Progress in Scale Modeling
Kozo Saito Editor
Progress in Scale Modeling Summary of the First International Symposium on Scale Modeling (ISSM I in 1988) and Selected Papers from Subsequent Symposia (ISSM II in 1997 through ISSM V in 2006)
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Editor Kozo Saito University of Kentucky Dept. Mechanical Engineering and Institute of Research for Technology Development Lexington KY 40506-0503 151 RGAN Bldg. USA
[email protected]
ISBN: 978-1-4020-8681-6
e-ISBN: 978-1-4020-8682-3
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Special Acknowledgements
We would like to acknowledge the contributions of the following people and groups for hosting the previous International Symposia of Scale Modeling. They have contributed much to this work through their time and effort. ISSM I: Richard I. Emori, Japan Society of Mechanical Engineers ISSM II: Kozo Saito, University of Kentucky ISSM III: Tadao Takeno and Yuji Nakamura, Nagoya University ISSM IV: Vedha Nayagam and Simon Ostrach, National Center for Microgravity Research ISSM V: Toshi Hirano and Lijing Gao, Chiba Institute of Science We would also like to extend a special acknowledgement to Bob Gregory, for his editorial work, and to Allison Hehemann, for her editorial work and for her role in communicating with all of the authors and editors throughout the entire course of this special volume’s production.
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Foreword: Significance of Scale Modeling in Engineering Science Forman A. Williams
Introduction Further amplification of a number of the ideas expressed by Kozo Saito in the Preface to this volume may be based on an address given at ISSMIII and dedicated to the memory of Professor Richard I. Emori, whose vision of the enjoyment and utility of scale modeling sparked the series of symposia that is covered in the present book, which chronicles many of the most significant papers presented at the symposia, updated as necessary to account for more recent developments. Dr. Emori was an atypical professor with a unique view of relationships between engineering and science. I had the good fortune to interact with him on one occasion, during an early visit to Japan, and I found him to be remarkably patient, kind, knowledgeable and prepared to embrace and understand the viewpoints of others. He especially admired creativity and art in engineering. He was, however, also quite adept in the sciences and therefore well positioned to evaluate the interactions between science and engineering. His paper [1] that was given by Professor Kozo Saito at the second of these symposia expresses some of his logic underlying that evaluation. Emori says [1] “. . .engineers. . .make new things. . .require creativity. . .do not even care whether. . .new products violate Newton’s law, as long as they work. . ..” He quotes Th. von K´arm´an, paraphrased more recently by the civil engineer Petroski [2] as having said that “a scientist studies what is, while an engineer creates what never was.” Petroski includes this quotation in an impassioned plea for greater public respect for the engineering profession, citing newspaper articles that, for example, credit space-exploration successes such as the Apollo manned moon landing and the Pathfinder exploration of the surface of Mars to rocket or space scientists, but attribute space-exploration failures, as that of a more recent Mars mission, to the inability of engineers to find or fix the problem. On the other side, responding with an unmistakable element of derision, if not poorly concealed envy, to the list of the twenty greatest engineering accomplishments of the twentieth century, as selected Forman A. Williams Department of Mechanical and Aerospace Engineering University of California, San Diego La Jolla, California vii
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by a committee of the US National Academy of Engineering, physicists in an article in Physics Today [3] go to great lengths to point out how physics and fundamental science were involved in these advances and so often absolutely essential to them. The battle lines thus are drawn. With such animosity, how can there be anything called “engineering science”? How can scale modeling have anything to do with such an oxymoron?
Interactions Between Science and Engineering We all know that engineering makes strong use of scientific principles. In the logical progression, the scientist makes the discovery, and the engineer takes that discovery to build or create something new and useful. Reality, however, is seldom ever logical, at least not in so simple and straightforward a sense. There is a plethora of instances in which the engineering application preceded the scientific discovery. Consider, for example, the spark-ignition engine. The original idea was that the spark starts the chemical heat release which then occurs homogeneously, more or less everywhere in the chamber, all at once. Only later, through scientific investigations, of spark-ignition engines, was it found that in fact the spark initiates a flame, and the flame traverses the charge, so that flame propagation – actually turbulent flame propagation, that is, flame propagation in a turbulent medium – is the underlying physical mechanism by which the spark-ignition engine operates. This knowledge helped greatly to improve designs of spark-ignition engines, since it then became possible to determine much better the time that would be required for consumption of the charge under different conditions. It is curious that understanding and technology have now progressed to a point at which it is becoming conceptually possible to circumvent the flame-traversing-charge mechanism and to achieve operable homogeneous-combustion spark-ignition engines or, even more promising, homogeneous-charge compression-ignition (HCCI) engines, autoignition replacing spark ignition in the latter, as in diesel engines. At least on paper, these concepts, which, in a sense, revert to the original idea, can exhibit benefits in both fuel economy and pollutant reduction [4]. Step back and examine this example. The original idea was wrong, but the device worked, so it may be judged that the engineering preceded the correct science. Once the engineering device was created, it became an object of scientific investigation, thereby broadening the range of scientific inquiry. A great deal of science has now gone into studying spark-ignition engines, generating associated engineering revolutions in their performance. There is little resemblance of my present automobile to my grandfather’s Ford, which I dimly remember. And now, engineering may be on the brink of a new breakthrough, an HCCI engine, motivated by improved scientific understanding of how to implement the original vague concept. In this example, for more than a century there has been a two-way street between science and engineering, traversed in both directions again and again, resulting in both scientific advances and engineering improvements.
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Engineering and science are so tightly connected with each other in this example that it becomes difficult to identify the dividing line between them. How can controversy have developed between the two when they are so closely related? Perhaps it is a question of personalities. Perhaps there are people who call themselves scientists and others who call themselves engineers, and the two communities dislike each other. Science may then be considered to be what scientists do, while engineering is what engineers do. It seems to me, however that this approach to ascertaining a distinction fails. In HCCI studies, the same people often do both science and engineering. It might be thought necessary to consider a more pure science and a more pure engineering to find one-sided individuals. Even in so pure a science as astronomy, however, the astronomer certainly does engineering in considering the design of a telescope, for example. Th. von K´arm´an is best known for his many fundamental scientific contributions and probably would generally be considered to be a scientist, but the preceding quotation clearly would place him on the side of the engineer. Emori, who would be thought to have been a fairly pure engineer, made significant scientific contributions. It does not seem helpful to try to define the categories on the basis of what people actually do. The difference between science and engineering seems more nearly to be one of overall attitude or motivation. The engineer is motivated to create something new, while the scientist is motivated to develop new understanding. There is, of course, a continuous spectrum of individual motivations, involving desires for both creativity and understanding. Strong advocacy in favor of science, as opposed to engineering, or the other way around, then depends on the location on the sliding scale of this spectrum. Both types of activities are important for human advancement.
Scientific Aspects of Engineering Design is increasingly accepted as the central element of engineering. The socalled capstone courses in engineering curricula have become the senior-level design courses at many US universities. Design problems can afford the opportunity to exercise creativity and art in engineering. Good design problems do not have unique solutions and require esthetics in their evaluation. Scale modeling can play a role in design, as discussed later. Good designs respect scientific advancements but generally do not contribute to them. From this viewpoint, design appears to have little to do with engineering science, whatever that may be. The term engineering science is much more prevalent in engineering circles than in scientific circles. It is generally considered to connote the more-or-less more scientific aspects of engineering. In this sense, it might better be called scientific engineering instead, since it has clearly been part of engineering rather than of any particular science. Similarly, engineering physics or engineering chemistry are found
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more in engineering than in physics or chemistry. Engineering chemistry typically represents more scientific aspects of chemical engineering. Even though physical principles are widely applied in engineering, unlike chemical engineering, physical engineering is not a recognized discipline, so it cannot be said that engineering physics denotes the more scientific aspects of physical engineering; the wide range of different applications of chemistry for different chemicals has led to the discipline of chemical engineering as a recognized specialty. The idea of application prevails in all of these contexts. That is, there seems to be little or no distinction between engineering physics and applied physics (the title of a curriculum that still exists in some universities) or between engineering chemistry and applied chemistry. Similarly, applied science could be a synonym for engineering science, although the use of the word “engineering” as an adjective does seem to add a dimension of creativity perhaps not associated with the word “applied”. Possibilities for applications give rise to creative ideas concerning how to achieve applications and thereby the development of corresponding engineering disciplines. Educational curricula called engineering science or applied science were popular fifty years ago but have been losing favor in recent years. I was a member of a Department of Applied Mechanics and Engineering Sciences, but the name of my department changed (in fact, while I was serving as chairman of the department) to the Department of Mechanical and Aerospace Engineering. This trend could be thought to mark a decrease in respect for science in engineering disciplines. It may no longer be necessary to know basic science to enter engineering. Science may be becoming divorced from engineering. Technological development may be destined to stagnate for lack of knowledge of science. Such dire predictions fail to recognize the complexity of the modern world. Science is not becoming irrelevant to engineering. On the contrary, both science and engineering are growing and expanding, with increasingly varied interdependence, generating new specialties that have both scientific and engineering components. The relevance of science to engineering is becoming an implicit assumption that does not need to be called out in titles. The researchers in my Department of Mechanical and Aerospace Engineering do as much or more science than was done in the Department of Applied Mechanics and Engineering Sciences. New engineering departments are being formed, with new names that identify new specialties, each having strong scientific components. Any engineering specialty that loses contact with science is unlikely to survive. Science is essential. A difficulty in most engineering specialties is that the necessary science base has become too broad to be fully assimilated in the limited time available for studying for a degree. This is especially true in engineering research. Even at the undergraduate level, however, the scientific depth of proficiency in any particular area seems to be decreasing as the breadth increase. For example, with the mushrooming role of computers, topics of numerical methods and programming are increasing, and there is an associated evident decrease in abilities in mathematical analysis, with an unfortunate loss of the physical understanding that can be obtained in that way. A potentially helpful move for engineering research in this respect could be
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establishment of apprenticeship-like degrees beyond the PhD, involving perhaps three additional years of both study and research, resulting in a formal recognition somewhat akin to the German Habilitation. The increased knowledge required to truly master the science underlying any particular engineering discipline is bound to take more time to accumulate. And after all, people are making useful contributions later and later in life. To render such further study commonplace would seem to be a logical progression associated with the increasing knowledge base, instilling the engineering science that is needed for advancement of engineering.
A Definition of Engineering Science Engineering science thus may be defined as the science that is required for the advancement of an engineering discipline. In this sense, it really is a science and does not center on engineering design, for example. It is a scientific activity, engaged in by engineers advancing a scientific field relevant to their engineering discipline. Scientific creativity plays a role in engineering science, but the creativity associated with engineering, for example the invention of new and useful devices, is not central to the subject. The quest is for scientific understanding. Engineering science is pursued to various extents in different organizations around the world. Industry, government laboratories and universities all are involved. The history of the partition of this involvement is of interest. Seventy years ago there was little work in government laboratories, so that most of the research was done at universities and in some industries. In vividly demonstrating the importance of science, the second world war led to rapid growth of research in government laboratories and in research laboratories of a number of industries. The heyday of these highly respected research organizations now seems to be finished. During the past 30 years, economic factors have limited growth of government laboratories and encouraged most industries to greatly reduce their large research laboratories, especially in the US, but to a lesser extent in Europe as well. Need therefore exists for universities to resume greater leadership in research. Alliances are strengthening in the US between universities and industry, with universities encouraged to generate increasing proportions of research results, often quite specific, product-oriented and bordering on proprietary. In this climate, there are pressures for university research to become more applied and to move away from engineering science, but to the extent that engineering science is maintained, it will largely be at universities, which therefore must assume greater responsibility for it. It must largely be an individual choice as to whether the creativity of engineering or the search for scientific understanding is the main drive for research. It is logical for the former to be centered more nearly in industry and the latter in universities. Students can be strongly motivated to enter engineering careers by professors with the former quality, but professors with the latter quality also can be inspiring and promote firm scientific foundations on which to base engineering ideas. It appears to me that in Japan, university faculty in engineering are comparatively strongly
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motivated to develop scientific understanding, and engineering creativity is largely located in industry, while in Europe and the US, there is a larger fraction of university engineering faculty interested in the engineering spirit exemplified by design. To maintain healthy engineering science, it seems important to not stray too far from this current Japanese paradigm. Although engineering spirit with design as a goal certainly is important, it is essential to retain and nurture the engineering science base from which such activities can be properly launched.
Scale Modeling in Engineering Science When engineers design a new large bridge or building, scale models often are constructed, exhibiting the final product in three dimensions at a much smaller size. These models often are useful for more than simply advertisement. They demonstrate visually the relative locations of different parts. By viewing and studying the scale model, engineers can get a better feeling for the relationships among the parts. Sometimes undesirable features can be seen in scale models that were not realized in the original design concept. Scale models thus can be used to test design ideas and to suggest improvements in design. This use of scale modeling in engineering is different from scale modeling for engineering science. Another use of scale modeling is in accident reconstruction. When this is done only as a convenient way to investigate the accident, without seeking scientific understanding, then this too is different from the use of scale modeling in engineering science. Scale modeling in engineering science is based on scaling laws. Laws are stated that are presumed to describe the system of interest, and from the associated nondimensional groups a smaller or larger model is constructed that will behave in a predicted way if the scaling laws are correct. If the system of interest is large, then the scale model is smaller, while if it is small, then the scale model is larger. The model is tested to determine whether it behaves as predicted, since it would be too expensive or too difficult to test the original system of interest, and improved control of variables affecting the system behavior may be achieved in the scale model. From results of the model tests, the degree of understanding of the system of interest can be assessed. In particular, the validity of the laws that were presumed to describe the system of interest can be evaluated. Examples of scale modeling in engineering science are too numerous to catalog [5]. There are continuing developments and advances in scale modeling [6]. Emori [1] relates an entertaining example concerning the trajectory of a sign post struck by a vehicle, in which two non-dimensional groups initially were hypothesized, and disagreement between observed and predicted model behavior eventually was traced to the shear strength of the bolts fastening the sign to the post. In an opposite extreme, twenty nine non-dimensional groups were identified that can have relevance to the scale modeling of mass fires [7]. Scale modeling finds roles throughout all areas of engineering science, including aerodynamics, heat transfer, fluid transport,
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chemical reactors, bioengineering, structural mechanics, combustion processes, atmospheric and meteorological phenomena, material synthesis and interactions between people and machines. As such, it has contributed to the advancement of engineering science in many different scientific disciplines. It is of interest to try to compare the contributions of scale modeling with those of other types of investigations. Four broad categories can be identified, namely, analytical modeling, numerical modeling, scale modeling and full-scale experimental testing. The last of these is the most direct and likely preferable, if it can be done well. Scale modeling becomes important when this is not possible or when there is interest in investigating greater ranges of variability than can be achieved with the full-scale system, for example effects of changing parameters not readily controllable at full scale. It is, however, also true that numerical modeling, also called numerical simulation, can uncover information of interest that would not be obtained by full-scale testing or scale modeling; such simulations can, for example, explore influences of varying parameters that cannot be controlled in either full-scale systems or scale models. In a similar vein, analytical modeling, that is, solving relevant equations and drawing inferences therefrom without resorting to full numerics or experimentation, is an excellent approach to developing needed scientific understanding in engineering science, when it can be accomplished. All of these different approaches thus are worthwhile and complementary. Scale modeling is only one of a number of different reasonable avenues of investigation. It is certainly not likely the dominant one in recent years, judging from the large numbers of papers presented at various numerical conferences. A fifth category may be added to the preceding four approaches to the development of scientific understanding, namely the approach that Saito terms kufu [8]. It is a much more abstract and mental approach, involving conception of the whole rather than breaking things down into quantifiable and scaleable parts, rooted in Eastern culture and therefore very difficult for a Westerner like me to understand. In the present context it relates to professional intuition, that is, accumulated understanding that can be brought to bear on a problem, with suitable sublime reflection, to advance understanding farther and possibly lead to an inspired breakthrough not achievable solely on the basis of methods of any of the previous four categories. This approach, too, is worthwhile for those who are capable of it and complementary to the others.
An Example of Successful Scale Modeling in a Scientific Sense As one example of a significant advance of scale modeling in engineering science, consider gas flows driven by buoyancy. The most important non-dimensional group for such natural-convection flows is the Grashof number, Gr = gL3 ⌬T T 2 , where g denotes the acceleration, L the characteristic length, T temperature, ⌬T the temperature difference driving the flow and the kinematic viscosity. The Reynolds number, Re = U L ν, the ratio of inertial to viscous forces, generates the Grashof
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number, the ratio of buoyant to viscous forces, by identifying the velocity U as a buoyant velocity determined by a balance between buoyant and viscous forces. When expensive and elaborate scale-modeling concepts are excluded, such as use of a centrifuge to adjust g or of temperature control to adjust T and ⌬T , then the Grashof number allows L to be varied with Gr maintained fixed only if is varied in proportion to L 3/2 . Since the kinematic viscosity of a gas is inversely proportional to pressure, this can be achieved by increasing the pressure in proportion to L −3/2 as the scale is decreased. The result is a scaling strategy that has been termed pressure modeling. Pressure modeling is ambitious because it requires experiments to be performed with a model at a different pressure than the normal pressure of the full-scale system. This is more expensive than simply changing the length scale. It does, however, achieve a great deal in rendering the flow in the model similar to that in the full-scale system. Even if the flow is turbulent, for example, since the turbulence is controlled by Gr, similarity is maintained. This same degree of fidelity can be retained even for combined forced and natural convection, laminar or turbulent, if the imposed velocities U are scaled in proportion to L 1/2 , since then Re is also fixed, according to its definition. Associated steady-state heat-transfer rates also are then expected to scale properly, since Nusselt numbers are functions mainly of Grashof and Reynolds numbers. Once the effort has been made to proceed with pressure modeling in this way, when care is taken in measurements with the model and results are compared with those for the full-scale system (or for a model of different scale), observed differences in behavior help to indicate what additional phenomena, not represented by Gr or Re, may be participating in the flow. Alpert [9] completed a careful investigation of pressure modeling for fires. He achieved reasonable agreement between measured and predicted burning rates and was able to develop some understanding of the reasons for the comparatively small differences that were observed. In addition, it was appealing to see the resulting miniature turbulent flames, having all of the apparent scaled-down characteristics of large turbulent flames in fires. Alpert concludes, however, quite reasonably that “the significance of this modeling technique is not its great precision but the elucidation of broad trends due to changes of size and geometry which would be prohibitively expensive to test at full scale” [9]. Pressure modeling of fires thus appears to represent an important success story in scale modeling. Jolly and Saito [10] review a number of other studies of scale modeling of fires, including some further successful pressure modeling, for example of ventilation-controlled fires. Despite an appreciable amount of effort in this area and a few notable successes, most studies of scale modeling of fires do not seem to have been as successful as Alpert’s pressure modeling in achieving similarity. It is nevertheless true that, although some scale modeling studies of fires continue today, pressure modeling no longer seems to be actively pursued. The most likely reason or this is that, because of expenses involved in constructing and maintaining large high-pressure working chambers, simpler scale-modeling strategies are applied for economic reasons. Understanding is deemed sufficient that less fidelity in
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modeling can be accepted while still retrieving the principal information of interest. Larger differences in the behaviors of the scale model and the full-scale system are tolerated for the sake of acquiring knowledge more quickly and economically. This is reasonable if understanding is sufficient to enable the necessary corrections to be made but nevertheless does tend to increase the risks of drawing some wrong inferences because of insufficient understanding. Although it would be fun to see pressure modeling emerge again as a widely applied scaling tool, the possibility of that happening seems remote. It represents a success story in the sense of achieving similarity but not in the sense of achieving wide applicability and acceptance. There are different value judgments in criteria for success, and appraisals always depend on the underlying values.
An Example of Successful Scale Modeling in an Engineering Sense There are other examples of scale modeling that are less successful in achieving similarity but more successful in a practical sense. One such example that was related to me a few years ago [11] pertains to a system for eliminating paint particles in automobile manufacturing environments. The problem in engineering science that was addressed concerned the mechanism by which the eliminator captured the particles. The mechanism was unknown for existing devices, and therefore a modeling study was undertaken to ascertain what it is. Quarter-scale models were constructed and tested, based on Froude-number scaling, that is, constancy of gL/U 2 , a procedure helpful in many other contexts as well, and a two-dimensional laminar-flow computational model was exercised for this three-dimensional turbulent-flow problem. Although the scaling in principle was poor, in less than two years of study a key mechanism was discovered, namely vortex entrainment of paint particles with surfactant-containing water mists. On the basis of this understanding, a new particle eliminator was designed, optimized and tested at full scale in a Toyota facility. It outperformed other available products, exhibiting a higher capture efficiency rate with up to a 40% energy savings. This new paint-particle eliminator, Vortecone, was jointly patented and has been installed in seven different Toyota plant booths in the US and Japan. It certainly is not true that there is an inverse correlation between fidelity of modeling and engineering success, as these two examples may suggest. It is, however, not essential to be rigorous in satisfying rules to achieve practical advances. From a viewpoint of kufu, under extreme conditions scale models can be useful even if they obey no scaling rules, as with bridge and building models previously mentioned. What is important in achieving breakthroughs is careful and sincere study and thought, from sound scientific background with objective motivation in a cooperative orientation. Although it is reasonable to employ as much scientific scaling knowledge as is conveniently available, excellent progress often can be made even when very little is available, given the variety of different criteria for success.
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Summary of the Significance of Scale Modeling In keeping with the idea that different values produce different appraisals, it is clearly possible to offer widely different evaluations of the significance of scale modeling in engineering science. In one extreme, scale modeling is viewed like playing with toys, as Emori emphasized [1]. We can decide that only children should play with toys. Engineers should have grown up and should no longer be wasting time on such things. If they are not smart enough to acquire the understanding that they need through purely analytical modeling, then they should construct numerical models and revise them until the numerical simulation performs reasonably in describing the full-scale system. They then should follow today’s trends and exercise numerical modeling with suitably varied parameters to achieve whatever knowledge and understanding they may need. They also should develop improved instrumentation and test their numerical predictions against experiments performed on full-scale systems. Scale modeling plays no role in this modern-day logical program. We need to mature and dispense with scale modeling. But with deeper thought, it is, however, not entirely so clear that numerical modeling, tested by full-scale experimentation, is the answer to our true needs. Although computer capabilities continue to grow exponentially and will do so for ten to twenty more years (not longer without tough technological breakthroughs), virtual reality is not reality, it is fantasy. However elaborate and seductive it may become to both young and old, it is not the real physical world in which we live. Wrong answers are readily provided, with authority, by computer modeling. Consider, for example, long-term climate prediction or shorter-term meteorological prediction. The models are constructed by humans, are replete with fudge factors and tend to be subtly unstable, always predicting eventual runaway global warming or, occasionally, another ice age, and numerical models are even notoriously inaccurate in 5-day weather prediction. It may be poor judgment to trust future global planning, fire safety or safety of nuclear stockpiles totally to computation and numerical modeling. No matter how attractive the fantasy world of the computer may seem, it is worthwhile considering returning to the real world and finding out more about engineering science from scale models, for example. Perhaps there should be less excitement with children playing computer games and more with real toys, as a prelude to scale modeling. A balance certainly is needed. Numerical modeling has a place in the balance, as does scale modeling. Neither should be accorded dominant significance in engineering science. Any attempt to quantify the significance further than that would be ill-conceived.
Conclusions Concerning Engineering Science and Scale Modeling We have seen here that, although controversies arise between engineers and scientists, and although usage of the term engineering science is decreasing, that subject
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is alive and well. It concerns fundamental science needed for engineering advancement. As such, it is related to research for design, a subject discussed by Saito in the Foreword. The difference between the two is one of shading in that specific design goals need not be kept in mind in engineering science. Worthwhile contributions are made in engineering science by engineers who are not design-oriented, as well as by some who are. The orientation towards fundamental science, however, is the main attribute that distinguishes an engineering scientist from other engineers. For engineering to remain healthy, continuing advancement of engineering science is needed. The center of that activity has been migrating from industry to universities in recent years. Universities therefore need to recognize their responsibility for nurturing this aspect of engineering. Scale modeling, along with numerical modeling, analytical modeling, full-scale experimentation and professional intuition, is an important element of engineering science that should not be overlooked. In recent years, increasing computer capabilities have engendered mushrooming growth of numerical modeling, to some extent at the expense of analytical modeling and scale modeling. It is essential to maintain these other aspects of engineering science for a reasonably balanced and effective delving into unknown fundamentals of nature that need to be understood for the long-term future progress of engineering. Scale modeling, which many engineers find to be a thoroughly enjoyable and challenging endeavor, is a significant contributor to advancement of understanding in engineering science. The articles in the present volume will help in progressing along this path.
References 1. R.I. Emori, “Toys and Scale Models”, Second International Symposium on Scale Modeling, University of Kentucky, Lexington, KY, June, 1997. 2. H. Petroski, “Making Headlines”, American Scientist 88, 206–209 (2000). 3. I. Goodwin, “Engineering Proclaims Top Achievements of 20th Century, but Neglects Attributing Feats to Roots in Physics”, Physics Today 53, No. 5, 48–49 (May, 2000). 4. Anonymous, “The Knocking Syndrome: Its Cure and Potential”, Automotive Engineering International (SAE), 64–68 (December, 1999). 5. R.I. Emori and D.J. Schuring, Scale Models in Engineering: The Theory and Its Application, Pergamon, 1977. 6. R.I. Emori, K. Saito and K. Sekimoto, Scale Models in Engineering (Mokei Jikken no Riron to Ohyoh), Gihodo Publishing Corp., Tokyo, Japan, 2000 in Japanese. 7. F.A. Williams, “Scaling Mass Fires”, Fire Research Abstracts and Reviews 11, 1–23 (1969). 8. K. Saito, “Kufu: Foundations for Employee Empowerment and Kaizen”, pp. 102–115, Principles of Continuous Learning Systems, K. Saito editor, McGraw-Hill, 1995. 9. R.L. Alpert, “Pressure Modeling of Fires Controlled by Radiation”, Proceedings of the Combustion Institute 16, 1489–1500 (1977). 10. S. Jolly and K. Saito, “Scale Modeling of Fires with Emphasis on Room Flashover Phenomenon”, Fire Safety Journal 18, 139–182 (1992). 11. K. Saito, personal communication, 2000.
Preface: The Art of Scale Modeling Kozo Saito
Introduction Professor Emori treated engineering as an art and emphasized the importance of professional intuition in his famous book, Mokei Jiken no Riron to Ouyou (Scale Modeling in Engineering: Its Theory and Application) [1]. The first edition was coauthored with D.J. Schuling and published in Japanese in 1973. The second edition was by the Professor himself in 1985. Unfortunately and unexpectedly Professor Emori passed away in 1996. Kozo Sekimoto and I, two of Professor Emori’s former students, received a request from the publisher to revise this popular textbook for college students as well as industry engineers and University researchers who want to learn how to solve practical engineering problems. The third edition was published in 2000 with three co-authors, Professor Emori and his former students, K. Sekimoto and me. The third edition has new sections to explain the expanded roles of scale models to validate numerical models, and to observe the prototype phenomena without establishing rigorous scaling relationships. Those roles were not included in Professor Emori’s first and second editions where scale models were defined as physical models validated by rigorous scaling laws. Both Sekimoto and I felt that this expanded definition of scale models was necessary to effectively validate predictions from the rapidly increasing capability of numerical methods. We sincerely hope that Professor Emori would have kindly accepted this expanded definition. Professor Emori had a passion for scale modeling, and the Professor himself is a founder of scale modeling theory, the so called “Law Approach [1],” which emphasizes professional intuition rather than the traditional three scientific methods to be explained later. He believed that professional intuition is the highest expression and the best tool that engineers can attain to solve practical engineering problems. Scale modeling covers almost all fields of engineering and is often applied to medicine, meteorology, biology etc. Because of its interdisciplinary nature, Professor Emori knew the need for international communication among a wide range of Kozo Saito Department of Mechanical Engineering University of Kentucky, Lexington, KY 40506, USA xix
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scale modeling researchers. He initiated the first international symposium on scale modeling in 1988 in Tokyo under the sponsorship of the Japanese Society of Mechanical Engineers [2]. After the successful first ISSM, unexpectedly, it took nine years to host the second symposium in Lexington, Kentucky under the sponsorship of the University of Kentucky. In the second ISSM, Professor Emori was invited to give the Keynote (Emori lecture) with the title: Toys and Scale Models [3]. Unfortunately, his presentation was never realized due to his sudden and unexpected death, which occurred during his early morning jogging exercise in December 1996. To keep Professor Emori’s will alive, Professor Takeno hosted the third ISSM in Nagoya in 2000, and the International Scale Modeling Committee formed just around that time decided to continue ISSM every 3 years. Based on that agreement, the fourth ISSM was held in Cleveland, Ohio in 2003, hosted by Dr. Vedha Nayagam under the sponsorship of the National Center for Microgravity Research, NASA Glenn Research Center. The fifth ISSM was held in Choshi, Chiba, Japan in 2006, hosted by President Hirano of the Chiba Institute of Science. During ISSM V, a special workshop was proposed to select papers from the past ISSM and publish them in a special ISSM volume. Accordingly, the University of Kentucky hosted the workshop May 28–29, 2007 in Lexington Kentucky. The following individuals agreed to serve as editors for the special ISSM volume publication: K. Chuah, D. Doherty, T. Hirano, M. Khraisheh, T. Konishi, A. Ito, H. Ito, K. Kuwana, J. Nakagawa, Y. Nakamura, V. Nayagam, J. Quintiere, K. Saito (editor-in-chief), K. Sekimoto, D.P. Sekulic, T. Takeno, and F.A. Williams. These editors met in Lexington and discussed the structure of this special volume: Progress in Scale Modeling and the method for selecting articles to be included. The editors decided to keep the length of this volume at less than 400 pages which means the number of papers to be included must be less than 45. This selection process was most difficult since more than 200 excellent papers were presented at ISSM II through V. The editors adopted the following criteria for selection. To be chosen, the paper must satisfy at least one of the following elements: Paper (1) has scaling and scale modeling elements, (2) contributes to the development of scaling concepts, (3) implies or indicates scaling relationships between different scale models, and (4) uses scale models or scale modeling to achieve final product design or control the original phenomena or mechanisms. The above definition of scale modeling is much broader than the one given by Professor Emori’s three editions of his textbook. The editors decided not to include independent papers from ISSM-I, which is nineteen years old, and would be difficult to contact authors associated with its copyright. Rather we decided to provide a summary of ISSM-I by Jim Quintiere, which appears in the beginning of this volume.
Professor Emori’s Fourth Engineering Tool: Kufu There are three conventional engineering tools known to exist: experiment, theory, and computation [4]. Professor Emori added professional intuition to the above list
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as the fourth tool in conjunction with scale modeling1 . Each of these three conventional tools has strengths and weaknesses. Experiments can be employed for pure observation as well as for confirmation of the predictions made by theory and computational methods. Theory helps us structure the thinking process and streamline logic and makes predictions based on assumptions. Thus, it can be called economy of thought. Computation, referred to as computer experiments, can provide detailed results in virtual reality conditions by numerically solving equations. The combination of two or more of these tools will increase not only the accuracy of the results but also the chance of getting correct answers, especially during the early stages of research and technology development projects [5]. For example, a simple experiment can offer vital information to researchers through observation from which theorists and computational specialists may be able to derive correct assumptions for a new theory and governing equations. Observation here means insightful observation which penetrates what we see physically to “sense” something that controls what we see [6]. It does not mean that something we can see physically is the final objective. Scale models can create scaled down or up versions of the full-scale phenomena. When researchers attempt to properly design these scaled up or down versions of prototypes, conduct experiments using these scale models, and observe the scaled phenomena, they may be able to gain at least the following two benefits: (1) Scaling relationships between the prototype and the scale models, and (2) Imagination to speculate on the behavior of the prototype phenomena. Computational methods not only save the time and energy of human calculation, but also provide details in virtual reality conditions under well controlled initial and boundary conditions, that may be difficult to achieve by experiments. However, all computational models require validation. For this reason, scale models can provide the third benefit to researchers as the validation tool for computational models. The fourth tool is not well known to scientific and engineering communities, although it has been used for years by scientists, engineers and skilled craftsmen [7]. I call it Kufu, the term that was used by D.T. Suzuki in his book: Zen and Japanese Culture [8]. The following provides some background information on how kufu (Professor Emori used to call it “professional intuition”) plays an important role in the breakthrough and discovery processes of scientific research and technology development [6]. Let’s see what Zen philosophy says about kufu; the following is an excerpt from Suzuki’s book [8] about kufu. “The term kufu is the most significant word used in connection with Zen and also in the fields of mental and spiritual discipline. Generally, it means ‘to seek the way out of a dilemma’ or ‘to struggle to pass through a blind alley.’ A dilemma or a blind alley may sound somewhat intellectual, but the fact is that this is where the intellect can go no further, having come to its limit, but an inner urge still pushes one somehow to go beyond. As the
1 In his Foreword, interestingly, Professor Williams [4] expended this original three scientific tools to five including kufu, which will appear later in this Preface. These newly defined five models are: analytical model, numerical model, scale modeling, full scale model, and kufu.
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intellect is powerless, we may enlist the aid of the will; but mere will, however pressing, is unable to break through the impasse. The will is closer to fundamentals than the intellect, but it is still on the surface of consciousness. One must go deeper yet, but how? This how is kufu. No teaching, no help from the outside is of any use. The solution must come from the inmost. One must keep knocking at the door until all that makes one feel an individual being crumbles away. That is, when the ego finally surrenders itself, it finds itself. Here is a newborn baby. Kufu is a sort of spiritual birth pang. The whole being is involved. There are physicians and psychologists who offer a synthetic medicinal substance to relieve one of this pang. But we must remember that, while man is partially mechanistic or biochemical, this does not by any means exhaust his being; he still retains something that can never be reached by medicine. This is where his spirituality lies, and it is kufu that finally wakes us to our spirituality.”
Kufu is a source of imagination and creativity, however and unfortunately, Suzuki says that no teaching and no methods can help to master the secrets of kufu, because technique is secondary in mastering kufu and each student and engineer must struggle to develop his or her own kufu from within [8]. Once they have mastered their own kufu in engineering, they become masters of engineering. This is exactly why Professor Emori said professional intuition is the best tool in solving engineering problems. A schematic illustration showing characteristics of Eastern culture (including Zen Philosophy) on which professional intuition is based, is shown in Fig. 1, in comparison to characteristics of Western culture on which scientific methods are based.
Scale Modeling and R4D The late Professor Emori who was famous for his engineering spirit and a strong advocate for engineers as problem solvers for industry problems, once said: “If we want to solve engineering problems, we must be curious about everything [9].” His belief in engineering problem solving resonates well with the founder of aerother-
Fig. 1 Comparison between scientific methods developed based on the western tradition of logical thinking and professional intuition (kufu) developed based on the eastern tradition of intuition and contemplation
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mochemistry, Professor Theodore von K´arm´an, who once declared, “Scientists see things that exist and ask why. Engineers dream things that do not exist and ask why not.” The engineers’ role to create new products, invent things, and find solutions for industry’s problems is clear. Therefore, Professor Emori claimed: “Engineering is an art but not a science.” He believed that the ultimate engineering problem solving is deeply related to an engineer’s psychological state of mind and on how the engineer sees the world rather than what kind of technical skills and scientific knowledge that the engineer has. This means that learning engineering and scientific knowledge and understanding those principles is not enough to solve engineering problems. Only professional intuition can find the solution, and the logical mind helps explain why the solution has worked. This is exactly what Einstein wrote [10], “First I imagine, then solution follows. My logical mind explains why that solution can work. . .(but) I never discovered anything by my logical mind.” A skilled craftsman can design parts or fix problems based mainly on his/her experience and professional intuition and not on scientific reasoning and understanding. His/her experience and know-how can help solve engineering problems as well. Three scientific methods: theory, experiment and computation, can help us to understand why the craftsman’s solution worked for a particular problem, but may not work for different types of problems. Here again, the craftsman’s role is the same as the engineer’s role in creation and problem solving, while a scientist’s role is needed here to understand why the solution worked. Thus, both engineering and scientific functions are required, if a company involved in research (R) and development (D) seeks the best possible R&D. It would be ideal for industry to have these two functions in its organization. However, the scientific function often finds difficulty in justifying its accountability on company costs. On the other hand, the University can be an excellent source for the company’s scientific function. There are two different types of University research: curiosity-driven basic research and purpose-driven applied research. R4D, defined below, is a good example of applied research, as we discussed earlier. It would be harmful, however, if University researchers only conduct R4D research by staying inside the boundary determined by a well-focused R4D plan, and ignoring curiosity-driven basic research. History has proven that many technological inventions were made by looking at the same problem from a different point of view [7, 9, 10]. A good balance between basic research and applied research, therefore, is clearly needed for a University researcher to effectively solve industry problems. In the Foreword of this volume, Professor Forman Williams stresses the importance of science in engineering, offering specific examples with his unique and in-depth analysis on why science plays important role in engineering, and finally offering balance to be made between basic and applied research in academic institutions. His emphasis on science coincides with my fruit tree concept of successful university-industry collaboration on research, shown in Fig. 2, where basic research is its roots, R4D is the branch to bear fruits, and the interdependent relationship between University and industries is the trunk. Figure 2 also supports the win-win concept of university-industry partnership. The University of Kentucky’s new Institute of Research for Technology Development (IR4TD) is a good example of university-industry collaboration. To stress the
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Fig. 2 Schematic of university-industry partnership to achieve win-win results
way research and development are integrated in our work, we call our approach R4D – research for development. The new institute’s purpose is to directly and effectively respond to requests from industries. R4D is a demand-pull rather than a supply-push approach; we respond to the needs of clients who approach us rather than approach companies with our research interests. The approach also provides an excellent education for our graduate students in tackling pressing industry problems, working as a team, accepting responsibility, coping with real budgets and real deadlines, communicating effectively with clients, and understanding their point of view. A client may see a problem with the current process; we can see, in fact, that they have come to the limits of a current technology so that a new generation of technology or even a radical new approach to the whole question is needed. The “R” of our work is not simply paired with the “D” but tied directly to needed innovations. Overall, this approach leads to: (1) a high probability of immediate in-plant benefits to the company, and (2) a high likelihood that new technology needs will be accurately identified – thus, new-generation technologies that fit efficiently into the company’s manufacturing systems, and the potential for discovering “quantum leap” (revolutionary) solutions that can be transferred to other industries.
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Summary Scale modeling can play an important role in R&D. When engineers receive some ideas in new product development, they can test how the new design looks by building scale models and they can get an actual feeling with the prototype through their imagination. Professor Emori often said: “When children play with a toy airplane, their mind is wondering about the prototype airplane which they haven’t ridden.” Children can use the scale model airplane as a means to enter into an imaginative world of wonder by testing in their own way how the actual airplane might function, how the actual airplane can maneuver aerodynamically, what might be the actual sound of a jet engine, how to safely land the actual airplane, and so on. This imagination that scale models can provide for children will help them later develop professional intuition. Physical scale models can never be entirely successfully replaced by computer screens where virtual models are displayed and fancy functions are demonstrated. Not only children but also adults can learn things by actually touching things only offered by physical models, helping all of us develop imagination and feeling eventually leading toward Kufu. Einstein’s famous “thought experiments [11],” which helped him to restructure modern physics may possibly and effectively be taught by letting researchers play with scale models!?
References 1. I. Emori, K. Saito, and K. Sekimoto, Mokei Jikken no Riron to Ouyou (Scale Models in Engineering: Its Theory and Application), Gihodo, Tokyo, Third Edition, 2000. 2. Proceeding of the First International Scale Modeling, Japan Society of Mechanical Engineers, 1988. 3. I. Emori, Toys and Scale Models, Special ISSM volume, to be published in 2008. 4. F.A. Williams, The Role of Theory in Combustion Science, Twenty-fourth International Symposium on Combustion, The Combustion Institute, 1992, pp. 1–17. 5. E.B. Wilson Jr., An Introduction to Scientific Research, Dover, New York, 1990. 6. K. Saito, Kufu, Principles of Continuous Learning Systems, Edited by K. Saito, McGrawHill, 1995. 7. E.S. Ferguson, Engineering and Mind’s Eye, The MIT Press, Cambridge, Massachusetts, 1992. 8. D.T. Suzuki, Zen and Japanese Culture, Princeton University Press, Princeton, New Jersey, 1973. 9. I. Emori, Significances of Hands-on Knowledge in Engineering Problem Solving Processes, in Mr. Honda Speaks on His Technology Principles, Kodansha, Tokyo, 1985. 10. Saito, K., A special lecture note on Asahi Sunac’s 50th anniversary lecture, April, 2007, Nagoya, Japan. 11. W. Isaacson, Einstein, His life and Universe, Simon & Schuster, New York, 2007.
Contents
Special Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Foreword: Significance of Scale Modeling in Engineering Science . . . . . . . . vii Forman A. Williams Preface: The Art of Scale Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix Kozo Saito ISSM 1, Tokyo, 1988: Summary Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxxi James G. Quintiere Part I Fire & Explosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T. Hirano, A. Ito, K. Chuah, H. Ito and K. Kuwana A Reduced Scale-Modeling Study on Wind and Smoke Interaction at a Refuge Floor in a High-Rise Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Richard K.K. Yuen, S.M. Lo and Charles C.K. Cheng
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Flame Spread over Polymer-Insulated Wire in Sub-Atmospheric Pressure: Similarity to Microgravity Phenomena . . . . . . . . . . . . . . . . . . . . . . . 17 Yuji Nakamura, Nobuko Yoshimura, Tomohiro Matsumura, Hiroyuki Ito and Osamu Fujita Mechanistic Aspects of the Scaling of Fires and Explosions . . . . . . . . . . . . . . 29 Forman A. Williams Modeling and Scaling Laws for Large Fires . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Howard R. Baum Modeling of Gas Explosion Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Toshisuke Hirano Period for Spontaneous Ignition of a Refuse Derived Fuel Pile . . . . . . . . . . . 75 Lijing Gao and Toshisuke Hirano xxvii
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Pressure Scaling of Fire Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Richard C. Corlett and Anay Luketa-Hanlin Scale Effects on Flame Structure in Medium-Size Pool Fires . . . . . . . . . . . . . 99 Akihiko Ito, Tadashi Konishi and Kozo Saito Scale Model Reconstruction of Fire in an Atrium . . . . . . . . . . . . . . . . . . . . . . 109 James G. Quintiere and Michael E. Dillon Scale Modeling of Quasi-Steady Wood Crib Fires in Enclosures . . . . . . . . . 121 Paul A. Croce and Yibing Xin Scale Modeling of Puffing Frequencies in Pool Fires Related with Froude Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Hiroyuki Sato, Kenji Amagai and Masataka Arai Scaling Sub-Surface Layer Circulation Induced by Pulsating Flame Spread over Liquid Fuels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Kozue Takahashi, Akihiko Ito, Yuji Kudo, Tadashi Konishi and Kozo Saito Part II Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 F.A. Williams, T. Takeno, Y. Nakamura and V. Nayagam Microgravity Droplet Combustion: An Inverse Scale Modeling Problem . . 169 Vedha Nayagam, Anthony J. Marchese and Kurt R. Sacksteder Modeling of Combustion Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Forman A. Williams Molecular Diffusion Time and Mass Consumption Rate in Flames . . . . . . . 197 Tadao Takeno and K.N.C. Bray Nitric-Oxide Emissions Scaling of Buoyancy-Dominated OxygenEnriched Methane Turbulent-Jet Diffusion Flames . . . . . . . . . . . . . . . . . . . . . 203 L.T. Yap, M. Pourkashanian, L. Howard, A. Williams and R.A. Yetter Numerical Simulations of Methane Diffusion Flame with Burner Rotation 211 Keng Hoo Chuah, Hiroshi Gotoda and Genichiro Kushida Numerical Study of the Effect of Model Scaling on Mixing and Flame Development in a Wake Flow Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Sadegh Tabejamaat and Takashi Niioka Scale Model Flames for Determining the Heat Release Rate from Burning Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 Gregory T. Linteris and Ian Rafferty
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Scale Modeling of Magnetocombustion Phenomena . . . . . . . . . . . . . . . . . . . . 247 John Baker, Mark Calvert and Kozo Saito Scaling Analysis of Diffusion Flame Attachment and Liftoff . . . . . . . . . . . . . 257 Indrek S. Wichman and Bassem Ramadan Scaling of Gas-Jet Flame Lengths in Elevated Gravity . . . . . . . . . . . . . . . . . . 269 Peter B. Sunderland, David L. Urban and Vedha Nayagam Some Partial Scaling Considerations in Microgravity Combustion Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 James S. T’ien Structure of Micro (Millimeter Size) Diffusion Flames . . . . . . . . . . . . . . . . . . 293 Yuji Nakamura, Heng Ban, Kozo Saito and Tadao Takeno Part III Materials Processing, Manufacturing and Environment . . . . . . . . . 307 D. Sekulic, J. Nakagawa, K. Sekimoto and M. Khraisheh Backdraft Experiments in a Small Compartment . . . . . . . . . . . . . . . . . . . . . . 313 Hiroshi Hayasaka, Yuji Kudo, Hideyoshi Kojima, Tsutomu Hashigami, Jun Ito and Takashi Ueda Development of a New Paint Over-Spray Eliminator . . . . . . . . . . . . . . . . . . . 325 Y. Tanigawa, R. Alloo, N. Tanaka, M. Yamazaki, T. Ohmori, H. Yano, A. J. Salazar and K. Saito Flow Visualization of Waste-Heat Boiler Using 1/20 Scale Model and Numerical Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 Tadashi Konishi, Susumu Akagi and Hironori Kikugawa Scale Modeling for Landing of a Lunar Probe . . . . . . . . . . . . . . . . . . . . . . . . . 357 Kazuya Yoshida, Shigehito Shimizu, Satoshi Yamaguchi, Kozo Sekimoto, Akira Miyahara and Takashi Yokoyama Scale Modeling of Steel Making Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 Junichi Nakagawa Scaling Laws for Sedimentation Process in Water Flow-Driven Sedimentation Tanks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 Kozo Sekimoto Scaling of Molten Metal Brazing Phenomena: Prolegomena for Model Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391 Dusan P. Sekulic
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Sound Insulation Analysis of a Resin Composite Material Using the Homogenization Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 Kohei Yuge and Susumu Ejima Toys and Scale Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 Richard I. Emori Part IV Medical – Conceptual, Practical, Translational into Practice . . . . . 429 D. Doherty, T. Konishi and T. Ida Characteristic Timescales for Adherent Mammalian Cells . . . . . . . . . . . . . . 433 John Kizito, Karen Barlow and Simon Ostrach Developing Scaling Parameters for Estimating Carbon Monoxide Levels in Structure Fires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 Brian Y. Lattimer, Uri Vandsburger and Richard J. Roby Monocyte Lung Retention During Normal Conditions (Health) and During Disease States (Endotoxemia): A Medical Application of Scale Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455 Dennis E. Doherty Lipolysaccharide-Induced Monocyte Retention in the Lung . . . . . . . . . . . . . 457 Dennis E. Doherty, Gregory P. Downey, Bill Schwab III, Elliot Elson, and G. Scott Worthen Scale Modeling of Medical Molecular Systems . . . . . . . . . . . . . . . . . . . . . . . . . 487 Tatsuhiko Kikkou, Shinichiro Iwabuchi and Osamu Matsumoto Scaling Human Bone Properties with PMMA to Optimize Drilling Conditions During Dental Implant Surgery . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 Mohamed I. Hassan, Varahalaraju Kalidindi, Aaron Carner, Neal Lemmerman, Mark V. Thomas, I.S. Jawahir and Kozo Saito
ISSM 1, Tokyo, 1988: Summary Review James G. Quintiere
Abstract A review is made of the papers presented in the first symposium on scale modeling in 1988. The breadth of the subjects ranges from phenomena dealing with fluid flow, structures, thermal comfort, and fire. Their scope shows the wide application of physical scale modeling and its accuracy in representing complex systems. The review is presented so that the reader can learn about the subject and appreciate the physical meaning of the dimensionless groups that govern. Nomenclature A area Ar Archemedes number B Buoyancy factor Br Buoyancy ratio c speed of sound, damping coefficient c p specific heat at constant pressure C coefficients Ca Cavitation number Cau Cauchy number D diameter E Young’s modulus f frequency Fr Froude number g force of gravity per unit mass h height of liquid H height of vent Ic Ice number l characteristic length m mass Ma Mach number p pressure J. G. Quintiere Department of Fire Protection Engineering, University of Maryland, College Park, MD e-mail:
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P pressure of sound wave ˙ rate of energy or heat Q Q ∗ Zukoski number r radius R hydraulic radius Sc Scruton number St Strouhal number t time T temperature v velocity w work x length coordinate z height coordinate β coefficient of volumetric expansion λ wavelength μ viscosity ρ density σ stress ω angular velocity ζ damping coefficient Subscripts atm atmosphere o vent s structure
Introduction In July 1988 a special conference on physical scale modeling was held at the Nihon Daigaku Kaikan in Tokyo [1]. It was sponsored by the Japan Society of Mechanical Engineers, and organized under the leadership of Richard Emori. Emori has used scale-modeling techniques in his research and applications, and this conference was aimed at highlighting the extent and value of a scale modeling approach. Scientists came from around the world, most from Japan, and illustrated the dramatic and extensive use of scaling. The very diversity and scope of the subjects addressed at this meeting were enough to make anyone recognize the value of its approach. Yet many scientists still scoff at its use, crying incompleteness and approximations are detriments. Increasingly, in a world of computer computations, it is even falling more in the background of valued scientific approaches. This conference and hopefully this review should help to bring scale modeling to the forefront. The use and value of the wind tunnel in the design and development of aircraft is well known among the general public. Even the Wright brothers had to rely on a wind tunnel in their bicycle shop to adequately design the power needed for the lift and drag of their aircraft. Today it is still a hallmark of sound aircraft design, with
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computations augmenting it. In other fields it is much less recognized. What does it have to offer, even in an incomplete rendition? Firstly, a sound model can reveal the overall nature of a complex system phenomena and its interaction of effects. Secondly, the ability to measure and display the results are relatively easy. Thirdly, the cost of the approach in time and money can be less than computer simulations and field tests. Fourth, the phenomena, even if slightly off-scale, behave as the physical laws intended them, and no ad hoc or complex modeling algorithms are necessary. Finally, the results of a physical scaled system can provide a range of data that should be essential for serving as the means for validating any computer simulation. An interesting aside from the substance of the meeting is the World Trade Center 9/11 event. It was suggested to the investigators that a scale modeling approach be taken for all of the reasons just given. Scale modeling could have addressed the aircraft collision, the fire growth and the effects of the fire on the structure and its subsequent collapse. Instead, the official government investigators took a nearly exclusive computational approach [2], with their costs at nearly $20 million. A scale model of the fire behavior on the 96th floor of WTC 1 was accomplished by a junior class project at the University of Maryland [3] for about $2000. Figure 1 shows a scene from that event, and Fig. 2 temperatures from the scale model and comparable temperatures predicted in the NIST (National Institute of Standards and Technology) simulation [4]. The NIST result is an average of the upper layer temperature, the rest of the curves are from the scale model at various locations. The dashed curve gives the upper layer temperature for the scale model at one location. The time is given in real (full-scale) time. The difference between the two approaches is primarily due to different fuel loadings assigned to the respective analyses. However, both investigations worked from the same office furnishing data; and this issue is still unresolved. Its lack of resolution displays the need for deeper scrutiny of such investigations. Unfortunately, scale modeling did not play a role in the WTC investigation. Indeed, NIST states (2007) on its website: “. . .NIST did not conduct reduced scale system-level tests because there are no generally accepted scaling laws that apply to fire propagation, temperature evolution, and structural response. . . .Therefore, NIST relied on high-fidelity finite element modeling of the aircraft impact event and subsequent fires [5].” The folly of this statement will be revealed in the review of the extraordinary problems tackled by scale modeling in the 1988 symposium. And it emphasizes the need for computer simulations to be tested against scale modeling for their validation in predicting complex system behavior. The 1st International Symposium on Scale Modeling [1] contained over 50 papers with many specially invited. They were organized into sessions corresponding to (1) Transportation, (2) Power, (3) Building and Structures, (4) Materials, (5) Environment, and (6) Nature. This review will track the papers in that order. But it should be recognized that the scope of the disciplines addressed include: (1) Fluid Mechanics – drag, stall, dispersion, and acoustics; (2) Solid Mechanics – strength of systems, vibrations, and collision; and (3) Thermal – power, propulsion, combustion, and fire. They range over the full range of conservation laws, and many phenomenological relationships involving transport and thermodynamic properties. Nearly all of the papers explicitly address the needed dimensionless parameters
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Fig. 1 Scale model of the fire on a floor of the WTC
Fig. 2 Comparison of temperatures from WTC scale model and NIST computations
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required for similitude. Most all approach the problem in geometric scale with at times a convenient distortion of one dimension. Hence, the scaling relationships can be expressed in general as Dimensionless Dependent Variables = Function(xi /l, t/t c , ⌸ s)
(1)
where xi represents the coordinate dimensions with l as the characteristic physical length, and t time with tc as a specified time scale. The ⌸ factors arise from the other variables and form the dimensionless groups that govern the dynamic scaling. It is generally impossible to satisfy the equality of all the dimensionless variables in scaling between a model and larger prototype. The selection of the “key” groups form the basis of “partial scaling”, and this is the state of most all scale model characterizations. Indeed, some groups are insensitive to the processes considered, and partial scaling becomes a perfectly reasonable engineering approximation for design and analysis. As the various applications are discussed from the Symposium, the dimensionless factors will be presented and explained. In this way, one can get a perspective on the range of phenomena treatable, and on the physics that underlies the scaling.
Review of Papers The papers will be examined in the topical subject list of the symposium. A scaling phenomenon will not necessarily be unique to a subject category. Indeed, aspects of fluid flow will be pervasive through many of the topics. As a new phenomenon is met, a discussion will be presented to elucidate the new dimensionless groups. In presenting the physics, the governing equations will be illustrated in symbolic phenomenological sense. A rigorous approach using the Buckingham theorem of dimensional analysis or a detailed differential equation representation will not be done. The interested reader can seek out more in the particular field of interest. Once a specific phenomenon has been addressed, its application will be emphasized as the subject categories are reviewed. In this way, a reader may see the physics, and appreciate the many areas of application. The Symposium presents a strong case for the consideration of physical scale modeling in design and investigation.
Transportation Transportation encompassed ships, aircraft, rail, autos and even an application to a rocket. Perhaps the earliest attempt to utilize scale modeling in design was for ships. Kajitani et al. report that William Froude in 1871 formulated the first useful relationship indicating that the power needed for ships depended on the forces of the waves and the force related to hull friction. The coefficient of resistance became
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a function of the Froude number (Fr) and Reynolds number (Re), later conceived by Osborn Reynolds. Cdrag ≡
Force 2 = f (Fr, Re) ρ v2 2 l
(2)
v2 ∼ inertia/gravity gl ρvl Re = ∼ inertia/viscous μ Fr =
The variables are described in the schematic shown in Figure 3 with v the velocity, ρ density, ω the angular speed of the propulsion shaft, and g the force of gravity per unit mass. Ship scaling offers a classic example of incomplete scaling. Maintaining geometric scaling and the same fluid media, it is impossible to satisfy both Fr and Re as v ∼ l −1 or l 1 /2 . The Fr is favored as long as Re is large enough to insure turbulent flow. These issues were discussed by Lin, who shows that the cavitation number (Ca), also known as an Euler number, is critical to determining the shaft torque power required
Ctorque = Ca
=
torque = f (Fr, Re, Ca) ρω2 l 5 ρgl + ( patm − pvapor )
(3)
1 ρv 2 2
Cavitation or vaporization can occur at high shaft speeds. Other examples of ship scaling include the dispersion of effluents into the ship’s wake, and the wave action on an elastic hull. The hull stress introduces Hooke’s law for stress (σ ) and strain (ε), σ = E ε with E the modulus of elasticity. An interesting example of analyzing the ability of a ship to cut through ice was described by Phillips and Tanaka. They introduce the Ice number (Ic) composed of the Cauchy number (Cau ) – elastic-hull-force/wave-inertia Cau =
E ρv 2
and the work ratio: elastic-hull-work/work-to-crack-ice (w)
Fig. 3 Ship dynamics
(4)
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Ic = Cau
2
El w
(5)
They used models of 1/40 to 1/20-scale. The use of Re is classic in aircraft analyses with the wind tunnel scaling velocity as v ∼ l −1 . But if one investigates the dynamics of stall and subsequent aircraft spin as described by Chambers, the Fr becomes more important as m
dv ∼ mg + Drag dt
(6)
Since the drag coefficient, Cdrag , for the aircraft is nearly constant and independent √ of Re, the dynamics can be represented in terms of Fr = f (t/ l/g). At high speeds, sound and shock wave effects enter and the Mach number (Ma = v/c, for c the speed of sound) becomes a factor. In a low temperature wind tunnel (Nitrogen at 100 K), both Re and Ma can be maintained constant! In other circumstances, the Ma might override the Re in high-speed applications regarding wing elastic deformation and flutter. Also Ma criterion can apply to helicopter rotor dynamics and its interaction with shedding vortices. The latter phenomenon introduces the Strouhal number, St = shedding speed, fl / v where f is the frequency of shedding. Thus, we see even for aircraft phenomena, the Re can play a subordinate role. The scaling applications to rail car phenomena are particularly fascinating. In particular, at 1/143 and 1/62 scales the design needed to reduce tunnel exit pressure wave effects is studied. Figure 4 shows the dynamics with respect to the compression in the tunnel ( p) and the external pressure wave (P). This shows that P p = f (vt/D, r/D, Ma, Re) and ρv 2 ρv 3 c
(7)
where Re and Ma can satisfactorily be ignored. Other rail applications examine a 1/10-scale study of wind and earthquake loads, and the propagation of rail vibrations through solid boundaries. There is even a 1/50-scale study of road noise accounting for road surface and grass terrain. Emori describes a most interesting study on vehicle collision effects. Figure 5 illustrates the dynamics that can be described by μmg + mg + σ l 2 ∼ mv/l 2 , t ∼ l/v. The friction term is needed for the post-crushing impulse following a two vehicle collision, the weight term is needed for three-dimensional effects as in motorcycle accidents, and the stress term is needed for the collision with road structures, such as poles as shown in Fig. 6.
Fig. 4 Rail tunnel pressure effects
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Fig. 5 Vehicle collision dynamics
Fig. 6 Scaling vehicle collision with a pole by Emori
The ⌸-terms become, accordingly, vehicle collision dynamics.
μgl gl σ l 3 , , v 2 v 2 mv 2
→
σ l2 , mg
and they describe the
Power Power applications in scaling were investigated for the erosion effects on hydrodynamic machinery where Ca enters, and the efficiency of combustion in diesel and rocket motors. Liquid rocket combustion efficiency can effectively be studied at a small scale by introducing a Pi-factor that represents the flow-time/dropletevaporation-time. The power output of a wind turbine is analyzed in a wind tunnel at constant Re and the wing-tip-speed to wind-speed ratio, ωl/v. The power coefficient is defined by Cp =
Power 1 πρv 3 l 2 2
(8)
Figure 7 shows the comparison for field and model tests at different pitch angles. The results confirm the benefit of scaling.
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Fig. 7 Wind turbine power
Buildings and Structures The use of wind tunnels is not exclusively for aerodynamic purposes. Wardlaw and Cermak review the history of wind tunnel use on structures. Apparently, Smeaton (1759) concerned himself with the simulation of the Earth’s boundary layer, vital for the study of wind on structures. The study of the collapse of the Tacoma Narrows Bridge in 1940 used the wind tunnel to reveal its aerodynamic instability. Murakami et al. and Ito et al. explain the techniques of simulating atmospheric turbulence in such wind tunnels. Figure 8 shows a bridge in a wind tunnel at 1/10 scale, and Fig. 9 shows the arrangement of spires and roughness blocks to promote turbulence. Typically, however, the overall Re is neglected along with Fr, and the Rossby number, Ro = u/lω which is related to angular-wind motion. In studying the wind effect on structures, the Cau is important along with the structure’s vibration characteristics where spring, (kl) and damping (cv) forces come into play. k is the spring constant, and c is the damping coefficient. Tanaka presents these effects in terms of the “damping ratio”, ζ ≡ c 2(ρs l 3 k)1/2 where ρs is the density of the structure. He combines ζ with the structure-to-air mass ratio to form the Scruton number, Sc ≡
ρs ζ ρ
(9)
Other examples of modeling for structural elements under non-wind loads, include a study of rock bolting fro tunnels, the effect of steel panel stiffeners, and 1/25-scale study of the design pitfalls on inflating the Tokyo dome roof structure. That study uncovered an instability on inflating the dome – a shaking motion – of the support cables.
xl Fig. 8 Model of a bridge in a wind tunnel
Fig. 9 Turbulent devices on the floor of a wind tunnel
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Indeed, the Tokyo Dome air-distribution for climate control was studied in a 1/50-scale model by Nagasawa et al. It included electric heaters to simulate the load of the sun and the people in attendance. The Archemedes number is introduced as the governing ⌸, Ar ≡
bouyant force gβ⌬T l ∼ v2 flow force
(10)
where β is the coefficient of volumetric expansion, 1/T for a gas. The heat flow 2 ˙ scaling follows the ⌸ Q/(ρc ˙ rate ( Q) p v⌬T l ). By satisfying the Ar (or Fr), with 1/2 0 v ∼ (gl) , then ⌬T ∼ l , and this ⌸ becomes Q∗ ≡
ρc p T
˙ Q √
gl 5/2
(11)
a parameter known by fire investigators as the Zukoski number. Figure 10 shows a photograph of such a climate control study in a gymnasium at 1/30-scale (from Kato). In another climate study, Poreh examined the passive solar heating design to establish the thermal performance of apartments. In addition to climate control, acoustics can be studied in buildings. In 1934 Spandok was the first to use scale modeling to study the acoustics of an auditorium. Figure 11 shows the similitude for the sound absorption coefficient of a rib-wall at 1/10-scale by Tachibana et al. From acoustic theory, wavelength (λ) and time (t) scale as l, while frequency ( f ) scales as l −1 , based on f t = constant. Actual recordings in the theater are made and then re-broadcast under the scaled criteria
Fig. 10 Thermal comfort scaling
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Fig. 11 Acoustic scaling of a material sound absorption
in the model. The effects of wind and temperature on sound propagation were even studied using a wind tunnel. A novel scaling technique common in geotechnics uses a centrifuge (∼ 200 g) to investigate the dynamics and structural characteristics of soil using ⌸ = σ/gl with time scaling as l for vibrations, or l 2 for diffusion phenomena.
Materials Although only two papers addressed scale model studies of material processing, it should not be taken as limited applicability. They addressed the roll-forming of aluminum, and dendritic growth in solidification.
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Fig. 12 Results for vertical buoyant flow in stably stratified atmosphere
Environment Most of these studies of the environment addressed dispersions in fluid systems, while one studied the rehabilitation at 1/45-scale of the Oregon Yaquina Bay jetty built in 1895 that had been damaged by waves. In the dispersion areas, Ohba et al. studies at 1/400-scale the behavior of abuoyant plume of initial velocity vo in a dρatm < 0 . The maximum, plume rise, z max /D is a stably stratified atmosphere dz D dρatm function of a modified Fr ∼ ρvo /g⌬ρ D and the Buoyancy Ratio, Br ≡ ⌬ρ dz (Fig. 12). Pollution dispersion is studied at 1/5000-scale over Mt. Tukuba subject to nocturnal conditions, and also in Kagoshima Bay with exchange of clear seawater. Fukuoka et al. also studies the sediment transport in a riverbed.
Nature The scaling rules for the sedimentation of particles in turbulent flow were outlined by Sekimoto. He shows different rules depend on particle size and mass density in the fluid. Figure 13 shows the Sedimentation Ratio (mass of sediment to original flow mass). For the case of low mass concentration and small particles, the viscous and gravity forces yield a dependence of particle diameter, d ∼ l 1/4 . This scaling is verified in Fig. 13. Wind effects are examined around Mt. Fuji in a water channel and around Mt Tsukuba in a wind tunnel. In the Mt. Fuji case, the flow patterns indicated high shear stress areas along the flow separation line which correlated with the region of actual accidental fall locations along hiking trails. This is shown Fig. 14. Most of the studies involved tidal flow models. The most impressive is a scale model of the Eastern Scheldt storm surge barrier in the Netherlands shown in Fig. 15. The scour depth at the barrier due to tidal action is predicted quite well
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Fig. 13 Scaling particulates in flow
Fig. 14 Mt. Fuji high flow stress areas where accidental falls occurred (indicated by • on the map), the E-areas found in the study where greatest wind speed changes occurred
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Fig. 15 Model of the storm barrier in The Netherlands
according to Fig. 16. Scaling is based on Fr and the Chezy equation for channel flow. v2 dz The latter requires ⌸ = as constant, where C is the channel roughness C R 1/2 dl coefficient, R its hydraulic radius, and dz , the water depth to length slope. In the dl Scheldt model: h ∼ 1/100, l ∼ 1/400, and time scales as 1/40. Other tidal models address water exchange between the Seto Inland Sea and the ocean at 1/2000-scale, and for Chita Bay at 1/5000-scale. Hayakawa et al. investigated the use of vertical rods to better simulate longitudinal turbulent diffusion in tidal models. Again, the Fr and Cau numbers entered into establishing the cause of wave damage that occurred in 1978 to the Doles breakwater at Sines, Portugal.
Fig. 16 Scour depth prediction from the tidal storm barrier model
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Fig. 17 Average wall temperatures in a compartment fire at various fire power and ventilation
The final area of physical scale modeling is fire, perhaps the most complex. As chemical reaction rates are generally fast, diffusion and turbulence controls the combustion rate; therefore, modeling is basically physical rather than chemical. The principal ⌸-groups have been discussed before: Fr, Q ∗ , and Re, the last generally neglected. However, physical scale modeling at elevated pressure can allow Re to also be satisfied. Figure 17 shows the wall temperatures in room fires can scale as ∗ the characteristic length scale is based on the ventilation a function of 1/Q √ where factor, l ∼ (Ao Ho )2/5 (Ao is the vent area and Ho is its height). Figure 18 shows how the smoke layer height scales in a closed corridor using a salt-water analog ˙ ρc p T l)1/3 and t ∼ l/v model; here, Q ∗ /Fr was taken equal to 1, so that v ∼ (g Q is the scaling with T ∼ l 0 .
Fig. 18 Smoke layer descent in a saltwater model
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Fig. 19 Large area fire plumes scaled by helium
Another analog technique uses helium to simulate large area fire plumes. The centerline buoyancy factor, B (like a dimensionless temperature rise) B≡
g ⌬ρ R ρ
1/3
(π vo )2/3
(12)
is plotted as a function of dimensionless vertical height with respect to radius, z/R. This result is shown in Fig. 19 by Poreh and Cermak, and compared to the fire data of Yokoi. The agreement is remarkable for such different media. Even flashover, the instability in enclosure fires that suddenly produces a bigger fire, can be studied at small scale. Perhaps, the most fascinating study was that of catastrophic fire whirls (tornado-fires) by Soma and Saito. They investigated the Hifukusho-Ato fire whirl that killed 38,000 people following an earthquake in Tokyo (1923). The large fire whirl spun off of the main conflagration. They also studied the Hamburg fire whirl resulting from a conflagration due to a WWII bombing raid in 1943. That event killed 20,000 with a whirl sighted at 5000 m high and 3000 m in diameter. Wind tunnel and a field test at 1/100- scale confirmed that these fire whirls were solely due to a wind effect on the conflagration. Figure 20 displays the characteristics of these whirls discerned from the model studies.
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Fig. 20 Fire whirl characteristics following the Tokyo earthquake (1923) and Hamburg bombing raid (1943)
Conclusions It should be apparent from the papers in this Symposium that physical scale modeling is viable, useful, and accurate. Its cost, scale, and reliance on the natural interactions of complex processes should make it a design and investigation tool of choice. Yet many still doubt its appropriateness and prefer computer modeling. It should be a right of passage for the credibility of a computer model to predict its scale model counterpart before it is solely relied on.
References 1. Proceedings of the International Symposium on Scale Modeling, July 18–22, 1988, Japan Society of Mechanical Engineers, Tokyo. 2. Final Report of the Federal Building and Fire Safety Investigation of the World Trade Center Disaster, Drafts for Public comment, NIST NSTAR 1, NIST, DoC, September, 2005. 3. J. G. Quintiere and A. W. Marshall, “A Collective Undergraduate Class Project Reconstructing the September 11, 2001 World Trade Center Fire”, 2007 ASEE Annual Conf. and Expo., Amer. Soc. Engrg. Education, Honolulu, HI, June 24–27, 2007. 4. J. G. Quintiere, “Questions on the WTC Investigation”, Urban Structures Resilience under Multi-Hazard Threats: Lessons of 9/11 and Research Issues for Urban Future Work, To be published Springer, Netherlands. 5. National Institute of Standards and Technology (NIST) Federal Building and Fire Safety Investigation of the World Trade Center Disaster, Answers to Frequently Asked Questions – Supplement (December 14, 2007), wtc.nist.gov/.
Part I Fire & Explosion T. Hirano, A. Ito, K. Chuah, H. Ito and K. Kuwana
Summary Fire and explosion phenomena are very complicated – knowledge of fluid mechanics, heat transfer, chemical kinetics, material science, and other areas is required to study these phenomena. The complicated nature of the phenomena can be seen in a number of different stages that they cover: for example, ignition, flame spread over combustible materials, flame propagation through combustible gases, and continuous burning of combustible materials such as pool fires. Each stage has a different length scale; ignition may occur in a relatively small space, while a large-scale wildland fire can burn an area of greater than 1 km2 . The time scale associated with a fire or explosion scenario also greatly varies. An explosion accident can cause a significant damage to our society in the order of one second or less, whereas a forest fire may last for more than one month. A number of dimensionless parameters (or ⌸ numbers) is associated with fire and explosion phenomena. Each fire or explosion scenario, in principle, has a different set of the parameters, each having a specific value to the scenario. Therefore, one way of studying a fire or explosion phenomenon is its full-scale reconstruction either experimentally or computationally. Full-scale experiments as well as numerical simulations, however, are usually costly and time consuming (if not impossible) as is clear if we imagine conducting an experiment of California forest fires. Another approach of the study is scale modeling based on an appropriate scaling analysis, the theme of this book. When designing a scale-model experiment, we need to disregard the effect of minor ⌸ numbers (otherwise full-scale experiment would be the only way of research). Consequently, a scale-modeling study is a journey to identify important parameters. Important ⌸ numbers are often different from scale to scale. For example, in small-scale fires the effect of viscosity may be important and the Reynolds number is a governing ⌸ number, whereas the buoyancy effect may be important for large-scale fires, making the Froude number an important parameter. On the other hand, a strikingly simple scaling law sometimes holds to different scales, enabling us to design a simple scale-model experiment as demonstrated by Emori and Saito (see, for example Refs. [1, 2]), pioneers of scale modeling in fire research. In Ref. [1], they identified, via dimensional consideration, two important ⌸ K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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numbers of a large-scale real forest fire: Froude number defined using the heat release rate, and turbulence intensity. By setting these ⌸ numbers equal to those of the forest fire, they reconstructed the forest fire in a small wind tunnel even without using fire. Fire and explosion are one of main areas discussed in the previous International Symposia of Scale Modeling: 4 presentations in the First Symposium are related to the fire and explosion phenomena; 12 in the Second; 13 in the Third; 9 in the Fourth; and 12 in the Fifth. Among these 50 papers, 12 are selected in this special volume based on their relevance to scale modeling and contribution to the development of new scale-modeling techniques. Many of the selected papers study the applicability of a known theory to different scales, propose new scaling laws, and/or conduct scale-model experiments based on scaling analysis. Papers published in other journals are not included. The selected papers are briefly summarized in the following.
Papers Selected from the Second Symposium 1. R.C. Corlett and A. Luketa-Hanlin. “Pressure Scaling of Fire Dynamics.” This paper reviewed and summarized pressure scaling of fires. The difficult problem of including radiation was discussed. This paper is selected in this book because of its contribution to resolving issues on selecting parameter for scale modeling. 2. J. Quintiere. “Scale Model Reconstruction of Fire in an Atrium.” An excellent overview of scale modeling in the building fire research is provided in this paper. Scale-model experiments are designed based on the scale-modeling theory and important insights into building fires are presented.
Papers Selected from the Third Symposium 1. A. Ito, T. Konishi, and K. Saito. “Scale Effects of Flame Structure in MediumSize Pool Fire.” The authors’ unique technique, the particle-track laser sheet method was applied to understand the detailed structures of pool fires. The results of different scale pool fires reveal the scale effect on the pool fire structure. 2. H. Baum. “Modeling and Scaling Laws for Large Fires.” Mathematical models of the convective transport induced by large fires are presented to illustrate the role of scaling laws in the mathematical development and computer implementation of simulations. 3. T. Hirano. “Modeling of Gas Explosion Phenomena.” Various important stages in the gas explosion phenomena are identified, for example, leakage of a flammable gas, ignition, flame propagation, and structure destruction. Scaling laws for each stage are presented.
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3
Papers Selected from the Fourth Symposium 1. K. Takahashi, A. Ito, Y. Kudo, T. Konishi, and K. Saito. “Scaling Sub-Surface Layer Circulation Induced by Pulsating Flame Spread Over Liquid Fuels.” An instability analysis for the liquid surface ahead of the spreading flame is presented to investigate the effects of dimensionless parameters on the onset of flame pulsation. 2. F.A. Williams. “Mechanistic Aspects of the Scaling of Fires and Explosions.” Scaling laws of fires and explosions are reviewed. The presented scaling laws cover those for burning rates, flame spread, room fires, explosions, turbulent combustion, and chemistry. This is a comprehensive paper of overall understanding of scale modeling. 3. P.A. Croce and Y. Xin. “Scale Modeling of Quasi-Steady Wood Crib Fires in Enclosures.” Scaling laws for crib fires are derived and experimentally evaluated. Experimental results of different scales support the validity of the scaling laws.
Papers Selected from the Fifth Symposium 1. L. Gao and T. Hirano. “Period for Spontaneous Ignition of a Refuse Derived Fuel Pile.” The period needed for the spontaneous ignition of a refuse derived fuel (RDF) pile is theoretically investigated. The limitation of the FrankKamenetskii theory is also discussed. The spontaneous ignition of a large-scale fuel is made clear. 2. H. Sato, K. Amagi, and M. Arai. “Scale modeling on puffing frequencies in pool fires related with Froude numbers.” The well-established Strouhal numberFroude number correlation for the puffing frequencies of pool fires is further examined by changing Froude number by spinning pool fires. 3. R.K.K. Yuen, S.M. Lo, and C.C.K. Cheng. “A Reduced Scale-Modeling Study on Wind and Smoke Interaction at a Refuge Floor in a High-Rise Building.” This paper presents the wind and smoke interaction at a refuge floor using scalemodel experiments, in relation to Hong Kong’s building code that requires refuge floors in high-rise buildings. This study contributes to solving modern issues of high-rise buildings. 4. Y. Nakamura et al. “Flame Spread over Polymer-Insulated Wire in Sub-Atmospheric Pressure: Similarity to Microgravity Phenomena.” Experimental results obtained in reduced pressure environments are found to be similar to those in microgravity environments. The similarity is explained by a dimensional analysis. This paper addresses the special but interesting issues on scale modeling of fire spread.
References 1. R.I. Emori, K. Saito, Fire Technol. 18 (1982) 319–327. 2. R.I. Emori, K. Saito, Combust. Sci. Technol. 31 (1983) 217–231.
A Reduced Scale-Modeling Study on Wind and Smoke Interaction at a Refuge Floor in a High-Rise Building Richard K.K. Yuen, S.M. Lo and Charles C.K. Cheng
Abstract Refuge floor is considered as a temporary safe place for evacuees in super high-rise buildings and is a prescriptive requirement in Hong Kong’s Building Codes. The degree of safety of refuge floors under fire situations may be impaired if the floor is affected by smoke from other floors. In the circumstance, Hong Kong’s code prescribes that cross-ventilation should be provided in refuge floor so as to prevent smoke logging. This article reports studies on wind and smoke interaction at a refuge floor by using reduced-scale experiments in wind tunnel and computational fluid dynamics models. Results have indicated that cross-ventilation induced by permanent opening to the external may not guarantee that smoke logging will not happen in refuge floor. Keywords Refuge floor · external smoke spread · reduced-scale model · wind tunnel tests
Introduction Rapid urbanization and concentration of people and facilities in the metropolitan areas causes huge demand of floor space in many cities. Super high-rise buildings are now constructed everywhere, in particular in many metropolitan areas in the Far East. Of all the issues of constructing super high-rise buildings, safety is the major concern of many building designers, the Government as well as the general public. One of the ways to mitigate the ill-effect to the occupants of super high-rise buildings under emergency situations, such as fire hazard, is to provide a good evacuation system for the building. The prolonged travel in the escape routes in a super high-rise building is a factor influencing the efficiency of an evacuation system. The provision of refuge space has been promoted in many building codes to handle this particular issue. Hong Kong’s Building Codes [1] prescribes the provision of a whole floor for refuge purpose in super high-rise buildings. Such floor is considered R.K.K. Yuen Fire and Disaster Prevention Group, Department of Building and Construction, City University of Hong Kong, Kowloon, Hong Kong K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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as a temporary safe place for evacuees so as to minimize their continuous effort to move down the building from a very high level. It can also act as an interim base for fire fighter to fight against the fire at high level. In order to maintain its function, such floor should be a safe place and that it should not be affected by fire or smoke. Accordingly, the Hong Kong Code has prescribed the fire resisting requirements of the refuge floor. It also recognizes that smoke logging in the refuge floor may impair its safety level, and stipulates that the floor should be opened in at least two sides so as to maintain cross-ventilation for the floor. However, external smoke spread from the fire at other floor may still be possible. The early studies by Lo and others [2–5] have discussed the functions of refuge floor and the problems of adopting refuge floors as a temporary safe place for evacuees in super high-rise buildings. Later he and his colleagues have performed further studies [6–12] concerning the effect of external smoke spread on refuge floors. Computational fluid dynamic models have been adopted to simulate the fire and smoke spreading situations under various wind conditions. Results have shown that smoke spreading from a fire floor to the external may re-enter the refuge floor when wind speed prevailing the high-rise building is not very high. They also pointed out that the external wind flow behaviour and the setting of refuge floor may have a significant effect on the flow pattern of natural cross-ventilation, especially when the refuge floor is located at mid-height of the building. In other words, effective cross ventilation could be induced by the prevailing wind if there the service core of the building is not bulky and of simple form. However, the air flow may be “trapped” in the refuge floor if there are more than one service core with complex and irregular shape. In the circumstance, venting smoke at refuge floor by “cross ventilation” may not be effective and that external smoke spreading into the refuge floor may happen and even endanger the evacuees using the floor. Further studies, including more computational studies and experimental works have been performing at the Department of Building and Construction to examine the effects in details. This chapter reports some of the studies.
Reduced-Scale Wind Tunnel Experiment With reference to the scale of super high-rise buildings, a full scale physical test is always too expensive (costs and time) and is considered not a practical method to be adopted for the investigation. A reduced-scale test in a wind tunnel is a widely accepted approach applying to investigate the wind induced flow behaviour over and inside a building [13–21]. However, it is still considered as an expensive investigation method. With the advancement of computer technology, computational fluid dynamics (CFD) studies become the pre-dominating method to examine wind flow [22, 23], smoke movement [24–27], and so on. The numerical experiments open a promising way to perform extensive parametric studies on different building design. Nevertheless, such approach may lack physical information of wind flow to assure the quality of the numerical models. Wind tunnel tests have then been
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initiated in associated with computational studies to provide a more comprehensive investigation and to improve the credibility of numerical studies. To establish the wind flow information for subsequent computer simulations, the authors have initiated wind tunnel experiments and data obtained in the experiments have been adopted as a basis for calibrating subsequent numerical models. The physical experiments have been carried out at a boundary layer re-circulation type wind tunnel whose working length is 11 m long with a cross section of 3 m × 1.7 m. Spires and roughness elements are used to provide at the model location a simulated atmospheric boundary layer of the open to suburban terrain type. The form of the reduced-scale model (height of building = H, length of the building = L, and width of the building = W) with a refuge floor under investigation are square-plan shape having full-scale dimension of 124.5 m tall and 20 m2 in plan. The model with a scale of 1:150 was constructed by wooden panels and placed in the wind tunnel as shown in Fig. 1. The geometry of the refuge floor (Fig. 2) is built in accordance with the basic requirements stipulated in the Hong Kong’s building codes [1]. The facade area of the building model covers 3% of the cross sectional area of tunnel working section. Wind tunnel experiments are performed with the mean wind speed and turbulent intensity at 850 mm above floor (reference height Href ) equal to 10.478 m/s and 0.088, respectively. This speed and intensity are used as the reference wind speed (Uref ) and reference turbulent intensity (Iref ). The measured mean wind speed and turbulent intensity profiles are observed to follow the Power Law with an exponent of 0.19 for gradient wind speed and that an exponent of −0.47 for gradient turbulent intensity (Fig. 3). In the experiments, measuring the velocity data in the gap-like refuge floor was a critical problem. It would be impracticable to capture the data by laser anemometry since unpredictable loss in power and internal reflection problems could happen
Fig. 1 Setup of wind tunnel test
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Fig. 2 Dimensions of the basic building model: (a) elevation and (b) plan
I/IH 0.9
1.0
1.1
1.2
1.3
1.4
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1.6
1.7
1.8
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LEGEND
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U/UH 0.7 z /H
I/IH Curves fitted by Power Law
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H = (z /H)
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0.4
= (z /H)
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0.3 0.2 0.1 0.0 0.6
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Fig. 3 Wind conditions established in the wind tunnel experiments
1.4
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x/b = – 0.2
x/b = 0.2
x/b = 0.4
x/b = 0.5
x/b = 0.75
x/b = 1.0
0.0 0.4 0.8 1.2
x/b = – 0.4
0.0 0.4 0.8 1.2
x/b = – 0.5
0.0 0.4 0.8 1.2
x/b = –1.0 x/b = – 0.75
0.0 0.4 0.8 1.2
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because of the semi-enclosed internal space. Wind field velocities were thus measured by hot-wire anemometry. The hot wires were operated with a constant temperature anemometer. The output voltages from the anemometer were collected and converted inside a computer, which also performed probe calibration and analysis of wind tunnel data. Miniature X-wire probes (Dantec 55P61, 55P63 and 55P64) were used to measure the velocity data on the vertical mid-width plane across the building model and on half of the horizontal plane at the level 0.61 Href ; i.e. midheight the refuge floor. In each measurement, the reference wind speed was taken by a pitot-static tube mounted at some height above the building model. This enabled the wind velocity components U, V and W to be normalized by the mean wind speed at Hh (Uh ). A refuge floor was built on the “25th storey” of the “building”. A rectangular block, covering 50% of the floor area, representing the main services core was inserted in the center of the model. Two sides of its external walls were opened. The height of the refuge floor provided in the model matched a full-scale value of about 3.75 m (0.03 H; height of the building). The data obtained in the wind tunnel experiments have been compared with the previous numerical data. Figures 4 and 5 illustrate the comparisons. Wind flow
1.20 1.15 1.10 1.05 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.0 0.4 0.8
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Fig. 5 Computed and measured velocity coefficient U U H of wind on horizontal half plane cuts at mid-height of refuge floor
patterns compiled by the wind tunnel data serve as the basis for subsequent numerical studies [28–31]. Further details of the experiments have been given in other publications [29, 31].
Application of Numerical Studies on a Typical Building Although a wind tunnel experiment can provide valuable results for studying smoke effect on refuge floor, it cannot facilitate the building designer to examine various design parameters of a building. Computational fluid dynamics (CFD) models have then been applied in many building design cases. The following section illustrates the use of a CFD model to simulate the smoke flow on the basis of the approach in Fig. 6. Figure 7 shows a typical floor in a super high-rise apartment building in Hong Kong and Fig. 8 shows the corresponding refuge floor layout. A CFD model has been established to simulate the hot gases dispersion so as to determine if the refuge
Reduced Scale-Modeling Study on Wind and Smoke Interaction
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CFD simulations
Covert the physical domains into computational domains with appropriate simplifications CONCLUSION
Determine the untenable conditions
Specify the boundary conditions (e.g. fire bed, open door and open vents)
Visualize simulation results Generate mesh schemes
NO
NO
Specify the model parameters (e.g. fire size)
Solve the dependent variables θ
Converged solution?
Grid independent solution ?
Fig. 6 Overall procedures for CFD simulations
floor may suffer from re-entering of smoke from the external. The Fire Dynamics Simulator (FDS) ver. 4.0 [32] of fire-driven fluid flow was adopted for the evaluation. It solves numerically a set of the Navier-Stokes equations appropriate for lowspeed, thermally-driven flow with an emphasis on smoke and heat transport from fires. FDS is based on the Smagorinsky model of Large Eddy Simulation (LES). The application of LES on fire dynamics is based on the separation of large scale eddies and small scale eddies by filtering process. It solves the large eddy motion by a set of filtered equations governing the three-dimensional, time dependent motions. While the small eddies are modeled by the sub-grid model independently. The basic conservation of mass, momentum and energy equations for a thermally-expandable, multi-component mixture of ideal gases [33] are as follows: ⭸ρ + ∇ · ρu = 0 (1) ⭸t ⭸ Conservation of Species : (2) (ρYl ) + ∇ · ρYl u = ∇ · ρ Dl Yl + m˙ ⭸t ⭸u Conservation of Momentum : ρ + (u · ∇) u + ∇ p = ρg + f + ∇ · τ (3) ⭸t
Conservation of Mass :
Conservation of Energy :
⭸ Dp − ∇ · qr + ∇ · k∇T (ρh) + ∇ · ρhu = ⭸t Dt
+ ∇·h l ρ Dl ∇Yl l
(4)
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Fig. 7 Layout plan a typical residential building in Hong Kong
In order to simulate the worst scenarios, fire location and fire size have been carefully selected. Simulations with fire located at various part of the flats one floor below the refuge floor have been performed. Maximum fire sizes at flashover situation have been taken. A series of simulation results were obtained for the analyses. Figures 9 and 10 illustrate some of the results. In this particular case, smoke will re-enter the refuge floor under certain wind profile. If architectural fins projecting outward are built at the floor level of the refuge floor, a substantial amount of smoke will be retarded to enter into the refuge floor. With the assistance of the CFD model, the design of the architectural fins can be effectively established. If the designer rejects the provision of architectural fins, other physical barriers, such as fire shutter or drencher, should be required to “stop” the re-entering of smoke. Moreover, with the assistance of an evacuation model, such as SGEM [34, 35], SIMULUX [36, 37], etc., the safety level of evacuees at a refuge floor can be evaluated.
Reduced Scale-Modeling Study on Wind and Smoke Interaction Fig. 8 Layout plan of the refuge floor for the residential building
Fig. 9 Temperature distribution at the vertical plan cutting the fire bed
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Fig. 10 Temperature distribution at 2 m AFFL of refuge floor
Concluding Remarks The provision of cross-ventilation for refuge floor cannot guarantee that the floor will be free of smoke logging. Previous studies by the authors have demonstrated the possibility of smoke logging by computational fluid dynamics models and reducedscale wind tunnel experiments. In view of the size of super high-rise buildings, full scale experiments can hardly be performed. Reduced-scale experiments and numerical studies are the only practical ways to investigate the problems. Moreover, in building design process, building designers are required to examine the effect of different design parameters in order to produce an effective layout. Numerical models can have the benefit in facilitating the designers to evaluate different design options. Acknowledgement The authors acknowledge the support of a RGC, Competitive Earmarked Research Grant No. CityU1172/01E, Hong Kong.
References 1. Code of Practice on Means of Escape, Buildings Department, Hong Kong Government, 1996. 2. So, A.T.P., Lo, S.M., Chan, W.L., and Liu, S.K. (1996), “Strategic fire escape from super highrise buildings”, Proceedings of ELEVCON’ 96, The International Association of Elevator Engineers, pp. 214–222.
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3. Lo, S.M. and Will, B.F. (1997), “A view to the requirement of designated refuge floors in high-rise buildings in Hong Kong”, Fire Safety Science – Proceedings of the 5th International Symposium, pp. 737–745. 4. Lo, S.M. (1998), “The use of designated refuge floors in high-rise buildings”, Journal of Applied Fire Science, vol. 7(3), pp. 1–13. 5. Lo, S.M. (1998), “On the requirements of designated refuge floors in high-rise buildings”, The Hong Kong Surveyor, vol. 9(1), pp. 25–33. 6. Yuen, K.K., Lo, S.M., and Yeoh, G.H. (1999), “A preliminary study on the smoke effect on a refuge floor”, Journal of Building Surveying, vol. 1(1), pp. 21–26. 7. Yuen, K.K., Lo, S.M., and Yeoh, G.H. (1999), “Numerical simulation of wind–smoke effect on designated refuge floor in ultra high-rise buildings”, paper presented in Interflam’99 – Fire Science and Engineering Conference, Edinburgh. 8. Kwok, W.K., Chen, D.H., Yuen, K.K., Lo, S.M., and Lu, W.Z. (2000), “A pilot study of the external smoke spread in high-rise buildings”, Journal of Building Surveying, vol. 2(1), pp. 4–9. 9. Lu, W.Z., Lo, S.M., Fang, Z., and Yuen, K.K. (2001), “A preliminary investigation of airflow field in designated refuge floor”, Building and Environment, vol. 36(2), pp. 219–230. 10. Lu, W.Z., Lo, S.M., Fang, Z., and Yuen, K.K. (2001), “A CFD study of air movement in designated refuge floor”, International Journal of Computational Fluid Dynamics, vol. 15, pp. 169–176. 11. Lu, W.Z., Lo, S.M., Yuen, K.K., and Fang, Z. (2001), “An investigation of the impact of floor setting on airflow and smoke extraction in designated refuge floor”, International Journal of Computational Fluid Dynamics, vol. 14, pp. 327–337. 12. Chen, D.H., Lo, S.M., Lu, W.Z., Yuen, K.K., and Fang, Z. (2001), “A numerical study of the effect of window configuration on the external heat and smoke spread in building fires”, Numerical Heat Transfer – Part A, vol. 40, pp. 821–839. 13. Liu, H. (1975), “Wind pressure inside buildings”, Proceedings of the 2nd US National Conference on Wind Engineering Research, Colorado State University, June 22–25, pp. III-3-1 to 3. 14. Aynsley, R.M. (1982), “Natural ventilation model studies”, Proceedings of the International Workshop on Wind Tunnel Modeling Criteria and Techniques in Civil Engineering Applications, Gaithersburg, MD, US, pp. 465–485. 15. Cook, N.J. (1985), “The designer’s guide to wind loading of building structure, Part II: static structures”, Building Research Establishment, UK. 16. Aroussi, A. and Ferris, S.A. (1987), “Air flow over buildings: A computer simulation of L.D.A. measurements”, Proceedings of the 2nd International Conference on Laser Anemometry – Advances and Applications, Strathclyde, UK, pp. 175–188. 17. Building Code of Hong Kong; PNAP 150: 1991, “Practice note for authorized persons and registered structure engineers: Wind tunnel testing of buildings”, Building Department of Hong Kong, 1991. 18. Lam, K.M. (1992), “Wind environment around the base of a tall building with a permeable intermediate floor”, Journal of Wind Engineering and Industrial Aerodynamics, vols. 41–44, pp. 2313–2314. 19. ASCE, ASCE manual on engineering practice No. 67 – Wind tunnel models on buildings and structures, New York, 1999. 20. Straw, M.P., Baker, C.J., and Robertson, A.P. (2000), “Experimental measurements and computations of wind-induced ventilation of a cubic structure”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 88, pp. 213–230. 21. Ohba, M., Irie, K., and Kurabuchi, T. (2001), “Study on airflow characteristics inside and outside a cross-ventilation model, and ventilation flow rates using wind tunnel experiments”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 89, pp. 1513–1524. 22. Paterson, D.A. and Apelt, C.J. (1985), “Computation of wind flows over building”, Research Report No. 63, Department of Civil Engineering, University of Queensland, Australia. 23. Stathopoulos, T. (1997), “Computational wind engineering: Past achievements and future challenges”, Journal of Wind Engineering and Industrial Aerodynamics, vol. 67 & 68, pp. 509–532.
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24. Satoh, K. and Kuwahara, K. (1991), “A numerical study of window-to-window propagation in high-rise building fires”, Proceedings of the 3rd International Symposium on Fire Safety Science, Hemisphere Publishing Corp., pp. 355–364. 25. Chow, K.W. and Fong, N.K. (1990), “Numerical studies on the sprinkler fire interaction using field modeling technique”, Proceedings of the Interflam ’90 Conference, Interscience Communications UK, pp. 25–34. 26. Chow, K.W. and Cheung, Y.L. (1995), “Numerical studies on sprinkler-smoke layer interaction”, Proceedings of an International Conference on Fire Science and Engineering, Hong Kong, pp. 421–438. 27. Chow, K.W. and Gao, Y. (2000), “Numerical studies on fire induced flow in a high-rise residential building”, Journal of Applied Fire Science, vol. 9(3), pp. 275–301. 28. Cheng, C.K. and Yuen, K.K. (2003), A review of designated refuge floor studies, The International Conference on Building Fire Safety, 20–21 November, Brisbane, Australia, pp. 170–177. 29. Cheng, C.K., Yuen, K.K., Lam, K.M., and Lo, S.M. (2005), “CFD wind tunnel test: Field velocity patterns of wind on a building with a refuge floor”, International Journal of Computational Fluid Dynamics, vol. 19(7), pp. 531–544. 30. Cheng, C.K., Lam, K.M., Yuen, K.K., and Lo, S.M. (2005), “Wind tunnel and CFD studies on wind flow around a high-rise building with a refuge floor”, The Sixth International Conference on Tall Buildings, Hong Kong, pp. 435–441. 31. Cheng, C.K., Lam, K.M., Yuen, K.K., Lo, S.M., and Liang, J. (2001), “A study of natural ventilation in a designed refuge floor with wind prevailing at different angles to the building”, Building and Environment, vol. 42, pp. 3322–3332. 32. McGratta, K. and Forney, G. (2004), Fire dynamics simulator (Version 4) – user’s guide. NIST Special Publication 1019, National Institute of Standards and Technology, Gaithersburg, MD. 33. McGrattan, K. (2004), Fire dynamics simulator (Version 4) – technical reference guide. NIST Special Publication 1018, National Institute of Standards and Technology, Gaithersburg, MD. 34. Lo, S.M. and Fang, Z. (2000), “A spatial-grid evacuation model for buildings”, Journal of Fire Science, vol. 18, pp. 376–394. 35. Lo, S.M., Fang, Z., Lin, P., and Zhi, G.S. (2004), “An evacuation model: the SGEM package”, Fire Safety Journal, vol. 39, pp. 169–190. 36. Thompson, P.A. and Marchant, E.W. (1995), “A computer model for the evacuation of large building populations”, Fire Safety Journal, vol. 24, pp. 131–148. 37. Thompson, P.A. and Marchant, E.W. (1995), “Computer and fluid modelling of evacuation”, Safety Science, vol. 18, pp. 277–289.
Flame Spread over Polymer-Insulated Wire in Sub-Atmospheric Pressure: Similarity to Microgravity Phenomena Yuji Nakamura, Nobuko Yoshimura, Tomohiro Matsumura, Hiroyuki Ito and Osamu Fujita
Abstract Flame spread over polymer-insulated wire in reduced pressure environments have been studied experimentally. Horizontally-placed polyethylene (PE) insulated NiCr wire is used as the burning sample. Ambient gas is the mixture of nitrogen and oxygen, and composition is fixed at constant as air. Total pressure is reduced from atmospheric (101 kPa) to sub-atmospheric (∼20 kPa) levels. Flame spread behavior over the sample wire followed by the forced ignition at the edge is examined. Experiments with backlight were also made to observe the deformation of molten PE during the spread event. Experimental results show that typical “teardrop” flame is gradually modified to round and even oval (wider in horizontal direction) as the total pressure decreases. Additionally, flame luminosity decreases, indicating the combustion becomes weaker, as the pressure decreases. Nonetheless, the spread rate does not drop in the “reduced” pressure condition, more precisely, low-pressured environment can bring faster spread rate depending under the condition considered in this study. This is due to the modification of mass and thermal transport processes depending on the pressure: relative importance of diffusive transport is pronounced while convective cooling becomes less important in the low-pressured environment. Similarity of the observed spread trend in sub-atmospherics pressure to that in microgravity with weak imposed flow via Grashof number correlation is discussed. Keywords Fire in space · flame spread · low pressure · microgravity
Nomenclature B d Da Fr
Frequency factor [1/s, 1/min] Diameter of core wire [m] Damkholer number [–] Froude number [–]
Y. Nakamura Division of Mechanical and Space Engineering, Hokkaido University, N13 W8, Kita-ku, Sapporo, 060-8628, Japan e-mail:
[email protected]
K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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g G Gr h l L P Q ΔP Re T t U β ρ μ Δθ
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Gravity acceleration (general) [m/s2 ] Gravity acceleration on the ground [9.81 m/s2 ] Grashof number [–] Thermal diffusivity [J/m2 K s] Thermal length along the wire [m] Characteristic length [m] Pressure [kPa, atm] Heat flux [W/m2 ] Pressure difference (between inside/outside the enclosure) [kPa, atm] Reynolds number [–] Temperature [K] Elapsed time [s] Characteristic velocity [m/s] Coefficient of thermal expansion [1/K] Density [kg/m3 ] Viscosity [kg/(m s)] Non-dimensionalized temperature difference (= [T − T0 ]) [–]
Subscript g s 0
Gas phase Solid phase (surface of core wire) Standard condition (temperature: 300 K, pressure: 101 kPa at normal gravity)
Introduction Necessary of Fire Studies in Depressurized Conditions Depressurized environment sounds unfamiliar when we stay on the ground (even underneath). Once we fly over the ground via airplane, balloons, spacecraft (furthermore, space habitats in future), instead, we are forced to stay in “depressurized enclosure”. Selection of reduced pressure over the standard pressure (101 kPa, P0 ) in such enclosure is quite simple: it has excellent advantage to simplify the structure. Due to the fact that the pressure difference between internal and outside of the enclosure, ⌬P, is the only matter to enforce the stress on the structure, reducing ⌬P is preferable choice from engineering point of view to hold mechanical safety [1]. As is well-known, the internal pressure in the aircraft cabin is maintained to 80 kPa (∼0.8 P0 ) during the flight in 30,000 ft altitude, at which ambient pressure is about 25 kPa (∼1/4 P0 ). Although current space shuttle or ISS (International Space Station) chose the normal pressure atmosphere in the cabin, sub-atmospheric pressure environment (∼65 kPa) is going to be applied to next generation of spaceship, called ORION [2].
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Fire in such artificial enclosure is quite dangerous and we must fight with our best knowledge. Thus, fire retardant evaluation is crucially important. In terms of the space vehicle, materials allowed to use must be passed “fire safety standard test” [3]. Important to note here is that the test is performed on the ground (i.e. normal pressure) although the working condition could be sub-atmospheric pressure as mentioned. The test is acceptable if the combustibility of the material does not depend on the pressure, however, if so, the test results are not sufficient to use as the safety measure unless appropriate corrections are made. Unfortunately, there are limited evidences about the pressure dependency (especially in low pressure range) on solid combustibility [4–6]. Frey [4] has reported that the pyrolysis temperature becomes lower (i.e. more fuel is ejected in the same temperature level) in the reduced pressure field. Saito et al. [5] made irradiated ignition test of the propellant to reveal the various mode of ignition and ignition delay time in the depressurized field. Goldmeer et al. [6] have studied the flame spreading behavior over PMMA rod in sub-atmospheric pressure and showed the flame spread rate is monotonically decreased with the pressure. Yang et al. [7] examined the burning characteristics of PMMA (poly-methyl metacrylate) sphere in sub-atmospheric pressure. By chance, these reports indicated that chance of fire becomes less as the pressure decreases, however, there is no guarantee to apply this conclusion to all possible cases of fire. For example, there is no evidence for electric wire combustion (including ignition and subsequent flame spread) in sub-atmospheric pressure, which is the one of most considerable fire chance in the aircraft and space vehicle [8–10].
Objective and Target of This Study: Similarity of Combustion in Depressurized vs. Microgravity Environments Combustion character of polymer-insulated wire is quite unique: it has extensive heat transfer through the wire and make molten phase during the combustion of polymer (combustion processes contains gas-liquid-solid phases). According to the previous studies [11, 12], the spread behavior strongly depends on the heat transfer through the electric wire to heat up the unburned material. This heat transfer is originated by the flame (to heat the bare wire), thus, gas-phase flame status, e.g. where and how to attach the flame to the wire, is crucially important to determine the flame spread event. Previously, in microgravity environment, flame spread of electric wire becomes faster than normal gravity, suggesting that flow “stagnant” situation could bring preferable condition on fire of electric wire. Now it is important to note that the sub-atmospheric pressure also provides “stagnant” situation since the convective transport process essentially depends on the ambient density (total pressure) [13]. If this is true, sub-atmospheric pressure would give faster spread rate than that in standard pressure; this is totally opposite to the previous sub-atmospheric solid combustion literature. It is interesting to see if there is certain similarity law, like Grashof number correlation, is retained. If this is done, we can “simulate” or “reproduce”
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microgravity phenomena virtually through the change in environmental pressure and we may not need expensive facility to obtain real microgravity environment. In this study, we made first look for the flame spreading phenomena of polymerinsulated wire in sub-atmospheric pressure and examined the similarity to microgravity combustion phenomena. As first step, pai number correlation is made to obtain the key physics to be concerned. Final goal of our study is to have better understanding of fundamental fire characters in sub-atmospheric pressure to provide an appropriate fire safety strategy in the aircraft and space.
Experiment Figure 1 shows the experimental apparatus used in this study. The chamber volume is 365 mm (L) × 260 mm (W) × 180 mm(H) and gas is fully sealed during the test. There are two gas-lines mounted in the chamber: one is from gas supplying system and the other is connected to vacuum pump. Sealing performance is well-checked prior to the experiment and we confirm the less than 1% fluctuation of internal pressure at least 10 min. Polyethylene (PE) coated NiCr wire (core diameter is 0.5 mm, thickness of PE is 0.15 mm) is used as test combustible sample throughout the study. Igniter (coil heater) is set on the one end of the sample to initiate the ignition and subsequent flame spread over the wire. Whole events are recorded by digital video camera (Sony: DCR-TRV900, 30 frames per second, denote “DV camera” hereafter) through the side window made by Pyrex. Each experimental run is made by the following manner. First, the sample is placed at the center portion of the chamber. Close the chamber and vacuum procedure is employed until below 3 kPa internal pressure is achieved. Close the vacuum line and open the gas supply line, then ambient gas mixture (21 vol.% of oxygen diluted by pure nitrogen) is supplied into the chamber until a target pressure condition (from 20 kPa to 101 kPa) is achieved. Leave the chamber at least 5 min. to ensure the internal gas motion is ceased. Then the igniter is turned on (we define this instance as t = 0 s) and continuous 5 s heating is employed on the sample.
Pressure Gauge Compression Air Spread
Flame
Ignitor
PE Sample Wire Sample Holder
Fig. 1 A schematic of experimental apparatus
To Vacuum
Combustion Chamber
To DC Supply
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Ignition and subsequent flame spread events (lasts about 30 s) are recorded by DV camera. Shutter speed and exposure of the camera are set to 1/250 s and full open, respectively. All experiments are done in the dark room to avoid any possible noise in the observed images. Visualizing molten PE deformation was done by backlight method.
Experimental Results General Description of Ignition and Flame Spread of Polymer-Insulated Wire At first, it is better to have general concern about how ignition occurs and flame spreads in the present system. Once igniter (coil heater set to near-by the sample wire) is turned-on, high heat flux is exposed onto the unburned PE. PE melts and evolves combustible gases into the atmosphere. The combustible gases mixes with ambient oxygen to form the combustible mixture. The mixture is heated by igniter and the forced ignition occurs when the flammable condition is attained. Followed by the ignition, diffusion flame is formed over the molten PE. The flame is formed a bit away from molten PE, one flame tip of downstream (unburned side) heats up the unburned PE through gas-phase conduction or radiation. Additionally, especially for insulated-wire combustion, the other flame tip of upstream is attached on the bare wire to heat up the wire, resulting in one more thermal transport along the wire to unburned PE is provided. The former (gasphase heat transfer to the solid) is conventional heating mode in the fundamental fire study (e.g. flame spread over PMMA, cellulose, wood etc.), but the latter (conduction through the wire) is specialized for wire combustion. According to Umemura et al. [12], the latter mode plays a role on insulated-wire combustion in microgravity.
Visible Flame Characters in Depressurized Fields Figure 2 shows the typical instantaneous flame shape observed during the flame spread (15 s after the ignition) with various sub-atmospheric pressure conditions. Flame becomes less luminous and the shape changes from “teardrop” to sphere or oval as the pressure decreases. It is suspected that such flow becomes weak in sub-atmospheric pressure. Figure 3 summarizes quantitative change of flame height and width, indicating that they are not linearly correlated to the pressure. In Fig. 4, typical instantaneous backlight images are shown. Larger molten PE is clearly obtained in lower pressure condition. Molten PE is elongated to downward by gravity force and suspended by the wire. Frequent dripping-off event of suspended molten PE has been notified especially lower than 0.4 P0 . This fact suggests
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(a) P = P0
(b) P = 0.9P0
(c) P = 0.8P0
(d) P = 0.7P0
(e) P = 0.6P0
(f) P = 0.5P0
(g) P = 0.4P0
(h) P = 0.3P0
Fig. 2 Direct still images of spreading flame in depressurized conditions (15 s after ignition). Flame travels from right to left
Length Scale [mm]
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Fig. 3 Change of outer shape of observed spreading flames
Flame Height 10
8
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4 0.02
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that molten PE does not consumed well during the spread event in lower pressure. This interesting notice is continuously investigated in our future study and no further concern is made here. At 0.3 P0 , flame extinction is observed immediately after the dripping-off of molten PE, indicating that flame in low pressure is weak enough to lead extinction against the fluctuation.
(a) P = P0
(b) P = 0.6P0
(c) P = 0.4P0
(d) P = 0.3P0
Fig. 4 Direct still images of molten PE during the flame spread in depressurized conditions via backlight visualization technique
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Quasi-Steady State Spread Behavior
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Flame Tip Position [mm]
Flame Tip Position [mm]
Figure 5 compares the typical time-history of the location of flame tip during the spread depending on the imposed pressure. Here, we only plot the data after 10 s of the ignition (t ∗ = 10 s in the figures) to avoid any ignition effect on the spread data. It is understood that the flame tip moves almost linearly against the time. Nonetheless, “go-and-stop (zigzag)” motion is clearly observed in lower pressure (less than 0.4 P0 in this study). This motion is related to the change in the shape of molten PE including the surface tension and no further discussion is made here. Although such motion is observed, averaged flame spread rate can be calculated as mean value and its reproducibility is fairly good to discuss about the qualitative trend. Linear relationship obtained here suggests the following three things. At first, the spread event observed is in “quasi-steady state” and the averaged spread rate can be defined uniquely as eigen value. Second, the combustion chamber is large enough and oxygen consumption during experiment does not play a role on the observable spread behavior. Lastly, effect of boundary layer formed over the wire, which may cause the change of the spread rate [14], on the spread is negligibly small. (a) P = 101 kPa 30 20 10 0
0
5 10 Elasped Time, t-t* [s]
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(b) P = 40 kPa 30 20 10 0
0
5 10 Elasped Time, t-t* [s]
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Fig. 5 Time-history of flame front in spreading flame
Flame Spread Rate: Fire Crisis Measure in Depressurized Field Flame spread rate calculated from the time history of the flame tip (during t = 10 s to 20 s) in sub-atmospheric pressure is summarized in Fig. 6. Interestingly, it is found that the spread rate does not decrease, rather slightly increase, as the pressure decreases although the reaction rate (i.e. heat release rate) becomes slower in low pressure (∼P2 : this will be explained in later). This trend is completely different from the previous studies [4–7]. Recall that the lower pressure case, at which higher spread rate is observed, induces the frequent dripping-off the hot molten PE; this makes further fire damage. These two facts reveal that the low-pressure environment is more dangerous than standard atmospheric environment in fire safety point of view. On the other hand, flames in low pressure are less-luminous and weakened as described (see Fig. 2), suggesting that low-pressured environment is rather safe. Thus, we have to have right measure to evaluate the possible fire damage depending on pressure. If the measure is based on the spread rate, current results indicate that
Fig. 6 Pressure effect on flame spread rate of model wire (PE-coated NiCr wire)
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Normalized Pressure, P/P0 [-]
evaluating combustibility in the ground for aircraft materials exposed in the depressurized environment may fail or underestimate the fire crisis in sub-atmospheric pressure.
Discussions Flame Spread Mechanism in Depressurized Field Now the question is why the enhancement of flame spread in sub-atmospheric pressure is observed. It is worthwhile to look for the possible change of physical processes according to the change of pressure. Considering the pai numbers appeared in the chemically reactive-fluid system under the condition of fixed gas composition, corresponding independent ones are only limited to Froude number (Fr = U2 /gL), Reynolds number (Re = ρUL/μ) and Damkholer number (Da = BL/U). Since we have no forced flow in the present system, thus, characteristics velocity on this system should be represented by the buoyancy-driven flow. Assuming that momentum force is equal to buoyancy force driven by a given temperature difference (∼Fr = 1), another pai number describing the ratio of gravity force and viscous term; namely Grashof number (Gr = ρ 2 gL3 Δθ/μ2 : note that U is scaled by (gL)1/2 ) is introduced. Now if only transport processes are of interest, Gr and Re are the system controlling pai numbers; Gr = ρ 2 gL3 Δθ/μ2 ∼ P2
(1)
Re = ρUL/μ = ρg1/2 L3/2 /μ ∼ P1
(2)
Consider that viscosity coefficient (μ) is independent on the pressure [15], gravity (g) and the characteristic length scale (L) is essentially independent of pressure. In addition, density is linearly correlated to the pressure according to the equation of state for ideal gas (P∼ρT). These facts give us their pressure dependency clearly; Gr ∼P2 and Re∼P1 . Thus, as the imposed pressure is decreased, both pai numbers are decreased. Considering that Gr is the ratio of gravity and viscosity (diffusion)
Flame Spread over Polymer-Insulated Wire in Sub-Atmospheric Pressure
25
and Re is the ratio of momentum and viscosity (diffusion), the diffusion becomes dominant transport process when the pressure decreases. This situation is basically the same as what we observed in microgravity, where the diffusion is dominant in whole transport processes. Round flame shape observed in lower pressure (see Figs. 2 and 3) supports this consideration. In polymer-insulated wire combustion process, thermal conduction through the core wire play crucial role as mentioned previously. Due to the conduction, unburned PE is heated up to enhance the spread. Simultaneously thermal wave through the wire travels to the burned bare wire, where the wire is expected to have convective cooling induced by the buoyancy-driven flow. This “convective heat loss” is described by following manner; Q = h(T s − T0 ), where h is thermal diffusivity and T s is the surface temperature of the heated core wire. Here, h is a function of the velocity induced by buoyancy and roughly estimated by Nusselt number (N u) for cylinder configuration. Total heat loss by buoyancy-driven convection can be estimated as dl × h(T s − T0 ), where l indicates the characteristic length of thermal layer along the wire. Since Nu has [Gr ]1/15 dependency for small value of Gr [16], total heat loss is scaled by P 2/15 l. Thus, the length of thermal layer along the wire, l, increases as the pressure decreases (l∼P−2/15 ). Therefore we can simply expect the thermal layer to the unburned portion (i.e. upward direction) also moderately increases in sub-atmospheric pressure. This might be the one of reasons to give higher spread rate and elongated (oval) flame shape observed in this study. Further study would be necessary to concrete the effects of pressure drop on the spread behavior. We now conduct the measurements of the temperature profile along the wire and gas-phase temperature distribution.
