Steam Boilers of Thermal Power Stations

the inlet (iE i 1,. 1 = i') and x = 1 at the outle t (i[ i 0 u t = i"), (Fig . 9.2). On the other ha nd, t he volume steam content ~ and the actual steam content rp, which both have zero initial values, increase sharply in the initial portion of a tube. Further in the tube, they increase less intens ively to the maximum value oE unity at the tube end. Wi th an increase in press ure, rp and ~ approach x . The pressure steam content q> is an i mpo rtant flow characteristic, since it describes the actual distribution of water and steam in a mixture and their individual velocities in the combined £low. The actual velocity of steam is

w,

=

w;trp

(9.37)

and the actual velocity of water is

~

If t~ere is no difference in velocity, that IS w, = Ww = Wm, c = 1 and (9.36)

Fig . 9.1. Relation between mass steam conlent z and volu.me steam content ~ at vunous pressures

f .O

cp<~

For a descending flow

w,

103

9.3. R egimes of Steam-water Mtztare Floro

The proportionality fac tor c characterizes the ratio of the velocity of the steam-water mixture Wm to the ~ctual velocity of steam w., and t hus 1t characterizes the relative velocity of steam w,. With a n increase in pressure, the relative velocity of steam decreases and, as pressure approac~es the critical value, c tends to uruty while rp tends to ~The mass steam content in a uniformly heated evaporating tube varies linearly along the tube length between its extreme values: x = 0 at

Ww

= w~/(1 -

rp)

(9.38)

The_apparent density of a steam-water m ixture, Pm• kg/m3 , is the density

4h

G, w'Qf

+ Gw

IDo/

(9.39)

The actual density of the steam water mixture, Pa• kg/m3 , i.e. the density at the actual v el ocities of s team and wa ter, can be found from the Eollowing consideration. Let us s eparate a tube element of height !J.h filled with a steam-water mixture (Fig. 9.3). L et steam and water i n the element be represented by corresponding elementary volumes. The fractio ns of the cross sections occupied by steam and water may be denoted as f , 1 and !w a nd thei r sum, as f. The masses of t he two components may be written as /, 16.hpw and fw!J.hp' and their s um is the mass of the sepa rate d volume of the steam-wa ter mixture, f!J.hp 0 • This gives us an expression for the actual density of steam-water mixture:

Pa = p' -

!p

(p' - P *) = (1 - cp) p' rpp. (9.40)

+

In an ascending tube, the steam has a relative velocity W ro which results in a decrease in the fractio n of tho cross section occupied by the steam, rp, and an increase in the fraction occupied by water, (1 - rp), s o t hat Pa > Pm· With increasing pressure, Pa tends to Pm· The circulation ratio K is an inverse of the mass steam content and is essentially the ratio of the quantity of circulati ng wa ter to the quantity of steam produced for the same time interval (see Sec. 1.2}: K = 1/x (9.41)

9.3. Regimes of Steam-water Mixture Flow f

Fig. 9.3. To derivation of the formula for the density or steam-water mixture

The intensity of heat removal from a heating surface substantially depends on the con ditions, or regimes, of the motion of the steam-water mixture on t hat surface. Under identical conditions, the s t ructure and

I

104

Ch. 9. Parameters an¢ Motion Equations of Working Fluid

·-

-•,_

--. ·a

_ _o _

-a

0

.

• . ..-·-

.... ..

--~~'­

'- -' _ G_ a_

-r--·

.

!~..

. . . .

••t

0

!..~

o__o_

•• •

--• -

-.-

(a)

{b)

••

-.!.-

.• '

•

••• •• •

.

••~ : •• • •0 • •

•• • •

• • • ••

•

•••

--~

••

0

.!...!..... 0

•

•

-'-·

...

.-.• ••

.,_qr_.

•

0 0

0

.

.

-·-

•

-

-

'-

(c)

•• • ••

·-. -

(d)

(e)

=

Fig. 9.4. Steam-water mixture flow modes in vertical tubes (a) bubble !low; (b) emu ls ion flow; (c) slug now; (d) dispersed annulnr flow; (c) inverse dispersed annular f low

I

regime of flow are determined by the spatial orientation of the heating tubes, which is used to organize the motion of th e working fluid in steam-generating tubes. Vertical tubes. An adiabatic flow of a steam-water mixture at a low steam content and slow velocity is essentially liquid with rare fine vapour bubbles distributed in it. This is what is called bubble flow (Fig. 9.4a). As the steam content increases and if wp is high, the moving mixture contains a larger number of fine vapour bubbles; this is the emulsion flow, or frothy flow (Fig. 9.4b). At low values of wp, an increase in steam content may result in the coalescence of fine bubbles into larger formations whose size may be comparable with the tube diameter and whose l ength may be many times the diameter. These formations are called 'slugs' and, correspondingly the flow regime is the slug regime (Fig. 9.4c). Behind a slug there is a thin liquid bridge containing fine vapour bubbles. With a further increase in the steam content, water bridges between the slugs disappear and the slugs merge into a continuous vapour column with atomized water droplets in it. This

column moves aloog the tube core and i~ ·surrounded hy a continuous annular water film which moves aloog the tube wall. The water film intensively cools the internal surface of the tube. This is what is called the disperse-annular (wet-wall) flow (Fig. 9.4d). The thickness of the water film depends on the ratio between the flow rates of water and steam. At a high pressure and high steam velociLy, the major mass of the film is broken off and carried as droplets by the steam flow, leaving only a very thin water film on tho wall, which soon evaporates. In heated channels, some specific flow regimes may take place. In film boiling, for instance, a vapour film may separate the liquid from the heat-exchange surface, while liquid fills in the core of the channel; this is called the inverse disperse-annular flow (dry-wall flow), Fig. 9.4e. The flow regimes described above are rather conditional since they gradually change from one typo to another with no distinct boundaries between them. Horizontal tubes. The flow of the steam-water mixture in a horizontal tube is characterized by a non-uniform distribution of structural flow components over the tube cross section. Since steam has a lower density, it moves primarily along the upper tube wall, while the main mass of water is concentrated at the lower wall. The asymmetry of flow relative to the horizontal depends on the velocity of the steam-water mixture and tube diameter. At higher velocities, the flow is less asymmetrical. In steam-generating tubes 30-40 mm in diameter and at relatively high inlet velocities (w > 1 m/s), vapour bubbles form in the initial tube section. They are detached from the tube surface and move along with the liquid (Fig. 9.5a). The vapour bubbles increase in number in the direction of the flow and begin to merge into larger · formations. An ever increasing quantity of steam is involved in the combined motion of

10!)

9.4. H ydraullc Resis.t.ances

•

..

-

(a)

•

(6)

Fig. 9.5. Two-phase flow modes in horizontal tubes at (a) high and (b) low inlet velocity

the two phases, so that at a high steam content the flow in a tube becomes almost axisymmetrical and resembles the; disperse-annular regime in vertical tubes. \Vith a low velocity of water at the inlet to a steam-generating tube (w < 0.5 m/s), asymmetrical motion of water and steam may result in the exposure of substantial portions of the tube surface (Fig. 9.5b). The flow then becomes essentially asymmetrical along the whole length of the tube, with the steam moving along the upper tube wall. In other words, the two-phase flow is separated, as it were, into two individual flows. This flow regime is unstable. With an increase in the flow velocity, waves may form on the separating surface with their tops periodically touching the superheated upper wall. At supercritical pressures, the working fluid is a homogeneous medium . Nonetheless, even with a directed motion of the fluid at supercritical pressure in a horizontal channel, free convection may take place in a transverse direction, resulting in density variation along the height of the flow. This inhomogeneity can be characterized by the motion of a lighter (less dense) medium along the upper surface of a tube and of a heavier (denser) medium, along the lower surface, with no distinct boun-

dary between them. The difference in densities increases with an increase in the vertical size of a channel or of the tube diameter. In tube bends, some portions of the tube surface may be washed less intensively by the fluid than others, which is due to the centrifugal effect by which water is thrown towards the outside surface of a bend, while the tube wall at the inside surface is insufficiently cooled by water. 9.4. Hydraulic Resistances Since tubes offer resistance to the motion of water, steam-water mixture or steam, a pressure gradient forms between any two sections along the length of a tube. The general equation of the total pressure gradient l~ns been given in Sec. 9.1. For practical calculations, it can be written in a more convenient form:

t:..p = t:..p/r

+

t:..p,

+

t:..Poc ±

t:..ph (9.42)-

i.e. the total pressure gradient between any two sections of a heated tube is the sum of pressure gradients due to· fdction, t:..p1,, local resistances t:..p, acceleration t:..Pac• and hydrostatic head t:..p h· The resistance due to friction is caused by the viscosity of the moving:

.• 1 06

Cit. 9. Parameters and Motion Equations of Working Fluid

fluid. For a single-phase isothermal flow in a straight channel of constant -cross section, this term is found from the formula: l

t.p,, =

Ik

whore t.p1, is the resistance due to friction, Pa, A. 0 = A.ld is the resolved friction coefficient, 1/m, l is the length of the channel , m, w is the velocity of the fluid, m/s, and p is the density of the fluid, kg/m 3 • Tho friction resistance for a twophase flow can be principally determined by tho formula for single-phase flows, by replacing the s ingle-phase Jlow velocity by the velocity o.E steamwater mixture wm, provided that tho two-phaseflowcan be considered homogeneous, i.e. obeying the following relationship: (9.44) Noting the law of mass conservation {soe Sec. 9.1), we can write: PmWm

=

pfwo

(9.45)

Noting equation (9.25), formula (9.44) can be re-written as foll ows: t.p,, = "-ol

The pressure loss due to friction for a flow of variable steam content can be determined from the formula: w~ [_1+XI!J - - ( rr p' l!.pfr = "-ol--fp'

(9.43)

• 0

~0

p' [

w+ w; (1 - ~:)] 0

noting equation (9.29):

I!.Ptr = Aol

4- pf [ 1+X(f.- -1) J (9.47)

I 11 most flow regimes, the structure {)[ a two-phase flow differs noticeably from a homogeneous structure (see F ig. 9.4), for which reason correction factor 'iJ is introduced into the last ~qu ation to account for the effect {){ the flow structure. With a constant steam content, we then have: t.p,, = A0 l

4-;P' [1+ x'IJ (f.- -1 )J (9.48)

J

where x is the average steam content in the channel and \~jXJ-IJ>t.:Z:j

"' = --'-....;___ Xf -

Xj

_

where 'IJ 1 and 'i'J are correction factors to account for the effect of the initial and final steam content, x 1 and x 1 , on tho flow structure. Pressure losses due to local resistances are explained by the energy consumption for detachment of the boundary layer from the tube wall and the formation of whirls in the flow. Local r esistances appear in places where the shape or direction of a channel changes; conditionally, they are considered to be localized in a particular section and do not include fr iction resistance. The pressure loss in local resistances to a single-phase flow is determined by a formula similar to (9.43) in which the resolved friction coefficient A.0 = Aid is replaced by the coefficient of local resistance ~~ (it may be found in reference books):

(9.46) {)f,

1)

(9.49)

-

(9.50) For a two-phase flow: [t.p 1 = 1:£{

L4p' [1+x ( :~ -1) J (9.51)

where !;! is a conditional coefficient of local resistance for a steam-water mixture, usually !;; > £1• For a s ingle-phase flow across a tube bundle, the hydraulic resistance is t.p,b =stb

w2

2

1.07

9.5. Thermoph ytlcal Properties of Working Fluid

p

(9.52)

The coefficient !; 1 for a flow across a tube bundle depends on the design of the bundle.

For a two-phase flow:

ilPtb =

s;b ~~ p'[ 1+ x( f.--1)](9.53)

The pressure loss due to acceleration is caused by a change in the volume, and therefore, in the velocity of a flow. It can appear as the steam -content of a fl ow increases due to heating, as the fluid passes through a reduced cross section, or both. The pressure loss due to fl9w accel eration can be found by the· formula: D.Pac

=tot wp dw

(9.54)

wl

For a steady-state flow:

wp = constant Therefore, at p >Per llPac = wp (w, - w 1) = (wp) 2 (v1 - v 1) (9.55) For a two-phase flow, p < p cr· Expressing v1 and v 1 through the mass steam contents: v1 = v' (1 - x1) u·x, u1 = u' (1 -xi) v •x 1 and substituting them into formula (9 .55), we finally have: llPoc = (wp) 2 (u • - u') X \xl - Xt) (9.56) The hydrostatic component of pressure loss for single- and two-phase v ertical· flows is: WtPt

= w 1 p, =

9.5. Tbermophysical Properties of Working Fluid in the Path of a Monobloc Unit Va1·iations of the parameters and physical properties of the working fluid in various sections of the watersteam path of a supercritical-pressure monobloc unit are shown in Fig. 9.6. T he highest pressure of the fluid is at the inlet to the high-pressure water heater, downstream of the feed water pump, Pw 1, and tho lowest pressure is in the turbine condenser, p c· For supercritical-pressure pl ants, this pressure range is from 32 MPa to 0.003 MPa and for high-pressure power plants, from 17 MPa to 0.003 MPa. In the condensate path, which includes a condensate pump, and in the feed water path with a feed water pump, the

t (A I I

+ +

h

t.p,. = g ) p dh =

pgh

---l'- I

''I .

(9.57)

0

For a single-phase flow, p is taken as the average density of the fluid in section h, and for two-phase flows is determined by formula (9.40). When determining the total pressure gradient, l!.p h is assumed to be positive for ascending flows since it increases the total resistance of a tube, and negative for descending flows where it ceases to be a resistance and, {)n the contrary, acts in the direction {)f the flow.

Mtrln

1/iglr· :;;

S11por- , prt.·~-sll ti

!JMior :ylintfe

I

II

"ill

IY

l ow·

Pl'l!~·svriJ

~ -ylri ufpr

..

Y

1!1.

~ ~

"l:l

.§

Y11

Fig. 9.6. Variations of parameters and thermophysical properties of the working flu id in the water-steam path of a supercriticalpressurc monobloc unit

i08

Ch. 9. Parameters and Motion Equations of Working Flulct

pressure of the turbine condensate is raised to a value equal to tho pressure at the inlet. to the high-pressure water heater, which ensures the motion of the working fluid through the entire water-steam path of the boiler. In tho turbine, steam moves due to a pressure gradient between tho inlet, where the pressure is equal to that downstream of tho boiler, and the outlet, where it is equal to the pressure in the condenser. The highest temperature of the working fluid is the temperature of superheated steam and the lowest is that in the condenser. In high-pressure and supercritical-pressure plants, this temperature interval is from 545° to 30°C. Turbine condensate is preheated in the low-pressure water heaters and the deaorator of the condensate path from 30° to 105-165°C aud further in the higl1-pressure water heaters of the feed water path to the feed water temperature t1w (usually 145-270°C). Water pressure in this path varies from p = 0.3-1.0 MPa to 15-17 MPa in high-pressure plants or to 30-32 MPa in supercritical-pressure pl ants. The total pressure gradient in the path, flp = flP ec flPdca flp31, constitutes 20-30% of the pressure of superheated steam. On the other hand, the temperature of the working fluid is raised substantially, from t1w to superheated-steam tomperature t ••. Superheated steam is fed into the turbine with the parameters t,. and p ••· As steam expands adiabatically in tho turbine, its pressure and temperature decrease. In power plants of high and supercritical parameters, the total efficiency is increased by taking off steam from an intermediate stage of t.he turbine (at a pressure of 3-4 MPa and temperature of 290-320°C) and recirculating it back into the boiler where it is reheated, usually to the initial steam temperature, 54SC, in an intermed iate steam superbeater (rehoater). Since t,he working fluid changes its pressure and temperatm·e in the wa-