Similarity to Microgravity Flames Figure 7 shows the comparison of visible spreading flame over the polymer-insulated wire in microgravity (left) [11] and in 0.3 P0 (right). As notified, the flame shape seems equivalent (although further elongated for microgravity flame as explain in later), suggesting that gas-phase transport process is similar to each other. However, obvious difference is found in the flame color, which is rather related to the chemical processes. Because the chemical reaction rate is linearly correlated to the collision frequency of the reactive molecules and the number of reactive molecules decreases as the pressure decreases, the general overall reaction order of hydrocarbon fuels (directly related to the pressure dependency) are mostly around 1.5∼2. As a consequence, the reaction rate decreases quickly when the pressure decreases. Reactions for soot formation also become slower even though the longer residence time is expected in low pressure. This might contribute to appear less-luminous flame as found in low-pressured cases. In microgravity condition, on the other hand, frequent collision in the stagnant field (i.e. longer residence time in the flame) is possible since considerable number of molecules exists. This is best condition to grow the soot, resulting in the high-luminous flame. In this case, thermal input via radiation
26
Y. Nakamura et al.
Fig. 7 Comparisons of still picture of spreading flames over polymer-insulated wire (left: microgravity flame, right: low-P flame (0.3P0 )
(a) Microgravity experiment [ref.11 ] [35%O2, micro-g with velocity: U] 4
3 0.01
exponent: –0.0754
out of thermal regime (radiation extinction regime)
0.1
1 10 2 2 2 (P/P0 ) × U /L, [m /s]
100
Flame Spread Rate, Vsp, [mm/s]
Flame Spread Rate, Vsp, [mm/s]
from the flame to the wire comes to play a role, resulting that longer thermal layer along the wire, i.e. further flame elongation to axial direction, is expected than that of sub-atmospheric flames. As suggested from above discussions, flame shape (especially flame width along the wire) found in low pressure and in microgravity conditions would be welldescribed by the thermal layer formed along the wire. Once we try to simulate “microgravity” flame spreading in “low-P” conditions, additional treatment to elongate the thermal layer along the wire (e.g. slight heating of the wire, external radiation input) would be effective. Lastly, let us see the Grashof number correlation to the present low-pressured data (in 21% O2 atmosphere) and microgravity data (in 35% O2 atmosphere with standard pressure) referred from Ref. [11]. Here, corresponding microgravity data are the spread rate under various weak imposed velocities. Since Fr is assumed as unity, therefore, equivalent gravity acceleration for the specific weak flow velocity, U, can be obtained by U2 /L. Since microgravity flame has lower flame temperature, let us assume the temperature is constant. Now the not-constant parameter in Gr is (P/P0 )2 × g, and under Fr ∼1 assumption, it can be transformed to (P/P0 )2 × U2 /L. Results are plotted (log–log) in Fig. 8, showing Grashof number correlation to the spread rate. Since microgravity data showed the peak of spread rate in certain imposed flow velocity, data categorized to the thermal regime, where the radiation
(b) Sub-atmospheric experiment [21%O2, normal-g, no forced flow] 3
exponent: –0.0526 2 0.01
0.1
1 2 2 (P/P0 ) × g, [m /s]
10
100
Fig. 8 Grashof number correlation to the spread rate in microgravity with weak flow (left) and in sub-atmospheric pressure (right)
Flame Spread over Polymer-Insulated Wire in Sub-Atmospheric Pressure
27
extinction mode is neglected, is concerned in the following. As indicated, exponent for both cases are fairly close and it is suggested that the ratio of buoyancy (or momentum) and diffusion transport may responsible to determine the spread behavior. Although the current estimation is quite rough, however, the scale modeling concept is valuable to consider what could be the dominant process and which we will look into deeply in the next.
Conclusions Flame spread behavior over the polymer-insulated wire under lower pressure field is examined experimentally and compared to the phenomena given in microgravity. Features of depressurized flame spread over the insulated-wire, such as “go-and-stop” motion, flame shape and quasi-steady spread, have been revealed. Dimensional analysis is employed to explain the observed flame shapes by looking up the thermal balance along the wire. It is suggested that microgravity flame could be “simulated” by applying low-P condition with additional thermal treatment. Acknowledgments This work is partially supported by Grants-in-Aid for Young Scientists (B) of #17710131, Japan Space Forum, and Noumura Foundation of Science and Technology. YN would like to express sincere thanks for their supports to work on the present subject.
References 1. Nakamura, Y., J. Space Tech. Sci. 21(2) (2005) 39–48. 2. http://www.nasa.gov/missions/solarsystem/cev.html. 3. NASA office of safety and mission quality, flammability, odor, offgassing and compatibility requirements and test procedures for materials in environments that support combustion, NHB8060.1C (1991). 4. Frey, Jr., E., Combust. Flame 36 (1979) 263–289. 5. Saito, T., Harayama, M., Iwama, A., J. Ind. Explosives Society of Japan 41(3) (1980) 131–140 (in Japanese). 6. Goldmeer, J.S., T’ien, J.S., Urban, D.L., Fire Safety J. 32 (1999) 61–88. 7. Yang, J.C., Hamins, A., Donnelly, M.K., Combust. Flame 120 (2000) 61–74. 8. Limero, T., Wilson, S., Perlot, S., James, J., SAE Tech. Paper 921414 (1992). 9. Paulos, T., Paxton, K., Jones, S., Issacci, F., Catton, I., Apostolakis, G., AIAA 93–1153 (1993). 10. Friedman, R., Fire and Materials 20 (1996) 235–243. 11. Fujita, O., Nishizawa, K., Ito, K., Proc. Combust. Inst. 29 (2002) 2545–2552. 12. Umemura, A.,Uchida, M., Hirata, T., Sato, J., Proc. Combust. Inst. 29 (2002) 2535–2543. 13. Gaydon, A.G., Wolfhard, H.G., Flames, Their Structure, Radiation and Temperature (4th edn.) Chapman Hall, London, 1979. 14. Nakamura, Y., Etoh, Y., Yamashita, H., Trans. JSME (B) 69(677) (2003) 192–199 (in Japanese). 15. Bird, R.B., Stewart, W.E., Lightfoot, E.N., Transport Phenomena. John Wiley & Sons, New York, 1960. 16. Katsutou, Y., Dennetsu-Gairon (Introduction to Heat Transfer) (29th edn.), Yoken-do, Tokyo, 1990 (in Japanese).
Mechanistic Aspects of the Scaling of Fires and Explosions Forman A. Williams
Abstract Mechanistic aspects of scalings are addressed that include burning rates, flame spread, room fires, explosions, turbulent combustion and chemistry (fire suppression and the production of soot and toxic materials), with attention focused on dimensions sufficiently large for turbulence to be fully developed. For burning pools and cribs, scalings of burning rates, flame heights and radiant emissions are suggested, and for room fires, modifications associated with the onset of ventilation control are considered. Both confined and unconfined explosions are addressed, including overpressure scaling and, for the latter, size and radiation scaling for the limit of instantaneous release with momentum and buoyancy control. Relationships to scalings of turbulent combustion of gases and roles of chemical kinetics are mentioned. Keywords Scaling · fires · explosions
Nomenclature Ao c D E f g H Ho hF
Area of opening Specific heat at constant pressure Diffusion coefficient Total rate of emission of radiant energy from the gas Stoichiometric ratio by mass of fuel to oxygen Acceleration of gravity Flame height Height of opening Lower heating value of the fuel (net chemical energy liberated per unit mass of fuel consumed)
F.A. Williams Center for Energy Research, University of California, San Diego, La Jolla, CA 92093-0411, USA
K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
29
30
hg L LP M m n p q R s T U V YO
F.A. Williams
Energy required for heating and vaporization of a liquid fuel or for heating and gasification of a solid fuel (energy per unit mass) Length scale Planck-mean absorption length Mass loss rate (mass per unit time) Burning rate (mass per unit area per unit time) Pressure exponent of inverse chemical time Pressure Heat flux to fuel (energy per unit area per unit time) Aspect ratio Surface to volume ratio of fuel elements Temperature Root-mean-square velocity fluctuation Velocity Mass fraction of oxygen in the atmosphere
Greek α ε κ λ ν ρ ρT σ σT τ χ
Thermal diffusivity Emissivity Packing fraction, fraction of total volume of bed occupied by fuel Thermal conductivity Kinematic viscosity Density Rate of change of liquid density with temperature Stefan-Boltzmann constant Rate of change of surface tension with temperature Overall chemical conversion time Radiant fraction
Subscripts a b c F f g i l O o s
Ambient atmosphere (typically air) Burning Crossover Fuel Flame Gas Initial Liquid Oxygen Opening Surface
Mechanistic Aspects of the Scaling of Fires and Explosions
31
Introduction Complexities of fire and explosion phenomena make rational approaches to their understanding difficult. Scaling is a way to try to develop rational understanding that can generate useful simplifications. From the underlying conservation equations, all of the dimensionless groups that arise can be identified [1]. When this is done, it is found that there are about 30 such groups, and scaling keeping all of these groups constant is manifestly impossible. It is therefore better to identify dominant groups from mechanistic concepts [2]. Different scaling procedures are then derived, depending on which groups are presumed to be in control, so that the scalings offered here differ somewhat from earlier [2] ones. Many different scaling protocols can thereby be obtained.
Pool Burning Burning rates, flame heights and radiant heat fluxes from plumes are among the items of interest in pool burning. Burning rates are determined by a balance between the heat feedback from the fire to the fuel and the energy required to vaporize the fuel, m = q/ h g
(1)
Although there are corrections for different initial fuel temperatures and for heat losses from the liquid, h g is often approximately the latent heat of vaporization, a fuel property, while q depends on the gaseous flow field and radiation. For heat transfer by turbulent free convection q = a ca (Tf − Ts )(a g)1/3
(2)
apart from near-unity factors involving the Prandtl Number of air and the ratio of the density difference of the gas to its mean density. Hence m is approximately independent of scale, so that M scales as L 2 with L the square root of the surface area of the pool. This well-known result is well justified experimentally [3] even with large, dominant radiant heat-transfer contributions, although modifications arise at small L where transitional and laminar flow occur. To obtain the scaling with L was, in fact, a major objective even in the original publication [3]. Beyond simple scaling with L, there have been studies of pressure modeling [1, 4] and ideas on acceleration modeling [1]. Applied to pool fires, the proportionalities M ∼ p 2/3 and M ∼ g 1/3 , implied by Eqs. (1) and (2) since a ∼ p and a ∼ 1/ p, could be exploited in various ways. If, for example, there is interest in fixing M at normal gravity, then increasing p with decreasing L according to p ∼ L −3 would test the formulas. Centrifuge experiments at reduced pressure with p ∼ g −1/2 and L fixed would test the prediction that M and m both remain constant. Air vitiation to reduce T f , or inert addition to fuel to modify T f and h g are other strategies of
32
F.A. Williams
comparable complexity. It is economically more practical to vary only L or fuel composition to test predictions. Flame heights are generally controlled by buoyancy. Under such conditions, again ignoring nearly constant factors as above and putting entrainment velocities proportional to buoyant velocities, the ratio of the fuel flow √rate into the fire plume to the air flow rate into it over height H is m L 2 /(H L √ a g H ), where the length L. in the denominator is now the perimeter, roughly L R. The flame height for meter-size or larger pools is thereby found to be 2 2 2 2 1 3 H=L m R f Y O a gL
(3)
Use of Eqs. (1) and (2) in Eq. (3) gives
H = L ca T f − TS
2 2 9 1 1 3 va g 9 (R L) 3 h g f YO
(4)
The consequent turbulent flame-height scaling as L 2/3 / p 2/9 g 1/9 could be tested and exploited in a variety of ways. Sooting is an especially complicating factor for poolfire flame heights which, depending on how H is defined (to the beginning of the smoke or to the top-most soot-hidden flame) can significantly decrease or increase H and modify scaling. Radiant heat fluxes depend on geometry and distances but are proportional to the total rate of emission of energy. For liquid fuels, such as methanol, that typically may have predominantly optically thin flames, E = 4σ T f4 H L 2 L p
(5)
For other liquid fuels that have smoky fire plumes the radiant transfer problem is much more complex, but in the optically thick limit the approximation E = εσ T f4 H L
√
R
(6)
may be employed with ε = 1 or with ε < 1 and adjusted to account for the fact that the temperature of the average emitting surface is less than the flame temperature. Combined with preceding equations, this last expression yields, for the fraction of the total energy release emitted by radiation, χ=
√
RεT f4
hF f
2
Y02
1 1 3 1 4 1 9 3 va g 9 (R L) 3 hg ca T f − TS (7) a
which is applicable only if the resulting value of is less than about 30% and √ in which Rε is to be replaced by 4L/L P < 1 for optically thin flames. Scalings implied here, ∼ p −8/9 g −4/9 L −1/3 R 1/6 , have the directions of their L and
Mechanistic Aspects of the Scaling of Fires and Explosions
33
R dependences reversed for optically thin flames, thereby further emphasizing the complexity. A reasonable compromise approximation may be to assume that is independent of L and R for large turbulent pool fires, resulting in radiant fluxes at geometrically similar distances being proportional to L 2 .
Crib Fires Although burning rates and flame heights of crib fires share much in common with pool fires, their burning mechanisms are more complex [5]. There are a larger number of geometrical parameters in crib fires. Different behaviors are exhibited in loosely packed limits (where each fuel element has sufficient oxygen and burns roughly independently) and in densely packed limits (where buoyancy-induced flow through vertical shafts in the crib, with heat and mass transfer, affects overall massloss rates) [6, 7]. As a first approximation, the same kinds of scaling indicated above for pools may be applied to cribs in the open. Within enclosures, burning rates of both cribs and pools can be reduced by oxygen deprivation and increased by radiation from walls and especially hot ceilings. This last effect appears to be larger for pools than for cribs [8]. In a rough first approximation, however, such effects might be neglected, and common enclosureindependent scaling may then be tested for both pools and cribs.
Room Fires As fires in compartments grow and begin to become ventilation-controlled, the enclosure independent burning rates no longer apply. Burning rates are very likely to be controlled by ventilation after flashover. When ventilation restrictions become important, burning rates can become dependent in complicated ways on positions, sizes and shapes of openings. The simplest case, namely that of a single rectangular opening, has been studied thoroughly [8]. Under ventilation-controlled conditions for this configuration, approximately [9] √ M = a g Ao H0 2
(8)
5/2 where √ a refers to the air outside the opening. The consequent scaling, M ∼ L p g, where L is now a characteristic linear dimension of the opening, is not excessively different from the corresponding results derived from Eqs. (1) and (2) in the absence of ventilation limitations (M ∼ L 2 p 2/3 g 1/3 , with L the fuel dimension). The differences between these two scaling, proportional to L 1/2 p 1/3 g 1/6 , could be difficult to detect experimentally. One might therefore be motivated to investigate possible nearly common scaling of burning rates over wide ranges of conditions, maintaining full geometrical similarity of room dimensions, fuel dimensions and object locations, but keeping sizes large enough to assure well-developed
34
F.A. Williams
turbulence. Burning times under such conditions may scale roughly as L 9/4 p 5/6 g 5/12 , the exponents here representing the arithmetic mean of the exponents of each of the two scaling. This approach would contrast with some previous scaling approaches in which different dimensions were scaled differently on the basis of presumed physical mechanisms. It should be emphasized that the preceding suggestions are rough approximations, at best. Different fuels do indeed behave differently in room fires, and more detailed considerations enable these differences to be addressed well [8].
Fire Spread Spread of flames is important in many fire scenarios [10–12], including room fires [8]. Flame spread can modify scaling and has not been addressed above. Complexity is introduced by the fact that there are numerous different mechanisms of fire spread [10], and different mechanisms generally imply different scaling. A general expression for spread rates, developed on the basis of an energy balance, can be written as [10] V =q
hg F
(9)
Consideration of the many different mechanisms for the relevant effective heat transfer flux q then leads to a wide variety of different formulas for V .
Explosions Explosions occur more rapidly than fires and have different scaling concerns [13], although there are some common elements. Confined and unconfined explosions are two limiting categories with different characteristics. In confined explosions interest focuses on overpressures achieved [13–15] and transition to detonation, as affected by the extent of partial confinement and by obstacles in the flow, as well as by fuel distribution and igniter location. Unconfined explosions have less of a propensity for transition to detonation and more often involve fireplume or fireball formation, with associated concerns about radiant energy emissions and durations. Steady-state concepts, so prevalent for fires, are less relevant for explosions, which involve timedependent fluid dynamics and compressible gas dynamics. For unconfined explosions [16], two limiting conditions can be defined, depending on the manner in which gaseous fuel is released to the atmosphere. If the release time is long compared with the mixing time, then a nearly steady-state fuel jet is established, usually with a core too rich in fuel to burn, while if the release time is short compared with the mixing time, then a time dependent fuel cloud is formed, which after ignition can develop into a fireball. Various combustion-time studies [16, 17] suggest two different controlling fireball combustion mechanisms. Neither of these mechanisms involves the most obvious possible controlling factor,
Mechanistic Aspects of the Scaling of Fires and Explosions
35
namely atmospheric turbulence, which would give a combustion time t of order L 2 divided by a turbulent diffusivity, the product of a root-mean-square turbulent velocity fluctuation with a turbulent integral length scale of the atmosphere. This would result in t increasing as the two-thirds power of the fuel mass, a much stronger dependence than observed. The reason that this is incorrect is that the fireball generates its own turbulence that overpowers ambient atmospheric turbulence, shortening t. The two controlling mechanisms for generating turbulence are buoyancy, involving g, or the momentum of the release of the cloud, involving the velocity m/a ,√where m is now an average mass flux during release. In the former case t scales as L/g, proportional to the one-sixth power of the fuel mass, and in the latter case t scales as Lm/a , proportional to the one-third power of the fuel mass. Since the most rapid process is the one that will be in control, estimates may be made on the basis of both of these mechanisms, and the mechanism that gives the shortest t may then be selected. The total rise height, gt 2 , will scale as L, proportional to the cube root of the fuel mass, for buoyancy control and as L 2 , proportional to the two-thirds power of the fuel mass, if momentum dominates buoyancy for the entire lifetime, which seldom occurs. The combustion times encountered rarely exceed 10 s, even for the largest fireballs. Scaling of radiant emissions from fireballs will vary with optical thickness. For optically thick fireballs, roughly E = εT f4 L 2
(10)
and in this formula ε must be replaced by L/L P for optically thin fireballs. Consequent radiant fractions, roughly χ = Et h F a L 3
(11)
increase with L for optically thin fireballs then level off and possibly even decrease slightly with increasing L after the fireball becomes optically thick, which occurs for sufficiently large values of L. The transition of an optically thick cloud occurs at sizes that are relatively strongly dependent on the fuel and that are generally smaller for higher hydrocarbons. These qualitative understandings help in scaling fireballs. If the cloud core is not fuel-rich at the time of ignition, so that a deflagration can consume all of the fuel, then the burning time generally is decreased. Under these conditions, for sufficiently large clouds, flame propagation can lead to significant pressure buildup and result in a self-similar time-dependent process in which a shock wave precedes the deflagration. Scaling relations exist for such so-called nonideal explosions [18, 19]. Overpressures depend on turbulent burning velocities, heat release, gas dynamic parameters and geometrical configurations.
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F.A. Williams
Turbulent Combustion In turbulent combustion, Damkohler and Reynolds numbers appear [20, 21]. Finiterate chemistry becomes important for flame extinction [22] and motivates studies of reduced chemistry [23]. Soot is a complicating factor that can sometimes influence net heat release [24] and that is produced by finite-rate chemistry [25]. For carbon monoxide [26] the rate of consumption can influence emission. Future progress may be expected in these important areas.
Concluding Comment As continuing research on fires and explosions is showing [27], there are numerous different mechanisms that can become relevant under different situations, and these different mechanisms in general will imply different scalings. There is much more work to be done on scaling of fires and explosions.
References 1. Williams, F.A. Scaling Mass Fires. Fire Research Abstracts and Reviews, 11, 1969, pp. 1–23. 2. Quintiere, J.G. Scaling Applications in Fire Research. Fire Safety Journal, 15, 1989, pp. 3–29; How to Use a Scale Model to Simulate the Fire and Structural Failure of the World Trade Center Towers. Proceedings of the Third Joint Meeting of the U.S. Sections of the Combustion Institute, Chicago, IL, March 16–19, 2003. 3. Blinov. V.I. and Khudiakov, G.N. Certain Laws Governing Diffusive Burning of Liquids. Academiie Nauk, SSSR Doklady, 113, 1957, pp. 1094–1098. 4. De Ris, J., Kanury, A.M. and Yuen, M.C. Pressure Modeling of Fires. Proceedings of the Combustion Institute, 14, 1973, pp. 1033–1044. ˜ Some Recent Progress. Proceedings of the 5. Thomas, P.H. Behavior of Fires in Enclosures N Combustion Institute, 14, 1973, pp. 1007–1020. 6. Block, J.A. A Theoretical and Experimental Study of Nonpropagating Free-Burning Fires. Proceedings of the Combustion Institute, 13, 1971, pp. 971–978. 7. Heskestad, G. Modeling of Enclosure Fires. Proceedings of the Combustion Institute 14, 1973, pp. 1021–1030. 8. Quintiere, J.G. Fire Behavior in Building Compartments. Proceedings of the Combustion Institute, 29, 2003, pp. 181–193. 9. Williams, F.A. Urban and Wildland Fire Phenomenology. Progress in Energy and Combustion Science, 8, 1982, pp. 317–354. 10. Williams, F.A. Mechanisms of Fire Spread. Proceedings of the Combustion Institute, 16, 1977, pp. 1281–1294. 11. Wickman, I.S. Flame Spread in an Opposed Flow with a Linear Velocity Gradient. Combustion and Flame, 50, 1983, pp. 287–304. 12. Pastor, E., Z´arate, L., Planas, E. and Arnaldos, J. Mathematical Models and Calculation Systems for the Study of Wildland Fire Behaviour. Progress in Energy and Combustion Science, 29, 2003, pp. 139–153. 13. Bradley, D. Dimensionless Groups in Fires and Explosions. Fire and Explosion Hazard of Substances and Venting of Deflagrations, Proceedings of the First International Seminar (Molkov, V., Editor), Russian Association for Fire Safety Science, 1995, pp. 8–17.
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14. Bradley, D. and Mitcheson, A. The Venting of Gaseous Explosions in Spherical Vessels. Combustion and Flame, 32, 1978, pp. 221–255. 15. Molkov, V., Korolchenko, A. and Alexandrov, S. Venting of Deflagrations in Buildings and Equipment: Universal Correlation, Fire Safety Science – Proceedings of the Fifth International Symposium, International Association for Fire Safety Science, 1997, pp. 1249–1260. 16. Makhviladze, G.M. and Yakush, S.E. Large-Scale Unconfined Fires and Explosions, Proceedings of the Combustion Institute, 29, 2003, pp. 195–210. 17. Roper, F., Arno, J. and Jaggers, H.C. The Effect of Release Velocity and Geometry on Burning Times for Non-Premixed Fuel Gas Clouds. Combustion Science and Technology, 28, 1991, pp. 315–338. 18. Kuhl, A.L., Kamel, M.M. and Oppenheim, A.K. Pressure Waves Generated by Steady Flames, Proceedings of the Combustion Institute, 14, 1973, pp. 1201–1215. 19. Williams, F.A. Qualitative Theory of Nonideal Explosions. Combustion Science and Technology, 12, 1976, pp. 199–206. 20. Peters, N. Turbulent Combustion. Cambridge University Press, Cambridge, 2000. 21. Williams, F.A. Turbulent Combustion. The Mathematics of Combustion (Buckmaster, J.D., Editor) Chapter III, Society for Industrial and Applied Mathematics, 1985, pp. 97–131. 22. Williams, F.A. A Review of Flame Extinction. Fire Safety Journal, 3, 1981, pp. 163–175. 23. Seshadri, K., Multistep Asymptotic Analyses of Flame Structures. Proceedings of the Combustion Institute, 26, 1996, pp. 831–846. 24. Brohez, S., Delvosalle, C., Marlair, G. and Tewarson, A. Soot Generation in Fires: An Important Parameter for Accurate Calculation of Heat Release. Fire Safety Science – Proceedings of the Sixth International Symposium, International Association for Fire Safety Science, 2000, pp. 265–276. 25. Saito, K., Gordon, A.S. and Williams, F.A. Effects of Oxygen on Soot Formation in Methane Diffusion Flames. Combustion Science and Technology, 47, 1986, pp. 117–138. 26. Pitts, W.M. An Algorithm for Estimating Carbon Monoxide Formation in Enclosure Fires. Fire Safety Science – Proceedings of the Fifth International Symposium, International Association for Fire Safety Science, 1997, pp. 535–546. 27. Hirano, T. Combustion Science for Safety, Proceedings of the Combustion Institute, 29, 2003, pp. 167–180.
Modeling and Scaling Laws for Large Fires Howard R. Baum
Abstract Mathematical models of the convective transport induced by large fires are presented. The models are chosen to illustrate the role of scaling laws in the mathematical development and computer implementation of simulations. The basic equations governing large fire dynamics are presented in a form suitable for these studies. The role of vorticity and heat release is emphasized in this formulation. Two different fire scenarios are examined; each with a unique analysis aimed at the phenomena of interest. First, a “kinematic” approach to fire plume dynamics is used to relate vorticity and heat release distributions obtained from plume correlations to fire induced winds. The utility of this approach is illustrated by appeal both to experiments on individual laboratory plumes and simulations of mass fires. The interaction of fire plumes with atmospheric winds is illustrated by a smoke dispersion model that couples a simplified description of the stratified atmosphere with a CFD based simulation of the large scale fire induced motions. Simulations of crude oilfire plumes compared with large scale experiments are shown to demonstrate the use of this model. A brief discussion of additional factors involved in the analysis of large fires is outlined. Keywords Combustion · fire plumes · fluid mechanics · mathematical models · oil spills
Nomenclature →
a Cp D F → g
Local acceleration of fluid element Specific heat of gas Isolated plume length scale Point source plume structure function Gravitational acceleration
H.R. Baum Building and Fire Research Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA e-mail:
[email protected] K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
39
40
k L → n p˜ p∗ p∞ P0 Pr → q → qR Qc QO Q r r R Re t∗ T T∞ T0 T˜ T∗ → u ur uz u U V V Vθ →
v v v∗ → w w∗ z z z∗ Γ γ θ Θ
H.R. Baum
Thermal conductivity of gas Vertical length scale associated with windblown plume Unit normal to surface used to define circulation Fire induced pressure field Dimensionless windblown plume induced pressure field Reference pressure in ambient atmosphere Vertically stratified pressure in ambient atmosphere Turbulent Prandtl number for windblown plume model Heat flux vector Radiative heat flux vector Chemical heat release rate per unit volume Total combustion heat release rate for individual fire Dimensionless heat release rate per unit volume Radial coordinate measured from isolated fire axis of symmetry Dimensionless radial coordinate in isolated fire Gas constant for dry air Reynolds number for windblown plume model Dimensionless timelike windward spatial coordinate Gas temperature Reference temperature in ambient atmosphere Ambient temperature in stratified atmosphere Fire induced temperature perturbation in windblown plume Dimensionless windblown plume temperature perturbation Fluid velocity vector Radial velocity component in isolated fire plume Vertical velocity component in isolated fire plume Dimensionless radial velocity in isolated fire plume Ambient wind speed Transverse velocity scale for windblown plume Dimensionless spherical radial velocity component in point source plume Dimensionless spherical angular velocity component in point source plume Solenoidal component of velocity Dimensionless vertical velocity in isolated fire plume Dimensionless transverse velocity in windblown plume Pseudo-velocity defined in Eq. (5) Dimensionless vertical velocity in windblown plume Vertical coordinate Dimensionless vertical coordinate in isolated fire plume Dimensionless vertical coordinate in windblown plume Circulation about closed circuit moving with fluid Specific heat ratio Spherical polar angle measured from centerline of isolated fire plume Potential temperature of undisturbed atmosphere
Modeling and Scaling Laws for Large Fires
κ μ χr ρ ρ0 ρ∞ τ φ Φ Ψ Φ Ψ → ω ωφ ω Ω
41
Adiabatic exponent in definition of potential temperature Cosine of spherical polar angle Radiative fraction of combustion energy release Gas density Density in stratified ambient atmosphere Reference density in ambient atmosphere Stress tensor Potential flow component of velocity field Large scale potential flow field Vector potential of solenoidal flow field Dimensionless large scale potential field Dimensionless large scale vector potential Vorticity field Azimuthal vorticity in isolated plume Dimensionless vorticity in isolated plume Vorticity structure function in point source plume
Introduction Large fires can be characterized by the nature of their interaction with the local environment. The environment as defined here consists of a description of the geometry and burning characteristics of the fuel bed, the properties of the ambient atmosphere, and the geography of the natural terrain and buildings in the spatial domain of interest. The physical processes that control these interactions determine the various length scales that define the dynamics of a given fire scenario. One of the most obvious features of any fire is the enormous range of dynamically active length scales, ranging from the sub-millimeter thickness of the active reaction zone in an individual flame to the kilometer sized convective transport scales in large smoke plumes. Since it has not yet proved feasible to develop approximate models that include such a wide range of phenomena, a plausible way to truncate this large dynamic range is required. An isolated fire in a quiescent laboratory environment can be described in terms of a single macroscopic plume length scale D , defined in more detail below. All combustion reactions, diffusion, and local turbulent mixing occur on scales small compared with D . Thus, the fire is described in terms of an overall heat release rate which determines D . This can be accomplished by making use of empirical correlations which have the consequences of the smaller scale dynamics built into them. Large fires then, possess additional length scales that are comparable to or larger than the plume length scale. These scales arise either because of the nature of the fire scenario, as in mass fires, or because the physical processes that must be considered occur at atmospheric dynamics scales. Examples of each of these will be given below. The paper is organized as follows: The “low Mach number combustion” equations governing the dynamics of fire plumes are presented in the next section.
42
H.R. Baum
The fluid mechanical properties of these equations are explored, with particular emphasis on the mechanisms of vorticity creation and volumetric expansion. The remainder of the paper consists of two sections that describe mathematical models of different fire scenarios. Each of these models is chosen because the role of scaling laws is of critical importance in both formulating the models and in obtaining solutions. The first is based on a “kinematic” approach, using the fact that the sources of vorticity and expansion in fire plumes can be readily inferred from standard plume correlations. The fire induced flow is then directly related to the strength of these sources. The results show that the concept of entrainment in fire plumes is much more precisely explained in terms of the buoyancy induced vorticity. Moreover, this simple model can be used to predict some highly complex flow phenomena observed in large fires. The second model introduces a simplified description of the interaction of a buoyant plume with a stratified atmospheric wind. The Boussinesq approximation together with the assumption that the component of the fluid velocity in the direction of the atmospheric wind is undisturbed by the presence of the fire permits the development of a high resolution plume dynamics computer code. The code has been used to calculate the three-dimensional dispersion of combustion products in the atmosphere based on the fundamental equations with minimal computer resources. These models can be thought of as representing two limiting scenarios of interest in the study of large fires. The kinematic model is an inherently “near field” description of an idealized urban mass fire. The dimensions of the fire bed are much larger than any individual fire. The collective behavior of the totality of fires is the prime object of interest in this context. The wind blown plume model is a “far field description”. The dynamics of the fire bed is completely lost in this analysis. Although both are idealizations of a much more complicated reality, the results outlined below indicate that even these simplified analyses capture a wide variety of observed phenomena.
Fundamentals The starting point is the equations of motion for a compressible flow in the low Mach number approximation. However, the equations as originally developed [1] must be modified to allow for an ambient pressure P0 (z), temperature T0 (z), and density ρ0 (z) that vary with height z in the atmosphere in the absence of the fire. Their equations assume that the fire induced pressure is a small perturbation about the time dependent spatial average of the pressure in an enclosure. For the present application, the fire induced pressure p˜ is a small perturbation about P0 (z). The ambient density and temperature are related to P0 (z) by the equation of state and the assumption of hydrostatic balance in the ambient atmosphere. The equations expressing the conservation of mass, momentum, and energy then take the form: D → + ∇ · u = 0 Dt
(1)
Modeling and Scaling Laws for Large Fires
→
⭸u → → −u×ω+∇ ⭸t C p
1 2 u 2
43
→
+ ∇ p˜ − ( − 0 )g = ∇ · τ
d P0 DT → −w = −∇ · q + Q c Dt dz
(2)
(3)
→
Here, ρ is the density, u the velocity, T the temperature, and p˜ the fire induced pressure in the gas. The unresolved momentum flux and viscous stress tensors are → lumped together and denoted by . The quantity, ω, is the fluid vorticity. The vertical component of the velocity is denoted by w in Eq. (3) and the hydrostatic relation between P0 and ρ0 has been used in Eq. (2). The specific heat is denoted by Cp. Similarly, the unresolved advected energy flux, the conduction heat flux, and the radiant → energy flux are denoted by q, while the chemical heat release per unit volume is Qc. The energy and momentum equations can be thought of as advancing the time → evolution of T and u respectively. However the pressure perturbation does not obey an explicit time evolution equation. Instead, it is the solution of an elliptic equation determined by the divergence of the velocity field. The instantaneous response of the pressure field implied by the above equations is a consequence of the low Mach number assumption. In reality, pressure changes are carried through the atmosphere at the speed of sound. However, the sound speed is assumed to be so much higher than the local ambient winds or fire induced flows that the transit time for the sound wave can be ignored. → The equations presented above also require recipes for , q, and the heat release from the fire. In principle, there is no difficulty writing down the well known expressions leading to the Navier–Stokes equations and the associated energy and species conservation equations. Using these expressions, there are no unresolved fluxes or stresses. If it were possible to solve the resulting equations for the problems of interest no further discussion would be needed. However, the range of dynamically active length and time scales in almost any fire scenario is much too large to be amenable to computation. Thus, approximate forms of these equations have to be employed if any results are to be obtained. The approximate equations inevitably contain assumptions about the nature and importance of the unresolved stresses and fluxes. Before considering such models, however, it is useful to extract some basic information from the most general form of the equations. First consider the decomposition of the velocity field into its irrotational and solenoidal components. The mass and energy conservation equations together with the equation of state can be combined to yield:
→
∇ ·w =
γ −1 − (P0 (z)/ p∞ ) λp∞ →
γ −1 γ
→
(−∇ · q + Q c )
1 →
w = (P0 (z)/ p∞ ) γ u
(4) (5)
Here, p∞ is a reference pressure in the ambient atmosphere far from the fire, and ␥ is the specific heat ratio. Equation (4) determines the divergence of the velocity field
44
H.R. Baum →
(or more precisely a “pseudo-velocity” w) in terms of the combustion heat release rate and the fluxes of sensible and radiant energy. Just as Eq. (4) describes the sources of the irrotational component of the velocity, → the source of the solenoidal field is the fluid vorticity ω. The evolution of the vorticity field can be related to the plume dynamics using Kelvins Theorem. Let ⌫ be the circulation about any closed circuit moving with the fluid. Then [2]: D⌫ = Dt
→
→
a · dr
(6)
→
Here, a is the local acceleration of the fluid and the integral is around the closed circuit. Using Eq. (2): D⌫ = Dt
→ 1 → (−∇ p˜ + ( − 0 )g + ∇ · τ ) · dr
⌫ is directly related to the vorticity by Stokes Theorem: → → → → ⌫ = u · dr = w · nS
(7)
(8)
S →
The unit vector n is normal to the surface S bounded by the closed circuit used to define the circulation. Thus, Eq. (7) is an integral relation between the rate of vorticity creation and the forces on the fluid. The above results can be exploited by explicitly decomposing the velocity field as follows: →
→
u = ∇φ + v
(9)
→
Then, and v satisfy scalar and vector Poisson equations respectively. This is particularly clear if the stratification of the ambient atmosphere can be ignored. The equations then become: ∇ 2φ = →
γ −1 → (−∇ · q + Q c ) γ p∞ →
∇×v =ω
→
∇·v =0
(10) (11)
Equations (10) and (11) demonstrate explicitly that the heat flux and heat release are the sources of the potential field and that the vorticity is the source of the solenoidal field. Moreover, Eq. (7) shows that in general, there are three sources of vorticity. The first term on the right hand side of this equation corresponds to the non-buoyant baroclinic vorticity generation caused by the misalignment of pressure and density gradients. Outside the fire plume it vanishes, and away from the active combustion zone this term is small. However, where most of the heat release takes place, this
Modeling and Scaling Laws for Large Fires
45
is a significant contributor to the vorticity [3]. The second term is the contribution of the buoyancy. It also vanishes outside the plume, but is pervasive everywhere in the plume. Because of this, it is the dominant source of the solenoidal component of the velocity field almost everywhere. The last term in Eq. (7) represents the effects of viscosity on vorticity creation. For almost any fire of interest, this mechanism operates at such small scales that its effects are unimportant. The sources of the potential flow also require a distinction between large and → small scale phenomena. The heat flux vector q can be decomposed into conduction and radiative components as follows: →
→
q = −k∇T + q R
(12)
The thermal conductivity k(T ) is small enough to ensure that the conduction flux → is highly localized in the fire plume. The radiative flux q R , on the other hand is significant at the largest scales. Thus, if the velocity potential is decomposed in an analogous way, a large scale expansion field ⌽ can be defined as: γ −1 φ= γ p∞ ∇ 2⌽ =
T
k(T )dT + ⌽
(13)
T∞
γ −1 → (−∇ · q R + Q c ) γ p∞
(14)
The temperature, T∞ , is a reference temperature in the ambient atmosphere. Note that the conduction induced velocity is a highly localized flow directed up the temperature gradient, while the large scale potential field is the solution of a Poisson equation with an essentially positive right hand side. This is true even if the combustion energy release is contained in a large number of individual flames, each of which is much smaller than any macroscopic plume length scale.
Fire Induced Flows The entrainment of air into a fire plume is a necessary condition for the fire to be sustained. However, there is no precise definition of this concept, and measurement of the “entrainment rate” has proved both difficult and controversial. The problem arises because the typical approach to determining the increase of mass in an isolated fire plume with height above the fire rests on measuring or inferring an inflow velocity at the edge of the plume. However, unlike the temperature field, the velocity does not undergo any sharp transition at the edge of the plume. Indeed, the flow quantity most like the temperature is the vorticity. Moreover, if the flow quantity to be determined is chosen to be the fire induced flow field rather than the “entrainment” then both the measurement and the modeling problem become tractable. The starting point is the decomposition of the velocity field as represented by Eqs. (11) and (14). Note that the right hand sides of these equations are
46
H.R. Baum
non-vanishing only in the fire plume. Moreover, they are linear in the relations between both the solenoidal velocity and the vorticity and the potential field and the heat release rate. Thus, if time averaged experimental data describing the structure of the vorticity and heat release fields inside the plume are available, then the time averaged velocity fields both inside and outside the plume can be determined. Similarly, if time resolved data is available, the corresponding velocities can be calculated. This observation is the basis for a “kinematic” approach to fire induced flows [4]. First consider an isolated laboratory scale fire. The time averaged plume is axially symmetric, and the net integrated radiative flux emitted from the fire is assumed to be a fraction of the combustion heat release rate Q c . Defining (r, z) as radial and vertical cylindrical coordinates measured from the center of the fire, the corresponding velocity components u r and u z can be expressed in terms of ⌽(r, z) and a vector potential ⌿(r, z) as follows: ur =
⭸⌽ 1 ⭸⌿ − ⭸r r ⭸z
uz =
⭸⌽ 1 ⭸⌿ + ⭸z r ⭸r
(15)
Similarly, the vorticity vector reduces to an azimuthal component (r, z). Now let Q O be the total combustion heat release rate generated by the fire. Then, it is possible to define a natural plume length scale D as: D =
QO √ p∞ C p T∞ g
2/5 (16)
The independent variables can now be made non-dimensional by introducing (r, z) = D (r , z ). The dependent variables are then scaled in the form: (u r , u z ) = (g D )1/2 {u (r , z ), v (r , z )}
(17)
(⌽, ⌿) = D (g D )1/2 {⌽ (r ∗ , z ), ⌿∗ (r , z )}
(18)
Finally the vorticity and heat release rate which act as the sources of the vector and scalar potentials are written in the form: ω = (g D )1/2 ω
Q c = [Q O /(D )3 ]Q
(19)
This choice of dimensionless variables is not arbitrary. The plume correlations developed by McCaffrey [5] can be compactly expressed in this form [4]. Moreover, if the temperature is made dimensionless with respect to T∞ and the fire induced pressure p˜ is normalized with respect to ∞ g D , then all the explicitly resolved terms in the dimensionless form of the fundamental conservation Eqs. (1), (2), and (3) depend only on the fraction of the combustion energy release emitted as radiation r . Finally the vector and scalar potentials satisfy the following equations, which exhibit the same parametric dependence:
Modeling and Scaling Laws for Large Fires
47
⭸2 ⌿ ⭸2 ⌿ 1 ⭸⌿ + − = r ω r , z ∗2 ∗2 ⭸z ⭸r r ⭸r 2 ⭸ ⌽ 1 ⭸ ⭸⌽ = (1 − χr )Q (r , z ) + r ⭸z ∗2 r ⭸r ⭸r
(20) (21)
Equations (20) and (21) must be supplemented by boundary conditions at the ground z = 0 and far from the fire. Since there can be no flow through the ground: Ψ (r , 0) =
⭸⌽ (r , 0) = 0 ⭸z
(22)
The far field boundary conditions are much more interesting. Since the heat release region is bounded in space, the potential field far from the fire corresponds to the point source solution. ⌽ =
1 − χr 2π (r ∗2 + z ∗2 )1/2
(23)
The asymptotic solenoidal velocity must be that associated with a point source plume. Since the velocity field decays proportional to (z)−1/3 in the plume, the vorticity and stream function must take the following form: ⌿ = (r ∗2 + z ∗2 )5/3
F()
(24)
ω = (r ∗2 + z ∗2 )−4/3
⍀()
(25)
Here, is the polar angle in a spherical polar coordinates measured from the plume centerline. The plume structure function F vanishes at = 0 and = /2, and satisfies the equation d2 F 10 + F = ⍀(μ) dμ2 9(1 − μ2 )
μ = cos(θ )
(26)
The structure of the vorticity function ⍀(μ) is determined from the assumed Gaussian form of the vertical velocity profile in the plume, with the width obtained from McCaffreys correlation. The results can be expressed in terms of a spherical radial component of the velocity field V and polar angle component V which take the form: V = (r 2 + z 2 )−1/3
V ()
(27)
V = (r 2 + z 2 )−1/3
V ()
(28)
The functions V and V are plotted in Fig. 1. Note that negative values of V near the plume centerline = 0 and V near the ground plane = /2 correspond to
48
H.R. Baum
Fig. 1 Angular dependence of normalized radial (Vρ ) and tangential Vθ velocities for point source plume [4]
inflows into the plume which are balanced by the vertical outflow through the plume carried by V near = 0. The flow pattern outside a point source plume was studied by Taylor [6] who replaced the entire plume by a line sink. His result is equivalent to that obtained here away from the plume, but becomes singular as the plume is approached. Using the above results as boundary conditions, Eqs. (20) and (21) can be solved in a cylindrical domain for ⌿ and ⌽ using fast direct elliptic equation solvers. The right hand sides of the equations are again determined from McCaffreys correlation. Details can be found in Ref. [4]. Figure 2 shows the ground level radial velocity, together with the component terms. Note that the solenoidal velocity is responsible for the entrainment, while the expansion flow is actually directed outward. The expansion flow is quite significant for distances from the plume comparable to the flame height (z = 1.3 in the present units). However, the vorticity induced flow dominates everywhere else. Moreover, the buoyancy induced component of the vorticity, which is all that survives in the far field, is by far the most important source of the vorticity. Since the computations described above are easy to perform (the discretized elliptic equations can be solved in less than a second on a twenty thousand point grid using any current generation workstation), this model can be used to calculate the flows induced by mass fires. Almost any such fire is actually a collection of discrete fires, due to either the discrete nature of the “fuel” (individual buildings, say) or because the oxygen supply to an individual fuel parcel is consumed by adjacent fires. If attention is focused on flows at or near ground level, then the plumes associated with each fire will be distinct. Since Eqs. (21) and (20) are linear and the vorticity
Modeling and Scaling Laws for Large Fires
49
Fig. 2 Calculated ground level radial velocity showing expansion (Dashed) and vorticity induced (Dotted) contribution to flow [4]
fields associated with each plume are separated, then the flows induced by each fire can be added vectorially. The combined asymptotic and numerical solutions for ⌽ and ⌿ then constitute a “computational element” that can be scaled appropriately for any size fire with a given radiative fraction. Using this technique it is not difficult to simulate the near ground flows induced by hundreds to thousands of individual fires. Such fires were in fact the motivation for this work. The model has been tested experimentally against large controlled burns by Quintiere and his collaborators [7, 8]. These field experiments, conducted in Canada in 1989, included wind tower measurements at five separate locations of velocities induced by fires whose ultimate strength reached several GW. Infrared photographs were used to discretize the fire into over 40 individual fires whose strength was estimated from separate analyses of the vegetation in the logged fields that constituted the fuel. Despite the fact that the terrain consisted of low rolling hills, and numerous uncertainties in the fuel characterization, the agreement between the calculated and measured horizontal velocity fields was quite encouraging. The comparisons were performed at several different times and the wind towers were several hundred meters apart, but the discrepancies between theory and experiment were almost all below 20% of the measured values in both magnitude and direction. Perhaps the most interesting application, however, is a study of the 1991 Oakland Hills fire by Trelles and Pagni [9]. This fire destroyed over two thousand buildings and affected an area of 600 hectares. The initial fire spread was strongly influenced by the dry 10 m/s ambient winds. However, between 11:45 AM and 12:00 noon the observed rate of spread of the fire slowed dramatically. Trelles and Pagni used the model described above to estimate the relative importance of the fire induced and ambient winds. They used estimates of the ambient wind field and the energy release rates associated with single and multiple unit dwellings together with the observed burning patterns at the two times in question. At 11:45 AM they assumed that the 38 observed fires each had a 50 MW heat release rate. The fire induced wind fields, shown in Fig. 3, are a small perturbation on the ambient winds. However, by
50
H.R. Baum
Fig. 3 Horizontal induced winds 20 m above ground plane showing 38 fires burning at 11:45 am [9]
noon 259 fires were burning at rates estimated to be between 50 MW and 330 MW each. The combined effect of all these fires generated winds up to 13 m/s in places. The computed flow patterns are shown in Fig. 4. These velocities are comparable to those in the ambient wind. Moreover, they are primarily directed towards the most intensely burning regions of the fire. Thus, they impede the spread of the fire on the downwind side of the burning region. This statement is valid whether the spread mechanism is convective and radiative heat transfer from the flames or (as was widely observed) spotting by burning leaves and shingles carried aloft by the winds.
Modeling and Scaling Laws for Large Fires
51
Fig. 4 Horizontal induced winds 20 m above ground plane showing 259 fires burning at 12:00 pm [9]
Comparison of this model with large scale field measurements and observations has yielded encouraging results. However, it is important that the model be tested against laboratory experiments, where sources of error can be more precisely defined. Gore and his collaborators have performed a series of experiments and analyses along these lines (Gore et al., 1996) [19]. In their most detailed experiments, measurements were made of the vorticity and heat release rate distributions in a 7.1 cm natural gas diffusion burner designed to mimic the hydrodynamic properties of a small pool fire. The vorticity was obtained from particle imaging velocimetry (PIV) measurements of the velocity field. Time averages of the velocity were then
52
H.R. Baum
Fig. 5 Comparison of vertical component of velocity with predictions based on measured source terms (Courtesy Prof. J. Gore)
differenced to obtain the vorticity. The sources of the expansion field were obtained by relating them to the local mixture fraction field (Baum et al., 1990). The mixture fraction was determined from measurements of the major species concentrations. Figure 5 shows a comparison between PIV measurements of the vertical velocity component and the calculated velocities using the measured sources. Zhou and Gore note, in describing their closely related Fig. 4 [18]: The agreement between the predictions and the measurement is excellent. The predictions are not only close to the data in absolute value, but also catch the saddle shape of the radial distribution of axial velocities at locations close to the burner surface. This agreement supports the present method of estimating the source term.
Modeling and Scaling Laws for Large Fires
53
Wind Blown Plumes There is considerable interest in the environmental consequences of large fires, since the transport of combustion products by a wind-blown fire plume can distribute potentially hazardous materials over a large area. Pools of burning oil and other petroleum products are of particular concern due to the vast flow of these materials through the global economy and because of the fragility of the environment in many regions where oil is extracted, transported, or stored. Buoyant wind-blown plumes have been studied since the 1960s, and an extensive literature has been developed. Summaries of recent work have been given by Turner [11] and Wilson [12]. Virtually all the models described in these reviews are integral models, where the profiles of physical quantities in cross-sectional planes perpendicular to the wind are assumed, together with simple laws relating plume entrainment to macroscopic features used to describe its evolution. Many of the models in use for air quality assessment simply use Gaussian profiles of pollutant density. Unfortunately, the plume structures actually observed are too complex to be described in terms of a few simple parameters. Most of the assumptions required by integral models can be removed by taking advantage of the enormous advances in computational fluid dynamics that have occurred since these models were developed. This is especially true if it is assumed that the component of the fluid velocity in the direction of the ambient wind is literally the wind speed. The neglect of streamwise perturbations to the ambient wind is an old idea in aerodynamics, where it has been used to study aircraft wakes since the 1930s [13]. Once this approximation is made the plume can be studied as a two-dimensional time dependent entity. The large scale structure of the plume can then be determined in detail at moderate computational cost. The small-scale “sub-grid” mixing and dissipation is represented with a constant eddy viscosity. This permits the mathematical structure of the Navier–Stokes equations to be retained. The effective Reynolds number, defined by the buoyancy induced velocity, plume height, and eddy viscosity, is chosen to be well above 104 . This permits at least two orders of magnitude of dynamically active length scales in all coordinate directions to be simulated. Thus, the model described here is a simplified form of large eddy simulation. The plume is described in terms of steady-state convective transport by a uniform ambient wind of heated gases and particulate matter introduced into a stably stratified atmosphere by a continuously burning fire [14, 15]. Since the firebed itself is not the object under study, only the overall heat release rate and the fraction of the fuel converted to particulate matter need be specified. The simulation begins several fire diameters downwind of the fire, where the plume is characterized by relatively small temperature perturbations, and minimal radiation effects. In this region the plume gases ascend to an altitude of neutral buoyancy, and then gradually disperse. The trajectory of the plume is governed by the ambient wind, the atmospheric stratification and the buoyancy induced convection. It is assumed that the ambient temperature profile as a function of height is available. The model has been extended to allow for multiple interacting plumes [16] and the presence of a
54
H.R. Baum
wind shear [17]. However, only the basic form of the model will be discussed in detail here. Assuming that the perturbations to the background temperature T0 (z) and pressure P0 (z) are small beyond a few diameters downwind of the firebed, the expansion component of the velocity field can be ignored and the equations describing the steady state plume reduce to the Boussinesq approximation. The uniform ambient wind speed U is taken to be constant. For mathematical consistency, U is much larger than the buoyancy induced crosswind velocity components, and the rates of change of physical quantities in the windward direction are much slower than those in the crosswind plane. These assumptions are quite realistic several flame lengths downwind of the firebed. Since U does not change, there is no need for a windward component of the momentum equations. The details of the firebed are not being simulated, so the only information about the fire required is the overall convective heat release rate Q O and the particulate mass flux. The initial temperature distribution in the plume cross section is assumed to be Gaussian and satisfy the following integral
∞
∞
∞
0 c p U T dzdy = Q o
(29)
0
The quantity T˜ is the fire induced temperature perturbation. The particulate matter (or any non-reacting combustion product) is tracked through the use of Lagrangian particles which are advected with the overall flow. The initial particulate distribution mimics the initial temperature distribution. If either more detailed experimental data or the results of a local simulation of the firebed dynamics were available, then they could be used in lieu of the Gaussian profile. The equations of motion are made non-dimensional so as to maximize the amount of information which can be extracted from each run. First, the windward spatial coordinate is replaced by a temporal coordinate t∗ =
V x UL
(30)
where the plume height L is given in terms of the potential temperature of the undisturbed atmosphere ⌰(z). L=
Q0 C p T0 0 U ⌰
1/3 ;
⌰ (z) =
z=0
1 d⌰ ⌰ dz
(31)
The potential temperature is related to the actual temperature through the relation P0−κ (z)T0 (z) = P0 (0)−κ ⌰(z)
(32)
where = R/C p and R is the gas constant for dry air. The characteristic velocity of the fluid is given by
Modeling and Scaling Laws for Large Fires
V =
55
Q0 g C p T0 0 U L
1/2 (33) z=3
The characteristic length L and velocity V scale the crosswind spatial coordinates (y, z) = L(y ∗ , z ∗ ) and velocities (v, w) = V (v ∗ , w ∗ ). The quantity ⌰ (z) is scaled by its value at the ground. The temperature perturbation T˜ is made nondimensional by the expression T˜ =
Qo T∗ C p 0 U L 2
(34)
Finally, the turbulent Reynolds and Prandtl numbers are defined Re =
0 V L ; μ
Pr =
μC p k
(35)
The viscosity and thermal conductivity are to be regarded as “eddy” coefficients whose primary role is to provide sinks of kinetic and thermal energy that are actually the result of subgrid scale dissipative processes. In practice, they are used to set the dynamic range of length scales employed in the simulation, which is typically 5 to 15 m. This range is needed to capture the large-scale fire-induced eddy motions. This requirement, together with the knowledge that the dissipative effects operate at a scale Re−1/2 times smaller than the overall geometric scale (the stabilization height of the plume for this problem), translates into Reynolds numbers of the order 104 . Thermal conductivity is treated in a similar manner to viscosity; thus the Prandtl number remains of order unity. The dimensionless form of the model equations is remarkably simple ⭸w ∗ ⭸v ∗ + ∗ =0 ∗ ⭸y ⭸z ∗ ∗ ∗ ⭸v ⭸ p∗ 1 ⭸2 v ∗ ⭸2 v ∗ ∗ ⭸v ∗ ⭸v + v + w + = + ⭸t ∗ ⭸y ∗ ⭸z ∗ ⭸y ∗ Re ⭸y ∗2 ⭸z ∗2 ∗ ∗ ⭸w ∗ ⭸ p∗ 1 ⭸2 w ∗ ⭸2 w ∗ ∗ ⭸w ∗ ⭸w ∗ +v +w + ∗ −T = + ∗2 ⭸t ∗ ⭸y ∗ ⭸z ∗ ⭸z Re ⭸y ∗2 ⭸z ∗ ∗ ∗ 2 ∗ ⭸T ⭸ T 1 ⭸2 T ∗ ∗ ⭸T ∗ ⭸T ∗ ∗ +v +w + ⌰ (z) w = + ∗2 ⭸t ∗ ⭸y ∗ ⭸z ∗ Re Pr ⭸y ∗2 ⭸z
(36) (37) (38) (39)
subject to the initial condition
T ∗ (y ∗ , z ∗ )dy ∗ dz ∗ = 1
(40)
The crosswind velocity components v ∗ and w ∗ are assumed to be zero initially, although this assumption can be relaxed if more detailed information is available.
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H.R. Baum
No-flux, free-slip boundary conditions are prescribed at the ground, consistent with the assumed uniformity of the prevailing wind and the resolution limits of the calculation. At the outer and upper edges of the computational domain, the perturbation temperature, perturbation pressure, and windward component of vorticity are set to zero. Figure 6 shows the results of a sample two plume simulation. The plume is visualized by interpolating the particle locations onto the computational grid, and plotting the isosurface on which the particulate density is a chosen value. Two large counterrotating vortices are associated with each plume. These vortices are responsible for much of the entrainment, mixing and cooling the combustion gases. These vortices are readily observed in actual large-scale experiments; see Figure 3 of Ref. [15]. The complexity of even a single plume structure is clearly nothing like that assumed in Gaussian plume models. The computational cost of this simulation is quite modest. A 512 cell (horizontal) by 128 cell (vertical) grid using 15,000 Lagrangian elements to represent the smoke particulate matter requires less than 5 min. on a current generation personal computer to advance the approximately 350 time steps needed to complete the calculation. In fact, over one thousand two plume simulations were performed to explore the large parameter space defined by the multiple plume generalization of this model. All the simulations were performed in the course of a few weeks. Other examples can be found in [16]. In these simulations, the particles do not simply follow the large scale velocity field. The background atmospheric motion plays an equally critical role in determining how rapidly the combustion products disperse. Atmospheric turbulence affects mixing on a wide range of scales, extending to scales which are smaller than the resolution of the calculations performed here. The “eddy” viscosity and thermal conductivity attempt to account for this sub-grid turbulence, but do not account for
Fig. 6 Two interacting 500 MW fire plumes generated by offset fires 500 m apart [16]
Modeling and Scaling Laws for Large Fires
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larger scale, background atmospheric motion. For the present purposes, this motion may be expressed in terms of variations of the prevailing wind over time scales of minutes to hours. These deviations can be measured, and are introduced into the model through random perturbations to the trajectories of the Lagrangian particles which represent the particulate matter. Thus, the motion of each particle is governed by the fire-induced velocity field found by solving the conservation equations above, plus a perturbation velocity field (0, v , w ) which represents the random temporal and spatial variations of the ambient wind. Details of the computation of the random velocity field and a description of the numerical methods employed in the simulation can be found in Ref. [15]. The smoke dispersion predicted by this model has been tested in a variety of large scale field experiments. In early September 1994, Alaska Clean Seas conducted at their Fire Training Ground in Prudhoe Bay, Alaska, three mesoscale burns to determine the feasibility of burning emulsified oil. Each burn consisted of burning an oil mixture within the confines of a fire resistant circular boom which floated in a pit filled with water. The boom diameter was roughly 9 m, and the rectangular pit was roughly 20 m×30 m. The first and third burns consumed emulsions of salt water and 17.4% evaporated Alaskan North Slope (ANS) crude. Emulsion breakers were applied to these mixtures. The second burn consumed fresh ANS crude. Heat release rates for the three burns were estimated to be 55, 186 and 98 MW, respectively. The mass flux of particulate was based on a smoke yield for ANS crude of 11.6%. Figure 7 summarizes the results of the experiments, showing the model prediction of ground level particulate concentration versus the actual measurements made in the field. The field measurements were averaged over the time of the burn. Except for a few stray points, the agreement between the time-averaged model predictions and field measurements is quite good, showing particulate concentrations ranging from 0 to 80 g m−3 along the narrow path over which the plume is lofted. In addition to ground level instruments, a small airplane was hired to fly in the vicinity of the plume and record plume positions at various times, as well as to photograph the burn site and the plume. According to flight track data, the plume from the first burn rose to a height of about 550 m and the plume from the second burn rose to about 400 m. These measurements are in very good agreement with model predictions, based on atmospheric profiles obtained with a helium blimp and a helicopter. More details can be found in Ref. [15].
Discussion The models discussed above represent two limiting cases of large fire scenarios. The kinematic model as applied to the study of mass fires is a case where the overall fire encompasses the entire domain of interest. Here, the details of the distribution of individual fires are all important, while the dynamics of the interaction of the fires with the atmosphere is ignored. If the individual fires are intense enough and persist for a relatively long period of time (tens of minutes, say), then the near ground winds
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Fig. 7 Predicted ground level particulate concentrations from the model (Shaded contours) shown with time averaged measurements for three Alaska clean seas emulsion burn experiments, September 1994 [15]
will be dominated by the fire induced flow, and the model is internally consistent. The wind blown plume model, on the other hand, addresses a scenario where the actual combustion zone of the fire is very much smaller than the spatial domain affected by the dispersal of combustion products. Here, the nature of the interaction of the plume with the atmosphere and with other plumes is critical. In the first case the largest length scale is determined by the geometry of the fire bed, while the individual fire scale D controls the local fire dynamics. In the
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latter scenario, the interaction of the plume with the atmosphere sets the largest scale L, while the fire bed is typically of negligible dimensions. Any plume interactions typically occur on the L scale. Clearly, each of these limiting cases represents a considerable idealization of any large fire scenario. Atmospheric winds usually cannot be ignored even in large urban fires. The immediate vicinity of the firebed associated with oil spill fires usually is so heavily smoke laden that the absorption of thermal radiation (and hence an absorption length scale) is a significant factor in determining plume dynamics. The geography associated with the natural and built environment is typically a major factor in most large fires. All these imply more length scales, and hence more dimensionless parameters whose influence must be studied, if the dynamics of large fires is to be understood.
References 1. Rehm, R.G. and Baum, H.R., 1978, “The equations of motion for thermally driven, buoyant flows”, Journal of Research of the Natural Bureau of Standards, Vol. 83, pp. 297–308. 2. Goldstein, S., 1960, Lectures on Fluid Mechanics, Interscience, New York, pp. 23–24. 3. Mell, W.E., McGrattan, K.B., and Baum, H.R., 1996, “Numerical simulation of combustion in fire plumes”, Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 1523–1530. 4. Baum, H.R. and McCaffrey, B.J., 1988, “Fire induced flow field – theory and experiment”, Fire Safety Science – Proceedings of the Second International Symposium, Hemisphere, New York, pp. 129–148. 5. McCaffrey, B.J., 1983, “Momentum implications for buoyant diffusion flames”, Combustion and Flame, Vol. 52, pp. 149–167. 6. Taylor, G.I., 1958, “Flow induced by jets”, Journal of Aerospace Sciences, Vol. 25, pp. 464–465. 7. Quintiere, J.G., 1990, “Canadian mass fire experiment”, National Institute of Standards and Technology Report NISTIR 4444. 8. Quintiere, J.G., 1993, “Canadian mass fire experiment”, Journal of Fire Protection Engineering, Vol. 5, pp. 67–78. 9. Trelles, J. and Pagni, P.J., 1997, “Fire-induced winds in the 20 October 1991 Oakland Hills fire”, Fire Safety Science – Proceedings of the Fifth International Symposium, Y. Hasemi, Ed., International Association for Fire Safety Science, pp. 911–922. 10. Zhou, X.C. and Gore, J.P., 1998, “Experimental estimation of thermal expansion and vorticity distribution in a buoyant diffusion flame”, Twenty-Seventh Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 2767–2773. 11. Turner, J.S., 1985, “Proposed pragmatic methods for estimating plume rise and plume penetration through atmospheric layers”, Atmospheric Environment, Vol. 19, pp. 1215–1218. 12. Wilson, R.B., 1993, “Review of development and application of CRSTER and MPTER models”, Atmospheric Environment, Vol. 27B, pp. 41–57. 13. Batchelor, G.K., 1967, An Introduction to Fluid Dymanics, Cambridge University Press, Cambridge, pp. 580–593. 14. Baum, H.R., McGrattan, K.B., and Rehm, R.G., 1994, “Simulation of smoke plumes from large pool fires”, Twenty-Fifth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 1463–1469. 15. McGrattan, K.B., Baum, H.R., and Rehm, R.G., 1996, Atmospheric Environment, Vol. 30, pp. 4125–4136.
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16. Trelles, J., McGrattan, K.B., and Baum, H.R., 1999a, AIAA Student Journal. American Institute of Aeronautics and Astronautics, Vol. 37, pp. 1588–1601. 17. Trelles, J., McGrattan, K.B., and Baum, H.R., 1999b, Combustion Theory and Modeling, Vol. 3, pp. 323–341. 18. Baum, H.R., Rehm, R.G., and Gore, J.P., “Transient combustion in a turbulent eddy”, TwentyThird Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 715–722. 19. Zhou, X.C., Gore, J.P., and Baum, H.R., 1996, “Measurements and predictions of air entrainment rates of pool fires”, Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 1453–1459.
Modeling of Gas Explosion Phenomena Toshisuke Hirano
Abstract This paper presents the results of a study on scale modeling for simulating an accidental gas explosion in an enclosure. Discussion has been concentrated on modeling of main processes of a gas explosion. Those include flammable mixture formation and pressure rise. Of various parameters, on which the flammable mixture formation depends, those representing the enclosure size, gas flow in it, ventilation, and turbulence generated at the flammable gas leakage are pointed out to be the most important for scale modeling. It is indicated that in a large enclosure, the flammable gas scarcely becomes uniform. For simulating the mixture formation in a scale model, the velocity of leaked gas should be increased by a factor inversely proportional to the reduction factor and the time should be reduced by a factor square of the reduction factor. The pressure rise depends on flame behavior, which is closely related to the flammable gas concentration. The difficulties for scale modeling of the pressure rise are indicated to be attributable to the non-uniformity of the mixture and independence of burning velocity from the enclosure size. Despite of those difficulties, the pressure rise can be simulated by controlling the time at break as it is proportional to the representative dimension. For establishing reliable scale modeling, there remain many other issues to resolve. Keywords Modeling · gas explosion · accident · disaster · flammable mixture formation · pressure rise
Introduction In order to establish a reliable systematic strategy to mitigate losses caused by accidental gas explosions, knowledge on the gas explosions is needed. For accumulation of knowledge about certain phenomena, experiments using practical systems are the most promised means. However, a large system where an accidental gas
T. Hirano Chiba Institute of Science, 3 Shiomi-cho, Choshi-city, Chiba 288-0025, Japan e-mail:
[email protected]
K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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explosion has occurred is generally not easy to reproduce in an experiment because of its expensiveness. Further, a system supplied for an experiment will suffer serious damage, so that the experiment for confirming the destruction processes cannot be conducted repeatedly by using the same system. For repeated experiments, a certain number of similar systems are needed. Thus, experiments using a large prototype model are not practical for accumulating knowledge on accidental gas explosions [1]. Even if one could provide a large prototype model for an explosion experiment, the data obtained through the experiment would be utilized for confirmation of knowledge accumulated through other studies including those using small-scale models. Thus, small-scale models are needed for gas explosion studies. Gas explosion phenomena depend strongly on the conditions and structure of the system where the explosion occurs. Those at leakage of gas to an open space are quite different from those of a flammable mixture in a long duct or tube [2–4]. Thus, approximate structure and size of the system for gas explosion research is in general assumed before starting research. In this paper, a gas explosion is assumed to occur in an enclosure such as a residential room, reactor, dryer, or fuel reservoir because the gas explosion in such a system has the most frequently occurred and caused serious disasters. Behavior of a gas explosion, even if it is assumed to occur in an enclosure, depends on so many factors that available data are in general not sufficient for the prediction of gas explosion hazards under an arbitrarily presumed set of conditions [4–14]. Further, systematic studies on gas explosions for all conceivable cases are practically impossible to carry out by any individual group. This may be the reason why most methods to predict gas explosion phenomena are crude in a sense of science. Gas explosion phenomena in an enclosure predicted by various empirical methods proposed in the past have been believed to be not much different from those to occur at real systems [4–10, 13, 15]. In the processes of the prediction of gas explosion phenomena in an enclosure, however, there remain a number of ambiguities, which have been in general approximated by changing factors on the basis of experience. The most serious issues are on selecting factors in prediction of the phenomena at systems of different sizes. The objective of this research is to elucidate the issues on scale modeling for each process of a gas explosion and to suggest methodology for solving those.
Processes of a Gas Explosion in an Enclosure Typical processes of an accidental gas explosion in an enclosure are shown in Fig. 1. The first process of an accidental gas explosion in an enclosure is leakage of flammable gas, which mixes with ambient air to form a flammable mixture. In some other cases, a combustible gas or vapor in a reservoir or tank mixes with air come from outside to form a flammable gas or the gas in a reservoir or reactor is of a nature to explode by exothermic decomposition. In these cases, main phenomena
Modeling of Gas Explosion Phenomena Fig. 1 Processes of gas explosion in an enclosure
63 Leakage of flammable gas Flammable mixture formation Ignition Flame propagation And pressure rise Structure destruction Pressure wave propagation And trajectile flying Fire occurrence
of gas explosions are not much different, so that the case of flammable mixture formation after leakage is assumed to be a representative case in this paper. If the flammable mixture formed in an enclosure ignites, combustion will occur and the pressure in the enclosure increases. The ignition is an important process in a gas explosion. Indeed, the ignition itself depends on the characteristics of the used ignition source and size and configuration of experimental apparatus. However, the ignition phenomena occur in a small space, and a small-scale experimental apparatus is enough for the study of ignition. Thus, we do not need scale models for understanding ignition phenomena. After ignition, a flame propagates in the enclosure and causes a pressure rise. The flame can propagate only through the flammable mixture. Since the mixture is likely non-uniform, the flame propagation should not be of a constant velocity even at its initial stage. Thus, this process is under strong influence of that of flammable mixture formation. In the prediction of this process of a representative gas explosion, the pressure rise at an initial stage should be evaluated on the basis of the flammable gas distribution. As aforementioned, the enclosure destruction would occur in this process. For scale modeling of this process it is needed to obtain basic knowledge of pressure rise at an individual gas explosion. The next process of a gas explosion is structure destruction caused by pressure rise. In a case study to explore behavior of a gas explosion, the analysis of this process is extremely important [2–4]. However, scale models for elucidating this process have been scarcely adopted. The reason seems to be that the mechanisms controlling behavior of structure destruction are much complicated compared to those of pressure rise. Also, the structure destruction has been studied not only for accumulating of knowledge about gas explosion phenomena but also for that about so many phenomena concerning safety. Thus, in this paper, scale modeling for structure destruction is not discussed. The damage at a gas explosion is also caused by pressure waves and trajectiles, and in some cases a fire occurs following to the gas explosion [2, 3].
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There is a well-known scale law about the damage caused by pressure waves, and only little remains to study. To the contrary, the behavior of trajectiles and transition into a fire are not the matters suitable for an experimental study using a reduced model. In this paper, therefore, scale modeling for these processes is not discussed.
Formation of Flammable Mixture Figure 2 shows a schematic representing flammable gas behavior in an enclosure. Flammable mixture formation in the enclosure depends on the volume and ventilation of the enclosure and the leakage mode and type of flammable gas. The overall aspects of the flammable gas distribution in an enclosure can be conveniently classified by using the following characteristic times [3, 4]: td = L 2 /D f : the characteristic time for overall diffusion, tld = l 2 /D f : the characteristic time for local diffusion, tc = L/U : the characteristic time for convection, tr = l/n : the characteristic time for ventilation, where L , D f , l, U , and n are a representative scale of the enclosure, diffusion coefficient of the flammable gas, representative scale of turbulence, representative velocity of convection in the enclosure, and ventilation frequency, respectively. The aspects of flammable gas concentration distributions categorized on the basis of the magnitudes of the characteristic times are presented in Table 1. An extreme case that has been assumed for the hazard assessments is of the Type III. Although this situation is hardly realized in an enclosure, the hazard assessments based on it has been accepted. The reason is simple. The situation and prediction based on it are comprehensible as follows:
Ventilation (inflow)
Ventilation (outflow) Convection
Diffusion
High concentration region Flammable gas leakage
Fig. 2 Aspects of flammable mixture formation in an enclosure
VI tc >> tr >> td
V tc >> td >> tr
IV tr >> td >> tc
III tr >> tc >> td
Uniform and low concentration
Uniform and high concentration Uniform and high concentration Non-uniform and low concentration
Uniform concentration Non-uniform concentration
I td >> tr >> tc
II td >> tc >> tr
Overall aspect
tc >> tdl
IVa tdl >> tc IVb tc >> tdl Va tc >> tdl >> tr Vb tc >> tr >> tdl
tc >> tdl
Ia tdl >> tc Ib tc >> tdl IIa tdl >> tc IIb tc >> tdl
Local situation
Uniform
Need time to be uniform Uniform Non-uniform Uniform
Uniform
Non-uniform Uniform Non-uniform Uniform
Local aspect
Flow out after becoming totally uniform Flow out before becoming totally uniform at special configuration space Realize only for a small-scale space Flow out after completely mixing Realize only for a small-scale and special configuration space Realize only for a small-scale and special configuration space
Remark
Table 1 Aspects of flammable gas concentration distributions under various conditions
Overall situation
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The increasing rate of the mean concentration in an enclosure increases with increasing of the rate of leakage and decreasing by ventilation, i.e., d(X f V )/d t = X f 0 Q − X f V n,
(1)
where X f , V, t, Q, and X f 0 are the mean concentration of flammable gas in the enclosure, enclosure volume, time from the starting of leakage, rate of leakage, and concentration of flammable gas of the leaked gas, respectively. When no flammable gas is in the enclosure before the leakage, the initial condition is X f = 0 at
t =0
(2)
Equation (1) can be solved for the initial condition (2). The result is X f = (Q/V n)(1 − exp(−nt))X f 0
(3)
This equation indicates the following: The final flammable gas concentration in the enclosure is Q X f 0 /V n. The time needed for flammable gas concentration increase is proportional to 1/n. The initial increasing rate of flammable gas concentration is Q X f 0 /V . At this situation, the hazard of an enclosure can be represented by a non-dimensional parameter, Q/V n and the scale models can be prepared by keeping the parameter constant. As aforementioned, however, this situation, Type III in Table 1, can be realized only for a small space. At this situation, the diffusive Reynolds number (LU )/(D f ) must be much smaller than 1. For realizing this situation, the convection velocity should be kept to be much less than 0.1 cm/s when the scale of the space is about 1 cm. Also, it is easily confirmed by experiments that this situation would not attain at a real accidental gas explosion of an enclosure larger than one meter span. Most situations at accidental gas explosions are apparently categorized into Type I and Type II. When the gas inside of the enclosure is strongly mixed by a fan or similar facility, the situation of Type I can be realized. In the case when convection is induced only by injection of the flammable gas into the enclosure, the convection is suppressed by the gravity force, which is induced by the density difference of the injected gas from the gas in the enclosure. The situation in this case should be categorized into Type IIa. Ohmori et al. [16] conducted an experimental study on the flammable gas behavior in a cubic enclosure as shown in Fig. 3. They injected propane into the enclosure from a tube at its bottom and measured concentration distributions under various conditions. The results are shown in Fig. 4.
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Fig. 3 Model experiments performed by Omori et al. [16]
Flow out
Propane injection
Ohmori et al. [16] tried to examine whether the measured concentration profiles can be represented by a simple diffusion equation as follows: ⭸X f /⭸t = D f (⭸2 X f /⭸x 2 )
(4)
where X f , t, and x are the mole fraction of the flammable gas, time, and distance from the floor respectively. The initial and boundary conditions for this case are X f = 0 for 0 ≤ x ≤ H
t =0
at
⭸X f /⭸x = −Q/(D f H 2 ) at x = 0, ⭸X f /⭸x = 0 at x = 0,
t >0
t >0
⎫ ⎪ ⎪ ⎬ (5)
⎪ ⎪ ⎭
where H is the height of an enclosure. The values predicted by solving Eq. (4) under conditions shown in Eq. (5) are well coincide with the measured values shown in Fig. 4. In the prediction, they assumed the value 0.14 cm2 for D f [16]. They 0.5 d (cm) 2.76 2.16 1.61 0.92
0.4
Fig. 4 Measured propane concentration distributions in a 2 m-cube enclosure, the injection tube diameter d being parameter (Injection rate: 67 cm3 /s, Time from injection starting: 5.76 × 103 s)
Xf
0.3 0.2 0.1 0
0
0.1
0.2 x/H
0.3
0.4
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attributed the fact that this value is a little larger than that for molecular diffusion of propane to the effect of initial turbulence induced by the jet. Also, it is seen in Fig. 4 that fairly long duration of time is needed for the concentration becoming uniform. Although the flammable gas in an enclosure at an accidental explosion becomes scarcely uniform, the controlling mechanisms of flammable gas formation are intrinsically of aerodynamics with diffusion and turbulent mass transfer. The scale modeling for this process can be performed based on knowledge of diffusion and turbulent flows. For scale modeling, the characteristics of a jet flow should be discussed at first (Figs. 2 and 3). If the characteristics are assumed to be expressed by the Reynolds number, similarity of the phenomena concerning the jet flow could be kept for a constant value of the Reynolds number i.e., Re = vd/ν = constant
(6)
where v is the jet velocity, v is the dynamic viscosity. The scale lv of the vortex induced by the jet can be assumed proportional to the mouth diameter d of the gas leakage. Then, the following relation should be valid for both prototype and scale models: lv /d = constant
(7)
The aspect of the mixture is assumed to be represented by the ratio of the dimension L of the enclosure and the diameter lv of the vortex, the scale model should keep the following condition: lv /L = constant
(8)
The strength of a gas explosion would depend on the ratio of the volumes of the flammable gas and the enclosure, so that this ratio should be the same for both prototype and scale models. Since the volume of the flammable gas flowing into the enclosure is approximately equal to Qti (Q: rate of flammable gas leakage; ti : time to continue the leakage) of leaked flammable gas, the following relation should be valid for both prototype and scale models: Qti /L 3 ∝ vd 2 ti /L 3 = constant
(9)
Further, the condition for the similar diffusion in the vortex is lv 2 /td = constant
(10)
and the condition for the similar convection effect is L/tc = constant
(11)
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For similar concentration profiles of the flammable gas in the enclosure, the relations represented by Eq. (6) through (11) must be satisfied. Thus, the following relations are derived for models of different sizes (the ratio of dimensions is a) in similar conditions for gas explosions: L 1 = a L 2 , d1 = ad 2 , v1 = v2 /a, ti1 = a 2 t12 , lv1 = al v2 , td1 = a 2 td2 , tc1 = a 2 tc2 (12) In the experiment, if all the dimensions are similar, the gas velocity to leak should be inversely proportional to the ratio a of dimensions, and the phenomena changes with the time proportional to the other scale in a factor a 2 .
Flame Propagation and Pressure Behavior After ignition, a flame propagates in the enclosure and causes a pressure rise (Fig. 5). The flame can propagate only through the flammable mixture. Since the mixture is likely non-uniform, the flame propagation should not be of a constant velocity even at its initial stage. This is one of difficulties for scale modeling of pressure behavior at a gas explosion. It would be easily supposed that no one could control the flame propagation velocity to be proportional to a −2 . If this were done, a similar scale law could be applied for pressure behavior in a reduced-scale model enclosure. Thus, another difficulty for scale modeling is due to the fact that the burning velocity cannot change with the size of the model. On the other hand, however, the flame behavior can be made similar in different models by controlling the scale and intensity of turbulence in those models. The simplest case under such conditions is of uniform concentration in the enclosure, although the uniform concentration in a prototype enclosure is hardly attainable as mentioned in the previous section. Flame propagation Flame
Fig. 5 Typical aspect of Flame Propagation in a flammable mixture filled enclosure
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If the flame propagation velocity can be assumed independent of the scale, the time tb needed for flame propagation across the enclosure should be proportional to the scale of the model. L/tb = constant
(13)
At the same time, the pressure rise in an enclosure just after ignition can be approximated as [4, 17]: ( p − p0 )/ p0 ∝ S 3 t 3 /V,
(14)
where p, p0 , S, and t are the pressure in an enclosure, the ambient pressure, the burning velocity, and the time from ignition, respectively. If the pressure rise pb − p0 at breaking can be assumed constant and the time from ignition to breaking of enclosure boundaries such as windows, doors, or fragile parts is proportional to tb , then the following relation can be obtained: pb − p0 ∝ tb 3 /L 3 = constant
(15)
In derivation of Eq. (15), V was assumed proportional to L 3 . Equation (15) represents a relation usually used for the prediction of the pressure rise in an enclosure at an accidental gas explosion. As already pointed out elsewhere [4, 18], even if the configuration, dimension, strength of a fragile part to break are constant, pb still depends on the pressure rising rate. To simulate the gas explosion phenomena, therefore, the rate of pressure rise (d p/dt)b at breaking is preferably kept constant, i.e., (d p/dt)b ∝ tb 2 /L 3
(16)
Considering the relation represented by Eq. (15), this relation can be rewritten as (d p/dt)b tb = constant.
(17)
Equations (14) through (17) indicate that the phenomena can be simulated by controlling tb as it is proportional to L. Although this simple situation is scarcely realized in practical systems, the prediction based on the assumption of uniform flammable gas concentration has been frequently performed in the past. As knowledge on large-scale gas explosions has been accumulated, effects of the non-uniformity of flammable gas concentration on pressure behavior gradually become subjects to study [12]. Hirano et al. [19] indicated in their experimental study on the explosion pressure of a layered flammable mixture in a vessel that the pressure behavior depends on the flammable layer thickness. Also, Harayama et al. [20] and Dobashi et al. [21] examined pressure behavior at explosions of non-uniform flammable mixtures and found that the effects of non-uniformity of flammable gas concentration on pressure behavior are significant.
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When the flammable mixture in an enclosure is non-uniform, Eqs. (16) and (17) are no more valid. For scale modeling of practical gas explosion phenomena, we need other relations. In an enclosure, for which we need to discuss mitigation of gas explosion hazards, a uniform concentration of a flammable gas would be hardly realized because of a small diffusion coefficient of the flammable gas and density difference of flammable gas from ambient air as discussed in the previous section. Even if the injection velocity of flammable gas is fairly high, the flammable mixture layer will be established as shown in Fig. 3. In such a case, the flame propagation velocity in vertical direction would be different from that in horizontal direction (Fig. 6). In an extreme case, which would be realized at early stage of leakage, a flame would propagate through a thin horizontal layer. In such a case, Eq. (13) would be still valid, but Eq. (14) should be replaced by ( p − p0 )/ p0 ∝ S 2 t 2 /V,
(18)
If the pressure rise pb − p0 at breaking of parts of enclosure boundaries such as windows, doors, or fragile parts can be assumed constant and the time from ignition to the breaking is proportional to tb , then the following relation can be obtained as derivation of Eq. (15): pb − p0 ∝ tb 2 /L 3 = constant
(19)
Equation (19) is different from Eq. (15) usually used for the prediction of the pressure rise in an enclosure at an accidental gas explosion. The pressure rising rate (d p/dt)b at breaking in this case is different from that for a uniform concentration gas explosion. To simulate the gas explosion phenomena in this case, therefore, the rate of pressure rise at breaking must satisfy one of the following relations: (d p/dt)b ∝ tb /L 3
(20)
(d p/dt)b tb = constant.
(17)
or
Flame front Flame propagation
Fig. 6 Flame Propagation in an enclosure when flammable mixture is established as a thin layer
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At a real gas explosion, the flammable mixture would not be uniform nor thin layer. Thus, for scale modeling we need to keep conditions represented by the following relations: pb − p0 ∝ tb 2+c /L 3 = constant
(21)
(d p/dt)b ∝ tb 1+c /L 3
(22)
where c is a constant between 0 and 1. The value c is a function of the nonuniformity. When the flammable mixture is completely uniform, c = 1, while it is of a thin layer, c = 0. Equation (17) is valid for every case.
Concluding Remarks Discussion in this paper has been concentrated on modeling of main processes of an accidental gas explosion, flammable mixture formation and pressure rise. After brief discussion, it is indicated that in a large enclosure, the flammable gas scarcely becomes uniform. When a reduced scale model is used for an experiment simulating an accidental gas explosion at an enclosure such as a residential room, reactor, dryer, or fuel reservoir, it is necessary to provide a system to be able to generate nonuniform flammable mixtures. Since the pressure rise depends on flame propagation through the formed flammable mixture, size and number of broken parts, and pressure at breaking of those parts, knowledge about flame propagation and structure breaking as well as the flammable gas behavior is needed for scale modeling. The difficulties for scale modeling of the pressure rise are indicated to be attributable to the non-uniformity of the flammable gas concentration and constant burning velocity independent of the enclosure size. Pressure behavior depends on uniformity of the flammable mixture. For a uniform mixture, the pressure increases in proportion to the third power of the time from ignition, while for a thin layered mixture, it increases in proportion to the square of the time from ignition.
References 1. R.I. Emori, K. Saito, K. Sekimoto, Scale Models in Engineering: Theory and Application, Gihodo, Tokyo, 2000, in Japanese. 2. T. Hirano, J. Japan Assoc. Fire Sci. and Technol. 28 (1978) 6–11. 3. T. Hirano, J. Japan Soc. Safety Engng. 19 (1980) 312–318. 4. T. Hirano, Technology for prevention of gas explosions, Kaibundo, Tokyo, 1983. 5. G.F.P. Harris, P.G. Briscoe, Combustion and Flame 11 (1967) 329–338. 6. C. Yao, AIChE Loss Prevention Symposium, 8 (1974) 1–9. 7. W.G. Chappell, AIChE Loss Prevention Symposium, 11 (1977) 76–86. 8. D. Bradley, A. Mitcheson, Combustion and Flame, 33 (1978) 221–236, 237–255.
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9. R.G. Zalosh, AIChE Loss Prevention Symposium, 13 (1979) 98–110. 10. D.M. Solberg, J.A. Pappas, E. Skramstad, Proc. Comb. Inst. 18 (1980) 1607–1614. 11. T. Hirano, Fuel-Air Explosions, J.S.H. Lee and C.M. Guirao, ed., Univ. Waterloo Press, Waterloo, (1982) pp. 823–839. 12. T. Hirano, Plant/Operation Progress, 3 (1984) 247–254. 13. V.V. Molkov, R. Dobashi, M. Suzuki, T. Hirano, J. Loss Prevention in the Process Industries 12 (1999) 147–156. 14. F. Tamanini, J.V. Valiulis, J. Loss Prevention in the Process Industries 13 (2000) 277–289. 15. V. V. Molkov, R. Dobashi, M. Suzuki, T. Hirano, J. Loss Prevention in the Process Industries 13 (2000) 397–409. 16. A. Ohmori, K. Shiota, T. Hirano, Paper No. 1 presented at the 13th Symposium on Safety Engineering (Japan) 1983. 17. B. Lewis, G. von Elbe, Combustion, Flames and Explosions of Gases, 3rd edn., Academic Press, New York, 1985. 18. H. Kaneko, Study on Gaseous Explosion in a Vessel With a Fragile Part (V), Tokyo Gas R&D Institute Report 26 (1981) 135–146. 19. T. Hirano, F. Okada, K. Akita, J. Japan Soc. Safety Engng. 18 (1979) 28–33. 20. M. Harayama, H. Ohtani, T. Hirano, K. Akita, J. Japan Soc. Safety Engng. 19 (1980) 266–271. 21. R. Dobashi, K. Sato, T. Hirano, K. Akita, J. Japan Soc. Safety Engng. 24 (1985) 9–16.
Period for Spontaneous Ignition of a Refuse Derived Fuel Pile Lijing Gao and Toshisuke Hirano
Abstract This paper presents the results of attempt to predict the period available for prevention of spontaneous ignition in a RDF (refuse derived fuel) pile. The heat transfer in a RDF pile was discussed for a case when the effect of convection is negligible. By analyzing the energy equation, it was inferred that the temperature in a large pile of RDF hardly becomes uniform. Assuming that the term representing the effect of the temperature rise on the thermal balance becomes appreciable compared to that representing the effect of the conductive heat transfer just before ignition, the period for the temperature rise to ignition was inferred. By comparing the period predicted by analysis to that observed at a fire, the size of the higher temperature region in the pile was inferred to be smaller than 3 m. Then, the available period from the detection of the temperature rise to the ignition of RDF piles of various sizes were predicted on the basis of the Frank-Kamenetskii theory. It is indicated that the available period drastically decreases with the increase of detection temperature. Also, the available period increases with the increase of the RDF size. Keywords Spontaneous ignition · ignition process · refuse derived fuel · large pile · fire
Nomenclature A C cp E ΔH l n
Apparent frequency factor Density Specific heat Apparent activation energy Heat of reaction Size Reaction order
L. Gao Faculty of Risk and Crisis Management, Chiba Institute of Science, 3 Shiomi-cho, Choshi-shi, Chiba 288-0025, Japan e-mail:
[email protected]
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R r T t V
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Gas constant Radius Temperature Time Gas velocity
Greek Θ α λ ρ ξ ω˙ f
Non-dimensional temperature Thermal diffusivity Thermal conductivity Density Non-dimensional distance Rate of chemical reaction
Subscripts c i 0 r
Critical condition Ignition Initial condition Surrounding
Introduction Recently, fires have repeatedly occurred at storage buildings of RDF (refuse derived fuel). The most serious one occurred on August 2003 at a power station in Mie Prefecture, Japan. Two explosions occurred during the fire. At the first explosion, four workers were burned, and at the second explosion, one worker was burned and two fire fighters were killed, who had been pouring water from the roof into the storage. It is true that efficient consumption of municipal solid waste is important for resolving the present issues on city lives. One of those methods is the use of RDF at power stations. The RDF is produced by shredding, screening, drying and palletizing. For efficient consumption of RDF, large-scale power stations are favorable. In such power stations, large storages are constructed for continuous operation. Once a fire occurs, however, they cannot continue operation, so that the prevention of fires at the RDF storages is extremely important. In the investigation about any specific RDF storage fire, no ignition source has been identified, and the cause of the fire was considered to be spontaneous ignition of piled RDF [1–6]. So far the critical temperature for spontaneous ignition has been studied on the basis of the Frank-Kamenetskii theory [7–8]. The critical temperature
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has been shown to decrease with the size of the RDF pile. The theoretically predicted results have been attempted to confirm by experiments [9]. The results obtained by those studies [3–9] to identify the critical temperature are useful to establish a rule that the temperature of an RDF pile should be kept lower than the critical temperature. However, those results do not give the knowledge on available period for the actions to cool the RDF pile when the trend of the temperature rise is detected. In order to prevent a fire caused by spontaneous ignition of a large RDF pile, we need the knowledge on the period available for making the RDF pile safe. Without the knowledge on the available period from the detection of a trend of the temperature rise to ignition, appropriate actions would not be performed for fire protection. In this study, therefore, it was attempted to find methods for prediction of the periods from the detection of the temperature rise to ignition.
Formulation of Problem Within a RDF pile, the pressure gradient and energy dissipation by fluid viscosity would be negligible, and the energy exchange by radiation would not be effective. For such a situation, the energy equation to describe the temperature profile and heat transfer in the RDF pile should be as follows: ρc p
⭸T + ρc p V · ∇T = ∇ (λ ∇T ) + ω˙ f ⌬H ⭸t
(1)
where ρ is the density, c p is the specific heat, T is the temperature, t is the time, λ is the thermal conductivity, V is the gas velocity, ΔH is the heat of reaction, and ω˙ f is the rate of chemical reaction. ω˙ f is assumed to be given by the Arrhenius equation as: ω˙ f
E = A exp − RT
(2)
where A is the apparent frequency factor, E is the apparent activation energy, and R is the gas constant. If the effect of convective heat transfer in the RDF pile is negligible, the governing equation to express temperature variation in the pile can be expressed as ρc p
⭸T = ∇ (λ ∇T ) + ω˙ f ⌬H ⭸t
(3)
Under the condition that Eq. (3) is applicable, ignition would occur when the amount of heat generated in the RDF pile exceeds that lost by conduction. In such a situation the left hand side of Eq. (3) is a finite positive value. On the other hand, the condition that the left hand side of Eq. (3) is zero represents a steady state in energy balance.
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The existing of physically meaningful solution of the equation ∇ (λ ∇T ) + ω˙ ⌬H = 0
(4)
means that the pile is in a state of steady, i.e., ignition would not occur. The limit of existing physically meaningful solution of Eq. (4) can be assumed to indicate the limit of ignition. This consideration is the base of the well known FrankKamenetsukii theory.
Local Temperature Profile Change In the cases of accidental fires of RDF storages, the period from the start of storage to ignition was observed to be several months. This fact means that the chemical reaction at the initial stage of spontaneous ignition at those cases can be assumed very low. In such a situation, if convective heat transfer is negligible as assumed at the formulation of the problem, the temperature profile change would mainly depend on conduction. In a huge RDF pile, there would be non-uniformity of the temperature, and ignition would occur at the site where the initial temperature is higher than its surroundings. It would be useful to know the process of the temperature profile change when a high temperature region exists in a pile as shown in Fig. 1 at the initial stage of spontaneous ignition. Assuming that λ is constant, that the temperature field is one dimensional, and that the heat release by chemical reaction is negligible, Eq. (3) becomes ρc p
⭸2 T ⭸T =λ 2 ⭸t ⭸x
(5)
Introducing non-dimensional temperature and distance: ⌰=
T − Te T0 − Te
(6)
Equation (5) can be rewritten as ⭸⌰ ⭸2 ⌰ =α 2 (7) ⭸t ⭸x where α is the thermal diffusivity = λ/ρc p . The initial and boundary conditions for the situation represented by Fig. 1 are at at
t >0
⎫ ⌰ = 1⎪ ⎬ ⌰=0 ⎪ ⎭ x → −∞ ⌰ = 0
t =0 −1≤ x ≤1 x < −1; 1 < x x → ∞;
(8)
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T Initial temperature profile
High temperature site To
Temperature profile presented by Equation (15) Te x=−
l 2
x=0
x=
l 2
x
Te = external temperature
Fig. 1 Model to evaluate temperature profile change when a high temperature site exists in a RDF pile
The solution of Eq. (7) to satisfy the initial and boundary conditions is 1−x 1+x 1 ⌰=1+ + erf erf 1 1 2 2 (αt) 2 2 (α t) 2
(9)
The time needed to increase the temperature at a site can be obtained from Eq. (9). In Fig. 1, the temperature at the central part is assumed to be higher than the surrounding temperature. When the temperature at the central part is lower than the surrounding temperature, the solution, Eq. (9) is the same. When the temperature at the central part becomes close to that of surroundings, Θ becomes 0. At such a situation, the following relation would be satisfied: 1
(αt) 2 ≈ l
(10)
This relation can be rewritten as tx ≈
ρc p 2 l λ
(11)
where tx is an approximate period needed to vanish the temperature difference at a part of a size l. Equation (11) is the same expression as the time needed to propagate a thermal wave for a distance l. The approximate time needed for temperature decrease at a higher temperature region of size l can be evaluated by using Eq. (11). The results are shown in Table 1. The data used for the evaluation are listed in Table 2. In the Table 2, in addition to the data for the evaluation of the periods shown in Table 1, those to be used in the flowing part of this paper are presented also. It is seen that the period needed to decrease the temperature of the high temperature region of 3 m in size is about 9.17 × 107 s, i.e., 35 months. This period is longer than the period from the start of the use of the storage to a fire. Thus, the temperature inside a large
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Table 1 The results of approximate period tx needed to vanish the temperature difference at a part of a size l l (m)
tx (s)
Corresponding days or months
0.1 0.5 1.0 3.0 5.0
1.02 × 105 2.55 × 106 1.02 × 107 9.17 × 107 2.55 × 108
About 1 day About 1 month About 4 months About 35 months About 98 months
Table 2 Values used to predict the time to ignition by numerical simulation Properties of RDF
Unit
Value
Gas constant, R Density, ρ Specific heat, c p Thermal diffusivity, α Thermal conductivity, λ Apparent activation energy, E Apparent frequency factor, A Heat of reaction, ΔH
J/mol K kg/m3 J/kg K m2 /s J/(s m K) J/mol 1/s J/kg
8.31 4.21 × 102 1.42 × 103 9.80 × 10−8 5.87 × 10−2 89.82 × 103 3.60 × 105 1.26 × 106
storage of RDF is necessarily not uniform and the size of a high temperature region can be inferred to be smaller than 3 m.
Period Needed to Start Ignition When the flow inside the pile can be assumed negligible, the temperature profile change can be predicted by solving Eq. (3). Since Eq. (3) is not linear, only the method to reach the solution is that by numerical simulation. By numerical simulation, the period from the initial state to ignition, when the rate of the temperature rise at the center of the volume becomes large, could be defined. Figure 2 shows the variation of period to ignition with initial temperature for a RDF volume of 3 m in size, which obtained by inferring on the basis of seven examples of numerical simulation about temperature profile histories [10]. The process of numerical simulation is not special, so that the details are omitted. It is seen that the time from its initial state to spontaneous ignition increases with the decrease of its initial temperature. Based on Fig. 2, we can evaluate the period from detection of temperature rise to ignition. If the action for preventing the spontaneous ignition is decided to start at 50 ◦ C, the available period can be inferred to be 4 days. Since the numerical simulation is expensive and the cases to evaluate are in usual limited, theoretical analysis would be favorable for understanding the effects of various parameters on the available period. Thus, in the followings, a theoretical analysis for evaluation of the available period for prevention of a RDF fire by spontaneous ignition. It is well known that we can evaluate the critical temperature Tc , a temperature higher than which a spontaneous ignition would occur, by using Eq. (4). The
Period for Spontaneous Ignition of a Refuse Derived Fuel Pile 100 Initial temperature, /°C
Fig. 2 Variation of period to ignition with initial temperature of RDF of 3 m in size
81
80
60
40
20
0
5
10 15 20 25 Time to ignition, /day
30
35
evaluation of Tc and its dependence on the pile size L are important for prevention of the RDF fires and have been performed in the previous studies [7, 8]. If the surrounding temperature would be Tc , however, the time needed to spontaneously ignite is infinite. For realizing a spontaneous ignition within a finite period, the temperature T at the periphery of the pile must be higher than Tc . When the spontaneous ignition caused by failure of temperature control or unexpected temperature increase at the periphery, T at the spontaneous ignition would be close to Tc . In such a situation the heat exchange caused by conduction would be almost the same, i.e., ∇ (λ∇T )c ≈ −ω˙ f c ⌬H
(12)
Assuming that the temperature rise is attributable to the heat release by chemical reaction, the following equation can be derived from Eqs. (3) and (12): ρc p
⭸T Tc ≈ ω˙ f ⌬H − ω˙ f c ⌬H = A⌬H exp − ⭸t T
(13)
Since the right hand side of Eq. (13) is independent of time, Eq. (13) can be rewritten as 1 dT 1 Tc ≈ (14) (ω˙ ⌬H − ω˙ f c ⌬H ) = A⌬H exp − dt ρc p f ρc p T Equation (14) can be solved if the initial condition is given. If at t = 0
T = T0
then the solution is ti ≈
Ti T0
ρc p Tc exp dτ ⌬HA T
(15)
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Equation (15) represents the period ti needed to rise temperature from T0 to Ti by chemical reaction. It is seen that as T approaches to Tc , ti becomes infinite, and that as the difference of T from Tc increases ti becomes small. On the basis of Eq. (15), a equation representing the available period ta after detection of temperature rise, i.e., ta ≈
Ti Td
ρc p Tc exp dτ ⌬HA T
(16)
where Td is the temperature for detection of temperature rise. The dependence of the available period on the size l of higher temperature region can be evaluated because Tc depends on the size. From the results of the FrankKamenetsukii theory, the relation between l and Tc can be expressed as
1 l ≈ Tc exp Tc 2
2
(17)
This equation implies that with the increase of the size l, Tc decreases markedly so that the available period becomes short. This result is consistent with the result derived on the basis of Fig. 2. The fact that the temperature rise in a small size of high temperature region implies that the heat release by chemical reaction exceeds the heat loss although the heat loss becomes significant with the decrease of the size.
Conclusions A study was conducted on prediction of the period available for prevention of spontaneous ignition in a RDF (refuse derived fuel) pile and the following conclusions were derived: 1. By analyzing the energy equation in a case when the effect of convection is negligible, it was inferred that the temperature in a large pile of RDF hardly becomes uniform. 2. Assuming that the term representing the effect of the temperature rise on the thermal balance becomes appreciable compared to that representing the effect of the conductive heat transfer just before ignition, the period for the temperature rise to ignition was inferred. The result is listed in Table 2. When the size of a high temperature region is 3 m, the evaluated period is about 35 months. 3. By comparing the period predicted by analysis to that observed at a fire, the size of the higher temperature region in the pile was inferred to be smaller than 3 m. 4. The available period from the detection of the temperature rise to the ignition of RDF piles of various sizes were predicted on the basis of the Frank-Kamenetskii theory. It is indicated that the available period drastically decreases with the increase of detection temperature. Also, the available period increases with the increase of the RDF size.
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Acknowledgments The authors wish to express their thanks to Drs. T. Suzuki, T. Tsuruda, and C. Liao, and Mr. Y. Ogawa for their stimulate discussion based on their experience conducting studies on RDF burning.
References 1. RDF power station accident investigation technical committee, Mie Prefecture, RDF power station accident investigation interim report (2003), 1–20. 2. Audit committee, Mie Prefecture, Regular audit debrief report (Mie Prefecture RDF power station audit debrief report) in 2003 fiscal year (2003), 1–50. 3. RDF propriety management study committee, The Ministry of the Environment, Proper management strategy of RDF (2003), 1–15. 4. Electric power safety subcommittee RDF power station accident investigation working group, The Ministry of Economy, Trade and Industry, Electric power safety subcommittee RDF power station accident investigation working group report (2003), 1–42. 5. RDF power station accident investigation technical committee, Mie Prefecture, RDF power station accident investigation final report (2003), 1–46. 6. The Ministry of Public Management, Home Affairs, Posts and Telecommunications Fire and Disaster Management Agency, Examination report of safety measures investigation of facilities related to RDF (2003), 1–234. 7. L. Gao, T. Tsuruda, T. Suzuki, Y. Ogawa, C. Liao, Y. Saso, Possibility of Refuse Derived Fuel Fire Inception by Spontaneous Ignition, Proceedings of 6th Asia-Oceania Symposium on Fire Science & Technology, 102–107, Daegu, Korea, March 17–20, 2004. 8. L. Gao, T. Tsuruda, Influence of RDF Properties on Spontaneous Ignition, Proceeding of Annual Meeting of Japan Association for Fire Science and Engineering (2004), 90–93. 9. T. Suzuki, T. Tsuruda, C. Liao, Y. Ogawa, Y. Saso, L. Gao, A Study on Self-heating of RDF-5, Report of National Research Institute of Fire and Disaster, No. 98 (2004), 91–96. 10. T. Tsuruda, The Numerical Simulation of Concerning Heat Ignition of RDF, Report of National Research Institute of Fire and Disaster, No. 99 (2004).
Pressure Scaling of Fire Dynamics Richard C. Corlett and Anay Luketa-Hanlin
Abstract Fundamental to fire behavior are convection/diffusion phenomena which are not quantitatively captured by subscale experiments in an ordinary atmosphere. It has been known for decades that combining pressurization with length scale reduction, via the L 3 P 2 preservation rule, offers the possibility of rigorous convection/diffusion scaling. But the potential usefulness of pressure scaling of fires is still not delineated. Other phenomena are not encompassed by pressure scaling theory and thus present scaling deficiencies. These must be evaluated and, as necessary, dealt with by compensation in experimental procedure or interpretation of results. Thermal radiation presents the most critical potential scaling deficiencies; others stem from difficulties with rate-dependent processes, such as pyrolysis. Pressure scaling theory is reviewed. For context, focus is on prototype length scale L from 3 to 10 m and length scaling ratios of from 2 to 5. Pressure scaling still holds out potential for cost savings in testing fire protection designs. Scaling of fire spread in enclosures appears feasible but only up to points in time where product recirculation or gas layer influence on fire dynamics becomes important. For optically thick fires with burning rates of both model and prototype controlled by energy feedback, accounting for radiation will force compromise modification of the L 3 P 2 rule itself. Keywords Pressure scaling · thermal radiation · fire
Introduction Much of the societal hazard of fires lies in their size and energy, attributes which impede experimental study. Typical full scale fires are difficult to control and replicate, which often degrades quantitative results. Parametric variation at full scale is rarely affordable.
R.C. Corlett Department of Mechanical Engineering, Box 352600, University of Washington Seattle, WA 98195-2600
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Investigators are thus compelled to scale down the fire, The full scale “prototype” is represented by a “model” of smaller length scale L. Scaling down at normal atmospheric pressure reduces the balance between convective and diffusive transport as characterized by the Reynolds number or, in the more usual fire case, the Grashof number Gr. The justifying reasoning is that large fires are turbulent with flows depending only mildly on Gr. So long as the model fire is large enough to also be turbulent the flows are argued to be similar in some degree. Similarity can be enhanced by requiring the balance between inertia and buoyancy to be the same for the model as the prototype. This is Froude scaling [1] wherein all imposed velocities, including the effective velocity of fuel entering the fire from a gasifying surface (that is, the local “burning rate”) are scaled as L 1/2 . The natural coupling between heat energy feedback and burning rate generally produces a model burning rate exceeding this requirement. A more basic problem is that, even if the large scale fire structure is captured by self-adjustment of turbulence, at some level of detail such as that of vortex formation or convective heating of objects, failure to preserve Gr will result in significant misrepresentation by the model. The only practicable way to preserve Gr over an attractive L-range is to raise the pressure P (atm) of the model. If it is hypothesized that the prototype and model temperature fields are homologous, then dimensional arguments show that preservation of Gr translates to preservation of L 3 P 2 . In a pioneering paper in 1973, de Ris et al. [2] presented a comprehensive theoretical discussion of P-scaling and reported a P-range to 40 corresponding to an L-ratio range to 12. Typical range of L (burning object maximum) was 0.04–0.3 m. Fuels were plexiglass (PMMA) and wood. The theory states that the surface convective heat flux and fuel mass flux required to support a stationary fire both scale as 1/L. The reported experiments were in reasonable agreement. Extension of the theory to coupling of gas-phase fire energetics and heat conduction in the condensed fuel suggests that fire spread can also be scaled. Model time is accelerated by a factor 1/L 2 corresponding to burning rate scaling as 1/L. In Ref. [2] also are discussed some “second order effects”, most importantly thermal radiation. Difficulties with radiation were anticipated, but the tone was optimistic. Over time, the view of the radiation problem in the fire research community has grown more pessimistic. It is certain that there can be found highly unfavorable conditions wherein radiation plays an essential role in fire energetics and, at the same time, does not pressure scale correctly. The delineation of fire regimes not subject to these dual conditions (importance of radiation and failure to scale) remains an open question. The roles of finite-rate chemistry in the gas phase as well as in the gasifying solid phase, e.g., in wood, are briefly addressed in Ref. [2], providing a foundation for the development to follow. The present paper reviews and summarizes pressure scaling of fires. Convective/diffusive scaling rules are put forward, with radiation disregarded, in the next section. Included are coupling with transient conduction in inert bounding materials (e.g., walls) and in condensed fuels. Then the difficult problem of including radiation is discussed.
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Convective/Diffusive Pressure Scaling Preliminary Remarks on Scaling Development In what follows, the “prototype” refers to a full-scale fire event about which knowledge is wanted, e.g., fire development, heat transfer to a surface. A “model”, typically smaller, is the subject of a real fire event intended to yield the desired information. This approach generally embodies two types of scaling rules: “operational” and “interpretive”. Adherence to operational rules assures that the model phenomena represent those of the prototype in respects essential to the determination at hand. The above-mentioned L 3 P 2 rule is operational. Interpretative scaling rules tell how to translate model measurements to prototype conditions. Interpretive rules may be “direct” dictates of scaling theory, e.g., velocity as L 1/2 , or “correcting” to account for “scaling deficiencies” as defined below. Scaling rule development may follow two paths, both utilized in Ref. [2] and here. One is based on preservation of parameter ratios identified from physical reasoning. The other is based on examination of a complete formulation consisting of conservation PDEs and their boundary conditions. Using scaling transformations the formulation is rendered dimensionless in space and time and derived variables, e.g., velocity, but not in temperature, to yield a version common to both model and prototype. The term “reduced” is here applied to the variables, PDEs, etc., resulting from this process. The solution of the reduced problem is common to both model and prototype provided the parameters therein, e.g., Gr, are invariant between model and prototype. Transformation of measured model results to reduced variables and then to prototype “predictions” is equivalent to application of direct interpretive rules. The dimensionless PDE approach is considered relatively rigorous. Of particular value is the possibility of isolating “scaling deficiencies”, that is, deviations from reality required to force the model and prototype formulations into commonality. A scaling deficiency is tantamount to insertion of a false relationship or false information into a mathematical model supposed to describe the real fire phenomena. The existence of scaling discrepancies does not necessarily destroy the usefulness of a scaling procedure. The pertinent issue is the extent to which the imperfection(s) in the mathematical model, reflecting scaling deficiencies, would lead to false or erroneous predictions of the information desired from the scale model experiment. Little research has been devoted to evaluating scaling deficiencies in this spirit. A suite of examples stemming from the chemical process descriptions in the energy and species conservation equations is next discussed.
Gas-Phase Chemistry Exact representations of chemical reaction source terms introduce reduced parameters which depend on characteristic times (for finite-rate reactions) and differ
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intrinsically for prototype and model. A way around this in pressure scaling is to replace the finite-rate terms by mathematical imposition of local equilibrium, that is, the “fast combustion” limit. In the simplest version, oxidation is required to proceed at every point at whatever rate is required to continuously exhaust either the local oxygen or the local fuel. If there is oxygen deficiency, additional rules must be invoked to allocate the deficiency, e.g., via hydrogen, CO or soot. Such rules are pressure dependent and hence not amenable to pressure scaling. A third difficulty arises with locally weak (typically lean) mixtures. If weak-mixture combustion is of interest, e.g., for ignition and flame spread in ceiling layers, pressure scaling demands modeling rules independent of pressure and not introducing a characteristic time. A modeling assumption consistent with pressure scaling would invoke only temperatures and/or composition as parameters, e.g., application of a critical local adiabatic flame temperature below which there can be no reaction and above which fast reaction to equilibrium. In the proceeding paragraph, three apparently potential scaling deficiencies in treatment of gas-phase chemistry are pointed out: replacement of finite-rate by fast chemistry, incorrect equilibrium of oxygen-lean mixtures, and artificial flammability rules for weak-mixture combustion. Most fire researchers would have little problem with the first two. They would dispense with the first on grounds that the main flow and energetics of fires are diffusion-controlled and the second on grounds that heat energy release correlates well with oxygen consumption alone (see the oxygen calorimetry literature [3]) so that the chemical allocation of oxygen deficiency is essentially irrelevant. The third is only relevant to special problems for which getting the flow and mixing right is sufficiently challenging that problematic simplifications of the chemistry might be tolerable. The heart of the PDE formalism for pressure scaling is reduction of the convection/diffusion terms to forms identical for both model and prototype. For brevity, the term “pressure-scalable gas reaction model” or “PSGR model” is used here for any description of the progress of the combustion process(es) which is compatible with such reduction. The approximations suggested in the preceding paragraph satisfy PSGR criteria. A global reaction chemical model with first order gas-phase chemistry also fits [2]. Henceforth a valid PSGR model is assumed. More threatening scaling deficiencies are consequences of thermal radiation phenomena. Radiation is ignored until reintroduced later.
Temperature and Concentration Field Similarity Non-subscripted and m-subscripted quantities refer to the prototype and model, repectively. Mass (as opposed to mole) fractions are chosen arbitrarily to characterize composition. A correctly scaled model fire is hypothesized to have a temperature Tm -field which is homologous to the prototype T -field in space (length scales L m and L) and time scales to be specified, depending on the type of problem.
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Also hypothesized to be homologous are all species mass fraction fields of interest. These hypotheses embody the conventional ideal gas thermophysical assumptions wherein the following are functions of composition and T : specific heats, ρ/P, and transport properties (of the form ρ D) where ρ is density and D is any diffusivity. In determination of the thermodynamic properties, P ≡ constant is assumed for any one fire event. Within the hypotheses of temperature and concentration similarity the fire gas-phase PDEs will accept virtually any level of thermophysical and combustion detail, except as constrained by the incorporation of a PSGR model.
Full Fluid-Mechanical Scaling Consider as a prototype a set of condensed material surfaces forming a partial enclosure with fluid-mechanical access to ambient air of density ρ∞ . Over a portion (at least) of this set combustible fuel is introduced. In general, over other portions of the surface, inerts, e.g., water vapor from char formation or applied spray, are introduced. Over the remainder, e.g., walls, there is no flow. Further flows may cross control surfaces such as windows or there may be a flow at infinity (wind). Prototype problem surface information (subscript sp) includes a set {Usp } of velocities which may include continuous variation over surfaces. Also included is a set {Ysp } of gas mass fraction compositions wherever the flow is into the fire system. The problem statement is completed by a set {Tsp } of temperatures over all material surfaces and other inflows or at infinity. Specification of these three information elements need not be explicit. The foregoing specifications, while amenable to pressure scaling, are excessively general for most needs. We might reduce {Tsp } to fuel surface and air temperatures T f and T∞ , {Ysp } to identification of the fuel, e.g., propane or wood pyrolysis products, and {Usp } to fuel supply velocity U f . The fuel surface mass flux m f = ρ f U f where the density ρ f is determined by the fuel identity, T f and P. With g denoting gravity, a set of characteristic flow quantities are L (length – from the problem geometry), t ∗ = (L/g)1/2 (time) and V ∗ = (Lg)1/2 (velocity). Reduction with these and incorporation of a PSGR model for chemical rate terms, reduces the prototype and pressure-scaled model PDE sets (independent variables x/L and t/t ∗ , velocity variable V /V ∗ ) to identify. (Here x represents a lengthdimensioned vector in full 3-D space, y a surface subset of x and z the local surface of x.) With the additional reduction of {Usp } to {Usp /V ∗ }, the complete model and prototype formulations become identical. The solution fields of reduced velocity V /V ∗ , mass fraction composition, and T are identical in dimensionless time and space. We can then deduce any properties of the prototype field(s) from knowledge of the corresponding model data. In the reduced formulation, surface T -gradients are in x/L space which implies that the surface heat fluxes, being proportional to the T -gradients in x space, scale as 1/L, as previously noted.