+

+

ter-steam path or a supercritical monobloc power unit, this involves certain changes in its thermophysical properties. As shown in Fig. 9.6, the water-steam path can be divided in to seven zones in which typical changes in the th ermophysical properties of the working fluid take place. The first zone includes the condensate and feed water path of the power unit with convective and radiationheated economizers. In this zone, feed water pumps create tho highest pressure in the water-steam path needed to produce steam of the required pressure. The working fluid in this zone remains liquid and therefore, its thermophysical characteristics are changed relatively weakly, notwithstanding the high rise in pressure; its dielectric permittivity e, however, decreases to a smoll rraction of its initial value. The most t.yp ical is the second (near critical) zone which is usually located in the boiler furnace. In this zone, the change from water to steam takes place, so that even a small rise in the temperature of the flow causes sharp changes in the thermophysical characteristics: near tho temperature of the highest heat capacity, the enthalpy of tho flow increases sharpl y, while the viscosity ll• heat conductivity A., and, what is especially important, the density p and dielectric permittivity e decrease substantially, though smoothly, not jumpwise. In the third zone, which iocl udes the main superheater, the temperature and enthalpy of the superheated steam increase further, but all other parameters, including density and dielectric permittivity, change less than in the previous zones. In the fourth zone (high-pressure cylinder of turbine), the thermal energy of the superheated steam is converted into mechanical work and its pressure and temperature decrease. Accordingly, the enthalpy and density of the steam decrease, the dielectric permittivity increases somewhat (due to temperature reduction), and tho

109

9.5. Thermophyslcal Properties of W orking Fluid

other properties (heat conductivity, heat capacity' and dynamic. viscosity) continue to decrease smoothly. [n tho fifth zone (reheater), steam temperature is raised again at an almost constant pressure roughly 3.5 MPa, resulting in an appreciable in crease in its enthalpy and slight increase in viscosity and beat conductivity. The dielectric permittivity of steam decreases by 67-80%, whereas the density and isobaric heat ca'pacity diminish only slightly. In the sixth zone (low-pressure cylinder of turbine), the physical parameters of steam are changed in a manner similar to the fourth zone, the only difference being that the pressure changes much more substantially t han in the fourth zone. For that reason, the density of steam decreases roughly to 1/300 or 1/400 o[ its init ial value. Its enthalpy also decreases Sllbstantially, wh ile changes in the other properties are rather s mooth. The seventh zone includes the turbine condenser. The condensing steam hero has constant parameters: pressure 0.003 MPa and a temperature of around 30°C. Only the enthalpy and steam content of the flow are diminished. As steam is condensed fully , the density, heat conductivity, heat capacity, viscosity and dielectric permittivity increase sharply. The specifics of subcritical pressure units are most pronounced in the second zone of the water-steam path, which is within the boiler furnace (Fig. 9.7). This zone is characterized by the conversion of water to steam (boiling); steam generation takes place at a constant temperature t' with two phases: water and steam, existing simultaneousl y (curve 1). For comparison, the figure shows temperature variations in the working flu id at supercritical pressure (curve 2). As may be seen from Figs. 9.6 and 9 .7, the thermo physical characteristics of the working fluid in the zone of high heat capacities at suporcritical pressures vary smoothly (though rapidly), whereas at subcritical pres-

p

Pu

I~ 2'::::,.·..... / / ~ /

/--x-:o

/://

:r:~t

t'

.

~

.....

\

~

'

~ r\Pm \

\

~ r-....

~ ._ '\em

\

....

.I!

-~

"" c::S"l::"

"'til~

:

' :>..,

I

~

._..,. -

f11rnaco ·~ ~ wafer walls ~\,.

•

•"' ~~~ c.a";-

Fig. 9.7. Variations of density p and dielectric permittivity e in evaporating zone

1- lcmperaturc or the working !luid at subcr!tical pressure; B- d!tto, at sul?ercri tical pressure (for compartson)

sures the change from the proper ties of water to those of steam suddenly takes place at the saturation temperature. As seen in Fig . 9.7, as the water to steam transition takes place, tho density of the water, Pw• abruptly changes to that of steam, p., which results in an increase in the enthalpy of the working fluid. Similarly, the dielectric permittivity of water changes abruptly to that of steam. In the zone of constant temperature at the saturation line and constant pressure, bot;h phases (water and steam) co-exist; in the whole range of steam contents of the two-phase flow, 0 < < x < 1. The dot-and-dash lines in tho figure show variations in the density· of the steam-water mixture, Pm, and in its dielectric permittiv ity em along the flow. The thermophysical properties of water and steam are determined by

i10

Ch. 10. Temperature Conditions on Heating Surfaces

\

,1/r

J11alt?r r t?!IID/1

e~

, Pcr,tcr

Fig. 9.8. Effect of pressure on the density of

wn ter aod steam, p, and dielectric pcrmi Uivity e at the saturation li ne

pressure. Figure 9.8 shows v ariations in the density and dielectric permitti-

vity of water and steam; as may be seen, these characteristics are substantially different in a wide range of subcritical pressures, but come closer and closer together in the critical point. The above relationships between the parame~ers and properties of the working £lu id determine the hydrodynamic and heat- transFer processes on heating surfaces and the carry-off by steam of impurities present in water; they also pl ay a v ital part in the formation of deposits on boiler and turbine elemen ls.

TEMPERATURE CONDITIONS ON HEATING SURFACES 10.1. Classification of Heating and Cooling Modes

U A knowledge of temperature distribution in the metal of heating surfaces, which operate under complicated and heavy conditions, is essential for estimating the reliability of a steam boiler. In boilers operat ing on organic fu el , there are three differen t regions of heat transfer. The first region includes the heating surfaces (water walls) arranged in the furnace; they receive heat mainly by radiation. The most important factor of heat transfer in this region is the pattern of distribution of the heat flow along tho height of the furnace (see Fig. 20.2) and over the cross-sectional periphery of waterwall tubes (see Sec. 10.4). The second heat-transfer region comprises the semiradiant heaLing surfaces which are arranged in the boiler zone where radiation from gaseous vo-

lumes is still subst,anLial and the gas temperature is quite high (1 2008000C). This group of heating surfaces includes primarily platens and water walls in the horizontal duct of the furnace. The heating surfaces in the third reg ion receive heat mostly by convection. T his r egion has a r elatively low temperature of combustion products (800-900°C at tho inlet, to the convective shalt and up to 100-150°C at i Ls • outlet) and accommodates convective heating surfaces: an economizer, air heat er, and some superheater banks . These heating surfaces have a small Lube pitch, i .e. small spaces between tubes for Lhe passage of hot gases. Under such cond itions, the fraction of radiant heat transfer from combustion products onto t ubes is not high . In the steam generators of nuclear power st ations , Lwo r egions of heat transfer are usually distinguished. The first r egion includes the heating sur-

1U

10.1. Claulflcatlon of Heating and Cooling .Modes

faces arranged in the reactor core. The heat in the reactor is liberated due to nuclear fission in ·a very restricted volume around the pl ace where nuclear fission occurs. This makes it. possible to ass ume that practically all the heat released by tho core is concentrated in tho volume of fuel elements. The maximum amount of heat released, qmax• through the s1.1rface of fuel elements is in mid-height and the zero value (in the absence of reflectors), a t the end faces. Reflect ors can substantially equalize the intensity of heat released. In the second region, heat transfer takes place by convection at a moderate temperature of the heat-transfer agent (water, liquid metal or gas) . For instance, in a water-healed primary circuit, water Lem perature does not exceed 330-350°C (at a pressure of 13-15 MPa); in ci rcuits heated by liquid metal or gas, this temperature may be higher, up to 700-800°C. Under such conditions, ther e is no immediate danger of tube burn-out should the heat-Lransfer conditions worsen, but the durability of the heating surfaces' metal can be impaired and cause emergency situations. Present-day engineering has made possible the release of enormous quantities of heat in the boiler furnace or the core of a nuclear power reactor. Irrespective of t,he type of power plant, the beat released must be actively r emoved through heating surfaces. This is ensured by the motion of the working fluid at a definite velocity. The motion of the steam-water mixture, and therefore, cooling of the evaporating tubes of steam boilers and steam generators can be organized in a different manner (Fig. 10.1). In free-·c irculation plants , the steamwater mixture moves under the freecirculation head that appears when the tubes heat up. With an increase in load, tho mass fl ow rate at the inlet, to the evaporating tu bes first

c

c'

D/Dr

Fig. 10.i. Effect or boiler load on mass. velocity J - gravlly clrculntlon; t-mulliple forced c irculati on: J-c lrculotlon In once-through boiler; 4-comblned circulation

increases sharply to a maximum value and is then almost stabilized or oven decreases somewhat , since the increasing steam generation at. a high unit volume of steam results in an increased resistance of the Lubes (curve 1 in Fig. 10.1). In mul t iple forced circulat-ion plants, the circulation of the water and steam-water mixture in evaporating tubes is effected b y a circulation pump , so that the mass flow rate of the working fluid is almost constant irrespective of boil er load (curve 2). In once-through boiler plants, tl1e mass flow rate is proporLional to t he boiler load (curve 3). At a low load, the mass fl ow rate may turn out t<> be inadmissibly low and cause burnout of tubes. For this reason , load shedding is restricted to no less than 30% of the rated load. Curve 4 in Fig. 10.1 depicts the characteristic of a boiler plant in which tho motion of the working fluid is based on the principle of mulLiple forced circulation at low loads and on the once-through principle at high loads. When operating on the principle of mult-iple forced circulation, the mass flow rate is expressed by the sum of the ordinates ab- the mass flow rate corresponding to recircul ation through the steam-generating surfaces, and be- the mass flow rate in the economizer and superheater in once-through operation. With a chan-

Ch. 10. T empera ture Conditfons on Heating Surfaces

112

ge to the once-through operation, the cross section of a tube (noting the mass flow rate is the same in all that heat supply or heat r emov al may the heaLing surfaces of the water-steam b e uneven around the periphery of a path, the ordinate a' c'. Thus, the tube}. comb ined circulation system ensures adequate cooling of all the heaLing 10.2. Heat-transfer Crisis surfaces irrespective of the load. Acin Evaporating T ubes cordingly, fo rced-circul ation singleFor a g iven heat release intens ity, pass motion of water and steam takes place in the economizers and super- the temperature conditions on an evaporating tube are m ainly determiheaters. The thermal conditions in the Lubes ned by the steam content, mass flow of tho steam-water path of a steam rate and pressure of the flow . Various inadequate temperature conboiler or steam generator are established depending on the ratio between ditions which may appear in evapothe quantity of heat s upplied by the rating tubes can resu lt in a substanheat-trans[er agent \.o the outside tial rise in tho temperature of the surface and tho quantity of heat metallic tube wall which carl someremoved by tho working fluid from times cause tube burn-out. One should the inside surface. T he si multaneous differentiate between tho inad equate processes of heat rel ease and heat temperature condition s in bubble El ow removal ensure that any point of a and in disperse-annular flow . With bubble flow of a s team-water heating surface is in the necessa ry t herma l s tate and has a specific mixture having a moderate steam t emperature. The temperatures in va- content, a thick layer of liquid coveL"S rious points of a heating surface form the tube wall (Fig. 10.2a) and the what is called the temperature field . temp erature of the tube is maintained One can distinguish between a tem- at a substantially low level (section perature field along the motion of 1-2). Even with intensive heating, it t he working fluid, i.e. along the length exceeds the saturat ion temperature of tu bes (assuming that t hey are hea- only by a few tens of degrees. As th e working fluid moves and is ted uniformly around their periphery) and a temperatu re field across heated in t he tube, more and more J I

-,

f

f'

2

t - - - -- -

t'- - -

q,

gUll.LLLI.Lj.J.lll.UJJ

. .......... . ... .. . .' . . : . .. ' . .' .. . . .

•

.

,.

(a)

•

.

• t

q2rrrrrn""T"T"i-rrhrTTTTTT1rTTTTT"M u~~~~~~~~

• •

I

(h)

Fig. 10.2_ General pattern of temperatures in a steam-generating lube at (a) bubble Oow and (b) dispersed nnnular Oow of steam-water mixture

10.2. Heat-tran•fer Crl1ll In" Euapor4tlng Tabu

vapour bubbles appear on tho tube walls; they coal esce with .o ne another and may eventually form a continuous vapour film· which will separate the flowing liquid from the heated tube wall and thus sharply impair the conditions of heat transfer. T he effect of a sharp worsening of heat transfer on a change fro m bubble boiling to film boiling is called tho boiling crisis (burn-out conditton.~) and t he corresponding heating · ·t oad is called the critical load qcr· On occurrence of the boiling crisis (point 2), the layer of superheated steam at the heated wall becomes thicker, the heat-transfer coefficient drops down sh arply, resulting in a sharp rise in the wall temperature and often in burn-out of the t ube wall (point 3). These temperature conditions can occur in bubble flow if the heating rate of one of the evaporating tubes is t oo high and a thick layer of steam accumulates oo the superheated tube wall. In disperse-annular (wet-wall) flow, saturated steam with susp!:nded liquid droplets moves in the core of a tube and a water film flows along the tube walls (Fig. 10.2b). Without heating, the thickness of th e liquid film depends on the ratio between the flow rates of water and steam, the quantity of moisture t hat is separated from the flow core and wets the wall, and . the. quantity of moisture r emoved from the wall due to break-off and mechanical carry-off by the steam flow. In heated tubes, the intensity of heating has a strong ,additional effect on the thickness of•'"the water film. A continuous water fil m can still ensure proper heat removal from the heated surface and the wall tempeL·ature can be maintained at an allowable lovel (line 1 ' -2' ). In further heating, the water film becomes thinner owing to ev aporation and break-off, so that only a very thin fil m (micro-film) re mai_ns on the wall. Under a particular heating load, t he microfilm is destroyed and separated into individual islets and streaks whose Iiumbor 8 -01524

113

and size diminish in the course of further vaporization. T hus, a continuous steam layer forms at the wall, while the core of the flow contains ii slightly superheated steam with wator droplets whose concentration decreases gradually in the direction of the flow. Under such condit ions , water dro plets do not roach the tube walls. Besides, on entering a hotter zone of the tube they evaporate. Since vaporization is more intensive at the walls, the water droplots are repulsed from tube walls back into the steam flow. T:Jnder such conditions, heat transfer occurs through a continuous steam layer, i.e. the heat-transfer · c.oefficient decreases sharply and the wall temperature increases (poin t 2' in F ig. 10.2b}, resulti ng in a boiling crisis . In contrasl. to , the previously mentioned case of a boiling crisis at a mode1·ate steam content during a cbange· from bubble to "film boiling, this type of boiling crisis is caused by a · change fro m disperse-annular to disperse flow with a complet e drying out of the liquid film at a high steam content of the £low. This type of boiling crisis can even · take place at a · low h eating load and rel atively high .heattransfer coefficien t as th e liquid phase evaporates almost completely. Since the unit volume of steam is much higher than that of water, the linear velocity of the flow increases substantially. In a boiling crisis when the liquid fil m dries out, the temperature of the tube wall rises less significantly (line 2' -3'), as in tho former case. Boiling cris is in the one-sided heating of evaporating tUbes. We have discussed the mechanism of boiling crisis in an ascending flow of working fluid in vertical tubes heated u niform ly all over their periphery. l n modern powerful steam boilers, th~ main steam-generating surfaces nrc formed by furnace water walls which are unevenly h eated over their periphery. The distribution pattern of the heating load over the periphery of a water-wall tube is shown in

114

Ch. 10. Temperature CondLttons on Heating Surfaces

Fig. 10.3. Heat distribution in a smooth tube heated from one side

10.9: Temperature Conditions Along the Channel

ce-through boilers are shown in Fig. 10.4. In boilers of any type, the temperature of feed water in the economizer, t 1w, is raised to the saturation point (in the limit), so that the heat absorbed by evaporating tubes is almost fully spent on vaporizatioi;I, and the temperature of the steam-water mixture t' remains almost constant. In the superheater. the temperature of steam is further r aised to the rated value t ••. In the economizer section I, the temperature of the flow t1 and that of the tube wall, tt. are below the saturation temperature: t 1 < t' and· t 1 < t'. The thermo physical properties of water in the layer near the walL vary only slightly with temperature. Under such conditions, heat transfer is mainly governed by the laws of convection:

Fig. 10.3. The front side of the tube, which faces the furnace, is heated most intensively and the rear side, (10.1) least intensively. Uneven heating causes transverse circulation of the work- Where ing fluid from the less heated to the o:d Re - wp1d Pr - cptf.Lr u N 1,_'J..!' ! ~lf. ,,, more heated portions of the tube periphery; some heat is also transThe subscript 'f' implies that the· ferred by conduction in the metal wall. These two circumstances en- flow temperature is taken as the decihance the cooling effect of the working sive parameter. For straight channels,. fluid, thus retarding the appearance c = 0.023 . Heat exchange occurs at a temperaof a boiling crisis. For this reason, burn-out conditions in tubes that ture gradient M = t 1 - t1 = qlrzzare unevenly heated across their pe. riphery can appear at substantially /! 3 / J :... higher values of qcr than in those 1>:1 8,8'-.../ / ,-J -c >Sl < which are heated uniformly from all i \ sides. This means that one-sided heat1:>. . ing surfaces can be designed for more ~ . forced heating, q~~ > q~;· (see Fig. l>:t -c >I f-.rcr ' z 10.3). The allowable heating load 2~ J 'B.o' ·C AI to avoid a boiling crisis can also be • increased by artificial turbulization "== "== ,_ of the flow with helical inserts, screw ...., ..... f 1 threading of the internal surface of tss trw t' tubes, etc. (b) (a)


~~~

-

//

i

10.3. Temperature Conditions Along the Length of a Channel

Fig. i0.4. Temperature variations in the water-steam path of (a) drum-type and (b)· once-through subcritical-pressure boilers

Straight channels. Curves of temperatures in the water-steam path of subcritical-pressure drum-type and on-

1- economizer: 2-evaporating tubes ; J-superbeater· A-temperature or the working !luld ~ B-wall temperature or a drum-type boil er; B'wall t empe rature or a once-through boile r; C-ailowa ble metal tempera ture

In the economizer section, heat exchange between the wall and the water takes place at a low heating intensity (q ~ 5-10 kW/m2 ) and high values o[ the heat-transfer coefficient [a. = = 2-5 kW/(m 2 K)}, so that the wall temperature is only a few degrees higher than that of the water. In section II, the temperature of the flow t 1 is lower than t', while the wall temperature is higner than t'. This means that vaporizatfon (surface boiling) has already started on the wall. As steam bubbles are formed, they pass into the water flow and are condensed. In this section, the water flow is heated in the temperature range up to t'. This section too, belongs to the economizer, but the heat transfer in it is more intensive than in section I. As heat is further supplied, stable bubble boiling begins in the tube: t1 = t' and t 1 > t'. In this boiling zone (section I II), heat transfer takes place irrespective o[ the flow velocity (at velocities typical for steam boilers), but is determined by the heating intensity q and the thermophysical properties of the liquid and steam at the saturation line, which depend uniquely on pressure p. In the pressure range 0.4-16 .MPa, the heat-transfer coefficient in the zone of intensive boiling can be approximated by the empirical formula ~ . - 0 · 31•po.4sqo.7 (10.2) . '-"bo II • Heat transfer in this section takes place at a substantially high heattransfer coefficient [rz 2 = 50-100 2 kW/(m K)J, and therefore, the temperature of the tube wall only slightly exceeds the temperature of the flow even with very intensive heating, as is possible in high-forced furnaces of steam boilers without running the risk of scale deposition (see Sec. 10.4). Such conditions exist along the whole length o[ evaporating tubes in drumtype boilers (section III) where the mass steam content x at the outlet 1s rather low (less than 20%) due to the high circulation ratio. In once-

H5

through boil ers, the steam content varies along the length of the evaporating tubes in the range 0 < x < 1. In tube portions where x is relatively low due to extensive boiling, a 2 is rather high and can be calculated by formula (10.2). Under such conditions, t 1 is close to t'. ·· Beginning hom a certain steam content Xcr. which depends on pressure and heating intensity 1 th_e temperature of the wall rises st~;bstantial­ ly (boiling crisis associated with ' water film drying, see Sec. 10.2),, which is indicative of deterioration of the heat exchange conditions (section. IV). For this section, i.e , in the zone x > > X cr. or upon occurr~nce of a. .boiling crisis, it may be assumed with a good approximation that the coefficient of heat transfer from the wall to steamwater mixture (rz1 ) varies . roughly proportionally to the linear velocity of the steam-water mixture to the power of 0.8; a similar relationship may be assumed fr9~ the. coefficient of heat transfer t.o · dry saturated steam a*. Therefore:

'wm

•

•

t ••

(10.3)

'. Assuming that the steam-water mixture in the zone of deterioration of heat transfer moves as a homogeneous medium, the coefficient of heat transfer can be determined as for dry saturated steam whose average velocity is equal to the velocity of the mixture: '

Wm

-. = x Ul

'

'

p• +-,.. (1-x) p

(10.4)

The formula for a 1 in the . zones of deterioration of beat transfer has been proposed by Z. L. Miropolsky [61]. I t includes a correction factor y to account for inhomogeneity of the fluid in the zone at a steam content that is slightly less than unity: Nu1 = c (Re")o. spro · 8 t' '

• ]0 8 +f,(1-x) ·. y [

X _x

(10.5)

·H6

Ch. 10. Temp erature Conditions on Heating Surfaces

~vh ere

Nu1 =

i/

y :: 1 -0.1 (

I •

I

I

where Nu 0 is the Nussel t nu mber under isothermal conditions:

kW/(m21()

and Re" = (w:~ d

'The correction factor y, w hich de-pe•~ds on the steam content and p' /p • rat1o, can be found ily the empirical form ula:

~: - 1

r·"

oc 15 +-~ - ---

10

·u nder impairment 'of heat transfer conditions, the coefficient a. 2 is substantially lower than in intensive boiling, but is still sufficiently high to ensure reliable operation of the m etal of the heating surfaces at a properly selected mass lvelocity of the ilow (see Sec. 10.2). vVilh an increase in pressure, surface tension decreases , so that impairment of heat transfer occurs at a lower value of Xcr· T he same effect on Xcr has an increase in tho heating load (due to quicker ovaporaLion of moisture in the tubes). The boundary of the transition to .deteriorated heat-transfer conditions ·can move along the length of an eva-

~

5

(1 - x("

On atlaining a maximum, the te m·perat ure of the heated tubes decreases. 'T his is due to the fact that heat "transfer is mor~ in tensive with an :increase in l.he linear velocity of :steam in the zone where the liquid pl1ase is evaporated completely (section V). A t the boundary between sections IIf. and IV for drum-typo boilers or lf and VI for onco-tllrough. boilers, tile• mass steam con tent be-comes equal to unity (x = 1) and the •enthal py is i •, so that any further :supply of hoat results i11 steam super~ .heatiug. '· In all types of boilers, in tho super:hoater region (section VI), heat translfer to s uperheated s team again wor:sens and the temperature of the tube metal increases. In this region, the laws of convective heat exchange for a s ingle-pllase medium become valid .again - but for superheated steam we .have: (10.6) N u ,, = cR e.0 · 6p rl0·8

.

20

-......

' 0

t

Fig. 10.5. Wall and flow temperatures in the water-steam path of a supercriti calp ressure boiler 1- tl ow temperature; 2- wnll temperature al low q;

HT

10.3. ·r emperatarc Conditions Along .the Channel

3-Wnll temperature at high q

porating tube d epending on certa in operating factors. T he metal at that boundat·y is subjected to temperature ch anges which may cause thermal fatigue. The amplitude of tempet·ature variations can be decreased by I imiting the temperature g•:adient between the in ternal wall Of a t ubo and the flow in the transition region (6.t :s;;;; ,s;;;; 80°C}. This is attai ned by maintaining a sufficientl y high flow velocity. Curves of the temperature variatio ns of the flow and tube wall in a vertical once-through circuit o[ supercritical pressure at various heating intensities are shown in Fig. 10.5. The entire region of steam generation cart be divided into three h eat-transfer regions: I or I' -water preheating; II or [['-pseudo-boiling; and IIIsteam Superheating. [n l'egiOil f , tho temperature oE the fl ow and woll at a given pressure is below the temperature of conditional phase transition, tph· The thermophysical prope.·ties of the working fluid in t he boundary layer on the wall vary only slightly. UndeL· such cond itions, h eal, Lransfer is governed by convection and can be calculated by formula (10.1). The wall temperature in r egion I increases slowly, following v adations in l,he flow temperature.