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An example is a water-cooled porous gas burner (length L) in a calm unobstructed atmosphere of standard air at P and T∞ . The fuel is characterized by surface supply velocity U f , mass air/fuel ratio (AFR), supply temperature and density T f and ρ f , and stoichiometric adiabatic flame temperature Tsaf (referred to T∞ and T f ). For a scale model experiment (length L m ), all of the problem-defining temperatures, and AFR, are the same. Also Pm /P = ρ f m /ρ f = (L/L m )3/2 and V f m /V = (L m /L)1/2 . Subject to the stated assumptions the model and prototype fires would be completely homologous per these scaling relations. The imposed fuel mass fluxes and the mean heat fluxes would satisfy m f m /m f = qsm /qm = L/L m
(1)
A more complex example would put the same burner in a room with a window. The room surfaces are assumed sufficiently massive and heat conducting as to retain the initial surface temperature for a significant fire duration. In this case the complete transient phenomena, including products layer buildup and eventual establishment of window in- and out-flows, would be captured by the model. Both velocities and time would scale as L 1/2 .
Thermally Simple Fuels A thermally simple fuel here means one which yields a gasification mass flux in direct proportion to the fire feedback heat flux. A common example is a liquid supplied near its evaporation temperature. Equation (1) implies that full fluid-mechanical scaling is also achieved if a prototype with a simple fuel is pressure modeled with the same fuel. The condensed-fuel regression rate scales as 1/L. The convective feedback flux need not be spatially uniform. Fuel geometry can be arbitrarily complex and may even vary with time as fuel locally burns out. Flow of liquid fuel in response to regression is not covered by this scaling principle.
Coupling with Heat Conduction: Matched Time-Scale Ratios In most cases of practical interest the surface temperature Ts varies over t and y in accordance with the heat conduction PDE. Full transient similarity requires matching of model- and prototype-ratios of tc (conduction PDE time scale) to t ∗ (gas phase). There are two possible strategies for scaling of heat conduction. One is to adjust solid-phase geometry (usually thickness) and, by material substitution, thermophysical properties. The other is to exploit the fact (not always true) that tc >> t ∗ thereby rendering the time-scale matching constraint irrelevant. In what follows, it is assumed without further discussion that, where conducting surfaces have backfaces – a slab has a backface and a crib element does
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not – backface boundary conditions are either prescribed temperature, zero heat flux or thermally thick, and the same for model and prototype. Now consider the material substitution strategy with matched time scale ratios for a thermally thick solid with constant properties ks (thermal conductivity) and (ρC)s (volume specific heat). In general the model properties are different. Let L c denote a conduction length scale to be determined. The heat conduction PDE must be reduced analogously to the gas-phase equations, from which appears a conduction time constant, tc = L 2c (ρC)s /ks . Preserving tc /t ∗ leads to the requirement (L m /L)1/2 (L c /L cm )2 (ksm /ks )(ρC)s /(ρC)sm = 1
(2)
Heat flux continuity at the solid surface, after reduction via the two length scales and noting that the model and prototype gas-phase thermal conductivities are the same, produces the additional requirement (L m /L)(ksw /ks )(L c /L cm ) = 1
(3)
Eliminating the L c ratio yields (ksm /ks )(ρC)s /(ρC)sm = (L/L m )3/2
(4)
This is a difficult requirement to meet in practice except perhaps when the prototype is a strong thermal insulator with both ks and (ρC)s much smaller than values for solids available for a model. If the solid is not thermally thick, then L c and L cm must be the same fixed fraction of the respective prototype and model physical thicknesses. The preceding equations (two independent) represent stringent constraints on selection of the model properties L cm , ksm and (ρC)sm .
Coupling with Heat Conduction: Time-Scale Ratios not Matched Radical material substitution appears generally incompatible with modeling of thermally controlled fuel gasification and such related phenomena as fire spread and char-layer growth. Consider a simplified fire situation with a condensed fuel surface and other surfaces which are inert. The condensed fuel gasifies to form a distinct gaseous fuel (as characterized by AFR and combustion energy) whose density is proportional to the pressure P and otherwise is fully determined by T f . The local fuel flux is characterized by fuel velocity V f . In general, V f and T f are functions of y, as is also the inert surface temperature Ts . Consider the gas phase of this fire from an IO standpoint. The three functions V f (y), T f (y) and Ts (y) constitute the Input. The Output is the feedback fire-to-condensed-phase surface heat flux distribution qs (y). The assumption is that, for any change in the Inputs, the Output readjusts itself in a time much less than tc . Thus we regard the gas phase of the particular fire geometry, fuel identity and pressure as embodying the functional (in the
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mathematical sense of a function of functions) qs (y) = Q s {V f (y), T f (y), Ts (y)}. Following the same reasoning as in Eq. (1), we obtain the reduced functional Q S R , L qs (y/L) = Q S R L m f ( y¯ /L) , T f (y/L) , Ts (y/L)
(5)
where the surface geometry presented to the gas-phase fire by the model is fully similar to that presented by the prototype, and the L 3 P 2 rule is understood. Note that the functional in Eq. (5) in no way depends on the thickness of the model surfaces or their heat conduction properties. But this functional does contain all of the information from the fire’s gas phase that is pertinent to the condensedphase problem. Now complete the specification of the problem by assuming that the model is perfectly “faithful” in that its entire construction is geometrically similar to that of the prototype and identical materials are used homologously. The 3-D heat conduction equation is reduced to model and prototype similarity by transforming to independent variables x/L and t/tc . (Faithful geometric modeling removes the distinction between L and L c .) We assume (temporarily for simplicity) that gasification is a phase- or chemical-transformation at temperature T f g and with energy ⌬h f g , both material properties. If Ts < T f g , m f = 0 and all of qs goes to conduction. The reduced surface boundary condition then reads qs L + ks [⭸T /⭸(z/L)]s = m f L ⌬h f g
(6)
where z/L is an appropriate scaled distance normal to the surface. Equation (6) applies at every surface point y/L for both model and prototype. Together with the reduced PDE, Eqs. (5) and (6) constitute a complete problem formulation identical for model and prototype. The solutions are homologous in space and time, with time scale, tc = L 2 (ρC)s /ks , i.e., time scales as L 2 and velocity as L. The above result is completely general respecting geometry. Upward, lateral and downward fire spread can be modeled simultaneously. Inhomogenous structures such as panel with stiffeners of different materials can be modeled. The thermophysics can also be generalized. Specifically, transient heat conduction similarity can be achieved provided that materials at homologous points can be described fully in terms of temperature-dependent properties, i.e., chemical transformations controlled by kinetic rates must be modeled as temperaturedependent. Anisotropy and composite construction are acceptable. Specific heat “delta functions” can represent sub-surface transformations such as virgin f uel → char + gas. In analogy with the PSGR models previously introduced for gas-phase chemistry, we specify “pressure-scalable fuel gasification models” or “PSFG models” as a generic requirement for transient conduction scaling. The implications of the corresponding scaling deficiencies have not been much explored. Applying scaling hypotheses essentially the same as derived above, Alpert reported experiments with wood cribs [4] and fire spread on vertical surfaces of both charring and noncharring fuels [5]. His results are encouraging. The most serious problems appear to
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stem from scaling deficiencies associated with thermal radiation rather than PSGR or PSFG modeling. We note three possible pitfalls: (i) Some enclosure fires exhibit recirculation of products into the “atmosphere” feeding the firec or buildup of a smoke layer which could alter fire dynamics. Then qs distribution would depend not only on the distributions of m f , T f and Ts but on that of the products fraction as well, which violates Eq. (5). Accordingly, this conduction/fuel gasification scheme can be used only in geometries for which the product stream escapes directly, e.g., no ceiling, or for cases where the influence of accumulated products on flame dynamics and energy feedback is deemed unimportant. (ii) Growth of an initially small fire is sensitive to the heating pattern at the time of ignition. For example, a vertical spread experiment ignited by heating of a strip at its base depends on the width of the strip, the heat flux and the exposure time. All of these must conform to the scaling rules. Obtaining a high ignition heat flux for the model in accordance with the 1/L rule can present difficulty. (iii) For a complex prototype structure, especially with composite materials, obtaining a faithfully scaled model may not be practicable. The prototype material may not even be available. If the phenomena of interest are deemed to entail only locally 1-D conduction, some relief may be obtained by adjustment of ks and L e . There are incentives to identify thermally thick prototype components wherever justified to develop criteria for convenient and inexpensive substitute materials and structures. It may be necessary to concede a degree of imperfect scaling and to develop correcting rules via parametric testing and computer simulations.
Water Spray Modeling Fire suppression or control by the thermal effect of water spray can be modeled consistently with pressure scaling. Space here allows only a bare outline of our work in progress in this area. Assuming geometric similarity of nozzle locations, cone patterns, etc., and with spray application time scaled according to the 1/L 2 rule, there remain three primary degrees of freedom: water mass flux (equivalent to a cooling energy flux), droplet velocity and droplet diameter. The mass flux has to scale in accordance per the 1/L rule. Velocity and diameter are then chosen to scale the thermal (droplet evaporation and flame cooling) and momentum interactions between flames and spray.
Adjustment of Fire Energy Level Via Modification of Model Ambient Oxygen So far, the fuel gasification temperature T f g has been taken as the same for model and prototype with identical fuels. For a phase change, the evaporation temperature increases with P (Clapeyron equation). For chemical transformations, T f g is determined from a (presumed) severely temperature-dependent controlling kinetic rate
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(e.g., high activation energy). This rate implies a characteristic time which, as T is increased, decreases from >> tc (conduction time constant) to << tc . The two characteristic times balance at T f g . Since, by the 1/L 2 rule for time scale, tcm < tc by an order of magnitude of more, T f gm > T f g . This has the effect of increasing the effective mass transfer B-number for the model experiment. Although T f g -shifting with P is probably not a major scaling deficiency, it can be explored and probably compensated for by enriching model atmosphere oxygen to adjust the fire T -level. There is even more of an incentive for such adjustment to cope with thermal radiation mismatch as discussed later. Our judgment is that an enthalpy range (relative to standard air) from roughly 0.75 to 1.35 can be achieved in practice without violating the fast chemistry assumption at the low end or excessive equilibrium-dictated incomplete combustion at the high end. Varying model atmosphere oxygen is inconsistent with the collapse of the model and prototype PDE sets to identity. Transport property distortion contributes to a mismatch in Gr. Fire dynamics are altered as the general buoyancy level is shifted. We propose to compensate for the altered dynamics by introducing characteristic temperature differential ⌬T and buoyancy b = ⌬T /T∞ and replacing the (implied) characteristic acceleration g in this paper’s earlier development by b g. This brings the convection and buoyancy terms of the reduced model and prototype PDEs more into line. The transport property variation for the above-stated oxygen range should not distort Gr by more than a factor of 2. Consistent with the burning rate versus Gr data in Ref. [2] we doubt that heat transfer and dynamics of a turbulent fire are sensitive to such a small Gr variation. A difficulty with the acceleration scaling sketched above is that b is not operationally defined. We estimate a value between 2 and 3 for a typical fire in a standard atmosphere. It should be possible to infer variation of b with atmosphere oxygen fraction by measurements of gas velocities at homologous points, for which we expect V ∝ b1/2 .
Thermal Radiation Attention is directed to luminous fires which are formally scaled per the L 3 P 2 rule. We reiterate interest in the 3 to 10 m prototype L-range. Flame radiation depths may in some cases be much less than L (as in spreading flames) and in others comparable to L (pool fires). Factory Mutual Research has produced several detailed studies of fire radiation, primarily luminous, at standard pressure [6–9] and one [10] of pressure scaling of radiation-controlled fires on vertical PMMA walls. The L-range of these valuable studies is mostly on the low end of the present range of interest. Understanding of the interaction between radiation and fire structure for larger fires and their corresponding P-models remains poor. For ease of discussion the luminous flame gases are assumed approximately gray. In addition to the heat flux qr at boundaries (z-component of vector q r ) radiation enters the problem via the source/sink term ∇ · q r in the energy PDE. The q r field is derivable from established transport equations, e.g., Modest [11], which require
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as an input the field of appropriately spectral-averaged mass absorption coefficient here generically denoted a M (units: area/mass). (There is also a scattering coefficient field, scaling implications of which are logically similar to those of absorption and are here omitted.) Scaling of the full radiation field requires that q r scale between model and prototype as 1/L and ∇ · q r as 1/L 2 . This, in turn, requires that the model and prototype a M fields scale at homologous points as L 1/2 . In other words the optical depth along every line through the model must be the same as that along the homologous prototype line. An additional requirement is scaleup of the model blackbody intensity field by a factor L/L m . Complete fulfillment of the latter requirement is beyond our reach even with oxygen enhancement. There is also evidence from soot yield measurements [12] indicating that a M increases with P. A possible representation is a M ∝ P n where n is around 1.0. This means that the optical depth of a P-scaled model is generally higher than that of the prototype. Consider the role of radiation in the prototype and its P-model as L is increased from very small to very large values. Meeting the 1/L requirement on model qrm in the optically thin limit with no adjustment of T -field requires n = 1/3. With the exponent n as high as suggested above, prototype qr would be overpredicted on the basis of an optically thin model. As L is increased such that optical depth is of order unity, an “optically intermediate” range is encountered wherein the whole or most of the fire contributes to qr but qr no longer increases linearly with L. For optical depth above 4 or so the fire gases exhibit “optically thick”, diffusion-like behavior [11]. In the optically thick regime qr varies with P and L at most only slowly. Hence, in the optically thick regime qrm cannot follow the 1/L rule and qr is severely underpredicted. It follows that somewhere in the optically intermediate regime strict L 3 P 2 scaling will correctly predict qr as well as the convective component qr . Radiation does not conform to the L 3 P 2 rule for optically thick fires. In that regime radiation is surely important but to an extent not yet delineated. There is no doubt that heat transfer from large luminous fires to condensed-phase surfaces is predominately radiative. Whether qc is actually negligible depends on the type of fire. Fires with complex geometry and vertically distributed fuel (as opposed to, say, symmetrical pool fires) should exhibit relatively high qc /qr . Moreover, because of flow laminarization near a surface where qc /qr is measured, this ratio does not quantitatively indicate the relative importance of convective transport in the fire interior. Regarding heat flow (hence T -distribution) in the overall flame body, our conjecture is that, even for the maximum L targeted here for P-scaling, radiation must play a major if not dominant role. On the other hand, we lack grounds for generally ruling out convection as an important, or even comparable, contributor to interior heat flow.
Concluding Discussion Pressure-scaling doubtless offers benefits as a research topic. But this paper is motivated by the goal of P-scaling as a practical tool in a prototype size range where repetitive full scale testing is hard to justify. Also, geometrical complexity of fire setting and flow fields is of more interest than simpler settings amenable to CFD
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analysis although the latter might be used to “calibrate” P-scaling. The comparative cost of P-scaling versus full scale testing is poorly known especially if such additional steps as oxygen enrichment are added. Demonstration of the reliability and resolution of P-scaling for specific classes of fires and test information needs appears prerequisite to definitive cost analyses. Gasification (PSFG) modeling assumptions merit refinement and further critical testing. However, it would appear that, if these were the only issues, a strong case could already be made for moving ahead aggressively toward a practical P-scaling capability and practice. The holdup is “the radiation problem”. For test fires in which burning rate can be artificially controlled, scaling per the L 3 P 2 rule should give useful indications of flame geometry and enclosure flow patterns. Inference of prototype heat flux from model data should be possible with suitable correcting interpretive rules, particularly for radiation. The previously mentioned possibility of combined radiative/convective scaling for heat feedback-controlled fires in the optically intermediate regime deserves further investigation. Oxygen enrichment may extend the margins where such scaling can be successful. However, the fact that a M is known to vary with air oxygen level [13] may introduce complications. For heat feedback-controlled fires in the optically thick regime we are forced to the conclusion that the L 3 P 2 rule itself must be compromised. We propose to replace L 3 P 2 by L 3(1−c) P 2 preservation where 0 < c < 2/3. To the extent that fire geometry does not distort too badly with this relaxation of strict convection/diffusion scaling, Froude scaling of velocity (∝ L 1/2 ) should automatically be retained. The fuel mass flux m f then scales as L −(2−3c)/2 . For any allocation of the relative contributions of prototype radiation and convection heat transfer a value of c can be found to correctly scale the combined heat transfer. Of course, heat flux would not be scaled exactly at every point of interest. However, with general magnitudes matched, detailed correcting data for parametric P-scale testing could be obtained from occasional full scale tests. For large fires de Ris [14] has earlier proposed c = 2/3, that is, P 2 L preservation. For this choice, pressure-scaling becomes more a correction of Froude scaling than true scaling of turbulent convection/diffusion. To the extent that flow field similitude is obtained, mass fluxes m f and m fm are identical. If also the optical depth per unit mass a M ∝ P, that is, n = 1 exactly, then model and prototype optical depths are also equal so that radiative heat flux is matched for all optical depths. As c increases, with fixed P-capability, there is an increasing advantage in scaling ratio relative to L 3 P 2 scaling. A major research need is to evaluate the tradeoff between abandonment of detailed convection/diffusion scaling versus improved modeling of radiation heat transfer. Acknowledgments This work was supported in part by ONR/University of Washington Grant N00014-94-1-0497. Also, as a look at the Reference list will reveal, we are indebted to researchers at the Factory Mutual Research for their predominant role in carrying pressure scaling technology to its present point.
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References 1. J.G. Quintiere, Fire Safety Journal, 15:3 (1989). 2. J. de Ris, A.M. Kanury and M.C. Yuen, Fourteenth Symposium (International) on Combustion, The Combustion Institute, pp. 1033–1044 (1973). 3. C. Huggett, Fire and Materials, 4:61 (1980). 4. R.L. Alpert, Combustion Science and Technology, 15:XXX (1976). 5. R.L. Alpert, Pressure Modeling of Fire Growth on Char-Forming and Laminated Materials, Report FMRC J.I.0G0N3.BU/RC83-BT-11, Factory Mutual Research (1983). 6. L. Orloff, A.T. Modak, and R.L. Alpert, Sixteenth Symposium (International) on Combustion, The Combustion Institute, pp. 1345–1354 (1976). 7. J. de Ris, Seventeenth Symposium (International) on Combustion, The Combustion Institute, pp. 1003–1015 (1978). 8. L. Orloff and J. de Ris, Nineteenth Symposium (International) on Combustion, The Combustion Institute, pp. 885–895 (1982). 9. G.H. Markstein and J. de Ris, Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute, pp. 1747–1752 (1992). 10. R.L. Alpert, Sixteenth Symposium (International) on Combustion, The Combustion Institute, pp. 1489–1500 (1976). 11. M.F. Modest, Radiative Heat Transfer, McGraw-Hill (1993). 12. J.S. McArragher and K.J. Tan, Combustion Science and Technology, 5:257 (1972). 13. G. Sugiyame, L. Xie, and M. Kono, Trans. JSME(B), 89-0180:3532 (1989). 14. J. de Ris, Radiation Modeling of Large Scale Fires, Factory Mutual Research Internal Memo (1988).
Scale Effects on Flame Structure in Medium-Size Pool Fires Akihiko Ito, Tadashi Konishi and Kozo Saito
Abstract Experiments using a particle-track laser sheet technique (PTLS) combined with a high speed video camera were conducted to reveal the flame structure and flow vector diagram in medium-size pool fires. To improve our understanding of the scale effects on buoyancy controlled flame structure, we employed four different size liquid pool fires whose pan diameters are 10, 20, 30 and 50 cm. These results were compared with numerical analysis previously presented by other researchers. The flow visualization results at the vertical plane along a center axis are in good agreement with numerical results. However, air entrainment through the flame is estimated to be at most 30% larger than that of axis-symmetric smooth flame because of an increase in the reaction surface area and the existing rotational velocity component around the wrinkled flame. For a medium-size pool fire below 20 cmdiameter pan, the flame height and the puffing frequency are close to an assembled small-size pool fire in which 3 cm-diameter pans are lined around a circle. The flame structure below 20 cm-diameter seems to be composed of several flame cells. While the flame structure above 30 cm-diameter is quite different from the aggregate of small-size pool fires. For a 50 cm-diameter pool fire a wrinkled flame having a high frequent disturbance of 12–14 Hz occurs near the base flame zone and grows along the flame surface. A pool fire beyond 50 cm diameter pan becomes a large-scale pool fire having a turbulent flow structure. Keywords Pool fire · flame structure · scale effect · air entrainment · flow structure
Nomenclature d D
Pan thickness Diameter of fuel pan
A. Ito Department of Intelligent Machines and System Engineering, Hirosaki University, Hirosaki 036-8561, Japan e-mail:
[email protected]
K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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fp h Hf q r t z
Puffing frequency Pan depth Flame height Coordinate of circular direction Coordinate of radial direction Time Coordinate of vertical direction
Introduction The flame structure and the mechanism of air entrainment in pool fires are of current interest because of both fundamental curiosity and practical concerns related to flame size and shape, smoke production, radiant emission and fuel regression. These parameters are important in models for various types of fires. Experimental studies have been conducted to determine these parameters in laboratory-scale pool fires [1–13]. McCaffrey [1] proposed three separate zonal structures: a continuous flame zone as the base of the flame, which is followed by an intermittent flame zone and above it a plume zone. We divided McCaffrey’s continuous zone into three subzones: the quenching zone, the primary anchoring zone (PAZ) and the post-PAZ. According to our study for small-scale pool fires [12], convective air entrainment likely occurs at the PAZ in order to satisfy mass conservation because of the rapid acceleration of the buoyant gases in the flame interior. The structure of the PAZ in a medium-scale pool fire is not substantially different from a small-scale pool fire [13]. In the post-PAZ region for a small-scale pool fire where the flame is a pseudo laminar flame, air entrainment to the flame surface is mainly controlled by diffusion. While in a medium-scale pool fire, beyond a 10 cm-diameter pan, the flame is a wrinkled flame where the rotational velocity component exists due to several vortexes. In the intermittent flame region, the flame is pulsating because of unsteady buoyant-momentum interaction [6–9]. Air entrainment in this region occurs mainly by relatively large-scale buoyancy induced mixing as explained by Weckman et al. [6, 7], Cetegen [8, 9], and Zhou and Gore [10, 11]. Even though the flame is puffing in the intermittent region the flame shape is axially symmetric in small-scale pool fires. While in medium-scale pool fires, a large-scale circulation ring around the neck of the flame surface is broken into several vortex cells, whose flow structure becomes 3-dimensional. The flame structure and the mechanism of air entrainment is different with both fire-scale and flame zone structure. The numerical simulation for a medium-scale pool fire has been conducted by Mell et al. [14] and Ghoniem et al. [15]. The numerical simulation is useful to estimate the behavior of a large-scale pool fire. To develop the numerical model for a large-scale pool fire, a better understanding of the scale effects on the flame structure is required. We conducted flow visualization using a particle-track lasersheet technique (PTLS) combined with a high-speed video camera to reveal the flow structure in medium-scale pool fires.
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Experimental Apparatus and Procedure To investigate the scale effects on flame structure, pool fire tests were conducted with stainless steel pans of four different diameters (10, 20, 30 and 50cm) whose dimensions are listed in Table 1. In preliminary tests we found a pool fire was stable during 3 to 6 minutes after igniting the fuel, so each test was performed within 5 min after ignition. Kerosene was used for the test fuel. Its initial temperature was around 22 ◦ C. According to our previous study [13], a medium-scale pool fire has a wrinkled flame except at the PAZ region and the vortex ring is broken into several vortex cells around a wrinkled flame surface, which looks like an aggregate of small-scale pool fires. A ranged number of 6 to 48 3 cm-diameter pool fires arranged around a circle (see Fig. 4 (a) to (d)) were examined to compare with medium-scale pool fires. Table 1 Dimensions of four different diameter stainless steel made open-top pan Pan diameter: D (mm)
100
200
300
500
Pan depth: h (mm) Pan thickness: d (mm) Number of assembled pan 30 mm(D) × 18 mm(h) × 1.8 mm(d)
20 2 6
20 5 17
20 4 28
63 4 48
Flame Shape Visualization A high-speed video camera was used for flame shape visualization. Only a 50 cmdiameter pool fire was tested in outdoor conditions because of its flame height reaching to above 2 m. In each experiment 1500 frame pictures were recorded at intervals of 20 ms for 3 second. From this data we analyzed an instantaneous flame height, visible flame shape and puffing frequency.
Flow Visualization and Velocity Vector Measurements A schematic of the experimental apparatus for PTLS is shown in Fig. 1. Using 4 W Argon-ion laser beam and a cylindrical lens, we established a thin laser sheet with an approximately 35◦ open angle. We conducted flow visualization at the vertical plane along a center axis, and found that the flow profiles, i.e. the velocity vector, possess the r and z components (Fig. 2). Pool fires were seeded with commercially available talc particles (its mean size was determined to be around 5 m by SEM), which were generated by a seeding bed located 10 cm below the pan. The particle injection velocity was less than 0.04 m/s, yet a sufficient seeding rate and density was achieved. The trajectories of these particles were recorded by a high-speed video camera with 500 flames/s through a band pass filter of 488 nm ± 5% and a UV image intensifier which was connected to a video system and a TV monitor for the real time observation of both flow field and visible flame shape.
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Laser sheet (PTLS)
Gate image intensifier
High speed video camera
Flame Power supply z Laser sheet (PTLS, LST)
r
Monitor
Filter
α = 0 deg.(Vertical plane) 45 deg. (Horizontal plane)
Recorder Talc particle
Computer
Pan Seeding bed Fuel Air Cylindrical lens
Argon ion laser Water Power supply
Fig. 1 Schematic of flow visualization apparatus
Results and Discussion For a 10 cm-diameter pool fire, the flow-vector diagrams of the r and z components at intervals of 20 ms are shown in Fig. 2. Air entrainment through the visible flame sheet occurs in the base flame at the PAZ. Below a 20 cm-diameter pool the fire flow in the base flame is similar to that of a small-scale pool fire [13]. In the postPAZ region, air stream flows along the visible flame sheet, then it is apart from the flame sheet and grows up into a relatively large-scale circulation about 5 cm downward from the brim. This circulation leads to a “mushroom shaped flame”. Only one mushroom shaped flame appears in a small scale pool fire, while beyond a 10 cm-diameter pool fire a couple of mushroom shaped flames are generated along the downward flame. The flow-vector diagram was compared with the numerical analysis previously presented by Ghoniem et al. [15] shown in Fig. 3. Despite assuming the axially symmetric in the numerical model, the computational result is qualitatively consistent with the measured flow vector diagram. However, the flame except at the PAZ region is a wrinkled flame. Increasing the reaction surface area due to wrinkled flame, we measured flame contour for each flame region by a laser sheet tomography [13]. As a result the reaction surface area of a wrinkled flame was estimated to be at most 20–30% larger than that of a co-axis smooth flame. We conducted flow visualization for r and θ plane (horizontal plane) using PTLS with a relatively thick laser sheet. The typical flow diagram for a 10 cm-diameter pool fire at horizontal plane of 3 cm
z (cm)
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Center axis
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103 Center axis
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100 ms 80 ms 60 ms
80 ms
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Fig. 2 Visible flame sheet at interval of 20 ms and flow vector diagrams at vertical plane for a 10 cm-diameter kerosene pool fire
above fuel surface is shown in Fig. 4. Air stream is parallel to visible flame sheet just above the PAZ region, and then a toroidal vortex appears downward. This vortex separates into several small vortexes, which are consistent with the number of wrinkles around the flame sheet. Flow visualization reveals that a small vortex has a radial velocity component. From the flow visualization results, air entrainment through the flame was attributed to be larger than that of the numerical model for
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10
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z (cm)
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5
1m/s 0
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Fig. 3 Comparison between a measured flow vector diagram and flame sheet (a) and a calculated one (b)
1
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(a) PTLS photograph (α = 45deg.)
0 1 Width direction position
1 (cm)
(b) Flow vector diagram at horizontal plane (α = 90deg.)
Fig. 4 PTLS photograph (a) and flow vector diagram (b) for 10 cm-diameter pool fire at z = 3 cm
the following reasons: (1) increasing flame surface area due to wrinkled flame, and (2) the existing rotational velocity component around the wrinkled flame.
Flame Structure Flame structure for a medium-scale pool fire seems to be composed of several flame cells. We conducted fire tests of assembled small-scale pool fires in which
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3 cm-diameter pans were lined around a circle shown in Fig. 5(a)–(d). A pool fire made of six of the 3 cm-diameter pans (3 cm × 6) is equivalent to a 10 cm-diameter pool fire. Figure 5(a) shows the instantaneous flame height and its puffing frequency of the 3cm × 6 assembled small-scale pool fires compared with those of 10 cmdiameter pool fire. Both flame height and puffing frequency for the 3 cm × 6 assembled small-scale pool fires are in good agreement with those for a 10 cm-diameter pool fire. Also the number of wrinkles is 6 for a 10 cm-diameter pool fire, which is consistent with the number of 6 assembled small-scale pool fires. The instantaneous flame height and puffing frequency for the 3 cm × 17 assembled pool fires and for a 20 cm-diameter pool fire are shown in Fig. 5(b). The results are not substantially different. Below a 20 cm-diameter pool fire, the flame behavior is simulated with assembled small-scale pool fires. For a 30 cm-diameter pool fire, however, the instantaneous flame height is much higher than that for 3 cm × 28 assembled pool fires as shown in Fig. 5(c). Also the puffing frequency for the former is less than that for the latter. Flame behavior for a 50 cm-diameter pool fire shown in Fig. 5(d) is quite different from that for 3 cm × 48 assembled pool fires. Figure 6 shows the flame photograph near the base of a 50 cm-diameter pool fire. The wrinkled flame
Hf (cm)
fp =
Hf (cm)
fp =
fp =
fp =
t(s)
t(s)
(a)
(c) fp =
Hf (cm)
Hf (cm)
fp =
fp =
fp =
t(s)
t(s)
(b)
(d)
Fig. 5 Flame height and the puffing frequency. (a) 10 cm-diameter kerosene pool fire and 3 cm × 6 assembled small-scale pool fires. (b) 20 cm-diameter kerosene pool fire and 3 cm × 17 assembled small-scale pool fires. (c) 30 cm-diameter kerosene pool fire and 3 cm × 38 assembled small-scale pool fires. (d) 50 cm-diameter kerosene pool fire and 3 cm × 48 assembled small-scale pool fires
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Fig. 6 Photograph of the base flame for a 50 cm-diameter kerosene pool fire
has a high frequency disturbance of 12–14 Hz occurs near the base flame zone and grows down the flame surface. A pool fire beyond a 50 cm-diameter pan transits to a large-scale pool fire having a turbulent flow structure.
Summary and Conclusions In reference to the specific objective addressed in the introduction, the conclusions obtained from this study are summarized here: 1. The flow structure around the visible flame sheet for a 10 cm-diameter pool fire is qualitatively consistent with the computational fire plume model which is based on a rising isothermal axis-symmetric plume. However, air entrainment through the flame is estimated to be at most 30% larger than that of the axis-symmetric smooth flame because of the increasing reaction surface area and the existing rotational velocity component around the wrinkled flame. 2. In a medium-scale pool fire below a 20 cm-diameter pan, the flame height and the puffing frequency is close to assembled small-scale pool fires. The flame structure below a 20 cm-diameter pool fire seems to be composed of several flame cells. While beyond a 30 cm-diameter pan, the flame height is much higher than that for assembled small-scale pool fires, and the puffing frequency of the former is less than that of the latter. 3. Beyond a 50 cm-diameter pool fire, the base flame is a wrinkled flame with high frequency disturbance of 12–14 Hz. A pool fire beyond a 50 cm-diameter pan transits to a large-scale pool fire having a turbulent flow structure.
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References 1. McCaffrey, B.J., 1983, “Momentum implications for buoyant diffusion flames”, Combustion and Flame, Vol. 52, pp. 149–167. 2. Zukoski, E.E., Cetegen, B.M. and Kubota, T., 1984, “Visible structure of buoyant diffusion flames”, Twentieth Symposium (International) on Combustion, The Combustion Institute, p. 361. 3. Schonbucher, A., Goeck, D., Kettler, A., Krattenmacher, D. and Schiess, N., 1986, “Static and dynamic radiance structure in pool fire”, Twenty-First Symposium (International) on Combustion, The Combustion Institute, pp. 93–100. 4. Delichatsios, M.A., 1987, “Air entrainment into buoyant jet flame and pool fires”, Combustion and Flame, Vol. 70, pp. 33–46. 5. Bouhafid, A., Vantelon, J.P., Joulain, P. and Fernandez-Pello, A.C., 1988, “On the flame structure at the base of a pool fire”, Twenty-Second Symposium (International) on Combustion, The Combustion Institute, pp. 1291–1298. 6. Weckman, E.J. and Sobiesiak, A., 1988, “The oscillatory behavior of medium-scale pool fires”, Twenty-Second Symposium (International) on Combustion, The Combustion Institute, pp. 1299–1310. 7. Weckman, E.J. and Strong, A.B., 1993, “Experimental investigation of the turbulence structure of medium-scale pool fires”, Combustion and Flame, Vol. 105, pp. 245–266. 8. Cetegen, B. and Ahmed, T.A., 1993, “Experiments on the periodic instability of buoyant plumes and pool fires”, Combustion and Flame, Vol. 93, pp. 157–184. 9. Cetegen, B., 1994, “Phase-resolved velocity field measurements in pulsating buoyant plumes of helium-air mixtures”, The Annual NIST Fire Research Conference, Gaithersburg, MD. 10. Zhou, X.C. and Gore, J.P., 1995, “Air entrainment flow field induced by a pool fire”, Combustion and Flame, Vol. 100, pp. 50–60. 11. Zhou, X.C., Gore, J.P. and Baum, H.R., 1996, “Measurements and prediction of air entrainment rates of pool fire”, Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, pp. 1453–1459. 12. Venkatesh, S., Ito, A., Saito, K. and Wichman, I.S., 1996, “Flame base structure of smallscale pool fires”, Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, pp. 1437–1443. 13. Ito, A., Nishi, Y., Shimasaki, S. and Saito, K., 1997, “Flame structure and air entrainment flow in small-scale and medium-scale pool fires”, Second International Symposium on Scale Modeling, Lexington, KY, pp. 133–145. 14. Mell, W.E., McGratan, K.B. and Baum, H.R., 1996, “Numerical simulation of combustion in pool fire”, Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, pp. 1523–1530. 15. Ghoniem, A.F., Lakkis, I. and Soteriou, M., 1996, “Numerical simulation of the dynamic of large fire plumes and the phenomenon of puffing”, Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, pp. 1531–1539.
Scale Model Reconstruction of Fire in an Atrium James G. Quintiere and Michael E. Dillon
Abstract Scaling principles are derived and explained for the simulation of smoke movement in building fires. The scaling is primarily based on representing transient inviscid flows characteristic of large Reynolds number. This form of scaling is sometimes called Froude number scaling since the momentum and buoyancy effects are modeled. A technique is used to compensate for the neglect of Reynolds number effects at solid boundaries. The scaling technique was applied to clarify the performance of a smoke control system which operated in an actual fire incident in a department store atrium. The scale model results confirmed a design flaw in the smoke control system. The high velocity inlet air was shown to be responsible for mixing and destratifying the hot smoke in the atrium and dispersing it throughout the department store. It is believed this the first time a scale model in fire was used as evidence in civil litigation case. Keywords Fire · scale modeling · smoke control system
Nomenclature c D g k L p Q t T v V˙
Specific heat Diameter Gravitational force per unit mass Thermal conductivity Length Pressure Energy release rate Time Temperature Velocity Volumetric flow rate
J.G. Quintiere Department of Fire Protection Engineering, University of Maryland, College Park, MD e-mail:
[email protected] K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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x,y,z α ρ ν
J.G. Quintiere, M.E. Dillon
Position Thermal diffusivity, k/c Density Kinematic viscosity
Subscript fan F m o w
Fan Full-scale Small-scale model Initial or reference Solid wall boundary
Superscript (˙ ) (∧ )
Per unit time Dimensionless
Introduction Many aspects of fire phenomena can be scaled using geometrically similar models. In general all of the variables cannot be completely scaled since too many dimensionless groups appear. However, usually the most relevant significant dimensionless groups can be preserved in a scale model study. This is referred to as partial scaling. A review of scaling techniques successfully used in fire problems has been described by Quintiere [1]. In particular, smoke flow scaling studies have been performed by Heskestad [2] and Quintiere et al. [3]. These two studies used reduced scale fires in a geometrically scaled enclosure representing building components. An analog technique using a water and salt-water system to simulate the buoyancy difference caused by hot smoke and cold air has been successfully used to describe fire induced flows in series of rooms [4]. A11 of these studies are based on a scaling principle which maintains a balance between the buoyancy and convective “forces”, while ignoring viscous and heat conduction effects. Based on the success of these studies, a scale modeling approach was used to study the motion of smoke in an actual atrium due to a fire. In this actual fire, a smoke control system was activated which extracted smoke from the roof of the atrium. However, in this incident an issue arose concerning the operation of the smoke control system and on the distribution of smoke throughout the building housing the atrium. The issue concerned whether the smoke control system was responsible for the improper dispersal of smoke. Since this problem was very similar to the dynamic features of the smoke movement in buildings previously studied [2–4],
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similar scaling techniques were used in developing a scale model study. These scale model results would ultimately be used in the litigation of the smoke control design issue. Because the scale model was used in litigation, there are not extensive results to demonstrate its complete characteristics. However, the video results were especially graphic in resolving the issue. A description of this fire will be described along with the atrium geometry and design features of the smoke control system. The theoretical basis of the scaling relationships will be developed. Some results of the scale model will be presented.
Description of the Fire Shortly before 6:45 am on December 17, 1988, a fire occurred in the atrium of the Hart Albin department store in Billings, Montana. The building had sprinklers and a smoke control system. The fire occurred on a polystyrene and wood Santa Claus and sleigh display suspended in the atrium as shown in Fig. 1. The burning display fell to the basement and 1st floor landings as shown in the schematic of the atrium in Fig. 2. The sprinklers were not activated, but the smoke control system was automatically initiated. It consisted of two 38,000 cfm fans mounted at the roof of the atrium, and two supplies. The primary supply fan injected 25 F ambient air through a 2 ft. diameter vertical duct at 25,000 cfm from the basement level of the atrium. A secondary supply diffusely injected 5000 cfm at the 2nd floor level. Smoke accumulated throughout the store which extended from the atrium at the basement
Fig. 1 Origin of the fire occurred on the Santa and sleigh shown here as they were displayed
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Fig. 2 Schematic of the atrium showing the smoke control flows and the fire locations
through the 2nd floor levels. The fires resulting from the falling Santa and sleigh did not propagate and were confined to relatively small regions. The cause of the smoke dispersal throughout the store became an issue of contention. One contended cause was the malfunction of dampers which were to automatically shut down the HVAC system on activation of the smoke control fans. Another proposed cause was the high velocity basement injector and its’ potential to stir and destroy the stratified smoke in the atrium. This injector would have an initial velocity of 132 ft/s (40 m/s). This velocity is significant since velocities in flames associated with the atrium fires would be less than one tenth of the injector velocity. Since the entrainment of air flow into both the buoyant fire plumes and the cold injector jet would depend on these velocities, the resultant upward flow in the atrium could be very complex. This complexity is compounded since the injector flow would have negative buoyancy as it brought in cold air (25 F) compared to the indoor atrium temperature (65 F). A smoke control system in the atrium is intended to extract the smoke from a fire while maintaining a stably stratified hot layer at the top of the atrium. Apparently, the rational for this design with the high velocity inlet air was to increase the entrainment of smoke flow to the ceiling. However, its high momentum
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could cause the destratification of the hot layer and the mixing of smoke to the lower portions of the atrium. In order to investigate these flow dynamics a scale model was constructed of the atrium and a limited region of the store to dynamically simulate the fluid motion as a result of the fire and the smoke control system.
Theoretical Basis for Scaling The previous studies [1–4] form the justification of the scaling relationships that are developed in the following. The basic theory is sketched and illustrated, without a loss in generalization, for a one dimensional, fluid system. The variables are normalized by the following characteristic parameters: characteristic length, L, characteristic velocity, (gL)1/2 , characteristic time, (L/g)1/2 , initial density, ρo , initial temperature, To , and initial pressure, po . Accordingly, the conservation equations can be written in dimensionless form. The normalized dimensionless variables are designated by (∧ ). ⭸ρˆ ⭸(ρˆ vˆ ) + =0 ⭸tˆ ⭸ yˆ ⭸ˆv ⭸ pˆ v ⭸2 vˆ ⭸ˆv + vˆ = (1 − ρ) ˆ − + 1/2 3/2 2 Momentum : ρˆ ⭸tˆ ⭸ yˆ ⭸ yˆ g L ⭸ yˆ Mass :
(1)
(2)
The pressure is given in terms of the reduced pressure, p , which is the difference between the pressure in the fluid and a corresponding point at the same elevation for the fluid at rest. It can be argued that the last term on the right-hand-side can be ignored (and will be) since for air v/(g 1/2 L 3/2 ) ∼ 10−6 /L(m)3/2 . The significance of dropping this term is to ignore the viscous effects which are negligible in the bulk of the flow, but would be important near solid boundaries. A related term will show up in the energy equation and it will be explicitly ignored along with the pressure work and viscous dissipation terms which can be shown to be negligible for this application [1]. Energy : ρ
⭸T ⭸T +v ⭸t ⭸y
= π Q = Q ∗L
(3)
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The dimensionless energy release rate term is given as: Q ∗L =
˙ Q ρo c p To g 1/2 L 5/2
(4)
˙ is distributed over the space of the combustion zone. If the The energy release rate Q diameter D of the fire is scaled geometrically, the flame height will also be geometrically scaled since correlations for flame height L f have been found to follow [5]: Lf ∼ function(Q ∗D ) where Q ∗D = Q ∗L D
L D
5/2 (5)
A consideration of equation of state for this application yields: ρˆ Tˆ = 1. This is approximate since the molecular weight of the gases is approximately constant and not expected to depart great from that of air. Also for free burning and normal building fire applications (where leakage occurs), the overall pressure is approximately constant for the system. Up to now the above presentation would suggest that all of the dimensionless dependent variables representing velocity, temperature, density and pressure will depend on the dimensionless space and time coordinates and the parameter, Q . In the case of this scaling application, the boundary conditions due to heat transfer to the solid “wall” surfaces, and the fan flows must be included. To include these effects will lead to two additional groups. First the wall heat transfer is considered. Radiation effects will be ignored due to the anticipated low temperatures. Surface radiation should scale under geometric scaling and with temperatures invariant, but flame radiation is not scaled. Under these conditions, the gas phase and solid (w) phase heat transfer must be equal at the boundary and given as: −k
⭸T ⭸y
gas
⭸T = −k ⭸y w
(6)
In order to compensate for neglecting viscous effects, the convective heat transfer is represented in terms of a convective heat transfer coefficient, h, which depends on the viscous and gas phase conduction previously omitted. In general for turbulent flow on flat surfaces: hL ∼ k
vL υ
0.8 υ 1/3 α
(7)
Since the left-hand-side of Eq. (6) can be replaced by h(T − Tw ) from the definition of h, a dimensionless form of Eq. (6) is
Scale Model Reconstruction of Fire in an Atrium
⭸Tˆw − = ⭸ yˆ w
h Lw kw
115
(Tˆ − Tˆw )
(8)
where L w is a characteristic length for normalizing the space coordinate yw into the wall. For thermally thin walls, it represents the thickness; for thermally thick walls, it can be selected as kw / h. A wall might be represented as thermally thick for times less than (L w )2 /αw . For a 1/2 inch plasterboard wall this time limit is about 15 min. In this application, times much less than this are of interest. Therefore, the thick wall case will be considered. Under this specification, the coefficient on the right-hand side in Eq. (8) becomes unity and the wall conduction equation in dimensionless form is ⭸2 Tˆw ⭸Tˆw = πw 2 ⭸tˆ ⭸ yˆ w
(9)
πw = h 2 (L/g)/(kρc)w
(10)
where
From Eq. (7) it can be shown, alternatively: 0.9 πw = g 0.3 v 1.6 k 2 (kρc)−1 w L
(11)
It remains to consider the issue of fan supply and extraction flows at the boundaries. At these flow boundaries, the dimensionless temperature, density and velocity must be preserved in scaling. In terms of volumetric flow rates usually specified for such flows, the dimensionless volumetric flow rate can be expressed in terms of the normalizing characteristic length and velocity selected as πfan =
V˙ g 1/2 L 5/2
(12)
where V˙ is the volumetric flow rate. The general solution to the problem posed above for this fire induced flow with heat loss and fan boundary flows becomes of the form: ⎧ T ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ To ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ v ⎪ ⎪ ⎪ ⎪ √ ⎪ ⎨ gL ⎪ ⎬ x y z t = f , , ,√ , π Q , πw , π f an ⎪ p ⎪ ⎪ L L L L/g ⎪ ⎪ ⎪ ⎪ ⎪ ρo gL ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ T w ⎪ ⎪ ⎩ ⎭ To
(13)
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J.G. Quintiere, M.E. Dillon Table 1 Scaling expressions Parameter
Scaling expression
Gas temperature Surface temperature Velocity Pressure Geometric position Time Heat release rate Volumetric exhaust rate Wall thermal properties
Tm = TF Tw,m = T√ w,F vm = v F L m /L F pm = p F (L m /L F ) xm = x F√(L m /L F ) tm = t F L m /L F ˙ m (tm ) = Q ˙ F (t F )(L m /L F )5/2 Q V˙ fan,m (tm ) = V˙ fan,F (t F )(L m /L F )5/2 (kρc)w,m = (kρc)w,F (L m /L F )0.9
This result gives the scaling conditions. Under geometric scaling, time will be distorted as indicated along with the pressures and velocities. The temperatures will be preserved provided the ’s are maintained equal in the scale model. The scaling relationships between a scale model, ()m , and a full-scale building system ()F are presented in Table 1. This form of scaling is sometimes called Froude modeling since the Q can be characterized as the ratio convective velocity due to energy release to buoyant velocity. Excluding the explicit role of the Reynolds or Grashoff numbers, containing the viscous effects, presents the problem as a nearly inviscid transient flow problem. The jets created by inlet fan flows would also ignore Reynolds number scaling. Since jet entrainment depends more on the inlet velocity this neglect may not be significant. The only requirement in such “Froude model” scaling is to maintain a sufficiently high enough Reynolds number to insure that flow regimes that should be turbulent are turbulent. In practice for fire induced flows it has been found that a scaling reduction of 1/7 for fire driven flows in 8 ft rooms was sufficient for achieving good results for temperatures and velocities [6].
Scale Model Design A 1/7 geometric scale model of the atrium is shown in Fig. 3 with a portion of the wall removed to reveal the inside of the atrium. The scale model included extensive architectural detail for the atrium, but the remainder of the building was only partially represented in the model. The fire was estimated from information about the materials burned (the sleigh and Santa composed of wood and polystyrene) and the observations of the fire by custodial staff (which included burning times and flames lengths). The estimated fires on the basement level (Q1) and on 1st floor (Q2) landing are shown in Fig. 4. These fires were estimated to range over areas of 2–3 m, and 1–2 m, respectively for Q1 and Q2. From Table 1, since L m /L F = 1/7, ˙ m = 0.0077 Q ˙ F, Q V˙ m = 0.0077V˙ F , and tm = 0.38t F .
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Fig. 3 Scale model
Figure 5 shows the scaled energy release rates of the fires. The simulated fires were created by propane burners consisting of glass funnels filled with glass beads which were mounted flush with the floor as shown in Fig. 6. The diameters of the funnels were selected to match the estimated extent of the fires: 2 m for Q1 and 2 m for Q2. Geometric scaling requires that Dm = D F /7 for their diameters. Three 15 cm
Fig. 4 Estimated fire energy release rates
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Fig. 5 Scaled energy release rates
diameter funnels were used to represent Q1 and one 15 cm funnel was used for Q2. The volumetric fan flow rates were simulated according to the scaling relationship, and the inlet air temperature was cooled in the model to simulate the cold outdoor ambient but only about 45 ◦ F was attained instead of the actual 25 ◦ F. The model and full-scale temperature should be identical under these scaling relationships, and the flow should be similar. The flow field was visualized in the model by the introduction of artificial white smoke (TiO2 or Zn oxide) introduced near the fire. Suspended strips of light paper were hung in openings to indicate flow direction. A large glass window, simulated by poymethylmethacrylate, allowed for ease in visualizing the smoke and flow movement. A vertical track of flood lamps was used to enhance visualization. The construction materials used in the model approximated the preservation of πw .
Fig. 6 Top view in atrium model showing burners and inlet vent
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Discussion of Results The results demonstrated that the cold high velocity inlet jet significantly contributed to mixing the smoke in the atrium, and its distribution throughout the store. Figure 7 attempts to illustrate the smoke movement. A video more definitively demonstrated the dominant mixing effect of the cold inlet jet. This is not unexpected since the cold jet velocity is of the order of 10 times the velocity in the fire regions. The interaction of the cold negatively buoyant jet and the positive buoyancy of the fires would produce a very complex flow pattern in the atrium. Extensive measurements were not taken but vertical temperature data shown in Fig. 8 show an unusual cold region at the 4th floor while the basement level has high temperatures. This vertical may was near the atrium walls. The results of this study, in particular the video data, proved definitive in settling the dispute on the cause of the smoke movement in this fire. It was probably the first time a scale model was used to settle a fire litigation dispute. The smoke control system had been an approved national code design, but was subsequently discontinued partly as a result of this work. The 1982 Uniform Building Code [7] required that the atrium smoke control system be designed with a minimum of 50 percent make-up air introduced vertically at the base of the atrium. The high momentum of the vertical jet of make-up air was cited as causing problems in full-scale atrium tests as reported by Dillon in as early 1983 [8]. But it took this fire and the subsequent scaling study to bring the issue to resolution.
Fig. 7 Smoke movement in the scale model showing a smoke eddy moving down and to the right
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Fig. 8 Vertical temperature distribution
References 1. J.G. Quintiere, Fire Safety J., 15, 1989. 2. G. Heskestad, “Determination of Gas Venting Geometry and Capacity of Air Pollution Control System at Factory Mutual Research Center”, FMRC Ser. No. 20581, Fac. Mutual Res., Norwood, MA, November 1972. 3. J.G. Quintiere, B.J. McCaffrey, and T. Kashiwagi, Comb. Sci. Technol., 18, 1978. 4. K.D. Steckler, H.R. Baum, and J.G. Quintiere, 21st Symp. (Int.) on Combustion, The Combustion Inst., Pittsburgh, PA, 1986, pp. 143–149. 5. G. Heskestad, Fire Safety J., 5, 1983. 6. B.J. McCaffrey and J.G. Quintiere, “Buoyancy Driven Countercurrent Flows Generated by a Fire Source”, Turbulent Buoyant Convection, 1976 Inter. Seminar, Inter. Centre for Heat and Mass Transfer, Dubrovnik, Yugoslavia, Hemisphere Publishing Corp., 1976. 7. Uniform Building Code, Section 1715 (b), 1982 edition, International Conference of Building Officials, Whittier, CA, 1982. 8. M.E. Dillon, ASHRAE Transactions, 89, Part 2B, 1983, pp. 832–834.
Scale Modeling of Quasi-Steady Wood Crib Fires in Enclosures Paul A. Croce and Yibing Xin
Abstract A scale modeling hypothesis for quasi-steady enclosure fires has been experimentally evaluated. The scheme utilizes geometric similarity and freeburn behavior of the source fuel to scale the fires in enclosure from one scale size to another. Measurements of burning rate, gas and wall temperature rises, combustion product concentrations and radiation flux were obtained in full-, half- and quarterscale enclosures using wood cribs as the fuel. The good agreement of reduced data among the different size enclosures strongly supported the modeling hypothesis. Relatively large scatters were observed with gas concentrations and radiation flux. In general, the scatters for all the above measurements were within those observed in freeburn crib fires. The experimental results validated the scaling laws, which can be used to predict the distributions of temperatures and combustion products in enclosure fires. Keywords Scale modeling · wood crib fire · enclosure fire
Introduction The scale modeling of enclosure fires – predicting full-scale behavior from the results of reduced-scale enclosure tests, is important when the cost of full-scale tests is considered. In the past, different modeling schemes have been proposed such as Froude modeling [1–4], pressure modeling [5–8], and recently radiation modeling [9]; and numerous studies [10–16] have been conducted with various degrees of approximation, scope and success. These studies have been surveyed and evaluated in a number of review articles [17–19]. Because of the complexity of the problem, one usually has to focus on major effects and neglect those unimportant according to the fire scenario of interest, which forms the modeling hypothesis. The hypothesis has to be tested against experiments to examine its validity. Therefore, the present work is directed to test the scaling hypothesis of Heskestad [2] for a quasi-steady
P.A. Croce FM Global, 1151 Boston-Providence Turnpike, Norwood, MA 02062, USA
K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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source fire. The scaling laws, if successfully validated, will scale not only burning rates, but also the room environment produced by the fire including gas and wall temperatures, combustion products, and radiation fluxes at homologous locations.
Scaling Theory The scaling laws of enclosure fires were derived based on free burning of wood cribs. For the free burning of wood cribs, Gross [20] identified two distinct burning regimes for loosely-packed and tightly-packed cribs. B1ock [21] later developed a theory for turbulent burning inside tightly-packed cribs. Combining the experimental findings of Block [21] and the correlating concept of Gross [20], Heskestad [2] proposed that the ratio of enclosure burning rate to free burning rate R/Rr , temperature rise relative to ambient T − T0 , and species concentrations ci would be reproduced in all geometrically similar enclosures as follows: R/Rr = f P, G, Ah 1/2 /Rr T − T0 , ci = f P, G, Ah 1/2 /Rr , x¯ /H
(1) (2)
where P is the crib porosity factor defined in Ref. [2], G the collective geometric similarity parameter, A the vent area and h the vent height, x¯ /H is the normalized position using enclosure height. To reproduce R/Rr , T − T0 and ci from one scale to another, quantities P, G and Ah 1/2 /Rr need to be preserved, which requires Rr ∝ As b−1/2 ∝ H 5/2
(3)
Equation (3) and preserved P require: Av s 1/2 ∝ H 5/2
(4)
where Av is the vent area, As the exposed crib surface area, and s the surface-tosurface stick spacing. With G preserved, the crib height h c scales linearly with the enclosure height H hc ∝ H
(5)
and the wood length l also scales linearly with H l∝H
(6)
Equations (3)–(6) can be expressed in terms of the basic crib quantities such as the crib thickness b, the stick length l, the number of sticks per layer n and the number of layers N , which, in turn, can be expressed as powers of H (i.e., l ∝ H l , b ∝
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H b , etc.). Introducing these relationships into Eqs. (3)–(6), we obtain the scaling relationships approximately as b ∝ H 1/2 ,
l ∝ H 9/8 ,
N ∝ H 1/2 ,
n ∝ H 5/8
(7)
These relationships were used in designing the experiment. Appropriate materials were also selected to satisfy the requirements of boundary conditions as discussed in Ref. [2]. It is recognized that the current scaling scheme is only approximately valid when considering the radiation process for energy balance. However, the experimental results shown later indicate that the discrepancies introduced by the approximation of radiation are not significant in the present study.
Experiment Tests were performed in geometrically similar vented enclosures with height to length to width ratios of 1:1.5:1, at full, half and quarter scale (H = 2.44, 1.22 and 0.61 m) with correspondingly scaled cribs. Full width, horizontal openings centered on the end walls were used as vents, as shown in Fig. 1. The walls were selected to be 15.9 mm thick, fire-rated gypsum wallboard for the full-scale enclosure, 12.7 mm thick, cement-asbestos board for the intermediate-scale, and 9.5 mm thick, alumina/silica board for the small-scale. All of the cribs used in this study were made of clear Sugar pine without knots and are described in Table 1 together with the measured free-burning rates. The
Fig. 1 Diagram of experimental setup. x – gas thermocouple; • – wall thermocouple; ⌬ – gas sampling port; x – load cell; – radiometer
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functional correlation between freeburn rate Rr and porosity factor P suggested by Heskestad [2] is shown in Fig. 2. The variation of ±20 percent is consistent with previous correlations of this type [2, 20, 21]. The transition from tightly-packed to loosely-packed cribs occurs at a value of P = 0.3–0.5 mm; above these values, the crib becomes loosely-packed and the influence of P is much less significant. For the scaling of cribs to different enclosure sizes, i.e., by conserving values of P, G and Ah 1/2 /Rr , the hypothesis requires that Rr ∝ H 5/2 , b ∝ H 1/2 , l ∝ H and h c ∝ H . Accordingly, a standard crib (Type A in Table 1), with given values of Rr , h c and P, was selected for the large enclosure and corresponding (Type A) cribs scaled to the intermediate and small enclosures. Various other combinations of Rr , h c and P were then used in the tests of cribs Types B–E. When changing h c , both P and Rr could not be preserved easily. Consequently, a crib with reduced crib height for a given scale is accompanied by a reduced freeburn rate for the same scale. Note that the freeburn rate for a given crib type varies approximately by a factor of 32 between large and small scale. Other crib types (F–J) were used in small scale only to investigate burning behavior. Note that, although cribs A and D have different internal structures (b, l, n and N ) in the same scale, they have similar values of Rr , h c and P and should, therefore, yield similar results according to Eqs. (3) and (4). In this paper, the experimental results of wood crib A and D are mainly
Table 1 Wood crib characteristics Crib
A
B
C
D
E
15.9-191-5-6 95.3 0.82 2.42
15.9-191-3-12 191 1.70 3.13
12.7-191-4-15 191 0.90 4.38
15.9-191-7-6 95.3 0.23 2.48
22.2-381-7-9 200 0.81 13.9
22.2-381-4-18 400 1.77 16.7
19.1-381-6-20 381 0.74 29.0
Small enclosure b-l-n-N hc P Rr
15.9-191-4-12 191 0.83 3.95
Intermediate enclosure b-l-n-N hc P Rr
22.2-381-6-16 356 0.72 21.3
Large enclosure b-l-n-N hc P Rr
31.8-762-8-24 762 0.77 108.7
31.8-762-10-12 381 0.81 69.0
31.8-762-6-24 762 1.57 88.4
28.6-762-8-27 772 0.81 123.0
31.8-762-14-12 381 0.23 57.9
Crib
F
G
H
I
J
15.9-191-8-6 95.3 0.11 2.00
15.9-191-9-6 95.3 0.046 1.36
15.9-191-6-12 191 0.22 4.90
15.9-191-8-12 191 0.056 2.10
Small enclosure b-l-n-N hc P Rr
15.9-191-4-6 95.3 1.60 2.02
Note: The quantities b, l and P are given in mm; Rr is given in g/sec.
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Fig. 2 Reduced free burning rate versus crib porosity. Solid symbols denote cribs for large enclosure tests, half-filled for intermediate enclosure tests and open for small enclosure tests
presented to validate the modeling hypothesis because of their completeness at different scales. Measurements of other types of wood cribs can be found in Ref. [22]. Each enclosure was equipped with bare-bead thermocouples monitoring gas temperatures and inner-surface wall temperatures at the locations shown in Fig. 1. A gas sampling port was located near one of the gas temperature thermocouples, and the aspirated gas analyzed continuously for O2 , CO2 and CO. A radiometer was located outside the enclosure so as to view an entire end wall. A load cell was utilized to monitor continuously the weight loss of the crib from which burning rates were deduced. Cribs were dried at 93 ◦ C for 24 hours prior to an experiment and located centrally within the enclosure for each test. Since the hypothesis was developed for quasi-steady burning, a special method was utilized to ignite the entire exposed crib surface as rapidly as possible. Shortly before the test, a modified acetone pan fire was placed below the crib and lined with a piece of asbestos paper to minimize the acetone charge. At time zero, the square pan was lighted to ignite the exposed crib surface. The quasi-steady burn interval was taken as the period of burning during which the crib mass varied from 80% to 30% of its initial mass. All plotted data shown later were averaged over this interval.
Results and Discussions Burning Behavior One of the important requirements of any fire modeling scheme is that burning behavior be reproduced from one scale to another. Four types of burning behavior, generally related to the degree of ventilation, were observed in the three enclosure sizes (Table 2). In the first type (Type C), which is associated with higher ventilation values, the flames remain attached to the crib as in freeburn and burn quite vigorously. With the smaller cribs (h c /H = 0.16), the flames impinged upon the ceiling
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P.A. Croce, Y. Xin Table 2 Burning behavior
h/H (Crib A) Small Intermediate Large
1.0 C C C
0.5 C C C
0.2 C C,C,W C
0.1 W
0.05 W F F
0.03 X
0.02 X
h/H (Crib B) Small Intermediate Large
1.0 C C C
0.5 C C
0.2 C C
0.1 C,C,W
0.05 F C,C,W
0.03 X
0.02 X
h/H (Crib C) Small Intermediate Large
1.0 C C
0.5 C C C
0.2 C C
0.1 W F
0.05 X
0.03 X
0.02 X
h/H (Crib D) Small Intermediate Large
1.0 C C
0.5 C C
0.2 C C
0.1 W
0.05 X F
0.03 X
h/H (Crib E) Small Intermediate
1.0 C
0.5 C C
0.2 C
0.1 F
0.05 F
0.03 X
h/H (Crib F) Small
1.0 C
0.5 C
0.2 C
0.1 C
0.05 X
0.03 X
(Crib h/H) Small
H, 0.5 C
I, 0.5 C
J, 0.5 C
W
F
Legend: C – Flame attached to crib, as in freeburn; W – Flame detached from crib and burning at windows of the enclosure; F – Flame detached from crib and wandering around floor of the enclosure; X – Combustion not sustained.
and splashed approximately halfway across the ceiling to the vents. With the larger cribs (h c /H = 0.31), the flames essentially filled the upper portion of the enclosure and overflowed slightly out the vents. The second type of burning behavior (Type W) is characterized by the flames burning languidly on the crib during the early stages of the fire, detaching from the crib and wandering over the floor of the enclosure, and finally moving to the vent opening where they burned vigorously. In a few cases, the flames moved back and forth between the window and the floor, but most of the time they were well established at the window. In the third type of burning behavior (Type F), languidly-burning flames detached from the crib and wandered around the floor of the enclosure for the duration of the quasi-steady interval. In a few cases, the flames reattached to the crib for short periods, and in a few other cases, the flames burned at the vents for brief periods. But in all cases, the flames wandered over the floor for most or all the quasi-steady interval. Both the second and third types of behavior produced oscillatory results with respect to time during the burning period, similar to the observations of Tewarson [23]; this oscillatory behavior was more pronounced with the third type of behavior (Type F) than with the second (Type W). In the fourth type of burning behavior (Type X), combustion
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of the crib following ignition was not sustained, so that a major portion of the crib mass was not consumed. Table 2 presents the burning behavior for all test conditions. In this table, a single letter entry means that all tests at those conditions exhibited the same behavior, as indicated by the letter. Multiple entries signify that there were differences in behavior between tests at those conditions and the behavior of each test is listed separately. For example, for the three tests performed in the small enclosure with type B cribs and h/H = 0.1, flames were attached to the cribs in two instances and burned at the window in one. In general, the observed behavior agrees well with that reported by Heskestad [2]. It can be seen that for all enclosure sizes and crib-types, the behavior appears to go from Type C to Type X as ventilation decreases. Also, the type of behavior is reproduced well for higher ventilation values, while at lower values of h/H , there are some differences, i.e., Crib A with h/H = 0.05 and 0.02, and cribs B, C and D with h/H = 0.05. It is difficult to determine whether these differences are real and anomalous, rather than due to experimental artifact, for the following reasons:
1. When h/H < 0.2, the type of behavior that occurs appears to be quite sensitive to ventilation conditions until combustion is no longer sustained. The observed differences indicate that, for a given vent ratio, the fire may have been better ventilated as the enclosure size increased. This is seen in the case of crib A with h/H = 0.05 and 0.02, and crib B with h/H = 0.05, for example. In support of this conjecture, the following observations are presented: the material used for the small enclosure was known to be porous, and hence the small enclosure was carefully wrapped with aluminum foil on the outer surface. This enclosure was very tightly sealed except for the vents. The material for the intermediate enclosure, though virtually non-porous initially, cracked noticeably when exposed to fires. The cracks worsened with additional tests, but, since this material was available on special order only, replacement of badly cracked panels was necessarily limited. As a result, for some intermediate tests, the wall porosity may have been a contributing factor. The sequence of testing in the intermediate enclosure was such that tests with h/H = 0.05 were performed early in the series while those with h/H = 0.2 were performed late in the series. In the large enclosure, for which gypsum wallboard was used, it was difficult to avoid warping of the end panels in most tests. Although the tests with high values of h/H were probably not greatly affected, those tests with low values of h/H (especially those with h/H = 0.05 and 0.02) may have experienced ventilation conditions slightly different from nominal values. 2. The ratio of wall thickness to vent height was not conserved for all enclosures. Although this should not be important for tests with large openings, it could be significant for low ventilation tests by affecting the distribution of influx and efflux flows.
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Effects of Ventilation Figure 3 shows the ratio of enclosure to free burning rate for crib types A and D (loosely packed) as a function of the reduced ventilation parameter, Ah 1/2 /Rr , for various values of h/H . Specific values of h/H are indicated on this and subsequent figures because variation of this ratio affects the relative position parameter G and the reduced ventilation parameter Ah 1/2 /Rr . Good agreement exists among the enclosures of different size and between the two crib types as anticipated. Below a value of Ah 1/2 /Rr = 10 m5/2 s/kg, the burning is controlled by ventilation flow through the enclosure opening, consistent with the observation of others [12, 24]. Above this value, the burning-rate ratio exceeds the value of unity – a somewhat unexpected result. The exact reason of this phenomenon is not known. However, a possible reason is the burning behavior changes significantly with ventilation parameter, or h/H increasing (see Table 2). As a consequence, the radiation heat exchange between wall surface and the crib changes, which affects the burning rate. Figure 4 shows the increase of gas temperatures measured near the ceiling and near the floor as a function of the reduced ventilation parameter. The symbols with tails denote measurements near the floor and those without tails near the ceiling. The data points, average values respectively of the two upper and two lower thermocouples monitoring gas temperatures, are indications of the temperature of the gases leaving the enclosure (near-ceiling values) and of the gases feeding the fire (near-floor values). It can be seen that for h/H > 0.02, the measured gas temperatures at different scales at the two locations correlate at given reduced ventilation parameter Ah 1/2 /Rr , which is consistent with the modeling hypothesis described in Eq. (2). For h/H = 0.02, only measurements at the full scale of Crib A are available. It should be noted that, in the full-scale enclosure, some tests were made without replacing all of the wallboard material, e.g., those tests with h/H = 0.1 and 0.05. For the other full-scale tests, the paper lining was not scaled to the smaller enclosures. As a consequence, its burning may affect the full-scale results.
Fig. 3 Burning rate ratio versus reduced ventilation parameter for cribs A and D
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Fig. 4 Near-ceiling and near-floor gas temperatures versus reduced ventilation parameter for cribs A and D
The time-averaged wall temperature rise is shown as a function of reduced ventilation parameter in Fig. 5. The data points representing average values of the two thermocouples monitoring inner surface temperatures correlate similarly to the gas temperatures in Fig. 4. The relatively low full-scale values for h/H = 0.1–1.0 are caused by the presence of moisture, either hydrated or absorbed, in the gypsum wallboard. In those tests with virgin wallboard, significant quantities of smoke and steam appeared to outgas from the walls, both before and somewhat after the paper burned away. The volumetric concentrations of O2 , CO2 (without tails) and CO (with tails) are shown in Figs. 6 and 7. As with other data, these values have been averaged over the quasi-steady burn interval. However, they have also been corrected prior to averaging for errors due to the slow response of the gas analyzing system [25]. As shown in Fig. 1, the gas sampling position is near the ceiling, therefore, O2
Fig. 5 Wall temperature increase versus reduced ventilation parameter for cribs A and D
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Fig. 6 O2 Concentration versus reduced ventilation parameter for cribs A and D
Fig. 7 CO2 and CO versus reduced ventilation parameter for cribs A and D
concentrations increase while CO2 and CO concentrations decrease with increasing reduced ventilation parameter. The scatter of these data at different scales for a given reduced ventilation parameter Ah 1/2 /Rr is greater than those of burning rate and temperatures shown in Figs. 3–5. As discussed at the end of scaling theory, the total radiant heat flow through the vents should scale as H 5/2 ∝ Rr for overall consistency with the enclosure has been scaled by the energy balance. Accordingly, the measured heat flux q˙ Rm 2 ratio Rr /H and is shown in Fig. 8 plotted against the reduced ventilation parameter. The scatter in these data is greater than with other data, but no systematic variation is apparent. Based on the analysis of radiation effects in Ref. [22], the scaling of radiation from wall surface is only approximately consistent with other quantities. Therefore, the different contributions from radiation sources with respect
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Fig. 8 Scaled radiation versus reduced ventilation parameter for cribs A and D
to the particular radiometer location and view field may cause the relatively large scatter in Fig. 8. For example, flame radiation was the primary contributor to the measured radiative heat flux for high ventilation conditions, while surface radiation from end walls might be dominant for the low ventilation conditions.
Summary and Conclusions Crib fires in enclosures were studied experimentally to evaluate a set of scale modeling hypothesis. The results show that burning rate, gas and wall temperatures, gas species concentrations and radiation flux seen from an exterior location of wood crib fires in enclosure are correlated well under the previously proposed modeling hypothesis. Therefore, the modeling hypothesis is valid for scaling enclosure crib fires. Correlations of reproduced quantities are generally within ±20%, which is consistent to the extent of reduced data in free burning fires. The gas concentrations and radiation flux exhibit larger scatter for low ventilation conditions. Enhanced burning rate was observed for larger ventilation parameters compared to free burning rate. A possible reason is the increased radiation from surface wall, which scales only approximately with other quantities. A limitation of the modeling method is that the freeburn behavior of the primary fuel element must be known before any model enclosure work may proceed. In addition, future work is needed to improve the scaling of radiation heat transfer while maintaining the simplicity of scaling modeling at atmospheric pressure.
References 1. 2. 3. 4.
Thomas, P.H., Proc. Combust. Inst. 9: 844–858 (1962). Heskestad, G., Proc. Combust. Inst. 14: 1021–1030 (1972). Heskestad, G., J. Fire Flammability 6: 253–273 (1975). de Ris, J., Appl. Polymer Symp. 22: 185–193 (1973).
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5. 6. 7. 8.
de Ris, J., Kanury, A.M., and Yuen, M.C., Proc. Combust. Inst. 14: 1033–1044 (1972). Alpert, R.L., Combust. Sci. Tech. 15: 11–20 (1977). Alpert, R.L., Proc. Combust. Inst. 16: 1489–1500 (1976). Lockwood, R.W. and Corlett, R.C., Proceedings of the ASME-JSME Thermal Engineering Joint Conference, Vol. 1, pp. 421–426, ASME, New York, 1987. de Ris, J., Wu, P., and Heskestad, H., Proc. Combust. Inst. 28: 2751–2759 (2000). Kawagoe, K., “Fire Behavior in Rooms,” Report No. 27, Build. Res. Inst. of Japan, 1958. Thomas, P.H., Research 13: 69 (1960). Gross, D. and Robertson, A.F., Proc. Combust. Inst. 10: 931–942 (1965). Waterman, T.C., Fire Tech. 5: 52–58 (1969). Thomas, P.H. and Nilsson, L., “Fully Developed Compartment Fires: New Correlations of Burning Rates,” Fire Research Note No. 979, FRS, Boreham Wood, UK, 1973. Parker, W.J. and Lee, B.T., “A Small-Scale Enclosure for Characterizing the Fire Buildup Potential of a Room,” Report No. NBSIR 75-710, National Bureau of Standards, 1975. Quintiere, J., McCaffrey, B.J. and Kashiwagi, T., Combust. Sci. Tech. 18: 1–19 (1978). Harmathy, T.Z., Fire Tech. 8: 196–217, 326–351 (1972). Friedman, R., “Behavior of Fires in Compartments,” International Symposium on Fire Safety of Combustible Materials, Edinburgh, Scotland, pp. 100–113, 1975. Quintiere, J., “The Growth of Fire in Building Compartments,” ASTM-NBS Symposium on Fire Standards and Safety, National Bureau of Standards, Gaithersburg, MD, 1976. Gross, D., J. Res. National Bureau of Standards, 66C: 99 (1962). Block, J.A., Proc. Combust. Inst. 13: 97 (1971). Croce, P.A., “Modeling of Vented Enclosure Fires Part I: Quasi-Steady Wood-Crib Source fires,” Technical Report, FMRC J.I.7A0R5.GU., 1978. Tewarson, A., Combust. Flame 19: 101–111 (1972). Heselden, A.J.M., Thomas, P.R. and Law, N., Fire Tech. 6: 123–125 (1970). Croce, P.A., Combust. Sci. Tech. 14: 221–228 (1976).
9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.
Scale Modeling of Puffing Frequencies in Pool Fires Related with Froude Number Hiroyuki Sato, Kenji Amagai and Masataka Arai
Abstract Quantitative investigation of the gravity effect was performed for small-sized acetone and kerosene pool fires. Several investigations on the behavior of pool fires have been conducted to understand the physical model. In their primary papers, it was mentioned that the buoyancy effect on the motion of pool fires was significant to understand the characteristics such as flame height, oscillatory frequency, and so on. Under these circumstances, in this investigation, a centrifuge was used to create elevated gravity fields and to examine the gravity effect. Small-scale pool fires were observed under various high gravity fields. Regions of stable flame, puffing flame and irregular oscillatory flame were categorized to make a map related with the gravity level and pool diameter. Flame height decreased and oscillatory frequency increased with an increase in the gravity level. Behavior of the flame height was agreed quantitatively with the scaling prediction presented by Orloff and Heskestad. Puffing phenomena observed under various gravity fields were summarized with the relationship between Strouhal and Froude number. As the result, an empirical equation expressed by St = 0.517Fr −0.502 could be obtained. From this equation, puffing frequency could be estimated for a flame of various pool diameters varying from 0.01 to 50 m. Keywords Fire · diffusion combustion · liquid fuel · flame stability · gravity · scale modeling · froude number · strouhal number
Nomenclature D f Fr G
Pool diameter Oscillatory frequency Froude number Non-dimensional gravity level
H. Sato Department of mechanical design engineering, Shonan Institute of Technology 1-1-25 Tsujido-Nishikaigan, Fujisawa, Kanagawa, 251-8511 Japan e-mail:
[email protected]
K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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134
g ⌬L f mf Qf Re St Vf Vl ρf ρfb τ τc
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Gravitational acceleration in normal gravity field Fluctuation length of flame height Mass flow rate of liquid fuel Volumetric flow rate of liquid fuel (burning rate) Reynolds number Strouhal number Evaporation velocity of liquid fuel Regression rate of liquid fuel Density of liquid fuel at room temperature Density of liquid fuel at boiling point Time-scale of large vortex motion defined by video image analysis Time-scale of large vortex motion defined by auto-correlation function
Introduction Laboratory scale investigations on the fire disaster have been carried out for the purpose of understanding the fire hazard, such as oil storage, oil spill and so on. In these researches, objective is in generally small- or middle-sized pool fires characterized their scale with less than about 50 cm in pool diameter. Therefore, it is important to consider the scale effect on the flame behavior, and scaling analysis using nondimensional parameters is a very significant perspective. Under these circumstances, analyses of flame height and oscillatory frequency caused by buoyancy-driven flow have been conducted [1–5]. On the scaling analysis of flame height behavior, several models are proposed. For instance, Orloff and Ris investigated the behavior of flame height with 0.38-m pool diameter, and discussed the effect of heat loss due to the radiation using a non-dimensional flame height parameter normalized by the pool diameter [1]. As for the analysis on oscillatory behavior, it has been reported that flame tip is oscillated spontaneously with a bigger pool diameter [2, 3]. For a non-dimensional analysis, Malasekera et al. carried out an experiment to clarify the relationship between pool diameter and oscillatory (puffing) frequency [2]. They reported that the frequency was proportional to the pool diameter to the power of 0.5. Schonbusher et al. [3] and Cetegen and Ahmed [4] have been reported to confirm that the relationship between oscillatory frequency and pool diameter is independent of the fuel. Furthermore, in another paper by Cetegen and Kasper [5], they investigated puffing phenomena using Richardson and Strouhal number for non-reacting helium plume characterized by the pool diameter ranging from 3.6 to 20 cm. They showed that tendency of the oscillation was distinguished by Richardson number. The authors have been conducted in quantitative analysis of buoyancy effect on the unsteady motion of the jet flame using a centrifuge [6–10]. Our approach is based on the concept that an experiment of super gravity filed is available to conduct a parametric study of understanding the buoyancy effect. In this study, the quantitative analysis of pool fires affected by buoyant flow is conducted because there are few reports to mention the buoyancy effect on the behavior of pool fires. Particularly, unsteady behaviors represented by puffing phenomena and turbulence
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were investigated experimentally. The Strouhal and Froude number relationship which could be applicable for various flames was proposed, and buoyancy effect on a turbulent flame was mentioned.
Experimental Appratus and Method Artificial gravity field was formed a rotating beam of the centrifuge to investigate the buoyancy effect on the unsteady motions of flames. In this study, gravitational level was elevated ranging from 1-G to 10-G by controlling the rotating speed of the centrifuge. The detailed description of the centrifuge was given in our previous papers [6–8]. A schematic view of the experimental apparatus including measurement system is shown in Fig. 1. Combustion test equipment consists of the pool vessel and the extinction system. The vessel was made from duralumin and the size is 10-mm in depth. Several configurations of diameter (D =10, 15, 20 and 30-mm) were equipped with considering the scale of flames. Acetone and kerosene were used in consideration of fuel volatility. In generally, experiment of pool fire was carried out with an embedded vessel in the ground to simulate the behavior of fire spread. So a plate of 100-mm diameter was equipped at near the rim of the vessel. The plate was connected to the shaft with a small rotary motor as an extinction system. The extinction system was used to quantify the expended amount of fuel. The behavior of the flames in the gondola was observed by using a CCD camera and was recorded directly by a video tape recording system. Luminosity of the flame was picked up by a photo-sensor. This signal was analyzed by a frequency analyzer.
Fig. 1 Combustion equipment and frequency analysis system
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The optical device was installed in the position of about two third of a flame height, which corresponded to the average height of an oscillatory flame. To clarify the effect of buoyancy on turbulent flames, high Reynolds number flames were observed in the centrifuge. In that case, methane-propane mixture gas (C3 H8 :H2 = 64:36 mol%) was used with a nozzle of 0.4-mm diameter. In the frequency analysis, power spectrum and auto-correlation functions were analyzed.
Results and Discussion Flame Characteristic of Elevated Gravity Field Flame stability of pool fires was investigated in various gravity fields to make clear the buoyancy effect on a pool fire. Flame characteristics as a function of gravitational acceleration are indicated in Fig. 2. Figure 2(a) and (b) show a flame stability map summarized by pool diameter and gravitational level relationship. Result from Fig. 2(a) is for acetone flames and Fig. 2(b) is for kerosene flames. In these figures, flame characteristic was determined by video images, and oscillatory motions were also checked with the images and power spectrum data obtained by the frequency analysis. Since it was difficult to make a sharp distinction of the boundary area between the puffing and the irregular flames from just a image, the irregular flame was defined by broadband frequencies without any dominant oscillatory modes in power spectrum data. There were four main regions: laminar stable flame, puffing and irregular unsteady flames, and blow-off limit. A laminar flame belonged to the stable region. In the puffing area, transitional flame such as laminar to turbulence transition was observed, and such a flame had a very periodic oscillatory frequency. Even if the
(a)
(b)
Fig. 2 Combustion characteristics of pool fires at various gravity levels: (a) D-G map for acetone pool fire, (b) D-G map for kerosene pool fire
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stable flame was obtained at a normal gravity field, it changed into a puffing flame when the gravitational level was elevated. This change suggested that natural convection caused by buoyancy was a very important factor in causing flame puffing motion. The flame characterized by irregular showed non-periodic oscillation. Blow-off limit indicated the extinction of flames. Considering the effect of fuel property, distribution of the flame characteristics region was almost the same in the case of the same pool diameter. This means that buoyancy effect on the pool fire is independent to fuel property, because flame scale is almost the same size in the case of the same pool diameter; scale of the pool fire is dependent on its pool diameter. Figure 3 shows photographs of typical flames such as puffing, irregular and before blow-off. These flames were in the conditions of acetone fuel, 30-mm diameter of the vessel. Puffing flame as shown in Fig. 3(a) was obtained at normal gravity field (G =1), and its oscillatory frequency was about 10-Hz from a series of photograph. Figure 3(b) showed an irregular flame at G = 4. The flame surface was nonaxisymmetric structure, and showed the blue flame region at the base of flame. In the case of Fig. 3(c), flame condition was before blow-off at G = 5, and observed a local extinction near the vessel rim. After the local extinction papered, the flame went out immediately.
(a)
Fig. 3 Typical flames at various gravity levels: (a) Puffing flame at G = 1, (b) Irregular flame at G = 4, (c) Irregular flame near blow-off at G = 5
(b)
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Effect of Buoyancy on the Puffing Frequency In this section, we’d like to discuss the effect of buoyancy on the puffing frequency based on the result of Fig. 2. To clarify the characteristic of flame oscillation, frequency analysis by FFT analyzer was conducted. Figure 4 shows the quintessential example of the analysis for acetone pool fire. For the flame of 20-mm pool diameter, Fig. 4(a)–(c) were under the condition of G = 1, G = 2 and G1 = 6, respectively. Measurement points were indicated on the G-D map. Fluctuation of flame instability was detected by the photo sensor, and the signal from the sensor output were shown in the upper section of the figure. The power spectra P( f ) derived from the flame
Fig. 4 Time series data of sensor output and power spectrum for puffing flames
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fluctuations were presented in the lower section. From the result of Fig. 4(a), it was found that puffing flame at G = 1 has a very periodic frequency (about f = 9-Hz). In the case of high gravitational level as shown in Fig. 4(b) and (c), a frequency peak in the spectrum shifted to the high-frequency side. Furthermore, it was found that shape of the spectrum was extended into broadband. Also, it seems that the change of spectrum corresponds to a turbulent flame. In the range of puffing flame, dependence of the buoyancy to the oscillatory frequency was investigated quantitatively. Figure 5 shows the buoyancy effect of puffing frequencies. For both the flames of acetone and kerosene, the frequency increased with an increase in gravitational level. The fitted line was the same against the different conditions of the flame. The correlation of the oscillatory frequency with the gravitational level could be summarized by the following formula; f ∝ G 0.74
(1)
In this study, parameter of pool diameter was considered ranging from 10 to 30 m. In these conditions, the relationship represented by Eq. (1) was independent to the pool diameter and the properties of fuel. Malasekera et al. [2], Schonbusher et al. [3] and Cetegen and Ahmed [4] reported that the oscillatory frequency was proportional to the pool diameter to the power of 0.5; however, in this investigation significant impact of the pool diameter effect was not confirmed because the parameter of pool diameter varied within a narrow range (D = 10, 20, 30-mm). Furthermore, when we consider that thermal convection provides unsteady motions of the flame, buoyant flow caused by combustion-driven rapid density changes near the flame surface influences puffing motions. Thus, scale effect of buoyancy influenced the puffing frequency more than that of the pool diameter.
Fig. 5 Gravity effect on puffing frequencies
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To predict the puffing frequency for various scale of pool fires, Cetegen and Ahmed [4] showed the relationship between frequency and pool diameter described by f = 1.5D −0.5 . However, buoyancy effect on the oscillatory frequency was indicated as shown in the result of Fig. 5. It is important, therefore, to analyze the unsteady motion of pool fires by considering the buoyancy effect. Hamins et al. [11] summarized oscillatory phenomena of flames by using the relationship between Strouhal number St and Froude number Fr. To apply the St–Fr relationship to pool fires, evaporation rate of the fuel should be estimated. Figure 6 shows a schematic of the pool fire for modeling evaporation rate. The gas-phase velocity V f , which is evaporation velocity of liquid fuel, was estimated from regression rate of the liquid fuel. Mass of the liquid fuel burned per second m f was derived by the following equation; m f = ρf · Q f
(2)
where ρ f is density of the liquid fuel and Q f is burning rate of the fuel characterized by volumetric. When the temperature of evaporated fuel was supposed to the temperature at the boiling point, evaporation velocity of the liquid fuel V f could be estimated as following relation; V f = ρ f ρ f b · Q f π D 2 4 = ρ f ρ f b · Vl
(3)
When the value of mass flow rate was calculated by volumetric flow rate using Eq. (2), the evaporation velocity V f could be obtained from Eq. (3). From the estimated values of evaporation velocity, Strouhal and Froude number relationship (St–Fr relationship) was investigated as shown in Fig. 7. To discuss theeffect of buoyancy, the Froude number was defined by the equation of Fr = V f2 gG D. To estimate the evaporation velocity of liquid fuel, result of the regression rate of the liquid fuel Vl reported by Blinov and Khudyakov [12] were used as shown
Fig. 6 Schematic of evaporation model for pool fire
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Fig. 7 Scale modeling by St–Fr relationship for puffing frequencies of pool fires
in Table 1. The Strouhal number was defined by St = f D V f . In this study, we could plot the data that included the buoyancy effect (G = 1–7) for a small-sized pool fire (D = 10–30 mm). As shown in the figure, it was found that all the data had a linear relationship. The empirical equation obtained from the present data was described by the following formula; St = 0.517Fr −0.502
(4)
When the result by Cetegen and Ahmed [4] was reflected into St–Fr relationship, the empirical equation was described by St = 0.48Fr −0.5 . This result indicated the same with the present result by Eq. (4). Furthermore, numerical results of non-reacting flow reported by Mell et al. [13] and Ghoniem et al. [14] were also expressed by Eq. (4). As for the data of very large-sized pool fires given by Takahashi et al. [15], which were results of 30 and 50 m pool fire, the oscillatory frequencies were also described by the same formula. As a general rule, the empirical equation obtained in this study was more significant to estimate the unsteady behavior of pool fires. Furthermore, signification of the super gravity experiment by using a centrifuge was come into focus.
Characteristic of Turbulence in Elevated Gravity Field From the result of Fig. 7, it was indicated that gravitational acceleration gave an influence to the puffing frequencies. However, we don’t make reference the flame structure between the flame of super gravity field and that of a large pool diameter.
Brotz et al. [17]
Byram et al. [18]
Mell et al. [13]
Ghoniem et al. [14]
2
3
4
5
6
Fuel
Helium (simulation) Helium (simulation)
Ethanol
Diesel Methanol
Acetone
Kerosene
0.1
–
0.076–2.4
0.045–18
–
–
1.50E −05–1.67E− 05∗
1.58E05 −5.83E − 05∗
4.17E − 05∗
0.2
6.00E − 06∗
50 0.3
V f (m/s) 1.26E − 02 (estimated) 1.20E − 02 (estimated) 1.45E − 02 (estimated) 1.11E02–1.75E − 02 (estimated) 6.96E − 03 –7.75E − 03 (estimated) –
Vl (m/s) 6.08E − 06∗
D(m) 30
Estimated by the result of Blinov et al. (Dokl, Akad, Nauk, SSSR, Vol. 113, No. 5, p. 1094, 1957).
Weckman et al. [16]
1
∗
Reference
Takahashi et al. [15]
No.
Table 1 Evaporation velocity and regression rate of liquid fuels f (Hz)
7.2
6–14.9
1.0–6.0
0.26–8.5
2.7
0.023
0.31
7.50E− 01–1.01E +02 3.6
5.87E+ 01–3.48E +02
2.81E+01 −3.92E +02
5.56E + 01
9.58E + 02
7.38E + 02
St
1.60E−00 –5.00E +02 24.5
1.23E+04 –2.46E +05
1.43E+03 –1.24E +06
1.38E + 04
3.40E + 06
1.85E + 06
1/Fr
142 H. Sato et al.
Scale Modeling of Puffing Frequencies in Pool Fires Related with Froude Number
143
In this section, we will mention the buoyancy effect on turbulent flame in various super gravity fields. To realize a high Reynolds number flame in the gondola of centrifuge, we contrived a turbulent flame with a sort flame-height using a 0.4-mm nozzle. In general, characteristic of turbulence was discussed by differential or integral scale of the local component of fluctuation. However, because the target flame in this study was large vortex structure and local measurement of fluctuation could not carry out, we discussed fluctuation characteristic of a high-Reynolds number jet flame. The discussion was based on the results of power spectrum and auto-correlation function obtained by fluctuations of a laser beam to the buoyant flow near the flame. The power spectrum indicated fluctuation characteristic such as regular or irregular. Also, the result of auto-correlation function provides a value of density changes in the structure of fluid body, which means a time-scale of large vortex structure. Figure 8 shows the results of power spectrum and auto-correlation function in Re = 2800. In this figure, the flame was laminar at G = 1. Gravitational level was elevated ranging from G = 1 to G = 7. At the normal gravity condition, the spectrum didn’t show any remarkable frequencies so that the flame was stable. The peak-frequency near 50-Hz in Fig. 8(a) was just an electric noise of power supply. In the case of G = 1, result of auto-correlation function was not indicated due to the steady flame. When the gravitational acceleration was increased to G = 4, the flame was oscillated with a frequency of 30-Hz, and continues spectrum was also observed. The low-frequency element was explained as a flickering flame [6–9]. However, flickering phenomena in very periodic oscillation and have just
0.001 Re = 2800
G=1
0 0.001 30 Hz
0 0.01
Auto-correlation C(˱)
Power spectrum P (f ) V
1
G=4
G=7
Re = 2800
G=4
0 –1 1
G=7
0 –1 –0.2
0 Time delay ˱ s
0.2
0
0
0.25 Frequency f kHz (a) Power spectrum
0.5 (b) Auto-correlation
Fig. 8 Frequency analysis of flame fluctuations under super gravity field: Re = 2800 (fuel jet)
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a single remarkable frequency. Therefore, the flickering flame observed at G = 4 in Fig. 8(a) was like a turbulent flame because it was characterized as a flame which included the element of irregular oscillatory frequency with the periodic motion of large-scale vortex. From the auto-correlation wave, it was indicated that time-scale of the periodic motion was expanded with an increase in gravitational acceleration. Figure 9 shows the results of Re = 3600 at various gravity fields. In the figure, gravitational level was changed from G = 1 to G = 3, and the flame was turbulence at G = 1. At normal gravity condition, the spectrum was like a broadband due to the turbulent flame. When the gravitational level was elevated, low-frequency modes appeared within 0.05-kHz. And especially, the spectrum of low-frequency mode was amplified obviously at G = 3. As for the behavior of auto-correlation function, the results showed almost the same tendency with Fig. 8(b). To discuss the time-scale of a large vortex motion in detail, a parameter of the half bandwidth 2τc for auto-correlation function was defined as shown in Fig. 9(b). If the vortex motion auto-correlates with the analysis, time range for a high level auto-correlation (C (τ ) ≈ 1.0) means the fluctuation associated with a large-scale vortex motion. Once again, the parameter by 2τc is represented as FWHM (Full Width at Half Maximum). Figure 10 indicates the behavior of FWHM at various gravity fields. In both cases of Re = 2800 and 3600, FWHM values were increased with an increase in gravitational acceleration. That means the scale of flame motion becomes large when the gravitational level is elevated. The reason why the vortex motion becomes large in the super gravity field is explained as follows: flame is accelerated by the effect of buoyancy influenced to high-temperature region of the
0.01
Re = 3600
1
G=1
Re = 3600
G=1 C(˱) = 1 0.5
0 0.005
G=2
0 0.005
G=3
Auto-correlation C(˱)
Power spectrum P (f ) V
0
2τc
–1 1
G=2
0 –1 1
G=3
0 0
0
0.25 0.5 Frequency f kHz (a) Power spectrum
–1 –0.04
0 Time delay ˱ s
0.04
(b) Auto-correlation and definition of 2τc
Fig. 9 Frequency analysis of flame fluctuations under super gravity field: Re = 3600 (fuel jet)
Scale Modeling of Puffing Frequencies in Pool Fires Related with Froude Number Fig. 10 Change of FWHM values at various gravity fields
145
10 z/Lf = 0.6
Pre-blow out
FWHM 2˱c ms
Re = 2800
5
Re = 3600
Pre-blow out 0
0
5
10
15
Gravity G
flame when the gravity is increased. Then, share flow would be produced in the layer between the flame surface and its surrounding ambient atmosphere. And also, a large-scale vortex is formed due to the share flow. Therefore, the large-scale vortex motion works closely with the buoyant flow, resulting in fluctuation scale of the vortex becomes large with an increase in gravitational level. To support the above thinking, flow visualization of the vortex motion or detailed measurement of velocity fluctuation is needed. Since it was difficult to make an experiment of the visualization in the gondola of centrifuge, fluctuation range of the unsteady flame height was investigated by video images. As an evaluation parameter for the fluctuation range of the flame height, difference in flame height between maximum and minimum was defined as a parameter of ⌬L f shown in Fig. 11. Figure 11 shows the G-⌬L f relationship in Re = 2800 and 3600. In both cases, the fluctuation range of the flame height is increased with an increase in gravitational acceleration. This increasing tendency corresponds to the result of Fig. 10. To discuss the results of Figs. 10 and 11, time-scale was estimated from two different analyses, which are based on video image of the flame height motion and auto-correlation function, respectively. At the normal gravity condition, estimated time-scale values are compared. The time-scale of the fluctuation estimated by video images was τ = 0.21-ms, and the value by auto-correlation function was τc = 0.30-ms. These results indicate to confirm that the change of ⌬L f corresponds to the behavior of time-scale τc calculated from auto-correlation analysis due to the same order with the time-scale of fluctuation obtained by video images: O(τc ) ≈ O(τ ).
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Fig. 11 Buoyancy effect on amplitude of flame oscillation
˂Lf
50
Flame oscillation ΔLf mm
Pre-blow out Re = 3600
25 Re = 2800
Pre-blow out
Laminar 0
0
1
5
10
15
Gravity G
Conclusions On the unsteady motion of pool fires, scale modeling based on the Froude and Strouhal number relationship was conducted to clarify the buoyancy effect on puffing frequencies by using a centrifuge. The centrifuge enables us to consider the buoyancy effect on unsteady phenomena directly. The remarkable conclusions obtained in this study were summarized as follows: 1. Flame stability maps of pool fires were obtained with including the buoyancy effect. As for the flame configurations, the regions of laminar, puffing, irregular and blow-off could be distinguished. 2. Puffing frequencies of the pool fires were increased with an increase in gravitational level. Considering the evaporation velocity of the liquid fuel, Froude and Strouhal number relationship was extended with including the buoyancy effect as a parameter of gravitational acceleration, and the puffing frequencies at various gravitational levels could be summarized by the relationship of St ∝ Fr −0.502 . 3. As for the characteristic of turbulent flame in a super gravity field, variable-scale of flame height was amplified with elevated gravitational level. This result corresponded to amplifying the time-scale of the fluctuation, and its characteristic depended on the magnitude of gravitational level.
References 1. Orloff, L. and Ris, J.D., “Froude Modeling of Pool Fires”, Proc. Combust. Inst., 19: 885–895 (1982).
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2. Malasekera, W.M.G., Versteeg, H.K., and Gilchrist, K., “A Review of Reaearch and an Experimental Study on the Pulsation of Buoyant Diffusion Flames and Pool Fires”, Fire and Materials, 20: 261–271 (1996). 3. Schonbusher, A., Arnold, B., Banharrdt, V., Bieller, V., Kasper, H., Kaufmann, M., Lucas, R., and Schiess, N., Proc. Combust. Inst., 21: 83–92 (1986). 4. Cetegen, B.M. and Ahmed, T.A., “Experiments on the Periodic Instability of Buoyant Plumes and Pool Fires”, Combust. Flame, 93: 157–184 (1993). 5. Cetegen, B.M. and Kasper, K.D., “Experiments on the Oscillatory Behavior of Buoyant Plumes of Helium and Helium-Air Mixtures”, Phys. Fluids, 8(11): 2974–2984 (1996). 6. Arai, M., Sato, H., and Amagai, K., “Gravity Effects on Stability and Flickering Motion of Diffusion Flames”, Combust. Flame, 118 (1–2): 293–300 (1999). 7. Sato, H., Amagai, K., and Arai, M., “Flickering Frequencies of Diffusion Flames Observed Under Various Gravity Fields”, Proc. Combust. Inst., 28: 1981–1987 (2000). 8. Sato, H., Amagai, K., and Arai, M., “Diffusion Flames and Their Flickering Motions Related with Froude Numbers Under Various Gravity Levels”, Combust. Flame, 123 (1–2): 107–118 (2000). 9. Sato, H., Kushida, G., Amagai, K., and Arai, M., “Numerical Analysis of the Gravitational Effect on the Buoyancy-Driven Fluctuations in Diffusion Flames”, Proc. Combust. Inst., 29: 1671–1678 (2002). 10. Ishii, T., Sato, H., Amagai, K., and Arai, M., “Effect of Gravity on the Turbulent Diffusion Flame”, JSME, Ser. B, 72(713): 194–201 (2006) (in Japanese). 11. Hamins, A., Yang, J.C., and Kashiwagi, T., “An Experimental Investigation of the Pulsation Frequency of Flames”, Proc. Combust. Inst. 24: 1695–1702 (1992). 12. Blinov, V.I. and Khudyakov, G.N., Dokl. Akad. Nauk. SSSR, 113(5): 1094–1097 (1957). 13. Mell, W. E., Mcgrattan, K.B., and Baum, H.R., “Numerical Simulation of Combustion in Fire Plumes”, Proc. Combust. Inst., 26: 1523–1530 (1996). 14. Ghoniem, A.F., Lakkis, I., and Soteriou, M., “Numerical Simulation of the Dynamics of Large Fire Plumes and the Phenomenon of Puffing”, Proc. Combust. Inst., 26: 1531–1539 (1996). 15. Takahashi, N., Suzuki, M., Dobashi, R., and Hirano, T., “Behavior of Luminous Zones Appearing on Plumes of Large-Scale Pool Fires of Kerosene”, Fire Safety J., 33: 1–10 (1999). 16. Weckman, E.J., and Sobiesiak, A., “The Oscillatory Behaviour of Medium –Scale Pool Fires”, Symp. (Int.) on Combustion, vol. 22, Issue 1: 1299–1310 (1989). 17. Br¨otz, W., Sch¨onbucher, A., Lucas, R., Schiess, N., “Coherent Short Time Structures and the Momentary Refraction Index, Density, and Temperature Profiles in a n-hexan-poolflame”; Ber. Bunsen. Ges. Phys. Chem. 87: 951 (1983). 18. Byram, G.M., and Nelson, R.M., “The Modeling of Pulsating Fires”, Fire Technology, vol. 6, No. 2: 102–110 (1970).
Scaling Sub-Surface Layer Circulation Induced by Pulsating Flame Spread over Liquid Fuels Kozue Takahashi, Akihiko Ito, Yuji Kudo, Tadashi Konishi and Kozo Saito
Abstract The pulsating flame spread over liquid fuels consists of main-pulsation with 0.5 to 2 Hz frequency and sub-pulsation with 5 to 10 Hz frequency. The former originates in existence of a cold temperature valley at the liquid surface ahead of the spreading flame. The cold temperature valley is formed by the surface wave in connection with a sub-surface layer circulation. In this study, the instability analysis for the liquid surface ahead of a flame leading edge was performed to clarify the onset of surface wave. Moreover the effect of gravity on surface wave generation was examined. The theoretical result shows that the onset of surface wave is firstly controlled by Marangoni force and secondary by buoyancy force. The critical condition for onset of surface wave was expressed to the non-dimensional form. Three dimensionless parameters, the Marangoni number, the Weber number and the Froude number include the ratio, h L, of the characteristic length, L, and the depth, h, of subsurface layer circulation (shown in Fig. 1). The circulation scale for seven different thickness of liquid fuel from 2 to20 mm was measured using a schlieren photograph and thermography. The ratio, h L, decreases with decreasing fuel layer thickness less than 5 mm and consists to g condition at the fuel layer thickness of 3 mm. Keywords Flame spread · liquid fuels · sub-surface layer circulation
Nomenclature C+ C0 FB FMa g
Dynamic wave velocity [m/s] Kinematic wave velocity [m/s] Buoyancy [N] Marangoni force [N] Gravitational acceleration [m/s2 ]
K. Takahashi Department of Intelligent Machines and System Engineering, Hirosaki University, Hirosaki, Japan e-mail:
[email protected]
K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
149
150
h h H k L q T ΔT U US u x y α β γ Γ λ λl μ ρ σ σT τ
K. Takahashi et al.
Sub-surface thickness [m or mm] Characteristic depth of circulation [m or mm] Liquid fuel thickness [m or mm] Wave number [≡ 2/ m−1 ] Characteristic length of circulation [m or mm] Heat flux [W/m2 ] Temperature [K] Difference of a flash point and bulk [K] Liquid velocity [m/s] Interface velocity [m/s] Average liquid velocity [m/s] Coordinate in flow direction [m] Coordinate normal to flow direction [m] Heat flow factor Momentum displacement thickness Cubical expansion coefficient [/K] Liquid volumetric flow rate per unit width of the tray [m2 /s] Wavelength [m or mm] Thermal conductivity [W/m K−1 ] Viscosity [Pa · s] Density [kg/m3 ] Surface tension force [N/m] Temperature coefficient of surface tension force [N/m K−1 ] Shear stress [Pa]
Subscripts i b
Gas-liquid interface Bulk
Introduction To understand the mechanism of pulsating flame spread, it is crucial to obtain detail thermal, fluid dynamic, and chemical structures of both gas and liquid phases near the flame leading edge during the flame spread process. Pulsating flame spread consists of the main-pulsation of about 0.5 to 1 Hz, and sub-pulsation of about 5 to 10 Hz [1]. The former originates in the generation and disappearance of a cold temperature valley in the liquid surface ahead of the flame. The pulsating flame spread model [2] was proposed that it was formed of sub-surface layer circulation and the surface wave. On the other hand, in numerical analysis [3], the phenomenon in g pulsating flame spread cannot easily happen and is not clarified to the ability to usually explain pulsating flame spread in 1 g.
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151
In our previous studies [2, 4], we applied six different experimental techniques, including laser sheet particle tracking, smoke tracing, single and dual wavelength holographic interferometer (HI), IR thermograph, and high-speed photography to measure detailed transient three-dimensional flow, temperature, and fuel species concentration profiles created by a pulsating spread over propanol. Five different processes on the pulsating spread are identified in our previous paper [2, 4]: (1) the onset of pulsation, (2) the formation of a cold-temperature valley in the liquid, (3) the disappearance of the cold-temperature valley and the formation of a flammable gas layer over the liquid surface, (4) a flame jump through the flammable gas layer, and (5) a temporal cessation of the spread connecting back step 1. One of the major conclusions obtained from our previous studies [2, 4] was a cyclic appearance and disappearance of a cold (liquid) temperature valley whose cycle frequency was well correlated with the frequency of the main flame pulsation. We also discussed a possible reason why there was no pulsating flame spread under micro gravity. Our thought was that convective heat transfer is the major mode of heat transfer from the flame to the liquid, and under micro gravity there is much weaker convection than in normal gravity, so the convection effect is not strong enough to cancel out the cold-temperature valley profiles once they formed in the liquid, allowing the cold valley to continuously exist (therefore, no pulsating spread). It may be interesting to review how numerical models can deal with liquid temperature profiles. Two-dimensional numerical modeling [5] showed a linear decay in the temperature of the liquid ahead of the flame leading edge and did not predict the existence of the cold temperature valley. At the beginning, we thought this was due to two-dimensional model assumptions being applied to actual threedimensional phenomena. Later, this lone of thought was proved to be wrong, when the NASA group [6] showed that there was a pulsating flame spread over a thin liquid layer pooled in a shallow circular pan where no cold temperature valley was thought to exist. To explain this disagreement, we searched for a clue in the temperature structure created in a shallow liquid pool during pulsating flame spread. We conducted a flame spread experiment using the same rectangular tray and an enclosure box (480 mm long × 20 mm wide × 20 mm high), described in our previous experiments [2, 4, 7], and measured the detailed temperature structure in the liquid using HI, shadowgraph (SG), and IR techniques, In particular, HI is very effective in measuring transient temperature profiles with high special resolution (our HI system can offer a microsecond time response and a better than 0.1 mm special resolution). Interestingly, we found there was a small-scale liquid surface wave which height of the crest is about 0.9 mm for 20 mm deep pool. In this paper, the instability analysis for the liquid sub-surface layer ahead of a flame leading edge was performed to clarify the onset of a surface wave, which was thought the cause of the cold temperature valley. Moreover, we introduced the non-dimensional parameter into the theoretical results, and examined the scale effects of sub-surface layer circulation ratio h L (shown in Fig. 1) on pulsating flame spread.
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Fig. 1 Schlieren photograph and the definition of the characteristic length, L, and the depth, h, of sub-surface layer circulation
Theoretical Analysis Basic Equation Our objective is to study the instability of sub-surface layer flow ahead of the spreading flame. The flow is assumed to be laminar. It is also assumed that the temperature coefficient of surface tension force and other physical properties are constant. A schematic of sub-surface layer flow is shown in Fig. 2. The various symbols are defined as follows: x is the flow direction coordinate, y is the normal direction to the wall, λ is wavelength, H is the fuel layer thickness, h is the sub-surface layer thick"h ness, U is the liquid velocity, u is the average liquid velocity u (≡ 0 U dy h , τb is the shear stress in the liquid, τi is the shear stress at liquid surface and qi is the heat flux from the liquid surface to gas-phase.
Flame
V
Flammable vapor Surface wave Diffusion coefficient D
δ
λ qi
Us
Wall
Ti
U y H 0
h
x
T
τi τb
Tb
Liquid
Wall
Fig. 2 Sub-surface layer flow model and symbol
Scaling Sub-Surface Layer Circulation Induced by Pulsating Flame Spread
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The continuity and momentum equations for the sub-surface layer are expressed as, h t + (hu)x = 0 (hu)t + 0
h
1 U 2 dy + gh 2 2
+ x
(1)
σ k 2 δh ρ
= x
1 (τi − τb ) ρ
(2)
where, g is the acceleration due to gravity, σ is the surface tension force and ρ is the density of the liquid. The subscripts t and x indicate the partial derivatives in time and in the x-direction, respectively. The third term on the LHS in Eq. (2) is due to the surface tension force, where, δ = A exp ik (x − ct) is the expression for the surface wave. Where k ≡ 2π λ is the wave number, λ is the wavelength and c is the wave velocity. In Eq. (2), τi is the surface shear stress due to Marangoni effect and is expressed as, τi =
⭸T ⭸σ = σT ⭸x ⭸x
σT ≡
dσ dT
(3)
" h If the momentum displacement thickness β ≡ 0 U 2 dy u 2 h and the continuity equation, Eq. (1), are substituted into Eq. (2), we obtain the following equation: hu t + (2β − 1) huu x + (β − 1) u 2 h x + βx u 2 h + ghh x +
σ k2 1 (δx h + δh x ) = (τi − τb ) (4) ρ ρ
The perturbation at the gas-liquid interface is very small and the independent variables (u, h, τ ) are expressed as, u = u + u , h = h + δ, τb = τ b + τb , τi = τ i + τ
(5)
where the superscripts bar and prime indicate time-averaged and perturbation quantities, respectively. If the velocity remains similar on perturbation, then β = β. With the substitution of Eqs. (1) and (5) into Eq. (4), and if the velocity is fully developed, u x = h x = 0, τ i = 0, τ b = 0, and the higher-order perturbation terms are negligible, the continuity and momentum equations can then, respectively, be written as, (6) δt + uδx + hu x = 0 2 δx 1 σk δx = (7) u t + 2β − 1 uu x + β − 1 u 2 + gδx + τi − τb ρ h ρh # u du ## If τ b is small as for the gap from time-average value τ b = μ = 3μ , it # dy y=0 h may be written as,
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u u − 3μ h h
u ∼ u u ∼ − = 3μ = 3μ h h h
(8)
This implies that no heat is stored in the sub-surface layer. All the heat is transferred qi at the gas-1iquid interface. If the flow is laminar, T i = T b − α h, where T b is λl time-averaged temperature in liquid, λl is the thermal conductivity of the liquid and α is heat flow factor (: the positive indicates the heat released from the surface to gas-phase, the negative indicates the heat absorbed at the surface). If the perturbation of the surface temperature is very small, then, Ti = T b − α
qi qi h = Tb − α h+δ λl λl
(9)
Differentiating Ti with respect to x, and substituting into Eq. (3), we obtain, τi = −α
qi σT δx λl
(10)
By substituting Eqs. (8) and (10) into Eq. (7) and differentiating with respect to x, and using Eq. (6) to eliminate u, we can obtain the following wave equation.
⭸ ⭸ + C+ ⭸t ⭸x
⭸ ⭸ + C− ⭸t ⭸x
δ+
3μ ρh
2
⭸ ⭸ + C0 ⭸t ⭸x
δ=0
(11)
where, $ C± = βu ±
h qi β − 1 βu 2 + gh + σ k 2 + ασT ρ ρλl
(12)
C0 = u The first term on the LHS of Eq. (11) represents the dynamic wave where C+ and C− are the forward and reverse propagation velocities. The second term on the LHS of Eq. (11) represents the kinematic wave, where C0 is the propagation velocity in the direction of flow. Therefore, in Eq. (11) the surface wave is represented as a linear combination of the dynamic wave and the kinematic wave. The Marangoni effect appears in the C± term in the dynamic wave expression. If the surface perturbation is expressed as δ = a exp i(kx − wt), then from Eq. (11) we obtain the following equation, (ω − kC− ) (ω − kC+ ) + i
3μ ρh
2
(ω − kC0 ) = 0
(13)
Scaling Sub-Surface Layer Circulation Induced by Pulsating Flame Spread
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Hence, ω may be approximated as
3μ 3μ (C − C ) (C − C ) + 0 0 − + kC− − i 2 ω ∼ = kC+ − i 2 (C+ − C− ) (C+ − C− ) ρh ρh (14)
The dynamic wave is unstable if Im (ω) > 0, and this indicates that C0 C+ . This gives rise to the “neutrally stable” condition C0 = C+ , and the following equation for generation of a surface wave may be obtained, h qi 1 − β u 2 = gh + σ k 2 + ασT ρ ρλl
(15)
If the liquid velocity is defined as U = Ay 2 0 ≤ y ≤ h and A = 1, the liquid "h 3 volumetric flow rate per unit width of the duct is Γ = 0 y 2 dy = 13 h , the average 2
liquid velocity is u = 13 h and the momentum displacement thickness is β = Equation (16) may be written as, 1
−3 3
4 4 1 ⌫cr 3 − 3 3 15
g+
σ k2 ρ
1
⌫cr 3 =
ασT qi ρλl
9 . 5
(16)
where Γcr is the critical flow rate required for surface wave to occur.
Conditions for Generation of a Surface Wave The neutral stable line obtained from the Eq. (16) is shown in Fig. 3 for the three different wavelengths into a parameter. The following values are used for calculation: σ = 24.17 × 10−3 N/m, σT = −8.16 × 10−5 N/m · K, ρ = 809 kg/m3 , λl = 151.7 × 10−3 W/m · K, α = 1. As the hot liquid flows ahead of the flame leading edge by Marangoni force, the liquid surface temperature is higher than the gas phase temperature. The qi in horizontal in Fig. 3 is positive for heat release from the liquid surface to gas-phase. The area above the neutral stable line in Fig. 3 shows an unstable region, which is corresponding to the generating region of a surface wave. A theoretical result
Fig. 3 The neutral stable line
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shows the follows: (1) shorter wavelength perturbation is easy to develop to a surface wave, (2) the liquid surface is more stable with increasing the heat flux from the liquid surface to gas-phase. In experiment, uniform flame spread changes to pulsation at certain temperature below the flash point. The Marangoni force is proportion to the temperature difference between the hot zone underneath the flame leading edge and bulk liquid temperature. The liquid bulk temperature is lower, the Marangoni force is greater. This may lead to sub-surface flow rate increase and a surface wave to be occurred.
The Non-Dimensional Parameter The following non-dimensional parameters are introduced, ασT qi ρλu 2 u , Ma = Fr = % , W e = σ ρλl u 2 gh
(17)
where, Fr is the Froude number, We is the Weber number and Ma is the Marangoni number. Equation (15) is rewritten to non-dimensional form using Eq. (17), we obtain the following equation: 1−β =
h 1 1 − Ma + 4π 2 2 Fr λ We
(18)
From the overall the energy and the momentum balances in sub-surface layer, the following equations are drawn, qi = μ
US h
λl ΔT αh = σT
(19) ΔT L
(20)
where, U S is the liquid surface velocity, ΔT is the temperature difference between a flash point and liquid bulk temperature, L and h is the thermal characteristic length and depth of the sub-surface layer circulation shown in Fig. 4. Using Eqs. (19) and (20), the three non-dimensional parameters can be rewritten as, σT ΔT 1 h Fr = √ 2 gμ h L 2 ρσT 2 ΔT 2 h λ We = 4μ2 σ L 2 h ρσT ΔT h Ma = 4μ2 L
(21)
(22)
(23)
Scaling Sub-Surface Layer Circulation Induced by Pulsating Flame Spread Fig. 4 Characteristic length and depth
157
L Flame
Surface wave
Gas Interface Liquid
h Sub-surface layer circulation
And also we rewrite Eq. (17) using Eqs. (21)–(23) and obtain the following equation, 1−β =
h 1 1 1 + 4π 2 − 2 Fr λ We Ma
(24)
Equations (21)–(24), all having the characteristic length scale ratio, h L, in their expressions, describe the generation of a liquid surface wave and its propagation. Therefore these four equations may predict the onset of flame pulsation and subsequent pulsating flame spread over liquids. Scales and ratio of the sub-surface layer circulation for n-butanol are compared the normal-gravity and the micro gravity conditions presented by H. Ross and F. Miller [3] in Table 1. Although the depth of circulation in g condition is much larger than that in 1 g condition, the ratio h L in 1 g is larger than that in g condition. The circulation in 1 g develops in the direction of depth due to the buoyancy force. Figure 5 shows the critical Marangoni number versus the Weber number obtained from Eq. (24) using the values of h L in Table 1 for 1 g and g conditions. Here, 1 g is corresponding to Fr = 0.773 and g (1×10−4 g) is corresponding to Fr = 20.8. The critical Marangoni number for g is higher than that for 1 g at the same Weber number. This is meaning that the gravity in a liquid affect to instability of the liquid surface. Figure 6 shows the relation between the critical Marangoni number and the subsurface layer depth at the constant Weber number. Here, 1 g is corresponding to W e = 0.859 and g (1 × 10−4 g) is corresponding to W e = 0.588. The sub-surface layer depth in g is about 3 times of the depth in 1 g. The critical Marangoni number in g is about 0.24 for 13.8 mm of h, which is still larger than that in 1 g (the critical Ma is about 0.1 in 1 g). When the liquid surface becomes instable and the surface wave is formed in g condition, the sub-surface layer depth should be deep and the circulation should be large. Table 1 Scales and ratio of sub-surface layer circulation for n-butanol [3] Characteristic length L Characteristic depth h h L
1g
g
6.67 mm 4.38 mm 0.67
43.3 mm 13.8 mm 0.32
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Fig. 5 Marangoni number versus Weber number
0.15
Ma
0.1 unstable 0.05
0
0
Fig. 6 Marangoni number versus characteristic depth
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Experimental Apparatus and Method The schlieren photograph method was used to measure the characteristic length and depth of a sub-surface layer circulation. Experimental set up is shown in Fig. 7. The experimental equipments for a schleiren photograph, a 5 mW He-Ne laser as the light source, a knife-edge, lens, mirror etc. were fixed on the optical bench with a magnet stand. The laser beam was expanded by a beam expander which was placed at the focus position of a concave mirror. The expanded laser light was reflected by a concave mirror and passed through the fuel container. The laser light was recorded by the motor driven camera with a 300 mm telephoto lens (15 flames/s). The behavior of flame spread was recorded by a digital video camera. The flame spread rate and pulsation frequency were measured from the recorded digital image. An IR camera with 8–13 m wavelength detector was also placed above the liquid container to measure the liquid surface temperature during the flame spread. Our previous test [8, 9] confirmed that the emissive of n-propanol was 0.95. A fuel container used for this experiment is shown in Fig. 7. It is having dimensions of 480 mm long × 20 mm wide × seven different heights (2, 5, 7, 10, 15 and 20 mm). The seven different tray heights were used to provide seven different liquid thicknesses by keeping all the other tray dimensions and the initial liquid surface level to the tray wall rim height the same. The fuel container bottom was made of brass and the both side were made of Pyrex. A n-propanol was used for test fuel. A fuel was filled in the container and was filled to the limit of a container in order
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Fig. 7 Experimental apparatus
to lose the influence of meniscus. A small pilot flame that was located at one end of the tray initiated the flame spread that propagated to the other end. The liquid temperature is hold by 290 K, which are the pulsating region of n-propanol.
Results and Discussion Effects of Gravity on Circulation Figure 8 shows the ratio of characteristic length and depth, h L, measured by schlielen photograph as a function of the initial propanol thickness, H. The ratio h L, is almost constant value of 0.5 over 5 mm of initial fuel thickness, while it sharply decreases with decreasing initial fuel thickness. The ratio in 1 g consists with that in g at the initial fuel thickness of3 mm. Substituting the experimental results of h L into Eq. (23), Marangoni number is plotted in Fig. 9 as a function of fuel layer thickness. Here, temperature difference, ΔT , in Eq. (23) is referred to 8 K. The Marangoni number is almost constant value
Fig. 8 Ratio of the characteristic length and depth of sub-surface layer circulation versus initial fuel layer thickness
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Fig. 9 Marangoni number versus initial fuel layer thickness
of 30 over 5 mm of initial fuel thickness, while less than 5 mm of H it decreases with decreasing initial fuel thickness. The Marangoni number in g condition is about 2 for 20 mm butanol thickness, which consists with that for 3 or 4 mm propnol thickness in 1 g. The ratio of buoyancy force and Marangoni force is expressed as follows, 2 γρg h L FB = FMa σT
(25)
Substituting the ratio of characteristic length and depth, h L, into Eq. (25), the ratio of buoyancy force and Marangoni force is plotted in Fig. 10 as a function of an initial fuel thickness. The ratio, FB /FMa , is almost 0.4 over 5 mm of initial fuel thickness. It is meaning the buoyancy contributes at most 40% to generate a surface wave for deep liquid fuel. The ratio, FB /FMa , steeply decreases less the 5 mm and reaches to 0.1 at the 4 mm. From above the results, we conclude that the buoyancy (gravity in liquid fuel) is affect to surface wave formation at most 40% for deep liquid fuel, while less than 3 or 4 mm of fuel thickness, buoyancy dose not affect to surface wave generation. This conclusion suggests the pulsation on the thin liquid fuel pool occurs same phenomena both 1 g and g condition.
Fig. 10 Ratio of the buoyancy force and Marangoni force versus initial fuel layer thickness
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Characteristic Length and Depth of Circulation Figure 11 shows the characteristic length, L, and depth, h, of the sub-surface layer circulation at 17 ◦ C of the initial fuel temperature as a function of initial fuel thickness. As the sub-surface layer circulation is restricted to develop in the direction of depth, the h decrease with decreasing the initial fuel thickness below 5 mm. On the contrary, the L has a minimum value at 4 mm, and then increases with decreasing the initial fuel thickness. The measured temperature gradient at the liquid surface in the direction of flame spread is shown in Fig. 12. The surface temperature gradient has minimum value at 5 mm of the initial fuel thickness. The surface velocity may decrease with decreasing the initial fuel thickness because of decreasing buoyancy force. This may lead to increase the surface temperature gradient below 5 mm as the Maragoni force is dominant force for sub-surface layer flowing. In g conditions, it is suggested a surface wave is easy to generate in thin liquid fuel pool. Fig. 11 Characteristic length and depth versus initial fuel layer thickness
Fig. 12 Temperature gradient versus initial fuel layer thickness
Conclusion A small-surface wave generates just ahead of the flame leading edge during pulsating flame spread. The instability analysis for the liquid surface ahead of a flame leading edge was performed to clarify the onset of a surface wave. Theoretical result shows the onset of a surface wave is firstly controlled by Marangoni force,
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the buoyancy contributes at most 40% for thick liquid fuel pool. While it becomes small below 3 mm of fuel thickness. The surface wave is related to a sub-surface layer circulation. The ratio, h L, of the characteristic length, L, and the depth, h, of a sub-surface layer circulation was 0.67 in 1 g condition and 0.32 in g condition for butanol. The ratio, h L, in g is smaller than that in 1 g. We measured the scale of sub-surface layer circulation using schlieren photograph and IR camera for changing the initial fuel thickness in 1 g. The ratio decreases with decreasing initial fuel thickness below 5 mm and consists to that in g at the initial fuel thickness of 3 mm.
References 1. Konishi, T., Ito, A., Kudo, Y., and Saito, K., (2002) Proc. Combust. Inst. 29: 267–272. 2. Konishi, T., Tashtoush, G., Ito, A., Narumi, A., and Saito, K., (2000) Combust. Inst. 28: 2819–2826 . 3. Ross, H. and Miller, F., (1996) Combust. Inst. 26: 1327–1334. 4. Ito, A., Narumi, A., Konishi, T., Tashtoush, G., Saito, K., and Cremers, C. J., (1999) J. Heat Transfer 121: 413–419. 5. Schiller, D.N., Ross, H.D., and Sirignaro, W.A., (1993) AIAA paper 93–0285. 6. Ross, H.D., (1994) Prog. Energy Combust. Sci. 20: 17–63. 7. Ito, A., Masuda, D., and Saito, K., (1991) Combust. Flame 83: 375–389. 8. Qian, C., Ishida, H., and Saito, K., (1994) Combust. Flame 99: 331–338. 9. Konishi, T., Ito, A., and Saito, K., (2000) Appl. Opt. 39: 6708–6714.
Part II Combustion F.A. Williams, T. Takeno, Y. Nakamura and V. Nayagam
Summary Combustion, which involves exothermically chemically reacting flows, is complicated in that it includes both physical processes, such as heat and mass transfer, and chemical processes of many different types. The topic is a broad one with applications in areas that encompass power-production and safety issues. The safety-related subjects of fire and explosions are addressed in Part I. The present section focuses on more fundamental aspects of combustion. Because combustion is a complicated phenomenon, it is important as a first step to identify the most dominant controlling processes. Dimensional analysis is a good way to investigate the dominant physics and chemistry. Since there are many nondimensional groups in combustion, it is challenging to pick out the few that are most important. Once this is done, there is appreciable simplification which then makes combustion a good candidate for application of scale modeling. The scalemodeling concepts help to simplify the problem and to expose the most important aspects, thereby affording a useful first step, prior to more detailed experimental and numerical work. Since there have been many fundamental combustion studies presented at the ISSM symposia, stringent criteria had to be enforced in selecting papers for inclusion in the present volume. Papers were excluded unless they were both highly contributing to the development of fundamental combustion science and strongly related to scale modeling. This required the omission of some excellent papers and finally resulted in the selection of only 12 papers for publication. Although most of these papers are experimentally based, some theoretical and numerical studies also are included. Figure 1 summarizes the number of papers in this area presented at the different symposia. That number is seen to have reached a maximum, in both absolute value and percentage, around ISSM-III and ISSM-IV, reflecting a trend in the fraction of scale modeling research devoted to fundamentals of combustion. Figure 2 summarizes the acceptance ratios for papers in fundamental combustion. Except for ISSM-II, in which 50% of the papers were both excellent and highly relevant, the acceptance ratio remains around 20%. The overall decrease with time in the
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Fig. 1 A summary of the number of papers
Fig. 2 Acceptance ratio
fraction of papers in this area that are both excellent and relevant may be attributed to the increasing capabilities and precision of direct numerical simulation. Since those capabilities, however, remain deficient for three-dimensional turbulent flows with ignition and extinction, for multiphase combustion and for other comparably complex combustion processes, further contributions of scale modeling to advances in these fundamental combustion areas may be anticipated in the future.
Papers Selected from the Second Symposium 1. F.A. Williams. “Modeling of Combustion Phenomena.” This paper reviews a wide variety of modeling and scaling questions in combustion. It emphasizes the relevance of partial modeling, in which certain groups of possibly lesser
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importance are purposely ignored. This paper was chosen because of its breadth of coverage and perspective. S. Tabejamaat and T. Niioka. “Numerical Study of the Effect of Model Scaling on Mixing and Flame Development in a Wake Flow Field.” This addresses the combustion of hydrogen injected into a supersonic air stream from the downstream side of a bluff body. It applies numerical methods to identify the mechanism of flame holding. This paper was chosen because of the importance of its establishment of the mechanism of flame stabilization and because it considers the effects of model scaling, pointing out the scales that are most relevant. T. Takeno and K.N.C. Bray. “Molecular Diffusion Time and Mass Consumption Rate in Flames.” This paper presents dimensional-analysis arguments for describing how non-uniform flow can affect combustion rates in flames. It addresses both premixed and non-premixed flames in flame-let regimes. It was chosen because of its contribution to understanding of the processes involved. L.T. Yap, M. Pourkashanian, L. Howard, A. Williams, and R.A. Yetter. “NitricOxide Emissions Scaling of Buoyancy-Dominated Oxygen-Enriched Methane Turbulent-Jet Diffusion Flames.” This paper contains detailed experimental and theoretical investigations of emissions of nitric oxide from turbulent flames to which oxygen has been added for the purpose of reducing harmful emissions. It develops and validates a scaling law for emissions based on a Froude number. This paper was chosen because of its discovery and elucidation of the most significant underlying mechanisms and its identification of the relevant scaling that occurs. I.S. Wichman and B. Ramadan. “Scaling Analysis of Diffusion Flame Attachment and Liftoff.” This paper presents a theoretical analysis of the attachment and liftoff of a flame downstream from a splitter plate separating fuel and oxidizer flows. It identifies the different regimes that occur and the existence of triple flames under suitable conditions. It was selected because of its contribution to understanding and its identification of the relevant non-dimensional parameters needed in scaling.
Papers Selected from the Third Symposium 1. V. Nayagam, A.J. Marchese and K. Sacksteder. “Microgravity Droplet Combustion: An Inverse Scale Modeling Problem.” This paper addresses droplet combustion questions for which there is some advantage in studying a scale model that is larger than the prototype. It identifies different regimes of droplet combustion and the relevant non-dimensional parameters in the regimes. This paper was chosen because of its insights and unconventional approach to considerations of scale modeling. 2. P.B. Sunderland, D.L. Urban, and V. Nayagam. “Scaling of Gas-Jet Flame Lengths in Elevated Gravity.” This paper considers gas-jet diffusion flames
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employing both theoretical and computational methods. It develops scaling laws for flame dimensions and tests the predictions against available data obtained in experiments in which gravity levels are effectively elevated by use of centrifuges in which the combustion occurs. This paper, which is a rewritten version that also includes results in a similar paper presented at ISSM-IV, was selected because of the notable advances in understanding of scaling of flame heights that it develops. 3. Y. Nakamura, H. Ban, K. Saito and T. Takeno. “Structure of Micro (Millimeter Size) Diffusion Flames.” This paper presents detailed numerical and experimental results on the structure of very small methane-air laminar diffusion flames. It was chosen because of its emphasis on the relevant non-dimensional scaling parameters and its clarifications of the combustion processes that occur under these atypical conditions.
Papers Selected from the Fourth Symposium 1. J.S. T’ien. “Some Partial Scaling Considerations in Microgravity Combustion Problems.” Based on considerations of conservation equations for various microgravity combustion processes, this paper identifies similarity parameters and tests them against computational and experimental results. It emphasizes the importance of radiant energy transfer under microgravity conditions. It was selected because of its contributions to our understanding of the relevant non-dimensional parameters under microgravity conditions. 2. J. Baker, M. Calvert, and K. Saito. “Scale Modeling of Magnetocombustion Phenomena.” This paper analyzes heights of laminar diffusion flames in nonuniform magnetic fields, employing both theoretical and experimental methods. It identifies relevant non-dimensional parameters and tests them experimentally. It was chosen because of its novel approach to this relatively unusual combustion scenario and its strong appeal to scale modeling. 3. G.T. Linteris and I. Rafferty. “Scale Model Flames for Determining the Heat Release Rate from Burning Polymers.” This paper investigates the utility of flame size for assessing heat release rates of burning polymers by testing six different materials in apparatuses of different sizes. It established the relevance of Froude numbers for correlations of the results. This paper was chosen because it is a new application of scale modeling in combustion that falls in the mainstream of the subject and that appropriately advances our knowledge and understanding of the processes involved.
Papers Selected from the Fifth Symposium 1. K.H. Chuah, H. Gotoda, and G. Kushida. “Numerical Simulations of Methane Diffusion Flame with Burner Rotation.” This paper presents numerical solutions
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of the conservation equations for combustion of methane diffusion flames on rotating burners. It exhibits pulsating flames and clarifies their mechanisms. This paper was chosen because it increases our knowledge of influences of rotation on such flames and addresses scaling laws for pulsation frequencies that can be tested by scale modeling.
Microgravity Droplet Combustion: An Inverse Scale Modeling Problem Vedha Nayagam, Anthony J. Marchese and Kurt R. Sacksteder
Abstract Scaling behavior of burning rate constant with initial droplet diameter is investigated for a single component, sooting fuel under going spherically symmetric combustion in microgravity. Three different regions were identified: the D2 -law region where the burning rate constant is independent of initial droplet size, the sooting region, and the non-luminous radiative loss region. In the last two regions the −1/4 where D0 is the initial droplet burning rate constant is shown to decrease as D0 size. This decrease is primarily due to temperature dependent property variation. An estimate for the critical diameter that divides the first two regions is developed using a semi-empirical formulation for sooting. Keywords Droplet combustion · microgravity · sooting and radiation
Nomenclature A B Cp D D0 D1 D2 D3 Dg E fs i K
Pre-exponential factor for soot formation Mass transfer number Specific heat Droplet diameter Initial droplet diameter Maximum droplet diameter in the D2 -law region Maximum droplet diameter in the sooting region Maximum droplet diameter in the non-luminous radiative loss region Mass diffusion coefficient Overall activation energy Fraction of energy lost Stoichiometric oxygen to fuel-mass ratio Burning rate constant
V. Nayagam National Center for Space Exploration Research, Cleveland, OH 44135, USA e-mail:
[email protected]
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L Q ˙r Q ˙ Qc R r S T t YO εg ρ
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Effective heat of vaporization Heat of combustion per unit mass of fuel Instantaneous radiative heat loss rate Instantaneous heat release rate Universal gas constant Radial coordinate Progress variable for soot formation Temperature Time Oxygen mass fraction Total emissivity Density
Subscript f g l s ∞
Flame Gas Liquid Droplet surface Ambient
Introduction On board orbiting space platforms it is now possible to perform combustion experiments with long microgravity time requirements. For spherically symmetric, isolated droplet combustion experiments, this implies that droplets with larger initial diameters (>∼ 3 mm) can be formed, deployed, and burned to completion in a microgravity environment over a range of ambient conditions [1, 2]. From an experimental point of view, droplet combustion experiments with large initial droplet sizes have several beneficial features [3], the principal benefit being the ability to obtain better optical resolution over the entire field of view with relative ease. However, experiments with large droplets introduce additional physical phenomena that are of fundamental interest, but are not observable with smaller droplets, e.g., radiative flame extinction [2]. In spray combustion applications the typical droplet sizes are of the order of 100 microns or less [4]. At these small sizes the droplet flames are not influenced by buoyancy. Then the question arises whether it is possible to extrapolate the results obtained from spherically-symmetric, large droplet combustion to smaller droplet sizes. In other words, is microgravity droplet combustion an “inverse scale modeling” problem, where the size of the model is larger than that of the prototype? Williams [5] first hinted at this possibility in the Second International Scale Modeling Symposium in the context of extinction diameters for methanol droplets measured as a function of initial size [1]. The objective of the present work is to
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further explore this possibility and delineate the range of parameters over which such “inverse scale modeling” is valid for a sooting fuel droplet. We accomplish this objective by examining the experimentally measured burning rate constants for isolated fuel droplets of varying initial diameters and comparing them with simplified theoretical scaling laws.
Classical Theory The classical theory for droplet combustion [6, 7] provides an ideal starting point for the investigation of scaling laws associated with spherically symmetric droplet burning under microgravity conditions. It captures the most essential features of a single droplet burning, namely that it is a diffusion-controlled process with the characteristic length being the droplet initial diameter D0 , and the characteristic time being D0 2 /Dg , where Dg is the mass diffusivity of the fuel. This simplified theory, also called the D 2 -law, predicts that the square of the droplet diameter D decreases linearly with time t: D 2 = D02 − K t
(1)
where K is the burning rate constant (−dD 2 /dt). The burning rate constant K is expressed in terms of Dg , the gas and liquid-phase densities ρg and ρl , and the transfer number B, as K = 8Dg (ρg /ρ1 ) ln(1 + B)
(2)
where the transfer number B is defined as B = Q(Yo∞ /i) + Cp (T∞ − Ts ) /L
(3)
In the above equation Cp is the specific heat of the gas, T∞ is the ambient temperature, Ts is the droplet surface temperature, Yo∞ is the ambient oxygen mass fraction, i is the stoichiometric oxygen to fuel-mass ratio, Q is the heat of combustion per unit mass of fuel and L is the effective heat of vaporization. The classical theory also predicts that the ratio of the flame diameter Df to the instantaneous droplet diameter is a constant, namely Df /D = ln(1 + B)/ ln(1 + Yo∞ /i)
(4)
The classical theory employs a number of assumptions in obtaining the results given in Eqs. (1)–(4) [8]. The most important assumptions are (1) gas-phase quasisteadiness (2) constant gas-phase transport properties (3) infinitely-fast gas-phase chemistry and (4) no radiative heat loss. Clearly, if an experiment duplicates the underlying assumptions in deriving Eq. (1), inverse scale modeling is feasible in a limited sense for microgravity droplet combustion since the predicted burning rate
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is independent of the initial droplet size. In other words, one could perform largedroplet experiments and measure the burning rate constants accurately and then apply those results to smaller droplets encountered in other applications. However, in practice a number of assumptions that underlie the D 2 -law model are violated and consequently the burning behavior predicted by the model is not observed during experiments. In the following we examine the deviations of the measured burning rate constant K from the D 2 -law predictions and explore the possible scaling laws governing the additional physical phenomena which cause these deviations.
Measured Burning Rates Figure 1 shows the measured burning rate constants for n-heptane burning in air at atmospheric pressure as a function of initial droplet diameter D0 [9–14]. Three different regions can be identified in Fig. 1. For small values of D0 (D0 < D1 ) the burning rate constant remains relatively constant, and this region may be called the D 2 -law region (D2R) for reasons explained below. In the region D1 < D0 < D2 sooting is observed during the experiments and K decreases rapidly with increasing D0 . This region is termed the sooting region (SR). When D0 is larger than a critical size D2 , sooting disappears, continuum radiation stops, the flame becomes blue, and the burning rate constant jumps to a higher value and then decreases gradually with increasing D0 . Further increase in D0 leads to inherently unsteady combustion and radiative extinction above a critical diameter D3 . This region between D2 and D3 can be identified as non-luminous radiative loss region (NLR). The available
Fig. 1 Variation of droplet burning rate constant K , as a function of droplet initial diameter D0 for heptane droplets burning in air at atmospheric pressure
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experimental data in the NLR is limited because long-duration microgravity environment is needed to burn droplets of this large size. It should also be noted that there is a certain amount of scatter inherent in the experimental data reported by different researchers due to the different experimental techniques employed; for example, in dispensing the droplet, support fiber characteristics if used, ignition method (hot-wire or spark ignition), and residual drift velocities present when the droplet is freely deployed. Limited experimental data for n-decane, another sooting alkane fuel in air, show a similar trend K with D0 [15]. Thus one could assert that the general trend observed in Fig. 1 is valid for all sooting fuels, though more experimental data is still needed over a wide range of initial droplet diameters, particularly in the D2R region and NLR region.
D2 -Law Region: 0 < D0 < D1 Sooting and gas-phase radiative heat loss can be neglected in this region. The flame diameter Df is small (since Df ∼ D0 ) and the flame temperature remains relatively constant as the droplet burns. Sooting is absent due to insufficient residence time for the fuel molecules to pyrolyze and form soot. As long as quasi-steady burning takes place, K remains constant independent of the initial droplet diameter as predicted by the D 2 -law. However, property values, namely ρg Dg that appear in the burning rate expression, Eq. (2) must be evaluated at a suitable reference temperature to accurately predict the experimentally observed K values using Eq. (2) (see, e.g., [16]). The ability of numerical simulations [17] with infinite-rate gas-phase chemistry and no gas-phase radiation effects, but with variable property effects to accurately predict n-heptane burning rates seem to support this idea. It is interesting to note that inclusion of finite-rate chemistry in the numerical simulations [18] does not change the calculated burning rate constants appreciably adding further support to the applicability of D 2 -law in this region. Experimentally for n-heptane burning in air at 1 atm pressure D1 is estimated to be ∼ 0.45 mm [9, 11]. Clearly, among other things, D1 in general will depend on the environmental conditions, the fuel’s propensity to soot, and the fluid dynamics of the problem.
Boundary of the D2 -Law Region An estimate for D1 can be made using a semi-empirical model originally proposed by Saito et al. [19] for soot formation heights in gas-jet flames. Let S be a progress variable measuring the progress toward soot formation with S = 0 initially and S = 1 when yellow radiant emission begins. Assuming S obeys a one-step Arrhenius law we have, dS/dt = A exp[−E/RT (t)]
(5)
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where A is the pre-exponential factor with units 1/s, E is an overall activation energy, R the universal gas constant, and T (t) temperature which a fluid element experiences as it travels from the droplet surface toward the flame sheet. Integrating Eq. (5) gives, t1 1= A
exp[−E/RT (t)]dt
(6)
0
where t1 is the time at which soot appears. For large values of E/RT, the above shown expression can be approximated as 1 ≈ Aεe−1/ T1 /T (t1)
(7)
where T1 is the temperature at which soot radiation begins, T (t1) is the derivative of T with respect to time evaluated at t1, and = RT1 /E. In the following we assume that T1 is known a priori either from measurements or from detailed chemicalkinetic modeling of soot formation. Now we relate t to the radial co-ordinate r for a droplet burning under quasi-steady conditions. For quasi-steady combustion, using conservation of mass and the definition of K it can be shown that ' & r 3 8 ρgr02 −1 (8) t= 3 ρ1 K r0 where r0 is the droplet radius. As a zeroth-order approximation we assume the temperature inside the flame varies as T (r) = Tf −
(Tf − T0 ) (rf − r ) (rf − r0 )
(9)
where rf is the flame radius and T0 is the droplet surface temperature. Using Eqs. (8) and (9) T (t1) can be evaluated in terms of radial coordinates: # dT ## (Tf − T0 ) 8ρg K r0 2 = dt #t1 (rf − r0 ) ρlr0 r1
(10)
Combining Eq. (10) with Eq. (7) we obtain the following expression for the critical radial distance needed for soot formation, namely r1 2 =
1 K 8g
(Tf − T0 ) T1
e1/ A
1 (rf /r0 − 1)
(11)
For quasi-steady conditions the ratio rf /r0 is independent of ro . The critical droplet diameter D1 can now be specified as the diameter for which the flame diameter Df1 is greater than twice r1 , namely,
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( )1/2 l K e1/ 1 Tf − T0 Df1 = 2 8ρg ε A T1 (rf /r0 − 1)
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(12)
It is interesting to note that each factor in Eq. (12) signifies a specific mechanism: the first factor corresponds to a ratio of fluid dynamic or residence time and chemical reaction time for soot formation and can be considered as a Damk¨ohler number for soot formation, the second factor shows the temperature dependence, and the third factor is a geometric effect which is a function of fuel stoichiometry and ambient oxygen concentration (see, Eq. (4)). The droplet size associated with Df1 can then be expressed using Eq. (4) as ( 2 D1 =
)1/2 ρl K e1/ 1 Tf − T0 8ρg ε A T1 (rf /r0 − 1) ln(1 + B)/ ln(1 + Yo∞ /i)
(13)
When the initial droplet size D0 is greater than D1 soot begins to form and K is no longer a constant independent of D0 . Note that Eq. (4) is well known to over-predict the flame-to-droplet diameter ratios. As an alternative, simplified theoretical models that include distinct binary-diffusion coefficients [20] can be used in deriving Eq. (13) instead of Eq. (4).
Sooting Region: D1 < D0 < D2 Soot formation during droplet combustion is a complex process and comprehensive theoretical models capable of quantitatively predicting soot formation are not yet available [21]. This limits our understanding of how sooting influences the droplet combustion process. However, many plausible reasons have been proposed to explain the reduction in droplet burning rates due to soot formation. The two major mechanisms that have been proposed for the decrease of K are the reduction in the effective heat of combustion [10], and gas-phase radiative heat loss (both broadband and non-luminous radiation) [11] due to the presence of soot. The D 2 -law ignores both these effects and therefore the burning rate expression, Eq. (2), needs to be modified to predict the correct burning rate. Note that the burning rate expression in the classical model Eq. (2) is derived without any regard to the flame temperature or the flame position [22] and as such it should remain the same as long as the chemical heat release implicit in the D 2 -law model takes place within the combustion zone surrounding the droplet. Assuming that the reduction in chemical heat release due to soot formation is the primary cause in lowering experimentally observed K values, we can correct Eq. (2) and write it as K = 8Dg (ρg /ρ1 ) ln(1 + Q(1 − f s )Yo∞ /i L)
(14)
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where f s = (Q lost /Q) is the fraction of the energy lost due to incomplete combustion (soot formation) of unit mass of fuel. In the above we have assumed that B ≈ QYo∞ /i L. The fraction f s is small since it is proportional to the amount of soot formed during combustion. Choi and co-workers have measured soot volume fraction during the combustion of n-heptane in air at atmospheric pressure. Less than 2% of the fuel consumed is turned into soot during quasi-steady n-heptane droplet combustion [11, 13]. For small f s values Eq. (13) can be approximated as K = 8Dg (ρg /ρl ) [ln(1 + B) − f s QYo∞ /i L(1 + B)] = K D2R − 8 f s Dg (ρg /ρl )B/(1 + B) (15)
where K D2R is the burning rate constant in the D2R zone. Estimating f s ∼ 0.02 and B ∼ 6 for heptane burning in air the reduction in burning rate predicted by Eq. (14) is much smaller than what is observed in experiments and shown in Fig. 1. Thus we conclude that the reduction in chemical heat release is not the primary cause for the observed decrease in K in the sooting region. Now we examine the effect of radiative heat loss from the flame zone as the possible mechanism for reduction in K . The overall instantaneous radiative heat loss form the flame can be expressed as [23], ˙r≈ Q
rf r0
2 r02 εg σB Tf4 ∝ r03 Tf4
(16)
where εg is the total engineering emissivity which for a thin gray gas is roughly proportional to the droplet radius due to its dependency on the optical path length. Note that Eq. (16) holds good irrespective of whether band radiation or continuum radiation due to soot is present, since the sooting region scales with D0 just as the flame location, as seen from the experimental correlations for soot-shell standoff ratios [2, 10]. Again, if we argue that radiative heat loss contributes to the decrease in K by reducing the effective heat of combustion Q, according to Eq. (14) K should decrease much less than what is experimentally observed due to the logarithmic dependency of K on Q. However, radiative heat loss can indirectly affect the burning rate through the temperature dependency of ρg Dg in Eq. (2). The reduction in gas-phase temperature due to radiative heat loss can be estimated by balancing the instantaneous heat ˙ r . The instantaneous heat release rate at the flame is given by release rate and Q ˙ c ≈ 1 πρl Q K r0 Q 2
(17) 1/2
Equating Eqs. (15) and (16), we find that Tf ∼ 1/D0 . Since ρg Dg is approxi1/4 mately proportional to T 1/2 [16], ρg Dg ∼ 1/D0 . Then from Eq. (2), neglecting reduction in effective heat release due to soot formation and radiative heat loss, we −1/4 have K ∼ D0 . The −1/4 power dependency of K on D0 is more reasonable and closer to the experimental value of approximately −0.24. Thus we conclude that the dominant cause for the decrease in burning rate is the lowering of ρg Dg
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through its temperature dependency. However, when heavy sooting occurs, both thermophysical property variation and the reduction in the effective heat of combustion could play a role as evidenced by the steeper slope as D0 approaches D2 in Fig. 1. As D0 exceeds D2 , the flame temperature drops below the threshold temperature for soot formation due to radiative heat loss, and sooting stops. For heptane a blue flame is observed around the droplet without the orange emission from soot. For heptane burning in air D2 is approximately 2 mm as seen from Fig. 1.
Non-Luminous Radiative Loss Region: D2 < D0 < D3 In this region radiant emission is primarily spectral due to radiating species such as CO, CO2 , and H2 O. Numerical calculations with spectral radiative loss (not including soot) for heptane burning in air show that the flame temperature is reduced by as much as 300 K [12]. The argument that radiative heat loss is proportional to D0 3 , presented in the previous section, is still valid, except that the total amount of heat loss is reduced due to the absence of continuum radiation. Again, following the arguments presented earlier, we see that the primary cause for reduction in K is due to the lowering of ρg Dg by the reduced flame temperatures caused by radiative heat −1/4 loss. In other words, in this region the K should decrease as D0 . Figure 1 shows that this is reasonable though there is not enough data to form a strong correlation for large droplet sizes. It should also be noted here that as the initial droplet size becomes larger than D2 , the burning rate constant jumps to a higher value compared to the SR region and then reduces as the droplet size further increases. This initial jump in K is due to the reduction in energy loss without the continuum soot radiation. The details of the transition from sooting to non-sooting region needs further study. When D0 reaches a critical diameter D3 , the radiative heat loss becomes substantial and quasi-steady combustion is no longer possible. The flame grows to a certain size and then extinguishes abruptly before full contraction. Experimentally this type of behavior has been observed for large alkane droplets as well as alcohol fuels [1, 2]. Chao et al. [24] have developed an activation-energy asymptotic model that predicts the extinction diameter due to radiative heat loss.
Concluding Remarks We have examined the dependence of burning rate constant for an alkane fuel on its initial diameter. When the droplet diameter is less than a critical value D1 there is no sooting and the radiative heat loss from the flame zone is negligible. Under these conditions the burning rate constant remains fixed, independent of the initial diameter. When D0 exceeds D1 sooting begins and the burning rate is suppressed due to lower values of the transport properties within the flame zone. The reduction in the effective heat of combustion due to soot formation is not a major factor. In this
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region K decreases approximately as D0 , consistent with the scaling arguments presented here. For D0 greater than D2 , a critical diameter above which sooting stops due to lowering of the flame temperature below the sooting threshold, nonluminous radiation causes the observed decrease in K . Scaling arguments show that −1/4 this decrease should as D0 . Clearly, our knowledge of soot formation and its interaction with droplet burning process is not complete. More experimental measurements of droplet burning as well as theoretical and numerical model studies are needed to further improve our understanding. Acknowledgments This work was supported by the NASA Microgravity Combustion Science Program.
References 1. D.L. Dietrich, J.B. Haggard, Jr., F.L. Dryer, V. Nayagam, B.D. Shaw, F.A. Williams, Proceedings of the Combustion Institute, 26 (1996) 1201–1207. 2. V. Nayagam, J.B. Haggard, Jr., R.O. Colantonio, A.J. Marchese, F.L. Dryer, F.A. Williams, AIAA J., 36 (1998) 1369–1378. 3. F.A. Williams, F.L. Dryer, Science requirements document for the droplet combustion experiment, NASA Lewis Research Center, Cleveland, Ohio (1994). 4. W.A. Sirignano, “Fluid dynamics and transport of droplets and sprays,” Cambridge University Press, 1999. 5. F.A. Williams, Second International Symposium on Scale Modeling, Lexington, Kentucky (1997) 147–163. 6. G.A. Godsave, Proceedings of the Combustion Institute, 4 (1953) 818–830. 7. D.B. Spalding, Proceedings of the Combustion Institute, 4 (1953) 47–865. 8. F.A. Williams, J. Chem. Phys., 33 (1960) 133–144. 9. H. Hara, S. Kumagai, Proceedings of the Combustion Institute, 25 (1990) 423–429. 10. G.S. Jackson, C.T. Avedisian, Proceedings of Royal Society of London A, 446 (1994) 255–276. 11. K.O. Lee, S.L. Manzello, M.Y. Choi, Combust. Sci. Tech., 312 (1998) 139–156. 12. A.J. Marchese, F.L. Dryer, V. Nayagam, Combust. Flame, 116 (1999) 432–459. 13. S.L. Manzello, M.Y. Choi, A. Kazakov, F.L. Dryer, R. Dobashi, T. Hirano, Proceedings of the Combustion Institute, 28 (2000) 1079–1086. 14. M.D. Ackerman, R.O. Colantonio, R.K. Crouch, F.L. Dryer, J.B. Haggard, G. Linteris, A.J. Marchese, J.E. Voss, F.A. Williams, B.L. Zhang, NASA/TM-2003-212553 (2003). 15. J.B. Haggard, Jr., M.H. Brace, F.L. Dryer, M.Y. Choi, F.A. William, J. Card, AIAA-90-0649, 28th Aerospace Sciences Meeting, Reno, Nevada, 1990. 16. C.K. Law, F.A. Williams, Combust. Flame, 19 (1972) 393–405. 17. I.K. Puri, P.A. Libby, Combust. Sci. Tech., 76 (1991) 67–80. 18. G.S. Jackson, C.T. Avedisian, Combust. Sci. Tech., 115 (1996) 125–149. 19. K. Saito, F.A. Williams, A.S. Gordon, Combust. Sci. Tech., 47 (1986) 117–138. 20. I. Aharon, B.D. Shaw, Microgravity Sci. Technol., 10 (1997) 75–85. 21. C.T. Avedisian, J. Propulsion and Power, 16 (2000) 628–635. 22. Glassman, Combustion 2nd Edition, Academic Press, New York, 1987. 23. A.J. Marchese, F.L. Dryer, Combust. Sci. Tech., 124 (1997) 371–402. 24. B.H. Chao, C.K. Law, J.S. T’ien, Proceedings of the Combustion Institute, 23 (1990) 523–531.
Modeling of Combustion Phenomena Forman A. Williams
Abstract Scale modeling of combustion phenomena is considered in different contexts, ranging from power production by fossil fuels to damage by hostile fires. Since descriptions of combustion require a relatively large number of nondimensional groups, combustion modeling is comparatively challenging. Rather than viewing this difficulty as a source of despair, the complexity can be considered to provide a wider range of options for extracting worthwhile information from careful observations performed in experiments designed on the basis of alternative approaches to scale modeling. Combustion offers more possibilities for utilization of inaccurate “partial modeling” for enhancing understanding. Specific examples addressed include cold-flow modeling, Froude-number scaling, pressure modeling and microgravity droplet combustion. Through these examples it is concluded that a rich variety of advances can be made by modeling of combustion phenomena. Keywords Scale modeling · combustion · fire · droplet burning
Nomenclature Ak cl cp c pi Di j Ek g h i0 K ck L Lα mi
Pre-exponential frequency factor for kth reaction Heat capacity per unit mass for fuel l Specific heat at constant pressure for gas mixture Specific heat at constant pressure for species i in the gas Binary diffusion coefficient for species i and j Activation energy for kth reaction Magnitude of body force per unit mass Standard enthalpy of formation per unit mass for species i at T0 Equilibrium constant for concentrations, for kth reaction Characteristic length measuring the overall size of the system Other geometrical lengths, α = 1, 2, . . . Molecular weight of species i
F.A. Williams Center for Energy and Combustion Research, Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, La Jolla, CA 92093 K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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M N p q¯ T Q R tb T T T0 Tl νw V V¯ i T W Yi Yl ⌫ Δh l κ¯ ν λ μ νik νik
ρ σ σ¯ ν τ¯T
F.A. Williams
Total number of chemical reactions occurring Total number of chemical species present Hydrostatic pressure Representative turbulent heat flux Gas-phase heat released per unit mass of fuel gases consumed Universal gas constant Burning time Temperature Vertical temperature gradient A fixed standard reference temperature Gasification temperature for fuel l Wind velocity Characteristic mass average velocity of the gas mixture Representative turbulent diffusion velocity of species i Fuel loading (weight of fuel per unit area) Mass fraction of chemical species i in gas Mass fraction of chemical constituent l in fuel, also other pertinent dimensionless fuel-type and fuel-density parameters not easily included in either W or La Magnitude of ambient swirl vorticity vector Heat of gasification per unit mass for fuel l Average absorption coefficient per unit mass for radiation Thermal conductivity coefficient Viscosity coefficient Stoichiometric coefficient for species i appearing as a reactant in Kth reaction Stoichiometric coefficient for species i appearing as a product in Kth reaction Density of the gas mixture Stefan-Boltzmann constant Average scattering coefficient per unit mass for radiation Representative turbulent stress
Subscripts a ad i j k l T w α ν
Ambient atmosphere Adiabatic; identifies adiabatic lapse rate of the atmosphere A chemical species in the gas ( i = 1, 2, . . . , N) A chemical species in the gas ( j = 1, 2, . . . , N) A chemical reaction (k = 1, 2, . . . , M) A type of fuel or a chemical constituent of a fuel (l = 1, 2, . . .) Turbulent Wind A geometrical quantity (α = 1, 2, . . .) Frequency of radiation
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Introduction At the dawn of civilization, humankind became distinguished from other biological forms through the desire to comprehend, both individually and collectively. Understanding is sought for its own sake, as well as for use to improve the quality of life. Scale modeling, the design and performance of experiments at different scales to obtain information about a prototype, is one of numerous human activities pursued to acquire understanding. The information gained is employed for engineering, namely to develop better devices, structures, processes or systems, or sometimes only for enhancing comprehension of phenomena, possibly to be put to later use. Scale modeling of combustion phenomena has been undertaken with both of these objectives in mind. It is one of the most versatile and least straightforward activities in scale modeling, as the present paper attempts to demonstrate. The basic principles of scale modeling are well known [1]. Although various approaches exist, they all ultimately involve identifying nondimensional groups of the relevant dimensional parameters and attempting to keep the values of these groups equal for the model and the prototype. If a complete set of equations is available that fully describes the phenomenon of interest, then, in principle, all of the groups can be obtained by nondimensionalizing the equations. If complete equations are not available, then guesses must be made about what processes are at work in order to obtain the parameters needed to form the nondimensional groups, and there will be greater uncertainty in the resulting scaling laws. Comparisons of results of model experiments with the behavior of the prototype, by use of the scaling laws, can then test the initial guesses or, indeed, test whether the set of equations is correct, if the approach is one that began with equations. Careful observation of the model thereby enhances understanding. For combustion phenomena, an underlying set of differential equations is available [2]. Nondimensionalization of these equations and their associated boundary conditions results in 17 types of nondimensional groups [3]. Introduction of additional fuel-property, atmospheric and radiative groups relevant to mass fires brings the total number of different types of relevant nondimensional groups to 29 [4]. In either event, there are too many independent groups for the model and prototype to have the same values of all of them. This is the source of the complexity in scale modeling of combustion phenomena. The inability to preserve all potentially relevant dimensionless groups in scale modeling has been known for a long time in combustion. This has led to the concept of partial modeling [5], as much an art as a science, for use in extracting desired understanding. In partial modeling, the modeling laws dictated by certain dimensionless groups are purposely ignored; only the laws associated with a subset of the groups are respected, so that only partial rather than full modeling is achieved. This is undesirable in that evident behavioral differences are anticipated in the model, as compared with the prototype. Use may nevertheless be made of observed differences to increase understanding. There is, furthermore, an added versatility, involved in the selection of which groups are to
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be respected. More than one kind of scale modeling experiment can be studied. Combustion phenomena can thus be subjected to a wide variety of partial scale modeling.
Limits That Reduce the Number of Nondimensional Groups Table 1 lists one possible set of nondimensional groups for combustion and fire phenomena. Most of the groups that appear in the table must be discarded, to be able to proceed with scale modeling. There are limiting situations in which various groups become irrelevant. For example, for steady states, the first, 0 plays no role, and in quiescent atmospheres that are not at very large scales, the last three, 26 , 27 , and 28 , do not appear. When radiation is unimportant, it is unnecessary to include 4 , 5 , and 8 , which can be viewed as a limit in which 18 approaches zero. Simplifications occur as 6 approaches zero or infinity, corresponding to limits of small or large Reynolds numbers, the latter usually producing turbulent flows, although there is also a limit of large Reynolds numbers for laminar flows. In the limit of large Froude number, 2 approaching zero, buoyancy becomes unimportant. The limit of low Mach number, in which 3 , approaches zero, reduces the relevance of 1 , for example, for some problems. There are simplifications associated with Prandtl, Schmidt and Lewis numbers being unity. Large Damkohler numbers can provide chemical equilibrium in some situations, removing 13k and 14k from the set of groups. There are a number of other limits in which many of the groups become irrelevant, reducing the number of choices to be made in partial modeling.
Cold Flow Modeling Perhaps the simplest combustion modeling involves no change in scale dimensions at all but rather merely elimination of combustion, for example by not injecting fuel or not igniting it. This has the advantage of affording easier approaches to measurement and access for instrumentation. It violates constancy of virtually all of the nondimensional groups that are of primary importance, such as Mach numbers, Reynolds numbers, Froude numbers and Damkohler numbers, maintaining potential constancy of only 0 , 7 , 19␣ , 20 , 26 , and 27 of Table 1. Keeping 0 and 20 constant means keeping the “burning time” tb constant by artificially controlling injection flow rates. For modeling time-dependent processes such as fires, all six of these groups are relevant, while steady flows in combustion and furnaces do not involve 0 . Despite the many inadequacies of this partial modeling, it can be useful for identifying possible flow patterns in complex configurations. It applies only under momentum-controlled situations of sufficiently high Reynolds numbers and low
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Table 1 Dimensionless groups relevant to scaling of combustion phenomena and of fires Dimensionless group
Physical meaning
0 = L/V tb
A measure of the flow-field unsteadiness caused by factors other than turbulence. A measure of the ratio of specific heats, ␥. A buoyancy quantity related to reciprocal Froude number, Fr (and therefore related to Grashof number, Gr, through Reynolds number). A quantity proportional to the square of the Mach number, M, and related to the scale height of the atmosphere through 1 and 2 . Ratio of characteristic dimension to radiation absorption length.∗ Ratio of characteristic dimension to radiation scattering length.∗ Reciprocal of the Reynolds number, Re. Ratio of effective turbulent stress to dynamic pressure. Reciprocal of the Prandtl number, Pr. Ratio of effective turbulent heat flux to rate of convection of enthalpy. Schmidt number, Sci j , for species pair i, j. Ratio of effective turbulent diffusion velocity to characteristic velocity. Ratio of molecular weight of species i to molecular weight of ambient air.
1 = pa /ρa c pa Ta 2 = gL/V 2 3 = V 2 /cρa Ta 4 = Lρa ¯ v 5 = Lρa ¯ v 6 7 8 9
= a /ρa V L = ¯ T /ρa V 2 = a /a c pa = q¯ T /ρa V c pa Ta
10i j = a /ρa Di ja 11i = V¯ i T /V 12i = m i pa /ρa R Ta
13k = (L Aka /V )(R Ta / pa ) 14k = (E k /R Ta )
N *
i=1
vik −1
N *
[ (vik −vik )] 15k = K cka ( pa /R Ta ) i=1 16 = Q/cρa Ta
16i = h i0 /cρa Ta 17l = c pia /c pa 18 = Ta3 /ρa V c pa 19␣ = L ␣ /L 20 = W/ρa V tb 21l = Yl 22l = cl /c pa 23l = Tl /Ta 24l = Δh l /c pa Ta
Ratio of flow time to chemical time for reaction k, reciprocal of Damk¨ohler’s first similarity group DI for reaction k. Dimensionless activation energy for kth reaction. Dimensionless equilibrium constant for kth reaction. Dimensionless gas-phase heat of combustion, a simplification of 16 i Ratio of enthalpy of formation of species i to ambient thermal enthaply. Ratio of specific heat of species i to specific heat of ambient atmosphere. Ratio of blackbody radiation flux to rate of convection of enthaply. Ratios of lengths specifying details of geometrical configuration to characteristic length. Ratio of time-average mass burning rate per unit area to convective mass flux. Dimensionless fuel composition parameters reflecting fuel type, moisture content, etc. Dimensionless heat capacities for fuel consitutuents. Dimensionless gasification temperatures for fuel constituents. Dimensionless heats of gasification for fuel consituents. (continued)
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Dimensionless group
Physical meaning
24 = [cl (Tl − Ta ) + Δh l ]/c pa Ta
Effective dimensionless total heat required to gasify a unit mass of fuel, a simplification of 22l , 23l and 24l . Dimensionless ambient atmospheric composition parameters (e.g., humidity). Dimensionless ambient wind velocity.∗∗ Dimensionless ambient circulation (swirl).∗∗ Dimensionless ambient atmospheric lapse rate parameter determining atmospheric stability.∗∗
25i = Yia 26 = vw /V 27 = Γ L/V 28 = Ta /Tad
∗ For each of these quantities it is better to specify a distribution (over radiation frequency) rather than to specify merely a single number. ∗∗ For each of these quantities it is better to specify a distribution (over position) rather than to specify merely a single number.
Mach numbers, generally in turbulent flows. Constancy of the turbulent parameter 7 often is maintained naturally, closely enough, at high Reynolds numbers. One early example [6] concerns flow measurements in gas-turbine combustors, illustrated in Fig. 1. Transverse velocity profiles in the primary zone were measured with pitot instrumentation for both water and air flow and also by flow visualization in water flow employing bubbles as tracers [6], in a transparent full-scale model, with the results shown in Fig. 2. Not only is reasonable agreement seen in the velocity profiles, but also the qualitative information in Fig. 1 is helpful conceptually. Although there are many differences in detail under hot-flow conditions, the cold-flow observation can help in improving understanding.
Fig. 1 Representative diagram of the flow pattern in an axial plane of a gas-turbine combustor, revealed by bubble-tracer studies in water flow [6]
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Fig. 2 Comparisons of cold-flow transverse profiles of mean axial velocities in the primary zone of the combustor of Fig. 1, from pitot measurements in air and in water and from bubble-tracer studies in water [6]
Simple Scale Reduction Since large systems are expensive to study at full scale, modeling based on scale reduction maintaining geometrical similarity (19␣ fixed) can be useful for economically acquiring insight into combustion behavior. This approach is especially attractive for large fires. A classical study of this type for pool fires [7] employed pan diameters ranging from 22.9 m to 3.7 mm, spanning nearly four orders of magnitude, clearly demonstrating size dependences of combustion behavior, as illustrated in Fig. 3, resulting from interchanges of different controlling nondimensional groups. Many properties vary with scale in such modeling. Good correlations can, however, be obtained for judiciously selected properties. Figure 4 can be considered to be an example of a successful correlation; here the time dependence of the radiant energy flux received by radiometers located at geometrically scaled positions is
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Fig. 3 Dependence of the measured quasisteady burning rate on the pan diameter for pools of liquid hydrocarbon fuels in quiescent air [7]
Fig. 4 Time dependence of the irradiance E received by radiometers at geometrically scaled positions five pan diameters from the center of the pan, for burning hexane pools in pans of two different diameters in the turbulent-flow regime [8]
shown for hexane pool fires in pans of two different diameters [8], with the initial liquid depth kept the same for each pan to maintain an approximately constant burning time. This result demonstrates that there are some relationships which do not depend strongly on the controlling physical and chemical mechanisms of combustion.
Froude Number Scaling Many combustion processes in the atmosphere, especially open fires, are largely dominated by the Froude-number groups 2 . This leads to the concept of Froude number scaling, in which the model and prototype have the same value of the nondimensional group 2 , or, more precisely, of the generalization thereof in which g is multiplied by the ratio of a density difference to a characteristic density, better reflecting the ratio of buoyant to inertial forces. With this scaling, when density fields are unchanged, at fixed g the velocities are proportional to the square root of the length, as is evident from the expression for 2 in Table 1. Figure 4 actually involves Froude-number scaling because wind velocities were applied in these particular experiments, keeping 26 fixed based on this scaling; if there had been no wind, then results like Fig. 4 would not rely on Froude-number scaling.
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Froude-number scaling has been employed successfully for crib fires as well [8], and it has been extended to the reconstruction of fire whirls for specific accident scenarios [9]. It can work well for heat transfer in pool fires [10]. An attractive and useful recent fire-spread review including the subject is available [11]. Froude-number scaling also applies to heights of turbulent diffusion flames, as illustrated in Fig. 5 [12], and it has been extended as well to production rates of oxides of nitrogen in turbulent-jet diffusion flames [13], a topic of interest not for fire safety but rather for air pollution. In this last application, summarized in Fig. 6, it works mainly because the pollutant production is a finite-rate, mainly irreversible chemical process whose overall rate is not too strongly dependent on the particular fuel (except for hydrogen and mixtures of hydrogen and carbon monoxide which, lacking the “prompt” mechanism and therefore restricted to the “thermal” mechanism, produce points lying low in Fig. 6). The total rate of pollutant production then becomes proportional to the volume of the turbulent flame, which scales with the Froude number because it is controlled by buoyancy. This last example helps to illustrate how remarkably widely Froude-number scaling can apply to combustion phenomena. Figures 5 and 6 contain information beyond the statement that Froude-number scaling applies. They show the functional dependences of certain “output” quantities, namely h in Fig. 5 and E in Fig. 6, on the Froude number. Since Froudenumber scaling could be valid irrespective of what these dependences might be, the dependences themselves give further information about modeling the combustion processes in question. Theoretical models can be developed for predicting these dependences (and, indeed, have been developed for the curves in Figs 5 and 6), and comparison of theory with experimental results at different values of 2 then tests the theory. This extension of scale modeling, to determine dependences on
Fig. 5 Ratio of the average flame height h to the horizontal scale for turbulent diffusion flames of different sizes, as a function of the ratio of the square of the fuel burning rate per unit area m (g/cm2 s) to the length (cm), which is approximately proportional to a Froude number, 1/2 , illustrating Froude-number scaling of flame heights [12]
F.A. Williams
Eρ0u0/d0 (g/m3s)
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10
5
10
4
C3H8, Buriko & Kuznetsov
Theory, 44Fr3/5
C3H8, Takagi et al. C3H8, Turns & Lovett C3H8, Turns & Myhr C3H8, Roekke et al. C3H8, Present study CH4, Present study
10
3
CH4, Turns & Myhr CH4, Chen & Driscoll C2H4, Turns & Myhr CO/H2, Turns & Myhr H2, Chen & Driscoll H2, Lavoie & Schlader H2, Bilger & Beck
10
2
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1
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2
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3
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4
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6
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7
Froude number
Fig. 6 The measured emission index E for oxides of nitrogen (g NO2 /kg fuel), scaled by the exit density ρ0 , exit velocity u 0 and exit diameter d0 of the turbulent fuel jet, as a function of the Froude number, l/2 , for a number of different fuels, as found by a√number of different investigators [13]; in scale √ modeling with ρ0 fixed and u 0 proportional to d0 so that 2 is fixed, it is not E but rather E/ d0 that will be the same for the model and the prototype according to this figure, demonstrating that suitable scaling in general must be applied to the “output” property of interest, as well as to the “input” properties controlled by the modeler performing the scaling
nondimensional modeling parameters, is worthwhile for advancing combustion science and engineering.
Salt Water Modeling A technique for observing buoyancy-driven flows is to work with dyed mixtures of fresh and salt water or of other miscible liquids [11]. The approach relies on Froudenumber scaling and is restricted to turbulent-flow regimes. It has been applied in scale modeling of thermally produced fire and smoke plumes for fires in enclosures. An underlying theory is available [14], as well as experimental modeling results [15]. Both ceiling jets and comer fires have been studied in this manner [11]. In principle, travel of smoke and hot gas through multiple compartments can be scalemodeled well by this technique, as continuing research is demonstrating [15].
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Pressure Modeling Froude-number scaling involves changes only in scale and applied gas velocities, with velocities proportional to the square root of the length scale. Especially when interactions between gaseous and condensed phases are important, this approach suffers modeling deficiencies as a consequence of its failure to keep certain other relevant nondimensional groups constant. The most important of these other groups usually is the Reynolds number. Combustion experiments have been performed in which both the Froude number and the Reynolds number are held fixed, through scale adjustment not only of the velocity, to keep 2 constant (if external velocities are imposed) but also of the density ρa , to keep 6 constant. The viscosity μa is independent of pressure p, but the density ρa is proportional to p, and therefore if the product p 2 L 2 remains invariant (as well as V 2 /L), then both 2 and 6 are fixed. Experiments based on this so-called “pressure modeling” are very attractive for scale modeling of fires [16]. Laboratory-scale fires at high pressure often accurately model large-scale fires at normal atmospheric pressure when the proportionalities p ∼ L −3/2 and V ∼ L 1/2 are enforced. It is also appealing to observe resulting miniature turbulent diffusion flames having all of the apparent scaled-down characteristics of large turbulent diffusion flames in fires. Figure 7 illustrates the kinds of burning-rate correlations achievable with pressure modeling. This figure applies for horizontal pools of polymethyl methacrylate, illustrated in the figure [17]. Corresponding correlations were obtained for vertically oriented fuels, for fuel elements of different shapes and for different combustible materials [16, 17]. The Grashof number Gr, proportional to the square of a Reynolds number divided by a Froude number, 2 26 is held fixed in this scale modeling. Figure 7 shows how the nondimensional burning rate depends on this nondimensional scaling parameter. When the flow velocities are all generated internally and not applied externally, as is the situation in the pressure modeling experiments that have been performed, neither the Froude number nor the Reynolds number plays a separate role, and pressure modeling then reduces to Grashof-number scaling, quite analogous to the Froude-number scaling discussed previously. It can be reasoned that, provided that Damkohler numbers are large enough for finite-rate chemical kinetics to be unimportant, and radiant heat-transfer fluxes are either unimportant or proportional to combustion rates, then this pressure modeling (or Grashof-number scaling) scales not only the gas-phase and relevant condensedphase behavior but also the turbulence [16]. There are conditions under which flame spread, as well as steady burning, can be modeled in this way. Besides finiterate chemistry, radiation phenomena can contribute to inaccuracy of this pressure modeling. It has been observed [4] that 2 and 4 (as well as 5 ) might be kept constant by making p ∼ L −1 , while 2 and 18 are constant when p ∼ L −1/2 , and therefore radiation effects scale at least in the same general direction needed for pressure modeling. Perhaps keeping p ∼ L −n with 1/2 < n < 2 can often provide even better scaling of both convective and radiative heat transfer in combustion.
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103 Symbol
p(atm) 5–10 10–20 20-30 30-37
⎫ ⎪ ⎬ ⎪ ⎭
L = 5 – 25 cm m" = m / L2
m" L/µw
p = 5 – 38 atm L = 7.3 cm 1/3 Slope
⎫ ⎪ Circular ⎬ Pools ⎪ ⎭
102 p = 1 atm L = 23 – 122 cm
PMMA Pool
L
GrL = 1.457 x 104 ρ2L3 µ = 3.215 x 10–4 (g/cm s)
10
108
109
1010
1011
1012
Gr L
˙ Fig. 7 The nondimensional burning rate m¯˙ L/μw = m/Lμ w where m denotes the mass loss rate of fuel, L the horizontal width of the pool and μ the gas viscosity at the fuel surface, as a function of the Grashof number Gr L = gL 3 ρa2 Ta (T f − Ta )/(Tw2 pa μ2w ), where T f is the flame temperature taken to obey (T f − Ta ) = 6Ta , and Tw the gas temperature at the burning fuel surface taken to be 673 K, measured for pool fires of polymethyl methacrylate (PMMA) at different pressures, illustrating pressure modeling [17]
Other Scaling Ideas Scaling possibilities abound well beyond pressure modeling. Instead of changing pressure, consideration can be given to changing ambient temperature or molecular weight [4]. By varying the speed of sound, such changes could provide a
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basis for Mach-number scaling of compressible flows, that is, keeping 3 constant. Damkohler-number scaling also can be considered by focusing attention on 13k for flows not in chemical equilibrium, addressing variation of pressure or temperature. An alternative to velocity variation in Froude-number scaling is to vary g, the acceleration of gravity. Increasing g with decreasing L, as approximated by experiments in a centrifuge, can keep 2 fixed even if V is constant [18]. In general, each new element of parameter control enables additional nondimensional groups to be held fixed, and therefore the centrifuge approach can be considered for maintaining invariance of both convective and radiative transfer, for example, especially if coupled with suitably extended pressure modeling [4]. Opposite to increasing g is to decrease it, as is done in microgravity combustion experiments. At sufficiently small values of g, the group 2 can be omitted from Table 1, thereby simplifying scaling problems. A great deal of research currently is being pursued on microgravity combustion modeling [19]. Part of this work concerns microgravity droplet combustion [20]. As an illustration, it will be worthwhile to describe one particular problem in droplet combustion.
Microgravity Droplet Combustion Because of practical interest in the combustion of fuel sprays in air, studies have been performed on the burning of single, isolated fuel droplets, a process that often occurs in spray combustion. Sufficiently small individual droplets are influenced negligibly by buoyancy when they burn, but experimentally it is difficult to isolate and observe a single small droplet as it burns. It is easier in the laboratory to work with larger droplets, about 1 mm in diameter, in experiments on droplet combustion. The combustion of such large droplets is, however, affected appreciably by buoyancy. For this reason, experiments on droplet combustion were performed in freely falling chambers, to reduce influences of earth gravity [21]. The results can help in interpreting how individual droplets burn in dilute sprays. Different liquid droplet fuels burn differently. Unlike most other fuels, methanol absorbs appreciable amounts of water as it burns. Water is fully miscible with methanol, and water produced by the combustion in the flame surrounding the droplet diffuses back to the liquid and is absorbed during combustion. This absorption influences the droplet combustion history in a number of ways. After sufficient water accumulates in the liquid, it begins to vaporize along with the fuel, and the consequent reduction in the amount of heat released per unit mass of liquid vaporized reduces the buming rate of the droplet. In addition, in roomtemperature atmospheres droplets extinguish when they become sufficiently small that the residence time is less than the chemical conversion time (the grouping 13k e−14k Ta /T f / 6 8 , a Damkohler number DII , formed from the nondimensional reaction rate D I e−14k Ta /T f and a Peclet number 1/6 8 becomes too small), and water vaporization along with the methanol reduces the flame temperature T f , thereby strongly reducing DII and leading to extinction for larger droplets.
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Fig. 8 Comparison of theoretical and experimental extinction diameters for methanol droplets burning in normal atmospheric air; the solid line is the result of numerical integrations and the dashed lines are the results of simplified theory for three different initial water mass fractions Y0 of the liquid, while the open circles are results of experiments in freely falling chambers and the solid circles results of spacelab experiments
Theoretical modeling predicts that this droplet diameter at extinction increases roughly linearly with increasing initial droplet diameter, as shown in Fig. 8. In this respect, methanol droplet combustion is qualitatively quite different from the combustion of other liquid fuels, whose extinction diameters are predicted to be nearly independent of the initial diameter in this size range. Extinction diameters for methanol droplet combustion predicted by full numerical integrations and by simplified theoretical modeling are in good agreement, as the solid and dashed curves in Fig. 8 indicate [20]. A few data on extinction diameters were obtained in freely falling chambers and are shown by the open circles in Fig. 8. These results agree well with prediction. Measurements at initial diameters smaller than these are impractical, but the prediction can be tested by measurements for larger initial diameters. Freely falling chambers do not allow sufficient time
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for complete combustion of larger droplets. Therefore predictions were tested by burning droplets in an experiment performed in spacelab [20]. The results, shown by the solid points in Fig. 8, verify the predicted increase of extinction diameter with increasing initial diameter, but the values of the observed extinction diameters are larger than predicted. A possible explanation is absorption of water by the fuel from the natural humidity of the spacelab as the large droplets were formed, prior to ignition. Calculations for droplets initially containing 20 percent water by mass (Y O = 0.2) are seen in Fig. 8 to agree well with the spacelab measurements. This is an example of scale modeling in which the size of the model is larger than that of the prototype, and the increased size revealed an effect (possible water absorption before ignition) not evident from experiments at smaller scales.
Fires in Enclosures There is strong motivation for developing techniques for scale modeling of fires in enclosures because of the expense of full-scale testing. Interest focuses not only on steady burning but more importantly on fire histories, especially the question of whether flashover occurs, that is, whether the enclosure suddenly becomes fully involved in flames. For situations exhibiting flashover, the time from ignition to flashover is of great practical importance. Complexities of time-dependent fires in enclosures cause modeling of flashover times to be particularly challenging. Only limited scaling success has been achieved [22]. Although there have been some investigations at one-eighth scale, it is more common to study enclosure fires at one quarter scale because model behavior departs too strongly from that of the prototype beyond that degree of scale change. Even tests at one-quarter scale afford some economic advantage. A fundamental difficulty in scale modeling of fires in enclosures stems from the fact that such fires often become ventilation-controlled, that is, the burning rate becomes dependent on the rate of air supply into the enclosure. If the enclosure has an opening of area A and height H , then mass and momentum balances show √ that the total rate of consumption of fuel within the enclosure is proportional to A H under ventilation-controlled conditions [12]. On the other hand, Figs. 3 and 7 indicate that under turbulent conditions this rate of fuel consumption is approximately proportional to the square of the fuel surface area, L 2 , when there is sufficient air that the burning is fuel-controlled rather than ventilation controlled. If all dimensions are decreased proportionally, to keep 19␣ of Table 1 fixed, then the total fuel mass-loss rate is seen to be proportional to L 5/2 under ventilation-controlled conditions and to L 2 otherwise. The scaling of the burning rate therefore depends on whether the combustion is ventilation-controlled. There are ways to try to circumvent this inconsistency. For example, √ for rectangular openings of area A = B H , the width B may be scaled as L, instead of L, to achieve identical burning-rate scaling under fuel-controlled and ventilation controlled conditions. Although this may be desirable for some purposes, for other
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purposes it would be detrimental. For typical fires in enclosures that begin fuel controlled and later become ventilation-controlled, scaling of the time to ventilation control would be affected by this scaling modification. Flashover may occur under fuel-controlled or ventilation-controlled conditions, and even in the former circumstance, the smaller interior model wall area under the revised scaling may affect the time to flashover, while influences on flashover also are to be anticipated under the latter circumstance. Despite these difficulties, some progress has been made on scale modeling of enclosure fires [22–24]. The importance of radiative energy transfer and the influence of soot on radiation have been documented in this work. Although enclosure fires have not been investigated by pressure modeling, consideration of that approach could afford greater freedom. Use of a large pressure chamber at the end of the arm of a centrifuge would provide even greater possibilities for improved modeling, perhaps even allowing flashover times to be scaled. These potential advantages, however, need to be weighed against increased costs that ultimately could lead to scale modeling becoming more expensive than full-scale tests of prototypes.
Concluding Remarks The discussions that have been given here do not constitute a thorough review. In particular, there are many relevant references that have not been cited, although further entries into the literature can be found in some of the references that are given. The examples that have been selected here for brief discussion are, moreover, incomplete. There are numerous other investigations of scale modeling of combustion phenomena. Although many significant advances have been made, a wide variety of future accomplishments are achievable by new applications of partial modeling in combustion. This endeavor in increasing understanding for human benefit continues to be a highly promising long-term activity.
References 1. R.I. Emori and D.J. Schuring, Scale Models in Engineering: The Theory and Its Application, Pergamon, 1977. 2. F.A. Williams, Combustion Theory, 2nd edn, Addison-Wesley, 1985. 3. A. Linan and F.A. Williams, Fundamental Aspects of Combustion, Oxford, 1993. 4. F.A. Williams, Fire Research Abstracts and Reviews, 11:1 (1969). 5. D.B. Spalding, Ninth International Symposium on Combustion, Academic, p. 833 (1963). 6. A.E. Clarke, A.J. Gerrard and L.A. Holliday, Ninth International Symposium on Combustion, Academic, p. 878 (1963). 7. V.I. Blinov and G.N. Khudiakov, Doklady AcademieNauk, SSSR, 113:1094 (1957). 8. R.I. Emori and K. Saito, Combustion Science and Technology, 31:217 (1983). 9. S. Soma and K. Saito, Combustion and Flame, 86:269 (1991). 10. T. Yumoto, Combustion and Flame, 17:108 (1971). 11. T. Hirano and K. Saito, Progress in Energy and Combustion Science, 20:461 (1994). 12. F.A. Williams, Progress in Energy and Combustion Science, 8:317 (1982).
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13. N.A. Rokke, J.E. Hustad, O.K. Senju and F.A. Williams, Twenty-Fourth International Symposium on Combustion, The Combustion Institute, p. 385 (1992). 14. H.R. Baum and R.G. Rehm, Combustion Science and Technology, 40:55 (1984). 15. K.D. Steckler, H.R. Baum and J.G. Quintiere, Twenty-First International Symposium on Combustion, The Combustion Institute, p. 143 (1987). 16. J. de Ris, A.M. Kanury and M.C. Yuen, Fourteenth International Symposium on Combustion, The Combustion Institute, p. 1033 (1973). 17. R.L. Alpert, Sixteenth International Symposium on Combustion, The Combustion Institute, p. 1489 (1977). 18. R.A. Altenkirch, R. Eichhorn, N.N. Hsu, A.B. Brancic and N.E. Cevallos, Sixteenth International Symposium on Combustion, The Combustion Insitute, p. 1165 (1977). 19. M. Kono, K. Ito, T. Niioka, T. Kadota and J. Sato, Twenty-Sixth International Symposium on Combustion, The Combustion Institute, p. 1189–1199 (1996). 20. D.L. Dietrich, J.B. Haggard, Jr., F.L. Dryer, V. Nayagam, B.D. Shaw and F.A. Williams, Twenty-Sixth International Symposium on Combustion, The Combustion Institute, p. 1201–1207 (1996). 21. S. Kumagai and H. Isoda, Sixth International Symposium on Combustion, Reinhold, p. 726 (1957). 22. S. Jolly and K. Saito, Fire Safety Journal, 18:139 (1992). 23. B.J. McCaffrey, J.G. Quintiere and M.F. Harkleroad, Fire Technology, 17:98 (1981). 24. S. Jolly, M.P. Menguc, K. Saito and R.A. Alternkirch, First International Symposium on Scale Modeling, Japan Society of Mechanical Engineers, p. 373 (1988).
Molecular Diffusion Time and Mass Consumption Rate in Flames Tadao Takeno and K.N.C. Bray
Abstract The recent interest in laminar flamelet concept in turbulent combustion modeling makes it necessary to understand correctly the behavior of laminar premixed and diffusion flames in nonuniform flows. It is well known that nonuniform flow affects flames through stretch and flame curvatures. However, it has not been made clear yet how the nonuniform flow can affect the combustion rate in flames. In order to understand the mechanism, we have to elucidate the roles played by convective flow, molecular transport processes and chemical reactions in flames. In this paper we develop a very simple dimensional analysis argument to identify these roles. The argument is restricted to steady laminar flames, which are stable and far from the extinction condition. The chemical reaction is characterized by high activation energy, and hence the reaction time scale is much shorter than those of the flow and molecular transport processes, leading to a laminar flame structure composed of a thin reaction zone and thick molecular diffusion layers. On the basis of this asymptotic flame structure, we make a dimensional analysis to elucidate the respective roles to derive a universal relation between the molecular diffusion time and the mass consumption rate of both premixed and nonpremixed laminar flames in general flow fields. It is shown that an increase in chemical reaction rate alone cannot increase the local combustion rate. In the case of a diffusion flame an increase in the local flow velocity is an effective way to increase the local combustion rate. Keywords Flames in nonuniform flow · dimensional analysis
Introduction One important characteristic of combustion phenomena is the wide range of time and length scales of the processes involved. For example, the time scales of the controlling chemical reaction may range from micro seconds to several minutes or hours, depending on the specific problem under consideration. If we want to T. Takeno Nagoya University e-mail:
[email protected] K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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understand correctly what is going on in a certain combustion phenomena, we have to know at the outset the time and length scales of the rate controlling process. Therefore, scale modeling is extremely important in combustion science and engineering. If we successfully make use of the modeling, we can find out the essential physics and chemistry of a given combustion phenomena in terms of a simple analysis. The recent interest in laminar flamelet concept in turbulent combustion modeling makes it necessary to understand correctly the behavior of laminar premixed and diffusion flames in nonuniform flows [1]. It is well known that nonuniform flow affects flames through flame stretch and flame curvature [2]. However, it has not been made clear yet how the nonuniform flow can affect the combustion rate in flames. In order to understand the mechanism, we have to elucidate the roles played by convective flow, molecular transport processes and chemical reaction in flames. In this paper we develop a very simple dimensional analysis argument to identify these roles. The analysis is an extension of the dimensional analysis described in Tsuji’s text on combustion phenomena [3]. The argument is restricted to steady laminar flames, which are stable and far from the extinction condition. The chemical reaction is characterized by high activation energy, and hence the reaction time scale is much shorter than those of the flow and molecular transport processes, leading to the laminar flame structure composed of a thin reaction zone and thick molecular diffusion layers [4]. On the basis of this asymptotic flame structure, we make a dimensional analysis to elucidate the respective roles to derive a universal relation between the molecular diffusion time and the mass consumption rate of both premixed and nonpremixed laminar flames in general flow fields. In addition, we seek the most effective way to increase the local combustion rate.
Diffusion Flame Figure 1 shows schematically the asymptotic structure normal to the reaction zone of a diffusion flame [5]. The flame is composed of a thin reaction zone in the center surrounded by thick molecular diffusion layers of fuel and oxidizer on both sides. The thickness of reaction zone is δ and of diffusion layers are B. In the species conservation equation, it is the molecular diffusion and the chemical reaction that balances in the thin reaction zone, and convection does not affect what happens in this zone. On the contrary, convection and molecular diffusion balance in the outer diffusion layers. In the outer diffusion layers of thickness B, the molecular diffusion time τ D is given as τ D = B 2 /D
(1)
where D is the diffusion coefficient. The fuel diffusion velocity V is given as V = B/τ D = D/B
(2)
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Fig. 1 Schematic illustration of the asymptotic structure of diffusion flame
The aerodynamic flow time τa is given by τa = B/v
(3)
where v is the local convective velocity normal to the reaction zone. The balance between convection and diffusion gives τa = τ D or B = D/v and v = V
(4)
In the thin reaction zone, the chemical reaction time τc is given by τc = ρ/w
(5)
where ρ and w are the density and the mass consumption rate of fuel per unit volume. The molecular diffusion time τ D is now given by τD = δ V
(6)
where the diffusion velocity V is now given by V = DYδ /δ = D/B
(7)
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where Y␦ represents the fuel mass fraction in the reaction zone. Equation (2) is used in the last equality. The balance between diffusion and reaction yields τc = τ D , or wδ = ρV
(8)
In view of Eqs. (1) and (7), we have wδ = ρ D/τ D
(9)
In this way we demonstrate that the mass consumption rate of fuel is inversely proportional to the square root of the diffusion time. This is consistent with the results of our numerical calculations with detailed chemistry [6, 7].
Premixed Flame Figure 2 shows schematically the asymptotic structure of the normal premixed flame [4]. The flame is composed of a thin reaction zone with thickness of δ and a thick molecular diffusion layer, or the preheat zone, of thickness B upstream of the reaction zone. In the species conservation equation, it is the molecular diffusion and the chemical reaction that balances in the thin reaction zone and convection will not affect what happens in this zone. On the contrary, convection and molecular diffusion balance in the preheat zone. The same argument holds as that of the diffusion flame. In the preheat zone, the molecular diffusion time τ D is given by Eq. (1). In the same way, the diffusion velocity V of the reactant is given by Eq. (2). The aerodynamic flow time τa is given by τa = B/Su
(10)
where Su is the burning velocity of the mixture. The balance between convection and diffusion gives τa = τ D , or B = D/Su and Su = V
Fig. 2 Schematic illustration of the asymptotic structure of premixed flame
(11)
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In the thin reaction zone, the chemical reaction time τc is given by τc = ρ/w
(12)
where ρ and w are the density and the mass consumption rate of the reactant. The molecular diffusion time τd is given by τd = δ/V = δ B/D
(13)
where the diffusion velocity V is given by V = DYδ /δ = D/B
(14)
and where Yδ represents the reactant mass fraction in the reaction zone. The balance between diffusion and reaction in this zone yields τc = τd or wδ = ρV
(15)
In view of Eqs. (8) and (15) we have m = wδ = ρ D/τ D
(16)
where m is the mass burning velocity of the mixture. In this way we notice that the dependence of the mass consumption rate on the diffusion time is identical for the premixed and diffusion flames. However, in the premixed flame, the burning velocity Su and preheat zone thickness B are given functions of mixture properties, whereas no corresponding general functional relationships exist for the diffusion flame.
Discussions We now study the effect of the chemical reaction time and local convective velocity on the mass consumption rate. Equations (5) and (12) show that the fuel or reactant mass consumption rate w increases with a decrease in the reaction time. In the limit of zero reaction time, the mass consumption rate becomes infinitely large. On the other hand, Eqs. (8), (14) and (15) reveal that δ and Yδ should become infinitely small. This is the case of the well known flame sheet model. However, the product wδ must remain finite as can be seen in Eqs. (9) and (16). That is, even if the reaction rate becomes infinitely large, wδ remains finite since the reaction zone thickness becomes infinitely small. Note wδ represents the fuel or reactant mass consumption rate per unit flame surface area. This is more important than w, since this is the quantity that determines the actual local combustion rate. The result that this quantity should remain finite for the infinite reaction rate is a natural consequence of the
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fact that the combustion rate is controlled by the supply rate of the reactant by the molecular diffusion, as can be seen in Eqs. (8) and (15). In the diffusion flame, when we increase the local convective velocity v, the thickness of the diffusion layer B decreases accordingly to reduce the diffusion time τ D . Then the quantity wδ increases to increase the local combustion rate. Equations (4) and (8) show that wδ = ρV
(17)
indicating that the local combustion rate is directly proportional to the local flow velocity normal to the reaction zone. In the diffusion flame an increase in the local flow velocity is an effective way to increase the local combustion rate. On the other hand, in the case of the premixed flame, the local flow velocity is equal to the burning velocity, Su , which is a given quantity as a function of mixture properties, and cannot be specified arbitrarily. Acknowledgments The authors would like to extend their sincere thanks to YAMAHA MOTOR Foundation for its support in the initial stage of our cooperation. TT would like to extend his sincere thanks to JSPS for its support of this study.
References 1. Peters, N., Twenty-First Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1986, pp. 1231–1250. 2. Williams, F.A., Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1992, pp. 1–17. 3. Tsuji, H., Diffusion flame, combustion phenomena (7) (in Japanese), Science of Machine 28 (1976), 1335–1358. 4. Williams, F.A., Combustion Theory, Second Edn., Benjamin/Cummings, Menlo Park, 1985, pp. 154–160. 5. Takeno, T., Twenty-Fifth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1994, pp. 1061–1073. 6. Takeno, T., Effects of Flow Field on Diffusion Flame Structure, 3rd Workshop on Modeling of Chemical Reaction Systems, Heidelberg, June 1996. 7. Nishioka, M., Takemoto, Y., Yamasshia, H. and Takeno, T., Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1996, pp. 1071–1077.
Nitric-Oxide Emissions Scaling of Buoyancy-Dominated Oxygen-Enriched Methane Turbulent-Jet Diffusion Flames L.T. Yap, M. Pourkashanian, L. Howard, A. Williams and R.A. Yetter
Abstract Theoretical predictions and measurements of nitric-oxide emissions from buoyancy-controlled weak (<10%) oxygen-enriched as well as air-fired non-piloted methane turbulent-jet flames are presented. Numerical examination of strained opposed-flow diffusion flames underscores flamelet features for air as well as oxygen enrichment. For air and oxygen-enriched conditions, the NO production is dominated by the sequence CH + N2 → HCN + N and N + OH → NO + H. Peak NO formation shifts from stoichiometric to fuel-rich conditions with oxygen enrichment. Oxygen enrichment increases the Zel’dovich contribution more than the prompt contribution. However, the contribution of thermal NO, as defined by the classical Zel’dovich mechanism, to the total NO remains small even with (<10%) oxygen enrichment. Higher strain rates reduce this effect. A previously developed laminar-flamelet-based estimate is extended to incorporate oxygen enrichment. The theory uses reduced chemical-kinetic mechanisms for the flamelet and simplified transport equations for the buoyancy-controlled flame height. Average NO production rates are obtained from asymptotical examination of a two-reaction-zone oxygen-enriched laminar flamelet with an approximated joint probability-density function for mixture fraction and scalar dissipation. Experimental NOx emission indices derived from NO and CO2 measurements of oxygen-enriched (0 ≤ ΔXO2 ≤ 0.09) methane flames (3.5 × 103 ≤ Fr ≤ 4.4 × 104 ) are in excellent agreement (average deviation 13.5%) with the theoretically derived Froude-number correlation. Decreasing downward shifts about the correlation with increasing oxygen enrichment are observed and are consistent with liftoff phenomena. Comparisons with more extensive (633 ≤ Fr ≤ 1.6 × 106 ) methane-air results show better agreement (average deviation 22%) with the proposed correlation than previously obtainable.
Nomenclature do E
Exit jet diameter (m) Emission index
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Function of ΔXO2 obtained in theoretical analysis Froude number Gravitational acceleration (m/s2 ) Flame height (m) Characteristic flame radius (m) Reynolds number Average exit velocity (m/s) Average turbulent-flame volume (m3 ) Oxygen-enrichment mole fraction Jet-exist density Jet-exit viscosity
Introduction Oxygen enrichment has been used to increase thermal efficiencies in industrial combustion processes [1–3]. Increased flame temperatures enhance heat-transfer rates and hence thermal efficiencies [4–9]. High NOx emissions, however, are a potential trade-off for these gains in thermal efficiencies [10]. Specifically, at moderate oxygenenrichment levels, the flame-temperature increase affects NOx-formation rates much stronger than the reduction in N2 availability to the flame. Hence, the regime of moderate oxygen enrichment, where potentially many cost-effective industrial-process gains can be obtained, may be restrained by higher NOx emission. As premixing may present severe safety problems when applied to large flow rates, most industrial burners inject fuel and oxidizer as separate streams. Hence, for most commercial applications, gaseous combustion can be characterized with turbulent diffusion flames. As a result, there is a need for dependable techniques to assess nitric-oxide emission from oxygen-enriched turbulent diffusion flames. Unlike the situation that exists for oxygen-enriched turbulent diffusion flames, NOx formation in air-fired turbulent diffusion flames has received wide interest. Previous studies include both confined [e.g. 11, 12] and unconfined [e.g. 13] configurations for hydrogen [e.g. 14] as well as hydrocarbon fuels [e.g. 14–17]. The earlier uncertainties concerning the controlling mechanisms resulted in NO predictions varying by three orders of magnitude around the experimental emission levels despite careful theoretical analysis [12]. Since that time, knowledge of the underlying kinetics as well as of the flame structure has improved. More recently, it has been demonstrated that effective scaling behavior for air-fired turbulent diffusion flames can be obtained entirely from the asymptotic analysis of flamelet structure, chemical kinetics, and buoyancy-controlled jet behavior [17]. Unlike what was suggested by earlier studies [e.g. 13, 16], the noteworthy scaling of a wide variety of experimental data for various fuels implied, to leading order, the insignificance of radiation. A scaling law could then be developed [17]. In addition, this NO-emissions scaling law was applied successfully by the present authors to experimental as well as computational results of two geometrically scaled (65 kW and 260 kW) complex commercial natural-gas burners [18].
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The flamelet-like structure for weak (<10%) oxygen enrichment, as presented in the next section, motivates the current extension of Røkke et al.’s [17] NO scaling law to atmospheric oxygen-enriched turbulent-jet diffusion flames. A comparison with new experimental data demonstrates that the extension to oxygen enrichment is effective. Implications for practical oxygen-enrichment strategies where NOx emissions are of importance are discussed. Since an extended version of this work has now been published [19], only a summary of the scaling aspects of the work is presented here.
Oxygen-Enriched Chemical Kinetics Detailed baseline opposed laminar-flame calculations were performed for air and oxygen-enriched oxidants [20] for various strain rates. The GRI 2.1 mechanism [21] was used for air and 9% oxygen enrichment (XO2 = 0.3). The results [19] show spreading in mixture-fraction space of peak fluxes with oxygen enrichment for rate-limiting steps N2 + O → NO + N and CH + N2 → HCN + N [17]. The maximum total NO-production rate is central to these peaks underscoring the interaction between the prompt and the extended Zel’dovich mechanisms. Examination of the fluxes for the methane-air flame shows the dominance of the NO production by the prompt mechanism consistent with earlier studies [22–24]. Even with the (<9%) oxygen addition current results indicate the dominance of the prompt mechanism. From a flux analysis, the prevalent reaction sequence leading to NO was found to be CH + N2 → HCN + N and N + OH → NO + H. This sequence highlights the importance of transport in the NO production mechanism for diffusion flames; the N and OH responsible for the most prolific step N + OH → NO + H are produced in the fuel-rich and the fuel-lean zones, respectively. To examine the applicability of flamelet analysis to oxygen-enriched conditions, estimates of flame thickness were compared with Kolmogorov length scales. Using the thickness of the fuel-rich heat-release zone where most NO is formed, a decrease in flame thickness of 9% was estimated. Using a gradient method on the mixture-fraction profile, an increase in flame thickness of 4% due to (9%) oxygen addition was estimated. The Kolmogorov length scales were estimated to increase by 18% at the calculated flame temperatures. These results suggest the extension of the flamelet formalism to oxygen-enriched conditions.
Extension of Laminar Flamelet-Structure Analysis to Oxygen Enrichment The analysis of NO-scaling behavior for oxygen-enriched turbulent diffusion flames followed the developments of Røkke et al. [17] closely [19]. The rate estimates detailed above apply on a spatially and temporally resolved basis and are used with
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a flamelet model which distinguishes oxygen-consumption and fuel-consumption zones with thicknesses and and ␦ in mixture-fraction space, respectively [17, 25, 26]. With increased oxygen enrichment, the activation energies in the thermal mechanism are sufficiently high to make the Zel’dovich mechanisms peak sharply at the stoichiometric mixture fraction where the temperature is enhanced, making the use of activation-energy asymptotics increasingly accurate. The flame temperature is tempered by finite-rate chemistry and enhanced by oxygen enrichment. Radiant losses also reduce the peak temperature but are mostly less important than the finitechemistry effects [17]. The local average rate of production of NO per unit volume was analyzed in detail [19] leading to an explicit expression for the emission index E referenced to NO2 (g/kg fuel). To evaluate E, the average turbulent-flame volume was estimated from V ≈ R2 H(m3 ), where R is a characteristic flame radius and H is the flame length. Extending the buoyancy-controlled jet theory of Røkke et al. [17] to include the effect of oxygen enrichment through the stoichiometric mixture fraction, an expression for H was obtained [19] in terms of the Froude number, Fr = u2o go do , as was an expression for R. This enabled deriving a scaling law for E [19]: E(o uo )/do f(⌬XO2 )) = Fr3/5
(1)
f(⌬XO2 ) = 26 exp(10⌬XO2 0.7 )
(2)
where
Experimental Results and Comparison The experimental methods and procedures for extracting values of E from the experimental results have been given in detail [19]. Measurements for air-fired as well as oxygen-enriched flames are presented in Figs. 1 and 2. Results for nonpiloted axi-symmetric turbulent-jet methane diffusion flame with 2500 ≤ Re ≤ 4500, 3.5 × 103 ≤ Fr ≤ 4.4 × 104 , where Re = o do uo o , 17 mm ≤ do ≤ 3 mm, 10 m/s ≤ uo ≤ 38 m/s and 0 ≤ ΔXO2 ≤ 0.09 are plotted in Fig. 1. The average deviation of the data from the theoretical correlation is 13.5%. The transition from attached to lifted turbulent flames is indicated. It can be seen that the lifting reduces the emissions to a lower regime. Despite this shift, the trend as proposed by the theoretical correlation, however, is still followed. These liftoff-induced shifts are larger with smaller oxygen enrichment. At the higher oxygen enrichments (ΔXO2 ≥ 0.07) these shifts become negligible. This behavior is consistent with the larger liftoff heights generated at lower oxygen enrichments. Significant oxygen levels were found throughout the lifted flames at the lower (ΔXO2 ≤ 0.07) oxygenenrichment levels. This larger degree of pre-mixing at the lower oxygen-enriched lifted flames is compatible with trends exhibited by the oxygen-induced emissions
Nitric-Oxide Emissions Scaling of Turbulent-Jet Diffusion Flames
Fig. 1 NO-emissions correlation with oxygen-enriched turbulent-jet methane flame data
Fig. 2 NO-emissions correlation with data for all methane flames
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shift. Although the range of data is limited, the ability of the theoretical formula to correlate the oxygen-enriched results is remarkable. Figure 2 shows the oxygen-enriched flame data of Fig. 1 in addition to air-fired methane turbulent-jet diffusion-flame data from the literature. Here, the data spans 2500 ≤ Re ≤ 106 , 633 ≤ Fr ≤ 1.6 × 106 , 1.7 mm ≤ do ≤ 28 mm, 9.5 m/s ≤ uo ≤ 81 m/s and 0 ≤ ΔXO2 ≤ 0.09. Over this large range, the average deviation of the data from the scaling law was 22% which is well within the accuracy of the assumptions underlying the derivation. In addition to turbulent-jet diffusion-flame emissions, data for two geometrically scaled industrial burners [18] have been plotted in Fig. 2. The jet-flame correlation with appropriately evaluated characteristic lengths for the buoyancy effects yields promising results for even complex flames in the flamelet regime. It is anticipated that the increased levels of Dahmkohler numbers induced by general oxygen enrichment may make the NO-scaling analysis [19] increasingly applicable to complex burner configurations.
Conclusions Theoretical scaling characteristics for NO emissions from oxygen-enriched turbulent buoyancy-controlled methane flames were examined experimentally. Although the Froude number range for the experimental data was limited (3.5 × 103 ≤ Fr ≤ 4.4 × 104 ), the average deviation for oxygen enrichment up to 9% was only 13.5%. Liftoff-induced downward shifts for lower oxygen-enrichment levels were identified. Comparing air-based data from the current study as well as from the literature yielded an average deviation from the correlation of 22% for a much larger range of Froude numbers (633 ≤ Fr ≤ 1.6 × 106 ). The agreement appears to fall well within the uncertainties in the underpinnings of the theory. The general scaling behavior is controlled by the turbulent flame volume and the oxygen-enrichment-induced flame-temperature increase. Oxygen-enriched flame data over a larger range will help further test the current correlation.
References 1. T.L. Yap, Ceramic Engineering and Science Proceedings 11 (1990) 175–195. 2. M. Pourkashanian, T.L. Yap, A. Williams, Proceedings of the Institute of Energy Adam Hilger, Bristol (1990) 301–314. 3. M. Missaghi, T.L. Yap, S.H. Ahmadi, A.D. Al-Fawaz, E. Hampartsoumian, M. Pourkashanian, A. Williams, 1992 International Gas Research Conference, Vol. ii (1993) 1993–2002. 4. T.L. Yap, Glass Production Technology International, H. Rawson, Ed. (1991) 91–97. 5. M. Pourkashanian, T.L. Yap, Proceedings of the 125th TMS Annual Meeting (1996) 655. 6. R. Abernathy, J. McElroy, L.T. Yap, Proceedings of the 125th TMS Annual Meeting (1996) 1233–1239. 7. J.T. Brown, Ceramic Engineering and Science Proceeding 12 (1991) 594–609. 8. K. Congleton, Ceramic Engineering and Science Proceeding 16 (1995) 190–194.
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9. P.B. Eleazer, A.G. Slavejkov, Ceramic Engineering and Science Proceeding 15 (1994) 159–174. 10. J.T. Hedley, M. Pourkashanian, A. Williams, T.L. Yap, Combust. Sci. Tech. 108 (1995) 311–322. 11. T. Takagi, M. Ogasawara, K. Fujii, M. Daizo, Proc. Combust. Inst. 15 (1975) 1051–1070. 12. N. Peters, S. Donnerhack, Proc. Combust. Inst. 18 (1981) 33–42. 13. Y.Y. Buriko, V.R. Kuznetsov, Combustion Explosions and Shockwaves 14 (1978) 296. 14. R.W. Bilger, R.E. Beck, Proc. Combust. Inst. 15 (1975) 541–552. 15. S.R. Turns, J.A. Lovett, Combust. Sci. Tech. 66 (1989) 233–249. 16. S.R. Turns, F.H. Myhr, Combustion and Flame 87 (1991) 319–335. 17. N.A. Røkke, J.E. Hustad, O.K. Sønju, F.A. Williams, Proc. Combust. Inst. 24 (1992) 385–393. 18. A.D. Al-Fawaz, M. Missaghi, M. Pourkashanian, A. Williams, T.L. Yap, Proc. Combust. Inst. 25 (1994) 1027–1034. 19. L.T. Yap, M. Pourkashanian, L. Howard, A. Williams, R.A. Yetter, Proc. Combust. Inst. 27 (1998) 1451–1460. 20. A.E. Lutz, R.J. Kee, J.F. Grcar, Oppdif, A Fortran Program for Computing Opposed Flow Diffusion Flames, Sandia National Laboratories, Livermore, CA. 21. C.T. Bowman, M. Frenklach, W. Gardiner, D. Golden, V. Lissiansky, G. Smith, H. Wang, GRI Mech 2.11, Gas Research Institute Report, Chicago (1995). 22. M.C. Drake, R.J. Blint, Combustion and Flame 83 (1991) 185–203. 23. J.C. Hewson, F.A. Williams, Proceedings of the Eighth ONR Propulsion Meeting, G.D. Roy, F.A. Williams, Eds., ONR, VA (1995) 52–59. 24. M. Nishioka, S. Nakagawa, Y. Ishikawa, T. Takeno, Combustion and Flame 98 (1994) 127–138. 25. K. Seshadri, N. Peters, Combustion and Flame 73 (1988) 23–44. 26. H.K. Chelliah, F.A. Williams, Combustion and Flame 80 (1990) 17–48.
Numerical Simulations of Methane Diffusion Flame with Burner Rotation Keng Hoo Chuah, Hiroshi Gotoda and Genichiro Kushida
Abstract Numerical simulations have been conducted to study methane diffusion flame with burner rotation. The burner rotational speed is from 300 rpm to 1200 rpm; the burner diameter is 1 cm and 2 cm; the injection velocity is 10 cm/s and 15 cm/s. Quantitative data obtained includes the velocity profile, the temperature profile, and the frequencies of fluctuation. From the simulation data, the flame shape is obtained from the temperature data and reasonably agrees with the flame shape in the experiment. Because the flame is buoyancy dominant, the frequency scales to the square root of the burner’s diameter. Vortex flow, found around the burner cylinder and induced by the burner rotation, causes the flame to be unstable at the burner exit for rotational speed larger than 800 rpm. Rotational speed increase also reduces the pulsation frequency, but not as significant as a change in burner diameter. The length of the burner cylinder and the fluctuations of the flame alter the vortex propagation shapes and directions, as well as the frequencies of the flame. It is clear that the burner length is the medium for generating instability. Keywords Buoyancy · flame · instability · swirling flow
Nomenclature Cp D d f h N q T t ui
Constant pressure specific heat Mass diffusivity Burner diameter Flame pulsation frequency Burner height Rotational speed Heat of combustion Temperature Time Velocity
K.H. Chuah Department of Mechanical Engineering, University of Kentucky, Lexington, KY, 40506 U.S.A.
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uI Yi λ μ ν ρ
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Fuel injection velocity Mass fraction Thermal conductivity Dynamic viscosity Mass stoichiometric index = 4.0 Gas density
Subscripts F O r z θ
Methane Air Radial direction Axial direction Tangential direction
Introduction Buoyancy-induced flame flickering in a small scale laboratory setting is a subject of thermo-fluid dynamics. When a buoyancy-dependant flame is coupled with a rotating burner, fluid interaction with the ambient air increases. Then, the physical properties around the combustion become important. Using this basic assumption, this paper reports numerical results of flow structure and temperature profile of a jet diffusion flame with burner rotation, under normal gravity condition. Experiments of buoyancy flames with a rotating burner for premixed flames are well-documented in the literature. Sheu et al. reported flame flatting and instability in a Bunsen flame with Burner rotation [1]. Subsequently in a more extensive study, Cha and Sohrab reported an extension of flame stabilization region because flame can anchor to the burner at a larger Reynolds number when the burner is rotating [2]. Transient flame tip motions in experiments with burner rotation have been investigated under normal gravity condition and reduced-gravity condition by Gotoda et al. [3] and subsequently by Gotoda Ueda [4]. The paper is outline as follow: First the numerical simulation model is presented with assumptions, governing equations, and implementation details. Then, the results are shown for temperature profiles, pulsation frequencies, and velocity profiles, followed by discussions and conclusions.
Numerical Simulation Model Model Assumptions To simulate flames with burner rotation, a numerical simulation model is created using the time-dependent Navier-Stokes equations with temperature-dependent physical properties and a one-step global oxidative reaction. The reaction rate is
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Arrhenius type and low Mach number is assumed. The model is assumed to be axisymmetric in a cylindrical coordinate system (r, θ, z), where the center of the burner exit is defined as the origin. The burner is rotating at a specific speed while injecting fuel with a tangential velocity component proportional to the radius and at a constant fuel rate. The r -axis is a fixed boundary blocking all flows. The outer boundaries are in convective conditions and normal gravity is assumed.
Governing Equations Equations governing the model with the assumptions above are shown below. The relevant equations are a mass conservation equation for gas, three momentum conservation equations, an energy conservation equation, and two species conservation equations for Methane and air. Mass:
1 ⭸rρu r ⭸ρu z ⭸ρ + + =0 ⭸t r ⭸r ⭸z
(1)
r -Momentum: ⭸ρu r 1 ⭸ ⭸ ρu 2θ ⭸P 4 ⭸u r ⭸u r + rρu r2 − r μ + ρu z u r − μ = − ⭸t r ⭸r 3 ⭸r ⭸z ⭸z r ⭸r 1 ⭸ ⭸u z ⭸ ⭸u z 2 μ 2u r ⭸u r ⭸u z 2 1 ⭸μu r + rμ + μ − − − − 3 r ⭸r r ⭸r ⭸z ⭸z ⭸r 3r r ⭸r ⭸z (2) θ -Momentum: ⭸ρu θ 1 ⭸ ⭸ ρu r u θ ⭸u θ ⭸u θ + rρu r u θ − r μ + ρu z u θ − μ =− ⭸t r ⭸r ⭸r ⭸z ⭸z r 1 ⭸μr u θ μ ⭸u θ − 2 + r ⭸r r ⭸r
(3)
z-Momentum: ⭸ρu z 1 ⭸ ⭸ ⭸u z ⭸u z 4 + rρu r u z − r μ + ρu 2z − − μ ⭸t r ⭸r ⭸r ⭸z 3 ⭸z 1 ⭸ ⭸u r ⭸P 2 ⭸ μ ⭸r u r + (ρ∞ − ρ)g − + rμ =− ⭸z 3 ⭸z r ⭸r r ⭸r ⭸z
(4)
Energy: ⭸ρC p T 1 ⭸ + ⭸t r ⭸r
⭸ λ ⭸C p T λ ⭸C p T ˙ rρu r C p T − r + ρu z C p T − = qM C p ⭸r ⭸z C p ⭸z (5)
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Methane-Species: ⭸YF ⭸YF ⭸ ˙ rρu r YF − rρ D + ρu z YF − ρ D = −M ⭸r ⭸z ⭸z
(6)
⭸ ⭸YO ⭸YO ˙ rρu r YO − rρ D + ρu z YO − ρ D = −ν M ⭸r ⭸z ⭸z
(7)
⭸ρYF 1 ⭸ + ⭸t r ⭸r Air-Species: 1 ⭸ ⭸ρYO + ⭸t r ⭸r
Model Implementation The model implements finite volume method with SIMPLE algorithm [5, 6] and the chemical parameter by Coffee et al. [7]. The grid of the model is structured 100×200 and the grid size is 0.5 mm × 1.0 mm. The relatively coarse grid size implies that all flow details smaller than the grid size will disappear in the result. Nevertheless, the Kolmogorov length is estimated to be in the order of 1 mm. The time step is adaptive based on the convergences of temperature. It is at 2 s during the ignition period, but returns to 50 s after the ignition. The small errors introduced during the initial ignition period are expected to have no significant effect on the temperature and velocity profiles of interest. For t > 1 s (20,000 time steps), the maximum changes of relative pressure is ±1 Pa per time step, with a convergence error of ±0.01 Pa per iteration. The area with the largest error is at the corner of the burner exit. Additional study has been performed at doubled grid of 200 × 400 and grid size of 0.25 mm × 1.0 mm. It is discussed in the results below, following the findings of vortex motion around the burner.
Results and Discussion Results of the numerical simulation are presented for temperature profile, frequency of pulsation, and velocity profile. The important parameters affecting the simulation are: 1. The burner rotational speed, N controls the strength of the vortex generated from the injected fuel as well as the flow around the burner due to viscous diffusion. It is expected that the tangential velocity profile will be affected by this parameter. The simulated speeds are 300 rpm, 400 rpm, 600 rpm, 800 rpm, and 1200 rpm. 2. The diameter of the burner, d is a length scale that controls the flame height and the flame pulsation frequency. According to Burke-Schumann theory and scaling analysis, the flame height is a function of squared diameter. If the flame in the simulation is buoyancy dominant, where Fr number is near constant, scaling analysis shows that the relation between the flame pulsation frequency and the burner diameter is [8]:
Numerical Simulations of Methane Diffusion Flame with Burner Rotation
f = f
d d
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1/2 (8)
3. The simulated diameters are 1 cm and 2 cm. 4. The length of the burner, h is another length scale that changes the flame pulsation frequency, but to a lesser degree. Burner length controls the number of vortex rings generated around the burner due rotational instability. The simulated burner lengths are 1.9 cm and 3.8 cm. 5. The fuel injection velocity, u I linearly scales with the flame height. Unfortunately, the flame is almost as tall as the simulated domain. The simulated fuel injection velocity is 10 cm/s and 15 cm/s.
Temperature Profile N = 800 rpm, d = 1 cm, h = 3.8 cm, u I = 10 cm/s: Time-averaged temperature is calculated from the numerical simulation as a function of radius for a number of heights above the burner exit, as shown in Fig. 1(a). Near the burner exit, the temperature increases from the z-axis to a maximum temperature of 1700 K before diffusing to the ambient temperature, 300 K. The temperature does not peak at the z-axis because fuel is injected at a temperature of 300 K. Due to flame pulsation and thermal diffusion, the high temperature region of the flame at 6.2 cm is slightly more wide spread than the high temperature region near the burner exit at 2.2 cm. But the peak temperature has shifted to the z-axis at this height. The peak temperature started to drop above this height, where at 8.2 cm above the burner, the peak temperature is only 1500 K. N = 300 rpm, d = 2 cm, h = 3.8 cm, u I = 10 cm/s: Time-averaged temperature data in Fig. 1(b) shows similar trends. With the diameter increased to 2 cm, the temperature at the z-axis at 2.2 cm above the burner drops to 800 K as the amount of injected fuel at 300 K has increased. The temperature increases radially to a maximum temperature of 1600 K before diffusing to the ambient temperature, 300 K. At the height of 8.2 cm above the burner, the temperature inside the burner is almost flat at 1600 K. N = 300 rpm, d = 2 cm, h = 1.9 cm, u I = 10 cm/s: The temperature profile for this case is similar to Fig. 1(b), indicating that burner length does not change the temperature profile.
Flame Pulsation Frequency The flame pulsation frequency depends on the type of flame simulated. For buoyancy-dominant flame, flame pulsation frequency is a function of diameter. The flame pulsation frequency is obtained from temperature data at the z-axis, using Fourier transform.
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4.2 cm cm 4.2
6.2 cm cm 6.2
8.2 cm cm 8.2
2000 1800
Temperature (K)
1600 1400 1200 1000 800 600 400 200 0 0.0
1.0
2.0 3.0 Radius (cm)
4.0
5.0
(a)
2.2 cm cm 2.2
4.2 cm cm 4.2
6.2 cm cm 6.2
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1800
Temperature (K)
1600 1400 1200 1000 800 600 400 200 0 0.0
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5.0
(b) Fig. 1 Time-averaged temperature of a rotating burner at different heights above the burner exit specified in the legend (a) N = 800 rpm, d = 1 cm, h = 3.8 cm, u I = 10 cm/s; (b) N = 300 rpm, d = 2 cm, h = 3.8 cm, u I = 10 cm/s
N = 800 rpm, d = 1 cm, h = 3.8 cm, u I = 10 cm/s: Figure 2(a) shows that the dominant frequency of the flame is 10 Hz. The magnitude of the frequencies is smaller near the burner exit. At the height of 10.2 cm, the temperature fluctuates a lot, but the frequencies remain the same. N = 300 rpm, d = 2 cm, h = 3.8 cm, u I = 10 cm/s: Figure 2(b) shows that the dominant frequency of the flame is 6.5 Hz. Nevertheless, the magnitude of this
Numerical Simulations of Methane Diffusion Flame with Burner Rotation 2.2 cm
10.2 cm
0.3 0.25 Mognitude [z]
Fig. 2 Frequency analysis with Fourier transform of temperature data at the z-axis at different heights above the burner exit specified in the legend (a) N = 800 rpm, d = 1 cm, h = 3.8 cm, u I = 10 cm/s; (b) N = 300 rpm, d = 2 cm, h = 3.8 cm, u I = 10 cm/s
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0.2 0.15 0.1 0.05 0 0
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20 30 Frequency (Hz) (a) 2.2 cm
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10.2 cm
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Mognitude [z]
0.25 0.2 0.15 0.1 0.05 0 0
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20 30 Frequency (Hz) (b)
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frequency reduces as the height increases, a complete reversed as compare to the first case. A low frequency of 1.5 Hz is also present in the graph. At the height of 10.2 cm, the number of major flame frequencies increases, but the dominant frequency remains the same. From a comparison of the frequencies in Fig. 2(a) and (b) shows that Eq. (8) discussed above holds. Therefore, the flame simulated is buoyancy dependant. N = 300 rpm, d = 2 cm, h = 1.9 cm, u I = 10 cm/s: Figure 3 shows that the dominant frequency of the flame is 7 Hz. The magnitude of this frequency also reduces as the height increases. A low frequency of 1.5 Hz is also present in the graph. Since the only change between this case and Fig. 2(b) is the burner length, the small shift in frequency of 0.5 Hz is attributed to physical structure of the burner.
Velocity Profile N = 800 rpm, d = 1 cm, h = 3.8 cm, u I = 10 cm/s: The time-averaged radial and tangential velocity above the burner is plotted in Fig. 4. The flow resembles a
218 2.1 cm
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0.3 0.25 Magnitude (z)
Fig. 3 Frequency analysis with Fourier transform of temperature data at the z-axis at different heights above the burner exit specified in the legend, N = 300 rpm, d = 2 cm, h = 1.9 cm, u I = 10 cm/s
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0.2 0.15 0.1 0.05 0 0
10
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(a)
2.2 cm
4.2 cm
6.2 cm
8.2 cm
7.0
Fig. 4 (a) Time-averaged radial velocity and (b) tangential velocity of a rotating burner at different heights above the burner exit specified in the legend (N = 800 rpm, d = 1 cm, h = 3.8 cm, u I = 10 cm/s)
Velocity (cm/s)
6.0 5.0 4.0 3.0 2.0 1.0 0.0 0.0
1.0
2.0 3.0 Radius (cm)
(b)
4.0
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fire whirl vortex compressed radially to a short distance in the burner region [9]. The vortex is supported by secondary inflow and axial up flow.
Vortex Motions Around the Burner The results presented so far is about the flow and temperature profiles above the burner. Around the burner and invisible from the temperature data are vortex flows due to rotational instability. Figure 5 shows the temperature profile and tangential velocity of a time frame in the simulation. Clearly, vortex rings, as strong as the main vortex above the burner, are being generated around the burner. The stream function and tangential vorticity are plotted in Figs. 6 and 7. It is believed that the vortex rings around the burner is disrupting the regular frequencies of the flame.
Fig. 5 (a) Temperature profile and (b) the corresponding tangential velocity profile of a rotating burner in the numerical simulations (N = 800 rpm, d = 1 cm, h = 3.8 cm, u I = 10 cm/s)
T (K)
vθ (cm/s)
2200
50
1820
40
1440
30
1060
20
680
10
300
0
Rotational Speed N = 400 rpm, 800 rpm, and 1200 rpm, d = 1 cm, h = 3.8 cm, u I = 15 cm/s: The frequency of pulsation decreases when the rotational speed increases as shown in Figure 8. This is consistent irrespective of height. The fluctuation of temperature is almost non-existent near the burner exit at 400 rpm. The fluctuation increases with rotational speed.
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Fig. 6 Stream function of the flow around a rotating burner in the numerical simulations (N = 800 rpm, d = 1 cm, h = 3.8 cm, u I = 10 cm/s) 6
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z (cm)
4
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r (cm)
Fig. 7 Vorticity of the flow around a rotating burner in the numerical simulations (N = 800 rpm, d = 1 cm, h = 3.8 cm, u I = 10 cm/s)
Numerical Simulations of Methane Diffusion Flame with Burner Rotation N = 400, H = 6.2
Tn(K)
Fig. 8 Frequency analysis with Fourier transform of temperature data at the z-axis at different heights above the burner exit specified in the legend N = 400 rpm, 800 rpm, and 1200 rpm, d = 1 cm, h = 3.8 cm, u I = 15 cm/s (a) at height = 6.2 cm; (b) at height = 0.5cm
45 40 35 30 25 20 15 10 5 0
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20 15 10 5 0
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f (Hz) (b)
Conclusion Numerical simulations conducted to study methane diffusion flame with burner rotation resulted in quantitative data of the velocity profile, the temperature profile, and the frequencies of pulsation. The flame shape obtained from the temperature data reasonably agrees with the flame shape in the experiment. Because the flame is buoyancy dominant, the frequency scales to the square root of the burner diameter. Vortex flow, found around the burner cylinder and induced by the burner rotation, causes the flame to be unstable at the burner exit for rotational speed larger than 800 rpm. Rotational speed increase also reduces the pulsation frequency, but not as significant as a change in burner diameter. The length of the burner cylinder and the fluctuations of the flame alter the vortex propagation shapes and directions, as well as the frequencies of the flame. It is clear that the burner length is the medium for generating instability.
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References 1. Sheu, W.J., Sohrab, S.H., and Sivashinsky, G.I., “Effect of rotation on Bunsen flame”, Combustion and Flame, 79: 190–198 (1990). 2. Cha, J.M. and Sohrab, S.H., “Stabilization of premixed flames on rotating Bunsen burners”, Combustion and Flame, 106: 467–477 (1996). 3. Gotoda, H., Maeda, K., Ueda, T., and Cheng, R.K., “Periodic motion of a Bunsen Flame with Burner rotation”, Combustion and Flame, 134: 67–79 (2003). 4. Gotoda, H. and Ueda, T., “Transition from Periodic to Non-Periodic Motion of a BunsenType Premixed Flame Tip with Burner Rotation”, Proc. of The Combustion Institute, 29: 1503–1509 (2003). 5. Kushida, G., Proc. Com. Heat Mass Trans. 3: 233–242 (2003). 6. Patankar, S.V., Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980. 7. Coffee, T.P. et al., Combustion and Flame, 58: 59–67 (1984). 8. Emori, R.I. and Saito, K. “A study of scaling laws in pool and crib fires”, Combustion Science and Technology, 31: 217–231 (1983). 9. Chuah, K.H. and Kushida, G., “The Prediction of Flame Heights and Flame Shapes of Small Fire Whirls”, Proc. of The Combustion Institute, 31–2: 2599–2606 (2007).