.....-::

/,.... ......

!;

v

""""~ t'<

J

\ 4

8

Rc,Prt N u 0 = ------=~-=----

I

2

1.07 -l- 12.7

!'...

5 2000

Other quan liLies needed fo1· the cal cul ation: Gr is the :G t·ashof number:

JrJ/Irg

I

Fig. 10.6. Effect of the working fluid enthalpy and of heat flux on the }teat-transfer coefficient at supercritical pressure P - 24 MPa, wp = 700 kg(m' s); q, k\V/m': 350; 2-520; 3-64 0; 4-7 50; S- 870

J-

ln region II, the temperature of the flow remains lower than tp 1., but the temperature of the wall is higher th an tp 1, . For this reason, the tbermophysical properties in the boundary layer and in the main fl ow may differ substantially (see Sec. 9.5) resulting in the features s pecific to the heat transfer in that region : heat transfer is intensified at low values of q (line 2 in Fig. 10.5) and, on the con trary, is impaired at high values of q (line 3). Figure 10.6 shows the effect of q on a. 2 in the phase transition region. As may be seen , a. 2 has a maximum at a low q and decreases to a minimum at higher values of q. With a decrease in the flow velocity or an increase in the heating load, the region of unit enthalpies typical of the im paired beat tr ansfer becomes larger. Ats'upercritical pressures, heat transfer in this region is caused by two m ain factors: tho effect of varying properties of the fl ow on the processes of turbulent mass exchange and the appearance of noticeable thcrmogrnv itational forces (free convection). Th errnogravilutional forces can be characterized by the ratio Gr/Re 2 . At Gr/Re2 < 10 - 2 , the effect of free convection ca n be neglected and boat transfer in a vertical ascending flow can be calcul ated by the formula proposed by V.S. Protopopov:

Nu, =- Nu 0

(.2_)n (_E_I_ )"' c ,t PJ . 1

(Pr2f'-1)

(10.8) l

IJOO

V{

(10.7)

Cr -

g

(Pt -r.~!l'!:. . VJPt

~ is the coefficien t of hydraulic resi-

s

stance, = (1.82 log Re - 1.64) - 2 ; cp is the mean specific henl.: -c

It - it - _..:.......__,_ p -

It -

It

is the specific heat of the flow~. and Pt and p 1 arc the How density at. the flow temperature and wall temperature, respectively. The exponents' n and m can be foun d by empiricaL formulae. At Gr/Re 2 = 1 0 -~-0.4, the contribution of gravitational forces is large· and heat transfer deteriora tcs owing: to a partial degeneration of the turbu-lence in an ascending flo w. For such• condi tions , the calculation should be· corrected for the effect of free convection, i.e. for Lhe ratio Gr/ Re 2 • The conditions described by curve 3. (see Fig. 10.5) can ap pear at q > · qt,. at a given value wp or at qlwp >> lq (wp)Jb 122). In region III, the temperature of' the flow exceeds t 1, 11 and heat transfer is governed b y the laws for superheated steam [formula (10.6)]. Bent channels. T he tubing of a boiler· or steam generator has straight tubular portions and numerous tube bends , such as bent tu bcs in cylindrical cyclone primary furna ces , coi led tubebanks in nucleat· steam generators, bends in multi-p ass sections of water wall, bent tubes around burner ports m a nholes, etc. ' Tlto motiou of flui ds in bent channels can be characterized by the appenl'ance of centrifugrll forces directed towards the outsid e of a beud. The· cp 1

i20

Ch. 10. Tempuatu.rc ·Conditions on Heating Surface.s

at that point should t)le heating . be uniform with a heat flow qmnx· . Non-uniformity of the temperature field is most essential for horizontal tubes of subcritical-pressure plants and also for tubes of any orientation of supercritical plants in zones where the working fluid has a high heat capacity. At supercritical pressures, the thermophysical properties of the \\rorking fluid may substantially change in a rather narrow temperature range (Fig. 9.6). In vertical heated tubes, this may result in a density gradient along the radius and the formation of a zone of lower density and lower conductivity near the heating surface whose temperature is naturally higher. This can lower the intensity .of heat transfer and worsen the temperature conditions on the heating surface. In horizontal tubes of a diameter more than '15-20 rom,. even if h eated uniformly over the periphery, in Lernal heat transfer in the upper portion is much worse than in the lower, which is due to asymmetry of the mixture flow under the effect of gravitational forces. F or this reason, the range of deteriorated heat transfer is larger in horizontal tubes than in vertical. In inclined tubes, even when heated uniformly over the periphery, unsymmetrical two-phase flow can also appear under certain conditions, resulting. in poor beat transfer in the top portion of a tube. Thus, the region of deteriorated heat transfer is l arger in inclined tubes than in vertical, but smaller than in horizontal tubes. At subcritical pressures and separated flow of the working fluid, heat transfer is unsymmetrical and the temperatures on the upper and lower surfaces of tubes are different (Fig. 10.9). Heat transfer at the upper tube surface, where the wall temperature is close to the saturation point, is worse than at the lower surface. This is associated with particular conditions of two-phase flow in horizontal tubes where the flow can be separated

10.4. Temperature Conditions around Periphery of Channel

For a ,platen wall, the. t.emperatur& of a fin root 'is found froui the formula

180" 0.9 0.8 0.7 0.6

I

2

......... qfurl' =0.2!! /7 ~~ 0.42 ./ /I ,\ VI

~

0.5,2{10

(1! ~) J

\ "--._0.53./ I "0.84 / 1600

v

'(10.16)

2fl01l t.lrJ/Ir!!

3 o 9o tou 27fl Jofl" An!lle from lower· line of tube

Fig. 10.9. Overheating of the upper surface of a horizontal tube with a separated flow inside, relative to its lower surface J-p

= 11 MPa;

Z-p =

1 B MPa; 3-p = 22.4 MPa'

by gravitational forces (see Sec. 9.3). Waves which form on flow separation can periodically splash onto the over., heated wall. Repeated water splashes cause a sharp cooling of the tube wall. Temperature variations in Ute metal can cause fat igue phenomena. For this reason, in free-circulat ion boilers, which are characterized by low velocities of flow in evaporating tubes, horizontal tubes are not heated. In once-through boilers, flow velocities are substantially higher, and therefo-. re, flow separation does not occur within a v,rider range of heating loads. The superheating /:;.t of the upper portion of a tube relative to i ts lower portion (upon flow separation) can be somewhat diminished by increasing, the thickness of the tube wall and • the heat conductivity of the tube metal, which causes heat to spread thr~>Ugh the tube metal. At supercritical pressures, the wor-. king fluid can separate in horizontal tubes by density in the vertical direction. For th is reason, under identical conditions, Lhe temperature of the upper portion of a horizontal tube turns out to be higher than the wall temperature of a vertical tube. The ratio a.h";,~/a ocr depends on the enthalpy of the flow and the parameter q/wp (Fig. 10.10). F inned tubes. As has been given earlier, under id en tical conditions the

Fig. 10.10. Ratio a~~Javer at supercritical pressUJ'e (p = constant)

heating load near the front wall on a smooth and a finned tube is roughly the same. This makes it possible to calculate the wall temperature on the front surface of finned tubes of water walls (equal one-sided heating of parallel tubes) as for smooth tubes [see formula (10 ..12)1. To estimate the reliability of the tube metal, it is essential to know the temperature of metal at the tip of fins . According to (14], with a symmetrical temperature . field (the same diameter of welded tubes and the same temperatures of working fluid and h eat -transfer coefficients a 2 in the tubes), the temperature at the tips of the fins can he found from the formula: (10.13) The coefficient lew considers the effect of welded seams; this can be taken from reference data. The temperature gradient between the root and tip of a fin can he found as: (10.14)

where A is the coefficient of the fin shape depending on the geometrical characteristics hlbr and b11br of fins (to be taken from reference data) . The t emperature in the root of the fin s of a furnace water wall can be expressed by the formula: 1.

tr = t}l + ~J.Lrqmax [ a 2

+ Am (1~~) fit

121

J

(10.15)