Numerical Study of the Effect of Model Scaling on Mixing and Flame Development in a Wake Flow Field Sadegh Tabejamaat and Takashi Niioka
Abstract Study of the effect of model scaling on combustion and flame-holding is very much warranted because of its theoretical and practical importance. In this study the effect of model scaling was investigated for combustion of hydrogen in supersonic airflow. Parallel Fuel injection is done from the base of a bluff body through a nozzle. Of high interest is how recirculation region behind the bluff body affects combustion and flame-holding. Two scales which directly affect the recirculation region are the width of the base of bluff body and diameter of nozzle. The effects of variation of these two scales on recirculation region, mixing and flameholding were numerically investigated. The governing equations in conjunction with full chemistry were solved by a high order numerical code. It has been shown that the flame-holding depends on the expansion of mixing region. Moreover, variation of velocity, mixing efficiency and combustion development are given for various geometry of the base and nozzle. Keywords Supersonic combustion · flame-holding · wake
Introduction Interest in the development of supersonic combustion ramjet (scramjet) has initiated many research works on the nature and the mechanism of supersonic combustion. Some of the main problems concerning with the scramjet are ignition and flameholding as well as supersonic combustion itself. Although, at high Mach number flight, a self-ignition can surely be achieved, for low Mach number flight a selfignition is impossible thus a stable combustion region cannot be established without special techniques [1]. It is well-known that supersonic combustion is a mixing-dominant phenomenon. Even for low Mach number flow the residence time is too short, consequently, a poor mixing efficiency cannot enable ignition and flame-holding. For the past three S. Tabejamaat Department of Aerospace Engineering, Amirkabir University of Technology, Tehran, Iran e-mail:
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decades, many experiments as well as theoretical and numerical studies have been directed toward supersonic combustion [2]. Increasing surface area between the two streams of fuel and air greatly enhances the mixing and reaction rates. This phenomenon is primarily controlled by turbulent flow. In this regard, generating instability or turbulence in the form of large coherent structures inside the reactant streams has been the focus of many researches. For this purpose, parallel fuel injection from the base of a strut has been considered as an appropriate means which provides a region of large coherent turbulent flow behind the base. As an effort to solve the aforementioned problems, one possibility is the use of recirculation region which can be established by for example a backward-facing step or a thick base. The characteristics of subsonic flame holding by recirculation zone have been investigated in early works [3]. However, a few efforts have been made for studying the characteristics of supersonic flame-holding by recirculation zone. Particularly, effects of model scaling on the flame-holding by recirculation zone have not been studied comprehensively. Studying the effects of model scaling on development of mixing region and flame-holding is the focus of the present study. In this regards, parallel injection of fuel from the base of a bluff body has been considered. By changing the scales of the base and injector, the processes of expansion at the corners, mixing layers, recompression and redevelopment are changed, which in turn change the flow field and recirculation zone. Consequently, mixing efficiency, combustion process, ignition and flame development are changed. The flame-holding mechanism for the present model with a preburner has been discussed in the authors previous reports [4, 5], and for more information regarding numerical scheme and code or chemical mechanism one may refer to these reports.
Modeling Analysis A physical model shown in Fig. 1 describes a two-dimensional supersonic flow behind a thick base, with a parallel fuel injection at the wake. This model may actually characterize the fuel injection in the Scramjet engine. In order to provide a condition of self-ignition, temperature of hydrogen as a fuel is increased using preburning before injection into supersonic flow. The upstream conditions of supersonic airflow and initial conditions of preburner are given in Table 1. The governing equations used to describe the flow and the combustion in the physical model of Fig. 1 are including of two-dimensional, unsteady, compressible, Navier-Stokes equations, a turbulence model, the state equation and the full chemistry of combustion process. The Navier-Stokes equations at a generalized curvilinear coordinate may be given as: →
→
→
⭸F j ⭸ Fv j → ⭸U + = +S ⭸t ⭸x j ⭸x j
(1)
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Fig. 1 A schematic layout of physical model
Table 1 Conditions at preburner and main flow
Supersonic airflow Preburner Nozzle
Pressure [MPa]
Temperature [K]
Mach number
Species mole fraction
0.05
293
1.5
21%O2 + 79%N2
0.09 0.049
293 1241.1
– 1.0
65%H2 + 35%(21%O2 + 79%N2 ) 52%H2 + 33%N2 + 15%H2 O
⎡ ⎡ ⎤ ⎤ ρYk ; k = 1..N S ρu j Yk ; k = 1..N S ⎢ ⎢ ρu 1 u j + δ1 j P ⎥ ⎥ ρu 1 ⎢ ⎢ ⎥ ⎥ → → ⎢ ρu 2 u j + δ2 j P ⎥ ⎥ ρu U =⎢ F = 2 j ⎢ ⎢ ⎥ ⎥ ⎣ ⎣ ρu 3 u j + δ3 j P ⎦ ⎦ ρu 3 ρE ρHu j ⎤ ⎡ ⎡ ⎤ ⭸Yk ρ D ; k = 1..N S ω˙ k ; k = 1..N S ⎥ ⎢ ⭸x j ⎥ ⎢ ⎢ ⎥ 0 ⎥ → ⎢ ⎢ ⎥ → σ1 j ⎥ ⎢ ⎢ ⎥ 0 Fv j = ⎢ S=⎢ ⎥ ⎥ σ2 j ⎥ ⎢ ⎣ ⎦ 0 ⎦ ⎣ σ3 j 0 u i σi j + q j
(2)
where U is a vector of conservative variables; Fj is a vector of convective variables; Fvj is a vector of viscous fluxes, and S is a vector of source terms. In addition, u, , P, E, Yk , H, , and are respectively, velocity, density, pressure, total energy, mass fraction, enthalpy, chemical production and stress tensor. The details of the above equations and Thermochemical properties can be found in Ref. [4]. Manipulation of turbulence model with Navier-Stokes equations and full chemistry model by numerical scheme demands a simple and computational efficient turbulence model. Therefore, the Baldwin-Lomax algebraic eddy viscosity model [6] has been used for closing the Navier-Stokes equations. It is assumed that the flow in Fig. 1 is symmetric, and so the calculation is done for only half of the flow field. The inflow is always supersonic with a fully developed turbulent boundary layer on the wall. An adiabatic wall is assumed, and the upper boundary always lies in the free stream; namely, the normal gradient vanishes along
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this boundary. A symmetric condition is employed for the lower boundary. These conditions provide non-reflective conditions which pass disturbances through the boundary rather than reflecting them into the numerical domain. The initial conditions for the whole domain are chosen as those at the inflow boundary. The boundary and initial conditions for fuel jet are determined based on the preburner calculation. Velocity, pressure, temperature and species concentrations are determined for a choked nozzle based on equilibrium combustion calculation. In the present study, a full mechanism chemistry model has been used [7]. In this model, nine species (H2 , O2 , H2 O, H, OH, HO2 , O, H2 O2 , and N2 ) in which N2 is assumed to be inert, have been considered. The specific reaction rate constant is usually evaluated by the Arrhenius law, and the net rate of change in mole concentration of species is calculated using full reaction mechanism.
Numerical Scheme Based on the total variation diminishing (TVD) condition, several kinds of TVD scheme have been generated. These schemes are successfully and widely used for shock capturing and strongly discontinuous surface waves. In this study, the secondorder implicit upwind TVD scheme proposed by Yee and Harten [8] in conjunction with LU-SGS scheme [9] has been employed for chemically reacting flow. A H-type grid system with 101 × 81 points were used for computational domain after base. Moreover, 20×40 points were used for region ahead of the base. 101×41 grid points just were used in wake to ensure high resolution in this region. 101 × 7 grid points were inserted in jet region with a minimum spacing of 0.0019 Hb in y direction to get a high resolution in shear layer region between jet and airflow. In addition, in wake region near corners of the base where shear layers produce a high gradient zone high resolution of 101 × 12 grid points with a minimum spacing of 0.013Hb in y direction were used.
Mixing Efficiency Mixing between air and fuel has a paramount importance in supersonic combustion. In order to obtain a quantitative feature of mixing, we define the mixing efficiency as H Meff = 0
4φ dy/H (1 + φ)2
(3)
where φ and H are the equivalence ratio and the lateral distance of computational domain, respectively. By this definition the mixing efficiency takes a maximum value of 1 at stochiometric case and 0 when any of hydrogen or oxidizer mole fraction is vanished.
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Results and Discussion Ignition is one of the important problems concerning with supersonic combustion in particular, at low Mach number. To obtain a self-ignition condition the mixture temperature must be above a certain level. There are several methods for ignition in supersonic airflow. Using Spark-plug igniter, Argon/Hydrogen plasma jet, and shock induced ignition are some example of ignition methods. In addition to these methods, a self-ignition of a hydrogen/air mixture can be also obtained by increasing the temperature of a mixture. For this purpose one may use a preburner to raise temperature of the injected fuel. In this method which was adopted in this study, a very fuel rich mixture burns inside a preburner and product of this combustion is injected into supersonic airflow. Minimization of the Gibss free energy approach to chemical equilibrium has been used for obtaining equilibrium state in the preburner [10]. The products of this combustion and its equilibrium thermodynamic properties are given in Table 1. According to Zukoski and Marble [3] the principle of subsonic flame stabilization is due to the structure of recirculation zones downstream of an injection. They found that as an approximate estimation, for the subsonic flame stabilization, the residence time is proportional to the length of the recirculation zone and inversely proportional to the velocity upstream. Therefore, considering a case with a little change in reaction time the flame-holding is directly proportional to the length of recirculation zone. It is thus seen that the residence time strongly depends on the geometrical expansion of recirculation zone. A longer recirculation zone is, a larger residence time and more stable flame are. The following results will show to what extent such concept works for supersonic flame stability. The governing equations were solved on a Cray-YMP by a computer code developed by the authors. A validation of the computer code has been given in the previous reports [4]. Scales of the physical model of Fig. 1 is considered to be changed in two ways. First, for the same nozzle size the width of the base, Hb is changed. Second, the nozzle diameter is changed while Hb is kept constant. Getting a background from subsonic flame-holding we intended to know how scale of model may affect combustion process. On the other hand, as different scales provides different recirculation zones, it is important to know the aforementioned relationship between recirculation length and flame-holding in subsonic flow is valid for combustion in supersonic flow or not. In Fig. 2 the variation of axial velocity at the centerline along X is shown for various Hb . At the first, it must be noted that the distance from the base, X , in Fig. 2 is non-dimensionalized by Hb = 15 mm. Fuel injection velocity for a choked condition is obtained as Uinj = 1022.1 m/s. Velocity profiles in Fig. 2 generally show a high velocity near the base because of injection, then fuel flow is decelerated by shear layer viscosity and finally in redevelopment region it is accelerated again. Experimental results [11] for base flow without injection predict that impingement of the shear layers occurs at approximately, X/Hb = 1.37. Considering the effect of injection as well as combustion to expand the recirculation region, the impingement point moves downstream. At Hb = 20 mm there is a strong reverse flow in recirculation zone with comparably long recirculation region. As Hb
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Fig. 2 The variation of axial velocity at centerline along X
decreases the reverse flow region becomes smaller, so that, for Hb < 6 the reverse flow region is very small. The second step is to find the relationship between recirculation region and combustion development. On the other hand, to find the effect of recirculation region on mixing efficiency that was defined before in this paper. The variation of mixing efficiency along X is shown in Fig. 3 for different Hb . Clearly, it can be seen that mixing efficiency takes two maxima: one near the base and the second one just around impingement point. The first maximum is due to large scale vortices near the base, particularly, in the corners which provide a high mixing efficiency. On the other hand, the second maximum corresponds to another large scale vortex in trailing region of the recirculation zone. Between these two maxima the fuel mixes with air in a narrow region of mixing layer. At this mixing layer, a strong turbulent
Fig. 3 The variation of mixing efficiency along X
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region is restricted to a narrow area and mixing is carried out by small scales of vortices. The comparison of the mixing efficiency curve with the velocity profile in Fig. 2 shows that a region with high mixing efficiency remains inside the recirculation region. It can be seen from Fig. 3 that the efficiency of the second strong mixing region considerably reduces with decreasing of Hb . It affects strongly the development of combustion in downstream. In order to have a two-dimensional feature of combustion development, distribution of OH mole fraction is shown in Fig. 4. It has been shown that the reactions involving OH production are slow and dominate the combustion. Therefore, in combustion of hydrogen, OH is a very important radical and its distribution can demonstrate combustion development. Clearly, it can be seen from Fig. 4 that combustion region laterally becomes smaller by decreasing of Hb . At Hb = 20 mm a large recirculation region enables a well mixing between fuel and oxidizer. The most important characteristics of such large recirculation zone are the enhancement of mixing throughout the recirculation zone. Of particular interest is expanding of mixing region between the two strong combustion zones; which are shown in Fig. 3. On the other hand, there are two strong combustion zones enabled by two strong mixing regions; shown in Fig. 3. One of these two combustion regions is established near the base, but another is a substantial region separated from the base. Existence of this substantial combustion region is very important for flameholding. Otherwise, flame is limited to a small region near the base. However, the
Fig. 4 Distributions of OH mole fraction; (a) Hb = 7 mm, (b) Hb = 10 mm, (c) Hb = 15 mm, (d) Hb = 20 mm
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development of substantial combustion region strongly depends on the development of combustion after the primary combustion region. Therefore, what we want to conclude from Fig. 4 is that combustion in this transition region as well as substantial combustion are enhanced by increasing Hb . This means the flame-holding strongly depends on the length of recirculation zone. For Hb < 7.0 combustion region can not be established at all. This limit was discovered by doing a lot of calculation for Hb = 4–10 mm. In Fig. 5 the variation of maximum temperature in combustion region is given against the Hb . As Hb becomes larger the maximum temperature increases, for a small Hb , recirculation zone becomes drastically small, leading to an extinction at Hb < 7.0. The nozzle width, h, is the second scale which was considered here. Considering the outlet condition at nozzle exit as is given in Table 1, any change in nozzle width, h, is resulted in a change in flow rate of injected gas. Nozzle scale as the same as the base scale affects the establishment of mixing region. It must be noted here that the mesh resolution in recirculation region and particularly in injection region is adequately high enough which can handle high gradient in mixing layer between jet and airflow. Velocity profiles and mixing efficiency variation are shown in Figs. 6 and 7, respectively. Velocity profiles show a great change in recirculation region by increasing of nozzle width, h, that is mainly due to the change of flow rate. Change in wake flow field for a small nozzle width, (h = 0.2 mm) is very small compared with a large nozzle width, (h = 0.8 mm). Development of mixing regions in Fig. 7 shows a proportional relationship between h and the length of mixing region. A rough measurement at this figure shows that the mixing region length and h increase by the same ratio. For instance, at h = 0.8 mm the length of mixing region reaches about X/Hb = 6.0 just about 4 times of this length for h = 0.2 mm. Consequently, it increases the residence time approximately by an order of 4 times. This fact can
Fig. 5 The variation of maximum temperature in combustion region against the base width, Hb
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Fig. 6 Variation of axial velocity at centerline along X against nozzle scale, h
be understood from development of combustion regions which are shown in Fig. 8. Numerical results predict a very well flame-holding for h > 0.4 mm. By increasing of h the substantial combustion region is intensified, expanded and a little shifted downstream. This behavior can be seen from the variation of temperature along centerline in Fig. 9.
Fig. 7 Variations of mixing efficiency along X against nozzle scale, h
232 Fig. 8 Distributions of OH mole fraction; (a) h = 0.2 mm, (b) h = 0.4 mm, (c) h = 0.6 mm, (d) h = 0.8mm
Fig. 9 Variation of temperature along centerline for various h
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Conclusion A numerical study on the effect of model scaling on combustion and flame-holding in supersonic airflow has been done. Hydrogen is injected from the base of a bluff body through a nozzle. Two scales which directly affect recirculation region and combustion development are the width of base and nozzle. The effects of the variation of these two scales on recirculation region, mixing and flame-holding were investigated. It has been shown that for combustion in supersonic airflow similar to subsonic flame, the residence time is directly proportional to the length of recirculation region. A wide base generates a large mixing region enables a well developed combustion downstream of the base. On the other hand, increasing of nozzle width greatly change the recirculation region, leading to a very intense mixing and enhanced flame-holding.
References 1. T. Niioka, K. Terada, H. Kobayashi, S. Hasegawa, Journal of Propulsion and Power, 11:112, 1995. 2. F.S. Billig, Journal of Propulsion and Power, 9:499, 1993. 3. E.E. Zukoski, F.E. Marble, Proc. Gas Dyn. Symp., Northwestern Univ., Evaston, 1956. 4. S. Tabejamaat, Y. Ju, T. Niioka, AIAA Journal, Vol. 35, No. 9, 1997. 5. S. Tabejamaat, T. Niioka, Proceeding of the Combustion Institute, Combustion Inst., Pittsburgh, PA, Vol. 28, 2000. 6. B. Baldwin, H. Lomax, AIAA Paper 78–257, 1978. 7. G. Stahl, J. Warnatz, Combustion and Flame, 85:285, 1991. 8. H.C. Yee, A. Harten, AIAA Journal, Vol. 25, No. 2, 1987. 9. J.S. Shuen, S. Yoon, AIAA Journal, Vol. 27, No. 12, 1989. 10. S. Gorden, B.J. Macbride, NASA SP-273, 1971. 11. V.A. Amatucci, J.C. Dutton, D.W. Kuntz, A.L. Addy, AIAA Journal, 30:2039, 1992.
Scale Model Flames for Determining the Heat Release Rate from Burning Polymers Gregory T. Linteris and Ian Rafferty
Abstract The utility of flame size for the assessment of the heat release rate of burning polymers has been studied. Six polymers were tested in the NIST cone calorimeter to determine their heat release rate, and their flame height, area, and volume. A reduced-scale burner was developed for producing non-flickering, laminar flames, and tests were conducted with four gases, three liquids, and three polymers; subsequent automated image analyses again determined the flame size. The scaling for the flame size was shown to be reasonably well described by Froude modeling for turbulent pool fires or by laminar jet diffusion flame theory. Keywords Heat release rate · polymers · fire · cone calorimeter
Introduction The heat release rate of a burning object is important for quantifying fire growth and spread in a building [1]. To estimate the heat release rate of full-scale objects, smallscale samples of representative materials are subjected to controlled radiant heat fluxes, and the heat release is measured. Various methods have been developed to measure the heat release rate of the reduced scale samples [2, 3], and they are accurate and effective, but unfortunately require expensive equipment and are relatively time consuming (0.5 h to 2 h per sample). If a less expensive, faster test method could be developed, heat release rate measurements might be more widely used by the polymer industry in their development of materials with lower flammability; such a method could also be used in high-throughput testing, allowing combinatorial techniques to be applied to the development of fire-safe materials. The present paper investigates the potential of measurements of flame size as a surrogate for heat release [4]. As a first step, various polymer samples were burned in the NIST cone calorimeter and their heat release rate was determined. G.T. Linteris Building and Fire Research Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA e-mail:
[email protected]
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Simultaneously, the flame images were captured and then analyzed to determine the flame height, area, and volume. An image analysis procedure was developed which allowed flame size determinations from a large number of frames using an automated image analysis program with various filtering techniques. In the second set of tests, a new burner was designed which would limit the flames to the laminar regime. To achieve non-flickering, laminar flames, this burner used smaller samples, provided a co-flow of oxidizer, and the geometry was controlled. Flames of solid, liquid, and gaseous fuels were produced, and the heat release rate was determined from the measured fuel consumption rate and the calculated heat of combustion. This paper describes the scaling relationships observed for the flame height, surface area, and volume with respect to the heat release, and discusses the utility of these for estimating the heat release.
Background Our search for a correlation between flame size and heat release is motivated in part by the observation by Orloff and de Ris [5] that turbulent pool fires have an approx3 ˙m imately constant heat release rate per unit volume of the flame, Q c (1200 kW/m ). The scaling laws for pool burners have been investigated by many researchers, and good reviews exist [6–8]. While these investigations have been most interested in turbulent flames typical of fires, they can also be applied to the present results obtained in the cone calorimeter. For the reduced-scale flames, however, it is more appropriate to use laminar flame theory, for which descriptions appear in the literature [9, 10]. Although all of these mathematical descriptions employ significant simplifications, they are expected to provide useful scaling relationships for correlating and interpreting the present data.
Experiment Two distinct sets of experiments were conducted. In the first, the NIST cone calorimeter [11] was used as the test bed for the burning polymer samples. This apparatus consists of a cone-shaped electric resistive heating element (hence the name), which provides radiant fluxes up to 100 kW/m2 on a polymeric sample of dimensions typically 7.5 cm to 10 cm diameter. In addition to other parameters, the exhaust is tested for mass flow, and volume fraction of oxygen (CO volume fraction measurements were not available for the present experiments). From these, the heat release rate of the burning sample is estimated using oxygen consumption calorimetry (which is based on the approximation that the heat release is proportional to the mass of oxygen consumed, times a constant of 13.1 kJ/g [12]). In the present experiments, the cone heater was off, and the sample decomposition was due entirely to the heat provided by the flame radiation and convection to the sample surface. A second experimental apparatus was specifically developed to reduce the transition to turbulent flow. For solid samples, a smaller sample was used (2.5 cm
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diameter, 2.5 cm tall), and it was positioned concentrically in a laminar co-flowing oxidizer stream of controlled velocity (16.7 cm/s). The configuration was a variant of the cup burner [13], and has been used previously in tests of halon replacements for suppressing solid-sample flames [14]. The gas and liquid fuels were tested in a separate cup burner, that has been described previously [15]. It consists of a cylindrical glass cup (28 mm diameter) positioned inside a glass chimney (53.3 cm tall, 9.5 cm diameter); glass beads and screens provide flow straightening for the fuel and oxidizer flows. For the liquid and gaseous fuels, the chimney was cut off at a point lower than the burner rim to avoid reflections from the flame image. Gas flows were measured by mass flow controllers (Sierra 8601 ) which were calibrated so that their uncertainty is 2% of indicated flow. For liquid fuels, syringe pumps (Yale Apparatus model YA-12) supplied the fuel at a known rate, which was manually adjusted to keep the fuel level flush with the edge of the cup rim. For the solid fuels, the mass consumption rate was determined with a laboratory scale (Mettler, PE-360). The syringe pump or the scale output was recorded with a computer. The fuels used were methane (Matheson UHP, 99.9%), propane (Matheson CP, 99%), ethylene, propylene (Matheson, CP), methanol (Aldrich, 99.8%), ethanol (Warner Graham), heptane (Mallinckrodt), trioxane (Aldrich, 99+%), and various commercially available polymers, including poly(methyl methacrylate) PMMA, polypropylene, paraffin, ethylene vinyl acetate (EVA), Nylon-12, and high density polyethylene (HDPE). The air was house compressed air (filtered and dried) which is additionally cleaned by passing it through an 0.01 m filter, a carbon filter, and a desiccant bed to remove small aerosols, organic vapors, and water vapor. The flame images for all tests were recorded with a digital color video camera (Sony, TRV-730) having a pixel resolution of 720 × 480 and framing rate of 30 Hz. The flame images were analyzed to determine the flame height, area, and volume using an automated image analysis system based on two software packages. The NASA image processing freeware program Spotlight 1.1 provided the flame outline from the color image (for PMMA and Nylon-12 in the cone, it was necessary to determine the flame outline manually, and a single, representative image was used). A custom-written code subsequently interpreted the outline and calculated the flame surface area and volume. In determining the flame outline, no attempt was made to distinguish between the yellow soot emission and the blue emission from radicals in the reaction zone; both delineated the presence of a flame. The various filtering options in Spotlight were adjusted for each flame sequence so that the determined flame outline matched the visual luminous flame location. For the small, non-flickering, laminar flames, estimation of the flame height and area from the flame outline was straightforward, obtained by measuring the flame tip location and cord width, and assuming axial symmetry, summing segments as described below. For the convoluted flames in the cone calorimeter, however, we 1 Certain commercial equipment, instruments, or materials are identified in this paper to adequately specify the procedure. Such identification does not imply recommendation or endorsement by NIST, nor does it imply that the materials or equipment are necessarily the best available for the intended use.
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used the method described by Orloff [16], in which the vertical flame is divided up into slices (determined by the vertical pixel resolution). Across each slice, the software determines the presence or absence of the flame, assumes that any segment of the cord containing the flame is a cylidrical disk, and sums the volume or area for each segment of the vertical slice. The total surface area or volume of the flame is the sum for all vertical slices. Using this approach for complicated turbulent flame shapes, Orloff was able to produce flame locations within about 5% of those obtained from integration of the flame presence probability density function. Hence, we estimate that at the 95% confidence level, the luminous flame area or volume for the cone flames are within about 10%. For the small laminar flames which have very regular shapes, this uncertainty is less than 1%. Note that in many of the figures which follow, if the uncertainty is shown on the data points, the error bars represent the standard deviation (66% confidence level) for the variation in the flame area for the 30 frames of data. This uncertainty is much larger than that due to the flame area determination techniques described above. An uncertainty analysis was performed, consisting of calculation of individual uncertainty components and root mean square summation of components. All uncertainties are reported as expanded uncertainties: X ± ku c , from a combined standard uncertainty (estimated standard deviation) u c , and a coverage factor k = 2. Likewise, when reported, the relative uncertainty is ku c / X . The expanded relative uncertainties for the theoretical heat release for the gaseous and liquid fuel flames are 4% and 2%. For the solid fuels, the theoretical heat release, determined from the mass loss rate and heat of combustion, varies according to how constant the heat of combustion is for that polymer. For PMMA, paraffin, and trioxane, the uncertainty is estimated to be 4%; for polypropylene, it is 10%.
Results Figure 1(a–c) show the measured flame height (a.), area (b.), and volume (c.) for the six polymers tested in the cone calorimeter; the dotted lines are linear least-squares fits to the data. The closed symbols are used for the samples for which automated image analysis could be performed (EVA, HDPE, PP, and trioxane), while the open symbols are used for Nylon-12 and PMMA, for which image analysis was performed manually. For data points determined automatically, each point shown is the average from 30 flame images, and the error bar is +/− one standard deviation. As indicated, the standard deviation is around 18%, 29%, and 15% for the height, area, and volume, respectively, for the flames in the cone. While there is significant scatter in the points representing the averaged data, the height, area, and volume of the flame are clearly correlated with the measured heat release. Although the cone calorimeter would appear to be a good test apparatus for comparing the flame size with the heat release, several features make it less than optimum. Geometrical factors influence the flame shape; for example, the sample holder support is not optimized for smooth flow, causing the exhaust-induced air flow to be highly irregular and disturbing the flame. Also, the edge of the typical sample holder
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Fig. 1 Measured flame height (a), area (b), and volume (c), as a function of heat release rate for polymers tested in the cone calorimeter. Open symbols denote manual image analysis; closed, automated; dotted lines are linear curve fits to the data
can trip the flow to turbulent flow [16, 17], changing the flame size-heat release rate relationship. The typical sample size creates flames which are in-between laminar and turbulent flow, making them hard to describe analytically, and causing the oxygen transport rate to the flame to vary. If the conical heater element is being used, it
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can obstruct the view for tall flames. Finally, the flame images are highly irregular, making the determination of the flame area difficult. As a result, we conducted tests in the reduced-scale burner described above as the cup burner. For the cup-burner flames, the theoretical heat release of the flames was calculated from the measured fuel input rate and the heat of combustion of the gaseous reactants. An implicit assumption in the present work is that the combustion efficiency is high (>97%). The polymers selected for the tests were those with relatively constant and known heats of combustion. Since we are interested in the oxygen demand of the gas-phase reactants, the heat of combustion used was for gas-phase reactants to gas-phase products. Figure 2(a)–(c) shows the flame height, area, and volume as functions of the theoretical heat release. (Note that the heptane point is scaled by 1/2 for both variables to put it on the same plot without expanding the scales.) It is clear from the figure that the gaseous flames (square symbols) have the least variation between images, and their flame height, area, and volume are very well correlated with the predicted heat release. The reduced-scale, cup burner produces flames which have little variation between images, typically 3%, 6%, and 10%, for the gaseous, liquid, and solid fuels, respectively, regardless of whether height, area, or volume. For turbulent diffusion flames above pool fires, Zukoski [6] outlines various theoretical scaling relationships which have been developed based on Froude modeling. These typically are power-law functions of the form Z f /D ∼ Q ∗n , in which Z f is the flame height (normalized by the burner diameter D), and Q∗ is the nondimensional square root of the Froude number expressed in terms of the heat release ˙ c /(ρ∞ Cp T∞ (g D)1/2 D 2 ), in which Q ˙ c is the heat release in the flame, Q∗ = Q ρ∞ , Cp , T∞ , are the density, specific heat, and temperature of the oxidizer, and g is the acceleration due to gravity. Figure 3 shows the normalized flame height Z f /D as a function of Q ∗ for the gaseous, liquid, and solid fuels in the reduced-scale cup burner (solid symbols) as well as for the solid fuels in the cone calorimeter (open symbols). Also shown are the power law relations for Z f /D suggested by Zukoski 2/5 2/3 [6], each applicable in a range of Q ∗ , with a Q ∗ dependence for Q ∗ > 1, Q ∗ for 2 0.15 < Q ∗ < 1, and Q ∗ for Q ∗ < 0.15. The dotted black line is a linear curve fit to the data in the reduced-scale cup burner. The present data, from either burner, are clearly in the transition regime. The laminar flame theory of Roper [10] for co-flow jet diffusion flames can also be used to predict the flame height in the reduced-scale cup burner flames. The calculated flame height from Roper’s correlation is shown in Fig. 3 as the dotted red 1 line, which indicates a Z f /D variation with Q ∗ , which is consistent with the curve 1 fit through the reduced-scale cup burner data which also gives a Q ∗ dependence. (The offset of the Roper prediction with the curve fit through the data is likely due to the wide burner used in the present flame, which gives a non-zero flame area at zero height.) Our ultimate goal in the present work is to relate the measured heat release to the measured flame size (height, area, or volume). Simple scale arguments of the type suggested by Orloff and de Ris [5] can be used to determine the predicted and actual scaling relationship between the heat release and the height, area, or volume.
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To do this, it is useful to plot the heat release normalized by the flame height, area, or volume, as a function of the heat release, as done in Fig. 4. From the power-law fits to the data, it is possible to extract the relationship between the heat release rate ˙ c , or volume Q ˙ ˙ c , area Q normalized by the height Q c , and the heat release rate.
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Q*
Fig. 3 Normalized flame height Zf /D as a function of Q ∗ (cone calorimeter data, open symbols; reduced-scale cup burner, filled symbols)
From these, we can then estimate the power-law relationship correlating the heat ˙ c ∼ An a , or Q ˙ c ∼ Vn v . ˙ c ∼ Zn f , Q release with the height, area, or volume; e.g. Q f f f Table 1 lists the power-law scaling coefficients n f , n a , n v , for the heat release based on the measured flame height, area, or volume as observed in either the cone or the reduced-scale cup-burner flames; values are also given for the laminar flame theory prediction of Roper [10], as well as the turbulent flame theory predictions from Froude modeling as outlined by Zukoski [6]. As shown, the experimental results for the cone calorimeter flames are midway between the theoretical results for turbulent flames in the 0.15 < Q ∗ < 1 and Q ∗ > 1 regimes. For the flames in the reduced-scale cup burner, the results are midway between the theoretical prediction of Roper for laminar jet flames, and the Froude modeling turbulent flames in the 0.15 < Q ∗ < 1 regime. Two additional features of the flames were observed to be important for the data analysis. First, the image recording and analysis used the visible image, which includes both the blue emission from flame radicals in the reaction zone, as well as the much stronger black body emission from soot particles. We observed the luminous flame shapes to be larger than the blue reaction zone flame shapes; other researchers have found the luminous shapes to be 10% to 60% larger [18, 19]. Second, as the sample size gets smaller, the physical effects which may contribute to flame retardancy, for example, barrier layers on the burning polymer, can be affected by the small size.
Scale Model Flames for Determining the Heat Release Rate from Burning Polymers Methane Ethylene Propane Propylene
1000000
Qc''' = 10000Qc–2/3
/ Volume
100000
Methanol Ethanol Heptane Paraffin Polypropylene PMMA HDPE (Cone) EVA (Cone) PP (Cone) PMMA (Cone) Nylon-12 (cone) Trioxane (Cone )
Qc''' = 8000Qc–1/4
10000
1000
100
/ Area
Qc'' = 75Qc–1/4 Qc'' = 55Qc1/7
Qc' = 3Qc–1/10 10
1 0.01
Qc' = 7.7Qc1/7
/ Height
Heat Release per Flame Height, Area, or Volume kW/m, kW/m2, kW/m3
243
0.10 1.00 Heat Release Rate kW
10.00
Fig. 4 Heat release normalized by the measured flame height, area, or volume as a function of the heat release rate for flames in the reduced scale cup burner (solid symbols) and the cone calorimeter (open symbols); the lines are the results of a power-law curve fit to the data, together with the equation
Conclusions Experiments have been performed to measure the heat release rate as well as the flame height, area, and volume of burning gaseous, liquid, and solid fuels. Flames from samples in the NIST cone calorimeter had relatively high variability in these measured parameters from image to image, and were reasonably well described by Froude modeling predictions for turbulent pool flames, but in a regime where viscous effects are starting to be important. A reduced-scale burner similar to the
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Table 1 Power-law scaling coefficient for the heat release from the measured flame height, area, or volume, as observed in either the cone or the reduced-scale cup-burner flames, as well as that predicted by theory Scaling relationship
Power law scaling coefficient, n i Observed
˙c ∼ Q ˙c ∼ Q ˙c ∼ Q
Z fn z ; Anf a ; Vfn v ;
nz = na = nv =
Theory
Cup burner
Cone
0.91 0.8 0.4
1.2 1.2 0.8
Laminar flame, Roper [10]
Froude modeling [6] 0.15 < Q ∗ < 1
1 < Q∗
1.0 0.5 0.25
1.5 0.75 0.5
2.5 1.25 0.83
cup burner produced flames with much lower scatter and image to image variation. The variation of the height of these flames with heat release was well-predicted by the theoretical model of Roper. The small laminar flames showed scaling behavior of the heat release with respect to the height, area, and volume, midway between that of laminar co-flow jet diffusion flames and turbulent pool flames in the transition regime. Further research is necessary to determine if these measured parameters (flame height, area, and volume) can be determined accurately enough to be useful for predicting the heat release rate, especially for a wider range of test materials with actual heat release data based on oxygen consumption calorimetry. Acknowledgments Helpful conversations with David Urban, Peter Sunderland, and Jiann Yang added greatly to this work. This research was supported by NIST and NASA’s Office of Biological and Physical Research.
References 1. V. Babrauskas, R.D. Peacock, Fire Safety J. 18 (3) (1992) 255–272. 2. B.A.L. Ostman, I.G. Svensson, J. Blomqvist, Fire Mater. 9 (4) (1985) 176–184. 3. A. Tewarson, Flammability of polymers and organic liquids, Part I, Burning intensity, FMRC Serial 22429, Factory Mutual Research Corp., Norwood, MA, 1975. 4. Lyon, R., FAA, Personal Communication, 2003. 5. L. Orloff, J. de Ris, Proc. Combust. Inst. 19 (1982) 885–895. 6. E. Zukoski, Fluid dynamic aspects of room fires, In: Fire Safety Science: Proc. of the First International Symp., Hemisphere, New York, 1984, pp. 1–30. 7. B.J. McCaffrey, Flame height, In: SFPE handbook of fire protection engineering, SFPE (Ed.), National Fire Protection Assoc., Quincy, MA, 1988, pp. 298–305. 8. J.G. Quintiere, Fire Safety J. 15 (1) (1989) 3–29. 9. S.P. Burke, T.E.W. Schumann, Ind. Eng. Chem. 20 (10) (1928) 998–1004. 10. F.G. Roper, Combust. Flame 29 (3) (1977) 219–226. 11. W.H. Twilley, V. Babrauskas, User’s guide for the cone calorimeter, SP-745, National Institute of Standards and Technology, Gaithersburg, MD, 1988. 12. C. Huggett, Fire Mater. 4 (2) (1980) 61–65. 13. B. Hirst, K. Booth, Fire Technol. 13 (4) (1977) 296–315. 14. M.K. Donnelly, W.L. Grosshandler, Suppression of fires exposed to an external radiant flux, NIST IR 6827, National Institute of Standards and Technology, Gaithersburg MD, 2001.
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15. G.T. Linteris, G.W. Gmurczyk, Prediction of HF formation during suppression, In: Fire suppression system performance of alternative agents in aircraft engine and dry bay laboratory simulations, R.G. Gann (Ed.), National Institute of Standards and Technology, Gaithersburg, MD, 1995, pp. 201–318. 16. L. Orloff, Proc. Combust. Inst. 18 (1981) 549–583. 17. V. Babrauskas, W.H. Twilley, W.J. Parker, Fire Mater. 17 (2) (1993) 51–63. 18. R.E. Mitchell, A.F. Sarofim, L.A. Clomburg, Combust. Flame 37 (3) (1980) 227–244. 19. A. Gomez, G. Sidebotham, I. Glassman, Combust. Flame 58 (1) (1984) 45–57.
Scale Modeling of Magnetocombustion Phenomena John Baker, Mark Calvert and Kozo Saito
Abstract The effect of a non-uniform magnetic field on the height of a laminar diffusion flame is examined. Non-uniform magnetic fields impact flame height due to the paramagnetic and diamagnetic properties of the constituent species. To date, much of the experimental data on magnetocombustion behavior has been conducted on small-scale flames produced in a laboratory. In order to develop magnetocombustion technologies, it will be necessary to formulate scaling rules for the experimentally observed behavior. Such scaling rules are discussed and a simple theoretical model for the flame height of a two-dimensional diffusion flame in the magneticallycontrolled regime is developed. A parametric study of the impact that the various dimensionless parameters have on the behavior of a magnetically-controlled flame has been conducted and the results of the study are discussed. Keywords Diffusion flame · magnetic field · magnetically-controlled regime · theoretical modeling · dimensionless parameters
Nomenclature a b B BM C FM Fr Frb Fr M,b g I
Buoyant acceleration Burner width Magnetic induction Dimensionless magnetic field gradient Dimensionless number group Kelvin body for term Frounde number based on flame height Frounde number based on burner width Magnetic Froude number Gravitational acceleration Momentum adjustment factor
J. Baker Department of Mechanical Engineering, University of Alabama, Tuscaloosa, AL 35487, USA e-mail:
[email protected]
K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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Lf Ng M Re T u Fo Y F,stoic z Z θf ρ μo χ
J. Baker et al.
Flame height Buoyant to magnetic force ratio Reynolds number Temperature Fuel exit velocity Stoichiometric fuel mass fraction Spatial coordinate Dimensionless spatial coordinate Dimensionless flame temperature Density Permeability of free space Magnetic susceptibility
Subscripts buoy f F M mom ∞
Buoyancy-controlled regime Flame Fuel Magnetically-controlled regime Momentum-controlled regime Ambient conditions
Introduction Paramagnetism and diamagnetism are responsible for the experimentally observed interaction between laminar diffusion flames and non-uniform magnetic fields. Paramagnetism is the slight attraction of a material to a magnetic field. Oxygen is typically the principal paramagnetic gas associated with gaseous non-premixed hydrocarbon combustion. Diamagnetic materials exhibit a slight repulsion to an applied magnetic field. Nitrogen, hydrocarbon fuels, and most of the products of combustion are diamagnetic in nature. While the forces associated with paramagnetism and diamagnetism are much smaller than those associated with ferromagnetism, it is well documented that diamagnetic and paramagnetic forces impact flame behavior. Since an applied magnetic field produces a body-type force, previous research has drawn an analogy between the magnetically induced behavior and that produced as the result of a gravitational body force [1, 2]. Conceptually, an applied magnetic field can be considered a selective body force, i.e. different species not only experience a different force magnitude but also a different force direction. This significantly complicates an analysis of the resulting physical transport behavior. This paper examines the scaling parameters associated with laminar diffusion flames in the presence of non-uniform magnetic fields. The specific objectives of this paper are to:
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1. theoretically describe in term of dimensionless numbers the regime where magnetic forces dominate the transport behavior in the vicinity of the flame, i.e. the magnetically-controlled regime, 2. develop a simple theoretical model, cast in terms of the above mentioned dimensionless parameters, and 3. use the theoretical model to examine the impact of non-uniform magnetic fields on laminar diffusion flames in the magnetically-controlled regime.
Scaling As previously mentioned, the forces associated with an applied magnetic field are body forces and may be considered to produce a selective magnetic buoyancy force under certain conditions. It is well known that ignoring gravitational buoyancy forces in models of circular burner port laminar diffusion flames does not adversely affect the ability of such models to predict flame height [3]. With regard to modeling flames produced using slotted burners, this is not necessarily true. Two distinct flame regimes have been identified for flames produced using slotted burners, the momentum-controlled regime and the buoyancy-controlled regime [4]. The respective regime is determined by an examination of the Froude number, defined as [4] 2 u F I Y F,stoic Fr = aL f
(1)
where I = 1 for a uniform port exit velocity or I = 1.5 for a parabolic port exit velocity and the buoyant acceleration may be approximated as a ∼ = 0.6g where T f /T∞ − 1 . In the momentum-controlled regime, Fr >> 1, the height of the flame can be predicted by the following theoretical expression [4] 1/3
L mom =
β 2 θ f Re
(2)
2 I 2 Y F,stoic
where u F I Y F,stoic b ν θ f = T f /T∞ Re =
(3) (4)
In the buoyancy-controlled regime, Fr << 1, the height of the flame can be found using [4] L buoy =
2/3
9β 4 Re2 Frb θ f 4 8I 4 Y F,stoic
1/3 (5)
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where
u F I Y F,stoic Frb = ab
2 (6)
In the above expressions a unity Schmidt number has been assumed and a power law expression for the mass diffusivity was employed following Roper. Note that in the expression for the buoyancy-controlled flame height there is a difference in the definition of the Froude number. While Roper [4] used the flame height to define the Froude number, the Froude number used in the expression for the buoyancycontrolled flame height, Eq. (5), is based on the burner width. When following the theoretical model developed by Roper, it is necessary to specify the form of the axial component of velocity for a flame produced using a slotted burner port. For a flame in the presence of an applied magnetic field, the form of the axial velocity is found using du 2z 2 = 2a + FM dz ρf
(7)
where the term on the left hand side is that associated with advection, the first term on the right hand side is that associated with buoyancy, and the second term on the right hand side is the Kelvin body force term associated with the influence of the magnetic field. This equation is identical to that employed by Roper but with the addition of the magnetic force term. The Kelvin body force per unit volume within a fluid may be expressed as FM = −
χO x B · ∇B μo
(8)
where it has been assumed that oxygen is the only gas under consideration. Since the magnetic susceptibility of oxygen is two orders of magnitude greater than that of the diamagnetic species, this assumption is justified and also significantly simplifies the expression. Assuming that the magnetic field varies only in the axial direction and integrating the above expression yields u 2z = u 2zo + 2az −
χO x 2 B − Bo2 ρ f μo
(9)
where for a magnetic field that is a linear function of the distance above the burner port u 2z = u 2zo + 2az −
χ O2 ρ f μo
dB dz
2 z 2 − Bo
χ O2 d B z ρ f μo dz
(10)
The effective axial component of velocity at the burner exit, u zo , is found from a momentum balance between the fuel and oxidizer required for complete combustion.
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For no secondary flow the effective axial component of velocity is given as u zo = u F I Y F,stoic
(11)
Introducing this expression into the equation for the axial component of velocity and non-dimensionalizing the equation gives u 2z 2 BM 2 1 =1+ Z+ Z + Z 2 u zo Frb Fr M,b Fr M,b
(12)
where Z = z/b (d B/dz) b BM = Bo 2 ρ f μo u F I Y F,stoic Fr M,b = − χ M O2 Bo (d B/dz) b
(13) (14) (15)
As in Roper’s work, the above equations can be used to determine under which regime the flame exists, i.e. Momentum-Controlled : Frb → ∞ and Fr M → ∞ Buoyancy-Controlled : Frb → 0 and Fr M → ∞ Magnetic-Controlled : Frb → ∞ and Fr M → 0
Theoretical Modeling When deriving a theoretical model for the flame height of a laminar diffusion flame produced using a slotted burner, Roper made the following assumptions [4]: (a) Temperature and diffusivity are constant in regions of the flame where concentration gradients are significant, (b) Combustion does not cause a net change in the number of molecules within the flame. (c) Axial diffusion is negligible, (d) The Schmidt (Sc) and Lewis (Le) numbers have values of unity, (e) The component of the gas velocity parallel to the flame axis has a characteristic velocity u z , which is a function of z coordinate only. Variation of u z as a function of x and y coordinates is negligible within the flame region, (f) The flame gas velocity in the vertical direction, u z , is equal to the axial component of velocity, u f , in the reaction zone, and (g) The flame gases start with an axial velocity u zo at the burner exit.
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In this study, one additional assumption is made. The additional assumption is that the flame exists within a non-uniform magnetic field of linearly decreasing strength above the burner port exit. For a flame produced using a slotted burner, Roper [4] showed that the following expression must be satisfied
1/3
β 2 Reθ f
2 I 2 Y F,stoic
L
= 0
uz dZ u zo
(16)
where Roper’s expression has been made dimensionless using the conventions defined above. For a magnetically-controlled flame, the first two terms in the expression for the axial velocity, Eq. (12), are dropped and thus
1/3
β 2 Reθ f
2 I 2 Y F,stoic
LM
= 0
1 BM 2 Z+ Z Fr M,b Fr M,b
1/2 dZ
(17)
is used to find the flame height. When B˜ L M <<1 the above equation can be simplified by dropping the second term in the integral and upon integration yields the following linearized expression for the flame height of a laminar diffusion flame produced using a slotted burner port in the presence of a non-uniform magnetic field LM =
2/3
9β 4 Frm,b Re2 θ f
1/3
4 4I 4 Y F,stoic
(18)
From Eq. (18) is is clear to see that for the linearized case, the magneticallycontrolled flame height has a similar functional form as that of a buoyancy-controlled flame. Recalling the definition of the flame height for the buoyancy-controlled regime, Eq. (5), the ratio of the flame height in the magnetically-controlled regime to that in the buoyancy-controlled regime is 1/3 2ρ f μo a LM Fr M,b 1/3 1/3 = 2 = − = Ng M L buoy Frb χ O2 Bo ddzB
(19)
The general nonlinear magnetic controlled flame height is found from the solution of % −1 2L M + B M L M + BM L M 2 ⎡ ⎛ ⎞⎤ 1 1 ⎣ ⎝ ⎠⎦ = C % + 3/2 log 2 2B M 2 BM L M + BM L M 2 + 2B M L M + 1
(20)
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where 1/3
C=
1/2
4β 2 Reθ f Fr M,b
(21)
2 I 2 Y F,stoic
and where the integration was evaluated using integral tables [5].
Results and Discussion Table 1 provides a listing of the baseline data used to generate the results presented below. The values are representative of a propane-air flame and are similar in magnitude to the conditions examined in Baker and Calvert [1]. Data from the theoretical models were generated using Mathcad 2001. Figure 1 provides information as to the influence of the magnetic Froude and Reynolds numbers on the magnetically-controlled flame height. As expected, an increase in the magnetic Froude number or the Reynolds number will increase the flame height. Note that the information provided in Fig. 1 was generated using the linearized theoretical model, i.e. Eq. (18). For the baseline value of the dimensionless magnetic gradient used, the percent difference between the results obtained from Eq. (18) and those from Eq. (20) was approximately 0.41%. A comparison was made between the predictions using the linearized theoretical model and previously published experimental data [1]. While the theoretical results were on the same order of magnitude as the Table 1 Baseline parameters β θf
5.5 6.0
I Y F,stoic
1.5 0.06
10−2 10−4
Re Fr M,b
Ng M BM
250 Re = 0.001 Re = 0.01 Re = 0.1 Re = 1.0
200
LM
150
100
50
0
10–5
10–4
10–3
10–2
FrM,b
Fig. 1 Linearized model of magnetically-controlled flame height
10–1
0.1 −0.02
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experimental data, the theoretical results tended to under-predict flame heights. This can be explained by considering that the fact that the Froude number in the experimental data was “small”. As previously mentioned, for the flames to exist in the purely magnetically-controlled regime the Froude number must approach infinity and the magnetic Froude number must approach zero. The experimental data was in a transition regime and since the model presented in this paper is for a purely magnetically-controlled flame, a direct comparison cannot be made between the experimental data and the magnetically-controlled theoretical model. Figure 2 is a plot of the ratio of the magnetically-controlled flame height to that predicted by Roper for a buoyancy-controlled flame using Eq. (19). As the dimensionless parameter relating the buoyancy forces to the magnetic forces, N g M , decreases the ratio decreases. This agrees with previously reported experimental finding that show the application of an applied magnetic field decreases the flame height. While not explicitly shown on the plot, for values of N g M greater than unity, the application of a magnetic field is predicted to produce flames larger than buoyancy-controlled flames. Unfortunately, only slot flames with N g M less than unity have been examined experimentally to date. Figure 3 provides a plot showing the influence of the magnetic field gradient on flame height. As can be seen in Eq. (20), the flame height is a strong function of the magnetic field gradient. As the magnetic field gradient increases, there is a decrease in the flame height. This behavior has again been observed experimentally. Contrast this behavior, for a slotted burner in a non-uniform magnetic field, to that for a circular burner in a uniform magnetic field. It has been previously observed that there is no change in the height of a laminar diffusion flame produced using a circular burner port when such a flame is placed in a uniform magnetic field. For the range in B M considered, there was a 2% decrease in the predicted flame height. Figure 4 is a plot of the impact that varying the dimensionless group defined in Eq. (21) has on the predicted flame height. Clearly, as the dimensionless group C increases the flame height increases. Since C contains information as to the stoichiometry of the flame, the inertia forces acting on the flow field in the vicinity of 1.0
LM/Lbuoy
0.8
0.6
0.4
0.2
Fig. 2 Impact of applied magnetic field on flame height relative to that of a buoyancy-controlled flame
0.0 10–5
10–4
10–3
10–2 NgM
10–1
100
Scale Modeling of Magnetocombustion Phenomena
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1.035
Fig. 3 Impact of magnetic field gradient on magnetically-controlled flame height
1.030
LM
1.025
1.020
1.015
1.010 –0.10
–0.08
–0.06 BM
–0.04
–0.02
3.0
Fig. 4 Impact of variations in dimensionless group C on magnetically controlled flame height
2.5
LM
2.0 1.5 1.0 0.5 0.0 0.1
1
10
C
the flame, the flame temperature, and the magnetic forces acting on the flow field in the vicinity of the flame, this plot can provide information as to the influence of the various parameters on a magnetically-controlled flame.
Conclusions This paper has focused on the scaling parameters associated with laminar diffusion flames in the presence of a non-uniform magnetic field. Specifically, a laminar diffusion flame produced using a slotted burner in the presence of an upward decreasing non-uniform magnetic field has been examined. From the information obtained during this study, the following conclusions may be drawn: 1. The magnetically-controlled regime is identified as the regime where the traditionally defined Froude number approaches infinity and the magnetic Froude number approaches zero. In this regime, the transport behavior in the vicinity of the flame is dominated by the magnetic field forces.
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2. A theoretical model has been developed for magnetically-controlled flame height. The linearized version of this model produced a closed form expression for magnetically-controlled flame height. 3. The flame heights predicted using the theoretical model are on the same order of magnitude as experimentally observed flame heights but the theoretical model typically under-predicts the flames height. The discrepancy between the theoretical and experimental flame heights is likely to be due to the assumption of a purely magnetically-controlled regime during the development of the theoretical model. Acknowledgments This research was supported by the NASA Office of Biological and Physical Research, Combustion Science and Chemically Reacting Systems Program (NAG3-2560). The authors would like to thank Dr. Peter Struk for serving as the NASA technical monitor for this project.
References 1. Baker, J. and Calvert, M.E., Combustion and Flame, 2003, 133/3, pp. 345–357. 2. Fujita, O., Ito, K., Chida, T., Nagai, S., and Takeshita, Y., 27th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, 1998, p. 2573. 3. Turn, S.R., An Introduction to Combustion, McGraw-Hill, New York, 2000. 4. Roper, F.G., Combustion and Flame, 1977, 29, pp. 219–226. 5. Beyer, W.H., CRC Standard Mathematical Tables, 27th Ed., CRC Press, Boca Raton, Florida, pp. 255–256.
Scaling Analysis of Diffusion Flame Attachment and Liftoff Indrek S. Wichman and Bassem Ramadan
Abstract Flame attachment and liftoff is examined using scaling methods. Three regimes of practical and theoretical interest are described: (1) a very slow flow regime; (2) a slow flow regime; (3) a moderate flow regime. Correlations for flame quenching distance and characteristic flame width versus flow rate are developed for regimes (2) and (3). Regime (1) is independent of the flow rate. For moderate to large values the flow rate dictates flame structure changes relative to liftoff height, whereas for low flow rates the sensitivity to reaction rate controls the flame response. Comparisons with four different groups of experiments are favorable despite the fact that the experimental conditions differ from the model configuration. A liftoff height versus flow rate plot based partly on present results is constructed. Keywords Flame liftoff · diffusion flames · theoretical analysis
Nomenclature D D Do i Le Li m n q Q Tf
Mass diffusion coefficient Damk¨ohler number Damk¨ohler number without mass flow, Do = ε2 D Dimensional lengths (i = r, q) [r ≡ flame tip reaction zone; q ≡ quenching] Lewis number, Le = α/D Dimensionless lengths (i = r, q) Order of reaction in oxidizer Order of reaction in fuel Heat release Dimensionless heat release, Q = 1 + φ Flame temperature, T f = To + qY F F /c p (1 + φ)
I.S. Wichman Department of Mechanical Engineering, Michigan State University, E. Lansing, MI 48824-1226, USA e-mail:
[email protected]
K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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w
Chemical reactivity, w = y Om y Fn exp [−β(1 − τ )/[1 − α(1 − τ )]] (see Ref. [34]) Mass flow ratio, x = ε1 /ε2
x
Greek α β ε φ τ
Dimensionless enthalpy ratio, α = 1 − To /T f ; Also thermal diffusivity, α = λ/ρC p Zeldovich number, β = α E/RT f Peclet number or dimensionless flow rate, ε = u /α Stoichiometric index, φ = νY F F /Y O O Dimensionless temperature, τ = (T − To )/(T f − To )
Introduction Real flames in nature and in the laboratory are bounded by material surfaces. In fire and flame spread, the material surface is an essential feature of flame spread because the fuel vapors for gas-phase combustion originate from the surface as it decomposes. In laboratory experiments and technological applications, flames are always either adjacent, or attached, to nearby solid surfaces. Combustion research, by contrast, generally treats the condensed phase merely as a means for directing the gas flow. In isolated cases the condensed phase is treated as a boundary at which semi-realistic conditions must be satisfied by the gas flow. See the review article [1]. A survey of the combustion literature has shown [2] that approximately 1 in 20 articles fully addresses the interaction of the gas and solid phases. An extreme version of the absence of solid/gas interaction was found in Ref. [3], in which an experimental study of flame holders in ducted premixed flames specified neither duct nor flame holder materials: the material existed only to channel the flow. In this study, we shall examine the attachment and liftoff of diffusion flames (DFs) near cold, chemically inert surfaces. The configuration that we shall examine is shown in Fig. 1. The problem of diffusion flame attachment near surfaces is relevant for many types of combustion problems that generally fall into two broad classes. One class is flame spread, where the diffusion flame is anchored at its tip (or leading edge) to the condensed phase over which it presently spreads. The second class is burner flame attachment, where the diffusion flame is held, in a streaming flow, in the vicinity of a divider that separates the oxidizer flow from the fuel flow. It is necessary to understand flame attachment, lifting, and blowoff because flame attachment is crucially important for practical devices like combustors, furnaces and boilers. Usually, the flow velocities in flame spread are low, whereas in burner flames they can be high, sometimes supersonic. The latter class of problems is most commonly discussed in the context of practical flame attachment using artificially-enhanced
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Fig. 1 The model configuration and dimensionless equations. The vertical walls are porous with constant temperature To . The wall boundary conditions are shown
recirculation [4, 5]. Precise explanations of the observed behavior are not available, and technological progress has largely occurred through experimental trial and error, ad-hoc methods, dimensional analysis, intuition and experience. In these two classes of problems there are two important limiting cases. In the first limiting case, the flame leading edge has been moved sufficiently far from the surface or divider that the influence of the solid dividing boundary is nil. This constitutes the adiabatic limit, for which a pure gas-phase examination suffices to characterize and explain the flame structure. This limit is attractive because it simplifies the physics and the mathematical analysis [6–11]. In the second case, the flame tip lies sufficiently close to the divider to be considered as attached to it. In actuality the diffusion flame extinguishes a certain distance from the lower (fuel) wall, and a dark quench zone separates the surface from the flame tip. The flame tip may possess a complicated structure, called a tribrachial flame [12–15]. The non-adiabatic problems are more difficult to solve than the adiabatic problems, since the explicit connection to the solid phase must be included in the calculations. At the very least, a rigorous accounting of the flame behavior near a solid surface must be had, with or without surface pyrolysis or in-depth solid phase chemical decomposition or pyrolysis. In some combustion applications, such as the construction of miniature burners, the interaction of flame and surface is the principal impediment to the development of functional devices. Physically, our model can represent a heterogeneous condensed phase that undergoes surface gasification followed by mixing and gas-phase reaction; or, it may describe flame spread [16], since the conformal mapping ω = sin(π z/2), z = x + i y, [12–14] produces a modified flame-spread-like configuration [12]; or, it may describe burner flame attachment in the presence of a cooled exit-plane porous plug that produces a gas flow resembling the one-dimensional slug flow considered here (see Fig. 1). The literature of diffusion flame attachment is large and diverse [12–15, 17–32]. Much of the research employs the round jet configuration, which is relevant to the
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configuration of Fig. 1 if only one side of a cross-section of the jet is considered, and if curvature effects in the direction orthogonal to the jet axis are negligible. The initial studies of attachment and liftoff employed parametric correlations of experimental data, which were gathered primarily in the turbulent flow regime [20, 21]. These correlations retain their general validity, hence present models must be able to explain them where they are valid and modify them where they fail. Alternative explanations of liftoff were provided in Ref. [19] based on large-scale turbulent flow features of the jet flows. Two detailed reviews of these and other original works may be found in Refs. [23, 24]: while disagreeing with some of the turbulence modeling features, these works nevertheless support the final correlations. The work of Takahashi and colleagues [25–28] employed sophisticated experimental diagnostics and provided clarification of certain features of liftoff, resulting in a theoretical argument supporting the idea of stoichiometric premixed flame propagation by the flame tip and stressing the importance of radical production in chemical reactions near the flame leading edge. Of interest are the plotted contours of constant species concentration and temperature, as well as velocity fields. These provide clues for understanding the fundamental structure of attached and lifted flames. Schefer and colleagues [29] emphasized experimental diagnostics under intense turbulence conditions. Chung and colleagues [30, 31] took a different approach and examined flame liftoff under laminar flow conditions, seeking to thoroughly understand laminar liftoff before examining turbulent liftoff. For lifted flames, an essentially identical theory to Ref. [25] was developed. The lifted flame was assumed to propagate along stoichiometric surfaces for the diffusion flame. The flame leading edge was modeled as a stoichiometric premixed flame. The stoichiometric surfaces of the diffusion flame may change in response to the global equivalence ratio. The premixed flame leading edge remains invariant. Calculated liftoff heights compared well with experimental values; blowout and liftoff velocities were given as functions of fuel stream fuel mass fraction [31]. Such studies provide improved understanding of empirical correlations [20, 21] developed mostly through dimensional analysis. In this work we shall provide a method deepening our understanding of flame attachment and liftoff. We shall accomplish this by deriving liftoff and attachment formulae from first principles without recourse to a priori postulates such as stoichiometric premixed flame-tip propagation. The resulting formulae are used to draw a flame liftoff versus flow rate plot that can be adapted for flame spread.
The Model The model problem shown in Fig. 1 consists of a rectangular domain whose lower sector in y < 0 houses initially separated streams of flowing fuel and oxidizer. Along the y < 0 axis the splitter plate has non-dimensional width h, which can become vanishingly small without influencing the heat losses since all of the boundaries are maintained at To . The uniform, steady flow has non-dimensional mass
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flux ε, the gas-phase properties are assumed constant. Chemical reaction occurs in one irreversible, exothermic step. Three equations describe the process, the fuel and oxidizer species equations, and the energy equation, which contain convective (ε⭸(•)⭸y), diffusive (⭸2 (•)/⭸x 2 + ⭸2 (•)/⭸y 2 ) and reactive terms. There are six nondimensional parameters: α, β, D, ε, Le, φ. When Le = 1, Q and T f take the forms given in the Nomenclature. We note that the Damk¨ohler number D can be written as Do /ε2 , indicating that it is inversely proportional to the square of the Peclet number, ε.
Scaling Analysis The model of Fig. 1 can be scaled by using the integral form of the equation for conservation of energy, ρc p u A
⭸T dA = ⭸x
⭸T −λ d + qwd A ⭸n
(1)
A
where we have used d V = 1 · d A and d A = 1 · d since the geometry of Fig. 1 employs unit depth. The strongest gradients occur in the region A = r q over a distance q from the lower wall, whereas the dominant heat release occurs in the region A = π ( r /2)2 . Research [6, 10, 13] has demonstrated that the vicinity of the flame tip has a heat release of the order of 10× the trailing diffusion flame (labeled DF in Fig. 1). Equation (1) becomes ρc p uΔT r + λΔT r / q = γ qw · π ( r /2)2 , where γ is a fraction of the total heat release in the domain. Rearrangement gives ε + 1 = (π γ /4)(1 + φ)DL r L q . There are two cases to consider.
Case > O(1) Here ε = (π γ /4) · (1 + φ)DL r L q , which leads to the formula L r L q = (4/π γ ) ((1 + φ)Do )−1 ε3 = const · ε3 /[(1 + φ)Do ]. Now, the time required for a fluid particle to convect from the exit plane to the reaction front is tconv = q /u, and the time required for the particle to diffuse from the divider plane to√the opposite edge of the reaction zone is tdi f f = r2 /D. Equating gives L q /L r = εLe. Combining the preceding two relationships for L q and L r yields 5/4 const · ε5/4 L r1 ε1 ⇒ = : Lr = 1/2 1/4 [(1 + φ)Do ] Le L r2 ε2 7/4 L q1 const · Le · ε7/4 ε1 Lq = ⇒ = , [(1 + φ)Do ]1/2 L q2 ε2
(2)
when all parameters other than ε are fixed. If ε is fixed and β is allowed to vary, we obtain
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L r1 1 β1 − β2 : = exp L r2 2 α
) L q1 1 β1 − β2 , = exp L q2 2 α
(3)
indicating a strong sensitivity of L r and L q to β.
Case < O(1) Diffusion and reaction are dominant, giving 1 = (π γ /4) · (1 + φ)DL r L q . Previous analyses [12, 14] of quenched diffusion flames in the limit of very low flow gave L q = const. f (φ)(1 + φ)5/2 β (m+n+1)/2 D−1/2 /(4φ 3/2 ). In this limit we obtain [14] const · g(φ) ε Lr1 ε1 ⇒ = : 1/2 (m+n+1)/2 β Lr2 ε2 Do ) L q1 ε const · β (m+n+1)/2 ε1 · 1/2 ⇒ = . Lq = (1 + φ)g(φ) L q2 ε2 Do
Lr =
(4)
When ε is fixed we find Lr1 = Lr2
β2 β1
(m+n+1)/2
(m+n+1)/2 L q1 β1 − β2 β1 β1 − β2 : . exp = exp 2α L q2 β2 2α (5)
The numerical constant in Eq. (4) contains γ , π and other numerical factors. Also, g(φ) = φ 3/2 /[(1 + φ)7/2 f (φ)]. Note that L q increases with β, L q ∝ β (m+n+1)/2 exp(β/2α). L r has an algebraic decrease coupled to an exponential increase, L r ∝ β −(m+n+1)/2 exp(β/2α), with a minimum at β = (m + n + 1)α. We observe that Eq. (4) are not valid as ε → 0 because D can be defined without reference to a convective velocity. The factor ε2 , which appears naturally in D with convection, is replaced when there is no convection by the characteristic diffusion velocity ␣/ : L r and L q in Eq. (4) then become independent of the flow rate. This is true for low flow rates, ε < O(10−1 ). Linear dependence occurs when 10−1 < ε < 1. The scaling Eqs. (2)–(5) are compared with the numerical solution of the boundary-value problem of Fig. 1. In the numerical solutions, q is defined as the shortest distance from the cold lower surface to the point of maximum chemical reactivity, see Fig. 1. The point at which the flame quenches is very close to the point at which the reactivity w is maximum [14]. To compare the L q -ratio of Eq. (2), we fix ε2 = 5 and vary ε1 from 1 to 5. From Fig. 2, when x = ε1 /ε2 lies between 0.5 ∼ 1, we find (L q1 /L q2 ) = x 1.75 , as predicted by Eq. (2). To compare the L q -ratio of Eq. (4) with numerical solutions, we fix ε2 = 0.1 and vary ε1 between 0.1 and 0.9, so that the abscissa of Fig. 3 ranges from 1 to 9. Figure 2 shows the predicted linear behavior for 0.1 < ε1 < 0.7, followed by a change to x n behavior with n > 1, consistent with Fig. 2 when x ∼ 1. In Figs. 2 and 3 we used β = 6. Plots with β = 9 (not shown here) are similar in all respects to Figs. 2 and 3. When 0.01 < ε < 0.1,
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Fig. 2 Liftoff height ratio versus flowrate for moderate flowrates. Here ε2 = 5, 2 ≤ ε1 ≤ 5 and β=6
as ε decreases the linear behavior L q1 /L q2 ∝ (ε1 /ε2 ) is lost. For the case β = 9 in particular, the independence from β becomes very apparent. By contrast to the comparisons of quenching distances, which were facilitated by the unambiguous definition of the flame quench point, the study of the flame
Fig. 3 Same as Fig. 2 for small to moderate flowrates. Here ε2 = 0.1, 0.1 ≤ ε1 ≤ 0.9 and β = 6. The linear and numerical profiles coincide until ε1 /ε2 = 7
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Table 1 Ratios of L q and L r for ε = 0.1 and ε = 5 and -pairs (β1 , β2 ) = (6, 7), (7,8) and (6,8) from numerical computations and analytical predictions ε
(β1 , β2 )
(L q1 /L q2 )num
(L q1 /L q2 )an
(L r 1 /L r 2 )num
(L r 1 /L r 2 )an
0.1 0.1 0.1 5.0 5.0 5.0
(6,7) (7,8) (6,8) (6,7) (7,8) (6,8)
0.463 0.478 0.221 0.584 0.584 0.341
0.647 0.515 0.333 0.553 0.205 0.113
0.333 0.50 0.167 0.20 0.833 0.167
0.736 0.714 0.525 0.584 0.584 0.341
structure via L r is more complicated and less definite. The length L r is a measure of the extent of the leading edge flame structure. The best procedure would be to compare chemical reactivities through constant-w plots using a cutoff value like wc = 0.05wmax . We have not carried through this comparison. Equation (3) show that when ε > 1 L r and L q scale identically with β, i.e., L r /L q ∼ constant, whereas when ε < 1 Eq. (5) show that the ratio becomes L r /L q ∼ β −(m+n+1) : for large β the flame width decreases rapidly in comparison with the quenching distance. This behavior is consistent with the theoretical discussions of Refs. [12, 13] and also with experimental observations of attached flames, which show a quenched flame leading edge (tip) without a visible triple flame structure. Reference [33] calls this degenerate triple flame structure a “flame nub.” Equation (2) show that ε > 1 gives L q /L r ∼ ε1/2 : as ε increases, L q grows faster than L r by the factor ε1/2 . By contrast ε < 1 gives L q /L r ∼ constant indicating independence of this ratio from ε as it diminishes. In sum, ε > 1 gives L q /L r independent of β but dependent on ε(L q ∼ ε1/2 L r ) whereas for ε < 1, L q /L r depends strongly on β: L q ∼ L r β m+n+1 independent of ε. Thus, in the liftoff limit of large ε, the flow dictates changes in the flame structure (L r ) relative to its liftoff height (L q ), but in the attached limit of small ε the flow rate becomes less important. In this limit the reaction sensitivity β dictates changes in flame structure (L r ) relative to quench distance (L q ). A comparison between the predictions of Eqs. (3) and (5) on the basis of changes in β is shown in Table 1 for the two cases ε = 0.1 and ε = 5. For ε = 0.1 we employ Eq. (5), for ε = 5 Eq. (3). The comparisons are between (β1 , β2 ) = (6,7), (7,8) and (6,8). From Table 1 we see that the analytical and numerical trends are similar in all cases, but that the exact numerical values of the ratios differ. The numerical and analytical L q ratios are more consistent. For L r , we defined the numerical flame width as the distance between the two locations in the x-direction where w = e−1 wmax . We observe that L r is not a reaction zone width, such as a premixed flame or diffusion flame reaction layer width L f which varies as β −1 . The dependence of L r on β, L r ∼ β −(m+n+1)/2 exp(β/2α), may be important for describing heat flux signatures imparted by attached flames to nearby surfaces. We speculate that the transverse extent of the heated surface should scale with L r , not with L f ∼ β −1 . The ratio L r /L f ∼ β −(m+n+3)/2 exp(β/2α) has a minimum value at β = (m + n + 3)α.
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Comparison with Experiments There are four groups of experiments to which comparison of our correlations may be made. The first group is the laminar flow experiments of Refs. [30, 31] for narrow fuel jets. Lee and Chung find, consistent with our results, the existence of a very-low flow constant q regime followed for higher flow rates by a linear q regime [31]. A strict comparison is not possible because both exit geometry (circular opening) and boundary conditions (no enforceable constant temperature condition resembling Fig. 1) differ from ours. The second group is the pool fire study of Venkatesh et al. [15] in which the flow and attachment regions of a pool of burning fuel were examined. Once again, a strict comparison is not possible. However, using numerous diagnostic methods, it was shown in Ref. [15] that the flame tip (leading edge) structure is not that of the free, isenthalpic triple flame described in Ref. [6]. The flame tip is narrow, consistent with the “flame nub” description in Ref. [33], with a characteristic width that differs from the downstream flame width. Also, slightly downstream of the flame tip a double flame structure appears, consisting of what resembles the main diffusion flame adjacent to (and inside of) an outer lean premixed flame. Consistent with [28], these experiments show leakage of oxidizer and fuel through the flame tip. In this third group of experiments [25–28], careful measurements are made of velocity fields, concentrations and flame tip position using sophisticated experimental diagnostics. The flame leading edge (tip) for attached flames does not possess the characteristic triple flame shape, although the full stoichoimetric range has not been studied. In addition (and in agreement with [30, 31]), a strict comparison cannot be made partly because the fuel jet exit velocity is much larger than the outer coflowing oxidizer stream velocity. This velocity difference may have an influence on the appearance of the double flame structure slightly downstream of the flame tip, where the lean premixed flame bulges out from the diffusion flame arc into the oncoming oxidizer stream. The fourth and final group of experiments are the turbulent jet experiments of Schefer et al. [29] in which the flame standoff distance and flow rate were both measured, yielding q = 30 mm when the flow velocity was 21 m/s and q = 50 mm when the velocity was 37 m/s. The ratio q2 / q1 = 50/30 = 1.67, which is close to the ratio u 2 /u 1 = 37/21 = 1.76. Thus, in these experiments (and in many other round-jet experiments for large Peclet numbers) the flame stand-off distance q was linearly proportional to the flow rate (u), unlike our theoretical prediction, q2 / q1 = (ε2 /ε1 )7/4 . Our integral analysis does not exclude turbulent flow, but neither does not include a high-velocity fuel flow into a quiescent oxidizer atmosphere. Furthermore, our analysis is two-dimensional whereas the work of Schefer et al. [29] is strongly three-dimensional. Finally, the Pe-scale is different, since we have Pe ∼ O(10) whereas the experiments use much larger Pe values, Pe ∼ O(10)2 ) or larger. The experiments of Schefer et al. [29] suggest that prior to flame blowoff the detached flame follows the linear dependence q ∼ Pe, not q ∼ Pe7/4 , which might be expected for Pe-values between 1 and 10, say.
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I.S. Wichman, B. Ramadan high −ε blowoff
low −ε extinction
Lq1/Lq2
slope = 1 lifted flame
104 103 102 slope = 7/4 101 attached flame 100 slope = 1
10–1
ε1/ε2 10–1
100
101
102
103
104
Fig. 4 Flame standoff height versus the flow rate showing attached flame regime consisting of linear (see Eq. (4)) and 7/4 (see Eq. (2)) regimes, and the subsequent linear lifted flame regime (see e.g., Refs. [29–31]). Also shown is the condition of blowoff (high-ε) and the condition of extinction (low-ε). This graph is qualitative
In sum, qualitative agreement is found with four groups of experimental observations, each employing different flow conditions, experimental diagnostics, and apparatus dimensions. The latter range from needle tubes [30, 31] to large-diameter tubes [28, 29]. In addition, a pool fire [15], whose flow conditions are probably closest to ours, gave results consistent with our predictions. A composite flame standoff height (L q ) versus flow rate (ε) graph is shown in Fig. 4.
Conclusions An integral analysis of the governing equations produces several correlations of the flame height versus standoff distance. These are examined in Figs. 2 and 3 against the full numerical solutions of exactly the same model problem. The correlations for L r , a quantity which is not as clearly defined as L q , are somewhat less satisfactory. We suspect that L r is important for determining the characteristic widths of the heat flux signatures from the flame to the solid surface beneath it. Armed with this knowledge, it appears that a more considered examination of the detailed numerical model of flame attachment can be made. In these models, the full Navier-Stokes equations should be used, and variable properties, viscosity, etc. are retained, in contrast with our simplifying restrictions. Despite these restrictions,
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however, the scaling analysis has proved robust in its agreement with experiments and bodes well for pointing the way toward a more satisfying theoretical understanding of this difficult and technologically important problem. A lengthier article on this same subject by the same authors was published in Phys. Fluids A [34]. The interested reader is referred to that article for additional details of diffusion flame attachment and liftoff. An urgent scientific and engineering need is very careful non-intrusive measurements of liftoff heights. Acknowledgments This research was funded by NASA μg-Combustion grant NAG3-1626 and NSF CTS grant CTS-9415073. Students working on this project have included Dr. Robert Vance, Dr. Bala Varatharajan, Mr. Nandu Lakkaraju, Ms. Zornitza Pavlova and Mr. G. Qin. The encouragement of Dr. Vedha Nayagam of NASA is greatly appreciated.
References 1. Kashiwagi, T. Proc. Comb. Inst. Vol. 25 (1994) 1423–1437. 2. Wichman, I.S., Survey of articles in Transport Phenomena in Combustion (S.H. Chan, ed.). ISTP-8 Taylor and Francis, Vol. 2 (1996) 885–1828. ` 3. Perez-Ortiz, R.M., Sivasegaram, S., and Whitelaw, J.H., Transport Phenomena in Combustion (S.H. Chan, ed.), Taylor and Francis, Vol. 2 (1996) 1342–1353. 4. Glassman, I., Combustion, NY, Academic Press, 1977. 5. Williams, F.A., Combustion Theory, Benjamin/Cummings, Menlo Park, 1985. 6. Dold, J.W., Combustion and Flame 76 (1989) 71–88. 7. Dold. J.W. and Hartley, L.J., Combustion Science and Technology 80 (1991) 23–46. 8. Buckmaster, J. and Matalon, M. Proc. Comb. Inst. Vol. 22 (1988) 1527–1535. 9. Kioni, P.N., Rogg, B., Bray, K.N.C., and Li˜na´ n, A., Combustion and Flame 95 (1993) 276–290. 10. Grosch, C.E. and Jackson, T.L., Physics of Fluids A 3(12) (1991) 3087–3092. 11. Reutsch, C.R., Vervisch, L., and Li˜na´ n, A., Physics of Fluids A 7(6) (1995) 1442–1454. 12. Wichman, I.S., Combustion Science and Technology 64 (1989) 295–313. 13. Wichman, I.S., Lakkaraju, N., and Ramadan, B., Combustion Science and Technology 127 (1997) 141–165. 14. Wichman, I.S., Pavlova, Z., Ramadan, B., and Qin, G., Combustion and Flame 118 (1999) 651–668. 15. Venkatesh, S., Ito, A., Saito, K., and Wichman, I.S., Proc. Comb. Inst. Vol. 26 (1996) 1437–1443. 16. deRis, J.N., PhD Thesis, Harvard University, 1968. See also Proc. Comb. Inst. Vol. 12 (1969) 241–252. 17. Vanquickenborne, L. and van Tiggelen, A., Combustion and Flame 10 (1969) 59–69. 18. Peters, N. and Williams, F.A., AIAA Paper 81-011, January 1982. 19. Broadwell, J.E., Dahm, W.J.A., and Mungal, M.C., Proc. Comb. Inst. Vol. 20 (1984) 303–310. 20. Kalghatgi, G.T., Combustion Science and Technology 26 (1981) 233–239. 21. Kalghatgi, G.T., Combustion Science and Technology 41 (1984) 17–29. ˜ and Gollahalli, S.R., Combustion and Flame 73 (1988) 221–232. 22. Sherkarch, S., Savas, O., 23. Pitts, W.M., Combustion and Flame 76 (1989) 197–212. 24. Pitts, W.M., Proc. Comb. Inst. Vol. 23 (1990) 661–668. 25. Takahashi, F., Mizomato, M., and Ikai, S., Journal of Heat Transfer 110 (1988) 182–189. 26. Takahashi, F., Mizomoto, M., Ikai, S., and Futaki, N., Proc. Comb. Inst. Vol. 20 (1985) 295–302. 27. Takahashi, F. and Schmoll, W.J., Proc. Comb. Inst. Vol. 23 (1991) 677–687. 28. Takahashi, F. and Goss, L.P., Proc. Comb. Inst. Vol. 24 (1993) 351–359.
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29. Schefer, R.W., Namazian, M., and Kelly, J., Combustion and Flame 99 (1994) 75–86 [see refs. therein to earlier work of Schefer et al.]. 30. Chung, S.H. and Lee, B.J., Combustion and Flame 86 (1991) 62–72. 31. Lee, B.J. and Chung, S.H., in Transport Phenomena in Combustion (S.H. Chan, ed.), ISTP-8, Taylor and Francis, Vol. 1 (1996) 370–380. 32. Kibrya, M.C., Karim, G.A., and Wierzba, I., Proc. 33rd ASME Int. Gas Turbine & Aeroengine Congress and Exhibition, ASME Paper No. 88-CT-106, Amsterdam, June (1988). 33. Wichman, I.S., Combustion and Flame 117 (1999) 384–393. 34. Wichman, I.S. and Ramadan, B., Physics of Fluids A 10(12) (1998) 3145–3154.
Scaling of Gas-Jet Flame Lengths in Elevated Gravity Peter B. Sunderland, David L. Urban and Vedha Nayagam
Abstract There are two well known scaling laws for lengths of laminar jet diffusion flames on circular burners. The more prevalent of these is a linear relationship between normalized flame length and Reynolds number. The other, invoked in most past studies at elevated gravity, relates these lengths to a function of Reynolds and Froude numbers. The Reynolds scaling indicates stoichiometric flame lengths are independent of gravity level, while the Reynolds-Froude scaling indicates lengths decrease at elevated gravity. The ability of both approaches to correlate flame lengths is examined. Published lengths of laminar hydrogen, methane, ethane, and propane flames in 1–15 times earth gravity are considered. The Reynolds scaling yields better correlations of flame lengths for all fuels except hydrogen. The Reynolds-Froude scaling has a weaker theoretical basis and does not account as accurately for variations in fuel flowrate. Further, it does not admit microgravity flames and past predictions for its limiting behavior at low and high Froude number are not supported. Observed reductions in luminous flame length at elevated gravity are attributed to soot interference. The Reynolds scaling is recommended for flame lengths at microgravity, normal gravity, and elevated gravity. Keywords Centrifuge · flame shape · microgravity · slot burner · soot
Introduction Lengths of laminar jet diffusion flames are considered in most combustion textbooks. Most studies of such flames invoke a linear scaling between normalized flame length and Reynolds number. An alternate scaling, based on Reynolds and Froude numbers, was introduced by Altenkirch [1] for measurements at elevated gravity. The choice of scaling relationship is important because the Reynolds scaling indicates flame length is independent of gravity whereas the Reynolds-Froude scaling indicates flame lengths decrease at increased gravity. A critical analysis of these two P.B. Sunderland Department of Fire Protection Engr., University of Maryland, College Park, MD 20742, USA e-mail:
[email protected] K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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approaches was considered by Sunderland et al. [2]. That analysis is summarized and extended in this chapter. Beginning with Burke and Schumann [3], many studies have measured the lengths of gas-jet flames in normal gravity [4–12]. Recent work has emphasized microgravity conditions [4, 13–18]. Flame lengths in elevated gravity have been measured in fewer studies, namely those of Altenkirch and co-workers [1, 19, 20], Durox et al. [21], and Arai and co-workers [22–25]. Sufficient measurements now exist to evaluate the possible effects of elevated gravity on flame length. The objectives of this study are to consider the relative merits of the Reynolds and Reynolds-Froude scaling laws for flame lengths in elevated gravity. Extensive past measurements are examined under both scaling.
Length Scaling for Round Burners The Reynolds scaling of flame length on round burners can be derived in many different ways [4, 5–11]. It states: L/d ∼ Re
(1)
where L is flame length, d is burner inside diameter, ∼ represents proportionality, and Re is Reynolds number (defined below). Length is defined by most models as stoichiometric flame length, but by most experimental studies as luminous flame length. Nonbuoyant flame studies use the Reynolds scaling exclusively. Roper [6] famously predicted this behavior to hold for circular burners regardless of gravity level, his main argument being that the increase in flow acceleration caused by buoyancy in the axial direction is compensated for by the narrowing of the boundary layer thickness in the transverse direction, leaving the flame height independent of gravity. The Reynolds scaling has been used widely to correlate length measurements at microgravity and earth gravity [3–16]. The Reynolds-Froude scaling was introduced by Altenkirch et al. [1]. This began with a balance between fuel and oxidizer supply rates following Jost [5]. Note that this reduces to the Reynolds scaling Eq. (1) when diffusion length scales with flame width, which is a reasonable assumption. Altenkirch et al. [1] instead assumed the diffusion length to scale as the thickness of a boundary layer on an isothermal vertical flat plate: δ/x ∼ (gx 3 /ν 2 )−1/4
(2)
where δ is momentum boundary-layer thickness, x is streamwise distance from the leading edge, g is local acceleration of gravity, and ν is kinematic viscosity. The scaling of Eq. (2) neglects transverse curvature of the boundary layer, which typically is significant for gas-jet flames on round burners. The fuel-oxidizer balance and Eq. (2) lead to
Scaling of Gas-Jet Flame Lengths in Elevated Gravity
L/d ∼ Re2/3 Fr 1/3 (w/d)−4/3
271
(3)
where the Reynolds and Froude numbers are Re = u d/ν and Fr = u 2 /(g d)
(4)
Here w is the maximum flame width and u is the average gas velocity in the round burner. Evaluating Re requires fuel kinematic viscosity, which here is based on fuel density (at ambient pressure p and 298 K) and published dynamic viscosities of 8.76, 10.9, 9.22, and 8.05 mg/m-s for H2 , CH4 , C2 H6 , and C3 H8 , respectively. Altenkirch et al. [1] observed w/d to be nearly constant for any given fuel and oxidizer. They thus predicted two limiting trends from Eq. (3): L/d ∼ Re2/3 nonbuoyant flames (large Fr)
(5)
L/d ∼ Re
(6)
2/3
Fr
1/3
buoyant flames (small Fr)
Invoking the buoyant Eq. (2) in the nonbuoyant scaling of Eq. (5) is questionable. For nonbuoyant flames it would be more acceptable to invoke the flat-plate boundary-layer thickness for forced convection: δ/x ∼ (u x/ν)−1/2
(7)
Note that this does not resolve the problem of using a planar scaling relationship for axisymmetric flames. When Eq. (7) is invoked instead of Eq. (2), the Reynolds scaling Eq. (1) is obtained. This is yet another way of deriving the Reynolds scaling. Three drawbacks are now apparent in the derivation of the Reynolds-Froude scaling: 1. This scaling is predicated on the buoyant flat-plate relationship (Eq. (2)). However, transverse curvature is significant for most flames on laboratory-scale round burners. 2. The nonbuoyant limit of Eq. (5) is based on a buoyant flat-plate solution (Eq. (2)). 3. Constant w/d is assumed. Although constant flame widths are observed in microgravity flames at large Re [4, 16], they are not seen at lower Re or in normalgravity [4]. Despite these drawbacks, the Reynolds-Froude scaling of Eqs. (5) and (6) led to a choice of plot axes that yields reasonable correlations of flame lengths [1]. The same axes were later used for flame lengths at elevated gravity by Durox and co-workers [10, 21], Rosner [26], and Sato et al. [25]. The resulting plots suggest a decrease of flame length with increasing gravity.
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Length Scaling for Slot Burners Although measurements for slot burners are limited, the scaling relationships for slot burners can yield insight into those for round burners. Roper’s analysis [6] was applied to circular, square, and slot burners. This predicts flames on circular and square burners to scale according to Eq. (1). However it predicts flames burning on slot burners to scale as: L/b ∼ Re nonbuoyant flames (large Fr)
(8)
L/b ∼ Re2/3 Fr 1/3 buoyant flames (small Fr )
(9)
where b is slot width and where Re and Fr are based on b. Note the similarity of Eqs. (6) and (9). It is informative to consider a development parallel to Eqs. (2), (3), (4), (5) for slot burners. The appropriate diffusion length scales are the planar boundary layer thicknesses of Eqs. (2) and (7) for buoyant and nonbuoyant flames, respectively. This yields the Roper scaling of Eqs. (8) and (9). This analysis avoids the three drawbacks (above) that arise in the derivation of Eqs. (5) and (6) for axisymmetric flames. The Altenkirch et al. [1] and Roper [6] methods yield the same scaling for slotburners, but different scaling for round burners. Roper avoids the above drawbacks in both configurations, whereas Altenkirch avoids them only for slot burners. These facts indicate that for round burners there is a stronger theoretical foundation for the Reynolds scaling than for the Reynolds-Froude scaling.
Empirical Correlations of Flame Length Existing measurements of flame lengths at normal and elevated gravity were considered for empirical tests of the two scaling laws. As summarized in Table 1, these comprise 690 tests from seven research groups [1, 4, 11, 13–15, 19–21, 23–25, 27, 28]. This table and the subsequent plots include all published measurements of steady laminar flame lengths at elevated gravity for the fuels considered: hydrogen, methane, ethane, and propane. Various studies used co-flowing or quiescent air, but this is not expected to affect flame length [7, 12]. Nomenclature introduced in this table is gravity ratio G = g/ge where ge = 9.81 m/s2 , and fuel mass flowrate m. Altenkirch et al. [1] measured the largest number of elevated gravity flame lengths available to date. They plotted these measurements using Fr and (L/d) Re−2/3 Fr −1/3 as ordinate and abscissa. These axes were also used by others [10, 21, 25, 26] and are shown in Fig. 1 for the measurements of Table 1. The scatter about the correlations for the Reynolds-Froude scaling of Fig. 1 is reasonable. However these axes have three unfortunate characteristics: L/d is not plotted alone; Fr appears in both axes; and microgravity flames cannot be included. The
Air Co-flowing Quiescent Co-flowing Quiescent Co-flowing Quiescent Quiescent
Fuel
H2 , CH4 , C2 H6 , C3 H8 CH4 , C3 H8 CH4 H2 , CH4 CH4 CH4 , C2 H6 CH4 , C2 H6 , C3 H8
b
Altenkirch et al. [1]; Brancic [19]; Cevallos [20]. Arai et al. [23, 24]; Sato et al. [25]. c Cochran and Masica [13]; Cochran [14]; Haggard and Cochran [15]. d Ban et al. [27]; Nakamura et al. [28].
a
a
1–15 1–9 1–8.5 1 1 1 1
G 0.8–2.1 2–7.5 2.2, 12 1.02–8.84 16 0.41 0.19–5.5
d mm 1 1 1 0.98 1 1 0.25–1.97
p bar
0.16–2.63 0.29–11.7 0.90–4.16 0.47–7.90 0.94–5.41 0.06–0.44 0.04–4.60
m mg/s
Table 1 Summary of flame length measurements considered in the present work, all burning in air on circular burner
Altenkirch and co-workers Arai and co-workersb Durox et al. [21] Cochran and co-workersc Li et al. [11] Saito and co-workersd Sunderland et al. [4]
Study
190 57 99 67 32 14 231
# Tests
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Fig. 1 Empirical test of the Reynolds-Froude scaling law for flame lengths at elevated and normal gravity. The legend entries are defined in Table 1. The lines and equations shown are least-squares power fits, where y is (L/d) Re−2/3 Fr −1/3 . Reproduced from [2]
correlations shown indicate flame length decreases with increasing gravity according to, approximately, L ∼ G −0.1 Altenkirch et al. [1] and subsequent researchers claimed to observe two limiting slopes in such plots: a slope of 0 at low Fr [1, 10, 26] and a slope of −1/3 at high Fr [1, 26]. These slopes are predicted by Eqs. (6) and (5), respectively. Compared to the initial work [1], Fig. 1 includes Fr values that are four orders of magnitude lower and one order higher. Nevertheless, empirical support is lacking for either prediction of limiting slope. The measurements of Fig. 1 are considered empirically under the Reynolds scaling in Fig. 2. As quantified below, the data are well correlated. For each fuel the data have a slope that is slightly larger than the unit slope prediction of Eq. (1). This increased slope is attributed to flames at low Re, many of which attach below the burner tip, and flames at high Re, which can be slightly lifted. One advantage of the axes of Fig. 2 is that microgravity flames are admitted [4, 12–16]. Microgravity flames are longer than normal gravity flames at otherwise matched conditions [4, 16]. Figure 2 lends empirical support to the Reynolds scaling of L/d ∼ Re at all gravity levels.
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Fig. 2 Empirical test of the Reynolds scaling law for flame lengths at elevated and normal gravity. The lines and equations shown are geometric mean fits with unity slope. Variable c is a factor for plot convenience. Reproduced from [2]
The data scatter about the correlations of Figs. 1 and 2 can be evaluated statistically. The ratio of correlated to measured flame length (L correlated /L measured ) was found for each measurement. The L correlated values are given by the fit equations in Figs. 1 and 2. The geometric means of these ratios is unity for every fuel under both scaling. The geometric standard deviations of the ratios, σg , quantify the data scatter associated with the length correlations. The results are given in Table 2. In general, the σg are higher (up to 91% higher) for the Reynolds-Froude correlations than for the Reynolds fits. The only exception is hydrogen, for which the scatter is slightly higher for the Reynolds scaling. The Reynolds scaling correlates flame lengths with less scatter than the Reynolds-Froude scaling for all fuels except hydrogen. Under both scaling the scatter increases with increasing fuel carbon number, possibly owing to complications of soot luminosity. The L correlated /L measured ratios allow an evaluation of how well the two scaling laws account for variations in flame length with the four independent quantities that define the test conditions: G, d, p, and m. Such an evaluation was accomplished by plotting L correlated /L measured ratios with respect to these independent quantities for every fuel under both scaling. (Most these plots are not shown here.) In each case
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Table 2 Vertical Scatter in the Correlations of Figs. 1 and 2, Quantified by the Geometric Standard Deviations of Ratios of Correlated to Measured Flame Lengths for Different Fuels Fuel
# Tests
σg of L correlated /L measured Re-Fr Scaling
Re Scaling
H2 CH4 C2 H 6 C3 H 8
61 351 127 151
0.145 0.280 0.349 0.413
0.167 0.191 0.199 0.216
a power-law fit of the data was used to identify possible systematic deficiencies in the correlations. In general, both scaling laws accounted well for variations in G, d, and p for all fuels. However this was not the case for variations in m under the Reynolds-Froude scaling. Fig. 3 shows the methane measurements of Figs. 1 and 2 plotted with L correlated /L measured and m as axes, for both scaling. The Reynolds scaling shows a fit with negligible slope, indicating little or no systematic overprediction or underprediction of methane flame lengths as a function of m. The Reynolds-Froude scaling, conversely, yields a fit with a steep downward slope in Fig. 3. Both behaviors also occur for the three other fuels (not shown here). This indicates that flames with low and high flowrates are likely to have their lengths overpredicted and underpredicted, respectively, by the Reynolds-Froude correlations. Those correlations are unable to account properly for variations in fuel mass flowrate. All the centrifuge studies of Table 1 reported decreased luminosity lengths at elevated gravity. The possibility that this arises from soot interference, not changes in stoichiometric flame length, is considered next. Luminosity lengths of earth-gravity hydrocarbon-fueled flames have been found to exceed their stoichiometric lengths by 10–60% [8, 12, 16, 29] in a way that can be correlated [9, 12]. An increase in gravity decreases residence time and can change a hydrocarbon flame from yellow to blue [1, 22–25], but may have no significant effect on stoichiometric flame length.
Fig. 3 Ratios of correlated to measured flame lengths for methane, potted with respect to fuel mass flowrate. The methane fits of Figs. 1 and 2 are considered for the Reynolds- Froude scaling (upper) and the Reynolds scaling (lower), respectively. The lines and equations shown are least-squares power fits, where y = L correlated /L measured
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Fig. 4 Effect of gravity level on flame lengths. The open symbols are individual measurements. The other symbols are geometric means of earth-gravity measurements. The lines and equations shown are least-squares power fits of the open symbols. Reproduced from [2]
An empirical test of soot interference effects is shown in Fig. 4. Here flame length normalized as L/(d Re) is plotted versus G for the measurements of Figs. 1 and 2. This choice of axes is motivated by the empirical support for Eq. (1) apparent in Fig. 2. Data trends in Fig. 4 are a convenient way to assess the dependence of flame length on gravity level. The measurements for hydrocarbon flames in Fig. 4 indicate a trend of decreasing lengths as gravity increases. Note that these are luminosity lengths and that trends for stoichiometric lengths may have little or no decrease with increasing gravity. Soot interference is minimized at the highest gravity levels. At the highest gravity levels, hydrocarbon flame luminosity lengths are close to the mean earth-gravity stoichiometric lengths of Ref. [4], shown as plus symbols in Fig. 4.
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In contrast to hydrocarbon flames, no soot is formed in hydrogen flames. Figure 4 indicates that hydrogen flame lengths have the smallest decrease in flame length at elevated gravity of the present fuels. Part or all of this decrease for hydrogen could occur because coriolis effects increase with gravity and produce curved flames. This was estimated by Ref. [1] to bias measured flame lengths downward by up to 6% at elevated gravity. Unfortunately, experimental uncertainties are high for hydrogen flame lengths owing to dimness [15, 19], particularly at their tips. It is remarkable how well both the Reynolds and the Reynolds-Froude scaling correlate the lengths of diverse gas-jet flames. This is in spite of the phenomena neglected by these models: soot interference, axial diffusion, radiation, unsteadiness, burner heat loss, flame attachment below or above the burner tip, reactant leakage, and coriolis effects.
Conclusions The two most common scaling laws for lengths of gas-jet diffusion flame were examined, emphasizing conditions at elevated gravity. Published lengths of H2 , CH4 , C2 H6 and C3 H8 flames were considered. The major conclusions are: 1. Within experimental uncertainties, elevated gravity has no effect on stoichiometric flame lengths. Soot interference is primarily responsible for the observed decrease in luminosity lengths at elevated gravity. 2. The Reynolds scaling correlates flame lengths with less scatter than the ReynoldsFroude scaling for all fuels except hydrogen. The Reynolds scaling has stronger theoretical support and it admits microgravity flames. 3. The Reynolds-Froude scaling does not account properly for variations in fuel mass flowrate. It neglects transverse curvature and thus is better suited to slot burners. 4. Past predictions for the limiting behavior of the Reynolds-Froude scaling at low and high Fr do not have empirical support. Acknowledgments The authors acknowledge the supported of NASA Grant NNC-05GA59G, under the management of Merrill K. King, and helpful discussions with James E. Haylett, John L. de Ris, and Gregory T. Linteris.
References 1. R.A. Altenkirch, R. Eichhorn, N.N. Hsu, A.B. Brancic, N.E. Cevallos, Proc. Combust. Inst. 16 (1976) 1165–1174. 2. P.B. Sunderland, J.E. Haylett, D.L. Urban, V. Nayagam, Combust. Flame, accepted (2007). 3. S.P. Burke, T.E.W. Schumann, Ind. Eng. Chem. 20 (10) (1928) 998–1004. 4. P.B. Sunderland, B.J. Mendelson, Z.-G. Yuan, D.L. Urban, Combust. Flame 116 (1999) 376–386.
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5. W. Jost, Explosion and Combustion Processes in Gases, McGraw-Hill, New York, 1946, p. 212. 6. F.G. Roper, Combust. Flame 29 (1977) 219–226. 7. F.G. Roper, C. Smith, A.C. Cunningham, Combust. Flame 29 (1977) 227–234. 8. R.E. Mitchell, A.F. Sarofim, L.A. Clomburg, Combust. Flame 37 (1980) 227–244. 9. K. Saito, F.A. Williams, A.S. Gordon, Combust. Sci. Tech. 21 (1986) 117–138. 10. E. Villermaux, D. Durox, Combust. Sci. Technol. 84 (1992) 279–294. 11. S.C. Li, A.S. Gordon, F.A. Williams, Combust. Sci. Tech. 104 (1995) 75–91. 12. K.-C. Lin, G.M. Faeth, AIAA J. 37 (6) (1999) 759–765. 13. T.H. Cochran, W.J. Masica, Proc. Combust. Inst. 13 (1970) 821–829. 14. T.H. Cochran, Experimental Investigation of Laminar Gas Jet Diffusion Flames in Zero Gravity, NASA TN D-6523, 1972. 15. J.B. Haggard, Jr., T.H. Cochran, Hydrogen and Hydrocarbon Diffusion Flames in a Weightless Environment, NASA TN D-7165, 1973. 16. K.-C. Lin, G.M. Faeth, P.B. Sunderland, D.L. Urban, Z.-G. Yuan, Combust. Flame 116 (1999) 415–431. 17. P.B. Sunderland, S.S. Krishnan, J.P. Gore, Combust. Flame 136 (2004) 254–256. 18. C. Aalburg, F.J. Diez, G.M. Faeth, P.B. Sunderland, D.L. Urban, Z.-G. Yuan, Combust. Flame 142 (2005) 1–16. 19. A.B. Brancic, Effect of Increased Gravity on Laminar Diffusion Flames, M.S. Thesis, University of Kentucky, Lexington, 1976. 20. N.E. Cevallos, Experimental Studies of Effects of Elevated Gravity on Gaseous Hydrocarbon Diffusion Flames, M.S. Thesis, University of Kentucky, Lexington, 1976. 21. D. Durox, T. Yuan, F. Baillot, J.M. Most, Combust. Flame 102 (1995) 501–511. 22. K. Amagai, Y. Ito, M. Arai, J. Jpn. Soc. Micrograv. Appl. 14 (1) (1997) 3–9. 23. M. Arai, K. Amagai, Y. Ito, Proc. Second Intl. Symp. Scale Modeling, Lexington, Kentucky, 1997, pp. 197–210. 24. M. Arai, H. Sato, K. Amagai, Combust. Flame 118 (1999) 293–300. 25. H. Sato, K. Amagai, M. Arai, Combust. Flame 123 (2000) 107–118. 26. D.E. Rosner, Transport Processes in Chemically Reacting Flow Systems, Dover, Mineola, NY, 2000, p. 435. 27. H. Ban, S. Venkatesh, K. Saito, J. Heat Transfer 116 (1994) 954–959. 28. Y. Nakamura, H. Ban, K. Saito, T. Takeno, Proc. Spring Tech. Mtg. Central States Section, The Combustion Institute, Pittsburgh, 1997, pp. 160–163. 29. A. Gomez, G. Sidebotham, I. Glassman, Combust. Flame 58 (1984) 45–57.
Some Partial Scaling Considerations in Microgravity Combustion Problems James S. T’ien
Abstract The importance of flame scale is discussed related to role of radiation in microgravity flames. Several types of simulation between microgravity flames and normal gravity flames are discussed. The emphasis is on reproducing selected microgravity features in a normal gravity environment since complete simulation appears to be difficult. Keywords Microgravity flames · radiation · length scale
Introduction Combustion processes in microgravity offer a number of unique features that are not common for flames in normal gravity. In the absence of buoyant driven flow, flow velocity around the flame can be very small (for example, forced velocity of the order of a few centimeters per second) or absent. Since flow velocity affect flame length scales, the smaller convective velocity amplifies the flame thickness. Physical mechanisms that are of secondary importance in normal gravity can become influential in microgravity because of this scale change. One of the importance processes that have been discovered in recent microgravity research is radiation heat transfer in smaller scale flames.
Radiation in Small Scale Flames Thermal radiation from flames has traditionally been thought to be important only in large-scale fires [1]. However, due to the absence of buoyant convection, the effects of radiation are amplified in microgravity for small-scale flames. In many cases, radiation becomes a key player in determining the combustion behavior. In the past J.S. T’ien Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, Ohio 44106, USA e-mail:
[email protected]
K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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decades, a number of theories and experiments have demonstrated the contribution of radiation (see references cited in [2, 3]). Basically, the effects of radiation include (1) lowering flame temperature due to heat loss, (2) a change of flame color and structure (including the possibility of eliminating soot) due to flame temperature decrease, (3) a heat feedback mechanism in addition to conduction/convection in condensed-fuel combustion and (4) causing flame quenching. Some of the radiative effects are quantitative in nature but others cause a qualitative change of the flame behavior. The latter is especially important in flammability studies and has implication to spacecraft fire safety. To better see how radiation becomes important, we can examine the non-dimensional parameters containing the radiative terms. We will use the equations of flame spreading over a solid fuel surface for illustrative purpose. In additional to flame (gas-phase) radiation loss, surface radiative emission/absorption and interaction with flame are also present in the burning of solids [4]. Therefore, it represents a more complicated case than a pure gaseous flame from the point of view of radiation heat transfer. Using L R = α ∗ /U R as the reference length scale (here ␣∗ is the reference thermal diffusivity of air and U R is the reference flow velocity), the nondimensional gas-phase energy equation contains the radiation term is given below [2]. Note that this length scale represents the balance between convection and upstream conduction in a stabilized flame anchored over a flat fuel surface. It is the proper scale to define the size of the flame stabilization zone or equivalently the flame standoff distance from the solid. Energy equation:
ρ Di c Pi
DT 1 → = ∇ · (κ∇T ) + ∇ · qr − (∇Yi · ∇T ) − i h i (1) Dt Lei Bo i=1 i=1 2 −E where i = f i F = f i Daρ 2 Y F Y O2 exp T g and Da = α ∗ ρ ∗ B g /U R . f i = stoichiometric mass ratio of species i and fuel. T is temperature, ρ is density, c p is specific heat at constant pressure of the mixture, is coefficient of heat conduction, → D is diffusion coefficient, Yi is mass fraction of species i, q r is radiation flux vector, i is the mass reaction rate per unit volume for species i and h i is the enthalpy of species i., E g and B g are the activation energy and the pr-exponential factor of the gas-phase reaction respectively and superscript − denotes dimensional quantity and superscript ∗ is referred to a reference temperature in the gas flame. 1 → The gaseous radiation term is represented by ∇ · q r where Bo N
N
ρc P
3
Bo = (ρ ∗ c∗P U R )/(σ T ∞ )
∇ · q r = K (4T 4 − G)
(2)
Here σ is the Stefan-Boltzmann constant, G is the total incident radiation. A nondimensional mean absorption coefficient, K , is used (the dependence of K on length
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or velocity scale will be discussed later). The entire nondimensional gaseous radiation term can be expressed as: 3
4
)
KσT 4T 4 − G K σ T ∞ (α ∗ /U R 1 = (4T 4 − G) ∇ · q r = ∗ ∗∞ · α ∗ 2 / ) Bo ρ cP ∗ UR λT ∞ (α /U R 4
=
Kσ T ∞LR / λT ∞ L R
(4T 4 − G) ∼
radiation conduction
(3)
From this we see that gas radiation increase its importance as the convective velocity decreases or the thermal length increases. If K is constant (i.e. at the Planck-mean 2 2 limit), the non-dimensional gas radiation is proportional to 1/U R or L R . As the flow velocity U R decreases or the flame thickness scale L R increases, radiation effect is amplified. One half of the radiation amplification is from the thickening of the radiating layer of the combustion products (∝ L R ) and the other half is from the reduction of convective flux (∝ 1/L R ). This simple scaling is rigorous only in the optical-thin limit. Unfortunately, at the optical-thin limit (very thin flames), flame radiation effect is normally not significant [5]. For the cases that flame radiation needs to be accounted for, flame often is neither optically thin nor optically thick [5]. If we represent the mean absorption coefficient using K = C K P , where K P = K P L R , K P is the Planck-mean absorption coefficient and C is the calibration factor, the value of C is between 0 and 1 [6], depending on the flame optical thickness. The non-dimensional radiation term is therefore modified to be b b proportional to 1/U R or L R where 1 < b < 2. The effect of surface radiation and the interaction between gas flame radiation and the surface can be seen from the surface boundary condition. Here again we use the one for flame spread over a thin solid [2]: y
qc +
dh s dTs qr + ⌫h s =⌫ [−L + c(Ts − TL ) + (TL − Ts )] Bo dx dx
(4)
where ⌫ = (ρ s cs V f )/(ρ ∗ c∗P U R ) c = c∗P /cs L = L/(cs T ∞ ) dT qc = κ dy w qry = −εs (Ts4 − 1)
(if only solid radiative loss)
where εs is the emissivity of the solid surface, cs is the solid heat capacity, L is the term on the latent heat of the solid fuel and V f is the flame spread rate. The first y left, qc , is the conduction from the gas phase and the second term, qr Bo, is the net
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radiation term onto the solid surface. The latter includes incident radiation, reflection and surface emission. The essential massage from this nondimensional term is that surface radiation is proportional to 1/U R or L R (through Bo). From the above, we see that both gas radiation and surface radiation amplify (in term of their effect not necessarily in dimensional magnitude) with increasing flame thickness or decreasing convective velocity. Gas radiation amplifies faster than surface radiation (b > 1). For a typical solid fuel (e.g. PMMA), the surface temperature can be high (∼ 700 K) so the surface radiation loss can be much larger than the gas radiation in high-speed normal gravity flame. But because the gas radiation is amplifies faster, in low-intensity microgravity the contributions from these two sources can be comparable. For liquid fuel with low boiling temperature, surface emission is small. Flame is the only radiation source. Flame radiation can be both a loss from the flame and a gain on the surface. Computed results with burning rate exceed that by adiabatic theory have been reported because of the additional radiative feedback to the solid or liquid surfaces [7].
Simulation Between Microgravity and Normal Gravity Flames Because of the limited opportunity and high expense, there is relatively few longduration microgravity combustion experiments conducted. Repeated tests such as screening materials for flammability in microgravity are even more prohibitive. Tests in normal gravity that simulate the combustion performance in microgravity are therefore highly desirable. From a rigorous theoretical point of view, complete similitude requires the same non-dimensional governing equations, boundary conditions and the values of non-dimensional parameters. This complete match appears to be not feasible, so a partial similitude that retains the essence of microgravity behavior is explored here. From the scaling analysis in the last section, we see that it is essential to keep the flame thickness scale L R at the value at the microgravity condition (i.e. relatively large) in order to retain the importance of radiation with reduced convective flows. Several examples are given below in this attempt.
Stagnation Point Diffusion Flames Stagnation point flames are one-dimensional. The flow parameter is the flow strain rate or the flame stretch rate a (1 s−1 ). The only characteristic length is the flame thickness, L R = (␣/a)1/2 ∼ (D/a)1/2 ∼ (ν/a)1/2 . Note that because the flow parameter in this configuration is different from that in a spreading flame, the expressions for L R are different but the relative importance between surface and gas radiation is similar to the previous case. Inserting this new L R into Eqs. (2) and (3), we get the scaling relations: gas radiation amplifies with 1/a and surface radiation with 1/a 1/2 .
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In microgravity, flames are characterized by small stretch rates. In normal gravity, small stretch rate can be generated by buoyant flow near the bottom of a solid fuel with large radius of curvature, i.e. ab ∼ (g/R)1/2 , where g is gravity and R is the radius of curvature. Using a mixed forced and buoyant flow formulation [8] with 1 a mixed flow stretch rate defined by a = (a f + ab ) /2 = a f (1 + φ)1/2 , where a f is the forced flow stretch rate and φ is the densimetric Froude number (= ab /a f ), the computed flammability boundaries are shown in Fig. 1. In this computation, gas radiation is not included so the surface emissivity εs = 0 cases are the adiabatic flame while the εs = 1 cases are the ones with full surface radiative loss. The first observation from Fig. 1 is that the boundaries with and without radiative loss are qualitatively different at low stretch rate, as first pointed out in [9]. The boundaries with loss have a quenching branch at low stretch rates and produce a fundamental low oxygen limit at the merging point between the quenching branch and the high stretch blowoff branch. The second observation is that the three boundaries: purely forced (φ = 0), purely buoyant (φ = ∞) and mixed (φ = 1) are close to each other. Computed results also show that global quantities such as maximum flame temperature and burning rate are also close. Thus, an approximate similitude exists. This may be first surprising since there are differences in equations and boundary conditions, but it shows that the major controlling parameter in this geometry is the length scale L R . When this scale is matched, a number of the essential global properties in the flames can be simulated approximately. This idea has been explored in Ref. [10] in the experimental investigation of the bottom burning of PMMA. Samples with different radii of curvature have been
Fig. 1 Flammability boundary: limiting oxygen mass fraction vs. mixed – flow-stretch rate [8]
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Fig. 2 PMMA surface regression rate vs. stretch rate. Low stretch data are obtained using a normal gravity device [10]
tested in normal gravity. As sample radius increases (buoyant stretch rate decreases) flame color turns blue (an indication of flame temperature drop) and extinction is reached eventually. Figure 2 shows the burning rate data of PMMA is extended to the low stretch regime by the use of this burner. This idea of using a normal gravity devise to help screen material flammability for space application has been explored further in Ref. [11]. A buoyant porous burner of large radius of curvature (∼ 500cm or a ∼ 1s−1 ) has also been used to study the gaseous diffusion flame behavior at low stretch rates [12]. In this setup, the gaseous fuel is ejected from the porous plate. This is different from the solid fuel case where fuel burning rate is coupled to the flame. In Fig. 3, the low-stretch methane diffusion flame is labeled and extinction can be achieved by either diluting the methane or by decreasing the injection rate. This setup is similar to the well-known Tsuji burner. In the typical Tsuji burner, stretch rate is generated in a forced flow wind tunnel. There is a low stretch rate limit below which the result is contaminated by buoyancy. In the present setup, buoyant is used and controlled (through the radius of curvature). By using the approximate similarity just discussed, low-stretch flame behavior, missing in Tsuji’s experiments has been obtained. We note that low-stretch flame thickness is relatively large (∼ 1–2 cm) and in both setups, the bottom burners are large in lateral extent. This insures a flame diameter to thickness ratio much greater than unity, hence a quasi-one-dimensional flame. The quasi-one-dimensional flame is needed to eliminate the both the curvature effect and the influence of lateral heat conduction loss. Although buoyant stagnation flames can be a useful tool in simulating lowstretch flames in microgravity as just discussed, its applicability to screen solid material flammability (extinction) limits is limited to non-charring material with little ash contents. Char forming is known as one important mechanism to reduce material flammability. A charring solid with an extinguished flame in the stagnation
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Fig. 3 (Top) Diagonal view from underneath of the low-stretch bottom burner. (Bottom) The schematic [12]
configuration may be able to support a flame that spreads from one location to the other with only the top surface layer involved in the burning process. Simulation of spreading flames will be discussed next.
Spreading Flames over Solid Fuels in Opposed Flows In opposed-flow diffusion flame spreading over solids, the primary length scale is the thermal-diffusional distance L R = α ∗ /U R . As mentioned previously, this scale defines the size of the flame stabilization zone. In opposed flows, the stabilization zone is also the propagation front. So the processes occur in this zone determine both the spread rate and the extinction limit. In forced flows, the relative velocity between flame and air, is given by L R = U ∞ + V f , where U ∞ is the forced velocity far upstream relative to the laboratory coordinate and V f is the flame spread rate. In buoyant flows, L R = U b + V f , where U b is the buoyant induced air velocity near the flame front given by U b = (gL R )1/2 ≈ (α ∗ g)1/3 . Using these expressions, two sets of computed flame spreading results in low-speed forced flow and in reduced gravity buoyant flow were compared in [13]. Figure 4 shows that the spreading rates agree favorably. Again, as in the stationary stagnation-point flame case, the equations and boundary conditions are different and the detailed velocity distributions are different, but the major global results are very close if the major controlling length scale matches.
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Fig. 4 Computed flame spread rate of PMMA versus reference velocity with and without surface radiative loss [13]
In concurrent flame spread over solid surfaces, the situation is more complex. There are two major length scales: the thermal-diffusional distance, α ∗ /U R , that is important at the flame stabilization zone and the flame or pyrolysis length which is approximately proportional to U R . Because of the difference of flow structures between upward spread in gravity field and purely forced concurrent flow in zero gravity, it is not possible to match both these two scales. Hence, any simulation has to be more limited in scope. An attempt to simulate the rate of flame spread in partial gravity (gravity level less than that on earth) with that in normal gravity has been attempted and will be described in the next section.
Pressure Modeling As discussed previously, it is essential to preserve the key length scale in simulating a micro- or partial gravity flames in normal gravity. One way to do this is by varying the pressure in the experiment. Varying pressure changes the density hence the flame thickness or the flame standoff distance from a solid surface. If the key scale is preserved by varying pressure, the phenomenon associated with this scale can be simulated. A couple of examples are given below. Candle Flame It is known that in microgravity a candle flame in air is hemispherical in shape with a blue color (Fig. 5 top). Candle flame in normal gravity at sufficiently low pressure has a similar shape, size and color as shown at the bottom of Fig. 5. The reason that the low pressure flame assumes this shape and size is as follows. Buoyant induced velocity is estimated as U b = (gL R )1/2 and L R = α ∗ /U b. So L R is proportional to p −2/3 . As pressure decreases, the flame standoff distance at the flame stabilization zone increases. When the flame standoff becomes large enough, the candle wick
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Fig. 5 Candle flames in 21% O2 . (Top) microgravity, 100kPa [14], (Bottom) normal gravity, 13.6 kPa [15]. These are from two separate experiments with different candles and different camera settings
appears relatively short by comparison and acts like a point fuel source. Hence a hemispherical shaped flame is resulted. Both the microgravity and the normal gravity low-pressure candle flames exhibit near-limit oscillations as ambient oxygen is depleted. But the oscillating frequencies are different. In microgravity the frequency is about 1 Hz [14] and in normal gravity, 2 2 it is about 8 Hz [15]. Their ratio is close to (L R /␣)0g /(L R /␣)1g , where L R is the flame radius and α is the thermal diffusivity of the gas. Since the radii of the flames are close, this is approximately the density or the pressure ratio. It is also possible to produce hemispherical flame on earth by controlling the length scale to be sufficiently small. This has been demonstrated in the micro-jet diffusion flame experiment [16]. We will refer the readers to this reference for details. Upward Flame Spread over Solid in Partial Gravity The rate of upward flame spread rate is correlated with flame length which is related to the total solid mass burning rate. The solid burning rate depends on the flame standoff distance from the solid surface which depends on gravity level and pressure. It was found by performing partial gravity experiments in reduced-gravity airplane that the upward spread rates can be correlated by keeping p 1.8 g 0.95 constant [17, 18].
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Fig. 6 Steady upward flame spread over narrow Kimwipe samples. (Top) Different pyrolysis lengths at different gravity levels. (Bottom) Similar lengths using pressure-gravity scaling
Thus, it may be possible to infer the upward spread rate in partial gravity using an experiment in normal gravity. Figure 6 shows the direct photos of three flames with p 1.8 g 0.95 at approximate the same value. Note that this p-g correlation is close to p 2 g which can be derived if Grashof number is preserved. Note that because pressure affects chemical kinetic rates, a successful relationship to simulate the rate of flame spread by varying pressure may not be extended to the extinction limits.
Flame Spread in Narrow Channels In flame spread over solid surface in low-speed opposed flow in microgravity, radiative heat loss is a main contributor to its unique character. On earth, it is possible to reproduce a number of microgravity flame features by using a narrow channel device (of the order of 1 cm height or less) that enhances the conductive losses from the flame [19, 20]. These features include the qualitative trend of flame spread vs. opposed velocity and oxygen percentage. Despite the success of the qualitative trends, a quantitative comparison or matching has yet to be demonstrated.
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It is also noted that near-limit finger type instability has been observed using the narrow channel device on earth [19, 20]. Similar type instability has also been found in microgravity experiment [21]. Discussions on the mechanism for near-limit instabilities as a result of heat losses can be found in [22].
Concluding Remarks The importance of radiation in microgravity flames has been examined through nondimensional parameters. Both gas and surface radiation effects are amplified with the decrease of flow velocity and the increase of flame thickness. In situations where there is only one dominant length scale, it may be possible to find an approximate similitude between flames in microgravity and flames in normal gravity by matching up this scale. For the more complex cases that have multiple length scales, such a matching is more difficult. Judicious selection of suitable parameters may still be possible to simulate certain aspect of microgravity flame behavior. Acknowledgments This research has been supported by NASA grant NNC04AA58A, with Drs. Gary Ruff and Kurt Sacksteder as the grant monitors. The author would also like to thank Mr. Sheng-Yen Hsu for helping with the preparation of this manuscript.
References 1. de Ris, J., Seventeenth Symposium (International) on Combustion, The Combustion Institute, pp. 1003–1016 (1979). 2. T’ien, J.S., Shih, H.Y., Jiang, C.B., Ross, H.D., Miller, F.J., Fernandez-Pello, A.C., Torero, J.L. and Walter, D. “Mechanisms of Flame Spread and Smolder Wave Propagation”, Chapter 5 in Microgravity Combustion: Fire in Free Fall, pp. 299–418, (H. Ross, ed.), Academic Press (2001). 3. Ronney, P.D., Proceedings of the Combustion Institute 27: 2485–2506 (1998). 4. Kumar, A., Tolejko, K.D. and T’ien, J.S., Journal of Heat Transfer 126: 611–620 (2004). 5. Bedir, H., T’ien, J. S., and Lee, H. S., Combust. Theory Modelling 1: 395–404 (1997). 6. Rhatigan, J. L., Bedir, H., and T’ien, J. S., Combustion and Flame 112: 231–241 (1998). 7. Rhatigan, J. L., Sung, C. J. and T’ien, J. S., Proc. Combust. Inst. 29: 1645–1652 (2002). 8. Foutch, D. W. and T’ien, J. S., AIAA J., 25(7): 972–976 (1987). 9. T’ien, J. S., Combustion and Flame, 65(1): 31–34 (1986). 10. Olson, S. L. and T’ien, J. S., Combust. Flame, 121: 439–452 (2000). 11. Olson, S. L., Beeson, H. D. Hass, J. P. and Bass, J. S., Proc. Combust. Ins. 30(2): 2335–2343 (2005). 12. Han, B., Ibarreta, A.F., Sung, C.J. and T’ien, J.S., Proc. Combust. Inst. 30(1): 527–535 (2005). 13. West, J., Bhattacharjee, S. and Altenkirch, R. A., Combust Sci. Technol., 83: 233–244 (1992). 14. Dietrich, D. L., Ross, H. D., Shu, Y., Chang, P. and T’ien, J. S., Combust Sci. Technol. 156: 1–24 (2000). 15. Chan, W. Y. and T’ien, J. S., Combus. Sci. and Technol. 18(3,4): 139 (1978). 16. Ben, H., Venkatesh, S. and Saito, K. J. Heat Transfer, 116(4): 954–959 (1994) 17. Feier, I. I., Kleinhenz, J. E., T’ien, J. S., Ferkul, P. V., Sacksteder, K. R., Pressure Modeling of Upward Flame Spread Rates in Partial Gravity, AIAA paper-2005-0716, 43rd AIAA Aerospace Sciences Meeting (2005).
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18. Kleinhenz, J. E., Flammability and Flame spread of Nomex and Cellulosic in Space Habitat Environments, PhD thesis, Department of Mechanical and Aerospace Engineering, Case Western Reserve University (2006). 19. Zik, O. and Moses, E., Proc. Combust. Inst. 27, 2815–2820 (1998). 20. Olson, S. L., Miller, F. J. and Wichman, I. S., Combustion Theory and Modelling 10(2): 323–347 (2006). 21. Olson, S. L., Baum, H. R. and Kashiwagi, T., Proc. Combust. Inst. 27: 2525–2533 (1998). 22. Bechtold, J. K., Cui, C. and Matalon, M., Proc. Combust. Inst. 30(1): 177–184 (2005)
Structure of Micro (Millimeter Size) Diffusion Flames Yuji Nakamura, Heng Ban, Kozo Saito and Tadao Takeno
Abstract Tiny jet diffusion flames (called “micro flames” hereafter) with hydrocarbon fuels were established over a submillimeter-diameter hypodermic needle in a quiescent atmosphere. Because of the small flame height, on the order of magnitude of one millimeter, there is hardly any buoyancy effect, and the observed flame shape is almost spherical when Re = O(1). Experimental and numerical studies were pursued to investigate their structure and behavior near the extinction limit. The burner was modified from a previous study by adding a temperature-controlled plate surrounding the needle to control the boundary conditions, which may affect calculated flame characteristics. Previously preliminary comparisons were made for only one condition (1 m/s methane flow rate), and agreements were good, so our numerical model could be a useful tool to examine the flame structure in detail. This paper reports a series of further numerical calculations to examine the effect of exit velocity (Re) on the flame shape and height. Comparison of calculated and experimental results shows that our numerical model produces fairly good agreement for the flame shape and height. This result also indicates that such flame characters are essentially independent of the chemical and thermal structure of the flame edge because a one-step reaction model applied in the present study cannot describe the edge structure perfectly. It is found that flame height increases linearly with the methane flow rate under the conditions considered in this study. This is qualitatively consistent with the classical theory and observations (flame height of the order of centimeters), although the gradient for the micro flame was slightly steeper. Further evaluation of the axial transport is made from numerical results, and it is found to be important only when the flow rate is small. The axial diffusive transport becomes less important at higher flow rates due to the thermal expansion through the flame, not the buoyancy-driven convection. Keywords Micro flame · flame height · flame structure · numerical study
Y. Nakamura Division of Mechanical and Space Engineering, Hokkaido University, N13 W8, Kita-ku, Sapporo, 060-8628, Japan e-mail:
[email protected]
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Nomenclature A cp D d E Fr g g h ni Pe p q R Re r T T u ud ue Yi z ρ λ μ ν νι ω
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Frequency factor (= 1.92 × 1018 cm6 /g · s) Heat capacity Diffusion coefficient Burner diameter Activation energy (= 31.2 kcal/mol) Froude number (∼u2e /gd) Gravity vector Gravity acceleration Flame height Stoichiometric coefficient based on mole for ith species (nf = 1, no = 2) Peclet number (∼ue /ud ) Dynamic pressure Heat of formation per unit mass of methane (= 11352 cal/g, see Ref. 11) Universal gas constant (= 1.987 cal/mol · K) Reynolds number (∼ue d/) Radial direction Stress tensor Temperature Velocity vector Characteristic molecular diffusion velocity Methane velocity at the needle exit Mass fraction of ith species Axial direction Density of fluid Thermal conductivity of fluid Viscosity Kinematic viscosity Stoichiometric coefficient of species based on mass (o = 4, f = 1) Reaction rate
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Fuel (methane) Oxidizer (oxygen) Ambient (T∞ = 300K, Yo,∞ = 0.233, Yf , ∞ = 0.0) Maximum
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Introduction Laminar-jet diffusion flames can be classified into three types: the Burke-Schumann flame [1] controlled by diffusion, the Roper flame [2] controlled by buoyancy, and the micro flame [3] controlled by diffusion and convection. The first and second types of flame have been investigated extensively resulting in a rich literature [4]. However, the third type of flame was only recently investigated by Ban et al. [3] and Nakamura et al. [5]. Flame shapes of micro flames were found to be almost spherical [3]; different from the more commonly observed candle-like laminar diffusion (the Roper) flames and with little or no buoyancy effects. Considering its uncommon character, there would be a number of reasons that the micro flame is important to be studied. Firstly, because of its spherical flame shape, it is possible to become a model for microgravity flames. Second, due to the fact that its size is so small, the amount of heat release from the flame is very small, whereas the heat loss to the burner would be extensively large. This indicates that this flame may be established always under near-limit conditions and therefore may constitute a useful tool for studying the limiting behavior of flames. Third, the thickness of the diffusive transport layer is of the same order as that of the reaction-influenced layer [4], again because of its size. This suggests that micro flames could be useful in applications for investigating in detail the structure of diffusion-controlled phenomena in general or diffusion flames themselves. Before dealing with this “unknown” as well as “uncommon” flame, it is essential to start to investigate its fundamental characteristics; flame structure, flame shape and height. Previously, Ban et al. [3] conducted micro-diffusion-flame experiments using different kinds of C2-class hydrocarbon fuels (ethane, ethylene and acetylene) at various flow rates. They found that the flame shapes of these micro flames were almost spherical, indicating no buoyancy effect. A similarity analysis (without a buoyancy term) was also conducted in their study. The analysis clearly reveals the significance of axial diffusion for the flame shape of micro flames, as suggested by Savage [6] and Edelman et al. [7]. In terms of the flame height, their analytical solution shows that the flame height of micro flames increases linearly with the exit flow rate and therefore with Re. Their results are somewhat different from those of Savage [6] and Roper et al. [8], although Savage stated that the uncertainty of the data obtained for small flames would be large due to measurement error. As the authors mentioned in their paper [3], however, the similarity solution might not be correct near the burner port where the far-field boundary assumption is inadequate. To understand what is the real effect of the axial diffusive transport on flame behavior, it is necessary to set appropriate boundary conditions at the burner port [6].
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Furthermore, it is interesting to see when or how buoyancy effects [7, 9] come to play in the height, shape and structure of micro diffusion flames. To overcome the points raised above, we developed a 2-D numerical model with one-step finite-rate chemical kinetics and temperature-dependent transport and thermal properties to calculate the thermal and dynamic structures of methane-air micro flames [5]. The 2-D steady-state profiles of major species concentrations, temperature, reaction rate and flow field were calculated by the model under normal gravity condition at 1 m/s of methane flow rate (Re = O(1)). These calculations agreed fairly well with the experimentally observed micro flame shape except in the vicinity of the flame edge where the chemical structure becomes important. In this paper, a new series of numerical calculations is performed to examine the effect of exit flow rate (Re) on the flame shape and height and its structure. Calculated results were compared with the experimental results. To eliminate previous uncertainty in the thermal boundary condition, the burner was modified by adding a water-cooled plate surrounding the needle, instead of the free jet [3]. The fuel flow range considered corresponds to Re between about 1 and 2. The inner diameter of the burner was fixed at 0.4 mm. Methane was used as the fuel in this study to avoid the effects of diffusivity induced by using different fuels. Discussions about the gravity effect which were not given in the previous analysis [3] were also presented in this paper.
Features of Micro Flames The micro flame as defined by Ban et al. [3] has the following characteristics: Fr(= u 2e /gd) >> 1 and Pe(= u e /u d ) = O(1)
(1)
where ue , ud and d represent the exit methane flow rate at the burner port, the characteristic molecular diffusion velocity and the inner diameter of burner. A scaling analysis [4] showed that a typical flame (u e = 0.1 m/s, d = 1 mm, and Fr >> 1) has little effect of buoyancy. The physical meaning of Fr >> 1 is that a characteristic acceleration time by buoyancy is very large as compared to a characteristic flow time, whereas that of Pe = O(1) is that a characteristic flow time is comparable to a diffusion time. The shortest time scale here is the flow or diffusion time; therefore the micro flame is classified to the category of a “diffusion-convection (or Pe) controlled flame”. The volumetric flow rate of the jet remains small at high exit flow rates because the burner port size is sufficiently small.
Experimental Methods The needle burner apparatus used for this experiment (Fig. 1) is somewhat different from our previous one [3], because the present one has a water-cooled copper plate. The burner system consists of a stainless-steel needle burner with an inner diameter
Structure of Micro (Millimeter Size) Diffusion Flames Fig. 1 A schematic of applied micro flame burner apparatus and computational domain
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of 0.4 mm and a water-cooled copper plate (20 mm long × 20 mm wide × 8 mm thick) surrounding the needle burner. The burner was pressed into the plate to keep the burner port and the plate surface at the same level. The flow rate of methane (99.99% purity) was measured by a soap-film flow meter, whose accuracy in the flow rate range between 10 cc/s and 0.1 cc/s is better than 98%. A fine thermocouple (copper vs. constantan; wire diameter = 0.1 mm) was welded on the backside plate surface, and the temperature of the plate was kept at approximately 20 ◦ C. A steady and stable laminar methane-air micro flame was established over the burner port in quiescent ambient air at normal atmospheric condition. Color photographs of the flames were taken using a camera with a macro-lens. From the magnified image of the photographs, the flame shape was clearly identified, and the dimensions of the flame were measured using a technique developed by Saito et al. [10]. The reproducibility of this technique is better than 99%.
Experimental Results The diffusion flames observed were in a laminar regime. In Fig. 2, the experimentally determined visible flame shape is shown for various exit methane flow rates between 1 m/s and 5.15 m/s. A spherical flame was established over the burner port especially at the lower flow rates, whereas a candle-like flame shape was formed at relatively higher flow rates. This is because the spherical flame shape can be seen only when the molecular-diffusion velocity is comparable to the convection velocity of methane, as shown in the previous study [3]. As discussed later, the flame height increases linearly with the methane flow rate, indicating this flame-height feature is the same as that of Roper-type diffusion flames classified as “buoyancy-controlled diffusion flames” [10]. Due to the heat loss to the cold plate, a dark quenching zone was formed between the bottom of the visible flame edge and the burner port, producing an edge of the visible flame. As expected, the quenching distance, which is the height between the burner port and the visible flame edge, is larger for the flame with the water-cooled plate than for the flame without the cooling plate. However, the overall flame shape remained approximately the same with/without a cooled plate. This suggests that
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Fig. 2 The experimentally determined eight different flame shape of laminar methane-air micro diffusion flames as a function of the exit methane velocity: u e . The burner diameter: d = 0.4 mm
the effects of heat loss to the burner port and the flow boundary condition have little effect on the overall flame shape. The quenching distance remained the same in the range of the methane velocity, between 1 m/s and 2.5 m/s. For methane flow rates such that u e < 1 m/s, no flame was sustained at the burner port due to a large heat loss to the cooled burner port. For methane flow rates such that u e > 10 m/s, the flame started to lift off from the burner port to blow-off with any further increase of methane flow rate. The fact that the lower methane flow-rate limit for the flame to be sustained is somewhat higher for the flame with the cooling plate than for the flame without the cooled plate supports our explanation that the lower velocity limit is determined by the heat loss to the burner port.
Numerical Model and Applied Scheme The major assumptions made for the numerical model are as follows: (I) completely axisymmetric geometry; (II) ideal gas law for all the gases species; (III)
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temperature dependent thermo-physical and transport properties for all the species (they are equal to those of air); (IV) an overall one-step irreversible process for methane-air reaction; (V) laminar and low-Mach-number flow; and (VI) a 2-D coaxial Poiseuille flow for the incoming methane flow at the burner exit. Calculations were performed as a time-dependent problem starting from an estimated initial solution (homogeneous, quiescent atmospheric condition), and they were continued until a steady-state solution was achieved. With these assumptions, the governing equations can be written (D/Dt denotes the substantial derivative): Mass : Dρ/Dt + ρ div u = 0
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All chemical properties, like A, E, n f , n o , were obtained from the reference [11]. The boundary conditions and the schematic model of the calculation are shown in Fig. 3. Above equations were solved using the finite-differential method in staggered grid systems. The SIMPLE procedure [12] was employed to handle the pressure term in the momentum equation. A Hybrid scheme was applied to the flux terms on the grid cell surface and Euler’s implicit method was used for the time integration. In each time step, iteration by using a line-by-line method coupling with SOR (Successive Over Relaxation) was performed to maintain stability. The total number of mesh points is 91 for radial, 131 for axial direction, respectively. The entire region of the calculation is about 20d for radial, 60d for axial direction, where scales are nondimensionalized by jet diameter; d. Non-equivalent meshes were applied in both directions to set the outer boundary away from the flame region. The minimum grid scale generated at the equivalent mesh region corresponds to d/10. The calculation was started with an initial time step of 10 s and was continued until a steady state was reached. The steady-state solution was checked by showing that increasing the time step had no effect. Effects of mesh size and numerical domain on the converged solutions were carefully checked and ensured that the present numerical condition works well.
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Fig. 3 A schematic of the numerical model and boundary conditions
Numerical Results and Discussion Flame Height Figure 4 shows an excellent agreement between the numerically and the experimentally determined flame height vs. the exit methane flow rate in the range from ue = 1 to 5 m/s. Here, the numerical flame height was determined as the outer contour of the reaction rate, ω = 0.001 g/cm3 s; this corresponds to approximately 20% of the maximum reaction rate and the major C-H emission occurs [13]. The result shows that the numerical prediction of the flame height is slightly higher than the experimental measurement. This might be because of following reasons; (i) artificially introduced criteria of outer reaction zone numerically was inappropriate or (ii) diffuse back of ambient gas components into the burner needed to be taken into account or (iii) a fixed convective exit boundary condition of methane (Poiseuille distribution and fuel only) would be too idealized. Since diffusive flux of fuel would be considered in addition to convective flux at the exit (although it is small), the total flux of fuel was slightly over-estimated in our calculation. To improve this inconsistency, numerical code should be modified to solve the components inside the burner [14].
Structure of Micro (Millimeter Size) Diffusion Flames Fig. 4 Comparisons of experimentally and numerically determined flame height as a function of the exit methane flow rate: u e
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Flame Shape Figure 5 (5-1 and 5-2) shows numerical results for u e = 1 m/s and 2.5 m/s, respectively. Each case includes four different plots: (a) 2-D velocity vector plots, (b) 2-D temperature contour, (c) 2-D color coded methane concentration (gray scale) and oxygen concentration (solid line), and (d) 2-D color coded reaction rate (gray scale). All these plots are shown in the same non-dimensionalized 2-D coordinate. A comparison of numerical (in Fig. 5-1, 2) and experimental flame shape (in Fig. 2) shows that the numerical flame shape can simulate the experimental flame shape except the vicinity of the flame base, which is often called “flame edge”. The calculated flame near the edge has somewhat wider shape and narrower quenching distance in comparison with experimentally observed one. This discrepancy is expected because flame quenching due to radiation is not included in our model and our one-step finite chemical kinetics may not be accurate in the flame edge. It is reported that the temperature at the edge is often substantially (200 ◦ C) lower than the fully developed (adiabatic) flame temperature [15] and radical-species play a role significantly [16]. Our calculated profiles indicate that the flame edge temperature is 1400–1500 K,
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whereas the flame tip temperature reaches 1700–1800 K. The temperature difference between the flame edge and flame tip is about 300 K. On the other hand, the difference between the flame edge temperature and the adiabatic flame temperature for methane (∼2230 K) is over 700 K. The structure of the flame edge is known to be complex, however, our model can serve as a first order approximation to predict the overall shape of the micro flame.
Flame Structure and Characteristics Figure 5 clearly shows the thermal and chemical structure of micro flame at different fuel flow rate. For low or high methane flow rates, there is limited buoyancy effect on the flow field because the velocity induced by buoyancy is a function of gravity constant and residence time of the flow. The buoyancy-induced velocity is estimated to be on the order of 10−2 m/s, whereas the fuel exit velocity is 1–5 m/s. The vertical velocity does increase after the reaction zone due to the thermal expansion through the flame and to a much less extent, buoyancy. This accelerated flow elongates the temperature as well as species distributions as shown in figures, suggesting that their changes in axial direction become milder. Nonetheless, the flame is still controlled by diffusion-convection, since buoyancy is not significant. In Fig. 5, the air flow passing through the quenching region into the fuel flow can be clearly observed at higher exit rates, although weaker entrained flow also exists at lower flow rates. The existence of entrained flow was consistent with the experimental observations and numerical prediction [16, 17]. Since this entrained flow carries ambient oxygen inside the flame, the structure of diffusion flame would be affected somehow [15]. The difference in the amount of entrained air between low Re and high Re flames could also add to the difference in flame characteristics. Such entrain air flow would not happen when the flame sheet model is used. In this sense, our numerical model with finite rate reaction assumption could provide more precise flame structure than that of flame sheet model. Figure 6 shows the flame structure along the center axis at various exit flow rates. (z/d)∗ indicates relative distance from the reaction region (define zero at the location of maximum temperature); positive and negative denote the oxygen and fuel side, respectively. Since high Re flow broadens the distributions in axial direction, weaker axial diffusion transport is attained at higher flow rates. At lower flow rates, on the other hand, the sharp changes in quantities are predicted, suggesting the higher diffusive transport in axial direction near the reaction zone. Clear double-peak structure of heat release rate is predicted for all the conditions in this study. This is due to the entrained air through the quenching zone. The first peak is caused by premixed combustion, whereas the second peak is caused by non-premixed combustion. The first and second peaks tend to be closer at lower flow rates. This trend suggests that micro flame could be categorized neither as pure diffusion (non-premixed) flame nor premixed flame. Quenching distance exists in all flames. Its effect on micro flames is expected to be greater because the entrained air is relatively larger for micro flames in comparison to flames of, for instance, centimeters in size.
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Fig. 7 Comparison of maximum radial and axial heat conduction on center line in various exit flow rates
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significant under such conditions. This could be the reason why the axial diffusive transport becomes less important in higher flow rate.
Conclusions Both experimental and numerical studies were conducted to understand the structure of laminar methane-air micro diffusion flames with a thermally controlled boundary. These studies offer the following conclusions: 1. Methane micro flames of the burner diameter 0.4 mm and the exit methane velocity 1–3 m/s have little effects of buoyancy, and their flame shape is nearly semispherical, independent whether there is a cooled plate around the burner. 2. The flame height increases linearly with the exit flow rate in micro flames, and the linear function is found to be slightly steeper than that of the Roper flame, which does not include the axial diffusion transport effect. 3. A numerical model with a one-step overall finite-rate chemical reaction was developed to understand the structure of the micro diffusion flames established over a water-cooled burner port. The numerical calculations agreed with the experimental results fairly well except in the vicinity of the flame edge where wall quenching and detailed finite-rate chemical kinetics becomes important. 4. The axial diffusion transport becomes strong at lower exit flow rates in micro flames, but becomes weaker at higher flow rates due to the thermal expansion through the flame, not the buoyancy-driven convection. Acknowledgments We wish to acknowledge Professor F. A. Williams for his suggestions on the early development of micro flame model and editing entire of the manuscript to improve the quality. Advice from Professor Paul Libby to use a water-cooled copper plate to obtain a fixed-flow boundary is quite valuable. This research was supported by Japanese Ministry of Education, Science, Sports and Culture Grant (No. 11750162).
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
Burke, S. P. and Schumann, T. E. W., Ind. Eng. Chem. 20 (1928) 998–1004. Roper, F. G., Combust. Flame 29 (1977) 219–226. Ban, H., Venkatesh, S. and Saito, K., J. Heat Transfer 116 (1994) 954–959. Williams, F. A., Combustion Theory (2nd Ed.). Addison-Wesley, New York, 1985. Nakamura, Y., Ban, H., Saito, K. and Takeno, T., Proc. of 1997 Meeting of the Central States Section/The Combustion Institute, Point Clear, AL U.S.A., April 1997, 160–163. Savage, L. D., Combust. Flame 6 (1962) 77–87. Edelman, R. B., Fortune, O. F. and Weilerstein, G., 1973, Proc. Combust. Inst. 14 (1973) 399–412. Roper, F. G., Smith, C. and Cunningham, A. C., Combust. Flame 29 (1977) 227–234. Cochran, T. M. and Masica, W. J., Proc. Combust. Inst. 13 (1971) 821–829. Saito, K., Gordon, A. S. and Williams, F. A., 1986a, Combust. Sci. Tech. 47 (1986) 117–138. Coffee, T. P., Kotlar, A. J. and Miller, M. S., Combust. Flame 58 (1984) 59–67. Patankar, S. V., Numerical Heat Transfer and Fluid Flow. McGraw-Hill Inc., 1980.
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13. Gaydon, A. G. and Wolfhard, H. G., Flames, Their Structure, Radiation and Temperature (4th Ed.). Chapman Hall, London, 1979. 14. Nishioka, M., personal communication. 15. Saito, K., Williams, F. A. and Gordon, A. S., J. Heat Transfer 108 (1986) 640–648. 16. Takahashi, F., Schmoll, W. J. and Katta, V. R., Proc. Combust. Inst. 27 (1998) 675–684. 17. Venkatesh, S., Ito, A., Saito, K. and Wichman, I. S., Proc. Combust. Inst. 26 (1996) 1437–1443.
Part III Materials Processing, Manufacturing and Environment D. Sekulic, J. Nakagawa, K. Sekimoto and M. Khraisheh
Summary Over the years, scale modeling has been applied for materials processing and manufacturing but primarily in domains of complex multidimensional problems involving transport phenomena and advanced thermodynamics, such as modeling of convective flows in materials processing, surface tension driven phenomena, combustion related processes, etc. It should be added that the general applicability and suitability of scale modeling involving multidisciplinary topics and phenomena experienced at multiple scales would most likely mean a significant increase in the visibility of these techniques in the future. There are multiple reasons for such a trend and these may be found in particular in the increased interest in non-traditional manufacturing and related materials processing. An increased awareness of impacts that well developed but also new engineering fields may have on environmental and on societal well being is also a driving force for an increased role of large scale phenomena studies – hence a need for scale modeling and analysis. Developments in new technologies have very aggressively been applied in both large- but also micro- and nano- scale domains. These novel trends are continuing to uncover more questions than answers, in particular as far as the modeling of phenomena is concerned. Because the governing laws at multiple scales are intricate and still only partially understood – and even if they were more generally understood, might still be applicable only in part – all of this would lead initially to the increased prominence of heuristic approaches. Identification of the physical laws involved would necessarily precede a rigorous deterministic model building. It is to be expected that the complex feedback loops within and between multi-field domains (such as the interactions of man-made processes with the natural environment) will become of ever greater importance to society. At the same time, a lack of deterministic models and our inability to tackle such large- or multiplescale manufacturing-environment systems with comprehensive modeling and with real time and in-situ experimentation will inevitably lead us to the increased use of scale modeling, model experimentation, and analysis. On the other hand, nanotechnology and nano-manufacturing will require us to abandon a number of continuum laws assumptions; hence, new scaling laws will be needed.
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In light of these predictions, a review of scale modeling and related methods is timely and relevant. In addition, scale analysis and dimensional analysis (techniques not necessarily representing scale modeling but often using complementary approaches), presented in this section to a certain extent as well, illustrate the strength and broad applicability of these methods in the fields of materials processing, manufacturing, and environment studies. While not comprehensive – and given the space available, no selection could be – this collection of papers very clearly illustrates a variety of engineering and natural settings that may be studied by using either scale modeling, and/or model experimentation, as well as dimensional and/or multi-scale analysis.
Papers Selected from the First Symposium (with permission) 1. K. Sekimoto. “Scaling Laws for Sedimentation Process in Water Flow-Driven Sedimentation Tanks.” A sedimentation process is an inherently three-dimensional phenomenon. This process may involve (1) different physical size scales of system components and (2) different specific mass densities of involved particles. Such engineering setting represents an ideal test bed for an application of the scale modeling for materials processing and/or an environmental application. A need for preserving the geometric similarity as well as establishing the existence of the limited set of governing physical laws (for both a small model and a full scale setting) is promoted. Sekimoto’s study offers an insight into a selection of scaling laws for four considered cases characterized with a specific selection of particle size and mass density. Subsequently, multiple scale model experiments were discussed. It is shown that the selected scaling laws can be validated with the experiments for the two cases of practical importance.
Papers Papers Selected from the Second Symposium 1. R.I. Emori. “Toys and Scale Models.” A philosophy of solving engineering problems by using both experimentation and theoretical analysis, but based on an establishment of scale models, is discussed in this paper. Starting with a notion of engineering as an art of making new things vs. science as an enterprise of exploring natural phenomena, Emory outlines the need for a “play with mental toys” of scale modeling. This metaphoric language though has its rigor in the fundamental aspects of similarity of the phenomena evolution at different scales under conditions of proper selection of physical laws and assisted by building the relevant models. Both natural and man-made settings were offered as illustrations of successful scale modeling. 2. H. Hayasaka, Y. Kudo, H. Kojima, T. Hashigami, J. Ito, and T. Ueda. “Backdraft Experiments in a Small Compartment.” Small scale models’ experiments are quite appropriate for an analysis of physical settings otherwise very difficult to
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control/monitor as real-scale phenomena (like large-scale fires). Also, scale models are convenient for studies of the events that may otherwise require extensive resources to be observed in real settings. This paper offers a detailed discussion of an 1/3 scale model experiment involving an appearance of the so-called backdraft phenomenon – the rapid deflagration moving through a compartment featuring a fire after ignition consuming the accumulated excess pyrolizates. Multiple experiments were performed within the model environment and the backdraft conditions were successfully reproduced in a number of situations. The ease of monitoring of a small-scale model featuring the same full-scale phenomenon assists very efficiently a clear formulation of the backdraft onset scenario. In easily repeated experiments, an onset of the backdraft can be initiated by repeating an uncovered set of the steps, involving the uncovered pre-onset phenomena (a production and accumulation of combustible gasses, and mixing with oxygen). 3. K. Yuge and S. Ejima. “Sound Insulation Analysis of a Resin Composite Material Using the Homogenization Method.” This study presents a topic involving multiple scale effects in a system exposed to external perturbation. The system under consideration consists of a composite featuring a significant variation in properties. Namely, a microscopic reinforcement material is distributed within the matrix of a composite material serving the role of an acoustic insulator. The suggested approach of the analysis illustrated by Yuge and Ejima in this paper is the so-called homogenization method that distinguishes a periodic microstructure within the overall macroscopic domain. Mathematical modeling is followed by a finite element numerical analysis. The macro- and micro-domain equations were both used in this simulation. In such a manner, the homogenization method for linear elastic analysis was successfully extended to the viscous-elastic kinematics of the composite material.
Papers Selected from the Third Symposium 1. Y. Tanigawa, R. Alloo, N. Tanaka, M. Yamazaki, T. Ohmori, H. Yano, A.J. Salazar, and K. Saito. “Development of a New Paint Over-Spray Eliminator.” Manufacturing systems and processes require at an increasing rate the research and development that are in full accord with increased sustainability awareness. The energy more efficient and environmentally friendlier manufacturing has to satisfy high product quality and offer significant economic benefits. An example of solving an engineering challenge and achieving these objectives discussed in this paper involves painting in automotive industry. This paper offers an overview of a series of studies: (1) plant site observation, (2) modeling, (3) CFD analysis and (4) full scale experiments performed for design of a paint over-spray wet scrubber. The main objective of this effort was development of a new product. Tanigawa et al. demonstrate how lean manufacturing principles in conjunction with the tools of rigorous engineering analysis, assisted by scale modeling, can successfully contribute to a design process.
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2. D.P. Sekulic. “Scaling of Molten Metal Brazing Phenomena: Prolegomena for Model Formulation.” Understanding underlined physical phenomena that govern materials processing in a state-of-the art manufacturing is essential for developing efficient tools needed for related process analysis. Application of these tools may assist required improvements and/or offer entirely new venues of materials processing for manufacturing. In this paper, Sekulic addresses a host of intricate phenomena featuring molten metal flow. The metal filler/clad micro layer behavior before joint formation in a joining process by brazing is the subject of the study. A perceived model involving brazing of, say, (i) light metals, or (ii) low temperature joining by using lead-free solders, feature highly reactive substrateliquid interactions (solid state diffusion, liquid metal penetration, dissolution of a solid in liquid, erosion, etc.). The flow phenomena governed by surface tension within such complex metal systems (for which many constitutive and property relations are still unknown) is very difficult to scale. Hence, understanding of the importance of main dimensionless parameters controlling the process, evaluation of their scales, and identification of applicable physical laws are necessary. This paper offers an overview of such an inquiry.
Papers Selected from the Fourth Symposium 1. J. Nakagawa. “Scale Modeling of Steel Making Processes.” Steel making represents a complex materials processing task, very difficult to model both analytically and numerically. The process involves spatial and temporal variations difficult or even impossible to determine in real time. Nakagawa demonstrates how successful scale model experiments, featuring the fluids other than molten steel, may be devised under conditions of well matched dimensionless parameters (such as Reynolds and Froude numbers). The paper elaborates in detail a scale modeling procedure, emphasizing the relevance of three important scaling laws involving (1) fluid steering, (2) mixing and (3) chemical reactions. 2. T. Konishi, S. Akagi, and H. Kikugawa. “Flow Visualization of Waste-Heat Boiler using 1/20 Scale Model and Numerical Simulation.” Energy recovery and reduction of the presence of solid particulates within the effluents of a manufacturing process require highly efficient devices. A representative of such a process is analyzed by Konishi et al. It involves a waste-heat boiler for heat recovery and an elimination of the flue dust from the off-gas. Design of such a device assumes good understanding of flow conditions inside the boiler. This understanding may conveniently be obtained by performing process modeling. The paper provides an insight into: (1) an identification of physical laws governing the considered phenomenon, (2) an establishment of dimensionless π numbers, and (3) a discussion of possible relaxations. A brief discussion of the physical model and the related experimental apparatus are presented as well. Results show that the flow phenomena evolution inside the boiler can also be verified with numerical calculations.
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Papers Selected from the Fifth Symposium 1. K. Yoshida, S. Shimizu, S. Yamaguchi, K. Sekimoto, A. Miyahara, and T. Yokoyama. “Scale Modeling for Landing of a Lunar Probe.” A lack of an access to actual environmental and physical conditions to which a space vehicle would be exposed on another non-terrestrial (space) object constitutes a severe limitation in any effort to design components of a probe/vehicle under terrestrial conditions. Different gravitational conditions can only be simulated with a limited duration, but more importantly, a synergy of a myriad of geological and other influential factors is very difficult to replicate. So, the scaling laws can be identified to design the scale model experiments under terrestrial conditions. In this study Yoshida et al. summarize an analysis devoted to identification of relevant dimensionless parameters to properly simulate physical phenomena of a real extra terrestrial environment. An additional important aspect of such an analysis is a consideration of the consequences of a relaxation of some of these laws (otherwise required for performing scale model experiments under terrestrial conditions). This paper offers the scale modeling and some experimental data needed for the verification of such a model.
Backdraft Experiments in a Small Compartment Hiroshi Hayasaka, Yuji Kudo, Hideyoshi Kojima, Tsutomu Hashigami, Jun Ito and Takashi Ueda
Abstract This paper describes results of preliminary backdraft experiments in a 0.85 m high, 0.78 m wide, 1.08 m long compartment, a roughly one third scale residential room. Each surface of the compartment was made with two layers of insulation board to obtain a highly insulated condition. The compartment had a small opening in the middle of the front wall to realize a low-ventilation condition. Interior wall surfaces including the ceiling were partially or fully covered with 12 mm thick wood to simulate a room fire. This wood was the fuel for the fire. A total of 17 experiments were carried out to find backdraft occurrence conditions for the low-ventilation, highly insulated compartment, and to understand backdraft phenomena. In every experiment, two small pine wood cribs (about 2.2 kg total weight) were set in the right rear corner of the compartment. These cribs served as an igniter. Fire in the compartment gradually spread from the cribs to side walls and the ceiling. The total weight of wood used in any one experiment varied from around 2.5 to 15 kg. About one third of the wood remained as char after an experiment. Usually, after a series of backdrafts, an ordinary ventilation controlled fire was established. A water spray was used to extinguish fire and to cease the experiment. Temperature and oxygen concentration at several locations in the compartment were measured by thermocouples and an oxygen meter. Fire progress and the fire balls (spouted flame) produced along with backdrafts were observed visually and recorded by a video. 10 of the 17 experiments resulted in backdrafts. In this paper, one of these 10 experiments, namely Experiment 13, is described in detail to show the backdraft scenario in the compartment. In Experiment 13, backdrafts occurred seven times which is the largest number among the 17 experiments. Temperature and oxygen concentration measured at 0.15 m below the ceiling showed a very unique change shortly before and after a backdraft. From these experimental results, the backdraft scenario observed in these experiments is as follows:
H. Hayasaka Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan e-mail:
[email protected]
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1. Before a backdraft occurs, the compartment fire is much reduced due to the lack of oxygen in the upper layer of the compartment. 2. Pre-backdraft phenomena starts. In this process, pyrolyzate from the fuel (wood) accumulates in the upper layer. At the same time, as the fire dies back due to lack of oxygen, the room cools and fresh air from the outside of the compartment is drawn in and mixed into the upper layer. Thus a flammable, premixed gas which can be ignited in many ways is made. Partially burned wood and char on the side and ceiling walls can act as the igniter. This process usually takes a few minutes in the experiments. 3. Suddenly, a backdraft occurs. The backdraft consumes all vapor phase combustible products or oxygen in the compartment and makes a fire ball which erupts out of the compartment. After the backdraft the above mentioned prebackdraft phenomena starts again. By repeating the above mentioned processes, a series of backdrafts were observed in these preliminary experiments. Keywords Backdraft · pyrolyzate · self-extinguishment · fire ball · low ventilation
Introduction A backdraft is defined as a rapid deflagration following the introduction of oxygen into a compartment filled with accumulated unburned fuel [1]. The dangerous consequences of a backdraft are well recognized in Sapporo, Hokkaido, Japan. In the northern part of Japan, especially in Hokkaido, highly insulated houses are built to keep out of the cold. Fire services, especially in heavy snowfall and cold regions should anticipate and understand the backdraft problem, because fires in air-tight houses give firefighters many chances to meet backdrafts and to be injured or to lose their lives. It is necessary to establish the fire fighting methods which protect against backdrafts. Unfortunately there has been only a small amount of research on backdrafts [1–4]. It is also known that backdrafts occur not only in the above mentioned closed compartments but also in poorly ventilated compartments – those with a small opening. Recently, a number of reports of backdrafts in the Tokyo area have been received. Backdrafts also occur in reinforced concrete compartments, wellinsulated wooden houses and reinforced concrete houses in warmer place like Tokyo and other areas in Japan because their compartments are relative air-tight and highly insulated [5]. One of these, a freezer warehouse fire [6] in Koutou-ward, Tokyo, is a good example. On May 13, 1977, fire started in the warehouse and several backdrafts occurred due to self-extinction of the insulation in the warehouse. The backdraft scenario proposed by one study [1] is the following: “Fires can produce more fuel than the locally available oxygen can consume. This surplus
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fuel is called ‘excess pyrolyzates.’ If the compartment containing the fire is wellventilated, the excess pyrolyzates fuel long flames that extend out openings in the compartment, rapidly spreading the fire. If the compartment is closed, the excess pyrolyzates accumulate, ready to burn when a vent is suddenly opened, for example, as may happen when a window breaks due to the fire-induced thermal stress or a fire fighter enters the compartment. Upon venting, a gravity current carries fresh air into the compartment. This air mixes with the excess pyrolyzates to produce a flammable, premixed gas which can be ignited in many ways. The rapid deflagration moving through the compartment after ignition, consuming the accumulated excess pyrolyzates, is called a ‘backdraft’.” In this paper, preliminary experimental results on backdrafts are reported. They present backdraft scenarios in an one third scale compartment with a small opening in the middle of the front wall.
Experiments Figure 1 shows a schematic of the apparatus giving the internal dimensions of the compartment. The inside dimension are 0.78 m(W) × 0.85 m(H) × 1.08 m(D). The compartment volume is 0.716 m3 . The floor area is 0.84 m2 . The compartment is about a one third scale residential room. An asbestos slate board (t = 5 mm) and a fireproof insulation board (Mitsubishi Chemical Maftec board: t = 25 mm) were chosen for the walls of the compartment. All walls are fundamentally made by two pieces of fireproof insulation board. The outside of all walls was covered with asbestos slate board. On the floor of the compartment, two pieces of fireproof insulation (Mitsubishi Chemical Maftec blanket: t = 25 mm) were also installed to increase the heatproof
Fig. 1 Schematic view of experimental compartment
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and fireproof performance of the floor surface. Gaps between the walls were tightly filled with heatproof sealing material and covered with heatproof tape. In all, seventeen backdraft experiments are conducted. The experiment numbers given in Column 1 of Table 1 are used throughout this paper. The number of backdraft pulses and maximum flame length of exterior fire ball are listed in Columns 2 and 3 of Table 1. The experimental parameters are also summarized in other Columns of Table 1, including the opening dimension, ventilation parameter AH1/2, fuel material, total weight of fuel and wall configuration (fuel shape). The five different wall configurations used are shown in Fig. 2. The total weight of wood (fuel) was gradually increased as show in Fig. 2 and Column 7 of Table 1. For some tests, as shown in Fig. 2(e), the rear and side walls were perforated with about 120, 10 mm diameter holes, staggered and with a 50 mm pitch. Wood combustion was more rapid with these holes present. An opening in the center of the front wall, shown in Fig. 1, permitted fresh air to enter the compartment. The size of the opening was empirically determined by preliminary experiments, 1–6, shown in Table 1. This opening was kept open during a fire test to promote fire in the wood cribs which were the igniter. When a fire in the compartment had reached flashover or had become an ordinary room fire, in some tests, the opening was closed to extinguish the fire. Two pine wood cribs each weighing 1.1 kg were used as igniters. Cribs were set in the right rear corner of the compartment as shown in Fig. 1. The cribs were ignited by an LPG torch burner. Two vertical thermocouple trees were placed as shown in Fig. 1. Thermocouple trees were placed on the vertical center line of the front wall, that with the opening. The distance between thermocouple trees and the front wall were 270 mm and 540 mm respectively. The thermocouple trees were made of steel angles. The thermocouples were 0.8 mm Type K thermocouple wire with a stainless steel overbraid. One thermocouple tree had three thermocouples on it. They were placed at equal intervals of 420 mm. The highest thermocouple was placed 85 mm below the ceiling. Every measured point was given a short name like TF as shown in Fig. 1. The data collected was recorded every one second by a hybrid recorder (NEC Sanei RD3500) and was stored on a 1 mega-byte SRAM memory card. The temperatures reported here are uncorrected values. Gas concentrations in the upper and lower layers in the compartment were measured with two copper probes on the front thermocouple tree. One probe (GT) was placed at 85 mm below the ceiling. Another probe (GB) was placed at 85 mm above the floor. Due to the lack of gas analyzers, only oxygen concentration was measured by a gas analyzer (Testterm Testo33) and recorded by a data recorder (Kyowa Electric RTP- 772A) every 2 seconds. The response time of the oxygen analyzer was about 60 seconds including delay time due to the sampling line and the detector response time. Blast velocity at the opening was measured by the Pitot tube placed at 200 mm out from the opening wall. The difference between static pressure and dynamic pressure was translated to an electric signal by low pressure sensor (Kyowa Electric PDL-40GB) and recorded by a thermal array recorder (Graphtec WR8000). Blast velocity was calculated by pressure difference with the Bernoulli’s equation.
5 1 7
6 3 4 2
14 15 16 17
2.00 1.70 1.00 1.20
2.25 1.60 2.50
1.75
0.20 × 0.24
2
8 9 10 11 12 13
None
3
7
1.50
0.26 × 0.24
1
0.12 0.01
0.40 × 0.46 0.15 × 0.20
0.02
0.03
0.05
Ventilation parameter 5/2 AH1/2 m
Opening dim. W×Hm
0.28 × 0.30
1.00
Max. flame length m
5 6
None
Number of backdrafts
3 4
1 2
Exp. No.
Plywood (t = 5.5mm, Density = 550–600 kg/m3)
(t = 12mm, Density = 410–860 kg/m3 )
Plywood (Form)
Pine crib
Material
Fuel
Table 1 Experimental conditions and results
8.6 13.3 4.4 4.8
15.0 12.7 10.3 12.0 13.9 13.3
9.7
8.4 10.6
8.2
2.5 4.2
Total weight kg
Rear and Side Perforated Walls and Ceiling (see Fig. 2(e))
Rear Wall, Two Short Side Walls and Ceiling (see Fig. 2(c)) Rear Wall, Two Side Walls and Ceiling (see Fig. 2(d))
Hung ceiling with Ribs (see Fig. 2(b))
No Wall Hung ceiling (see Fig. 2(a))
Wall configuration (see Fig. 2)
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Fig. 2 Various wall configurations
Two video cameras were set at the left side and the front of the compartment to record exterior fireballs, smoke color and thickness, and interior fires in the compartment through the opening.
Results and Discussion Backdraft Occurrence Conditions In Experiments 1 through 7, varied mainly by changing the ventilation opening dimension and the weight of fuel, as shown in Table 1, the first backdraft was observed during Experiment 6. Results from Experiments 6–11 approximately fixed the backdraft conditions for this compartment. As shown in Table 1, 10 of the 17 experiments resulted in backdrafts; these are Experiments 6 through 8 and 11 through 17.
Experiment 13 In this paper, the results from Experiment 13 are described in detail. In Experiment 13, the most severe and frequent backdrafts were observed. A few minutes after ignition, smoldering smoke from the pine crib started to come out from the opening. Six minutes after ignition, the rear wall started to burn. Smoke flow gradually became severe. After ten minutes, smoke was still more severe and the color of the smoke became yellowish. The pre-backdraft condition was reached. The color of smoke gradually became dark yellow or brown just before a first backdraft. At 17 minutes 7 seconds after ignition, a first backdraft was observed after the fire had virtually self-extinguished. The color of the smoke became thin but thickened again soon after the backdraft. A second backdraft occurred at 18 minutes 9 seconds after the fire start. Similar changes were repeated until after the fourth backdraft. After the
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fifth backdraft, the color of smoke became thinner and the intensity of the backdrafts became smaller compared with that of the first through fourth backdrafts. Observation inside of the compartment is possible only under thin smoke conditions. Ghosting flames were observed just before every backdraft. Ghosting flames were also observed in poorly-ventilated pool fires within a compartment by Sugawa et al. [7] Takeda et al. [8] described ghosting flames that were observed just before flashover and backdrafts.
Temperature Histories in Experiment 13 Temperature histories in Experiment 13 are shown in Fig. 3. Temperatures near the ceiling (measuring points, TF and TC) are relatively higher than mid-height and floor points (MF, MC, BF and BC). The first temperature peak at about 30 seconds in Fig. 3 corresponds to dieback of the crib fires. Temperatures of the upper layer (TF, TC, MF and MC) rose again just after 1 minute 30 seconds. Temperature at TC reaches nearly 400◦ C at about 16 minutes after fire start. This high temperature of 400◦ C suddenly started to drop to 300◦ C at about 16–17 minutes after ignition. This temperature drop is due to self-extinguishment of the fire. The self-extinguishment was due to oxygen depletion. Surplus fuel called “excess pyrolyzates” accumulates because the fire produces more fuel than the locally available oxygen can consume. In other words, oxygen is completely consumed in the upper layer and the fire self-extinguishes due to lack of oxygen. Accompanying this rapid temperature drop is a drop in pressure within the room which induces an air-flow in through the vent. Mixing of pyrolyzates from fuel and oxygen from this fresh air starts. This mixing leads to a backdraft. Thus, the rapid temperature drop is one of the most important and apparent signs of an impending backdraft.
Fig. 3 Temperature histories in the compartment
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After the rapid temperature drop, a backdraft occurs. Temperature at TC rises very rapidly from 310 to 480◦ C. This rapid temperature rise signals that a backdraft occurred. Just after temperature at TC reaches its highest point of 480◦ C, temperatures at all points start to drop again. This means that oxygen in the compartment has been mostly consumed by the backdraft and fire self-extinguishment has happened again. The above mentioned temperature drop and rise process is observed repeatedly after the first backdraft. After the third backdraft, cycles of the temperature drop and rise proceed over a shorter time interval and temperatures at all points tend to fluctuate about a higher average temperature.
Oxygen Histories in Experiment 13 Oxygen concentration histories in Experiment 13 are shown in Fig. 4. Oxygen concentration near the ceiling (measuring point, GT) quickly drops to 14% due to cribs fires (1 minute after ignition). Next the plywood fire further reduces the oxygen concentration to about 7% (7 minutes after ignition). Between about 7–10 minutes after ignition, oxygen concentration stays at about 7% but then starts to drop again. At 16 minutes after ignition, the oxygen concentration had reached about 1.5%. The fire self-extinguished mainly due to lack of oxygen. The oxygen concentration rose rapidly because of the fire self-extinguishment, gas temperature drop and air inflow. When the oxygen concentration exceeded 10%, the first backdraft came. The first backdraft consumed oxygen in the compartment and the oxygen concentration dropped rapidly to about 3%. Then, fire self-extinguishment again occurred, mainly due to lack of oxygen. The above described drop and rise process of oxygen concentration was observed repeatedly after the first backdraft. After the fourth backdraft, intervals of
Fig. 4 Oxygen histories in the compartment
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the oxygen concentration drop and rise tended to become shorter and the oxygen concentration at GT tended to fluctuate about a lower average concentration range. Oxygen concentration at GB was measured in the similar manner. Its location was in the so-called lower layer. Oxygen concentration at GB dropped only to about 19% at a minute after crib ignition. A very gentle change compared to the GT oxygen concentration change because air flow is always supplied to the lower layer first.
Other Backdraft Phenomena in Experiments 6 Through 8 and 11 Through 17 When a backdraft occurred, the backdraft flame propagated through the compartment consuming oxygen and the accumulated excess pyrolyzate in the compartment. The accompanying thermal pulse drove additional excess pyrolyzate out from the opening. The pyrolyzate and smoke could mix with air outside the opening to produce combustible products in the smoke. In this experiment, fireball growth outside the compartment was observed. Fireball growth was recorded by the video camera. The typical fireball growth process is showed in Fig. 5 – a sequence photographs taken over a total 1.5 seconds. As soon as the backdraft occurred, a mass of smoke came out from the opening in the compartment (see in Fig. 5(2)). A small flame like tongue appeared in the opening following the mass of smoke (Fig. 5(3)). This small flame rapidly spread in the mass of smoke near the compartment and formed a big fireball in the form of a rugby ball (Fig. 5(4)). This fireball consumed combustible products in the smoke near the compartment vent. The fireball became smaller, supported only by combustible products from the compartment (Fig. 5(5) and (6)). This flame became small rapidly because fire self-extinguishment inside the room occurred due to lack of both oxygen and combustible products (Fig. 5(7) and (8)).
Backdraft Scenario From the above experimental results, a backdraft scenario in a small scale room under highly insulated and low-ventilation conditions is thought to be as follows: 1. Self-extinguishment of the compartment fire: Before the compartment fire was self-extinguished, the temperature near the ceiling gradually rose with a rate of 0.125◦ C/s (Fig. 3) and the oxygen concentration near the ceiling gradually dropped toward to 1.5% (Fig. 4). These trends continued until 30 seconds before the first backdraft. The compartment fire is thought to have self-extinguished mainly due to lack of oxygen in the upper layer. 2. Pre-phenomena of backdraft (Production and accumulation of combustible gases and mixing with oxygen): The temperature dropped very rapidly with a rate of 1.6◦ C/s (Fig. 3). On the other hand, the oxygen concentration rose rapidly with a rate of 0.2%/s (Fig. 4). This lasted about 30 seconds. When the rapid temperature
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Fig. 5 A typical fireball growth process in the backdraft (Experiment 13)
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drop gradually ceased and oxygen concentration reached nearly 10%, the first backdraft came. 3. Onset of backdraft (Explosive combustion and energy release): Just after the first backdraft, the temperature rose from 310 to 480◦ C in several seconds (Fig. 3) and the oxygen concentration dropped from 10 to 3% (Fig. 4). The temperature dropped again just after it had reached 480◦ C which was nearly the maximum temperature, 500◦ C, in the compartment. The oxygen concentration went up again just after the oxygen concentration reached 3% which was nearly the minimum concentration, 1.5%. These post-backdraft phenomena are almost the same as the above mentioned pre phenomena, item 2 namely just after self-extinguishment of fire. By repeating the above mentioned process 2 and 3, a number of backdrafts occurred in Experiment 13.
Conclusions Preliminary backdraft experiments were carried out by using actual wood and backdraft phenomena caused by actual pyrolyzates from wood were observed. Results obtained from preliminary backdraft experiments in a one third scale compartment under highly insulated and low-ventilation conditions suggest the following backdraft scenario conditions: Before the first backdraft occurs, the compartment fire is virtually self-extinguished due to the lack of oxygen in the upper layer. Then, pre-backdraft phenomena start. In this process, pyrolyzates from the fuel (wood) accumulate in the upper layer. At the same time, fresh air from the outside of the compartment flows into the compartment and mixes with the upper layer. Thus a flammable, premixed gas which can be ignited in many ways is made. Partial burned wood of the side walls and ceiling can act as an igniter. This process usually takes a few minutes in the experiments. Suddenly, backdraft occurs. The backdraft consumes all combustible products and/or oxygen in the compartment and makes a fire ball which erupts to the outside of the compartment. The above mentioned pre-backdraft phenomena starts again after the backdraft. By repeating the above mentioned processes, a series of backdrafts were observed in these preliminary experiments. Future work will focus on the onset of backdrafts in a compartment. A newly developed refractory glass will be used as a side wall. We will be able to observe the inside of the compartment provided the side wall glass can keep its transparency throughout experiments. We also have a plan to make more precise temperature distribution maps in a compartment. Gas analysis of upper and lower layer in a compartment will be carried out by measuring THC, O2 , CO2 and CO. From these experimental results, a more sophisticated and comprehensive compartment fire model incorporating backdraft phenomena may be developed.
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Acknowledgments The authors wish to thank to Dr. John A. Rockett for his good suggestions and editorial assistance.
References 1. Fleischmenn, C. M., Pagni, P. J. and Williamson, R. B., “Exploratory Backdraft Experiments”, Fire Technology, 29-4, pp. 298–316, 1993. 2. Fleischmenn, C. M., “Backdraft Phenomena”, Report NIST-GCR-94-646, 1994. 3. Fleischmenn, C. M., Pagni, P. J. and Williamson, R. B., “Quantitative Backdraft Experiments”, Fire Safety Science-Pro. of the Fourth Int. Sympo., pp. 337–348, 1994. 4. Bukowski, R. W., “Modeling Backdraft”, NFPA Journal, 89-6, pp. 85–89, 1995. 5. Himeji Fire Bureau, Monthly Firefighting (Japanese), 15: 24, 1993. 6. Murakami, Y., “Outline of Shinko Kairiku Transport Warehouse Deflagration Fire” (Japanese), Fire, 113, 1978. 7. Sugawa, O., Kawagoe, K., Oka, Y. and Ogahara, I., “Burning Behavior in a Poorly Ventilated Compartment Fire – Ghosting Fire”, Fire Science and Technology, 9, pp. 5–14, 1989. 8. Takeda, M., Mashita, K. and Okanda, I., “Study on the flashover (Series 5)” (Japanese), Report of Fire Science Laboratory, Tokyo Fire Dept., pp. 22–29, 1992.
Development of a New Paint Over-Spray Eliminator Y. Tanigawa, R. Alloo, N. Tanaka, M. Yamazaki, T. Ohmori, H. Yano, A. J. Salazar and K. Saito
Abstract The design of a new over-spray paint eliminator is presented as an example of a successful research and development (R&D) project performed by a team of engineers including representatives from a user company of the product, a manufacturer of the product and an academic institution. The combined effort of plant-site observation, a limited full-scale data, scale modeling, and computational fluid dynamic (CFD) modeling were first applied to solve technical problems related to an old wet scrubber and to enhance the physical understanding of the phenomena. With the insight gained during this process, a new wet scrubber was invented and reduced to production.
Nomenclature E F g Re v
Total electrical power Force Acceleration of gravity Characteristic length Reynolds number Velocity
Greeks ⌬p π ρ
Pressure drop Scaling pi number Density
Subscript a f
Air Fans
K. Saito Department of Mechanical Engineering, University of Kentucky, Lexington, KY 40506, USA e-mail:
[email protected]
K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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gw i ia iw p w
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Gravity action on water Relative to scale model Inertia of air Inertia of water Pressure Water
Superscript
Relative to scale model
Keywords Overspray capturing · spray painting · scale modeling
Introduction The development of a new product is always an important event for a company to remain competitive in the global market [1, 2]. When a new product hits the market, customers (but not engineers who designed the product) will judge it based on its quality, price, delivery time, safety, environmental friendliness, esthetics, etc. New products as well as improved versions of old ones, can be developed effectively by applying the principles offered by the Toyota Production System (TPS) or Lean Manufacturing (LM) [1]. TPS or LM conceives the manufacturing process as a continuous-flow system consisting of people, materials, machines and information as the input parameters and products as the output. Although it was originally realized in an industrial manufacturing environment, the basic principles of LM can readily be applied to R&D. Figure 1 shows a schematic of the LM system applied to our research project. Notice that materials have been omitted because, contrarily to manufacturing processes, it is not relevant to R&D projects. When the LM system is applied to a new product development process, it will offer an effective R&D strategy that helps streamlining the process, from the creation of ideas to the commercialization of a new product. It also provides guidelines to
Fig. 1 A schematic of LM system applied to R&D
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form an interdisciplinary team of professionals who can work cohesively to achieve the common goal by using their diversified talents [1]. Kaizen (a Japanese term for continuous improvement) is a general method for process improvement. When it is applied to a manufacturing process, it helps to produce high quality products with the minimum cost and time by finding all different types of waste and eliminating them one by one. When it is applied to a R&D project, “Kaizen” provides a step-by-step self re-definable strategy for gathering and managing, identifying problems and finding root causes. Kaizen helps not only to effectively solve the initial problem but also to eventually lead to innovative solutions and inventions. This paper describes the process of developing a new over-spray paint eliminator as an example of effective R&D based on LM principles. This project combined the efforts and expertise of a multidisciplinary team of engineers coming from Toyota headquarters plant in Japan and two other Toyota plants in Kentucky, USA (Toyota), Trinity Industrial Corp. in Japan (TIC) and the University of Kentucky (UK). Our paper is organized as follows. First, automotive paint booth systems and the background of our problem are presented. Next, the different modeling approaches used simultaneously in our investigation, including the results of our full-scale and small-scale experiments, our CFD simulation, and plant-site observations, are discussed. Finally, a new type of wet scrubber – namely Vortecone – is explained and subsequently, our concluding remarks are presented.
Automobile Paint Booth System Customers demand vehicles with a better surface appearance [2, 3] that can withstand a variety of weather conditions while maintaining an everlasting original quality of finish. Few people may realize, however, that the transfer efficiency of the paint, the percentage of sprayed paint that actually coats vehicle, is only 50–60% and that the remaining is unused over-sprayed paint that must be captured before it reaches the outside environment. Automobiles are painted in spray booths. An automotive spray booth is an enclosure that directs over-sprayed paint particles and solvent emissions toward an entrainment section by means of downdraft airflow moving from the ceiling vertically downward to a capturing exhaust system below the grating floor. Figure 2 presents a schematic of a typical automotive spray booth consisting of an upper (spraying) section, the portion above the floor grating, and an under (capturing) section, the portion below the floor grating. The upper section of a typical paint booth could be a 150-m long corridor through which the automobiles are longitudinally conveyed and within which workers and/or robots spray paint the moving auto bodies. Manual and automated robotic zones may be alternated along the booth according to manufacturing requirements. To increase the transfer efficiency, robotic spray guns are purposely charged while the body of the vehicle remains grounded. An average downward airflow velocity in
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Fig. 2 Schematic of a typical automotive spray booth
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excess to 0.5 m/s is required by US Occupational Safety and Health Administration (OSHA) standards in the upper section of the manual spray zone of the booth [4], which translates into a minimum blowing airflow rate of 450 m3 /s of fresh air for the 150-m long booth. This requirement is less stringent in the robotic spraying zone, where only 0.3 m/s airflow speed is required, which translates into a minimum blowing airflow rate of 270 m3 /s. These high airflow rates have a direct impact in the operational cost of the booth, especially when pressure drop through the booth is high. It is not surprising that, in a typical automobile assembly plant, spray painting operations may account for up to 40% of the total energy consumption of the plant. Contrary to the upper section configuration, which is similar in all booths, the under section configuration changes according to the manufacturer. Each design is targeted to trap as much overspray paint as possible with the minimum pressure drop. Due to the large amount of paint used by automakers, water scrubbing or water washing is the preferred method to capture the overspray [5]. A detackifying agent added to the water is used to remove the stickiness of the trapped paint. A trench is provided to collect the paint sludge and water mix coming out from the under section of the booth. During the wet scrubbing process, the supply water flows into and through the outlet structures to mix with the paint-laden air passing downwardly and it assists in the transfer of the overspray-paint from the air to the water, so that the air leaving the lower ends of the outlet structures is substantially free of entrained overspray. This cleaner air exiting the scrubbing section may still contain minute water drops. To capture this water, the exhaust air is usually passed through a set of mist reducer baffles.
Background of the Problem At one of Toyota’s automobile manufacturing plants, a paint particle eliminator started to decrease its capturing efficiency. To meet the environmental regulation, the company installed a down-pipe filtering system to capture the remaining paint particles escaping from the eliminator. This filtering system, however, created substantial financial burden to the company and concerns about the future performance of similar system that has been installed in their other plants. After several unsuccessful trials to fix the problem, the company finally decided to ask UK to study the capturing system thoroughly and to find the root cause of the problem so that a remedy can be implemented to prevent the recurrence of similar type of problems in the future. Feasibility studies conducted by the UK researchers revealed that the mechanisms for particle capturing in the existing commercial booth systems to be not well understood, even by the manufacturers of the equipment. Although impingement of the paint particles on the flooded water pond as well as the interaction of the paint-laden air with the shear-generated water mist – possibly created by a venturi effect – had been suggested as key mechanisms, there are neither detailed experimental data nor theory that successfully support the claim. Due to the inherent complexity of the capturing process, the design of the current spray booth systems relies largely on experience and trial-and-error approaches.
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Four different techniques were applied to solve the problem: full-scale experiments, scale modeling, CFD simulations and plant-site observations. Each played unique and complementary role to reach the solution. One of the important outcomes of this project is that the vortex interaction of the particle-laden airflow with the water mist was identified as the key small-particle capturing mechanism. Using all the above-mentioned capturing mechanisms to lead the basic design concept, a novel paint particle wet scrubber, namely Vortecone, was conceived.
Experiments, Modeling and Observations Before building and testing a full-scale Vortecone proto-type, it is more economical and time saving to design a reduced scale model and test its performance. This scale model can help not only identify possible operational problems but also give insight about how the capturing phenomenon actually takes place in the equipment. A 1/4 scale model of Vortecone was built at Trinity and tested in their R&D laboratory; it showed a promising performance. Subsequently, a full-scale Vortecone was built and tested: it outperformed any of similar products in the market with its low energy consumption rate and high capturing efficiency, especially for metallic-base paints [6]. In this section we discuss details about the implementation of the different research techniques employed in this project, i.e., full-scale experiments, scale modeling, CFD simulations, and plant-site observations.
Full-Scale Experiments At one of Toyota’s automobile paint booths, engineers built a course wire mesh that stands vertically and covers the entire cross section of the upper section of paint booth. A tuft was placed on each intersection of the mesh to obtain the flow direction under a fixed downward flow near and around an assumed to be painted automobile body. A portable anemometer was used to measure the velocity at the intersection. Based on these measurements, a steady state 2-D velocity-vector profile across the paint booth upper section was obtained.
Scale Modeling Two different types of scale models were designed. The first type is to simulate overall 2-D downward flow profile at the upper section of the Toyota’s paint booth and the second type is the Vortecone scale model with the aim to simulate a full scale Vortecone performance. Scale models should be developed based on strict scaling laws for the purpose of scientific understanding [7, 8]. The scaling laws can be described as: πi = πi ,
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where π stands for pi-number, prime stands for the scale model, and i = 1 . . . n. The pi-number is a dimensionless number and holds physical meaning. For example, Reynolds number, Re = [inertia forces]/[viscous forces]. To derive the scaling laws for the current problem, governing forces need to be identified. As Williams explained in his paper [7], however, strict scaling laws often require unrealistic and unachievable requirements for scale modeling due to many parameters involved in the system. The concept of partial scaling can help to reduce the number of parameters by identifying only major ones, keeping them and ignoring other minor ones. In partial scaling, the key point is how to make assumptions that can correctly represent physics that governs the full scale and reduce the scaling requirements to achievable ones. In our example, it is to keep only the major forces and to ignore minor ones. Once scaling laws are derived, they provide design criteria and experimental conditions for the scale model. Scale model experiments have dual aims: confirmation of the scaling laws (confirmation tests) and performance optimization of newly designed and already-existing products (production tests). To conduct the confirmation tests, two different size scale models can be designed based on the scaling laws. Then, scale model experiments can be conducted under the experimental conditions provided by the scaling laws. Finally, the experimental results can be compared to the scaling law predictions. If they agree, the scaling laws are validated by the confirmation tests. If they don’t, then the original assumptions need to be changed and new scaling laws will be derived for confirmation tests until they agree. The confirmation test is important before conducting a series of production tests. According to Emori [8], production tests without the confirmation tests often make wrong forecast and some of them created historical disasters. It is interesting to know, however, that some scale models can be used without the confirmation tests for the purpose of qualitative observation only (qualitative scale modeling). Because the confirmation tests often require painstaking effort, the qualitative scale modeling may be the solution for the new product R&D, where the timing is crucial. When the qualitative scale modeling is conducted, the scaling laws should be developed and used to evaluate the scale modeling results, although they are not directly applicable to the scale models. The scaling laws will help us to understand pros and cons of the qualitative scale modeling. To clarify the role of qualitative scale modeling, the following provides two examples of the qualitative scale modeling. The Upper Section Scale Model For the first type scale model, the major governing forces are assumed to be the inertia and the pressure forces, and the viscous and the gravity forces to be negligible, except in the vicinity of walls and automobile body surface where a boundary layer is formed and both the inertia and the viscous forces become important. This assumption is reasonable by knowing the fact that circulation of air inside the upper
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section paint booth is turbulent (the estimated Re number is in the order of 105 –106 ) and there is no water and paint particles. Thus, π1 = Fia /Fp = ρa va2 /⌬ p
(1)
where Fia = the inertia force of air and Fp = pressure force, ρa = density of air, va = characteristic air velocity, ⌬ p = pressure loss. A typical paint booth has a 150-m long horizontally stretched corridor section that may not be feasible to simulate in our scale model design due to the limitation of space. Considering our objective is to simulate downward airflow near and around a single automobile body, we thought a 10 m long corridor section to be sufficiently long enough for our 1/12 scale model to simulate the full scale airflow. Accurate measurement of pressure distributions inside the booth requires a nonintrusive measurement technique but we failed to find one, so the measurement of pressure distribution was not conducted, instead we used this scale model for the purpose of qualitative observation of airflow. Employing a flow visualization device described by Emori et al. [8], dry ice and incense smoke were used to generate smoke streaks from the ceiling. Smoke streaks were illuminated by a halogen lamp and recorded by a video camera. The average downward air flow velocity for the full scale is 0.5 m/s, so the corresponding air flow velocity for a 1/12 scale model should be, va = 0.5 ⌬ p −1/2 m/s. In this experiment, however, pressure was not adjusted; instead the average velocity of the airflow, 0.2–0.3 m/s was changed. Figure 3 shows a typical airflow pattern observed at the 1/12 scale model.
Fig. 3 Typical airflow pattern observed at the upper section of the 1/12 scale model of a spray booth
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Vortecone Scale Model The air is circulated through inside the booth by operating fans against pressure drop that is mainly caused at the wet-scrubber section by the interaction of water, paint particles and air. The forces associated in the process include the inertia force of air and water, the gravity force acting on water and paint particles, the viscous force of a paint-particle contained volatile organic compound, the viscous force of air in the vicinity of the particle surface, the viscous force of water, and the pressure force acting on the system. These eight forces yield seven pi-numbers [8] and it is not possible to satisfy simultaneously all these seven pi-numbers in our scale model. So, a simplification was made by assuming that the air is particle free and the inertia force of air and water and the gravity force acting on the water are only major forces and the rests are minor. Electric fans installed at the top of the paint booth provide the total energy input to operate the system. The total power that is required to operate these fans, E f needs to follow the scaling laws. This simplification yields three pi-numbers: π2 = Fia /Fgw = ρa va 2 /ρw w g
(2)
π3 = Fiw /Fgw = vw / w g
(3)
2
π4 = E f /Fia va = E f /ρa a va 2
3
(4)
where Fia = the inertia force of air, Fiw = the inertia force of water, Fgw = gravity force acting on the water, ρa = the density of air, ρw = the density of water, va = characteristic velocity of air, vw = characteristic velocity of water, and a = characteristic length of airflow and w = characteristic length of water flow. Using a common characteristic length, , for both airflow and water flow, and the same physical properties of air and water for both the full scale and the scale model, a = w = , ρa = ρa , ρw = ρw . Since, both tests will be conducted under the normal gravity condition, g = const. Thus, the above three pi-numbers yield, va ∝ vw ∝ 1/2 and E f ∝ 7/2
(5)
The obtained scaling relationships predict the following. If we build a 1/4 scale model that is geometrically similar to the full scale, and if we conduct a scale model test according to the above experimental conditions, the pressure loss that is measured inside the booth at points corresponding to the full scale booth should satisfy π1 relationship. After this confirmation test is done, then the scale model can be applied to a series of production tests in which optimization for the best design can be conducted using the scale model [8]. Due to the restricted time schedule, the confirmation test of the scale model was not conducted and a transparent plastic-made 1/4 scale model was only used for qualitative observation of water flow pattern. Even with such a limited use of the scale model, we obtained much of valuable information through careful observation
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Fig. 4 A typical visualization test at the 1/4 scale model of the new scrubber
that eventually helped to improve the short passing of water flow and instability of the flow near and at a high velocity water impingement point. Figure 4 presents a typical scale model visualization test for the new scrubber.
CFD Modeling To investigate whether computational fluid dynamics (CFD) model can be a useful tool to investigate the paint particle capturing mechanism inside the spray booths, we employed first 2-D, then 3-D CFD models. With the 2D model, we studied the effect of the particle diameter on the capturing performance and found that the larger the diameter is, the easier is to capture the particles [9]. This finding was later verified with some experimental results and plant-site observations. A 3-D CFD model was then created to understand the main factors that influence the capturing efficiency on two typical commercial paint booths [5]. The overall pressure-drop and paint particle trajectories were well simulated against the plant-site observations despite several assumptions and simplifications employed due to the complexity of the multiphase flow inside the booth. Assumptions employed include that the flow is laminar and incompressible (although the actual flow is turbulent), the volume fraction of paint particles in the spray cloud is very small, and no inter-particle and electrostatic interactions take place. The rationale of each of these assumptions was discussed [5] and is not available here. The two phases considered were the air (continuous phase) and the paint particles (dispersed phase). Two-phase
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Eulerian–Lagrangian modeling approach was applied to describe a more detailed inter-phase response. To identify the key capturing mechanism of paint particles, two different type paint booths, a tube type PB#1 and venturi type PB#2 were selected for the 3-D CFD simulation. The intention of this study is that detailed CFD flow structure analysis associated with particle capturing on PB#1 and PB#2 can help us understand how particles can be captured by the two different mechanisms and which mechanism is more efficient than the other in capturing. Figures 5 and 6 respectively show a schematic of spray booth #1 and #2. Each of these 3-D CFD models showed the detailed fluid dynamic structure inside the paint booth. As a result, the interaction of airflow contained paint particles with the water mist by a vortex mixing was found to be the key mechanism of the particle capturing. Figure 7 compares 2-D velocity profiles between the full-scale experiment and the corresponding 2-D CFD simulation. In addition to the velocity data, pressure distribution was calculated by the same CFD code, but comparison was not available because no pressure distribution was measured in the full-scale. The highest pressure is in the upper left of the diagram while the lowest pressure is in the area under the car. The numerical velocity vector results have been plotted every eight grid points horizontally and every four grid points vertically. All the velocity vectors measured at the inlet of the full-scale testing section show lateral velocity components in the same direction which are the remaining effect of the lateral inlet in the air supply plenum. To quantify the accuracy of the CFD results, a systematic error analysis based on the experimental vector data and the computed velocity vectors at the given measurement stations has been performed. An estimation of the rootmean-square error in the entire flow field, computed using the formula described in [5], showed the agreement to be approximately 82%. Considering uncertainties associated with the experiment and assumptions employed for the calculations, the agreement is remarkably good. Comparison with Plant-site Observations To evaluate the accuracy of our 3-D CFD model in predicting performance of the wet scrubber, plant-site observations and measurements were conducted [5]. Detailed quantitative comparisons may not be possible because of the qualitative nature of the plant-site data. The plant-site observation and measurements, however, should not be underestimated. They contain valuable information. If interpreted correctly, they can validate the predictions made either by numerical modeling or scale modeling. Here we carefully compared the plant-site observation against the prediction made by the 3-D CFD simulations on pressure drop through the scrubber and the maximum jet velocity in the capturing system. The agreement on the pressure drop was found to be greater than 75% for PB#1 and 79% for PB#2 and that on the maximum jet velocity was better than 90% for both PB#1 and PB#2. The results are presented in Tables 1 and 2.
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Fig. 5 3-D BFC computational grid employed in PB#1 simulation
Performance Comparison Between PB#1 and PB#2 Our 3-D CFD model calculations showed that the capturing efficiency decreases with the decrease of the paint particle diameter for both PB#1 and PB#2. For particle diameter 50 m or larger, both configurations are equally efficient. For particle diameter between 20 m and 50 m, PB#1 performs better than PB#1. For particle
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Fig. 6 3-D BFC computational grid employed in PB#2 simulation
diameter less than 20 m, PB#1 lost slightly its capturing efficiency, while PB#2 lost it abruptly. A close look at the flow results revealed that for PB#1 there is a strong circulation flow which creates long residence time on the air-water-paint particle mixing process, while for PB#2 there is no circulation and a very short residence time on the mixing. The estimated residence time for PB#1 is 0.8 s and that for PB#2 is 0.1 s, suggesting that longer residence times can help capturing smaller particles.
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Fig. 7 Top: Experimental full-scale airflow velocity data. Bottom: A corresponding 2-D CFD calculation assuming laminar flow
Table 1 Comparison of PB#1 simulation with plant-site measurements
⌬ pscrubber (mm H2 O) vupper-section (m/s) vjet-maximum (m/s)
Plant-site measurement
3-D simulation
Error (%)
104.1–132.1 0.36–0.51 34.0
99.4 0.508 31.92–34.41
(+4.5, +24.7) b.c. (−6.1, +1.2)
Table 2 Comparison of PB#2 simulation with plant-site measurements
⌬ pscrubber (mm H2 O) vupper-section (m/s) vjet-maximum (m/s)
Plant-site measurement
3-D simulation
Error (%)
88.5–130.0 0.39–0.52 –
103.2 0.508 32.23
(−20.6, +16.6) b.c. –
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Examining the vertical velocity distribution for the capturing system of PB#2, we found three high-speed downward velocity zones – one at the nozzle exit and two at the deflectors – and two upward velocity zones – next to the nozzle jet at the water pond. The maximum downward velocity for PB#2 reached approximately 32 m/s, which is the same order of that achieved at PB#1. This suggests that high velocity and sharp turns are not sufficient to guarantee high capturing efficiency of small diameter particles, e.g., particles smaller than 20 m.
Vortecone We started this project with the aim of identifying the key mechanisms for capturing over-spray paint particles, hoping that this finding will help us fix the trouble-making wet scrubber. After being validated against scale modeling, fullscale experiments, and plant-site observations, CFD modeling were used extensively during this study. Several different types of wet scrubber configurations, specifically designed for the automobile spray applications, were commercially available. As explained in the above section, of all these scrubber configurations, we selected two typical ones for a thorough CFD analysis. The first scrubber configuration (PB#1) had a good capturing efficiency with a relatively high-pressure loss (high-energy consumption). The second scrubber configuration (PB#2), which corresponded to the trouble-making scrubber, presented a low capturing efficiency with an acceptable degree of energy consumption. By means of our CFD analysis, we found that there might be a critical residence time required for the water mist to capture the paint particles. We found the two major sources of pressure loss during the scrubbing process to be the energy dissipation by small and large turbulent eddies and the impingement of a high speed air flow into the water pond. The energy dissipation generated by the turbulent eddies can be improved by streamlining the flow passage, while the energy dissipation generated during the impingement process was believed to be a necessary penalty to capture the paint particles. This second factor is responsible for an old widely accepted belief within the professionals in the overspray-capturing field – the higher the pressure loss, the higher the capturing efficiency. Our CFD analysis, however, showed that this belief was only partially true and that smooth circulation of the paint-laden air and the water mist could actually enhance capturing efficiency without creating high pressure loss. Based on these findings, the newly designed scrubber was invented. Vortecone has several unique features that are intended to enhance paint capturing efficiency and simultaneously reduce pressure drop. Figure 8 presents a schematic of Vorte1 provides smooth acceleration of the airflow a and cone. The cone-shaped entry 2 create water film b with a minimum pressure loss. Two vortex-chamber drums circulation of the paint-laden air c and the water d through which the smaller paint particles are trapped in the center providing an enhanced residence-time which
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Fig. 8 Schematic of the newly developed wet scrubber, Vortecone
increases the chances for these paint particles in the air stream to be captured by the water droplets. The larger paint particles and water droplets are pushed together to the water film d covering the chamber wall enhancing the capturing process. A 1 was attached to the exit of each vortex chamber and helped to recover volute pressure loss. Vortecone is particularly effective in capturing the less-than 20 m diameter particles that were not possible by any of the conventional wet scrubbers. Further information on Vortecone can be found in [6].
Conclusions In this paper we described the process of developing a new wet scrubber that can capture oversprayed paint with high capturing efficiency and low energy consumption. Full-scale experiments, scale modeling, CFD modeling and plant-site observation played a complementary role in identifying the key paint-particle capturing mechanism on which a new wet scrubber – named Vortecone – was designed. Even at its preliminary test, Vortecone outperformed any of the similar products in the market. The underlying essence of this paper is the practical demonstration of how LM principles can be employed to lead an effective R&D project in which engineers from a paint booth manufacturer and a major automaker – as the users of the painting
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technology product, and engineering scientists from a research university cohesively worked as an interdisciplinary team to develop an innovative product. Acknowledgments This study was co-sponsored by Toyota Motor Manufacturing North America, Erlanger, KY, USA, Trinity Industrial Corporation, Toyota-shi, Aichi, Japan, and by the Center for Robotics and Manufacturing Systems and the Center for Computational Sciences, both at the University of Kentucky, Lexington, KY, USA.
References 1. Cho, F., 1995, “Toyota production system,” Principles of Continuous Learning Systems, K. Saito Ed., McGraw-Hill. 2. Tanigawa, Y., 2000, “Toyota’s view on the future auto-motive paint booth systems,” presented at the 2000 Painting Technology Workshop, Lexington, KY, USA. 3. Parker, J. M. and Ackman, J., 2000, “The role of the small-scale prototype in designing a robust vision system to assess surface appearance,” ISSM III, Nagoya, Japan. 4. Occupational Safety & Health Administration (OSHA), U.S. Department of Labor, 1993, “Criteria for design and construction of spray booths – 1926.66,” OSHA Regulations (Standards – 29 CFR), 58 FR 35149, (b)(5)(i). 5. Salazar, A. J., 1998, “Computational fluid dynamic study of automobile assembly plant painting systems,” Ph.D. dissertation, University of Kentucky, Lexington, KY, USA. 6. Salazar, A. J., Saito, K., Alloo, R. and Tanaka, N., 2000, “Wet scrubber and paint booth including the wet scrubber,” US Patent No. 6,024,796. 7. Williams, F. A., 2000, “Significance of scale modeling in engineering science,” ISSM III, Nagoya, Japan. 8. Emori, R. I., Saito, K. and Sekimoto, K., 2000, Scale Models in Engineering, Gihodo, Tokyo, in Japanese. 9. Salazar, A. J., McDonough, J. M. and Saito, K., 1997, “Computational fluid dynamic simulation of automotive spray painting process,” Computer Modeling and Simulation in Engineering, Vol. 2(2), pp. 131–144.
Flow Visualization of Waste-Heat Boiler Using 1/20 Scale Model and Numerical Simulation Tadashi Konishi, Susumu Akagi and Hironori Kikugawa
Abstract A flash smelting furnace for copper smelting is equipped with a wasteheat boiler for heat recovery and the elimination of flue dust from off-gas. Water tubes in the boiler are exposed directly to the corrosive environment by high temperature SO2 gas and also by flue dust. Therefore, it is very important to know the flow behavior of the gas and the dust. The purposes of this study are to grasp the flow pattern both in the entire boiler and in the local area, and also to optimize the injection method of the slag cleaning furnace off-gas injected for the oxidation of sticky sulfide dusts. A 1/20-scale model, 1.5 m long × 0.3 m wide × 0.9 m high, made of transparent acrylic sheets and pipes, is adopted for this study. Air at room temperature is used as the working fluid and talc particles with an average diameter of 30 microns are used as a substitute for flue dust. The flow visualization in the local area is accomplished by laser-sheet techniques with a high-speed camera, whereas the entire flow pattern is observed using a smoke trace method. As a result, a vortex of about 10 cm diameter is observed to form in the vicinity of the castable refractories layer installed on the water tubes above the gas-inlet at the front wall of the boiler. Also, an optimum injection nozzle pattern of the slag cleaning furnace off-gas is proposed to provide the most effective mixing with flash smelting furnace off-gas and oxidation of flue dust. Keywords Waste-heat boiler · acrylic scale model · flow visualization · nozzle pattern · vortex
Nomenclature c d g
Specific heat (J/kgK) Diameter of particle (m) Gravitational acceleration (m2 /s)
T. Konishi Department of Mechanical Engineering, Oita National College of Technology, Oita 870-0152, Japan e-mail:
[email protected] K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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N P q Q R T u α ε γ ρ θ ζ σ μ
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Representative length (m) Number of particles occupied in the representative length (−) Pressure (Pa) Heat generation of the dust per unit mass (J/kg) Heat transfer (J) Curvature of radius (m) Time (s) Velocity (m/s) Coefficient of oxygen partial pressure Emissivity (−) Temperature coefficient Density (kg/m3 ) Temperature (K) Collision efficiency Bolzman constant (W/m2 K4 ) Viscosity coefficient (Pa · s)
Superscript g p
Gas Particle
Introduction Scale modeling is found to be useful when, for a variety of reasons, experimentation at actual size does not prove feasible. Using a scale model which expands or reduces length, time, force, velocity, temperature, etc. is a way to reproduce the otherwise unavailable phenomena by a more convenient means [1]. In the present case, a waste heat boiler is very difficult to work with experimentally because it is very large, internal flow can’t be observed and the boiler contains dangerous high temperature gas [2, 3]. Because of this, a properly-designed scale model for experimentation is called for. Results can then be examined to learn how to remodel a boiler to operate at high efficiency. Ideally, the scale model’s resemblance to the phenomenon or object to be studied would be complete – that is, all physical quantities, such as time, velocity, force, density, viscosity and temperature of the model should correspond exactly to the physical quantities of the real object. However, no scale model can be expected to reproduce the complexity of most actual phenomena. The purpose of the scale model in fact is to simplify a complex phenomenon, allowing researchers to see essential relationships more clearly. Since absolute similarity between scale model and real phenomenon is very rarely possible, performing a numerical simulation based on the data from the scale model experiment to capture the phenomenon’s behavior more completely is desirable using the knowledge acquired by the model experiment. In
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this way, it is possible to understand the flow phenomenon in a waste heat boiler in detail using a scale model for experimentation and also using numerical simulation, and to use this data as a basis for future studies.
Scale Modeling Cause and effect relationships between quantified variables, such as length, velocity, temperature, and a viscosity, provide the basis for modeling a real object or phenomenon. If a cause and effect relationship exists, then the functional relationship does not need to be known. However, experimentation using a scale model cannot be attempted without a certain amount of knowledge of the real phenomenon. Therefore, it is indispensable to observe phenomena carefully and enumerate the physical law or laws which govern them. The waste heat boiler is a very complex subject for a scale model experiment because dust-laden high temperature gas, chemical reaction, and heat absorption by water wall are all involved. Thus, we need first to examine what kind of physical laws govern the phenomena. Inertia force of gas: Fig = ρg 2 u 2g
(1)
Fvg = μg u g
(2)
Fbg = ρg β ⌬θ g 3
(3)
Viscosity force of gas:
Buoyancy force of gas:
Centrifugal force of gas: Fcg = ρg
u 2g R
3
(4)
Inertia force of particle: Fi p = ρ p d 2 u 2p N
(5)
Fvp = μg d u g − u p N
(6)
Viscosity force of particle:
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Gravity force of particle: Fgp = ρ p − ρg gd 3 N
(7)
u 2p 3 d N Fcp = ρ p − ρg R
(8)
Q e = qρ p d 3 N
(9)
Q c = c p ρg 3 ⌬θ
(10)
Q h = h 2 ⌬θ t
(11)
Q r = εσ 2 θ 4 t
(12)
W = ζ ρ p d 3 N u 2p 2 poα2 θ γ
(13)
Centrifugal force of particle:
Heat generation of particle:
Accumulation of heat:
Convective heat transfer:
Radiation heat transfer:
Quantity of corrosion:
As can be seen, a total of 13 physical laws govern the phenomena, eight concerning momentum balance, four that govern energy balance, and one for corrosion. Seven π -numbers are derived by Eq. (1) through Eq. (8) for momentum balance. ρg 2 u 2g Fig ug = = Fvg μg u g νg
(14)
ρg 2 u 2g u 2g Fig = = Fbg ρg β⌬θg 3 β⌬θg
(15)
π1 = π2 =
π3 =
ρg 2 u 2g Fig R = = 2 Fcg ug ρg 3 R
(16)
Here π1 to π3 are non-dimensional numbers referring to gas flow; they express the Reynolds number, the Froude number, and the swirl number (which strictly speaking, is different) respectively.
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π4 =
ρg 2 u 2g u 2g Fig 2 = = Fvp N dνg u g − u p μg d u p − u g N
(17)
π5 =
ρg 2 u 2g 2 u 2g Fig ρg 3 = = Fgp ρ p − ρg gd 3 N ρ p − ρg gd N
(18)
ρg 2 u 2g ρg Fig R 2 = = π6 = Fcp ρ p − ρg d 3 N u 2p d3 N ρ p − ρg R π7 =
ug up
2
ρg 2 u 2g Fig = Fi p ρ p d 2 u 2p N
(19)
(20)
π4 to π7 are non-dimensional numbers representing aspects of particulate flow. π4 and π7 determine the relative velocity of the direction of an axis of a gas and a particulate flows, π5 determines particle concentration distribution perpendicular to the flow, and π6 determines particle concentration distribution of the radius direction. An additional three π -numbers are derived by Eq. (9) through Eq. (12) for energy balance. qρ p d 3 N Qe = Qc c p ρg 3 ⌬θ
(21)
ht h Qh h 2 ⌬θ t = = = 3 Qc c p ρg ⌬θ c p ρg c p ρg u
(22)
c p ρg 3 θ c p ρg c p ρg u c p ρg 3 ⌬θ Qc ≈ = = = 2 4 2 4 3 Qr εσ θ t εσ θ t εσ θ t εσ θ 3
(23)
π8 = π9 = π10 =
π8 to π10 are non-dimensional numbers which determine the temperature distribution in the boiler and gas and particulate flow through change of buoyancy as well as the physical properties’ values according to temperature distribution. Although π8 is considered to be a non-dimensional number related to generation of dust, since the production mechanism of dust is unknown, it cannot be formulated. Equation (13), which showed corrosion loss, is derived based on the hypothesis of the pipe abrasion mechanism. Here it can be seen that a scale model experiment can’t satisfy the demand for complete resemblance between model and phenomena. Therefore, with secondary effects excluded, the analytical method is employed and the phenomenon is resolved spatially and temporally. Above-mentioned 23 equations of Eq. (1) though Eq. (23) are reduced to seven Eqs. (1) (3) (4) (5) (7) (8) and (23) as a result of simplifying the actual momentum balance relationships somewhat. Because flows of gas and particles can’t be separated, one phenomenon combines the particulate flow with the gas flow. The following relations are obtained when Eq. (1) and Eq. (4) are shown in -numbers.
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R≡ Fig R ↓ π3 = = −−−−−−−−−→ π3 = 1 Fcg From the above-mentioned relation, if the real object and the scale model are geometrically similar, the swirl number for each will be similar. The following relations will be obtained if the Eq. (1) and Eq. (3) are expressed with π -numbers.
π2 =
Fig = Fbg
ρg 2 u 2g ⌬ρ g 3
g = g ↓
−−−−−−−−−−−−−→
ρg u 2g ⌬ρ
The following relations are obtained if the flows in the real object and the model become similar as the inertia force and buoyancy have similarity. π2 = π2
(24)
The following relations can be obtained by Eq. (24). ρg u 2g
ρg u 2 g
−−−−−−−−−→ = = ⌬ρ ⌬ρ
ug u g
2
⌬ρ ρg ⌬ρ ρg
The above-mentioned relation leads to Eq. (25) and Eq. (26). =
ug u g
2
⌬ρ ⌬ρ = ρg ρg
(25) (26)
If a geometric similarity ratio and a velocity ratio are designed so that Eq. (25) may be satisfied in the real object and the scale model, then in order to reproduce a process involving mixed fluids, it is necessary to use the fluid which satisfies Eq. (26) in the model experiment. The sulfide generated by smelter passes a duct and flows into the boiler. It is necessary to reproduce the dust flow from the smelter exit to the waste heat boiler entrance in the model experiment. The following relations are obtained when Eq. (1) and Eq. (6) are expressed with π -numbers. π4 =
u 2g Fig 2 = Fvp N dνg u g − u p
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The following relations are obtained when Eq. (1) and Eq. (7) are expressed with π -numbers. g = g
s = ρ p ρg
π5 =
ρg 2 u 2g Fig 1 2 u 2g ↓ = − − − − − − − − − − − − − → Fgp (s − 1) d 3 N ρ p − ρg gd 3 N
The following relations are obtained when Eq. (1) and Eq. (8) are expressed with π -numbers. s = ρ p ρg R=
ρg 2 u 2g Fig 1 3 1 ↓ π6 = = − − − − − − − − − − − − − → u2 Fcp (s − 1) d 3 N ρ p − ρ f p d 3 N
ug up
2
Inertia force, gravity, centrifugal force and viscous force must be similar if the dust flow in the real object and the scale model is similar. π4 = π4
(27)
π5 = π5 π6 = π6
(28) (29)
The following relations can be obtained by Eq. (27) though Eq. (29). u 2g u 2 2 2 g = −→ N dνg u g − u p N d νg u g − u p
2 1 u 2 2 u 2g 1 g = −−−−−−−−−→ (s − 1) d 3 N (s − 1) d 3 N
3 1 1 (s − 1) d 3 N
ug up
2 =
3 1 1 (s − 1) d 3 N
u g
2
=
2
ug
2
2
u p
u g
=
−→
u g
N N
2
ug
3 =
d d
d d
d d
3
3
ν νg
ug − u p u g − u p
N s−1 N s − 1
N s−1 N s − 1
up u p
2
u g
2
ug
The following relation can be obtained by Eq. (28) and Eq. (29). =
up u p
2 (30)
If the same gas and dust are used in a model and real object, the dust mass ratio between the real object and the model (a mass ratio is the same as the dust number
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ratio if the same dust is used) is shown in the following equation as d = d and ρ p ≈ ρ p . N = N
d d
3 2 2 ρg 2 u g 2 ug s−1 =≈ ug s − 1 ρg ug
(31)
If the Similarity law is relaxed, the velocity ratio of the fluid and particles is the same in the real object and the model.
ug u g
=
up u p
(32)
Equations (30) and (31) are transformed to the next form by using Eq. (32).
2 ug u g ρg 3 N = N ρg =
(33) (34)
When Eq. (27) is transformed by using Eq. (30) and Eq. (31), the relative velocity ratio of the fluid to particles is obtained in the real object and scale model.
ug − u p u g − u p
2 2 μg ρg νg νg ug N = = = u g N νg ρg νg μg
(35)
Physical Model The material properties of the main stream, the uptake air and the Slag Cleaning Furnace off-gas are shown in Table 1. The density ratios of the uptake air to main air and Slag Cleaning Furnace off-gas are 1.6 and 0.95, respectively. The combination of fluids in main/blowing gas used in the scale model are examined for (a) air/carbon dioxide, (b) helium/air and (c) air/chlorofluorocarbon. It is found that actual flow can be reproduced in the model when air is used for the main stream and chlorofluorocarbon is used for uptake air and Slag Cleaning Furnace off-gas shown in Table 1. However, since use of a large quantity of chlorofluorocarbons is forbidden by air quality regulations, a substitute is required with a density equivalent to chlorofluorocarbon at a nominal temperature. The parameter which expresses tracking efficiency of particles to gas flow in the model is shown in Table 2. Real density is calculated from the properties of the smelter gas; since the kinetic viscosity is not available for the high temperature sulfurous acid gas, its value is replaced by using properties of nitrogen.
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Table 1 Gas used in real object and scale model Main gas Real object
Scale model
Uptake-air
Smelter gas 1300 K Air 300 K ρ = 0.447 kg/m3
ρ = 1.16 kg/m3 ⌬ρ = 1.16 − 0.447 = 0.713 ⌬ρ/ρ = 0.713/0.447 = 1.6
Air 300 K ρ = 1.16 kg/m3
Carbon dioxide 300 K ρ = 1.77 kg/m3 ⌬ρ = 1.77 − 1.16 = 0.61 ⌬ρ /ρ = 0.61/1.77 = 0.52 Air 300 K
Helium 300 K ρ = 0.16 kg/m3 Air 300 K ρ = 1.16 kg/m3
Slag cleaning furnace off-gas Air 400 K ρ = 0.87 kg/m3 ⌬ρ = 0.87 − 0.447 = 0.423 ⌬ρ/ρ = 0.423/0.447 = 0.95
ρ = 1.16 kg/m3 ⌬ρ = 1.16 − 0.16 = 1.0 ⌬ρ /ρ = 1.0/0.16 = 6.3 Felon R13 300 K ρ = 4.2 kg/m3 ⌬ρ = 4.2 − 1.16 = 3.04 ⌬ρ /ρ = 3.04/1.16 = 2.6
In Table 2, tracking efficiency of particles to gas flow in the water model is about 50 times as large as that of the air model, and the water model shows that a particle tends to follow fluid pattern as for the real object. On the other hand, although the tracking efficiency of the air model is on almost the same order as in the real object, the tracking efficiency is slightly worse than in the real object, and the relative velocity of the particle versus air flow is reduced. We confirm whether predominant physical laws in the real object are satisfied even with the 1/20 scale model. Figure 1 expresses a geometric similarity ratio to a horizontal axis, and expresses non-dimensional numbers shown on the vertical axis by Eq. (14) to Eq. (20), such as a Reynolds number and a Froude number. Table 2 Tracking efficiency of particles to gas flow in scale model Physical properties
Tracking efficiency
Smelter gas 1300 K = 42.7 mm2 /s (conjecture)
= 13.0 Pas (SO2 , 293K, 1atm)
Real object
ug − u p u g − u p
=
= 17.87 Pas (N2 , 293K, 1atm) = 49.39 Pas (N2 , 1300K, 1atm) Air Model
Air 300 K = 18.62 Pas
Water
Water 300 K = 854.4 Pas
18.62 = 0.44 42.7 854.4 = 20 42.7
μg μg
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Fig. 1 Examination of dominant physics laws in scale modeling
Experimental Apparatus It was found that a 1/20 scale model worked to reproduce the actual flow of waste heat boiler. Then, by carrying out numerical simulation of waste heat boiler flow using a 1/20 scale model, the particulate flow near water wall and the measurement of the air velocity and the mechanism of pipe abrasion due to the collision of the dust are solved. The experimental apparatus used to visualize the flow [4] is shown in Fig. 2.
Fig. 2 Experimental apparatus used to visualize the boiler flow
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Results and Discussion The entire flow inside the boiler in the model experiment and the numerical simulation is shown in Fig. 3. Comparison of numerical computation and the model experiment reveals higher flow discovered in the numerical computation. Since smelter gas temperature is 1280 degrees, this is considered to be the influence of an artefact of numerical computation. In Table 3, the attainment time from the gas inlet to front wall in the numerical simulation is compared with that of the model experiment. The attainment time from the gas inlet to front wall is 17–22 seconds in numerical computation, and is 13 seconds (value converted into real object) in the model experiment. The attainment time of the model experiment is measured from the locus of smoke. Because the time of swirl isn’t being added to the attainment time, it is considered that the attainment time of the model experiment becomes shorter than the time obtained in the numerical calculation. These results indicate that results of the modeling experiment and the numerical simulation are in close correspondance. The flow near the castable refractories in the front wall of the boiler is shown in Fig. 4. In the model experiment, a vortex with a diameter of 1 cm (20 cm in the actual object) occurs in the upper part of the castable refractories. On the other hand, in the numerical computation, since mesh size (10 cm) is equivalent to vortex size, no formation of a vortex is found. Next, the question of how to oxidize the dust contained in smelter gas by Slag Cleaning Furnace off-gas is examined. In order to mix the mainstream and Slag
(a)
(b)
Fig. 3 The entire flow of the boiler in (a) model experiment, and (b) numerical calculation
Table 3 Comparison of the scale model with numerical calculation Attainment time from the gas entrance to the front wall Actual model Numerical calculation 1/20 scale model
Unknown 17–22 seconds 13 seconds
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(b)
Fig. 4 The local flow near front wall in (a) model experiment, and (b) numerical calculation
Cleaning Furnace off-gas efficiently, the optimal nozzle shape and nozzle pattern are investigated. Two types of nozzle, i.e., the single type, which has one rectangular section, and the other, with four rectangular sections, are examined in the scale model. The nozzle pattern of each nozzle is shown in Fig. 5. The mixing process of the main stream with the Slag Cleaning Furnace off-gas is recorded by digital camera and analyzed by image processing. The evaluation index is defined by the rate of the mixed area of the Slag Cleaning Furnace off-gas to the entire mixed area. Figure 6 shows relations between the actual nozzle velocity and the mixing rate; it is found that the mixing rate is roughly proportional to the actual nozzle velocity. The model’s experiment results show that the most suitable nozzle pattern is B-4.
Fig. 5 Opening pattern of nozzles
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Fig. 6 Relations between actual velocity and the mix rate
Conclusions In this paper, 1/20th scale modeling and a numerical simulation are used to investigate the gas and particles flows inside a waste heat recovery boiler. Results show that the entire flow phenomena of the model experiment correspond very well with those in the numerical calculation. In the model experiment, a vortex with a diameter of 1 cm occurs in the upper part of the castable refractories. In the numerical computation, since mesh size (10 cm) is equivalent to vortex size, formation of a vortex is not observed. As a result of investigating the nozzle shape and the nozzle pattern for mixing the mainstream and Slag Cleaning Furnace off-gas efficiently, we found that the optimal nozzle pattern is B-4.
References 1. Emori, I., Saito, K. and Sekimto, K., Theory and Application of Scale Modeling, 3rd Ed., Gihoudo, 2000 (in Japanese) 2. Yang, Y., Jokilaakso, A., Taskinen, P. and Kyto, M., Modification of Waste-heat Boiler Design through Computer Simulation, Newsletter on Outokumpu Flash Smelting, 1999 3. Lilja, L. and Taskinen, P., Computational Fluid Dynamics-pushing up the Efficiency of Flash Smelting Technology, http://www.outokumpu.com/research/index.htm. 4. Ito, A. Narumi, T. Konishi, G. Tashtoush, K. Saito and C. J. Cremers., The measurement of transient two-dimensional profiles of velocity and fuel concentration over liquids, Transaction of the ASME Journal of Heat Transfer, Vol. 121, No. 2, pp. 413–419, 1999
Scale Modeling for Landing of a Lunar Probe Kazuya Yoshida, Shigehito Shimizu, Satoshi Yamaguchi, Kozo Sekimoto, Akira Miyahara and Takashi Yokoyama
Abstract In this paper, a scaling law on the landing behavior of a lunar probe is discussed. In order to derive an effective scaling law, all of possible non-dimensional numbers, called pi-numbers, were examined at first based on the principle equations of physics related to the phenomena. One strict relationship was then derived in terms of the size between a real model and a corresponding scale model. The relationship suggests that the scale models should have the size of one sixth of the real ones when studying the motion behavior of mechanical systems on the Moon. The fact has been well known in the space community. However, such a strict law is not always practical in laboratory experiments on the ground. Therefore, possibilities to relax the law were investigated; hence two candidate relationships were obtained. Experiments in a vacuum chamber using simulated lunar soil were carried out to validate these relaxed laws, and concluded was that inertia forces and soil-cohesion forces dominate over gravity forces for the landing dynamics. Elimination of the gravity forces from the primary consideration in the scale model experiments will make the verification process of the lunar landing systems easy and more practical. Keywords Lunar lending · lunar regolith · impact forces scaling
Nomenclature c d F g l mr ms
Cohesion force of the lunar soil Penetration depth Force Gravitational acceleration Representative length Mass of a lunar probe Mass of the associated lunar soil
K. Yoshida Department of Aerospace Engineering, Tohoku University, Aoba 6-6-01, Sendai, 980-8579, Japan e-mail:
[email protected]
K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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t V v α ρ μ π
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Time Volume Velocity Acceleration Density of the lunar soil Friction coefficient Dimensionless PI number
Superscript
Values in a scale model
Introduction In recent years, there is an increasing interest on lunar exploration missions and future in-situ resource utilization on the Moon. In order to establish a frequent access to the lunar surface, technologies around autonomous and safe landing is a key. In Japan, as for a next step program after on-going SELENE mission [1], an autonomous lunar landing probe has been studied. In such a landing probe, contact/impact dynamics in the final touchdown phase is most critical. The study of the touchdown dynamics on lunar soil is the central focus of this paper. Lunar surface is covered with fine granular or powdery soil called lunar regolith [2]. When a lunar probe makes a touchdown on the surface of regolith, we need to know how much impact forces are generated in which directions and make sure that the probe should not slip or bounce in an unexpected way, or tip over. Then, substantial understanding is required on the behavior of the landing probe which is caused by the physical interaction between the terrain and the legs of the probe. Experiments with hardware prototypes are necessary steps in the technology development and verification, but when we perform experiments on the Earth we need to pay attention to the differences between the laboratory models and the real ones in terms of size, atmosphere, and gravity. As for the atmosphere, the lunar surface is a vacuum environment, thus experiments in a vacuum chamber will provide a good simulation. As for the gravity, it is difficult to obtain 1/6 G in Earth-based laboratories. A remedy for this issue is to utilize semi-parabolic flights, but the duration of the experiments are limited and the size of the experimental models must fit in such an airplane. When we conduct experiments with a scale model, we need to comprehend the relationships between the model and the reality. The law of similarity suggests that if the non-dimensional ratios among equations of motions on the related physics between the model and the reality have a consistent number, called pi-number, the physical phenomena of a real model can be properly deduced from the experimental results [3]. But in practical cases the relationships become over-constrained, or even
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not over-constrained, too strict then unrealistic to conduct the scale model experiments. In such cases, the equations which do not play a major role for a given problem will be eliminated from the scaling law. This process is called relaxation. In this paper, we will provide a basic discussion on the scaling law for landing behavior of a lunar probe. We first examine all the related physics equations and derive non-dimensional relationships. The relationships lead to a strict law to constraint the size of the scale model. We then investigate the possibility for the relaxation of the law. In order to evaluate a couple of relaxed scaling laws, experiments are carried out in a vacuum chamber using simulated lunar soil. The behavior of the simulated lunar soil in the air and vacuum environments are also experimentally compared.
The Scaling Law for Landing Behavior of a Lunar Probe At first, we investigate the following principle equations that describe the physical phenomena of a lunar probe when it makes a touchdown on the lunar surface under the lunar gravity: Fi = ρl 3 (l/t 2 ) = ρl 2 v 2
(1)
Fg = ρgl 3
(2)
Fc = cl 2
(3)
F f = μFg
(4)
where Fi is representative inertia forces, Fg is representative gravity forces, Fc is representative cohesion forces of the lunar soil and F f is representative friction forces. Next, we derive non-dimensional relationships to define pi-numbers from possible pairs in the above equations. π1 =
Fi ρl 2 v 2 v2 = = Fg ρgl 3 gl
(5)
π2 =
Fi ρl 2 v 2 ρv 2 = = Fc cl 2 c
(6)
Ff =μ Fg
(7)
π3 =
As seen above, π1 is the ratio between the inertia and gravity forces, which is known as Froude number. π2 is the ratio between the inertia and cohesion forces. π3 is known as a friction coefficient. Particularly in case of soil-like deformable materials, the friction coefficient is modeled by μ = tan φ, where φ is the internal friction angle of the material.
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To properly deduce the physical phenomena of a real model from the experiments with a scale model, we need to match the pi-numbers between these two models. If the values in the real model are denoted by a prime ( ), we obtain the following ratios: for π1 , g l = gl
v v
2 (8)
for π2 , c ρ = cρ
v v
2 (9)
From Eq. (8) and Eq. (9), we can obtain the following equation: gc ρ l = l g cρ
(10)
Supposing that the scale-model experiments of the lunar landing are carried out on the Earth using simulated lunar soil which has the same characteristics as lunar regolith, the following relationships hold true: g =6 g c = c ρ = ρ
(11) (12) (13)
With Eq. (10) we obtain: 1 l = l 6
(14)
The law of similarity described above suggests that if the scale model uses l /l = 1/6 in size, the Earth-based experimental results shall properly simulate the motion of landing behavior on the Moon [4, 5].
Relaxation of the Scaling Law As confirmed above, 1/6 sized of the scale models are required for the experiments on the Earth. However this relationship gives a strict restriction on the size of the scale models. In practical cases, it is not always possible to comply with this law in conducting the scale model experiments on the Earth. We then investigated the possibility for the relaxation of the law with the following two options.
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Case A: Elimination of Scaling Law In this case, we consider that the dominating forces are inertia forces, friction forces and the gravity forces for the landing dynamics. Applying Eq. (8), we obtain the following equation: l g = l g
v v
2 (15)
Equation (15) suggests that the ratio of the size can be determined from the ratios of the gravities and velocities.
Case B: Elimination of the Gravity Forces In this case, we consider that the dominating forces are inertia forces, friction forces and cohesion forces for the landing dynamics. Applying Eq. (9), we obtain the following equation: v = v
$
c ρ cρ
(16)
Equation (16) does not include the length. This means that we can arbitrary choose the ratio in size regardless the differences of gravity. Notes on these relaxations of the scaling law are summarized in Table 1. In order to evaluate practical validity of these options, we carried out the experiments as described below. Table 1 Summary of the Relaxation of the scaling law Case
Eliminated physics
Relationship between the models
Size ratio
ν ρν , l c ν2 l ρν 2 c
ρc ρc 2 ν ν
2
None A
Cohesion forces
B
Gravity forces
2
(Arbitrary)
Experimental Procedure An overview of the experimental setup is depicted in Fig. 1. This setup consists of four major components: a chamber base (A in Fig. 1), an acrylic chamber (B), a guide rail (C) to support the vertical fall of test pieces, and a vacuum pump (D). For the soil, lunar regolith simulant [6], which has the same characteristic as real lunar regolith was used. The regolith stimulant was set in the steel container at the base
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Fig. 1 An overview of the experimental setup
and test pieces with different masses were dropped on the soil along the guide rail from different heights. The soil setting was controlled to have three distinguished conditions termed as soft, middle and hard, which are in the range from 2.1 to 10.1 [kPa] in terms of the shear strength. All the experiments were carried out in 100 [Pa] (1 Torr) environment. For each experiment, we measured the impact load under the bottom of soil container, the impact acceleration on the dropped test piece, and its vertical position. Measurement devises were a load cell, an accelerometer and a laser range sensor, respectively. Three test pieces were used throughout the experiments; the shape of each piece is a circular cone with a tip angle of 60 [deg], and the masses are 367 [g], 482 [g], and 991 [g]. The initial position of the test piece on the guide rail was adjusted so that the velocity of the landing (contact) was in the range from 1.4 to 2.7 [m/s].