When it is essential to obtain the· mass velocity of the flow, use is often made of multi-pass hydraulic systems in t.he form of individual banks or sections connected in series so that, as the working fluid [lows through them, its temperature· and . enthalpy gradually increase. 011 the qther hand,. these sections are arranged in parallel relative to the heat-transfer· agent (combustion products), so that each of them absorbs roughly the sam& quantity of heat. Under such conditions, an unsymmetrical tern perature field can appear in the extreme tubes of adjacent sections. If these tubes are welded together, as is done in gas-tight water walls, the temperature difference between connected fins can give rise to appreciable temperature stresses, sometimes causing fracturing in the welded sections. Temperature asymmetry in gas-tight (membrane) walls creates the problem of proper temperature distribution in such walls. The problem is solved by applying the superposition principle: with a number of external actions. it is assumed that their effects can be added together. The quantity of heat absorbed by a finned tube c,:onsists of two components: the heat absorbed in the cylindrical portion (from the front point to the fin root) and the heat absorbed in the fin proper. Each of these portions has a particular tempera Lure field which can be added together to obtain the total temperature field of a finned tube. P roblems with temperature symmetry (Fig. 10.11a) are solved by assuming that the heat absorbed by the· connecting piece between two tubes is distributed evenly between the tubes, and that the maximum of temperature is in the middle of the piece.

1.22

Ch. 10. Temperature Condition s on Heating Surfaces

0

Tubef

i!t =t,.,-Lr

• Tube2 t'

10.5. Heat Exchange In Steam Generators

0

H (a)

(a)

'L( l

s(IJ/tf

1

\ j· }r..

mH ( -m H II l~ig.

' {h)

10.11. Temperature distribution in n

connecting piece

t< 1l - t< 2l; (b) nsymmclricnl cond itions. t< 1 l > t< 1 >

h -......:...,

I

Y \

s(2)/lf

.

//Jjd

-<~ "

.

0

"'1 '/(

{<>) lbcrmnl symmetry ,

With Lam perature asymmetry (Fig. 10.11b), Lhe temperature maximum is shifted towards the tube with a lower temperature level, so that the distribution of heat between the tubes will be uneven: it will be divided in proportion to tho length of the piece from the point of the highest temperature to a particular tube, i.e. mH for the tube at a higher temper ature and (1 - m) H for that at a lower temperature, where m is the coefficient of displacement of the temperature maximum; its calculations can be found in reference book~ [141. Temperature conditions in a finned tube arc determined by its thermal and geometrical parameters . In Fig. 10.12, typical temperature fields are shown in terms of excessive temperatures, i.e. tempet·ature differences between t he metal and the working fluid, for a developed half-tube. For all tho curves shown, it is typical that tho highest temperature is in the front zone <>f a tu ho a nd at the tip of fins. Betw een these points, the tomperat1.1re decreases monotonically from the front point to tho fin root, then rises sub-

Fig. 10.12. Temperature distribution over the outer surface of a finned tube of water wall (a) at different values of internal hentt~ansfer coefficient a 2 (cd < ai < al); (b) at different relative pitch s/d (s 1 > s~ > s3) stantially c1t the fin tip and again decreases from the fin tip to the rear side of the tube. The effect of deposits on temperature conditions on heating surfaces. We h ave discllSSed temperature conditions on clean (deposit free) heating surfaces. S1.1ch conditions can be en- • sured by proper organization of the processes of steam generation. On the other hand, in boiler operation there is almost always a potential danger that deposits will form from impurities whi ch are presen L, in a d isso I ved or susp ended state, in water (see Chs. 14 and 15). When deposits are present on the inner surface of tubes, th e wall temperature is found from the formula: 1 1 t~n=tfz +qin(...!...+ ~' " ') as r!cp

(10.17)

With a larger thickness Odcp of the deposited layer and with a lower hea t conductivity 'J..dcP• the thermal re-

123

which always takes place over the cross section of the core (especially with intensive heating which is typical o£ nuclear reactors), the differences in the flow rates of the working fl1.1id in the cells and over the periphery of rods may result in different unit heaL absorp tion dq/d (wp) (per unit flow rate of the coolant) and the appearance of temperature gradients between the rods. Since there is no active turbulent mass exchange of the fluid through the narrow spaces between the rods in t he cells, the velocity field of the working fluid may be distorted oven more by deformation (bonding) of the rods undel' the action o[ temperature gradients. The critical heat flow at which detodorated conditions of heat transfer can appear on heating surfaces deponds on the following principal factors : steam content x , mass velocity wp, and pressure p. For a system of parall el channels in a boiling reactor, these parameters are average if each of the channels receives the same quantity of the working fluid, so that Lhe 10.5. Heat Exchange in Steam heat transfer crisis in rod bundles Generators of Nuclear Power Stations is qualitatively the same as in evapoThe unit heating load on the surface rating tubes, but the quantitative <>f fuel elements is quite high (1 000 relationships turn out to be substankW/m 2 or even more). This circum- tially different. Considering all the st ance makes the appearance of poor geometry specifics of rod assemblies cooling conditions in fuel elements and Lhe condi tions of their operation, differences in unit heat release or heat very probable. The steam-genet·ating channels of absorption can result in differences in nuclear reactors have an intricate sha- the flow rate wp and steam content x. pe. In reactor construction, wide uso Since qcr is a decreasing function of is made of heating surfaces in the form x, a boiling crisis is more likely to of bundles of heat-releasing rods bet- occur in the space between tubes at ween which the heat-transfer agent a lower limiting steam content than in tubes. flows in a longitudinal direction. Various types of flow whirlers are The geometry of chan nels formed b etween the rods may have a signi- mounted in tho outlet section of a reacficant effect on the hydrodynamics of tor channel to increase its power ; t he working flu id: the flow rates thro- they are often made integral with ugh the cells of a rod bundle may turn spacers. Under the effect of whirlers, out to be different or the velocity of water droplots are thrown from the the working fluid may vary over tho flo\v core onto the walls and replecross section of a cell; this may result nish the moving liquid film on the in the formation of diffori ng cooling walls . Thus, a boiling crisis caused by conditions over the periphery of Lhe Liquid film drying is delayed and at rods. With uneven heat absorption, the outlet the steam-generating reac-

sistance across the wall to the working fluid is higher, and thus, .the wall will have a higher temperature. The conduct ivity of deposits depends on the composition of impurities in the water and may vary within very wide limits-from 0.1 to 0.5 W /(m K) for mineral deposits and u p to 3-5 WI /(m K) for ferric oxides. Since the conductivity of deposits is substantially lower than that of the metal, even slight deposits, in a · layer of <>nly a few fractions of a millimetre, in the tubes of water walls, which are heated quite intensively, can raise the wall temperature to a value that is inadmissible for reliable operation <>f the t ube metal. Since d eposi t.s grow gr adually during boiler operation, t h is circumst ance limits the continuous operation of a plant. For this reason, one of t he most essential problems in boiler operation is to prevent or restrict the formation of deposits on the steam-water side of heating surfaces (for more detail see Ch. 15).

I

124

tor can operate at a Jaigh er s team content. I n steam generators operating in combination with pressurized water-cooled reactors or sodium-cooled fast-neutron reactors, during evapora tion the working fl uid passes through the same stages as in organic-fuel steam boilers . The only point of significance is that deteriorated heat tra nsfer in the steam generators of nuclear reactors does not involve failure of th e apparatus, since the temperature of its elem ents cannot exceed that of th e heat- tr~n s[er agent. However, . an increase m the length of the boiling cris is zone, where th e i nlcnsity of heat transfer is low (sec Sec. 10.2), r esults either in an increase in the steam generator size or in a loss o[ its capacity .