Results and Discussions The Penetration Depth and the Representative Length In order to evaluate the relaxed scaling laws A and B, we carried out a number of drop and landing experiments in the vacuum chamber, and the results were evaluated by the penetration depth of the dropped cone into the soil. Since our test pieces
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have a conic shape, the penetrated part always has the same shape regardless the penetration depth. In order to normalize the penetration depth with respect to the representative length, we introduce the value termed penetration ratio. As depicted in Fig. 2, we consider a virtual cone with the representative volume of the lunar probe (the test piece in the experiments). Let m r be the mass of the probe (test piece) and ρ the density of the lunar soil, the representative volume of the entire probe is constituted by the following equation: mr =V ρ
(17)
The representative length l is then defined by a cubic root of the representative volume: l=
mr ρ
1 3
(18)
Finally, the penetration ratio ε is defined as the ratio between the actual penetration depth d and l. ε=
Fig. 2 An image of representative length
d l
(19)
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Evaluation of the Relaxed Scaling Laws Based on the Penetration Ratio The experimental results are evaluated by the penetration ratio defined above, and depicted in Fig. 3 for case A and in Fig. 4 for case B. In the figures, the vertical axis is for the penetration ratio and the horizontal axis is for the characteristic non-dimensional number, and both axes are measured in the log scale. If the plots on the log-log plane constitute a single line, a meaningful correlation between the horizontal and vertical values is suggested. In this point of view, the plots in Fig. 3 are distributed in a scattered manner rather than forming a line. This indicates that
Fig. 3 Relationship between the characteristic non-dimensional value and the penetration ratio (case A)
Fig. 4 Relationship between the characteristic non-dimensional value and the penetration ratio (case B)
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the case A, the elimination of cohesion forces is not an appropriate relaxation. On the other hand, the plots in Fig. 4 are considered distributed on a line. This indicates that the case B, the elimination of gravity forces, is an appropriate relaxation. From this analysis, we can confirm that the inertia forces and the soil-cohesion forces dominate over the gravity forces for the landing dynamics.
Comparison of Impact Behavior in the Air and Vacuum Environments Before conducting the series of experiments shown in the above, we compared the landing behaviors in the air and the vacuum environments. The experimental conditions were as follows: The test pieces were of the same shape, mass and velocity. The regolith simulant was set to maintain the same soil condition in every test. The pressure was controlled as 1 [atm] in the air environment, while that was 100 [Pa] in the vacuum environment. The snapshots after the landing in each test are shown in Fig. 5. Compared between the in-the-air experiment (left picture) and the vacuum experiment (right picture), the penetration depths are apparently different. Particularly in the vacuum environment, the test piece penetrated deeper and a crater like dimple was formed. To observe the dynamic behavior of the soil, we also used an ultra high-speed camera and the following observation was made; in the air environment, the soil behaved like an elastic lump (a hard sponge) and the test piece seemed to bounce on the surface, while in the vacuum environment, the surface was fragmented in soil particles and flicked off by the landing impact. From the above comparison it is concluded that the lunar landing experiments must be carried out in the vacuum environment since the soil behavior in the vacuum is very different from that in the air.
Fig. 5 Appearances after the impact landing; left: in the air, right: in the vacuum
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Conclusions In this paper, the scaling law for landing behavior of a lunar probe and the possibility for the relaxation of the law were investigated. First, all principle equations of forces related to the phenomena of landing on the soil were examined to derive non-dimensional relationships. The relationships lead to a strict law to constraint the size of the scale model, which is well know as 1/6 in the size. Next, the relaxation of the law was investigated then a couple of candidate relationships were derived. To validate the relaxed scaling laws, the experiments were carried out in a vacuum chamber using simulated lunar soil, and the results were evaluated by the penetration ratio of the test piece into the soil, depicted as log-log plots. The results suggest that the dominating forces for the landing dynamics are inertia forces, friction forces and cohesion forces, but not gravity forces. The landing behavior in the air and vacuum environments were also compared by observing with a high-speed camera. As a result, it was observed that the soil behaved like an elastic lump in the air, while the soil behaved like particulates and an impact crater was formed in the vacuum environment. From this result, the experiments of the lunar landing are strongly suggested to be carried out in the vacuum environment. Acknowledgments The authors would like to acknowledge the Japan Aerospace Exploration Agency (JAXA) for their support of this research.
References 1. Japan Aerospace Exploration Agency, SELenological and ENgineering Explorer “SELENE”, http://www.jaxa.jp/missions/projects/sat/exploration/selene/index\ e.html, as of 2006. 2. G. Heiken, D. Vaniman, B. M. French, and J. Schmitt, Lunar Sourcebook: A User’s Guide to the Moon, Cambridge University Press, 1991. 3. I. Emori, K. Saito, and K., Sekimoto, Scale models in engineering (3rd ed), Giho-do, Tokyo, 2000. (in Japanese). 4. T. Yokoyama, H. Kanamori, and K. Higuchi, Estimate of Impact Force at Landing on Lunar Surface with Scale Model Experiment, Fifth International Symposium on Scale Modeling, 2006. 5. Y. Kuroda, T. Teshima, Y. Sato, and T. Kubota, Mobility Performance Evaluation of Planetary Rover with Similarity Model Experiment, IEEE International Conference on Robotics and Automation, 2004. 6. H. Kanamori, S. Udagawa, T. Yoshida, S. Matsumoto, and K. Takagi, Properties of Lunar Soil Simulant Manufactured in Japan, Proceedings of the 6th Int. Conf. and Exposition on Engineering, Construction, and Operations in Space, 1998.
Scale Modeling of Steel Making Processes Junichi Nakagawa
Abstract Steel making is a process in which hot metal tapped from blast furnaces is refined into steel of the quality specified by customers. Molten steel thus produced is then processed into slabs, blooms and billets as semi-finished products. The flow and chemical reaction in molten steel play an important role in these processes. However, it is impossible to measure these space distributions directly, because the temperature of molten steel is high and the scale of the equipment is large. Moreover, it is very difficult to obtain the space distributions by CFD, because the phenomena in molten steel are highly complicated. Fortunately, the kinematic viscosity of molten steel is almost the same as water. Therefore, in conducting a 1/1 scale model experiment with water, both the Reynolds number and the Froude number can be matched to a real plant. However, it is not easy to conduct this experiment because of the large size of the equipment. In addition, it is necessary to consider the influence of the gas injected into molten steel and the effect of the chemical reactions. This paper describes the procedures of scale modeling to clarify the complex phenomena in molten steel. Three scaling laws, that concern stirring, mixing, and chemical reaction respectively, are proposed. And we show that these scaling laws explain the experimental results of the scale models and the real plants. These results provide the guidance for operation improvement and process design. Keywords Steel-making · blast furnance · scaling laws
Nomenclature g u l ν
Gravitational acceleration Velocity Length Kinetic viscosity
J. Nakagawa Advanced Technology Research Laboratories, Nippon Steel Corporation, 20-1 Shintomi, Futtsu-Ciity, Chiba 293-8511, Japan e-mail:
[email protected]
K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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368
ρ ε R G T h P0 V Q S τ t K C
J. Nakagawa
Density Isothermal expansion energy Universal gas constant Gas injection flow rate Temperature Gas injection depth Atmospheric pressure Liquid volume in vessel Liquid recirculation flow rate Cross section area of snorkel Mixing time Time Rate constant or volume coefficient of mass transfer Concentration of chemical product
Subscript 0 m a r e i
Initial condition Mixing Advection Reaction External force Inertia force
Introduction Steel making is a process in which hot metal tapped from blast furnaces is refined into steel of the quality specified by customers. Molten steel thus produced is then processed into slabs, blooms and billets as semi-finished products. Figure 1 shows the schematic flow of the steel making process. Diverse types of equipment are used to make steel of a quality that meets the customer’s requirements. These are hot-metal pretreating equipment, BOF, secondary refining equipment and continuous casting machines. In the hot-metal pre-treating process, impurities such as silicon, phosphorous and sulfur are removed. In the BOF, oxygen is blown into the furnace vessel to remove mainly carbon from hot-metal and refine it into steel. Molten steel tapped from the BOF is further refined employing secondary refining equipment to make high-purity, high-sterility steel. Molten steel refined to suit specified applications is solidified employing continuous casting machines to produce slabs, blooms and billets. The flow and chemical reaction in molten steel play an important role in these processes. However, it is impossible to measure these space distributions directly,
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Fig. 1 Schematic flow of steel making process at Oita Works of Nippon Steel Corporation
because molten steel is high in temperature, ranging from 1700 K to 1900 K, and the equipment is large in size, ranging from 20 m3 to 70 m3 . Moreover, it is very difficult to get the space distributions by CFD (Computer Fluid Dynamics), because the phenomena in molten steel are highly complicated. They consist of a complex entanglement of chemical equilibrium factors relative to ferrous metallurgy and thermodynamics, and of fluid dynamic factors such as stirring force and mixing characteristics. In addition, it is necessary to treat the multi-phase flow, such as the gas-liquid phase or gas-liquid-solid phase structured by gas and powder injected into molten steel. To straighten out the entanglement and clarify the mechanism at work, I conducted scale modeling analysis. Even if the relational expression cannot be mathematically solved, the mechanism at work can be produced in a scale model experiment by using an appropriate scaling law. Then the mechanism can be clarified and quantified as the relational expression among the operation factors by confirming the validity of the scaling law in both the experiment and the real plant. This paper describes the procedures of scale modeling to clarify the complex phenomena in molten steel, especially the transport phenomena of mass and momentum in a reaction vessel, according to the idea mentioned above.
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Characteristics of Physical Properties of Molten Steel Fortunately, the kinematic viscosity of molten steel is almost the same as water. Therefore, both the Reynolds number and the Froude number can be matched to a real plant by conducting a 1/1 scale model experiment with water, as shown in Fig. 2. This means the flow pattern of the water model experiment corresponds to that of a real plant. Figure 3 shows the flow pattern of molten steel in the mold of the continuous casting machine at Oita Works of Nippon Steel Corporation. It is calculated by CFD, in which LES (Large Eddy Simulation) as the turbulence model is used. Here, one of the 1/2 sections of the mold is shown. On the other hand, Fig. 4 shows the flow pattern of water in the 1/1 scale model experiment. It is measured by PIV (Particle Image Velocimetry system). The flow pattern of Figs. 3 and 4 correspond macroscopically. However, with respect to costs and loads, it is not easy to conduct the 1/1 scale model experiment because of the large size of the equipment. In addition, it is necessary to consider the influence of the gas injected into molten steel and the effect of the chemical reactions.
Re =
ul ν
u l = u ′l ′
l = l′
ν ≈ ν ′ ≈ 1 m 2/ sec Fr =
u2 lg
u 2 u′2 = l l′
Fig. 2 Scaling law concerning single-phase flow of molten steel
Fig. 3 Flow pattern of molten steel in CC mold calculated by CFD [1]
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Fig. 4 Flow pattern of water in 1/1 scale model of CC mold measured by PIV [1]
Scaling Law of Stirring When a gas is injected into molten steel, the expansion energy of the gas is converted to the kinetic energy of the molten steel. The kinetic energy is caused by inertia force, Fi . The expansion energy is caused by external force, Fe , due to the injected gas. Their forces are written in representative form as: Inertia Force External Force
Fi = ρu 2 l 2 Fe = (ρl ε)/u 3
(1) (2)
where ρ = density of molten steel, u = velocity of molten steel, l = length, and ε is the isothermal expansion energy of the injected gas per unit liquid volume, as expressed below. ε = G RT ln(1 + ρ g h/P0 )/ρV
(3)
where G = gas injection flow rate, R = gas constant, T = molten steel temperature, g = gravitational acceleration, h = gas injection depth, P0 = atmospheric pressure, and V = liquid volume in vessel. From these forces, the first pi-number is formed as: π1 = Fe /Fi = {(ρl 3 ε)/u}/(ρu 2 l 2 ) = εl/u 3
(4) (5)
To verify the above-mentioned scaling law, a water model experiment was conducted by simulating the RH vacuum degasser, as shown in Fig. 5. This is a 1/5 scale model of the commercial RH vacuum degasser at Oita Works of Nippon Steel Corporation. The vacuum vessel and ladle were both evacuated to a vacuum P0 of approximately 100 Torr, and the liquid height in the vacuum vessel was kept
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Fig. 5 Water model experiment apparatus of RH vacuum degasser [2, 3]
geometrically similar to that in a commercial RH vacuum degasser by adjusting the pressure difference between the vacuum vessel and ladle. Though it is difficult to determine the velocity u in Eq. (5) explicitly, it is possible to define the velocity u as follows for the RH vacuum degasser. Q = uS
(6)
where Q = liquid recirculation flow rate, and S = cross sectional area of snorkel. When Eq. (5) and Eq. (6) are rearranged, Q can be expressed by 1/3 Q = 2ηG RTρ 2 S 2 ln(1 + ρ g h/P0 ) /ρ
(7)
where η = work efficiency (= (2π1 )−1 ). Figure 6 compares the measured values of Q in the model experiment with the calculated values of Q by Eq. (7). Q is measured by the anemometer set up in the snorkel. Equation (7) was found to be able to rationally explain the measured values despite some differences in P0 , G, S, and h. The work efficiency η is set at 0.06 according to the slope of the straight line. The validity of Eq. (7) was verified in the real plant by Mori [4], as shown in Fig. 7. This figure shows Eq. (7) can well explain the measured values in the real plants. 1/3
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Fig. 6 Comparison of measured and calculated values of Q in model experiment [2, 3]
Scaling Law of Mixing Next, the transport of impurities such as silicon, phosphorous and sulfur in the flow field formed by stirring is considered. It is possible to use Eq. (5) as the scaling law concerning the flow field. Concerning the transport of impurities, the effect due to diffusion can be disregarded, because the flow field formed by gas stirring is usually turbulent. Therefore, two transport masses are considered such as: Mm = ρ l 3
(8)
Ma = u ρ l τ 2
(9)
where τ = mixing time. Equations (8) and (9) represent the effects of the amount of mass and advection, respectively. From these transport masses, the second pi-number is formed as: π2 = Ma /Mm = u ρ l 2 τ/ρ l 3 = uτ/l
(10) (11)
The scaling law is shown below. u εl π1 = 3 −→ = u u
εl εl
1/3
u −1 l τ uτ π2 = −→ = l τ u l
# # −2 −1/3 # #−→ τ = εl # τ εl −2 #
(12)
To verify the above-mentioned scaling law, a water model experiment was conducted using the ladle shown in Fig. 8. To determine the mixing time of the experiment, a salt solution was injected in pulses near the gas discharge hole, and the
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Fig. 7 Comparison of measured and calculated values of Q in real plant [4]
where D = snorkel inner diameter, P2 = atmospheric pressure, (the same as P0) and P1 = P0 + ρhg
change in the electrical conductivity of the water was measured by the conductivity meter installed in the ladle side-wall. The mixing time was defined as the time at which conductivity reached 98% of its ultimate value, as shown in Fig. 9. Figure 10 shows the relation between the mixing time τ and εV −2/3 in the experiment. εV −2/3 is equal to εl −2 in representative form. Here, to confirm the influence of the contribution factors in scaling law, three kinds of similar model experiments with a different size were conducted. Equation (12) is verified by the fact that the slope of the straight line on the logarithmic graph of Fig. 10 is −1/3.
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Fig. 8 Water model experimental apparatus of ladle [3]
Fig. 9 Method of determining mixing time
T (sec)
V (m3) ○
0.049
■
0.014
△
0.006
‒1/3
ε ⋅ V −2 / 3 (W /m 5 )
Fig. 10 Relationship between τ and εV −2/3 in water model experiment
Scaling Law of Chemical Reaction Finally, the scaling law of the chemical reaction is considered. It is necessary to consider the source term of the chemical reaction in addition to the terms of amount
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of mass and advection mentioned above. The transport mass due to the chemical reaction is shown as: Mr = K ρ l 3 τ
(13)
where K = rate constant or volumetric coefficient of mass transfer. From Eq. (8) and Eq. (13), the third pi-number is formed as: π3 = Mr /Mm = K ρ l 3 τ/ρ l 3 = Kτ
(14) (15)
The scaling law is shown below: π1 =
εl Fe εl −→ 3 = 3 Fi u u
uτ uτ Ma = π2 = −→ Mm l l π3 =
# # # #−→ εl −2 1/3 τ = εl −2 1/3 τ # #
Mr −−−−−−−−−−−−−−−−−−−−−−→ K τ = K τ Mm
(16)
(17)
The rate constant K when benzoic acid was dissolved in water was measured in the experimental apparatus shown in Fig. 8. The experiment consisted of floating benzoic acid impregnated liquid paraffin on the water bath surface, stirring the bath with lance-injected nitrogen, and measuring the ratio of benzoic acid dissolution in the water with a conductivity meter. Some of the experimental data are shown in Fig. 11. When the benzoic acid concentration C/C0 is plotted against time on a simply logarithmic graph, a linear relation is obtained and is found to follow Eq. (19) derived by the transformation of Eq. (18). dC = −K C dt ln C/C0 = −K t
(18) (19)
where C = difference between saturation concentration and concentration at time t of benzoic acid, and C0 = difference between saturation concentration and initial concentration of benzoic acid. K is determined from the slope of the straight line. Figure 12 shows the relation between the rate constant K and (ε/S)1/3 in the water model experiment. ε/S is equal to εl −2 in representative form. S is the surface area of a vessel in the stationary state. ε/S is able to explain the influence factors of K based on the scaling law, Eq. (16) and Eq. (17), despite the differences in vessel type. Here, TPC stands for Torpedo Car which is shaped like a rugby ball. BOF stands for Basic Oxygen Furnace which is shaped like a jar.
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C/C0 (-)
. PLQ
C = [C 6 H5COOH]saturated - [C6H5COOH]t C 0 = [C6H5COOH]saturated - [C6H5COOH]t = 0
Time (min)
Fig. 11 Measured dissolution rate of benzoic acid in water [3]
1
k (1/min)
Type
0.01 1
k (1/min)
Fig. 12 Relationship between K and (ε/S)1/3 in dissolution of benzonic acid in water [5]
0.1
S (m2）
○
TPC
0.4
□
Ladle
0.066
▲
Ladle
0.029
×
BOF
0.42
10 (ε/S )1/ 3 ( (W / ton ⋅m −2 )1 / 3 )
100
Type
S (m2 )
○
TPC
37.7
●
TPC
7.5
■
Ladle
2.9
□
Ladle
0.45
▲
Ladle
0.03
×
BOF
33.6
(ε/S )1/ 3 ( (W / ton ⋅m −2 )1 / 3 )
Fig. 13 Relation between K and (ε/S)1/3 in dephosphorization in molten iron
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Figure 13 shows the relationship between the rate constant K and (ε/S)1/3 in the dephosphorization in molten iron including plant operation data. The dephosphorization is a reaction by which phosphorous in molten iron is removed with oxygen. ε/S is able to explain the influence factors of Fig. 13 as well as Fig. 12.
Conclusion To clarify the complex phenomena in molten steel, three scaling laws, that concern stirring, mixing, and chemical reaction respectively, were quantified as relational expressions among the factors of operation and equipment. And, these scaling laws explain the experiment results of the scale models and real plants. These results provide the guidance for the operation improvement and process design.
References 1. Kawai, Y., Nakagawa, J., Komori, T., 1993, The 26th Autumn Meeting of the Society of Chemical Engineers, Japan, I105. 2. Nakagawa, J., Yamamoto, S., Kato, H., Wake, M., 1985, Tetsu-to-Hagane, 7(12), S909. 3. Nakagawa, J., Komori, T., Ogura, M., 1991, Nippon Steel Technical Report, No. 48. 4. Mori, K., Kuwabara, T., Mimura, M., Umezawa, K., et al., 1987, Tetsu-to-Hagane, 73(4), S176. 5. Nakagawa, J., Yada, Y., Komori, T., Morita, M., 1989, CAMP-ISIJ, 2(1), 135.
Scaling Laws for Sedimentation Process in Water Flow-Driven Sedimentation Tanks Kozo Sekimoto
Abstract This paper addresses scaling laws on sedimentation tanks whose aim is to separate particles from particle-containing water. Sedimentation process was categorized for four typical cases: Case 1 through Case 4; then scaling laws for each case were developed using law approach method. Case 1: Relatively large diameter particles, Case 2: Relatively small diameter particles, Case 3: Small diameter particles with low specific mass density, and Case 4: large diameter particles with high specific mass density. Two scale model sedimentation tanks were designed for sedimentation experiments. These two tanks were geometrically similar. The large tank (prototype) is twice as larger than the small tank (model). Experiments were conducted for Case 3 and Case 4 using prototype and model. The flow rate of water and the feeding rate of particles for prototype and model were adjusted based on scaling laws derived for each case. Sedimentation ratio (dimensionless parameter), defined as the ratio of sedimentary particle weight of particular size to the original weight of the corresponding size of particles with known size distribution, was measured in the above experiments and used to validate scaling laws. As a result, the proposed scaling laws for Case 3 and Case 4 were successfully validated. Keywords Sedimentation · scaling laws · sedimentation tank
Nomenclature d Fg Fi Fv L Lt N
Particle diameter Gravitational force Inertial force Viscous force Length Length of tank Number of particles
K. Sekimoto Sekimoto SE Engineering, 5-1-18 Higashi-Sendai, Miyagino-ku, Sendai, 983-0833 Japan e-mail:
[email protected]. K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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Re V μ ν ρ g
K. Sekimoto
Reynolds number – width of the tank defined as the characteristic length Velocity Viscosity Kinematic viscosity Density Gravitational acceleration
Subscript f p
Fluid Particle
Superscript
Indicate the model
Introduction Sedimentation tanks have been used to remove particles from particle-containing liquid systems, such as for the water purification process in water treatment systems. The process of sedimentation is a complex phenomenon involving a transient 3-D interaction of particles with the liquid whose interface has free surface boundary with outside airflow. In addition, for many practical sedimentation tanks, particles usually consist of different shape, sizes and material properties, and the liquid can be multi-component, making accurate numerical modeling effort very difficult, if not impossible. Small scale model experiment of sedimentation tanks can be an attractive alternative to full scale experiments and numerical modeling when we seek improvement in performance of the currently existing sedimentation tanks and plan to design a new one. Thompson’s classical work [1] addresses the essential difficulty in finding general scaling laws that can be applied to all different types and sizes of sedimentation tanks. In this paper, therefore, the sedimentation processes are classified into four different typical types and scaling laws are developed for each type. A geometrically simple sedimentation tank which is similar to Thompson’s experiment [1] was used. To validate the scaling law prediction, ideally the result of the scale model experiment can be compared to the full scale test, if available. However, there was no reliable full-scale test database for comparing to this study. To overcome this, the law approach developed by Emori [2], where two different sized scale models designed for relative comparison was used for this study. The law approach requires two conditions: (1) these two different size scale models must have geometrical similarity, and (2) these two different sized scale models are assumed to be governed by the same physical laws that govern the full scale. The law approach has particular merits over other two approaches [3], as detailed
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by Emori [2], when the full scale phenomenon is very complex and requires partial scaling laws to realize scale model experiments from which designers can predict the needed full-scale behavior.
Scaling Laws Cross-section of the full-scale sedimentation tank to be scaled down is shown in Fig. 1. Typical flow condition is roughly in the range of Re = 30,000, which is well within turbulent regime. Therefore, assumptions were made here that the dominating forces on the flow are inertial and gravitational forces, while viscous force is secondary except very near the wall surface. Regarding the motion of particles, smaller particles may well follow the liquid flow, while larger particles will be separated from the liquid flow by inertia and gravity. The sedimentation particles in fluid are governed by the resistive force created by difference in velocity between the liquid and the particle. The terminal velocities of spherical particles in the air have been studied; results of the experiment are shown in Fig. 2 [4]. In the range where the particle diameter is small, the slope of the line shows 2:1, meaning that the resistive force due to relative motion of particle and fluid is mainly dominated by the viscous force. For larger particles, the slope becomes 1:2 meaning that the inertial force becomes predominant.
Case 1: Relatively Large Diameter Particles Both the fluid and sedimentation particles will be dominated by gravitational and inertial forces, so that the Froude (Fr) Number, the ratio of the inertia force to gravity, is a governing pi-number. Gravitational force acting on the fluid and particles Fg = ρ g L 3 Inertial force of the fluid and particles
Fig. 1 Cross section of a typical sedimentation tank
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Fig. 2 Terminal velocity of particles as a function of particle diameter
Fi = ρ L 2 V 2 Then, Fr number will be formed as the ratio of gravity to inertia forces. Fg ρ g L3 = π1 = Fi ρ L2 V 2
L = −−−−→ L ↑ g=g
V V
2 (1)
The incoming horizontal velocity of fluid in the two different scale model tanks should be scaled based on Eq. (1); then prediction the falling speed of particles can follow Eq. (1). The latter prediction will be tested by scale model experiments which will appear later. Note that in describing gravitational and inertia forces, the same length, velocity and density were used for both the fluid and the particles. These representative parameters (somewhat similar to characteristic parameters) differ from specific parameters. Representative parameters usually represent only important parameters which have the same dimension and have some role in controlling the full scale phenomenon. For more information on representative parameters, see Emori [2].
Case 2: Relatively Small Diameter Particles The fluid motion will be governed mainly by gravity acting on the fluid and the inertial force of moving fluid, while viscous force of fluid becomes negligible when compared to the inertial force of fluid. For the motion of particles, gravity will act on the particles and will influence vertical velocity. Small particles will easily follow
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the fluid flow, and therefore velocity difference between the particle and the fluid will be small. The drag force associated with this mechanism will be viscous force of fluid. Although the viscous force of fluid is small compared with the inertia force, drag force acting on the particles associated with the motion of small particles relative to the fluid motion will be governed by the viscous force of fluid. Therefore, the major governing forces for Case 2 are: Inertial force of fluid and particles Viscous force of fluid acting on the particles Gravity force acting on fluid and particles
Fi = ρ L 2 V 2 Fv = μ L V Fg = ρ g L 3
From the above three forces, π2 and π3 are obtained. LV Fi LV −−−−−→ = Fv ν ν ↑ μ ν≡ ρ 2 V L Fi = π3 = −−−−→ Fg L V ↑ g = g π2 =
# # # # 3 # ν #→ = L 2 # ν L # # #
(2)
Pi-numbers: π2 = π2 and π3 = π3 (where the left side of the equation represents the prototype and right side (‘) the model) can be satisfied by changing kinetic viscosity of fluid based on Eq. (2), resulting in the discovery that the same fluid cannot be used for prototype and model. Note that the length L represents both the tank and the particles; thus, the particle diameter be adjusted based on the above scaling laws.
Case 3: Small Diameter Particles with Low Specific Mass Density (d < 0.2 mm) If the particle size is sufficiently small, and the amount of the particles per unit volume of the fluid is small, the viscous force has the dominant effect on the motion of particles. The inertial force of moving particles is negligible. Although the particles are accelerated by the fluid, the exchange of momentum has little effect on the overall fluid motion. The effective range of the viscous force is restricted to the immediate vicinity around the particles and hardly affects the overall motion of the fluid; hence gravity and viscous force are dominant for particle motion while gravity and inertial force are dominant for the fluid motion. This two-separate-scaling concept, one for the fluid and the other for particles, is validated by the fact that the flow is hardly influenced by adding particles into the fluid. This two-separate-scaling concept can offer a useful scale modeling technique if particles are relatively few,
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so that the motions of fluid and particles can be considered independently, leading to the following scaling laws: Flow of fluid; Fg f = ρ f g L 3t
Gravitational force on fluid Inertial force on fluid
Fi
f
= ρ f L 2t V 2
We obtain the pi-number as: π4 =
Fg f ρ f g L 3t = −−−−→ Fi f ρ f L 2t V 2 ↑ g = g
L t = Lt
V V
2 (3)
Motion of one particle: Gravitational force on one particle Viscous force between fluid and particle
Fg p = ρ p − ρ f g d 3 Fv p = μ d V
We obtain the pi-number as: π5 =
Fv p μd V = Fg p ρp − ρ f g d3
−−−−→ ↑ ρ f = ρ f ,
μ = μ ,
ρ p = ρ p
d d
2 =
V V
(4) Four forces are identified as affecting motion of the fluid and particles, producing three pi-numbers. However, the magnitude of forces’ action on the fluid is much bigger than forces’ action on particles. This can justify the use of two independent length scales: L for the fluid, and d for the particles, and to justify ignoring the third pi-number to be formed between the motion of the fluid and particles. As a result, the remaining two pi-numbers can yield the following scaling relationship. L t = Lt
d d
4 (5)
Case 4: Large Diameter Particles with High Specific Mass Density (d > 0.2 mm) With an increasing number of particles, the overall flow of fluid is affected by the increasing apparent fluid density; thus, the exchange of momentum between particles and the fluid becomes important. Therefore, the de-coupling assumption made for Case 3 between the motion of the fluid and small and low density particles invalid. As a result, the following four different forces are important: the inertial force and
Scaling Laws for Sedimentation Process in Water Flow-Driven Sedimentation Tanks
385
gravity acting on the mixed fluids (fluid and particles), and viscous force and gravity acting on each particle. These forces can be written using the representative parameters as follows: Fg f
Gravitational force on fluid Inertial force on fluid
Fi f Fv p = μ d V N Fg p = ρ p − ρ f g d 3 N
Viscous force between fluid and particle Gravitational force on particles
From these four forces, π4 , π5 and following pi-numbers are formed: Fg f ρ f g L3 π6 = = Fg p ρp − ρ f g d3 N
−→ ↑ ρ f = ρ f , ρ p = ρ p
N = N
L t Lt
3
d d
3 (6)
As a practical matter, it is not easy to adjust sand particles based on the scaling laws (6). Thus, it makes sense to use the same particles for both prototype and model. Using water as the fluid, this requirement can be satisfied by adjusting the temperature of the water, since viscosity of water is a strong function of temperature while density of water remains almost unchanged with a change in the temperature of water. As a result, the following scaling laws will be obtained. π7 =
π6 =
Fv p μd V N = Fg p ρp − ρ f g d3 N
Fg f ρ f g L3 = Fg p ρp − ρ f g d3 N
ρ f = ρ f ,
ρ f = ρ f ,
−→ ↑ ρ p = ρ p , d = d −→ ↑ ρ p = ρ p ,
d = d
μ V = μ V N = N
L t Lt
(7) 3
(8) Therefore, from π4 and π7 , L t = Lt
μ μ
2 (9)
Scale Model Experiments Scaling laws for Case 1 and Case 2 are rather general and have less practical value compared to the more specific Case 3 and Case 4. The following two different types of scale model experiments were, therefore, designed to validate Case 3 and Case 4 scaling laws.
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The Case 3 Scale Model Experiment Figure 3 shows two geometrically similar open channel sedimentation tanks with key dimensions (the numbers in Figure 3 are in millimeters and the numbers in parentheses are for 1/2 scale model). Water was used as fluid; incoming velocity from the nozzle was adjusted by the scaling laws π1 and π4 . Garden sand whose particle diameter ranges from 1 mm to 10 micron was refined by using several fine mesh screens to obtain approximately normal distribution of particle sizes whose average particle density was approximately 3–4 g/cm3 . Sedimentation ratio is defined as the ratio of sedimentary particle weight of particular size to the original weight of the corresponding size of particles with known size distribution. Small styrofoam particles of approximate average diameter (2–3 mm) were sprinkled on the free surface of running water; average velocity was measured by measuring the time required for the Styrofoam particles to move from the inlet of the sedimentation tank to the outlet. This observation confirmed that the surface flow is nearly uniform along the width direction. Movement of small sand particles in the water was observed from the side; flow pattern along the depth of sedimentation tank was very complex creating a stable large circulation accompanied with a few unstable periodically appearing small circulations. Given the sedimentation ratio as defined above, it can be expected that the ratio will increase with an increase in particle diameter. Figure 4 plots the sedimentation ratio as a function of particle diameter. When the scaling laws π1 and π4 are satisfied in the above scale model experiments, the Fig. 4 plot is expected to behave according to the trend shown in Fig. 2 where the sedimentation velocity is plotted as a function of particle diameter. The feeding time of particles was relatively short compared with the time associated with particle transport and sedimentation;
Fig. 3 Schematic of cross-section of scale model sedimentation tank
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Fig. 4 Sedimentation ratio vs. particle diameter
therefore, the particle feeding time was not adjusted by scaling laws. Particles were continuously fed into the water stream with little disturbance of the water flow, and distribution of particle diameter was measured by a micro-photographic method [5]. Figure 4 shows the relationship between particle diameter and sedimentation ratio. For large diameter particles, a single length scale represents dimensions of the tank and the diameter of particles. Therefore, when d/L is kept the same for both prototype and model, the sedimentation ratio is expected to be the same for both. The sedimentation ratio plotted against d/L is shown in Fig. 5, which reveals, as expected, that the sedimentation ratios of prototype and model are the same for large particles, but that they become different for small particles. For small diameter particles (d < 0.2 mm), the sedimentation ratio is expected to be equal, when d/L 1/4 is kept the same in prototype and model. The experimental results
Fig. 5 Sedimentation ratio vs. d/L
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Fig. 6 Sedimentation vs. d/L 1/4
in Fig. 6 show that the sedimentation ratio of prototype to model is almost the same for small diameter particles (d < 0.2 mm), while for larger diameter particles (d > 0.2 mm) the sedimentation ratio remains the same for both model and prototype. Figure 4 shows that there is a critical particle diameter (0.2 mm) that can sharply separate the sedimentation ratio into two different regimes. The existence of this sharp transition caused by the 0.2 mm particle diameter justifies separating the sedimentation process into four different regimes and developing scaling laws for each case. Without the sharp transition, this categorization idea would not work as well as in this study.
The Case 4 Scale Model Experiment Sand particles whose diameter ranges from 0.05 mm to 0.1 mm can satisfy the condition for Case 4. The mixed fluid with a weight ratio of 5:2 for water to particles was fed into the apparatus shown in Figure 3 with the feeding time adjusted by scaling law (8). To satisfy the scaling law (7), water temperature for model was adjusted to 12◦ C and for prototype to 24◦ C. Sedimentation ratio was then measured for each run and some experiments were repeated several times to obtain better than 90% repeatability. Figure 7 shows the relationship between sedimentation ratio and Lμ2 , validating the scaling law prediction.
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Fig. 7 Lμ2 and sedimentation ratio
Conclusion This study has shown that sedimentation problems can be dealt with in four different cases. For each case, scaling laws were developed. Case 1: Relatively large sedimentation particles, Case 2: Relatively small sedimentation particles, Case 3: Sedimentation particles with low specific mass density and relatively small diameter, and Case 4: Sedimentation particles with high specific density. Two scale models of different size with geometrical similarity were designed and sedimentation ratio was measured. Scale model experiments were designed to validate the two most typical cases with highest practical applications: Case 3 and Case 4. For Case 3, two independent length scales were introduced and scaling laws (3) (4) and (5) were developed. For Case 4, a single length scale represents both dimensions related to the sedimentation tank and particle diameter, requiring particle diameter to be changed based on the scaling law (6). To avoid this difficult condition, a scaling law (7) that allows the same particles for both prototype and model was developed from the concept that viscosity of water strongly depends on water temperature while density remains almost unchanged, finally resulting in scaling laws (8) and (9) for Case 4. As a result, scale model experiments validated the above scaling laws for Case 3 and Case 4. Acknowledgments I would like to acknowledge the late Professor Ichiro Emori of Seikei University, who inspired me to study scale modeling research and provided me with continuous support and encouragement through this study. I also would like to acknowledge Professor K. Saito of University of Kentucky, who read the manuscript, provided many useful comments and edited this paper to its final form.
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References 1. D. M. Thompson, “Scaling laws for continuous flow sedimentation in rectangular tanks,” Proc. Inst. Civ. Eng. Vol. 43, 387, 1969. 2. I. Emori, K. Saito, and K. Sekimoto, Mokei Jikken no Riron to Ohyou (Scale Models in Engineering), in Japanese, Third Edition, Gihodo, Tokyo, Japan, 2000. 3. G. Murphy, Similitude in Engineering, Ronald Press, New York, NY, 1950. 4. Japan Society of Mechanical Engineers Handbook, Vol. 6 Fluid Mechanics, p. 24, 1966. 5. J. Volckens, T.M. Peters, J. Aerosol Science, Vol. 36, 1400–1408, 2005.
Scaling of Molten Metal Brazing Phenomena: Prolegomena for Model Formulation Dusan P. Sekulic
Abstract This paper discusses a model of heat, momentum, and mass transfer prior to formation of an equilibrium membrane of the free surface, but after formation of a molten metal micro layer and/or metal filler liquid drop during brazing. Empirical evidence related to joint formation performed in a controlled atmosphere brazing is reviewed first. Aluminum brazing is considered as an example. This evidence includes the topology and morphology of a joint zone before and after joint formation. Based on understanding of involved phenomena, an analytical model of a molten metal micro layer of a sessile drop is discussed. A set of dimensionless parameters that governs the process is extracted from the model, and the orders of magnitudes of these parameters are assessed. Keywords Modeling · scaling · brazing
Nomenclature c D cp F g k L Lx n p q q
Concentration, (characteristic c∗ ) Diffusion coefficient, m2 /s Specific heat, J/(kg K) Body force, N Acceleration of gravity, = 9.81 m/s2 Thermal conductivity, W/(m K) Length, m Wetting length, m Unit normal vector pointing out of liquid, m Pressure, Pa Heat transfer rate, W/m2 Rate of internal heat generation, W/m3
D.P. Sekulic Department of Mechanical Engineering, University of Kentucky Center for Manufacturing; College of Engineering, University of Kentucky, Lexington, KY 40506, USA
K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
391
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rc R Sgen Sc t t T T u v v x, y
D.P. Sekulic
Volumetric mass generation rate, kg/(s m3 ) Curvature, 1/m Entropy generation rate, W/K Entropy generation rate (diffusion), W/K Time, second Unit tangent vector Temperature, K Stress tensor, Pa Velocity component in x direction, m/s Velocity component in y direction Velocity vector, (u, v), m/s Cartesian coordinates, m
Special Symbols ℵ O(.)
Reaction rate coefficient, m/s2 Slip coefficient, m Order of magnitude
Acronyms and Dimensionless Parameters AA Re Sc Bo Ca Da Pr
Aluminum alloy Reynolds Number, dimensionless Schmidt Number, dimensionless Bond Number, dimensionless Capillary Number, dimensionless Reaction Number, dimensionless Prandtl Number, dimensionless
Greek Letters Φ β γT γc κ μ θ ρ σ
Dissipation function, 1/s2 Coefficient of thermal expansion, 1/K Thermal Marangoni effect coefficient, J/(m2 K) 3 Solutal Marangoni effect coefficient, J/(m2 kg/m ) Tanner law constant, m/s Dynamic viscosity, Pa s Static advancing contact angle, radian Density, kg/m3 Surface tension, N/m
Scaling of Molten Metal Brazing Phenomena
393
Subscripts free init rad w, y = 0
Free surface, gas-molten metal interface Initial Radiation at the wall (core metal interface)
Introduction Joint formation of a molten cladding during brazing is a complex surface tension driven phenomenon. Transient nature of the process, intricate physics-chemistry of the interaction between molten alloy and its substrate, chemical reactions between molten flux, oxide layer, molten metal and background atmosphere, mass transfer due to diffusion and core metal dissolution, and last but not least, diffusion controlled melting and re-solidification, make the joint formation extremely difficult to model [1–3]. First, a review of empirical evidence and an identification of relevant physical processes will be discussed. Second, a general analytical model of the molten metal micro layer of a sessile drop after melting but prior to formation of the joint free surface during brazing will be compiled. Physical setting featuring the so-called brazing sheet and/or filler sessile drop will be considered. Third, a selection of a set of dimensionless parameters that govern the process based on appropriate scales will be offered. Aluminum brazing will be considered.
Empirical Evidence A brazing sheet presents a composite of a core metal and a cladding layer(s), Fig. 1a–c. The cladding layer represents usually between 5 and 10% of the total sheet mass. An alternate physical setting (considered here) is a sessile drop configuration, Fig. 1d (AA4343 disc melts over AA3003 substrate). Clad (brazing sheet) or filler metal (sessile drop), say an aluminum alloy with increased content of silicon (AA4343), has a liquidus temperature lower than the
Core
AA3003 Detail A
Cladding
AA4343
38 microns Detail B Interface
Si particles
(a)
(b)
Detail A
(c)
Detail B
1mm
(d)
Fig. 1 Aluminum brazing sheet: (a) fin-tube segment; (b) brazing sheet cross section; (c) a SEM image of the detail B from (b), rotated; (d) a sessile drop filler spreading
394
D.P. Sekulic 700 690
o T C
1-100-3
680 670 660
Heater temperature
650 640 630 620 610
Cladding Surface
605 deg. C
600 590 575 deg. C
580 570 560 550 540 530 520 510
(a)
Run # 042500 AA4343/AA3003
Braazed in 99.999 Nitrogen
600
1-100-18
(b)
500 660
720
780
840
900
960
Time, seconds
Fig. 2 Brazing process: (a) Surface temperature history; (b) process outcome: a brazed joint of Fig. 1a
liquidus temperature of the core (AA 3003, an alloy with a small Si content and often increased Mn and/or Mg content). Following a precisely guided temperature ramp and a dwell at the peak brazing temperature, the molten micro layer is formed. Liquid metal flows into joints (if a mating surface exists) governed predominantly by surface tension, and upon joint formation, solidifies, see Fig. 2. The joint free surface shape at the onset of solidification represents an equilibrium membrane characterized by a geometry that corresponds to the minimum potential energy of the free surface [3]. The process of joint formation is fast, and the period of time between liquefaction and equilibrium membrane formation is of the order of magnitude of 10−2 –100 seconds. Characteristic dendrite structure of Al alpha phase, [1] is noticeable along with the eutectic needle-like phase, Fig. 2b. Very often, dissolution of the core metal in the molten cladding is present [3]. Typical brazing conditions for aluminum alloys are listed in Table 1. The order of magnitude of physical properties of liquid/solid materials involved is given in Table 2. At the end of the molten metal flow phase, a joint features an equilibrium membrane shape of the free surface of molten metal. Its overall geometry, as indicated
Table 1 Order of the magnitude of the parameters defining conditions at the peak brazing temperature Variable
Units
Order
Temperature range Time span Length scale Pressure Background atmosphere O2 level Flux coating
K Sec m Pa ppm
102 –103 10−2 –101 10−2 –10−5 10−1 –105 101
g/m2
100
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395
Table 2 Order of the magnitude of the physical properties Property
Units
Order
Density Viscosity Diffusion coefficient Surface tension Thermal conductivity Thermal diffusivity Specific heat Prandtl number
kg/m3 Ns/m2 m2 /s N/m J/(s m K) m2 /s J/(kg K) –
103 10−3 10−6 100 102 10−5 103 10−2
Inert atmosphere Radiation heating
Re-solidified clad y = y(t, x) Molten clad
y
Si Diffusion Solid clad or filler to be melted
Filler
Dissolution
Clad
x
Clad AA4343 Core AA3003
Substrat
Setting of the
Fig. 3 Physical setting: (a) schematic; (b) Cladding-substrate interface after brazing
above, depends also on mating surfaces’ shape and orientation, see Fig. 1a and 2b for a typical fin-tube joint of a compact heat exchanger. The molten metal phase takes place between the initial cladding solid state condition, presented in Fig. 1b and c (i.e., an initial solid state), and the final re-solidified state, Fig. 2b, see Fig. 3a for a complete sequence. Molten metal wets the substrate/mating surface core metal, and interacts with the core metal of both mating surfaces and, in general, with the surrounding atmosphere. Dissolution of the core in the molten metal may be considerable, Fig. 3b. Hence, the flow of molten metal is dependent on not only wetting conditions dictated by surface conditions, viscosity and inertial forces, but also on the associated reactions, including the influence of flux (potassium fluoraluminate), as well as the background atmosphere interaction with the molten alloy and flux.
Model of a Reactive Cladding/Filler Flow System Configuration The object of our inquiry is the molten cladding after melting but before solidification, exposed to a thermal radiation, governed by surface tension and gravity toward
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the joint region between mating surfaces and retarded by viscosity forces. In this preliminary model building, we will consider a 2-D configuration. A schematic of the physical situation under consideration is presented in Fig. 3a (filler in the form of a sessile drop is taken as an example). Let us summarize again the main phenomena involved. (1) Molten cladding flows under the influence of capillary forces due to a substantially reduced contact angle between the liquid metal and substrate (caused by the action of flux). (2) The influence of gravity is present but not dominant. (3) Uniform radiation heat flux provides the energy for the phase change, but it is not necessarily considered as a direct governing force of the flow. (4) The molten micro layer exchanges heat with substrate by conduction and convection. In addition, heat transfer by free and/or forced convection and radiation (dominantly) takes place between the cladding and the surroundings. (5) The substrate temperature is not necessarily constant if a non-eutectic Al-Si alloy is used as cladding (such as AA4343). This is because the melting process requires a range of temperatures to be accomplished. Still, the high thermal conductivity of aluminum ensures that the temperature of the substrate stays roughly constant. (6) During molten metal flow, a silicon rich liquid metal is in contact with substrate lean in silicon. Consequently, a substantial diffusion of Si may take place if the peak brazing temperature is sufficiently high for a prolonged period of time. Hence, this phenomenon must be included when considering reaction on the interface between the core and molten cladding. (7) In the surroundings, a high purity Nitrogen (99.999) is used with very low dew point temperature (−45 ◦ C or lower) and very low oxygen level concentration (see Table 1). Consequently, interactions at the free liquid surface may be considered as not significant. Due to improved wetting (as a consequence of the flux action), the contact angle between liquid and base metals may be expected to be small [of an order of magnitude of O(101 ) degrees.]
System of Governing Equations The physical problem described in previous section has never been modeled in its entirety, except for soldering [4]. However, studies of wetting of organic fluids, and most recently solders over a plane surface, in particular spreading without reaction with the substrate [5, 6, 7, 8, 11] or with reaction processes [4], [12], have been published. A process in which an interface between molten metal and substrate plays a key role in spreading is extremely complex and defines so far all the efforts to be fully described, even for significantly lower temperature situations, such as soldering [4]. Hence, the present discussion is an effort directed toward only a qualitative description of the main features to be included in a model, and it is based on the corresponding model for soldering [4]. In general, a 3-D configuration must be considered, imposed by a complex geometry of non-planar and non-orthogonal mating surfaces. Thus, the initial set of governing equations is as follows.
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(i) continuity for total mass D + ρ∇ · v = 0 Dt
(1)
(ii) momentum ρ
Dv = −∇ p + μ∇ 2 v + F Dt
(2)
(iii) energy ρcp
Dp DT = ∇ · (k∇T ) + βT + μΦ + q Dt Dt
(3)
(iv) concentration of a single species ρ
Dc = ∇ · (ρD∇c) + rc Dt
(4)
(v) entropy Sgen =
k T 2 (∇T )2
+
μ ⌽ + Sc T
(5)
Based on the empirical evidence reviewed in the previous section, the following set of idealizations may be invoked. (i) The problem may often be considered as two-dimensional. A typical cladding sheet application, such as the one presented in Fig. 1b, involves cladding thickness of an order of magnitude of 10−6 –10−5 m and the distance between the two joints of an order of magnitude of 10−3 –10−2 m. The length scale in the third direction (z direction) is of an even larger order of magnitude, e.g., 10−2 m. The empirical evidence (see Fig. 4) clearly indicates that a 2D configuration is often a sufficient representation. In the example considered here (a sessile drop configuration, Fig. 1d) clearly, a 2-D representation suffices. (ii) Thermophysical properties are idealized as constant. This idealization should be considered as a first approximation. Strictly, it is not possible to consider either density or other properties as constant. Therefore, a continuum mixture model should be adopted for a more realistic representation (not included here). If a non-eutectic Al + Si alloy is present, at a given moment in time, and given temperature at the peak brazing temperature level, only a portion of the cladding is in the liquid state. So the system’s boundary encloses a non-homogeneous region. The triple line speed, if cladding is represented by an advancing layer (an elevated “drop”) of molten metal may
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(iii) (iv)
(v)
(vi)
(vii)
D.P. Sekulic
be fast [O(100 –101 m/s)] and the temperature changes in a narrow range. Still the joint formation may last much longer [e.g. O(101 s)] to fill the joint at a distance L of O(10−2 m). So, the property values are considered as bulk (average) values. Surface tension depends linearly on temperature, and concentration; i.e., in general, surface tension may be described as follows: σ = σw −γT (T −Tw )−γc (c−cw ), σw = σ (Tw ). However, the Si concentration change is small, but not negligible [< O(100 %)], and the temperature change during the molten phase is limited (< 101 K), but still sizable. So, if thermocapillary effects have to be included, the surface tension will be considered as a linear function of temperature. The order of magnitude of thermophysical properties is given in Table 2. The flow is considered as incompressible. This assumption is justified for a molten metal flow. The only body force is gravity and any influence of electromagnetic and other forces may be neglected. The influence of gravity is sizable only for very large joints [the Bond number is usually of the order of magnitude of O(10−5 –10−2 )] Molten cladding is considered as a fluid in which the stress associated with motion depends linearly on the instantaneous value of the rate of deformation and it is isotropic, i.e., the fluid is Newtonian. This idealization should be considered as a first approximation because molten cladding is not necessarily isotropic. Energy source and energy dissipation terms in the energy equation may be neglected in the first approximation. This is possible because, first, O{[ρcp ] × [u] × [⌬T /L]} >> O{μ(⌬u/L)2 } (see Table 2 for the order of magnitude of thermophysical properties) and dissipation is negligible. Second, the molten metal is considered as a mixture model continuum [see the comment (ii) above]. So, Eqs. (3) and (5) may be simplified accordingly. Although chemical reaction is possible on the molten metal boundaries, it is idealized that the species generation term in mass conservation equation for a diffusion process between core and clad can be neglected. Diffusion coefficient is considered as constant in the first approximation because the temperature change is relatively small. The free surface does not interact with the inert atmosphere. Also, diffusion contributions to the entropy generation would not exist and Eq. (5) can be simplified accordingly.
Boundary Conditions A rather difficult task in setting-up a mathematical model of the phenomena under consideration is the selection of boundary conditions. The free surface of the molten sessile drop is described by y = yfree (t, x), i.e., it is not a constant. The free surface of a molten clad micro layer may be considered as constant, i.e., the substrate interface, see Fig. 3a, at y = 0, t = 0, is defined as y = yfree = const and at t > 0, y = yfree = const.
Scaling of Molten Metal Brazing Phenomena
# v # y=0 = 0 # ⭸u u # y=0 = ℵ ⭸y # T # y=0 = Tw # # D ⭸c c ## y=0 = + c∗ ⭸y
399
(6) (7) (8) (9)
In Eq. (7), ℵ represents the slip coefficient which in general may be different than zero. The slip coefficient may be considered as equal to zero, i.e., no slip ℵ = 0, except close to the contact line of advancing liquid over a substrate [8]. Equation (9) models the dissolution rate at the interface. Dissolution is omnipresent in brazing whenever the reaction rate (controlled by the coefficient in Eq. (9), [4]) is different than zero. At the free surface, y = yfree (t, x) = const, one may adopt the same dynamic conditions involving balancing normally and tangentially the stress components as suggested by [6]: n · T · n = Rσ
(10)
t · T · n = t · ∇σ
(11)
In Eq. (10) R represents the free surface curvature. The heat transfer condition must be consistent with the imposed relatively rapid heating [O(101 –102 K/s)] as often present in a brazing process [10]. A standard brazing process is accomplished by radiation heating, therefore, −kn · ∇T = qrad v−
(12)
⭸yfree ⭸yfree = u ⭸t ⭸x
(13)
n · ∇c = 0
(14)
Equation (13) represents the kinematic condition on the free surface. At that surface, there is no mass transfer (as far as the selected single species is considered), Eq. (14). Initial conditions include a given initial shape of the molten layer (say, yfree = const., or, in the more general case a shape that depends on x coordinate, as for the sessile drop), and the temperature, and concentration in the molten metal at t = 0. To complete the problem formulation, additional conditions regarding constant volume of the molten cladding/filler and the magnitude of the contact angle between the molten mass and substrate should be specified [4].
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Dimensionless Parameters Scales Based on the phenomenological description of heat, mass, and momentum transfer processes given in previous two sections, a selection of scales may be suggested. The scales are compiled in Table 3. Table 3 Scales Entity
Scale
Length
x-direction y-direction x-direction y-direction Length/velocity Energy balance at yfree Momentum balance Driving potential
Velocity Time Temperature Pressure Concentration
Lx Lx × tan() × tan() Lx /() (qrad Lx )/k ()/(Lx ) cinit − c∗
Parameters Using the scales given in Table 3, and rewriting the governing equations and boundary conditions one may arrive at the set of dimensionless parameters that control the process. Due to the limited space, the cumbersome but straightforward algebraic manipulation of these equations is omitted and the selected dimensionless numbers (only the most prominent) were compiled in Table 4. Table 4 Dimensionless parameters Name
Dimensionless parameter
Reynolds number Prandtl number Schmidt number Bond number Capillary number Reaction number
(Lx )/(/) (/)/(k/cp ) (/)/D (gLx 2 )/ ()/() (Lx )/D
Re Pr Sc Bo Ca Da
Discussion The selection of dimensionless parameters compiled in Table 4 does not include all the parameters that may be devised from a proposed model if some of the imposed idealizations are relaxed. For example, if the surface tension variations with temperature and concentration become sizable, the thermocapillary and solutocapillary effects must be included. In other words, both thermal and solutal Marangoni
Scaling of Molten Metal Brazing Phenomena
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numbers may be defined as discussed in [4] for soldering. In that case, the spreading may be retarded because γT > 0 [9], and γ < 0 (assumed). If not steady state, a Biot number devised from a heat transfer balance will indicate the transient nature of the process. The significance of dimensionless numbers involving entropy, in particular in the light of the process evolution (i.e., the dendrite growth and solidification) will be discussed elsewhere. However, the key problem in any further development of the model of this process is not necessarily an approach to the solution of the model equations, but a lack of reliable data for molten cladding properties and process parameters. These include diffusion and reaction coefficients, viscosity, thermal conductivity and surface tension of the mixture of molten cladding and molten flux. To make the situation worse, the influence of flux (for example, Kx Aly Fz , that melts prior to the cladding) on the process and properties is not sufficiently known. Some data on properties of the molten fluorides (such as K3 AlF6 − KalF4 ) had been investigated (see, for example, [15]). Also, the influence of this eutectic mixture on the process has been considered [14], [16], but many aspects of the phenomena are still unclear. The influence of gravity, as indicated by the small Bond number, is evidently small but it cannot be neglected if the joint becomes larger, and if the curvature of the mating surfaces has to be included into consideration. These influences are not included in the model discussed here. It may be speculated that dimensionless parameters relevant for this type of modeling would include the following: Re > 103 , Pr < 10−1 , Sc < 103 , Ca > 10−2 , Bo < 100 , and Da < 102 .
Conclusion The phenomenological study of molten cladding behavior during aluminum alloy brazing indicates that main influences may be identified, despite of its complexity. The model considered follows a similar model suggested for soldering. These include the trade offs between surface tension and gravity, viscosity and pertinent dynamic forces including reaction with the substrate, and topology of the configuration. As a prerequisite of a reliable prediction of this behavior, a thorough study of thermophysical properties of molten cladding/filler (including flux) is mandatory. Furthermore, the process parameters at the micro level are still not known and the verification of any such model must wait their determination. Acknowledgments This work was supported in part by the National Science Foundation (NSF Grant DMI-990831 monitored by Dr. Delcie Durham) and Kentucky Science and Engineering Foundation (KSEF Grant KSEF-829-RDE-007). The assistance of Dr. C. Pan and Mr. R. Anderson in preparing metallographic micrographs and SEM images at the early stages of the research is gratefully acknowledged. This article represents a modified version of a paper presented at the Third International Symposium on Scale Modeling, September 10–13, 2000, Nagoya, Japan, under the title: “Molten metal micro layer prior to joint formation during brazing. Prolegomena for a scaling analysis.”
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References 1. Sekulic, D.P., Galenko, P.K., Krivilyov, M.D., Walker, L., and Gao, F., 2005, International Journal of Heat and Mass Transfer, Vol. 48, pp. 2385–2396; Part 2, International Journal of Heat and Mass Transfer, Vol. 48, pp. 2372–2384. 2. Zhao, H. and Sekulic, D.P. 2006, Heat Mass Transfer, Special issue (Ed. Prof. C Amon), Vol. 42, pp. 464–469 3. Sekulic, D.P., Gao, F., Zhao, H., Zellmer, B., and Qian, Y.Y., 2004, Welding Journal, Research Supplement, Vol. 83, No. 3, pp. 102s–110s. 4. Braun, R.J., Murray, B.Y., Boettinger, W.J., and McFadden, G.B., 1995, Phys. Fluids, Vol. 7, pp. 1797–1810. 5. Dussan V., E.B., 1979, Annu. Rev. Fluid Mech., Vol. 11, p. 371-. 6. Ehrhard, P. and Davis, S.H., 1991, J. Fluid Mech., Vol. 229, pp. 365–388. 7. Gennes, de, P.G., 1985, Reviews of Modern Physics, Vol. 57, No. 3, Part 1, pp. 827–863. 8. Greenspan, H.P., 1977, J. Fluid Mech., Vol. 84, Part 1, pp. 125–143. 9. Hutch, J. E. (ed.), 1984, “Aluminum, Properties and Physical Metallurgy,” ASM, Metals Park, OH, pp. 15–16. 10. Humpson, G. and Jacobson, D.M., 1993, “Principles of Soldering and Brazing,” ASM International, Materials Park, OH, pp. 27–28. 11. Hocking, L.M., 1995, Phys. Fluids, Vol. 7, pp. 1797–1810. 12. Meier, A., Chidambaram, P.R., and Edwards, G.R., 1998, Acta mater., Vol. 46, No. 12, pp. 4453–4467. 13. Rivas, D. and Ostrach, S., 1992, Int. J. Heat Mass Transfer, Vol. 35, pp. 1469–1479. 14. Takigawa, J. and Okimoto, T., 1993, Kobelco Technology Review, No. 16, pp. 34–38. 15. Thomson, W.T. and Goad, D.G.W., 1976, Can. J. Chem., Vol. 54, pp. 3342–3349. 16. Yamaguchi, M., Kawase, H., and Koyama, H., 1993, Furukawa Review, No. 12, pp. 145–149.
Sound Insulation Analysis of a Resin Composite Material Using the Homogenization Method Kohei Yuge and Susumu Ejima
Abstract We propose a numerical method to predict the noise transmission loss of a resin composite cover, which considers the effect of the shape and the material properties of the microscopic reinforcements in a resin-composite. The mean material properties of the material are calculated with the homogenization method and the acoustic structural coupling analysis is made with the obtained material constants. The calculated results show that the sound insulation levels are affected seriously by the shape or rate of the reinforcements in the material, which suggests that the present method can be a good numerical method to determine the reinforcements in a resin to improve the sound insulation ability. Keywords Multi-scale · visco-elastic homogenization method · sound insulation analysis · resin
Introduction Resin composite materials are being used in a wide variety of structures. Their primary purpose in most cases is to increase the strength and reduce the weight of the structure. For this reason, composites are being used in engine covers of automobiles and aerospace vehicles where such features are highly advantageous. Furthermore, resin composite materials have a damping effect with their viscosity, so composite materials also play a major role in controlling noise and vibration problems in industry. However, most of the time, noise and vibration problems happen after the structure is developed, and designers do not anticipate these unexpected problems. The reason is that structures not only exist in isolation but also are attached to other structures or are surrounded by air. What is more important is that structural damping has a great influence on these problems. Usually, the phenomena of structure-sound interaction can be solved with simple, ideal formulations because of the complex geometry and non-linear behavior of the material. These simple classical solutions K. Yuge Department of Mechanical Engineering Seikei University, Kichijyoji Kitamachi 3, Musashino-city, Tokyo, Japan
K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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are convenient for understanding the phenomena in an experimental measurement, but these solutions are not detailed enough for real structural problems such as automobiles. Therefore, detailed computational prediction methods are important to help the engineer predict the various noise and vibration problems. We present a numerical prediction method of the sound insulation level of a cover composed of resin and microscopic reinforcements such as glass fibers. Although it is known that the shape or size of microscopic reinforcements has a significant influence on the damping characteristic of the resin composite material as well as stiffness, a numerical prediction method of the dynamic behaviors of a resin composite material considering these effects had not been established when we began our work. The homogenization method [1], whose finite element implementation for linear elastic analysis was shown by Guedes and Kikuchi [2] in 1991, is promising in that this method gives mean material constants of the composite material without any empirical assumptions if the material constants of each component are known. This method has been applied to the elasto-plastic analysis of a composite material by Terada and Kikuchi [3]. In the homogenization, method it is usually assumed that the composite material is locally formed by very small periodical microstructures compared with the overall “macroscopic” dimensions of the structure of interest. Hence the material properties are periodical functions of microscopic variables where the period is very small compared with the macroscopic variable. We extend this method to the visco-elastic kinematics of a resin composite material, where the constitutive equations of a resin are expressed with Zener model while those of reinforcements are assumed to be elastic. The obtained result is applied to the two dimensional acoustic-structure coupling analysis where both an acoustic area and a structure are discretized by the finite element method and the direct time integration scheme is employed. As a numerical example, sound insulation levels of a cover made of a resin composite material are calculated, where several kinds of reinforcements are assumed. The calculated results show that the sound insulation levels are affected seriously by the shape or size of the reinforcements in the material, which suggests that the present method can be a good numerical method to determine the reinforcements in a resin to improve the sound insulation ability.
Visco-Elastic Finite Element Analysis Based on the Homogenization Method Visco-Elastic Constitutive Equations for Resin Material The constitutive equations of resin were modeled by the generalized Zener model, which is composed of a spring unit (Unit 1) and spring-dash-pot one (Unit 2) as shown in Fig. 1. Unit 1 gives the elastic relation while Unit 2 gives the viscous property of the material. The uniaxial stress σ can be expressed as the sum of σ e and σ v .
Sound Insulation Analysis of a Resin Composite Material Fig. 1 Zener model
405
Unit 1
σe E
σ
Unit 2
σv Ev
εv ε
σ = σe + σv
(1)
where σ e is the stress of Unit 1 and σ v is the stress of Unit 2. Using E and E v , we obtain the next equation σ = Eε + E v (ε − εv )
(2)
When we extend this theory to be a two dimensional problem, here it is assumed that the stress-strain and strain-displacement relations are v σi j = σiej + σivj = E i jkl εkl + E ivjkl εkl − εkl (i, j, k, l = 1, 2) ⭸u v 1 ⭸u k ⭸u l 1 ⭸u vk v εkl = + = + l εkl 2 ⭸xl ⭸xk 2 ⭸xl ⭸xk
(3) (4)
v is the strain viscosity. Differentiating the strain viscosity with respect to where εkl time, we assume v ε˙ kl
=γ
σ¯ − σ¯ e E
⭸⌽ ⭸σi j
(5)
v is obtained by the summation of the viscous where E is the Young’s modulus and εkl strain at every step analytically.
v εkl
t =
v ε˙ kl dt
(6)
0
Assuming E to be constant, E v is represented as follows. E ivjkl = β · E i jkl
(7)
where Φ is the flow potential and is chosen as the von-Mises yield criterion. The value of β, γ , n were determined such that the consequent stress strain curves at various strain rates were in good agreement with the experimental ones.
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Application of the Homogenization Theory Let us consider the two-dimensional structure composed of a periodical microstructure as shown in Fig. 2. The composite material is formed by spatial repetition of a microstructure made of resin and reinforcement. The resin is assumed to be viscoelastic and the reinforcement is assumed to be elastic. Now the dynamic equilibrium equations of a composite body may be described by ⭸σi j + X i − ρ u¨ i = 0 ⭸x j
(8)
where ρ is the density and X i is the body forces. On the boundary, both the traction and displacement may be applied. For instance, the following conditions are possible: ti = n j σi j
u i = Ui
(9)
where ti is the surface force (or traction) on the boundary ⌫t and Ui is the prescribed displacement on the boundary ⌫d . Substituting Eq. (3) into Eq. (8) we obtain the following equation. ⭸ ⭸x j
(
⭸u ε E i jkl k + E ivjkl ⭸xl
⭸u εk ⭸u εv − k ⭸xl ⭸xl
)
− ρ u¨ iε = 0
(10)
where the body force is ignored. uε represents an arbitrary displacement of the composite body. Since the reinforcement is assumed to be elastic, the governing equation of resin and reinforcement satisfy simultaneously the above equation. In the case of an elastic body, we assume the Young’s modulus of Unit 2 as follows. E ivjkl = 0
(11)
Multiplied by a weighting function vε and integrated in the whole domain, Eq. (10) becomes t i : Traction
Γ Ω
Γt
Xi : Body force
Γd X2
Reinforcement Resin
ui = Ui Prescribed displacement
X1
Y2
Y1
Fig. 2 Structure composed of a periodical microstructure
Sound Insulation Analysis of a Resin Composite Material
407
) ( ⭸2 u εk ⭸2 u εv k ε v v ε vi E i jkl + E i jkl − ρ u¨ i d⍀ = 0 − E i jkl ⭸x j ⭸xl ⭸x j ⭸xl
(12)
⍀
Applying Green’s theorem, we obtained the following weak form:
E i jkl + E ivjkl
⍀
⭸viε ⭸u εk d⍀ − ⭸x j ⭸xl
⍀
E ivjkl
⭸viε ⭸u εv k d⍀ − ⭸x j ⭸xl
ρviε u¨ εk d⍀ =
⍀
viε f iε d⌫
⌫
(13) Here we introduce both the global and local coordinate systems so that u can be represented by two different scales. One is X (x1 , x2 ) in the global coordinates of the microstructure, and the other Y (y1 , y2 ) in the local coordinates of the microstructure and ε(Y = X/ε) is the order of X-coordinates compared with the Y-coordinate. Entreating the higher order terms, the displacement at uε (x, y) can be expressed as the sum of the global and the microscopic displacement. ε
u εk = u 0k (x) + εu lk (x, y) + ε2 u 2k (x, y) + · · ·
(14)
where u0 is the average displacement at the microstructure and u1 , u2 are the microscopic displacements which are Y -periodic. Also uεv can be expressed as an asymptotic expansion with respect to the parameter ε. 0v 1v 2 2v u εv k = u k (x) + εu k (x, y) + ε u k (x, y) + · · ·
(15)
Partial derivative of Y-periodic function Ψ (x, y) with respect to x we obtain the next equation. ⭸Ψ ⭸Ψ ⭸y ⭸Ψ 1 ⭸Ψ ⭸Ψ (x, x/ε) = + = + ⭸x ⭸x ⭸y ⭸x ⭸x ε ⭸y
(16)
Here, the weighted function vε can also be expressed as an asymptotic expansion, and we obtain the next equation. 2 1 ⭸vk (x, y) 1 ⭸vk1 (x, y) ⭸vkε (x, y) ⭸v 0 (x) ⭸vk (x, y) 1 ⭸vk1 (x, y) + ε2 + ··· = k +ε + + ⭸xl ⭸xl ⭸xl ε ⭸yl ⭸xl ε ⭸yl =
⭸vk0 (x) ⭸vk1 (x, y) + + εR ⭸xl ⭸yl
(17)
where v1 , v2 is Y-periodic function and v0 is the zero on the boundary ⌫d . If ε is sufficiently small, substituting Eq. (17) into Eq. (13) we obtain as follows.
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E i jkl +
⍀
E ivjkl
⭸vk0 (x) ⭸vk1 (x, y) ⭸u iε + d⍀ ⭸xl ⭸xl ⭸x j
⭸vk0 (x) ⭸vk1 (x, y) − + ⭸xl ⭸xl ⍀ − ρvi0 u¨ εk d⍀ = vi0 f iε d⌫ E ivjkl
⭸u iεv d⍀ ⭸x j (18)
⌫
⍀
If Eq. (18) is rearranged using terms ⭸vi0 /⭸x j and ⭸vi1 /⭸x j with the first order perturbation u1 , u1v pq
u 1k (x, y) = −χk (y) pq
u 1v k (x, y) = −κk (y)
⭸u 0p (x) ⭸xq
(k, p, q = 1, 2)
⭸u 0v p (x)
(k, p, q = 1, 2)
⭸xq
(19)
where these χ (y), κ(y) are a sort of an independent quantity of characteristic deformations in the macrostructure. we get ⍀
⍀
⎡( ) ⎤ ⭸χrkl ⭸u 0k v v (E + E ) − (E + E ) i jkl i jr s i jkl i jr s ⎢ ⭸xl ⎥ s ⎢ ⎥ d⍀ − ρv 0 u¨ 0 d⍀ = v 0 f ε d⌫ ⭸y 0v kl i k i i ⎦ ⭸vk ⭸x ⭸x j ⎣ − E ivjkl − E ivjr s r ⌫ ⍀ ⭸ys ⭸xl (20) ⭸vi0
⭸vi1 ⭸y j
( (E i jkl + E ivjkl ) − (E i jr s + E ivjr s )
⭸χrkl ⭸ys
)
⭸u 0k ⭸κ kl ⭸u 0v k d⍀ = 0 − E ivjkl − E ivjr s r ⭸xl ⭸ys ⭸xl (21)
Here, we separate the macro- and microscopic equations and then derive the homogenization formulae. Equation (20) represents the macroscopic equation and Eq. (21) represents the microscopic equation. These equations are accomplished by taking the limit of ε to zero and the integral formula such that 1 Ψ (x, y) dY d⍀ (22) lim Ψ (x, x/ε) d⍀ = ε→0 |Y | ⍀
⍀
Y
where Y represents the base cell of the composite structure and |Y | stands for the area of the cell. Ψ (x, x/ε) is a Y-periodic function. If we assign a definite value to χ kl , κ kl which satisfies the following condition, Eq. (21) is formed naturally.
Sound Insulation Analysis of a Resin Composite Material
( Y
409
) ⭸χrkl ⭸v 1j E i jkl + E ivjkl − E i jr s + E ivjr s dY = 0 ⭸ys ⭸y j ⭸κ kl ⭸vi1 E ivjkl − E ivjr s r dY = 0 ⭸ys ⭸y j
(23)
(24)
Y
Solving Eqs. (23) and (24) on the periodicity condition, we are able to find the χ kl and, κ kl functions. With these functions we can define the homogenized material constants as follow. ) ( ⭸χkpq 1 E i j pq + E ivj pq − E i jkl + E ivjkl dY (25) E iHjkl = |Y | ⭸yl Y pq 1 vH v v ⭸κk E i jkl − E i jr s dY (26) E i jkl = |Y | ⭸yl Y
If Eq. (20) is rearranged using Eqs. (25) and (26), We can simplify the macroscopic equation as ⍀
⭸vi0 ⭸x j
E iHjkl
0v ⭸u 0k H ⭸u k − E ivjkl ⭸xl ⭸xl
d⍀ −
ρvi0 u¨ i0 d⍀ =
vi0 f i0 d⌫
(27)
Here we represent the weak form of the governing equations which consider the viscosity of the resin composite material.
Free Vibration of Cantilever Beam To verify the proposed constitutive equations, free vibration of the cantilever beam of the resin composite material as shown in Fig. 3(a) was simulated by the finite element method. The beam was assumed to be composed of an infinitely small periodic square microstructure which has glass particles as shown in Fig. 3(b). The radius of a glass particle r is changed depending on the glass content of the composite material. The material property of glass and resin is shown in Table 1 and the parameters (β, γ , n), included in Eqs. (5) and (7), are assumed by the experiment of free vibration of the cantilever in Ref. [4]. Parameter A (Room temperature) : β = 0.6, n = 2.0, γ = 5.0 × 105 . Parameter B (High temperature) : β = 0.6, n = 2.0, γ = 5.0 × 107 The beam was divided into 10 elements (1 × 10) and an initial velocity of 2.0 m/s was given at one end. Then several cases of different values of the glass content were calculated. The displacement-time relation at the free end is shown in Fig. 4 and
410
K. Yuge, S. Ejima 0.12m
Fig. 3 Two dimensional structure composed of a periodical microstructure
2.0 m/sec
0.0032m
X2 (a) Cantilever beam
1
X1 Glass Resin
3
ρ2
E2 ρ 1r E1
Y2
Y1 (c) Base cell
(b) Composite structure
Table 1 Material property of glass and resin Material
Young’s modulus (MPa)
Poisson’s ratio
Weight density (kg/m3 )
Glass Resin (room temp.) Resion (120 ◦ C)
65000 3000 1500
0.2 0.45 0.45
2450 1120 1120
Fig. 5. Figure 4 shows the room temperature and Fig. 5 shows the high temperature. As the radius of the glass particles becomes smaller (decreasing the weight percentage of the glass material), the damping effect is represented with the resin viscosity and also the number of vibrations becomes small because of a reduction in the rigidity of the cantilever. At the high temperature its effect is revealed remarkably. Because of the low numerical resolution the magnitudes of displacement at certain points are larger than the initial values in both figures.
Two Dimensional Acoustic-Structural Coupling Problem In this section, the sound insulation effect of the resin composite material is calculated by the finite element analysis based on the algorithm for two dimensional acousticstructural coupling problems. The structural element employed herein has four nodes with two degree of freedom at each node and acoustic element has four nodes with one degree of freedom at each node. And the explicit time integration scheme is used. The governing equations of the acoustic area are introduced by the linear wave equation
Fig. 4 Free vibration of cantilever at room temperature
Displacement mm
Sound Insulation Analysis of a Resin Composite Material
2 1 0 –1 –2 0.0
0.1
411
0.2
0.3
0.4
0.5
0.4
0.5
0.4
0.5
0.4
0.5
0.4
0.5
Displacement mm
Time sec
(a) Glass content 0% 2 1 0 –1 –2 0.0
0.1
0.2
0.3
Displacement mm
Time sec
(b) Glass content 27% 2 1 0 –1 –2 0.0
0.1
0.2
0.3
Displacement mm
Time sec
(c) Glass content 50% 2 1 0 –1 –2 0.0
0.1
0.2
0.3
Displacement mm
Time sec
(d) Glass content 75% 2 1 0 –1 –2 0.0
0.1
0.2
0.3
Time sec
(e) Glass content 100%
δρ ( p¨ ) d⍀ + ⍀
c (∇δp)(∇ p)d⍀ =
δρ
2
⍀
⌫c
⭸p d⌫c ⭸n
(28)
where ⭸ p/⭸n is the derivative in the direction normal to the boundary, ⍀ is the area, and ⌫c is the boundary of the acoustic-structural coupling surface. The governing equation of the structural area is introduced by Eq. (27). On the structural and acoustic interaction boundary, the acoustic particles are assumed to have the same velocity as that of the structure surface [5]. We use the staggered method [6] to solve those governing equations simultaneously. In this method Eqs. (27) and (28) are solved alternately in the same time step, exchanging each unknown quantity of each equation.
Fig. 5 Free vibration of cantilever at high temperature
K. Yuge, S. Ejima Displacement mm
412
2 1 0 –1 –2 0.0
0.1
0.2
0.3
0.4
0.5
0.4
0.5
0.4
0.5
0.4
0.5
0.4
0.5
Displacement mm
Time sec
(a) Glass content 0% 2 1 0 –1 –2 0.0
0.1
0.2
0.3
Displacement mm
Time sec
(b) Glass content 27% 2 1 0 –1 –2 0.0
0.1
0.2
0.3
Displacement mm
Time sec
(c) Glass content 50% 2 1 0 –1 –2 0.0
0.1
0.2
0.3
Displacement mm
Time sec
(d) Glass content 75% 2 1 0 –1 –2 0.0
0.1
0.2 0.3 Time sec
(e) Glass content 100%
Sound Insulation Analysis of Resin Composite Material To examine the noise reduction effect of the resin composite material, twodimensional acoustic-structural coupling problems are considered. The problems are shown in Fig. 6, where the sinusoidal pressure in the x-direction is given uniformly to the nodal points on the side s-s as a line sound source and a simple supported wall with both ends fixed, separates the acoustic area, which is divided into 200 elements (10×20). As shown in the figure, a radiation boundary is assumed to restrain sound reflection from the receiving room. The material properties of the resin and glass which are contained in the composite material, are also the same as
Sound Insulation Analysis of a Resin Composite Material Fig. 6 Line sound source covered by a composite material containing a glass particle
0.3 m
Plane wave
413
0.6 + tm t
C
S
0.3 m
Cover
b
Radiation boundary
X2 S'
X1
0.3 m
a
Wall
C'
Glass Resin
1 ρ2 E ρ 1 r
L
1
3
2
E1
Y2
Y2
ρ2
ρ1
E2
E1
Y1
Y1
(a) Glass particle
(b) Glass fiber
shown in Table 1. The visco-elastic constitutive equations using the homogenization method are applied to the resin composite material. For the purpose of comparison, the problems are also calculated with a resin composite material containing glass particles and glass fibers with the same surface density (13.7 kg/m2 ), so that the thickness(t) of the each noise barrier is changed depending on the weight percentage of the glass content as show in Table 2 and Table 3. The glass content is controlled by the radius of the glass particle r and the width of the glass fiber L in each microstructure. Figures 7 and 8 depict the Table 2 Noise barrier with glass particle Glass content (%)
Radius of Glass particle (r )
Thickness (mm)
0 27 50 75 100
0 0.2 0.3 0.4 –
12.2 10.4 8.82 7.25 5.6
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K. Yuge, S. Ejima Table 3 Noise barrier with glass fiber Glass content (%)
Width of Glass fiber (L)
Thickness (mm)
0 35 48 77 100
0 0.2 0.3 0.6 1
12.2 9.89 9.03 7.15 5.6
difference of mean sound pressure levels with glass particles at point a and b from time 0 s to 0.03 s for various frequencies of the source. Figure 7 shows parameter A and Fig. 8 shows parameter B. In both cases, transmission loss remarkably declined between 200 Hz and 400 Hz which is near the natural frequency of the noise barrier. Also 550 Hz, which is a point where the difference in distance from the sound source and the noise barrier multiplies integrally as against a half wave length, is the resonance frequency of the sound source room and the receiving room. So that in this frequency, the acoustic wave transmits the noise barrier without any loss. Generally it can be said that depending on the mass law, the wall which has the same surface density indicates almost the same transmission loss. But in this case it is different for each case. Figures 9 and 10 shows a composite material containing glass fibers. The Young’s modulus of resin composite material containing glass fibers is four times larger than that of material containing glass particles, so in general the bending stiffness of the noise barrier becomes rigid and the natural
40 35
Transmission loss dB
30 25 20 15 10 5
Fig. 7 Transmission loss for glass particle at room temperature
0
Glass 0% Glass 27% Glass 50% Glass 75% Glass 100% 100
1000
Frequency Hz
Sound Insulation Analysis of a Resin Composite Material Fig. 8 Transmission loss for glass particle at high temperature
415
40
Glass 0% Glass 27% Glass 50% Glass 75% Glass 100%
35
Transmission loss dB
30 25 20 15 10 5 0
100
1000
Frequency Hz
frequency also becomes higher. In the case of a high temperature there is a reduction in the rigidity of the noise barrier compared with room temperature. But each case indicates almost the same transmission loss as a noise barrier made of glass only (glass 100%).
40 35
Transmission loss dB
30 25 20 15 10 5
Fig. 9 Transmission loss for glass fiber at room temperature
0
Glass 0% Glass 35% Glass 48% Glass 77% Glass 100% 100
1000 Frequency Hz
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K. Yuge, S. Ejima
Fig. 10 Transmission loss for glass fiber at high temperature
40
Transmission loss dB
35 30 25 20 15 10 5 0
Glass 0% Glass 35% Glass 48% Glass 77% Glass 100% 100
1000
Frequency Hz
Conclusions The homogenization method for liner elastic analysis proposed by Guedes and Kikuchi (1991) was extended to the visco-elastic kinematics of resin composite material. This method was applied to an acoustic-structural coupling problem and the sound insulation effect of a resin composite material was calculated as a study to establish a method for predicting the noise reduction levels of resin composite materials. The obtained results show that the sound insulation levels are affected seriously by the shape or rate of the reinforcements in the material, which suggests that the present method can be a good numerical method to determine the reinforcements in a resin to improve the sound insulation ability.
References 1. Lions, J. L., 1981. “Some Methods in the Mathematical Analysis of Systems and Their Control”, Science Press. 2. Guedes, J. M., and Kikuchi, N., 1990. “Preprocessing and Postprocessing for Materials Based on the Homogenization Method with Adaptive Finite Element Methods”, Computer Method in Applied Mechanic and Eng., 83, 143–198. 3. Terada, K., and Kikuchi, N., 1995. “Nonlinear Homogenization Method for Practical Applications in Computational Methods in Micro-mechanics”, AMD Special Volume edited by S. Ghosh, ASME. ASME Winter Annual Meeting, November, ASME, 1–16 4. Yuge, K., Ejima, S., Udagawa, R., Kishikawa, Y., and Ksai, K., 1994. “Sound Insulation Analysis of a Resin Using Visco-plastic Constitutive Equations”, in Japanese, Transactions of Japan Society of Mechanical Engineers 60–570, A 535–542. (Journal Article)
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5. Zienkiewicz, O. C., and Bettess, P., 1978. “Fluid-structure Dynamic Interaction and Wave Forces and introduction to Numerical Treatment”, International Journal Numerical Method in Engineering., 113, 1–16. 6. Park, K. C., and Fellipa, C. A., 1977. “Stabilization of Staggered Solution Procedure for FluidStructure Interaction Analysis”, Computational Methods for Fluid-Structural Interaction Prob., ASME, AMD 26, pp. 95–124
Toys and Scale Models Richard I. Emori
Abstract Play is fun. With toys designed like real world objects – kitchen sinks, hot wheels, lawn mowers, baby dolls – children are socialized through play. By playing with these toys, children exercise their imaginations, creativity, and intuition. So, too, do adults exercise these mental muscles through play. Scale models are the toys that engineers and scientists use to solve problems. While children’s toys may be less than accurate representations of real world objects, the similarity between full scale objects and their scale models must be guaranteed before engineers start playing with these “toys”. Most real world problems come out without labels as to what analytical process is appropriate to solve them. Experiments, or “play”, with scale models are helpful in defining problem areas and then in helping engineers apply proper analytical techniques to define solutions. Sometimes it is enough to scale down real world phenomena with scaling laws and do experiments in our heads to perceive the physical mechanism of the phenomenon. However, the mental process of problem-solving is enhanced through “play”. Scale models provide a great help to basic understanding of real world phenomena and making inductive inferences. It is fun to pursue the rigorous accuracy in scale models, and more fun to play with them. Keywords Scale modeling · problem solving · similarity
Introduction Engineering is a profession which makes new things that have never existed before, while science is the study of existing phenomena for a more thorough understanding of that phenomena. Von Karman once said: “Scientists see things that are and ask ‘why?’ Engineers dream of things that were not and ask, ‘why not?’ ” Since engineers are to make new things, we require creativity and we do not even care whether or not the new products violate Newton’s law as long as they work for what R.I. Emori Former President of Accident Investigation Associates, Emori Engineering Co., Mitaka, Tokoyo 181, Japan (Deceased) K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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they were designed. Since chances of success are slim if we ignore natural laws, we respect evidence confirmed by scientists and use that evidence to its maximum potential. Experiments with scale models often give us both inductive inference for creativity and deductive reasoning for the comprehension of phenomena. Children expand their dreams by playing with toys. Like exercising the body increases its capacity for exercise, so exercising all facets of mental capacity, including imagination, increases the mind’s capacity to imagine and create. And, as Einstein declared: “Imagination is more important than knowledge.” Play is the exercise of the imagination. The engineer can play with scale models to obtain new ideas and understanding of the physical mechanisms of his product.
Engineering Spirit Engineering is an art to make new things. Since we engineers are to make new things, we stride into a new territory where we confront unknowns to some extent, and we must have enough courage and determination to try out our ideas in unknown areas. Scale models encourage pioneering and engineering spirit.
Scale Model as Playmate It seems important to play with a free mind in order to develop creativity which is essential in engineering. As children satisfy their imaginations by playing with toys, we can try out new ideas on scale models. When children are playing with toys, some discrepancy is permissible between toys and their full scale counterparts in the real world. However, if we want to try out new ideas on scale models and expect the full scale model to work in the same way, we must make sure the scale models are accurate representations of the full scale objects. Similarity has been established for many years in some fields of scale modeling, such as wind tunnel studies in aircraft development and water basin tests in naval architecture. In these fields, we can test new ideas with scale models by following established processes and if the results are encouraging, we expect the idea would work in the same way in the full scale. But if we go beyond the region of similarity in building our models to scale and we over-trust the test results of less than exact scale models in the design of the full scale products, we can expect to run into the inherent danger in such designs. During World War II, the Zero-fighter of Japan was designed based on the classic wind tunnel study, using a wooden scale model. However, the scale model could not predict the self-exciting torsional vibration of the main wind [1], and the plane and its crews had to go through painful disasters during test flights. I, myself, have had similar but, by far, less disastrous experiences in scale model studies of automobile collisions [2]. With my successful experiments in the scale model study of vehicle to vehicle collisions with traffic accident reconstruction, I tried to extend the same
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process to collisions of vehicles with high way signposts. I conducted experiments to create signposts and lightposts that were strong enough to stand up to the wind, yet no so dense as to cause major damage, injury, or death. When I tried to repeat the experiments at full scale, the results were not the same. It took me almost a year of struggle and embarrassment with the granting government agency for the project before I could find the reason why the two sets of experiments had such different results. During the year’s struggle, I often had the impression that I may have been fighting a losing battle. These examples show the importance of maintaining similarity in scale models. To specify the extent of similarity between full and scale models or to know why that similarity is not realized, we must further understand the physics of the phenomenon more thoroughly.
Pilot and Production Experiments There are many and varied reasons for using scale models in place of full scale. It may be too expensive or too dangerous to use the full scale at first, or the full scale may still be on the drawing board. If we want to use scale models for experiments instead of using their full scale counterparts, we need to confirm the validity of the substitution before we start those experiments. Let me call the preliminary experiment to verify the exactness of the scale the PILOT experiment, and the scale model experiment to try various new ideas the PRODUCTION experiments. Before enjoying PRODUCTION experiments with scale models, we need to make PILOT experiments successful. The most reliable method to verify the accuracy of the scale model to the full scale is to compare experimental results of the scale model to the corresponding full scale. But, in many cases, the full scale may not even exist. If we cannot verify the accuracy of the scale model to the full scale directly, we must find another course. One method may be to make scale models of two preferably three or more, different sizes and compare results of the experiments conducted on them. If the results are similar among the various scale models, then similar results in the full scale may be expected with a high possibility, although there is still some reservation. Engineers have analyzed and compared the experimental results from these scale models. Even if the results agree, chances are that the analyses verify only scale models, and neither the scale model nor the analytical model simulate the full scale at all. We should be very careful of this short circuitry.
Realization of Similarity All mammals, including humans, have evolved in the same environment (the earth) and it is not surprising that we are basically all similar genetically and biologically. First of all, we note that all the mammals have roughly geometrical similarity, i.e. larger mammals have longer extremities.
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Since all mammals have been living in the same environment, their life mechanisms may also be similar. That is, larger mammals consume larger amounts of food to maintain life. The amount of necessary energy to live may be proportional to the animals weight if the metabolism is similar. Let E be the necessary energy to keep the animal alive. Then, E∼W
(1)
where W is the body weight of the animal. The metabolism takes place through the surface of the mammal. For instance, absorption of nutrition is done through the surface of the intestines, and perspiration takes place through the skin surface. Hence the energy of metabolism, Em, becomes Em ∼ At
(2)
where A is the surface area and t is time. Since the surface area is proportional to the animal’s length, l, squared, A ∼ l2
(3)
Assuming that the body density is approximately the same, the weight would be proportional to l 3 , i.e. W ∼ l3
(4)
Hence the energy of metabolism should become, Em ∼ W2/3 t
(5)
Since the life mechanism of all the mammals are assumed to be similar, the necessary nutritious energy, E, may be proportional to the energy of metabolism, Em, for all mammals, i.e. the ratio of the two energies may become the same for all mammals. We call the ratio a pi-number and denote it as π , i.e. π = E/Em ∼ W1/3 /t
(6)
will be the same for all mammals. Let us check the consequence with actual observations. We will take the life span a representative time, t, and the results are shown in Fig. 1. Although the data scatter somewhat, the straight line in the logarithmic plot with a slope of 1/3 supports the assumption that the metabolism of all mammals may be basically the same [2]. The above example shows that if the full scale and the scale model phenomena become similar, major energies governing the phenomena should become proportional and the pi-number, as the ratio of the energies, becomes identical. The classic way to obtain pi-numbers is to assemble pertinent parameters relating to the
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(1) Mice (2) Hamster (3) Rat (4) Japanese Mice (5) Guinea Pig (6) Cat (7) Rabbit (8) Dog (9) Ape (10) Porcupine (11) Pig (12) Lion (13) Gorilla (14) Bear (15) Rhinoceros (16) Hippopotamus
Fig. 1 The scaling law relationship between mammals’ life expectancy and body weight (from Ref. [2])
phenomena to take the ratio of governing energies of the phenomenon. If we want to understand the phenomenon based on the natural laws and attempt to abstract governing energies, the derived pi-number portrays our understanding of the phenomenon [3]. Hence, if the pi-number does not show the identity between the scale model and its full scale counterpart, our understanding of the phenomenon is not justified and we are forced to examine the phenomenon more closely. To perceive the hidden nature of the phenomenon, it is important to know the physical meaning of the pi-number. The pi-number of the mammals designates metabolism taking place through surface areas in mammals. Other popular pinumbers also have important physical meanings. The Reynolds number is the ratio of inertial force and viscous force of fluid, while the Froude number is the ratio of inertial force and gravitational force. We observe that the Reynolds number is important in studies of fluid not because it is popular, but because we understand the phenomenon to be governed by inertial and viscous forces [4]. It is notable that each parameter in a pi-number does not designate a fixed value in the phenomenon. In the pi-number of mammal’s metabolism, e.g., where we have considered the life span as time, t, there is no reason that we must use the life span. We can consider the age at which a mammal first gives birth, or the age at which it is weaned to be t as well. All other parameters in the pi-number are also representative, and do not necessarily represent a particular parameter [2].
Representative Parameter As we understand that all the parameters in the pi-number are representative in nature, so, too, do we know that as a result the governing energies and forces are also representative. We should make it clear, however, to what extent the representativeness is to be observed. Let us consider, e.g., why the wind tunnel study of the Japanese Zero-Fighters failed to predict the previously mentioned flutter during World War II. Two major forces, lift and resistance on the airplane are affected by
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the sudden change of air movement around the airplane, and it is not enough to consider the inertial force of the air. But the flutter is the vibration of the airplane wing structure and the representative inertial force must also include that of the wing. This means that the mass distribution and elastic strength of the wing should be made similar in the scale model to realize the similarity. The difficulty of visualizing the extent of representativeness is shown by another previously mentioned example: that of the automobile collisions with road signposts. The structure of the signboard is basically a honeycomb paper, sandwiched and glued between two thin aluminum plates. The board is sturdy but very lightweight. The board is then bolted to wooden posts which are firmly embedded in the ground. Sometimes the broken pieces and the signboard fall down, and they may hit the passing vehicle again. We wondered if it would be possible to keep the falling pieces from hitting the vehicle to prevent secondary damages. Could it be done by making the wooden poles breakable with notches and/or holes in particular places? The mechanism of the phenomena is described as follows: When the vehicle strikes the signpost, the wooden pole deflects and breaks, delivering the stress force to the vehicle. The stress force of the post is one of the major forces governing the phenomenon. The broken pieces of the signboard are accelerated while the vehicle decelerates, thus, the inertial force is another force governing the phenomenon. The broken pieces fall and may hit the vehicle again, hence the gravitational force should be taken into account. There may be other minor forces that acted on the collision phenomenon. However, these forces are minor compared to the above three forces and we intentionally eliminated these minor forces from the similarity requirement. The three major forces can be written in representative forms as: Fs ∼ sl 2
Stress force
(7)
Inertial force Fi ∼ (W/g)(v /l) Gravitational force Fg ∼ W 2
(8) (9)
where s = stress of the wooden post and the damaged part of the vehicle, l = length, W = weight, v = velocity, all being representative. From these forces, two pi-numbers will be obtained. π1 = Fs /Fg ∼ sl 2 /W
(10)
π2 = Fi /Fg ∼ v /gl
(11)
2
Since both pi-numbers need to be identical for the full scale and scale model, sl 2 /W ∼ s l 2 /W 2
v /gl ∼ v /g l 2
(12) (13)
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As for the stress, s, if different material is used for the scale model than the full scale, the material of the scale model should be made so that the stress becomes proportional to that of the full scale at any strain. It is very difficult, if not impossible, to find or manufacture such artificial material. Thus, the common practice for scale model engineers is to use the same material for both the full scale and the scale model, satisfying s = s . However, since the vehicle in the full scale experiment is much stronger than the signpost and the damage to the vehicle is minimal, the scale model vehicle can be made rigid as an aluminum block rather than an exact replica of the vehicle. Thus, s in the pi-number of the scale model does not represent the pi-number of the actual vehicle. This is an intentional violation of the similarity rule, and is called a relaxation technique, which is sometimes necessary to obtain achievable similarity rules and sometimes helps to significantly simplify the scale model experiments. We may conduct the scale model experiment under the same gravitational acceleration, i.e., g = g . With these binding conditions, we obtain the similarity rule, a regulatory rule with which scale model experiments are to be performed: W/W ∼ (l/l )2
1/2
v/v ∼ (l/l )
(14) (15)
The length scale of the model was chosen as 1/16 of the full scale. According to the similarity rule, the weight of the model was made to 1/256 of the full scale with the same material as the full scale. How did we do it? By attaching dummy weight to the scale model signpost. This dummy weight scale-model-signpost was crushed by a scale model vehicle with the velocity scaled to v/v = 1/4. Things did not go as smoothly as we expected, however, as the motion of the signpost in the scale model did not even resemble a percentage of the full scale. For almost a whole year we struggled by putting dummy weight on the signboard and the wooden post, by putting paper honeycomb on the front end of the model vehicle so that the collision became non-elastic, and so on and on, with absolutely no luck. We were cornered and our wits had almost been exhausted. Since we had recorded the full scale experiments in high-speed motion pictures, we started to review them carefully. After several trials of the review, we found the culprit.1 The full scale signboard is made of paper honeycomb sandwiched by thin aluminum sheets. The board is fastened with bolts onto the wooden post. When the vehicle strikes the post, the broken post is carried along with the vehicle and the post tries to carry the board with it. Since the board has an inertia and the board faces are made with thin aluminum sheets, the fastening bolt head cut through the aluminum sheets. Hence, the motion of the board is governed by the resistive force of the bolt head cutting though the aluminum sheet of the signboard. In other words, the representative stress, s, also should include the cutting stress of the aluminum sheet 1
An interesting article about “Kufu [5],” which is the source of imagination and creativity may help readers better understand the process of this culprit-finding breakthrough.
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by the bolt head! How could we expect this level of understanding of the phenomena at the beginning of this project? Taking the resistive stress of the full scale into the similarity consideration for the scale model, finally, the motion of the scale model signpost hit by the scale model automobile became similar to the full scale. The solution we found after a year-long struggle now seems so simple and sounds like no more than common sense. After I had worked on many different kinds and types of engineering problems for more than 50 years, I came to believe that solutions for many engineering problems (if not all) may be as simple as common sense! The important lesson gained by “playing with the scale models” is that our understanding on the mechanisms of automobile collision with signposts was significantly enhanced. Thus, the basic principle that children can enhance their imaginations and creativity by playing with toys certainly can be applied to engineers [6].
Engineering Spirit Engineering is an art to make new things and we engineers start with new ideas. It is important to play freely with our mental tools of reason, intuition, and imagination to create these new ideas and experience breakthroughs. Scale models enhance this mental play and they deserve good playmates. At the same time, these scale models are relentless task masters if we do not comprehend the phenomenon we are studying correctly. But, if we choose not to be discouraged and, instead, delve deeper into our insight and creativity, our playthings (scale models) can be our instructors, who give us the true engineering spirit. VIVA, ENGINEERING SPIRIT AND SCALE MODELS!! Acknowledgments Dr. Richard I. Emori had sensed the need for international collaboration on scale modeling research and initiated the International Symposium on Scale Modeling. The first symposium was successfully held in Tokyo in 1988 with over 200 attendees from eight different countries. I acknowledge Dr. Emori’s wisdom in the art of scale modeling and his passion for engineering spirit! The author of this paper suddenly passed away on December 30, 1996. After his death, Ms. Yasuko Kawashima, the secretary and long-time assistant to Dr. Emori, found this manuscript written by him especially for ISSM II. The manuscript was almost completed but needed editorial work. Dr. Mary Elizabeth Glade kindly offered her professional editorial expertise without changing Dr. Emori’s intention. With her help, this article became understandable for people who have no engineering background. I, as Dr. Emori’s former and only Ph.D. student, would like to acknowledge Dr. Glade’s special help in the preparation of this article. Kozo Saito, March 18, 1997
References 1. G. Horikoshi, Zero-Fighter of Japan, Kohbun-sha, 1970, in Japanese. 2. R.I. Emori and D.J. Schuling, Scale Models in Engineering, The Theory and Its Application, Pergamon, 1977.
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3. E.B. Wilson, Jr., An Introduction to Scientific Research, Dover, 1990. 4. S. Goldstein, Ed., Modern Developments in Fluid Dynamics, Vols. I and II, Dover, 1965. 5. K. Saito, “Kufu-Foundations for Employee Empowerment and Kaizen,” in Continuous Learning Systems, McGraw-Hill, 1995. 6. R.I. Emori, Imagination and Creativity Gained by Playing with Scale Models, Kodansha, Blue Backs, 1985, in Japanese.
Part IV Medical – Conceptual, Practical, Translational into Practice D. Doherty, T. Konishi and T. Ida
Summary The human body is composed of a network of communicating molecules, proteins, cells, and organs that function in a uniform fashion during health and disease. These internal body components themselves vary in size and function – internal bodily “scale modeling”. These characteristics include differences in size/weight: DNA and genes (1 nm–1 μm), cells (e.g. red blood cells 5–8 μm, white blood cells 6.5–10 μm), and organs (e.g. lungs 0.6 kg, muscle 27 kg). It is imperative that living organisms (animal, human) function in an integrated manner (homeostasis) using complicated and elaborate mechanisms to orchestrate the preservation of health. The body is continuously exposed to a myriad of internal and external stimuli that may be harmful: such as viruses, bacteria, chemical substances, poisons, medicines, and even external forces such as automobile accidents which lead to internal injury (e.g. fractured bones, contused organs). We need to investigate and understand these mechanisms that allow the body to respond appropriately to combat disease and preserve health. Scale modeling can provide an environment in which these investigations can proceed. It is often not possible to study these mechanisms initially in the human body for practical or perhaps ethical reasons – accordingly cell and animal models are utilized for in vitro and in vivo experiments. These scale modeling experiments often elucidate mechanisms that can later be verified in well controlled and relatively safe experiments in the human body. In medical “scale modeling”, the models are cells, animals, such as a mouse or a rabbit, human phantom, artificially made organ and cell, an artificial substance or a natural substance - which are utilized for their structure and/or functional characteristics that resemble human systems. Experiments using these medical scale models (in vitro or in vivo in animals) often establish potential mechanisms that control health and disease in the functional human body, and specifically guide subsequent translational human experimentation (in vivo) to verify that these mechanisms are relevant in man. In this section, we present the conceptual, practical (experimental), and translational “scale modeling” investigations authored by five outstanding scientists who specialize in both medical and engineering science. The present era in the medical field requires this type of interdisciplinary approach applying established scale modeling and analysis methods K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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from both engineering and medical science to solve the evolving medical problems that face, and will continue to challenge, the maintenance of our health.
Papers Selected from the Second Symposium 1. B. Lattimer, U. Vandsburger, and R.J. Roby. “Developing Scaling Parameters for Estimating Carbon Monoxide Levels in Structure Fires.” This paper describes scaling laws and an experimental method to predict CO production during compartment fires using a reduced-scale room model. The authors describe the scaling parameters affecting both the air entrainment and the stoichiometry of gases in building fires. Using these scaling parameters, the CO-yield at locations distant from the burning compartment was predicted.
Papers Selected from the Fourth Symposium 1. J. Kizito, K. Barlow, and S. Ostrach. “Characteristic Timescales for Adherent Mammalian Cells.” This paper describes analysis-practical-cell modeling. It describes time scales associated with mechano- and biochemo-transduction processes in mammalian adherent cells. Deformation time scales of the cytoskeleton, diffusion and reaction time scales in the cytoplasm are discussed and new dimensional parameters are derived to predict the processes. 2. M.I. Hassan, V. Kalidindi, A. Carner, N. Lemmerman, M.V. Thomas, I.S. Jawahir, and K. Saito. “Scaling Human Bone Properties with PMMA to Optimize Drilling Conditions During Dental Implant Surgery.” This paper describes a use of Polymethylmetbacrylate (PMMA) as a surrogate material for human bone. The authors conducted a series of drilling tests to find the optimum drilling conditions during dental implant surgery which requires human bone temperature to be below 47 ◦ C. When human bone temperature increased above this critical temperature, bone did not grow over the implant causing the implant to fail. The use of “surrogate” is one of the applications that scale modeling techniques can offer.
Papers Selected from the Fifth Symposium 1. D.E. Doherty. “Monocyte Lung Retention During Normal Conditions (Health) and During Disease States (Endotoxemia); a Medical Application of Scale Modeling.” This paper describes practical (Experimental) and translational (rabbit and humans) scale modeling. This paper was the keynote lecture of the latest symposium, ISSM-V. This paper describes a filtration (6.5–8 m) model simulating the blood monocyte (7–10 m) flow in the capillary network (6–8 m) of the human lung. They confirmed that lipopolysaccharide induces monocyte lung retention by increasing monocyte stiffness and thus diminishing the cell’s
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ability to deform and transit the narrow pulmonary capillary network and that later; LPS would induce CD18-dependent monocyte adhesion to lung vascular endothelium, prolonging their retention. 2. T. Kikkou, S. Iwabuchi, and O. Matsumoto. “Scale Modeling of Medical Molecular Systems”. This paper was a keynote lecture and contributed to conceptual scale modeling as molecular. This paper describes the molecular stiffness and flexibility which are determined by the balance of the internal degree of freedom and number of restraints in the molecule. The structures of DNA and protein are discussed under the model.
Characteristic Timescales for Adherent Mammalian Cells John Kizito, Karen Barlow and Simon Ostrach
Abstract This paper examines timescales associated with mechanotransduction and biochemotransduction processes in mammalian adherent cells. The deformation timescales of the cytoskeleton dominate, in certain cases, during mechanotransduction. Viscous damping effects limit the possibility of vibrational instabilities. We conclude that extreme oscillations may lead to cell detachment, while damped oscillations provide favorable environment for the cell growth. Conversely, times associated with diffusion in the cytoplasm limit biochemotransduction. Reaction timescales which do not involve enzymes are larger than the values of all other timescales suggesting that in specific cases, these reactions might be the limiting step. Also, we derive non-dimensional parameters to predict conditions in which gravity has a significant role in mechanotransduction and biochemotransduction. Keywords Mammalian chemotransduction
adherent
cells
·
mechanotransduction
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bio
Introduction Adherent cells are the smallest functional units of tissue which constitute an organism. In some cases, adherent cells like bacteria found in biofilms do form vibrant complex interdependent structures. In cell culture laboratories, adherent cells may be a part of a film, or monolayer, grown on a substrate. All these cells have one thing in common: they need a substrate upon which to adhere. In this paper we are interested in examining whether adherent cells can sense gravity directly via specialized receptors, a process referred to as mechanotransduction, or indirectly by responding the environmental changes, a process called biochemotransduction. We will answer this question based on the observable characteristic timescales which J. Kizito Department of Mechanical and Chemical Engineering, North Carolina A&T State University, Greensboro, NC 27411 e-mail:
[email protected]
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describe living cells. Initially, we start by examining the process of cell adhesion where a single cell suspended in fluid medium anchors itself to a substrate. Our goal is to determine possible timescales that describe the process of anchoring on a substrate and the dynamic response to a disturbance, such as fluid flow (or shear stress). The balance of all forces acting on a cell will determine whether a cell prospers and multiplies, or dies in a process called apoptosis and/or necrosis. The balance of forces is tightly coupled to the transport of nutrients and metabolic products to and from the cell interface. We will identify the effects that are caused by a mechanical interaction due to a structure deformation, stress tensor, and body forces (if present), all of which will be grouped as mechanotransduction timescales. The remaining timescales are associated with the transport of oxygen, nutrients, removal of waste products, and the expression of proteins. These effects are influenced by fluid flow or transport phenomena such as buoyancy driven convection (driven by gravity), and will be grouped as biochemotransduction timescales. This method will aid our ability to separate the environment and the transport effects on cells cultured and grown in microgravity from the direct gravitational response of the cells.
Review Alberts et al. [1] describe animal cells (about 10–30 m) as consisting mainly of the following parts (Fig. 1): (1) The cell membrane which can be referred to as a bag consisting of a continuous sheet of phospholipid molecules (about 4–5 nm thick) in which various proteins are embedded. The proteins act as pumps and or channels connecting the extracellular space to the cytoplasm. (2) The nucleus (2–3 m), lying near the center of the cell, is the most conspicuous organelle. The nucleus communicates with the cytoplasm by way of nuclear pores. (3) Cytoskeletal networks, found in the interior of the cell, contain elaborate arrays of protein fibers that serve such functions as: establishing cell shape, providing mechanical strength, locomotion, chromosome separation in mitosis and meiosis, and intracellular transport of organelles. The cytoskeleton is made up of three kinds of protein filaments: Actin filaments (8 nm), intermediate filaments (10 nm), and microtubules (25 nm). Intermediate filaments Cell-membrane
Nucleus
Microtubule Cytoplasm Actin
Focal adhesion
Fig. 1 Schematic of major cell components
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(4) Inside the cell, the cytoplasm is the matter, which includes all non-nuclear cell organelles and the cytosol, or aqueous fluid surrounding these organelles. As an example, the fluid-phase viscosity of the cytoplasm within a fibroblast, a cell involved in wound healing, ranges between 1.2 and 1.4cP [2, 3], or slightly greater than water. Cell adhesion to the underlying substrate is comprised of a number of focal adhesions. Focal adhesions are complexes of intracellular signaling and structural proteins which serve a structural role in linking the extracellular matrix on the outside of the cell to the cytoskeleton on the inside. The major transmembrane proteins in focal adhesions are integrins. Cell attachment to the extracellular matrix is mediated by integrins, a widely expressed family of transmembrane proteins. In addition to anchoring the cell, integrins transmit signals that direct cell migration, proliferation, and differentiation. To facilitate adhesion, cells excrete polysaccharides and proteins which spontaneously assemble into a complex network known as the extracellular matrix. The polysaccharides form an aqueous gel-like substance into which the proteins embed. The proteins are of two main types: structural and adhesive. Collagen fibers strengthen and help to organize the matrix, while elastin fibers give it resilience. The adhesive proteins such as fibronectin help cells attach to the extracellular matrix in connective tissues via the extracellular parts of some members of the integrin family [4]. Geiger et al. [4] give examples of how endothelial cells sense shear stress produced by the blood flow, pressure from cells by neighboring muscular tissues, acoustic waves acting on the stereocilia of hair cells, and adherent cells exposed to mechanical perturbation via the extracellular matrix (ECM). They report that mechanical probing of the immediate environment is considered a critical mechanism for controlling such cellular processes as motility, morphogenesis, proliferation, and apoptosis. As a result, cells possess rather sophisticated mechano-sensory devices which can detect forces and respond to them. They conclude that the mechanism of action of such “force receptors” is still poorly characterized compared to classical “chemoreceptors.” Ingber suggest that living cell sensation of gravity may not result from direct activation of any single gravity-sensing molecule [5]. Instead, gravitational forces may be experienced by individual cells in the living organism as a result of stressdependent changes in cell, tissue, or organ structure that, in turn, alter extracellular matrix mechanics, cell shape, cytoskeleton organization, or internal pre-stress in the cell-tissue matrix. Also given are examples of how dense crystals called statoliths push on the ciliated cells of the inner ear in response to motion. Consequently, changes in the stress loading of the cytoskeleton of these cells cause a gravity sensation. Maniotis et al. [6] reported that living cells and nuclei are hard-wired such that a mechanical tug on cell surface receptors can immediately change the organization of molecular assemblies in the cytoplasm and nucleus. They concluded that connections between integrins, cytoskeleton filaments, and nuclear scaffolds may therefore provide a discrete path for mechanical signal transfer through cells as well
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as a mechanism for producing integrated changes in cell and nuclear structure in response to changes in extracellular matrix adhesion strength or mechanics.
Problem Formulation Mechanotransduction: Fluid Structure Interaction at a Cellular Level Consider a simplistic example where a cell is surrounded by a fluid medium and is anchored on a substrate by a number of focal adhesions, which we will refer to as “tethers”, as shown in Fig. 2 below. Using Newton’s laws we will write the equation of motion which describes the cell dynamics. The net force will produce the acceleration of the cell which results in motion. The motion is resisted by the deformation of the tethers and the viscous drag of the medium. In a normal gravity environment, the buoyancy forces may also be significant. Therefore, the sum of all forces acting on a cell is: Fnet,j + Fviscous + Fdeformation = Fapplied
(1)
where the index j applied can refer to a group of all other forces such as gravity, vibration or magnetic. Let the cell have a spherical shape with the following traits: radius R; tether length, diameter, modulus of elasticity, and number l, d, E, and n, respectively; and μ is the viscosity of its surrounding media. Also, let the mass of the cell be m, spring constant of the tethers be k, and viscous effect be represented as a dash-pot constant c. Equation (1) can be written as follows: m
dy d2 y + ky = Fapplied +c dt 2 dt
(2)
where the variable y represents the displacement of the cell, and variable t represents the time. The above expression is derived from the fact that the viscous drag forces, which are proportional to velocity, cause resistance to motion, and deformation forces are proportional to the extension of stretch with the spring constant k. Equation (2) can be written in non-dimensional form as follows: Fluid Medium Motion → y
Single Cell Fnet
r
Fig. 2 Single adhered cell onto a substrate
Spring constant of the adhesion tethers
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T 2 Fapplied kT 2 d 2Y cT dY + Y = + dτ 2 m dτ m mR
(3)
t y , τ = , and T is the characteristic where the variables are scaled as; Y = R T timescale. Equation (3) can be written in a standard vibration format as: d 2Y dY + ω2 Y = f + 2ξ ω dτ 2 dτ
(4)
where the major non-dimensional parameters are: $ ω=T
√ 3k 3c ,ξ = 3 4ρπ R 4 ρπ R 3 k
(5)
The parameter ω represents a non-dimensional frequency a ratio of elastic to inertia timescales and ξ represents a non-dimensional damping number which is a ratio of the viscous to elastic timescale. The non-dimensional parameter f represents a ratio of a body-force to inertia force. We can expand the mass, spring constant, and dash pot constant, as: m=
Enπ d 2 4ρπ R 3 ,k = , c = 6π μR 3 4l
(6)
Equation 3 has two characteristic timescales which are: 5 t1 =
4ρπ R 3 2ρ R 2 , t2 = 3k 9μ
(7)
The physical meanings of the timescales are as follows: t1 is the elastic timescale derived from inertia and elastic effects; t2 is the viscous timescale derived from inertia and viscous effects. Using properties in Table 1 we obtain the following timescales These tables show that the limiting timescale is due to the elastic deformation effects of extracellular matrix proteins. Therefore let the characteristic timescale be: 5 tR =
4ρπ R 3 3k
(8)
Let the applied force be due to gravity, therefore the effects of gravity can be estimated as: →
Fbuoyancy =
4π R 3 (ρ − ρ F )g 3
(9)
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J. Kizito et al. Table 1 A Case study of adherent mammalian cell properties [7] Quantity
Symbol
Value
Units
Diameter Average Density Elastic Modulus Actin Elastic Modulus Elastin Actin diameter Viscosity of medium Gravitational acceleration Density of medium Initial perturbation Number of tethers Length of tethers
D ρ E E d μ g ρf Y [0] n l
10−5 1010 109 106 10−8 10−3 9.8 103 0.01 10 10−5
m Kg/m3 N/m2 N/m2 m Kg/m-s m/s2 Kg/m3 – – m
Using the last term in Eq. (3) and Eq. (8) gives the non-dimensional parameter which determines the effects of gravity as: →
f = 4π R 2
(ρ − ρ F )g 3k
(10)
Now let us subject the cell to an initial perturbation 1% of the diameter and determine the resulting motion described by Eq. (3). The case study of a mammalian cell with the properties is listed in Table 1. Inserting the quantities from Table 1 into the basic Eq. (3) (if the applied forces are absent) gives the following solution: Y [τ ] = −0.00042e−4.97τ + 0.01e−0.2τ
(11)
The graphical presentation of Eq. (11) is Fig. 3. Figure 3 shows that during the adhesion process any disturbance is over-damped by the cell, leading to a stable environment to allow proper anchoring of the cell on the substrate. On the other hand, using the properties of actin for the modulus of elasticity gives Eq. (12) and its graphical representation is shown in Fig. 4.
Fig. 3 The temporal response to an initial perturbation is over-damped by the fluid medium when E is that of elastin, 106 N/m2
Characteristic Timescales for Adherent Mammalian Cells
439
Fig. 4 The temporal response to an initial perturbation under-damped by the fluid medium when E is that of actin, 109 N/m2
Y [τ ] = 0.01e−0.08τ Cos[0.997τ ] + 0.008e−0.82τ Sin[0.997τ ]
(12)
Figure 4 shows that any disturbance after adhesion is under-damped, suggesting a change of characteristic timescales depicted by Tables 2 and 3. The analysis shows that the elastic timescale is limiting during the damping process. Viscous effects promote cell adhesion by damping any perturbation. Table 2 Typical timescale values for extracellular matrix protein, elastin Quantity Elastic timescale Viscous timescale
Symbol 5 4ρπ R 3 t1 = 3k 2ρ R 2 t2 = 9μ
Value
Units
2.9 × 10−5
s
5.6 × 10−6
s
Table 3 Typical timescale values for intracellular protein, actin Quantity Elastic timescale Viscous timescale
Symbol 5 4ρπ R 3 t1 = 3k 2ρ R 2 t2 = 9μ
Value
Units
9.2 × 10−7
s
5.6 × 10−6
s
Biochemotransduction: Transport Phenomena Consider a cell attached to a substrate surrounded by medium containing dissolved oxygen and glucose. A physicochemical rate process occurs within the cell to reduce the glucose into carbon dioxide and water. A boundary layer type of region is formed as the cell depletes the oxygen and nutrients and metabolic products are produced and emitted into same region. As the process progresses, oxygen and nutrients must be transported to the surface of the cell by the self-generated gradients. Similarly, carbon dioxide must be transported away from the cell surface. The transport of these species must occur simultaneously and can be described by multiple timescales. These timescales will determine cell viability. The product/nutrient fields are due to the metabolic process in the cell. The spatial distribution of products
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is affected by the relative motion between the cell and the surrounding fluid, and by the body forces such as gravity. Figures 5 and 6 depicts how cells interact with their environment under various fluid transport modalities. Figure 5 shows that metabolites released into the local environment are influenced by convective fluid flow. In contrast, Fig. 6 illustrates how buoyancy driven convection may transport the metabolites away from the cell. However, in both cases, the depletion zone is due to the utilization rate of the nutrients and/or oxygen. The biochemical reaction where glucose is reduced to carbon dioxide and water can be written as: C6 H12 O6 + 6O2 → 6CO2 + 6H2 O
(13)
The equations for transport of species can be written in compact form as: Fluid flow Metabolic product (s) Cell
U Nutrient depletion zone (s)
Adhesion tether (s)
Fig. 5 Transport phenomena due to convective flow
g↓ Metabolic product(s)
Cell
Fig. 6 Transport phenomena due to buoyancy
Characteristic Timescales for Adherent Mammalian Cells
441
→ ⭸Ci ˙ i (t) + U · ∇Ci = Di ∇ 2 Ci + M ⭸t
(14)
with the boundary equations written as: # # Di ∇C ##
= ki e
# # C i ##
−E a /Ru T
r =R
(15)
r =R
where index i is species i, Ci is the concentration, Di is the diffusion constant, ki ˙ i is the is the reaction rate i, E a is the activation energy, Ru universal constant, M mass production rate, and T ambient temperature. The temperature and species are coupled through the reaction term. For simplicity, assume that the coupling occurs through an Arrhenius-type relation. In Eq. (16), i represent the species and products within the medium as shown in Eq. (13) where m˙ is the rate of product of species i. ⎫ ⎫ ⎫ ⎧ ⎧ ⎧ ˙ C6 H12 O6 ⎪ CC6 H12 O6 ⎪ DC6 H12 O6 ⎪ −m ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎬ ⎨ C ⎨ D ⎨ −m ˙ O2 ⎬ O2 O2 , Di = , Si (t) = Ci = ˙ C O2 ⎪ m ⎪ C C O2 ⎪ ⎪ DC O2 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭ ⎭ ⎭ ⎩ ⎩ ⎩ ˙ H2 O m C H2 O D H2 O
(16)
Equation (14) reduces to a non dimensional form as: S
⭸ci ⭸t
+u
⭸ci ⭸r
1 = Pei
1 ⭸ 2 ⭸ci ˙ r + Da1i m(t) ⭸r r 2 ⭸r
(17)
Equation (17) is subjected to boundary condition at the cell surface as: Da2i
⭸c ⭸r
r =R
# # = ci ##
(18)
r =R
For nutrients: cr =∞ = 1
(19)
cr =R = 0
(20)
Ci C Ri
(21)
For products:
Where, ci = S=
LR , UR tR
Pei =
Di , UR L R
Da1 =
˙ Ri L R m , UR
Da2i =
Di ki L R
(22)
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where index R refers to a reference parameter, U, t and L are characteristic velocity, time and length scale respectively. The above non-dimensional numbers defined as: the Peclet number, Pe, (ratio between convection and diffusion transfer timescales), the Strouhal number, S, (ratio between convection timescale and a characteristic time), Damkohler’s first number, Da1 , (ratio between homogeneous reaction timescale to convection timescale; and Damkohler’s second number), and Da2 , (ratio between heterogeneous reaction timescale to diffusion timescale). Momentum transport can be described using Navier-Stoke’s equation as follows: → 1 ⭸Ui → + U · ∇Ui = υ∇ 2 Ui + (1 + βC ⌬C − βT ⌬T ) g − ∇ p ⭸t ρo
(23)
Equation (23) can be written in a non dimensional form as S
⭸u i → 1 2 + u · ∇u i = ∇ u i + (1 + Fr S ci − Fr T T ) − ∇ p ⭸t Re
(24)
The non-dimensional parameters are: Re =
UR R , υ
→
Frs = (βC ⌬C Ri )
gR , U R2
→
Fr T = (βT ⌬TR )
gR U R2
(25)
where Re is the Reynolds number, Frs is the solutal Froude number, and Fr T is thermal Froude number. The equations which describe the transport have a range of timescales. Each physicochemical event has an associated characteristic timescale. In the following analysis we will examine all of the following relevant timescales which describe the transport process as: ρ f R2 μ R Convective timescale, t4 ≡ , UR ρ p R2 Cell response timescale, t5 ≡ μ $ βT ⌬TR R Thermal buoyancy timescale, t6 ≡ g $ βc ⌬C R R Solutal buoyancy timescale, t7 ≡ g Fluid viscous diffusion timescale, t3 ≡
Species diffusion timescale, t8 ≡
R2 Di
(26) (27) (28) (29)
(30) (31)
Characteristic Timescales for Adherent Mammalian Cells
Reaction rate timescale, t9 Production rate timescale, t10
443
≡ ≡
1 ki 1 ˙i m
(32) (33)
The case study of a mammalian cell with the properties listed in Table 1 results in timescales listed in Table 4 where the timescale associated with diffusion in the cytoplasm limits biochemotransduction is shown. Reaction timescales which do not involve enzymes are larger than the values of all other timescales suggesting that, in specific cases, this might be the time-limiting step. Table 4 Typical timescale values for mammalian cells. Diffusion coefficients in the cytoplasm were calculated using the Stokes-Einstein equation: D = ko T /(6π Rμ∗ cf /c0 ) where ko , cf , and co are constants [8] Quantity timescale Fluid viscous diffusion timescale Convective timescale Gravitational timescale Species diffusion timescale for O2 in media
Symbol ρ f R2 t3 ≡ μ R t4 ≡ U 5 R t7 ≡ g R2 t8m ≡ D O2
Value
Units
0.000025
S
0.000025
S
0.000714
S
0.0125
S
Species diffusion timescale for O2 in cytoplasm
t8c ≡
R2 D O2
∼ 0.015
S
Species diffusion timescale for glucose in media
t8m ≡
R2 DC6 H12 O6
0.050
S
Species diffusion timescale for glucose in cytoplasm
t8c ≡
∼ 0.060
S
Reaction rate timescale with enzymes present
t9enz ≡
5. × 10−7
S
Reaction rate timescale without enzymes present
t9i ≡
5.00
S
R2 DC6 H12 O6 1 kenz
1 ki
Conclusion This paper has examined timescales associated with mechano- and biochemotransduction processes in mammalian adherent cells. The characteristic timescale for mechanotransduction is associated with the deformation of the cytoskeleton. Viscous damping effects limit the possibility that vibrational instabilities. Extreme oscillations may lead to detachment and/or apoptosis of the cell, while damped oscillations provide an environment conducive to cell viability. On the other hand,
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timescales associated with diffusion of large molecules in the cytoplasm limit biochemotransduction. The examples examined in this paper are not limited to diffusion of glucose. Reaction timescales which do not involve enzymes are larger than the values of all other timescales suggesting that, in certain specific cases, non-enzyme reaction timescale might be the time-limiting step. Gravitational effects on mechanotransduction are minimal in that gravity does not affect the damping process for a single cell. However, the non-dimensional parameter f , which compares buoyancy to the mechanical timescales, will become large when cells exist as a tissue. In this case, gravitational effects will influence mechanotransduction. Gravitational effects on biochemotransduction occur when large thermal or concentration gradients exist in the system. However, in mammalian systems, thermal gradients are negligible. Conversely, concentration gradients are vital for most biochemical processes to occur and are influenced by gravitational timescale. The non-dimensional number Fr S may be used to determine whether the gravitational effects are important. Acknowledgments We are grateful to Jos´ee R. Adamson of the National Center for Microgravity Research for her timely suggestions and comments.
References 1. Alberts, B., Bray, D., Lewis, J., Raff, M., Roberts, K., Watson, J.D. (1994) Molecular Biology of the Cell, 3rd ed. Garland Publishing Co., New York. 2. Fushimi, K., Verkman, A.S. (1991) Low Viscosity in the Aqueous Domain of Cell Cytoplasm Measured by Picosecond Polarization Microfluorimetery. J. Cell Bio. 112, 719–25. 3. Srivastava, A., Krishnamoorthy, G. (1997) Cell Type and Spatial Location Dependence of Cytoplasmic Viscosity Measured by Time-Resolved Fluorescence Microscopy. Arch. Biochem. Biophys. 340, 159–67. 4. Geiger, B., Bershadsky, A. (2002) Exploring the Neighborhood: Adhesion-Coupled Cell Mechanosensors. Cell 110, 139–42. 5. Ingber, D.A. (1999) How Cells (might) Sense Microgravity. FASEB J. 13, S3–S15. 6. Maniotis, A.J., Chen C.S., Ingber, D.E. (1997) Demonstration of Mechanical Connections Between Integrin, Cytoskeletal Filaments, and Nucleoplasm that Stabilize Nuclear Structure. Proc. Natl. Acad. Sci. USA 94, 849–54. 7. Fung, Y.C. (1993) Biomechanics: Mechanical Properties of Living Tissue. 2nd Ed. SpringerVerlang, New York. 8. Mastro, A.M., Keith, A.D. (1984) Diffusion in the Aqueous compartment. J. Cell Bio. 99, 180–87.
Developing Scaling Parameters for Estimating Carbon Monoxide Levels in Structure Fires Brian Y. Lattimer, Uri Vandsburger and Richard J. Roby
Abstract The majority of victims in building fires are found at locations distant from the burning compartment. Experiments were conducted in a reduced scale facility to quantify the effects of air entrainment and stoichiometry of gases entering the hallway on the CO yield at locations remote from a burning compartment. Scaling parameters for the air entrainment and the stoichiometry were empirically developed and used to predict the CO yield at these remote locations. The air entrainment scaling parameters were based on the Froude number where the gases enter the hallway and the geometry of the opening relative to the hallway. The stoichiometry of the gases entering the hallway was a function of the compartment fire size and equivalence ratio. When using scaling parameters for both the air entrainment and stoichiometry of the gases entering the hallway, the CO yield was predicted to within 30%. Keywords Carbon monoxide · structure fire · air entrainment · stoichiometry of gases
Introduction Smoke inhalation accounted for 76% of the 3,425 deaths in building fires during 1994 [1]. The majority of the smoke inhalation deaths were caused by carbon monoxide (CO) poisoning. Nearly 80% of the CO poisoning victims were found at locations distant from the room of fire origin [2]. A study was performed to determine and quantify the effects of fluid mechanic and thermodynamic parameters on CO levels transported away from the burning room. The level of CO transported to remote locations is a function of 1. the air entrainment into the compartment fire gases flowing in the hallway, 2. the stoichiometry of the gases exiting the burning compartment, and 3. the heat losses to the surfaces in the hallway. B.Y. Lattimer Virginia Polytechnic Institute and State University, Blacksburg, Virginia; Hughes Associates, Inc., Baltimore, Maryland
K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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The focus of the study was to quantify the effects of the first two items on CO levels, while minimizing the heat losses by performing the experiments in an insulated facility. Based on these experimental results, parameters were developed to predict the level of CO transported to locations remote from the burning room.
Experimental Experiments were conducted in a reduced-scale fire facility at VPI&SU to study the transport of CO down a hallway adjacent to a burning room. As shown in Fig. 1, the facility consisted of a compartment, an air inlet duct and plenum, a hallway and an exhaust system. The compartment was 1.52 m wide, 1.22 m high and 1.22 m deep with walls constructed of 25.4 mm thick Fire Master, UL rated fire insulation board. A liquid n-hexane pool fire was located in the center of the room with the weight of the fuel constantly monitored by a load cell (located in the air distribution plenum). Pool fire diameters of 0.15, 0.20, 0.23 and 0.30 m were used in the study to vary the fire size in the compartment. Underneath of the compartment was an air distribution plenum which was connected to the surroundings via a 0.30 m diameter, 1.83 m long duct. During a fire, air was naturally entrained into the compartment from the plenum. The air entrainment rate was measured in the duct connected to the plenum using a hot film probe. The compartment was connected to a hallway by a variable size opening. Opening sizes of 0.12 m2 (0.50 m wide, 0.24 m high), 0.08 m2 (0.50 m wide, 0.16 m high) and 0.04 m2 (0.25 m wide, 0.16 m high) were used in the study. The hallway adjacent to the compartment was 1.22 m wide, 1.67 m high, and 3.66 m long. The hallway walls were constructed of 6.35 mm thick gypsum fire
Fig. 1 The reduced-scale fire facility at VPI&SU
Developing Scaling Parameters for Estimating Carbon Monoxide
447
resistant board lined with 1.5 mm thick Fiberfax fire proof paper. The ceiling was constructed of 25.4 mm thick Fire Master, UL rated fire insulation board. The inlet soffit (the distance between the top of the opening and the ceiling) was either 0.0 m or 0.20 m. A 1.5 m square hood was located at the end of the hallway to collect the fire combustion products. A blower was connected to the exhaust ducting to remove the products of combustion from the facility. Additional details on the fire facility can be found in Ref. [3]. Species concentrations measured in gases sampled from the exhaust duct were used to determine the yield of CO exiting the hallway. The CO yield, YCO =
m˙ CO , m˙ fuel
(1)
was calculated by dividing the mass flow of CO in the exhaust duct by the fuel mass loss rate in the compartment. The temporal CO yield for an experiment was reduced to a single data point by averaging over a 20 second time window during the quasi-steady state time of the compartment fire.
Scaling Parameters The study presented here focused on the effects of the entrainment into the fire gases entering the hallway, and the stoichiometry of the fire gases on the CO levels exiting the hallway. The entrainment of air into the gases entering the hallway was varied by changing the compartment opening size and the inlet soffit height (distance between the top of the opening and the ceiling). The stoichiometry of the gases entering the hallway was varied by changing the fire size and the opening size. The opening size affected the fire stoichiometry by partially controlling the mass flow rate of air into the compartment.
Air Entrainment The effect of the opening size and the inlet soffit height on the air entrainment into the gases entering the hallway was measured in overventilated compartment fire experiments. A compartment fire was considered to be overventilated when the compartment equivalence ratio, m˙ fuel m˙ air φ= m˙ fuel m˙ air
st
(2)
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was less than 1.0. The overventilated fire experiments used to measure the air entrainment had equivalence ratios of 0.3–0.4 making the gases entering the hallway relatively non-reactive. The air entrainment into the jet of fire gases entering the hallway was determined by measuring the dilution of the gases between two locations along the hallway. The dilution between the two locations was determined from an integrated average of the species profiles (measured from 0.05 to 0.4 m below the ceiling in 0.05 m increments) measured at these locations. The mass flow rate of air entrained into the compartment fire gas jet was measured from the opening to a location 0.90 m downstream of the opening. This region (from 0.0 to 0.90 m) was chosen because it is where the compartment fire gases buoyantly rise to the ceiling and spread horizontally to the walls. Past this point little entrainment is expected to occur because the gases flow along the hallway as a ceiling jet [4]. The entrainment was measured for experiments with all three opening sizes and both inlet soffit heights (0.0 and 0.20 m). The results of the entrainment experiments are given in Table 1. Also listed in the table is the Froude number at the opening, Fr =
VO2 , gdh (ρe − ρ O ) ρe
(3)
where Vo is the average velocity at the opening, g is the gravitational acceleration, ρe is the density of the gases being entrained, ρo is the density of the gases at the opening and dh is the hydraulic diameter of the opening. The hydraulic diameter was calculated by dividing four times the opening area by the perimeter of the opening. The Froude number at the opening is shown in Fig. 2 plotted with the normalized air entrainment mass flow rate (air entrainment mass flow rate divided by the mass flow rate at the opening). The normalized entrainment rate increases with a decrease in opening size and with an increase in soffit height. The data tends to follow two curves, one for the 0.0 m inlet soffit and one for the 0.20 m inlet soffit cases. This is due to the Froude number at the opening not accounting for the entrainment which occurs downstream of the opening (i.e. the gases rising to the ceiling and spreading horizontally to the walls). Two nondimensional groups were developed to account for the entrainment taking place when the gases rise to the ceiling and spread horizontally to the walls. Table 1 Results from air entrainment experiments Opening size, m2
Inlet soffit height, m
Velocity at opening, Vo, m/s
Mass flow rate at opening, m o , kg/s
Mass flow rate of air entrainment, m e , kg/s
Normalized air entrainment m e /m o , kg/s
Froude number Fr
0.12 0.08 0.04
0.0 0.0 0.0
0.74 0.94 1.29
0.063 0.053 0.037
0.0063 0.014 0.021
0.10 0.25 0.58
0.86 1.85 4.41
0.12 0.08 0.04
0.20 0.20 0.20
0.86 1.08 1.33
0.073 0.061 0.038
0.052 0.060 0.074
0.71 1.01 1.95
1.16 2.45 4.72
Developing Scaling Parameters for Estimating Carbon Monoxide 2.5
2.0
1.5 me/mo
Fig. 2 The normalized entrainment plotted against the Froude number of the gases at the opening. Opening sizes: • − 0.12 m2 , − 0.08 m2 , and − 0.04 m2 . Open symbols no inlet soffit and closed with 0.20 m inlet soffit
449
1.0
0.5
0.0 0
1
2 3 Froude Number, Fr
4
5
The two groups relate the opening of the compartment to the hallway geometry. The maximum distance the gases can rise vertically is equal to the distance between the bottom of the opening and the ceiling, z. The height of the opening, h o , was normalized by this maximum vertical rise distance z. The horizontal spread of the gases in the hall is regulated by the hallway width, whall . Subsequently, the width of the opening, wo , was normalized by the hallway width, whall . The normalized entrainment rate was, therefore, postulated to be a function of m˙ e
h o wo m˙ o = f nc Fr, , . z whall
(4)
Using the entrainment data in Table 1 and the parameters in Eq. (4), an expression for estimating the normalized entrainment rate, m˙ e
& m˙ o = 0.1 Fr
0.2
ho z
−1.6
wo whall
−0.8 '
,
(5)
was developed. The normalized air entrainment rate was plotted versus the estimated air entrainment rate from Eq. (5) in Fig. 3. The line in the on the plot is the result of a linear regression on the data. The regression line has a slope equal to 1.0 and corresponds to a r 2 statistic of 0.99. After quantifying the air entrainment in the hallway, the effect of air entrainment on the CO yield exiting the hallway was determined. Ewens [5] conducted a series of underventilated fire experiments in the VPI&SU facility where the CO yield exiting the hallway was measured for various air entrainment rates. The air entrainment rate
450
B.Y. Lattimer et al.
Fig. 3 The normalized entrainment plotted against the relation in Eq. (5). Opening sizes: • − 0.12 m2 , − 0.08 m2 , and − 0.04 m2 . Open symbols no inlet soffit and closed with 0.20 m inlet soffit
2.0
me/mo
1.5
1.0
0.5
0.0 0.0
0.5 1.0 1.5 0.1 Fr 0.2(ho /z)–1.6 (wo /whall) –0.8
2.0
was varied by performing experiments with three different opening sizes (0.12, 0.08 and 0.04 m2 ) for two inlet soffit heights (0.0 and 0.20 m). The CO yield from Ewen’s [5] experiments is plotted versus the normalized air entrainment (determined from Eq. (5)) in Fig. 4 for experiments with gases entering the hallway at approximately the same stoichiometry. In general, the experimental cases the higher predicted air entrainment had lower CO yields exiting the hallway. Except for the 0.04 m2 case 0.30
0.25
CO Yield
0.20
0.15
0.10
Fig. 4 The CO yield plotted against the relation in Eq. (5). Opening sizes: • − 0.12 m2 , − 0.08 m2 , and − 0.04 m2 . Open symbols no inlet soffit and closed with 0.20 m inlet soffit
0.05
0.00 0.0
0.5
1.0 1.5 2.0 2.5 0.2 –1.6 –0.8 0.1 Fr (ho /z) (wo /whall)
3.0
Developing Scaling Parameters for Estimating Carbon Monoxide
451
with no inlet soffit, the CO yield correlates well with the normalized air entrianment predicted using Eq. (5). A line representing these data, however, corresponds to one line of a family of curves for different stoichiometric conditions of the gases entering the hallway.
Stoichiometry of Gases Entering Hallway The stoichiometry of the compartment fire gases entering the hallway is also expected to affect the CO yield exiting the hallway. For underventilated fires, the stoichiometry of the gases entering the hallway is determined by the level of fuel in the gases. The mass flow of fuel entering the hallway is dependent on the compartment fire size and equivalence ratio. To estimate the mass flow of fuel entering the hallway, it was assumed that the air entrained into the compartment burned completely with a stoichiometric amount of fuel. Using this assumption, the mass flow of fuel entering the hallway was estimated using the following expression Q , m˙ o,fuel = 1 − 1 φ ⌬HC
(6)
where Q is the ideal fire size, ΔHc is the heat of combustion of the fuel burning in the compartment, and φ is the compartment fire equivalence ratio. Ewens [5] also measured the CO yield at the hallway exit for various compartment fire sizes and equivalence ratios. Using data from these experiments, the CO yield is shown plotted in Fig. 5 with the normalized fuel mass flow rate (fuel mass 0.30
0.25
CO Yield
0.20
0.15
0.10
Fig. 5 The CO yield plotted against the normalized mass flow of fuel entering the hallway. Opening sizes: • − 0.12 m2 , − 0.08 m2 , and − 0.04 m2 . Open symbols no inlet soffit and closed with 0.20 m inlet soffit
0.05
0.00 0.00
0.02
0.04
0.06
0.08
mf /m o
0.10
0.12
0.14
0.16
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B.Y. Lattimer et al.
flow rate normalized by the total mass flow rate through the opening). In general, an increase in the normalized fuel mass flow rate at the opening resulted in a higher CO yield, except for experiments with a 0.04 m2 opening. Similar to results in Figs. 2 and 4, the CO yield for experiments with a 0.0 m soffit followed one curve while the CO yields from 0.20 m inlet soffit experiments followed a different curve. Such a result was expected since the effects of the hallway geometry on air entrainment were not accounted for in the plot.
Estimating CO Yields It is evident from the previous sections that both the air entrainment into and the stoichiometry of the compartment fire gases entering the hallway must be considered to estimate the CO yield. Therefore, the CO yield is hypothesized as being a function of the normalized fuel mass flow rate and the normalized air entrainment rate (determined from Eq. (5)), YCO
˙ m˙ e m fuel = f nc m˙ O , m˙ O ,
(7)
Using the available experimental data, a relationship between the CO yield and these parameters was formulated 0.30
0.25
CO Yield
0.20
0.15
0.10
0.05
0.00 0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.18 (mf /mo)0.4 (m e /mo)–0.55 Fig. 6 The CO yield plotted against the relation in Eq. (8). Opening sizes: • − 0.12 m2 , − 0.08 m2 , and − 0.04 m2 . Open symbols no inlet soffit and closed with 0.20 m inlet soffit
Developing Scaling Parameters for Estimating Carbon Monoxide
0.4 −0.55 m˙ e YCO = 0.18 m˙ fuel m˙ O . m˙ O
453
(8)
The CO yields predicted using Eq. (8) are plotted against the CO yield data in Fig. 6. The line shown on the plot is a regression fit with a r 2 statistic of 0.80.
Conclusions The CO yield exiting the hallway was determined to be a function of both the air entrainment into the gases entering the hallway and the stoichiometry of these gases. The air entrainment into the hallway was a function of the Froude number at the opening, the height of the opening normalized by the distance between the bottom of the opening and the ceiling, and the width of the opening normalized by the hallway width. Using these dimensionless groups, the air entrainment data was predicted to within 5%. Accounting for both the air entrainment and the fuel mass flow rate (stoichiometry) into the hallway, the CO yield was predicted to within 30% of the data. Acknowledgments The authors would like to thank the Building Fire Research Laboratory at the National Institute of Standards and Technology for funding this project under Grant No. 60NANB4D1651. The comments and suggestions given by Dr. Craig Beyler are also greatly appreciated.
References 1. Karter, M.J., NFPA Journal, September/October (1995). 2. Gann, R.J., Babrauskas, V., Peacock, R.D., and Hall, J.R., Fire and Materials, 23: 3, (May/June) (1994). 3. Lattimer, B.Y., Ewens, D.S., Vandsburger, U., and Roby, R.J., Journal of Fire Protection Engineering, 6: 4 (1995). 4. Ellison, T.H. and Turner, J.S., Journal of Fluid Mechanics, 6 (1959). 5. Ewens, D.S., The Transport and Remote Oxidation of Compartment Fire Exhaust Gases, MSE Thesis, Mech. Engineering Dept., Virginia Polytechnic Institute and State University, Blacksburg, VA (1994).
Monocyte Lung Retention During Normal Conditions (Health) and During Disease States (Endotoxemia): A Medical Application of Scale Modeling Dennis E. Doherty
Abstract Under normal conditions blood monocytes flow through the capillary network of the lungs, but during certain conditions (infection, injury) they accumulate in the lungs and modulate pulmonary inflammatory and reparative processes via their elaboration of cytokines and growth factors. The mechanisms that regulate monocyte retention, accumulation, and migration in the lung microvasculature during these conditions are largely unknown. Endotoxemia is a condition that often precedes acute lung injury. We have previously shown in an in vivo rabbit model of LPS-induced endotoxemia, that monocyte lung retention is markedly increased (verses saline controls). It was hypothesized that initially lipopolysaccharide (LPS) would induce monocyte (7–10 μm diameter) lung retention by increasing monocyte stiffness and thus diminishing the cell’s ability to deform and transit the narrow pulmonary capillary network (6–8 μm diameter), and that later, LPS would induce CD18-dependent monocyte adhesion to lung vascular endothelium, prolonging their retention. These mechanisms were confirmed in vitro, in that LPS induced a rapid concentration-dependent increase in human monocyte stiffness, net filamentous actin (F-actin) assembly/organization, and retention in a filtration model simulating the pulmonary capillary network. These LPS-induced responses were dependent on the integrity of F-actin in that cytochalasin D, an agent that disrupts F-actin assembly, attenuated each of these processes. LPS, in a concentration- and time-dependent fashion, induced CD18-dependent and -independent human monocyte adhesion to unstimulated human endothelial cell monolayers in vitro. These in vitro mechanisms were active in vivo. Pretreatment of rabbit monocytes ex vivo with LPS enhanced their lung retention in vivo, suggesting that LPS was acting, in part, directly on monocytes. Initial monocyte lung retention in vivo during endotoxemia was attenuated by inhibiting monocyte F-actin assembly with cytochalasin D. Anti-CD18 antibodies caused only a slight decrease in initial monocyte lung retention in vivo, but led to a 90% inhibition of retention by 2 hrs. Control IgG had no effect. These data together suggest that initial lung retention of monocytes during endotoxemia D.E. Doherty Lexington Veterans Affairs Medical Center, Division of Pulmonary, Critical Care, and Sleep Medicine, Department of Medicine, University of Kentucky College of Medicine, 740 S. Limestone, Room K-528, Lexington, KY 40536-0284, USA
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is dependent on alterations in their stiffness and assembly/organization of F-actin, and that CD18-dependent adhesive mechanisms prolong monocyte lung retention during endotoxemia. Additional FDA-approved human studies have confirmed that monocytes marginate in the lungs of normal humans, and that altered monocyte accumulation occurs in patients with interstitial lung disease (including idiopathic pulmonary fibrosis-IPF).
Lipolysaccharide-Induced Monocyte Retention in the Lung Role of Monocyte Stiffness, Actin Assembly, and CD18-Dependent Adherence1,3 Dennis E. Doherty,2∗†‡ Gregory P. Downey,∗ Bill Schwab III,§ Elliot Elson,§ and G. Scott Worthen∗†
Blood monocytes and monocyte-derived macrophages accumulate in the lungs and can modulate pulmonary inflammatory and reparative processes through their elaboration of cylokines and growth factors. Endotoxemia, often a prelude to acute lung injury, induces a monocytopenia, likely resulting from monocyte accumulation in the lung. We hypothesized that LPS would induce monocyte lung retention by increasing monocyte stiffness and thereby diminishing the cell’s ability to deform and transit the narrow pulmonary capillary network, and that LPS would induce CD18-dependent adhesion of monocytes to endothelium, prolonging their retention. LPS induced a rapid and concentration-dependent increase in human monocyte stiffness, net filamentous actin assembly, and retention in a filtration model of pulmonary capillaries. These LPS-induced responses were dependent on the integrity of actin filaments in that cytochalasin D, an agent that disrupts filamentous actin assembly, attenuated each of these processes. LPS induced CD18-dependent and -independent human monocyte adhesion to unstimulated human endothelial D.E. Doherty ∗ Department of Medicine, National Jewish Center for Immunology and Respiratory Medicine, † University of Colorado School of Medicine, and the ‡ Denver Veterans Administration Medical Center, Denver, CO 80206; and § Department of Biochemistry and Molecular Biophysics, Washington University, St. Louis, MO 63110 Received for publication December 21, 1993. Accepted for publication April 8, 1994. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked advertisement in accordance, with 18 U.S.C. Section 1734 solely to indicate this fact. 1 This work was supported by a Veterans Administration Merit Review Award and National Institutes of Health Grants HL01804 and HL27353. Dennis E. Doherty is the recipient of a Veteran’s Administration Clinical Investigator Award. 2 Address correspondence and reprint requests to Dr. Dennis E. Doherty, National Jewish Center for Immunology and Respiratory Medicine. Room D508, 1400 Jackson St., Denver, CO 80206. 3 Original Article found in The Journal of Immunology, Vol. 153, pp. 241–255, 1994. Copyright 1994 The American Association of Immunologists, Inc.
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cell monolayers. In vivo, rabbit monocytes were retained in the lungs of animals rendered endotoxemic. Pretreatment of monocytes ex vivo with LPS enhanced their lung retention suggesting that LPS was acting directly on monocytes. Initial lung retention during endotoxemia was attenuated by inhibiting monocyte F-actin assembly with cytochalasin D. Anti-CD18 Abs caused a slight decrease in initial retention of monocytes, but led to a 90% inhibition of retention by 2 h. Control lgG had no effect. These data suggest that the initial retention of monocytes in the lung during endotoxemia is dependent on alterations in their stiffness and assembly/organization of F-actin, and that CD18-dependent adhesive mechanisms prolong monocyte retention in the lung during this process. The Journal of Immunology, 1994, 153: 241. Blood monocytes and monocyte-derived macrophages, which accumulate in the lungs during several disease states, modulate inflammatory and reparative processes through the elaboration of diverse cytokines and growth factors [1–6]. Because these leukocytes are potent effector cells in the lung, they may participate in the initial injury of lung tissue as well as in the fibroproliferative phase of inflammatory processes such as the adult respiratory distress syndrome (ARDS)4 . Hence, defining mechanisms that regulate the accumulation of monocytes in the lung during endotoxemia, which in humans is often a prelude to the development of ARDS, may lead to a better understanding of the initiation and resolution of this syndrome and other monocyte-dependent inflammatory events in the lung. Endotoxemia induces a rapid monocytopenia and neutropenia in humans [7–9] and in several experimental animal systems [10–12]. Although several studies have shown that the neutropenia that develops in response to i.v. LPS results from an accumulation of neutrophils in the pulmonary vasculature [10, 13–15], little is known about the kinetics or degree of blood monocyte retention in the lung during endotoxemia. The purpose of these studies was 1) to establish if monocyte retention in the lung is increased during endotoxemia, and if so, 2) to determine the kinetics of this process, and 3) to define mechanisms that regulate monocyte retention in the pulmonary vasculature during the initial hours of endotoxemia. The majority of capillaries in the human lung have a diametor of 6–8 μm [16–18]. Thus the caliber of these pulmonary capillaries is smaller than the diameter of many blood monocytes (range 7–10 μm [19, 20]). Accordingly, monocytes and lung vessels (endothelial cells) must deform for the monocyte to overcome these geometric constraints and transit the narrow pulmonary capillary network. Cytoskeletal protein assembly and reorganization, particularly of the microfilament network, have been reported to regulate alterations in leukocyte shape and mechanical properties [19, 21, 22]. Inflammatory mediators, including LPS and other activating agents, have been shown to stimulate net filamentous actin (F-actin) assembly and increase the stiffness of neutrophils and other mammalian 4 Abbreviations used in this paper: ARDS, adult respiratory distress syndrome; F-actin, filamentous actin; KRPD, Kreb’s Ringers phosphate dextrose; HIPP, heat-inactivated platelet-poor (plasma); ROI, region of interest; NBD, nitro-benzoxadiazole; RFI, relative fluorescence index; mcp, multiple comparison procedure; ANOVA, analysis of variance; LBP, LPS-binding protein; Vv , volume density.
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cells [14, 21, 23–25]. The effects of LPS on the mechanical properties of monocytes are not known, but this mechanism may be involved in the regulation of monocyte retention in the lung during endotoxemia. Because stimulus-induced alterations in mechanical properties (cell shape and microfilament assembly) have been shown, at least for neutrophils, to be transient [21, 26], other mechanisms may also be involved in prolonging monocyte accumulation in the lung. Monocyte–endothelial cell adhesive interactions are known to be mediated in part by the β2 subfamily of integrin receptors present on monocytes αL /β2 (CD11a/CD18), αM /β2 (CD11b/CD18), and αX /β2 (CD11c/CD18), which can serve as ligands for the lg gene superfamily of endothelial cell adhesion molecules [27–29]. Because LPS has been shown to induce adherence of monocytes to endothelial cells by direct actions on both the monocyte [30] and the endothelial cell 30–33], it is possible that adhesion events in the lung that involve these molecules might also contribute to the Initial or prolonged retention of monocytes in the lung during endotoxemia. Accordingly, we hypothesized that LPS would act on the monocyte to induce retention in the lung, and that the initial retention would be regulated by LPS-induced cytoskeletal F-actin assembly and alterations in the mechanical properties of monocytes; prolonged retention would in part involve CD18-dependent adhesion.
Materials and Methods Reagents Reagents and Abs utilized in these experiments were LPS-free (<0.01 ng/ml of LPS) as determined by the Limulus assay kit from Associates of Cape Cod (Woods Hole, MA). Percoll (colloidal silica coated with PVP) was obtained from Pharmacia Fine Chemicals (Piscataway, NJ). HBSS was obtained from Life Technologies, Inc. (Grand Island, NY). Salts used in KRPD (Kreb’s Ringer phosphate dextrose) buffer were obtained from Malinckrodt (Paris, KY). 111 In (DuPont NEN, Boston, MA) and tropolonate (Fluka AG, Buchs, FRG) were used to radiolabel monocytes. Nitrobenzoxadiazole (NBD)-phallacidin and rhodamine-phalloidin were obtained from Molecular Probes (Eugene, OR). Cytochalasin D, glycerol, p-phenylenediamine dihydrochloride, paraformaldehyde, poly-L-lysine hydrobromide (m.w. >300, 000) were obtained from Sigma Chemical Co. (St. Louis, MO). LPS from Escherichia coli O111:B4 (List Biologicals, Campbell, CA) was sonicated using a Branson bath sonicator for 30 min before use. The anti-CD18 mAbs 60.3 (obtained from Bristol-Meyers Squibb, PRI, Seattle, WA) and IB4 (a kind gift of Karl Arfors, Pharmacia Experimental Medicine, La Jolla, CA) were used in these studies. Murine lgG (Organon Teknika-Cappel, Malvern, PA) and murine lgG2 (a kind gift from Coulter Corp., Hialeah, FL) were dialyzed against KRPD to remove azide before use.
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Cell Isolation and Labeling Human [34] (>92% pure, >85% yield) and rabbit [35] (>90% pure, >75% yield) blood monocytes were isolated by methods that minimized LPS exposure, using a combination of discontinuous plasma-Percoll density gradients and counterflow centrifugation–cell elutriation in the absence of an adherence step. Monocytes were radiolabeled with 111 Inlabeled tropolonate [34–36]. The functional integrity of monocytes prepared in this fashion was not altered compared with that of unlabeled monocytes in vitro [30, 34, 37, 38] nor in vivo [35, 36, 39, 40]. Heat-inactivated platelet-poor (HIPP) plasma was made from fresh plasma obtained from the cell preparation.
In Vivo Experimental Design NZW rabbits of either sex (2.0–3.5 kg) were anesthetized with 2–3 mg/kg xylazine (Mobay Corp., Shawnee, KS) and 30–35 mg/kg ketamine (Veterinary Bristol Laboratories, Syracuse, NY) and were allowed to breathe spontaneously as previously described [35]. Cannulae were placed into a marginal ear vein and the contralateral central ear artery, LPS (0111:B4, 1 ng to 1 μg) was infused i.v. 10 min before the i.v. infusion of 111 In-labeled rabbit monocytes. In pretreatment studies, LPS (0.01– 100 ng/ml) or an equal volume of sterile saline was added to the vehicle HIPP plasma, and both were incubated with 111 In-labeled monocytes in a 1-ml vol for 10 min at room temperature before infusion. Saline was added to monocytes and plasma to control for the incubation period during pretreatment ex vivo. LPS was not washed away, as this would lead to increased cell loss from repeated centrifugations and adherence to the pretreatment vessel [30]. This protocol resulted in less than 5% cell loss before experimentation. Because infusion of the LPS used to pretreat monocytes was obligated by the methodology used, LPS concentrations were chosen such that the infusion of these amounts of LPS alone into untreated animals led to only a moderate (10 and 100 ng) or insignificant (0.1 ng) increase in monocyte retention in the lung. Retention of pretreated monocytes was compared with the retention of untreated cells infused i.v. into animals immediately after i.v. infusion of equivalent or higher amounts of LPS. In some experiments, monocytes were pretreated 10 min at 37◦ C with cytochalasin D (5 μg/ml) in a 1-ml vol before LPS pretreatment. Cell viability was >99% by trypan blue exclusion criteria. In other experiments, 111 Inlabeled monocytes were incubated for 10 min at room temperature with 60.3, IB4, murine IgG (40 μg/ml), or the vehicle HIPP plasma in a 1-ml vol before infusion into untreated animals, animals infused with LPS alone, or animals infused with LPS and 2 mg/kg of 60.3 or IB4 (an amount of Ab demonstrated to saturate circulating native lcukocytes and inhibit CD-18-dependent functions in vivo [41–43]), or 2 mg/kg murine IgG as a control Ab. Gamma camera scintigrams were obtained 5 min, 20 min, 40 min, 1 h, 2 h, 4 h, 6 h, and in some experiments, 18 h and 24 h after monocyte infusion and analyzed as
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previously described [35]. Briefly, a scintigram of the syringe containing the 111 Inlabeled monocytes was taken before infusion. The activity remaining in the syringe and needle after infusion was also measured. The activity in a region of interest (ROI) constructed around the lungs (excluding the liver) and around the syringe was measured. The activity of equivalent ROIs, constructed in an area away from the rabbit or syringe, was measured to determine background activity. Data were expressed as a percentage of total radioactivity infused (corrected for the t1/2 of 111 In) using the following formula: % Radioactivity infused = ((lung ROI – background lung ROI)/(syringe ROI – background syringe ROI – residual syringe activity)) × 100. Animals were killed by an overdose of pentabarbitol and the lungs were removed and counted in a gamma well counter. Activity was expressed as a percentage of total radioactivity infused [35]. In all experiments using 111 In-labeled monocytes, cells were infused into an untreated animal as a negative control, as well as into an animal rendered endotoxemic (as a positive control). We have confirmed in these studies that the radioactivity measured by scintigraphy correlates (r = 0.91) with lung radioactivity measured in a gamma well counter at necropsy [35, 36]. Because of the differences in the geometry of the syringe used and the rabbit lungs, we validated that the 111 In-activity measured in the syringe could be used as a reference for the 111 In-activity measured in the rabbit lungs. 111 In/saline was put into a syringe or into a lung phantom, and scintigrams were obtained and analyzed as above. Ten phantom/syringe pairs with equal 111 In-activity were scanned and compared. The amount of 111 In-activity was varied between pairs to reproduce the quantity of activity measured over 6 h in the in vivo rabbit experiments. There was an excellent correlation between the activity measured by scintigraphy in the syringe and phantom: r 2 = 0.997, p = 0.001, and y = 0.96x + 19.3. The activity of the syringes was slightly higher than that of the phantoms. 1.9 ± 1.2% (mean difference ± SD).
Tissue Morphometry In experiments where lung tissue was processed for morphometry, the heart and inferior vena cava were ligated and the lungs were fixed immediately in 10% neutral buffered formalin at a constant distending pressure of 25 cm H2 O overnight. The lobes were sectioned, counted in a gamma well counter, and then three blocks were obtained in a standardized location from each lobe (right upper, right lower, left upper, and left lower) yielding 12 blocks per animal. One 2-μm section was taken from each block and stained with hematoxylin-eosin azure. To determine the volume density of mononuclear cells in lung tissue, the following measurements were made on all 12 sections from each animal. The fraction of lung tissue present in each of the 12 sections was determined using a grid with 42 points arranged at the angles of equilateral triangles. Measurements were made at a magnification of 10× on 24 random fields (2 per section), the number of fields necessary to minimize variance. This was done to control for differences in the expansion of airspaces lung to lung. A square lattice test grid of 100 points was then used on the above 12 sections of each
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animal at a magnification of ×400 to determine the volume density of mononuclear cells present in the lung (alveolar and interstitial). In preliminary studies, 100 fields were examined on random slides and the plot of variance as a function of the number of fields examined was used to determine the number of fields necessary to reach the minimum variance for each experimental condition. Fields were selected in a predetermined stratified pattern using a stage micrometer. The volume density of mononuclear cells within the lung normalized to the volume density of lung tissue was calculated.
Actin Assembly and Organization The time course of F-actin polymerization in monocytes was determined by NBDphallacidin staining as described by Howard and Meyer [25]. Monocytes were suspended in 1% HIPP plasma in the presence or absence of LPS (0.001 to 1000 ng/ml) and immediately fixed (time = 0) or incubated for 5 to 60 min at 37◦ C. One-percent HIPP plasma was used because higher concentrations interfered with fluorescence measurements in the flow cytometer. Monocytes were stained for F-actin as previously described using NBD-phallacidin [14]. In selected experiments, monocytes were pretreated with 5 μg/ml cytochalasin D at 37◦ C for 10 min before assay. Cells were analyzed by a Coulter EPICs C cytofluorograph, Coulter Corp., Hialeah, FL. Log fluorescence units were converted to linear units [44] and expressed as the ratio of the experimental group over buffer-treated cells (Relative Fluorescence Index— RFI), thus yielding a quantitative assessment of F-actin present in the cell. To determine whether anti-CD18 Abs altered LPS-induced net F-actin assembly, monocytes were pretreated with 60.3 or IB4 (40 μg/ml) for 10 min before assay. These Abs did not alter the kinetics of LPS-induced net F-actin assembly (time course, dose response, nor magnitude of F-actin assembly, data not shown). To determine the organization of F-actin in control and LPS-stimulated cells, monocytes were prepared as described above except rhodamine-phalloidin, an agent more resistant to bleaching than NBD, was used. Cells were placed on coverslips coated with 0.03% poly-L-lysine and mounted on slides in a 1/10 solution of saline-glycerol containing p-phenylenediamine (0.1%) as a quenching agent. Edges were sealed with nail polish.
Measurement of Monocyte Stiffness Monocyte stiffness was measured directly using the “cell poker” as previously described [19, 45, 46]. Monocytes were studied in the cell poker over 1 h. The cell poker chamber contained KRPD with 1% HIPP plasma in the presence and absence of LPS. In selected experiments, monocytes were pretreated as above with cytochalasin D (5 μg/ml) before assay in the cell poker chamber which contained 1% HIPP plasma, cytochalasin D (2 μg/ml), and LPS (10 ng/ml). Data were expressed as
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individual cell stiffness (mdyne/μm) plotted vs time. In LPS concentration-response assays, the mean stiffnesses of all monocytes studied from 20 to 60 min after exposure to LPS were grouped and compared.
Monocyte Surface Ag Staining Human or rabbit monocytes isolated by elutriation were suspended in KRPD with 5% BSA (buffer) for 10 min, washed twice with buffer, resuspended in 0.1 ml of primary Ab (in increasing concentrations), and incubated for 20 min. Cells were washed twice with buffer, resuspended and incubated in 0.5 ml of a 1/20 goat antimouse-FITC Ab (Cappel, Durham, NC) for 30 min, washed twice and resuspended in buffer. The entire assay was done at 4◦ C, and cells were kept on ice until read in a Profile 1 cytofluorograph (Coulter Corp., Hialeah, FL). Unstimulated human monocytes were saturated with 40 μg/ml of anti-CD18 mAbs 60.3 or IB4 (RFI = 6 to 7 compared with cells stained with secondary Ab alone). These Abs cross-reacted with rabbit monocyte CD18, and elutriated rabbit monocytes were saturated with 40–50 μg/ml of 60.3 or IB4 (RFI = 6). Experiments were repeated in parallel, comparing the saturation kinetics of 60.3 and IB4 binding to untreated human or rabbit monocytes to that of monocytes treated for up to 1 h at 37◦ C in the presence of LPS (1 μg/ml). There was no significant up-regulation of CD18 on the surface and no change in the saturation kinetics for either anti-CD18 mAb in the presence of LPS. Other studies have shown that the saturation kinetics of 60.3 mAb binding to untreated monocytes is not different from that of PMA-stimulated monocytes [29].
Monocyte Adherence Assays Monocyte adherence was quantitated using a microtiter adherence assay as previously described [30]. Briefly, 111 In-labeled monocytes suspended in KRPD were coincubated at 37◦ C with monolayers of human umbilical vein endothelial cells (HUVEC) or on serum-coated tissue culture plastic wells in the presence or absence of LPS (1 μg/ml) for 15 min or 1 h in quadruplicate. In selected experiments, monocytes were treated with cytochalasin D (5 μg/ml) before assay as above, or pretreated in the wells with 40 μg/ml of 60.3, IB4, or the isotype control Ab mouse IgG2 for 10 min at room temperature on a rotating shaker before assay. The percentage of adherent monocytes for each condition was determined using the formula: % Adherence = ((cpm harvested – Background cpm)/(Total cpm added – Background cpm)) × 100 [30]. Because adhesion in the presence of buffer alone (baseline adherence) was different in 15-min assays (28 ± 2.5%) compared with that in 1 h assays (35 ± 4%), results were expressed as a precentage of baseline adherence using the following formula: % Baseline Adherence = ((% Adherence of Experimental Condition)/(% Baseline Adherence)) × 100, where baseline adherence was the percentage of monocyte adherence in the presence of buffer alone.
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Filtration Studies Filtration of monocytes was performed at room temperature as previously described [19]. An infusion pump (Harvard Apparatus, South Natick, MA) provided constant flow at 5 ml/min through 6.5-μm filters and 1 ml/min through 8-μm filters. These flow rates, which minimized pressure changes in the system, were used in an attempt to simulate the low shear stress present in pulmonary vessels in vivo [19]. Time course studies confirmed that a 10-min pretreatment time led to the greatest retention of monocytes in filters (see Results). 111 In-labeled monocytes were pretreated with 1% HIPP plasma in HBSS (filtration buffer) in the presence or absence of LPS (0.01 to 1000 ng/ml) for 10 min at 37◦ C before their perfusion through the filtration system (1-min assay and 6.5-μm filters or 5-min assay and 8-μm filters). In some studies, monocytes were pretreated with cytochalasin D (5 μg/ml), and the filtration buffer contained 2 μg/ml cytochalasin D. In other studies, monocytes were preincubated with the anti-CD18 mAbs (60.3 or IB4) or with murine lgG2 (40 μg/ml) in filtration buffer for 10 min at 37◦ C before their exposure to LPS and assay. The effluent (5 ml), filters, and proximal and distal chambers were counted in a gamma well counter. Recovery of 111 In-labeled monocytes averaged 98%. Every condition in each experiment was run in triplicate. Data were expressed as a percentage of monocytes retained in the filters.
Statistics All in vitro data are reported as mean ± SEM unless otherwise specified. All in vivo data are expressed as mean ± SD. Results were analyzed using the proprietary statistical package. Statistical Analysis Systems (SAS, Cary, NC) on a VAX 11/750 computer. For scintigraphy data (Figs. 1 and 7), comparisons between conditions in the first 5 min after monocyte infusion were analyzed using a one-way ANOVA [47], and a Tukey’s multiple comparison method (mcp) was used to determine pairwise differences. Further comparisons of monocyte retention over time in the various groups was determined by normalizing each individual animal’s data to the retention measured at 5 min, fitting a nonlinear curve to each animal’s data, and using a multivariate ANOVA model: % Radioactivity Infused = 1 −
a × (time − c) b + (time − c)
(1)
where a is the height of the asymptore, b is the half-life, and c is an offset parameter. This allowed for simultaneous comparison of all curve parameters between the different treatment groups. The data in Table 1 was analyzed using a two-way univariate repeated measures ANOVA [48], with percentage of retention as the dependent variable and time and pretreatment status as the independent variables. Actin assembly data (Fig. 2) was analyzed using two sample t-tests because the differences observed varied with time. The cell stiffness data was analyzed using a one-way
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ANOVA with time (Fig. 4A) or LPS concentration (Fig. 4B) as the independent variables, and a Dunnett’s multiple comparison procedure (MCP; 47) was done to determine significance compared with control values. A linear contrast within the ANOVA model was used in Figure 4B to determine if there was a linear trend in the LPS dose response. Adherence data was analyzed using a univariate ANOVA which was fit individually to the 15-min and 1-h data. A Dunnett’s mcp was used to compare the mean of each condition to that of the baseline condition. Linear contrasts were used to compare mAb values to LPS-alone values. Filtration data (Fig. 6) was analyzed using a univarate repeated measures ANOVA, and a orthogonal polynomial contrast was used to test for a linear trend in the data. To determine differences in treatment conditions (cytochalasin D or anti-CD18 mAb), a one-way ANOVA was used, and a Tukey’s mcp was used to determine differences. Data in Figure 8 were analyzed using a one-way ANOVA and the Dunnett’s mcp test.
Results Retention of Rabbit Blood Monocytes in the Lungs of Normal and Endotoxemic Rabbits The kinetics of 111 In-labeled monocyte retention in the lungs of untreated and endotoxemic rabbits is shown in Figure 1A. The small proportion of monocytes initially retained in control animals (monocytes alone) rapidly left the lung. The initial (5 min) retention of monocytes was significantly increased in those animals receiving as little as 1 ng LPS, and further increased in response to 10 and 1000 ng LPS in a dose-dependent fashion ( p < 0.001 for all LPS doses compared with controls). Monocytes remained in the lungs of those animals treated with LPS doses above 1 ng for up to 6 h ( p = 0.01), but approached control values by 24 h (data not shown). LPS induced a rapid increase of monocyte retention in the lung, that is, before the known induction of adhesion molecules on endothelial cells by LPS [30–32]. To determine if this increased retention was due, in part, to direct effects of LPS on the monocyte rather than as a result of other LPS interactions in vivo, 111 In-labeled monocytes were pretreated ex vivo with LPS (10 ng) or an equal volume of sterile saline in the presence of HIPP plasma before their i.v. infusion into untreated rabbits. The initial 5-min retention of monocytes pretreated with LPS was significantly greater than retention of untreated monocytes infused into animals immediately after i.v. infusion of the same amount of LPS (10 ng, p = 0.04; Fig. 1B) or of 100 ng LPS ( p = 0.04), and greater than that of saline/plasma pretreated monocytes ( p = 0.002; Fig. 1B). LPS-pretreated monocytes were significantly retained in the lung over 6 h compared with that in animals receiving 10 ng LPS alone and with that of saline and plasma pretreated monocytes ( p = 0.01). The retention of monocytes pretreated with saline in HIPP plasma (Fig. 1B) was initially greater than that of untreated monocytes (Fig. 1A) in untreated animals; however, retention was similar by 1 h
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Fig. 1 LPS-induced retention of rabbit monocytes in the lung: scintigraphy. A. LPS (1-ng open squares, n = 6, 10-ng closed squares, n = 6, 1-μg closed circles, n = 7) induced a significant increase in retention of 111 In-labeled monocytes in the lungs of rabbits compared with that observed in untreated animals (gray area: retention ± 2 SD, n = 10) at 5 min (∗ p < 0.001) and over 6 h († p = 0.01) except in response to 1ng LPS ( p = NS). B. There was an increase in retention of LPS-pretreated monocytes (closed squares, n = 7) in lungs at 5 min (‡ p = 0.04) and over 6 h (§ p = 0.01) compared with retention observed in animals rendered endotoxemic with 10 ng LPS before infusion of untreated monocytes (open squares, n = 6), or to that of saline- and plasmapretreated monocytes infused into untreated animals (open circles, n = 4, p = 0.002 at 5 min, p = 0.01 over 6 h). Data are expressed as the mean percentage of monocyte radioactivity infused ± SD. Statistical analysis: at 5 min (one-way ANOVA/Tukey’s mcp), over 6 h (multivariate ANOVA)
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Table 1 Retention of LPS-pretreated monocytes in the lungs of rabbitsa Time of Scan LPS Pretreatment
5 Min No
0.1 ng LPS n=4 1 ng LPS n=4 100 ng LPS n=6
24.3 (4.4) 29.0 (5.9) 30.7 (3.7)
Yes 38.3 (0.6)§ 41.0 (1.2)‡ 37.6 (3.2)†
2h No 12.0 (1.3) 13.9 (3.1) 20.7 (2.9)
Yes 23.9 (2.2)§ 28.7 (5.4)‡ 32.8 (4.6)‡
4h No 8.3 (1.3) 9.0 (4.0) 13.6 (1.3)
Yes 16.9 (0.4)§ 22.5 (5.9)‡ 26.7 (4.8)§
6h No 7.8 (1.2) 7.8 (1.1) 13.1 (3.1)
Yes 13.0 (3.0)§ 17.1 (6.1)‡ 18.7 (2.9)∗
Data are expressed as the mean percentage of radioactivity infused ± SD at the above time points after the infusion of untreated or LPS-pretreated 111 In monocytes and LPS. ∗ p < 0.02, † p < 0.01, ‡ p < 0.003, § p < 0.001: All compared with retention of untreated monoa
cytes infused i.v. into rabbits receiving the same amount of LPS i.v. Statistics: two-way univariate repeated measures ANOVA.
after infusion. Monocyte retention was increased by pretreatment with as little as 0.1 or 1 ng/ml LPS (Table 1), indicating the extreme sensitivity of monocytes to LPS. The pretreatment effect was no longer evident in any group by 24 h.
LPS-Induced Net F-Actin Assembly and F-Actin Reorganization in Human Blood Monocytes The LPS pretreatment studies in vivo suggested that LPS could act directly on monocytes to induce their initial retention in the lung. Because LPS is known to cause rapid alterations in the shape of neutrophils, requiring net assembly of F-actin within the cell [14], the effects of LPS on net F-actin assembly in human monocytes were investigated. LPS (10 ng/ml) induced an increase in monocyte F-actin by 5 to 10 min. This effect was greatest by 30 min and had returned to that observed in response to 1 pg/ml LPS by 1 h (Fig. 2A). The effects of 1 pg/ml LPS was not different from that of buffer alone (data not shown). As expected, pretreatment of monocytes with cytochalasin D, an agent that disrupts F-actin assembly, before their exposure to LPS (10 ng/ml) prevented any increase in F-actin (Fig. 2A). LPS induced an increase in net F-actin assembly in a concentration-dependent fashion (Fig. 2B). There was a significant increase in response to 100 pg/ml LPS, with the maximum response observed with 10 ng/ml LPS. The organization of F-actin in monocytes exposed to LPS was qualitatively assessed by fluorescent microscopy (Fig. 3). Monocytes in the presence of buffer alone revealed diffuse F-actin staining thoughout their cytoplasm (Fig. 3A). F-actin staining in monocytes treated with LPS (10 ng/ml) was associated with ruffles on the cells by 20 to 40 min (Figs. 3, B and C). The F-actin was again present in a more peripheral distribution by 1 h after LPS exposure, but the staining appeared more localized than that observed in control cells. Several monocytes exhibited areas of shape change with staining in cell membrane protrusions (Fig. 3D). The
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Fig. 2 Time course (A) and concentration response (B) of LPS-induced F-actin assembly in human monocytes. A. A net increase in F-actin assembly was observed as early as 5 to 10 min after exposure to LPS (10 ng/ml, closed squares, n = 6), was greater than that observed in response to 1 pg/ml LPS (open circles, n = 4) at 20 min (∗ p = 0.03), 30 min († p = 0.003), and 40 min (‡ p = 0.01), and returned to baseline by 1 h. Pretreatment of monocytes with cytochalasin D before exposure to LPS prevented any increase in F-actin (gray bar, mean ± SD, n = 3) over time. B. LPS induced F-actin assembly in a concentration-dependent fashion (n = 6). Maximum assembly was observed in response to 10 ng/ml LPS. Each condition was performed in triplicate in each experiment. Data are expressed as the mean relative fluorescence index ± SEM. Statistical analysis: 2-sample t-test
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Fig. 3 LPS-induced reorganization of F-actin in human monocytes (250×). A, F-actin was diffusely distributed thoughout the cytoplasm of untreated monocytes and present at the periphery of some cells. By 20 min (B) and 40 min (C) after exposure to LPS (10 ng/ml), F-actin staining was associated with ruffles. By 1 h (D) F-actin was present in a more peripheral distribution, and several monocytes exhibited F-actin in areas of shape change and cell membrane protrusion
distribution of F-actin in monocytes pretreated with cytochalasin D alone was not different from that observed in cells treated with buffer alone, however when these monocytes were subsequently exposed to 10 ng/ml LPS for 20 to 40 min, F-actin was observed in a more punctate distribution thoughout the entire cell (data not shown).
Time Course and Dose Response of LPS-Induced Human Monocyte Stiffness: Cell Poker Because increases in cellular F-actin have previously been associated with an increase in cell stiffness [14, 22, 26], we questioned if LPS would alter this mechanical property of monocytes. The average stiffness of monocytes treated with buffer alone over a 1-h time period was 0.157 ± 0.06 mdyne/μm (mean ± SD). LPS induced a time dependent increase in monocyte stiffness that was significantly different ( p < 0.05) from that observed in matched control cells at all time points after 5 min (Fig. 4A). The effect was concentration-dependent ( p = 0.0001, Fig. 4B). Although a wide range of stiffness was observed, at each LPS concentration the increase in monocyte stiffness was significantly greater than that observed in control
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Fig. 4 Time course (A) and concentration response (B) of LPS-induced human monocyte stiffness. There was a significant increase in monocyte stiffness as early as 5 min after exposure to LPS (10 ng/ml) which persisted for 1 h compared with monocytes exposed to buffer alone ( p < 0.05). Data for all cells studied between 20 and 60 min after LPS exposure were combined for B. LPS induced increased stiffness in a concentration-dependent fashion (1 to 1000 ng/ml LPS, p = 0.0001). This increase was absent when monocytes were treated with cytochalasin D (5 μg/ml) before LPS exposure (10 ng/ml). Each circle represents an individual cell stiffness (mdynes/μm). The black bars represent mean stiffness. The hatched bar in A represents mean stiffness ± SD of monocytes exposed to buffer alone over 1 h. Statistical analysis: one-way ANOVA/Dunnett’s mcp
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cells ( p < 0.05). The integrity of actin filaments was necessary for cell stiffening in that cytochalasin D treatment abrogated the LPS-induced increase in monocyte stiffness (Fig. 4B).
LPS-Induced Human Monocyte Adherence: Effects of Anti-CD18 Abs and Cytochalasin D To investigate if CD18-dependent adhesive mechanisms might play a role in mediating monocyte retention in the lung during endotoxemia, we first determined if LPS-induced adhesion in vitro [30] was CD18-dependent using two mAbs directed against CD18 (60.3 and IB4). Binding studies indicated that human monocyte CD18 surface molecules were saturated by coincubation with 40 μg/ml of either mAb in the presence (data not shown) or absence (Fig. 5, insert) of LPS (1 μg/ml). LPS did not induce an increase in human monocyte adhesion to HUVEC monolayers at 15 min, and neither anti-CD18 Ab attenuated monocyte adherence at this time point. By 1 h, LPS induced a significant increase in monocyte adherence ( p < 0.001) which was inhibited 59% and 54% by 60.3 or IB4, respectively ( p < 0.005 compared with LPS alone: Fig. 5). A similar inhibition of LPS-induced adherence to serum-coated plastic wells was observed (data not shown). The control mAb IgG2 did not alter adherence to either surface at 1 h. Cytochalasin D did not significantly attenuate LPS-induced monocyte adherence to HUVEC. Adhesion of 60.3or IB4-treated monocytes was not further attenuated when they were pretreated with cytochalasin D.
LPS-Induced Human Monocyte Retention in Model Pulmonary Capillaries of Fixed Diameter: Effects of Cytochalasin D Human monocytes were perfused through a filtration apparatus which was designed to simulate a parallel network of pulmonary capillaries of fixed diameter (6.5-μm or 8-μm pore filters). LPS (10 ng/ml) induced retention of monocytes in 6.5-μm filters which was increased above control by 5 min ( p < 0.05) and reached plateau at 10 min ( p < 0.001: data not shown). LPS-induced retention was concentrationdependent (Fig. 6). Retention was significantly increased in response to 1 ng/ml LPS ( p < 0.005 compared with buffer controls). The LPS effect was maximum using 10 ng/ml LPS ( p < 0.0005). Monocyte retention in this system was dependent on the integrity of actin filaments, as cytochalasin D treatment abrogated the LPSinduced increase in monocyte retention (Fig. 6). Pretreatment of monocytes with the anti-CD18 mAbs 60.3 or IB4, or with a control mAb (murine IgG2), did not significantly alter retention inthe presence or absence of LPS ( p = NS compared
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Fig. 5 The effects of anti-CD18 mABs or cytochalasin D on LPS-induced human monocyte adherence to HUVEC monolayers. The concentration of the anti-CD18 mAbs IB4 (black circles) or 60.3 (open circles) that saturated untreated monocytes (40 μg/ml) was determined by cytofluorograph analysis (insert). In a 15-min assay (n = 3), LPS (1 μg/ml) did not enhance monocyte adhesion (black bar) compared with that observed in buffer alone. Preincubation of monocytes with antiCD18 mAbs (60.3 or IB4, gray bars) did not alter their adherence (n = 3). In a 1-h assay, LPS (n = 10) increased monocyte adherence above that observed in response to buffer (n = 10) or to buffer plus either anti-CD18 mAb (white bars, n = 5 for each mAb, ∗ p < 0.001). Pretreatment of monocytes with 60.3 (n = 6) or IB4 (n = 6) before their exposure to LPS significantly attenuated the LPS-induced adherence by 59% and 54%, respectively († p < 0.005 compared with LPS alone), but adherence of pretreated monocytes was significantly increased above control values (buffer alone and buffer + mAbs). lgG2 (40 μg/ml, gray hatched bar) pretreatment did not alter LPS-induced adherence. LPS-induced adherence was not altered when monocytes were pretreated with cytochalasin D (hatched white bar, n = 5, p = NS). Each condition was performed in triplicate. Data are expressed as mean percentage of baseline adherence (buffer alone ± SEM) which was 28 ± 2.5% in 15-min assays and 35 ± 4% in 1-h assays. Statistical analysis: univariate ANOVA
with LPS alone), indicating that this process was not caused by CD18-mediated adhesion to the filters. Studies were repeated using filters with 8 μm pores. Monocyte retention under control conditions and in response to LPS was slightly diminished, but the pattern of the LPS concentration dependence and the effects of cytochalasin D were similar to that observed using 6.5-μm filters (data not shown).
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Fig. 6 LPS-induced retention of human monocytes in model pulmonary capillaries of fixed diameter. LPS induced a concentration-dependent increase in monocyte retention (closed circles, n = 12, ‡ p < 0.005, § p < 0.0005) compared with buffer (open circle). Pretreatment of monocytes with cytochalasin D significantly attenuated the retention of monocytes in response to buffer alone or LPS (closed squares, n = 5, p < 0.001). Each condition was performed in triplicate. Data are expressed as mean retention ± SEM. Statistical analysis: univariate repeated measures ANOVA/Tukey’s mcp
Retention of Rabbit Blood Monocytes in the Lungs of Endotoxemic Rabbits: Effects of Cytochalasin D and Anti-CD18 Abs To determine if F-actin assembly and organization in monocytes regulated their retention in the lungs of endotoxemic rabbits in vivo, rabbit monocytes were pretreated ex vivo with cytochalasin D (5 μg/ml), followed by LPS (10 ng/ml) in the presence of HIPP plasma before their i.v. infusion into untreated animals. Pretreatment with cytochalasin D abrogated the pretreatment effects of LPS on monocyte retention at 5 and 20 min ( p < 0.001, Fig. 7A) and over the 6 h time period ( p = 0.03; data not shown). To determine the contribution of CD18-dependent mechanisms in both the initial (5 to 20 min) and later phases of monocyte retention, monocytes were pretreated ex vivo with the mAbs 60.3 or IB4 (40 μg/ml) in the presence of plasma before their infusion into untreated or endotoxemic rabbits passively immunized with either 60.3 or IB4 (2 mg/kg). At 5 min, monocyte retention was significantly greater than controls in all animals receiving LPS ( p < 0.001). Retention was decreased in the IB4-treated endotoxemic animals at 5 min ( p < 0.001 compared with LPS alone). By 20 min, monocyte retention was significantly decreased in both 60.3- and IB4-treated animals ( p < 0.001) compared with animals treated with LPS alone. Monocyte retention in 60.3-treated animals was still greater than that observed in
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untreated animals ( p < 0.05) at this time point. By 2 h, the retention of monocytes in animals treated with either anti-CD18 mAb was indistinguishable from that observed in untreated animals, and significantly less than that in LPS-treated animals ( p < 0.001); Fig. 7B). Pretreatment of monocytes and passive immunization of animals with 60.3 or IB4 attenuated LPS-induced monocyte retention in the lung over 6 h ( p < 0.001). Pretreatment of monocytes and passive immunization of animals with control IgG Ab had no significant effect on monocyte retention in the lungs. Radioactivity in the lungs of animals killed 6 h after monocyte infusion paralleled that determined by scintigraphy (Fig. 8 A). Monocyte retention was increased only in those animals treated with LPS alone or with LPS and control IgG compared with CD18 Ab-treated animals ( p < 0.05) or animals not receiving LPS ( p < 0.001). We have previously shown that 111 In-monocyte retention in the lungs of rabbits is similar to that of the animals’ native monocytes [35, 36, 39]. This was reconfirmed morphometrically in this system by determining the Vv of mononuclear cells in the lungs of the animals studied above (Fig. 8B). The Vv of mononuclear cells in the lungs of those animals treated with LPS alone or with both LPS and control IgG was increased compared with untreated controls ( p < 0.05). There was a significant reduction in the Vv of mononuclear cells in the lungs of those endotoxemic animals treated with 60.3 ( p = 0.05) or IB4 ( p = 0.05) compared with those animals treated with LPS alone or to those animals treated with murine IgG and LPS. When data from all treatment conditions were compared, there was a highly significant correlation (r = 0.90, p = 0.004) between the Vv of mononuclear cells present in the lungs and the percentage of 111 In-labeled monocytes retained in the lungs 6 h after monocyte infusion, suggesting that the labeled monocytes were retained in a manner similar to that of the animals’ native unlabeled cells.
Fig. 7 Effects of cytochalasin D and anti-CD18 mAbs on LPS-induced monocyte lung retention: scintigraphy. A. Rabbit 111 In-labeled monocytes were pretreated with LPS (10 ng) or LPS/cytochalasin D in the presence of plasma before i.v. infusion into untreated rabbits. Cytochalasin D (gray bars, n = 4) abrogated monocyte retention induced by LPS (black bars, n = 7, ∗ p < 0.001) at 5 min and 20 min. There was no difference in retention of cytochalasin D/LPStreated monocytes compared with that observed in response to saline/plasma treatment (data not shown), or that of untreated monocytes infused into untreated animals (white bars, n = 10). B. 111 In-labeled monocytes were pretreated with anti-CD18 mAb 60.3 (open squares, n = 5) or IB4 (open circles, n = 5) in the presence of plasma before infusion into animals rendered endotoxemic by LPS (1 μg) and passively immunized with 2 mg/kg of 60.3 or IB4. At 5 min, retention was increased in the three LPS groups (± mAb, p < 0.001) compared with that of control animals (gray area, retention ±2S D, n = 16) or animals receiving mAbs alone (data not shown, n = 4). Retention in lungs of 60.3 or IB4-treated animals was reduced from 20 min on ( p < 0.001) compared with retention in rabbits receiving 1 μg LPS i.v. alone (closed circles, n = 10). Passive immunization of endotoxemic animals with murine IgG (closed squares, n = 3) did not alter retention compared with animals receiving LPS alone. Data are expressed as mean percentage of monocyte radioactivity infused ± SD. Statistical analysis: 5 and 20 min data (one-way ANOVA/Tukey’s mcp), data over 6 h (multivariate ANOVA)
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Fig. 8 The effects of anti-CD18 mAbs on LPS-induced monocyte lung retention: lung radioactivity and tissue morphometry at 6 h. A. Lung radioactivity (gamma well counter) was increased in animals rendered endotoxemic with 1 μg LPS (n = 6) compared with untreated animals (∗ p < 0.001, n = 7) or animals passively immunized with 60.3 or IB4 mAbs alone (∗ p < 0.001, n = 3 for each Ab). Treatment of monocytes and passive immunization with 60.3 (n = 5) or IB4 (n = 6) led to a decrease in retention compared with that in animals receiving LPS alone († p < 0.05). Murine IgG (n = 3) did not significantly alter the LPS effect. Data are expressed as mean percentage of monocyte radioactivity infused ± SD. B. The volume density (Vv ) of mononuclear cells in the lung was significantly increased in animals rendered endotoxemic with 1 μg LPS (n = 3) compared with untreated animals (‡ p < 0.05, n = 7) or animals passively immunized with either 60.3 or IB4 alone (‡ p < 0.05, n = 4). Treatment of monocytes and passive immunization with 60.3 (§ p = 0.05, n = 4) led to decreased retention in endotoxemic animals that was not statistically different from that in control animals. Murine IgG (n = 3) did not alter the LPS effect. Data are represented as mean percentage volume density of mononuclear cells in the lung per volume density of lung tissue ± SFM. Statistical analysis: one-way ANOVA/Dunnett’s mcp
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Discussion The data presented here implicate two mechanisms that regulate discrete stages of monocyte retention in the pulmonary vasculature during endotoxemia. Initial retention was dependent on LPS-induced F-actin assembly and reorganization in monocytes, whereas CD18-dependent adherence was required for prolonged residence of these leukocytes in the lung. LPS induced monocytes to change rapidly their mechanical properties and to be retained in capillary-sized pores in vitro. These processes were dependent on the integrity of actin filaments as cytochalasin D abrogated these LPS-induced responses. These events, which occurred before LPS stimulated monocytes to adhere to surfaces in vitro, appeared to account for the majority of the initial (5 to 20 min) retention of monocytes in the lung during endotoxemia in vivo. Additional data suggested that prolongation of monocyte retention (2 to 6 h), and to a minor degree the initial retention of these cells, in the lung required a CD18-dependent adhesive mechanism(s). If these later mechanisms were blocked with anti-CD18 mAbs, monocytes rapidly left the lung after their initial LPS-induced retention. The stiffness of neutrophils and other mammalian cells in their quiescent [19, 21, 49] or stimulated state [14, 50] has been shown to be dependent on the assembly of F-actin. LPS induced a concentration-dependent increase in monocyte stiffness in a substantial fraction of monocytes. This process was dependent on the integrity of actin filaments, as cytochalasin D prevented the increase in stiffness (Fig. 4B). The LPS-induced changes in stiffness appeared to be related to LPS-induced monocyte retention in filters and in the lungs of rabbits, as cytochalasin D also markedly reduced LPS-induced monocyte retention in these systems. We have previously shown that a difference of 0.1 mdyne/μm in stiffness is significant with regard to neutrophil vs monocyte retention in filters and in the lungs of rabbits under normal conditions [19]. The mean diameter of monocytes (8.3 μm) is similar to that of neutrophils (8.1 μm), yet the mean retention of monocytes in 8-μm filters (40%) is greater than that of neutrophils (15%) in the absence of stimuli. The stiffness of monocytes (0.14 mdyne/μm) in these studies was greater than that of neutrophils (0.05 mdyne/μm), a difference of approximately 0.1 mdyne/μm. We have previously shown that the retention of monocytes in the lungs of normal rabbits is greater [19] and their transit through the lungs is slower [51] than that of neutrophils. These data together with the data presented in the studies here suggest that the ability of monocytes to pass through filters or to transit the pulmonary vascular bed is inversely proportional to cell stiffness. This concept has also been suggested for neutrophils by Doerschuk et al. [52]. The quantity of monocyte F-actin assembled in response to LPS was much less than that observed in neutrophils, whereas the degree of stiffness was equivalent [14]. These data suggested that the organization, rather than simply the amount of assembled F-actin might be important in regulating monocyte stiffness. LPS induced monocyte shape change within minutes, with F-actin associated with cell ruffles and pseudopods. Importantly, although net F-actin assembly had returned to baseline by 1 h, the reorganization of F-actin persisted in some monocytes, as did stiffness.
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As expected, pretreatment of LPS-stimulated monocytes with cytochalasin D altered the organization or integrity of F-actin in the cell cytoplasm, and attenuated monocyte stiffness, suggesting that the assembly of actin filaments was involved in increasing cell stiffness. However, LPS induced a significant increase in monocyte stiffness earlier than it induced significant net F-actin assembly. Accordingly, other mechanisms may also be involved in LPS-induced increases in monocyte stiffness. Another factor which may contribute to cell stiffness is that of myosin-dependent contractile forces. Conventional myosin has been shown to be essential for capping and concomitant increases in stiffness of Dictyostelium cells in that contractile tension generated by actin-myosin interactions can drive both a change of cell shape and the capping of cross-linked surface receptors [53]. The persistence of LPSinduced monocyte stiffness beyond the time at which net assembly of F-actin filaments diminished might also be explained in part by the early formation of myosin “latch” interactions with actin. The organization of actin filaments at 1 h (Fig. 3D) may have also contributed in prolonging LPS-induced monocyte stiffness (Fig. 4 A). To determine the effects of LPS on monocyte deformability and adhesion, studies were performed using a filtration assay and a monocyte-endothelial cell adhesion assay in vitro. Retention of human monocytes in capillaries was initially modeled with a filtration system in which cells were perfused at constant flow across capillary-sized pores (6.5 or 8 μm diameter). These filters were used to simulate those narrow-caliber pulmonary capillaries that could potentially impede the passage of larger monocytes (7–10 μm) through the human lung. LPS induced a concentration-dependent increase in monocyte retention in these filters within 5 to 10 min after monocyte exposure to LPS, a time course which paralleled that of LPSinduced increases in stiffness. Retention was dependent on the intergrity of actin filament assembly and organization as pretreatment of monocytes with cytochalasin D abrogated their retention. Other studies have shown that the β2 sub-family of integrin receptors on monocytes mediates monocyte adherence to surfaces in response to several stimuli [28, 29]. We have shown that LPS induced monocyte adhesion to HUVEC monolayers by CD18-dependent and CD18-independent mechanisms, and that this process required more than 15 min to occur (Fig. 5). Indeed, monocyte retention in the filtration system was not significantly altered by anti-CD18 Abs showing that retention was caused by a mechanism other than CD18-dependent adhesion to the filter surface (Fig. 6). In summary, we have shown that LPS induced monocyte retention in capillary-sized pores within minutes and that this retention was regulated in part by an ongoing process of F-actin assembly, disassembly, and reorganization within the cell. LPS-induced changes in monocyte stiffness were also likely to influence the retention of these cells in the filters. LPS also induced monocyte adhesion to endothelial cells or plastic surfaces, however the time course of this response was delayed compared with that of LPS-induced stiffness and retention in filters. To determine if these mechanisms which involved in LPS-induced retention and adhesion, identified in vitro, were active in vivo, we monitored LPS-induced monocyte lung retention by scintigraphy in rabbits. Monocyte lung retention was markedly increased during LPS-induced endotoxemia in a dose-dependent fashion. Monocytes were very sensitive to LPS in that low doses of i.v. LPS induced signif-
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icant increases in lung retention (1–10 ng), and that ex vivo pretreatment of monocytes in the presence of HIPP plasma with low concentrations of LPS (0.1 ng/ml) led to significant increases in retention. These pretreatment studies suggested that initial monocyte retention in the lung resulted from the effects of LPS on monocytes, and not to other LPS effects in vivo, that is, on endothelial cell adhesion molecules. Additional studies were designed to determine if F-actin assembly and/or CD18-dependent adhesion were involved in monocyte retention in the lung during endotoxemia. Pretreatment of monocytes with cytochalasin D totally abrogated LPS-induced monocyte retention in the lung, suggesting that initial retention required F-actin assembly and reorganization, and increased cell stiffness. These studies did not unequivocally exclude adherence as a mechanism contributing to initial retention, even though cytochalasin D did not attenuate LPS-induced monocyte adhesion to endothelial cell monolayers in vitro. Because anti-CD18 mAbs (60.3 or IB4) did not alter LPS-induced monocyte net F-actin assembly in vitro, but did significantly inhibit LPS-induced monocyte-endothelial cell adhesion, these Abs were used to distinguish the role of CD18-dependent adherence from that of actin filament assembly on the initial retention of monocytes in vivo. The pretreatment of monocytes ex vivo with either mAb, in conjunction with the passive immunization of endotoxcmic animals with the same mAb, only partially affected monocyte retention in the lung 5 min after the induction of endotoxemia, but markedly reduced retention from 2 to 6 h (Fig. 7B). The fact that the CD18 mAbs slightly decreased monocyte retention at 5 min suggests that CD18-dependent adhesion may have contributed to some extent in the initial retention of monocytes, but that the majority of initial LPS-induced retention was CD18-independent. As in the human, a proportion of pulmonary capillaries have a diameter that is similar to or slightly smaller than [18] that of the rabbit monocyte (range 6–9 μm). Only a fraction of the infused radiolabeled monocytes were retained in the lungs during endotoxemia. Although speculative, it is possible that these retained cells may have corresponded to those monocytes with stiffness values in the upper range after exposure to LPS (Fig. 4B). It is also possible that increases in cell stiffness and adhesion could be interdependent. That is, CD18-dependent adhesion mechanisms might be enhanced by monocyte stiffening which could mechanically force interactions between the monocyte surface and the capillary endothelium. There are also pulmonary capillaries in the rabbit that have diameters greater than [18] that of the rabbit monocyte. In this situation, monocyte stiffness may be less important, and CD18-dependent and CD18-independent adhesion mechanisms may be more important in the regulation of monocyte retention in those vessels. The in vitro data given here (Fig. 5) and that of others [54, 55] have shown that monocyte-endothetial cell adhesion is CD18-dependent and -independent. Accordingly, other monocyte–endothelial cell adhesion molecules such as CD49d-VCAM1 or the selectin family [27, 55] may also be involved during the time course of monocyte retention in the lung during inflammatory states. The abrogation of retention by 60.3 and IB4 1 to 2 h after monocyte infusion in these studies suggests that
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CD18-dependent mechanisms are of major importance in maintaining monocyte accumulation in the lung during endotoxemia. In these in vivo experiments a pulse of radiolabeled monocytes was administered immediately after the induction of endotoxemia and used as a probe to monitor monocyte retention in the lungs during the early stages of this process. The interpretation of these data is dependent on the normal behavior of these cells in vivo. The functional integrity of the labeled rabbit monocytes used in these studies has been extensively tested in vivo. After i.v. infusion into rabbits, they circulate with a normal t1/2 and migrate into inflammatory lesions with the same kinetics as the animal’s native monocytes [35, 36, 39]. We showed that monocytes were transiently retained in the lungs of untreated animals (Fig. 1 A). The existence of a marginating pool of monocytes in the lungs which is in an equilibrium with circulating monocytes has also been described in rabbits [40] and in mice [56] by other investigators. Margination of these cells in the vasculature does not mandate their migration into long tissue. Indeed, we showed that labeled monocytes were not present in the pulmonary vasculature by 24 h after the induction of endotoxemia, and that they did not migrate into the interstitial or alveolar compartments of the lung, suggesting that the signal(s) for monocyte migration were not generated at a time when radiolabeled monocytes were present in the lung. Other investigators have shown in various animal systems of inflammation that leukocyte migration into the lung is CD18-dependent and -independent [41, 54]. Recent studies have shown in a rabbit system of protease peptone-induced peritonitis that mononuclear leukocytes utilize the integrins CD18 and CD49d during their migration into the peritoneum [57]. It remains to be determined if CD49d or other adhesion molcules are involved in the early stages of monocyte retention in the lung during endotoxemia, if signal(s) are present in the lung at later times during endotoxemia which could induce the migration of monocytes retained in the pulmonary vasculature, and, if so, whether these mechanisms are CD18- or CD49d-dependent or -independent. Recent studies have suggested that plasma proteins, that is, LPS-binding protein (LBP), can enhance the actions of LPS on monocytes [58, 59] and macrophages [60, 61]. Cell stiffness, F-actin, and filtration assays were performed in the presence of plasma in an attempt to better reproduce in vivo conditions where LBP is present and potentially interacts with CD14 on monocytes [61, 62]. Monocytes were incubated with LPS in the presence of HIPP plasma for the in vivo LPS pretreatment studies (Fig. 1B) so that the LPS could interact with these binding proteins ex vivo before infusion. Preliminary studies have shown that monocyte retention in the lung is less if monocytes are pretreated with LPS in KRPD rather than in plasma: however, it remains to be determined if plasma proteins modulate LPS actions on the monocyte in vivo. As mentioned above, monocytes and neutrophils differ in regard to their stiffness and their retention in the lung under normal conditions. There are also distinct differences between the response of monocytes and neutrophils to LPS. Monocytes are more sensitive to LPS than neutrophils. Monocyte retention in the lungs significantly increased after the i.v. infusion of LPS doses as low as 1 ng, whereas a minimum of 100 ng of LPS is required to induce an increase in neutrophil re-
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tention [10]. LPS induces a three- to fourfold increase in neutrophil net F-actin assembly [14] compared with only a 15 to 20% increase in monocyte net F-actin assembly, yet the mean stiffness induced by LPS (10 ng/ml) is similar for neutrophils (0.23 mdyn/μm) and monocytes (0.31 mdyn/μm), suggesting that monocytes may require less F-actin assembly to attain maximal stiffness because of their larger nucleus and higher baseline stiffness. Monocytes are induced to adhere to HUVEC monolayers with 1ng/ml LPS, whereas neutrophils require a minimum of 1–10 μg/ml LPS [30, 63]. Another major difference between these two leukocytes is that CD18-mediated mechanisms are important in prolonging monocyte retention in the lung during endotoxemia; however, neutrophil retention in the lung during this process is CD18-independent [14, 43]. LPS-induced alterations in F-actin assembly may persist longer in neutrophils and therefore overshadow CD18-dependent contributions, or mechanisms of detachment from the pulmonary vascular endothelium may differ for these leukocytes. If LPS-induced neutrophil retention in the lung is for the most part CD18-independent during endotoxemia, the use of anti-CD18 Abs in humans with sepsis and ARDS may not effectively prevent neutrophil-mediated lung injury. Anti-CD18 mAbs which prevent accumulation of monocytes in the lung could, however, inhibit this cell’s contribution to the later fibroproliferative phase of ARDS. In conclusion, the data presented here show that 1) low doses of LPS induced monocyte retention in the lungs of rabbits in part by a direct action(s) on the monocyte, 2) LPS induced a significant increase in net F-actin assembly and a reorganization of F-actin in monocytes within minutes, 3) LPS induced a rapid increase in monocyte stiffness, and 4) LPS induced a significant increase in monocyte retention in the capillary-sized pores of a filtration system. We have further shown that the rapid effects of LPS on monocyte stiffness and monocyte retention was dependent on the integrity of LPS-induced actin filament assembly. LPS induced an increase in monocyte adherence to unstimulated endothelial cell monolayers in vitro by a direct action on the monocyte [30] via CD18-dependent and CD18-independent mechanisms. These in vitro mechanisms were found to be active in vivo in that the initial phase of monocyte retention in the lungs of endotoxemic rabbits was dependent in part on the assembly of actin filaments in these cells, and less so on their CD18-dependent adhesion. CD18-dependent adhesive interactions between monocytes and the pulmonary vasculature, however, were involved in prolonging LPS-induced monocyte retention in the lung for several hours after the onset of endotoxemia. Acknowledgments The authors thank Dr. Eric Brown for the use of his elutriator to isolate monocytes for the Cell poker studies performed at Washington University; Dr. S. C. Erzurum for assistance with fluorescent staining: Lynn Ackerson for statistical analyses: Lynn Cunningham and Jan Henson for lung tissue preparation for morphometry studies; and Lynn Zagarella and Jeannine Leadbeater for their technical assistance in these studies.
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Scale Modeling of Medical Molecular Systems Tatsuhiko Kikkou, Shinichiro Iwabuchi and Osamu Matsumoto
Abstract Human body is mainly made by several biomacromolecules. The malfunction of proteins and nucleic acids set up our diseases; it would be considered that ca. 70% of human diseases occurred by that of receptor proteins, especially. Therefore the clarification of relationship between structure and function on biomacromolecule is one of the highest priorities in the pharmaceutical science field. Nowadays, several technical innovations on structural biology (sample expression by genetic technology, innovation of measurements; i.e. SOR (Synchrotron Orbit Radiation) or giant NMR (Nuclear Magnetic Resonance) and so on, structural analysis calculation by super computer) make easy to analyze stereo structure of macromolecules. However, number of determined structures would not clear up the relationship between structure and function on biomacromolecules systematically. On the other hand, the author found the molecular model on biomacromolecule resembles a “space truss structure” in the Building Engineeringtectonics or a “space link” in the Mechanics. Therefore the molecular model must be obeyed by the rules on these Kinematics at least, and a real molecule may be obeyed also. The simplest principle, the balance of internal degree of freedom and number of restraints in the molecule, would be determined the molecular stiffness or flexibility or mechanism. DNA and some protein structures will be discussed under the principle. Keywords Medical molecular system · degree of freedom · protein · nucleic acid · enzyme · receptor
Introduction In 1953, James D. Watson and Francis Crick found DNA double helical structure [1]. The structural model opened “the molecular biology world” and we could understand “Heredity” as a duplication of DNA molecule. The success was extremely beautiful. At that time we have an illusion when we can determine the stereo structure O. Matsumoto Department of Pharmaceutical Sciences, Chiba Institute of Science, Shiomi-cho 3, Choshi, Chiba, Japan, 288-0025 e-mail:
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of the target molecule, we can clarify the function of the biology spontaneously. Many people dived into the ocean of the structural biology with X-ray crystallography or NMR or cryo-electronmicroscopy. I also joined the project to determine proteinase: inhibitor complexes [2, 3], ribonuclease F1 [4], DNA repair enzyme [5, 6] by X-ray crystallography. As a result of many people, almost 40,000 structures are deposit in the Protein Data Bank (http://www.rcsb.org/pdb/) so far. However the relationships between structure and function of most of biological molecules have been still unknown. I found it is not necessary to determine so many structural determinations to understand the biological function. The key to understand the function will exist in the structure itself. Probably we need another approach. We usually use the molecular models to understand biomacromolecular structure. The usefulness to use molecular model was found world widely when Linus Pauling and his group proposed the ␣-helix and -sheet structure using CPK models in 1951 [7]. The success influenced Watson and Crick to propose DNA structure in 1953 [1]. At that time many people indicated the molecular model resembled architecture [8]. When we solved the new crystal structure of DNA repair enzyme, T4 endonuclease V [5, 6], the next interest was to understand the molecular mechanism to recognize the damaged DNA and to repair it. But we did not succeed in it from watching crystal structure thoroughly on the computer graphics. We were willing to build the conventional molecular model. Then the author found the molecular model on biomacromolecule resembles a “space truss structure” in the Building Engineeringtectonics or a “space link” in the Mechanics. Therefore the molecular model must be obeyed by the rules on these Kinematics at least, and a real molecule may be obeyed also. The simple principle, the balance of internal degree of freedom and number of restrictions in the molecule, would be determined the molecular stiffness or flexibility or mechanism.
Results and Discussion DNA (Flexible Molecule) When we watch the DNA model which built by Watson & Crick (Fig. 1) [9], I found the support rod in the middle of DNA model. Everybody could easily recognize if we remove the support rod from the DNA model, the model would be buckling. So the structure is very flexible. However the support is not found in the natural structure. Somebody told me that the reason why a real molecule differed from a molecular model. Therefore I thought that the difference caused by these circumstances in themself. In the nature, DNA is covered with plenty of water molecules. Checking the crystal structure of DNA, the water molecule bound to DNA tightly and fixed the structure [10, 11]. The water molecules are fixed the DNA stereo structure. As an additional bonus, Mashimo et al. remove the bounded water molecules using ethanol solutions and measure the number of water molecule using dielectric study [12]. When more than 7 bonded water molecules around one nucleotide on DNA, DNA is B-form. But the number of water is below 7, the structure suddenly
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Fig. 1 DNA model supported by rod. (Science Museum in London)
changed to Z-DNA. And the number of water is below 4, DNA changed to A-form. So the DNA itself has not a unique stereo structure. The DNA structure is strongly dependent on the circumstance. Another factor to controll the DNA structure is negative charge repulsion. Backbone of DNA is consisting of phosphate groups which have strongly negative charges in the solution. When we observed the 4,000 base pairs plasmid using Atomic Force Microscopy (AFM), the structure is open and spread on the mica surface (Fig. 2) [13, 14]. The driving forces of spreading are these phosphate negative charges in the backbone. So we reduce the repulsion force by adding cationic liposome. The results are shown in Fig. 3. Similarly the same long plasmid formed condensation when Chinese group added positive charged polyamine [15]. In general, DNA is wound up by positive charged protein, Histon, and forms chromosome in the Nuclei like a flexible string.
Structural Protein (Stiff Molecule) On the other hand ␣-helical structure has no degree of freedom in the structure. So the conformation is fixed and tight. Figure 4 shows the stiffness of ␣-helical structural model.
490 Fig. 2 DNA plasmid (ca. 4,000 base pairs) is spread by negative charged repulsion
Fig. 3 AFM image that cationic liposome reduced the negative charege repulsion
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Fig. 4 Stiffness of ␣-helical structure
The most famous one made by ␣-helical structure is our hair. There is an interesting story showed here. In old Japan, most of buildings were made by woods. When Higashi-Honganji temple in Kyoto, which is one of the biggest wooden buildings in the world, was constructing, the big and heavy columns were required to support the huge roof. Many people rose up the columns by ropes but the ropes were cut by the weight of columns. To solve the problem Japanese Ladies dedicated their hair to make the especially strong ropes (Fig. 5). The length of rope was 60 m. The rope can endure the weight of columns and the construction is succeeded. We can see the rope, “Ke-tsuna”, in the Higashi-Honganji temple now. The stiff structural proteins are also found in our nail, tendon of our muscle and so on.
Fig. 5 Ke-tuna made by human hairs
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Functional Protein (Mechanical Molecule) Most of the proteins have enzymatic functions and the shapes are almost globular. According to the X-ray crystallographic analysis, the main chains are tightly bound to each other by hydrogen bonds and keep stiffness. The stiffness of so called “secondary structures”, ␣-helix and -sheet etc., is formed by the continuous hydrogen bonding network. However the over all structure of protein is globular. The secondary structure will be bent in proper length. At the bending site, the continuity of the hydrogen bonding network is broken. The number of the restriction is lacking to keep stiffness and form mechanism. The most important functional protein is G-protein coupled receptor in our field. Almost 70% of human diseases would be caused by the error of these receptor molecules. When they accept their several signal molecules from outer of the cell, they transfer the information into the cell to regulate biological functions. These proteins consist of seven transmembrane ␣-helical structures. When the ligand is caught by the receptor, the bundle of 7 helical structures will change and the signal transfers to the G-protein. But the detailed mechanism is still unknown. In the human adrenergic receptor, G-protein activation site was specified at the third intracellular loop [16]. We synthesized the corresponding peptide and determined by NMR [17]. Also we found this concept could be applicable to another receptor, human Prostagrandin “EP3alpha” receptor [18]. We synthesized the receptor peptide and measured the activity to G-protein and determined the solution structure also. Our conclusion is that the activation sites of receptors are limited small region. The next problem is the switching mechanism of the receptor. When Negishi et al. trancated the long c-terminal loop of the receptor, the receptor activated G-protein constitutively without any signal ligands [19–22]. The results will make us to imagine when the receptor is resting states, the big c-terminal loop structure buried the active site. However once the receptor catches the ligand, the 7-transmembrane helical bundle is spread. According to the mechanism, the c-terminal loop will swing away from active site and it appeared to the outer side. The active site has strongly positive charge cluster. On the contrary G-protein ␣ subunit has strongly negative charged surface [23]. G-protein will quickly attack to the active site. After releasing the ligand, the receptor structure will get back to resting states (Fig. 6). Most of the space truss structures in the architectural field are satisfied with the Rule of Maxwell’s [24] that the structural stiffness is determined by the balance between number of degree of freedom and number of restraints. On the other hand, we don’t know the rule of biomacromolecular design, so far. The author would propose the simple idea in this paper will be applicable to almost all molecular structure to understand the functional mechanism. At that time when an enzyme protein binds the inhibitor molecule, or the Medicine, if the complex structure between protein and inhibitor will be satisfied with the Maxwell’s rule, the active site structural changes from a flexible state to a stiff state and lost the mechanical motion. So the inhibitor molecule will stop the enzymatic function of the target enzyme protein.
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Fig. 6 Hypothetical model on receptor mechanism
Some of the active site of the complex structure forms the -sheet structure which is another representative secondary structure of protein like ␣-helix. -sheet is also stiff structure. We can see the examples in the Bovine Pancreatic Inhibitor: Trypsin complex [25] or Streptomyces Subtilisin Inhibitor: Subtilisin comlex [26] and so on. If we keep the binding mode, we can substitute the structure of the inhibitor molecules. We found the fragment of Luteinizing Hormone-Releasing Hormone could bind trypsin and showed the inhibitory functions [27].
Conclusion The molecular model is still useful to consider the Kinematics of the real biomacromolecules. Probably the application of the architectural or mechanological principles could become the new key to understand the functional mechanism of biomacromolecules. Acknowledgments The author thanks, Dr. Katsuo Katayanagi, Dr. Mariko Ariyoshi, Dr. Masaaki Matsushima, Profs. Kousuke Morikawa and Morio Ikehara in Protein Engineering Research Institute and Prof. Eiko Ohtsuka in Hokkaido University who were X-ray crystallographic group for T4 endonuclease V. The author also thanks Profs. Manabu Negishi, Kunio Takeyasu and Atsushi Ichikawa in Kyoto University who are the bio-nanotechnology group. And I learned the architectural principle from Prof. Ken’ichi Kawaguchi in Institute of Industrial Science, The University of Tokyo.
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18. Kikkou, T., Matsumoto, O., Ohkubo, T., Kobayashi, Y., Tsujimoto, G. “NMR structure of an intracellular loop peptide derived from prostaglandin EP3alpha receptor.” Biochem Biophys Res Commun. 345: 933–7 (2006). 19. Hasegawa, H., Negishi, M., Ichikawa, A. “Two isoforms of the prostaglandin E receptor EP3 subtype different in agonist-independent constitutive activity.” J. Biol. Chem. 271: 1857–60 (1996). 20. Negishi, M., Hasegawa, H., Ichikawa, A. “Prostaglandin E receptor EP3gamma isoform, with mostly full constitutive Gi activity and agonist-dependent Gs activity.” FEBS Lett. 386: 165–8. (1996). 21. Ichikawa, A., Negishi, M., Hasegawa, H. “Three isoforms of the prostaglandin E receptor EP3 subtype different in agonist-independent constitutive Gi activity and agonist-dependent Gs activity.” Adv Exp Med Biol. 433: 239–42 (1997). 22. Hizaki, H., Hasegawa, H., Katoh, H., Negishi, M., Ichikawa, A. “Functional role of carboxylterminal tail of prostaglandin EP3 receptor in Gi coupling.” FEBS Lett. 414: 323–6 (1997). 23. Lambright, D. G., Noel, J. P., Hamm, H. E., Siegler, P. B. “Structural determinants for activation of the alpha-subunit of a heterotrimeric G protein.” Nature 369: 621–8 (1994). 24. Hangai, Y., Kawaguchi, K. “Keitai Kaiseki.” Baifukan, Tokyo, 1991, p. 67 (in Japanese). 25. Marquart, M., Walter, J., Deisenhofer, J., Bode, W., Huber, R. “The Geometry of the Reactive Site and of the Peptide Groups in Trypsin, Trypsinogen and its Complexes with Inhibitors.” Acta Crystallogr., Sect. B v39: 480 (1983). 26. Takeuchi, Y., Nonaka, T., Nakamura, K. T., Kojima, S., Miura, K.-I., Mitsui, Y. “Crystal structure of an engineered subtilisin inhibitor complexed with bovine trypsin.” Proc. Natl. Acad. Sci. USA 89: 4407–11 (1992). 27. Matsumoto, O., Taga, T., Higashi, T., Matsushima, M., Machida, K. “Complex formation by bovine trypsin and a tetrapeptide (Leu-Arg-Pro-Gly-NH2 ): X-ray structure analysis of the complex in the orthorhombic crystal form with low molecular packing density.” J. Protein Chem. 9: 589–593 (1990).
Scaling Human Bone Properties with PMMA to Optimize Drilling Conditions During Dental Implant Surgery Mohamed I. Hassan, Varahalaraju Kalidindi, Aaron Carner, Neal Lemmerman, Mark V. Thomas, I.S. Jawahir and Kozo Saito
Abstract Dental implant surgery is an effective alternative for replacement of missing teeth. The success of the implant depends on how well the bone heals around the implant. However, the excessive heat generated during drilling may create a necrotic zone in the drilled area, which prevents the growth of bone around the implant. Using human bone for the many experiments needed to investigate factors that affect heat generation during drilling, it is impracticable to obtain human bone so we substitute a material used as bone cement for the last 40 years by dental surgeons. This paper reports results obtained by drilling Poly Methyl Methacrylate (PMMA) under different conditions and discusses how these results are scaled to represent human bone. Keywords Dental implant surgery · osseo-integration · polymethylmethacrylate
Introduction Despite significant progress in treatment and prevention of dental disease, many teeth are lost due to disease and trauma. A number of options exist for the replacement of missing teeth. The most recent of these is dental implant. Modern dental implants are the treatment of choice for the replacement of missing tooth, all other things being equal. Most currently used dental implants consist of a root-shaped portion that is anchored to the bone, see Fig. 1. Various types of dental restorations (e.g., single crowns, bridges, and even complete over dentures) can be attached to the root-form implant. The surgical placement of the implant involves preparing a hole in the jaw that corresponds in size and shape to the implant. This is known as the osteotomy site. The implant is then threaded into the hole (in a manner somewhat similar to a wood screw) or is a tight press-fit. Over a period of time, bone becomes deposited on the implant surface, a phenomenon known as osseo-integration. While the nature M.I. Hassan Department of Mechanical Engineering, University of Kentucky, Lexington, KY 40508 e-mail:
[email protected] K. Saito (ed.), Progress in Scale Modeling, C Springer Science+Business Media B.V. 2008
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Fig. 1 Schematic of dental implant
of this interface has not been fully elucidated, it is robust. Many studies have shown implants to be a predictable method of tooth replacement, often achieving successful 5-year survival rates exceeding 95%. Implants do sometimes fail in service. This may occur due to a failure to be Osseo integrated (early failure) or during later service (delayed failure). Early failure is often a result of problems during osteotomy site preparation. One such problem is overheating the bone during the drilling process. It has been documented that bone cell death may occur when bone is heated over 47 ◦ C. In the absence of irrigation, bone temperatures during drilling may exceed 100 ◦ C, resulting in a failure of bone to bond to the implant as an early failure. Various strategies have been employed to reduce heat generation during implant site preparation, including variations in drill design and coolant delivery. However, there is lack of unanimity regarding the optimal combination of drill design features and coolant delivery and there is relatively little in the implant literature on these topics. Implant therapy involves some expense and inconvenience to the patient. It
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Table 1 Thermal properties of bone and PMMA Properties
Bone
PMMA
Thermal conductivity (W/mK) Specific heat (J/Kg K) Thermal diffusivity (m2 /sec) Density (Kg/m3 )
0.2–0.35 1300 0.3∗ 10−6 1800
0.15–0.4 1400 0.11∗ 10−6 1200
is important to improve outcomes and minimize treatment failures. Given the deleterious effect of heat on bone viability, one strategy for optimizing implant outcomes may be reduction of heat during osteotomy site instrumentation, a strategy likely to find application in other disciplines such as orthopedic and plastic surgery. There are many factors that contribute to heat generation during the drilling operation: drilling pressure, drilling status (continuous or graduated drilling), drilling speed; drilling time, drill design, drill sharpness, irrigation systems, and drilling depth. To check how each of these factors affects heat generation requires a series of experiments and thus a large number of consistent human bone samples. Since human bone differ its density and shape depending on gender, age and other factors, it is difficult to obtain a large quantity of consistent quality human bon samples. Polymethylmethacrylate (PMMA) is a good alternative material which is easily available and similar to bone in properties and functioning. PMMA is an acrylate and has been used as an effective bone substitute for the last 40 years by dental surgeons. It has been implanted in bone to improve implant fixation. PMMA is a vinyl polymer, made by free radical vinyl polymerization from the monomer, Methylmethacrylate. One of the main advantages in using PMMA is that it is readily available, its thermal properties are known and it is transparent. Thermal and physical properties of PMMA and bone are shown in the Table 1. The main objectives of this study are: (1) study the effect of drilling operation parameters on the bone thermal analysis, (2) create a thermal model that describes the temperature distribution in the bone (3) validate the thermal model using experimental data.
Experimental Approach PMMA specimens of 5 cm diameter and 2 cm thickness are prepared. Each specimen has two type K thermocouples inserted at 6 cm apart and at 6 cm to the drilling centerline as shown in Fig. 2. The thermocouple locations are chosen based on the images obtained from the infrared thermograph (taken by FLIR IR camera with a wavelength detector of 7.5–13 m) during drilling operation. Infrared images helped in determining the distribution of heat around the drilled hole, as shown in Fig. 3. The isothermal lines show that heat is in the radial direction conducted from the drilled hole. The thermocouples are connected to a 14 channel data acquisition system acquiring temperature data during the drilling process at the rate of 10 temperature samples/second.
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Fig. 2 Schematic of the experimental set up
The drilling, using a HAAS machine, was carried out at three different cutting speeds (1200, 1800 and 2200 rpm), three different depths (8, 12 and 16 mm) and with three different drill diameters (2, 3.5 and 4.3 mm) with a constant feed rate of 0.42 mm/s. Figures 4 shows the thermocouple temperature history using 2mm drill at 1200 rpm and 16 mm depth during the drilling operation, and Fig. 5 shows the thermocouple temperature history at 12 mm depth under the Fig. 4 condition.
Fig. 3 Heat generation and isothermal lines recorded by infrared camera during drilling
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Fig. 4 Thermocouple readings using 2 mm drill at 1200 rpm and 16 mm depth
Fig. 5 Thermocouple readings using 2 mm drill at 1200 rpm and 12 mm depth
Modeling Approach A model that can predict temperature and heat flux distributions in the bone created by drilling process will help dentists to choose proper drilling parameters that keep bone temperature below the critical temperature of 47 ◦ C. Infrared thermograph images were taken during the drilling process (Fig. 3) for comparison with a thermal analysis using ANSYS. Figure 6, 2-D thermal image of PMMA model using
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Fig. 6 Heat generation and isothermal lines on PMMA model using ANSYS software
ANSYS software, shows that heat is being generated in the center around the drill bit where the hole is being made and we can also observe that heat is spread outwardly in a radial direction. Consider the homogenous differential equation of heat conduction in the cylindrical coordination system [11], 1 ⭸T 1 ⭸T ⭸2 T = For a ≤ r < ∞ + 2 ⭸r r ⭸r α ⭸t
(1)
Where temperature T is a function of radius r and time t, and boundary conditions are as follows: At r = a,
⭸T q =− ⭸r k
(2)
Where q is the constant heat flux being generated, and a is the drill radius. We assume the heat flux is zero at the finite boundary: At r = ∞,
⭸T =0 ⭸r
(3)
we assume heat flux is zero at infinite boundary. Initial condition: For t = 0, T = TR
(4)
where TR is the room temperature. The assumptions used in developing the model are as follows: 1. Heat distribution in the body is in a radial direction. 2. The thermal conductivity of the material is small so the body is considered to be semi-infinite solid. The current problem was treated as a homogenous boundary condition problem without losing accuracy. The dimensionless parameters were introduced.
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T − TR ⇒ T = θ ⌬Tc + TR ⌬Tc r ⇒ r = ηrc η= rc t τ = Fo = ⇒ t = τ tc tc θ=
(5) (6) (7)
Where θ is dimensionless temperature, η is dimensionless radius, is dimensionless time and FO is Fourier number, rc is radius of the drill, tc is the time at which we k . start drilling and we define ⌬Tc = − qrk c = − qa By substituting equations in (5, 6, 7) we get, ⭸2 θ ⭸θ 1 ⭸θ = For 1 ≤ η < ∞ + 2 ⭸η η ⭸η ⭸τ
(8)
The boundary conditions are as follows: ⭸θ =1 ⭸η ⭸θ =0 At η = ∞, ⭸η At τ = 0, θ = 0. At η = 1,
(9) (10) (11)
After solving the above problem we get the solution as follows: a2 √ √ k tα a 4tα T = TR − 1.775 − π ∗ er f . e √ qa 2 2 tα
(12)
The heat released during the drilling process is given by the following equation: q = ⌬A.V.ρw .cw .⌬Ts
(13)
Here ⌬A - the area of the work piece V - Cutting velocity ρw - Density of the work piece cw - Specific heat of the work piece ⌬Ts - Temperature rise in the shear zone. Schmidt and Roubik found that 10% of the total heat generated during drilling remains in the work piece; the drill and the chips are absorbing the rest. q = 0.1.⌬A.V.ρw .cw .⌬Ts
(14)
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The final equation is as follows: T = TR −
√ √ k tα a a2 4tα 1.775 − e π ∗ er f √ 0.1.⌬A.V.ρw .cw .⌬Ts .a 2 2 tα
(15)
Results and Discussion Results obtained from the theoretical equation and experiments are compared in Fig. 7. A series of experiments were performed to check the dependence of temperature on the cutting speed, drill diameter and drilling depth. Figure 8 shows the maximum temperature obtained at three different speeds (1200, 1800 and 2200 rpm) using a 2 mm diameter drill with the same feed rate, 0.42 mm/sec for all three cases. It shows that the maximum PMMA temperature almost linearly increased with an increase of the drilling speed. Figure 9 shows the maximum temperature obtained at three different depths (8, 12 and 16 mm) using a 2 mm diameter drill with the same cutting speed, 1200 rpm for all three cases. It shows that the maximum PMMA temperature increases with an increase of drilling depth (8 and 12 mm), then starts to flatten due to an increased heat transfer surface area that help dissipate heat. Figure 10 shows the maximum temperatures obtained at three different (2, 3.5 and 4.3 mm) diameter drills at the same feed rate, 0.42 mm/sec and the same drill speed, 1200 rpm for all three cases. It shows that the maximum temperature increases with an increase of drill diameter. Particularly the temperature increase for the 4.3 mm diameter drill case is significant probably due to an
Fig. 7 Comparison of experimental results with theory
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Fig. 8 Temperatures measured at drilling speeds of 1200, 1800 and 2200 rpm
Fig. 9 Temperatures measured at drilling depths of 8, 12, 16 mm
increased drill surface area that can quickly generate heat with little heat dissipation to the surroundings. These results suggest that a thinner, slower and shorter depth drilling reduces the risk of gum inflammation and dead tissue.
Conclusion The scope of this study is to find the optimum drilling parameters for teeth implant methodology, as a replacement of missed teeth. Studies carried out on drilling parameters show that drilling with thinner diameter bits, at slower speeds and at more shallow depths reduces the risk of gum inflammation and dead tissue. This
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Fig. 10 Temperatures measured at drilling diameters of 8, 12, 16 mm
information allows the dentist to avoid drilling conditions that lead to gum inflammation. There are other factors that contribute to an increase in temperature; we plan to study these other factors in the near future and identify the optimal conditions under which the drilling operations should be performed. A mathematical model has been specified to describe the temperature distribution in the gum to calculate temperature profile and trace the maximum temperature locations. Acknowledgments We wish to thank the Kentucky Science Foundation and the UK Center for Manufacturing at the University of Kentucky for their support.
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