Moreover, the wall in the zone of liquid film drying is a lternately washed with liquid and steam, causingtemperatu re pulsations in the wall (which can be quite substantia l in. liqu id-metal heating) a nd varying stresses in the m etal, which can resu lt ifr tube cracking. All these phenomena arc probablein steam generators where the workingfluid mo ves in the narrow cells of a channel or in chann els of a substAntial length. - On the other hand, boiling crisis in the reactor core is extremely dangerous. To prevent i ls occunencc iu wat er-moderated water-cooled power reactors, th e heal-transfer agent of th o- . primary circuit. has a tom pornl.u re a few tens of degrees below th o hoi ling point (subcooling margin) .

125

11:1. Classification of Open Hydraulic Sydem1

Ch. 11. Hydrodynamics of Op en Hydrazlllc _S ystems

•

•

Heating surfaces '

. ..

..•

.

plalen-lgpe

ra diant

convective

.

.. I • I I

v . v· I/ \_i ._~ ~

.

B .

\

'

\

\

.

~

'(b)

"

•

I

l

F F

' 'I •

--

(ti}

(C)

'

' n

(h)

(g )

~~

I

l

~

••

(a) I

-

'-

\_ j

6

'

I

(i)

F

I

. (l)

F

t

'

.

•

(m}

{j)

{k)

(f)

feJ

Fig. 11.1. Principal types of hydrau lic circuits with forced motion o[ the working fluid ( a) horizon tally wound water wall tubes; (b) vertica l nrrnnl!Cment of water wa ll tubes; (c) U-sbaped water wa ll : (d) N-shaped water wall;(<) multl-pa'l.• water wnll witll vcrli cul tubes; (f) mulli-pa_ss wa ter wall with hor izontal tubes; (g) L-shaped platen: (h) double L-sllaped platen: (i) horizontal platen: (J) U-sbaped platen; ( k ) multi-pass vertica l platen; (I) vertica l convection bank; (m) horizontal con'l'eclion bank

HYDRODYNAMICS OF OPEN HYDRAULIC SYSTEMS 11.1. Classification of Open Hydraulic Systems The principal cliagrams of open hydraulic circu its in heating surfaces are sh own in Fig. 11.1. In any circuit the r eliabl e oporaliou of the steam~ generating channels depends substantially on stability of mot ion, i. e. a s table flow rate of the \vorld ug flu id through parall el tubes anct channels . Under parti cula r condi lions (pressure, mass velocity, cuthalpy of the wo rking flu id a t th e inl et heating intensity) a nd depending o~ the design of th o s tcam-generati ug channels. uns table motio n of the work ing fluid (i.e. with a variable flow rate) can appear in them. One must distinguish, b etween static a nd dynamic instabi-

liLy. S ince instability, per so, is a dynamic process, tho term 'static inst ability' is rather cond i tiona!. Under statica lly unstable conditions, the fl ow . rates through various tubes (channels) are different and may vary in limo with an apprecialJle hequ ancy. Th o flow rate in individual tubes may turn out to beinsufficient to ensure proper healtransfer conditions. Varying conditions of cooling of t he t.uLes aud variations of the wall temperature may cause ther mal fatigue of the metal. Jn som e cases, especially in operntion at, variable or off-design loads, dynamic (or oscillating) insta bility of motion appears in lh e for m of excessive flow pulsations which lead to variable flow r ate of the worki ng fluid .

.

.

.

d ecreased cri tical heating load, cyc- 11..1a), the length L of a single tube may be as high as a few hundred melic temperatu..re variatio ns in the heatres and tho tube has a large number t ed walls a nd, as a fi nal result, to of bends and therefore, a high hydrauemergency situations. lic resistance D.p hr· The hyd rostatic Out of all the causes or hydraulic component D.p,. of the total pressure i nstability, and therefore, of maldigradient in such a circuit is not large s trib ution of heat , special attention in view of the small heigh t of the s hould be g iven to the effect o[ a n circuit compared with the length u nsteady hydrodynamic cltaractorisof the developed tube, i.e. H « L. t ic, flow pulsat ions and hoadet'S on T ho resistance due to flow accelera; he distribution oE the flow between tion 11Pac is also not large, especially [) arallel tubes. The pressure grad ient at a high pressure. Therefore, t.he n _heated tubes can be represented as total pressure gradient in a circuit the sum D.p = 11Ptr D.p, 'D.P ac± ± D.ph (see Sec. 9.4). Combining t ho with horizontal or slightly inclined tubes is mainly determined by the h yd raulic resistances in a si nglo torrn, hydraulic resistance: 11p1, 'D.p 1 = flp 1.,, we obtain: D.p = 11Phr -1- 11Pac ± flp,, (1.1.2) . (11.1) B oiler circuits w ith ver tical ascenIn o nce-through boilers with hori- ding or ascending-descending motion zontal or slightl y inclined lubes (Fig. of tho working fluid (Fig . 11 .tb to e)

+

+

+'

•

126

Ch . 11. H ydrodynamics of Open Hydraulic Systems

.dp

t!p 0

2' I' 2

11

Fig. H .2. Hydraulic characteristics: stable, (2) unstable

(1)

are charac terized by a s mall number of passes, and therefore, by a relatively short tubes and low number of bends. Tho hydraulic resistance of such circuits is low. The hydros ta tic head in v ertical tubes, however, makes up a substantial portion of the total pressure gradient, especially at low loads when the contributio n of th e hydraulic res is tance is subs tantially lower. Thus, !::,.p = !::,.p hr

±

!::,.ph

{11.3)

The ratio between !::,.p ilr and !::,.ph in the total pressure gradient may have a vital effect on the hydraulic stability of the flow in straight-flow elements. The hydraulic s tability of flow is described by the hydraulic characteristic which gives -the total pressure gradient !::,.p as a function of the flow rate G of the working fluid: !::,.p = f (G). If all tubes in an element are of the same diameter , the hydraulic characteristic is a fu nc tion of the mass velocity: !::,.p = f (wp). The hydraulic characteris tic is u nambiguous if a particular to tal pressure gradient in the tube system has only one corresponding flow rate of the working flu id {curve 1 in Fig. 11 .2), and ambigt1ous if the same total pressure gradient can appear at two or more differen t flow rates {curve 2.) The hydraulic characteristic may b ecome ambiguous on a change i n the thermophysical properties of the working fluid, s ay, the unit volum e, which may be caus ed by a change from one flow ra te to anothe r (see S ec . 11.2) or u nder the effect of hydrostatic

11.2. Hydrod ynamic Stability of Flow In Horizontal Tubes

head {see Sec. 11. 3). The s ituation is complicated oven more by the fact t hat the effect of hydrostatic h ead in ascending and descending motion of the working fl uid is different. All this results in i ntri cate analytical relationships which are represented gra phically fo r each particular object: hyd raulic circuit , geom e Lrical pa rame ters of th e tube system , pressure, entha lpy of the working fluid at the inle t , etc. The hydra ulic operation of a ny circuit is de~cribed by its hydraulic ch aracteristic. H owever, becaus e of Lhe above-m entioned s pecifics of hydraulic s ystems with horizontal unc.l ver tical t ubes, t heir hydra ulic characteris tics will b e anal yser! separately. 1 1.2. llydrodynamic Stabilit y of Flow in Horizon tal Evaporating Tubes The decisive factor that determines the hydraulic characteristic of evaporating tubes is the temperature of the fluid at the tube inlet. It may be equal or close to the saturation temper a ture at the pressure at the tube inlet, t 1n ~ t', or be substantially lower than that temperature, t 1, < t'. If a tube is s upplied with subcooled water, st eam generation begins not immediately at fts inlet, but a certain dis tance downstream. The whole' length of the tube can then be divided into two portions: tho economizer portion and the evaporating portion {Fig. 11.3), their lengths being determined by the ratio between the heat rel"ase and flow rate of water.

c

UQ;i 0

t in
v';i';:r=O

x= :"

v;c;ix;:r"

t t t t t t h ley

lee

l

Fig. 11 .3. Vari ati ons of the working .fluid param eters in a heated tube a t tin < t'

For the same heat release rate, an increase in the water flow rate in·creas es the length of the economizer p ortion . while shortening that of the evaporating portion, which is associated with a lower quantity of s team produced by the heated tube. If a tube has an economizer portion {Fig. 11.3), we have:

{11.4) Tho unit volume of the working fluid in the economizer and evaporating portions is different. The lengths of these portions are different too. The unit volume of water varies only slightly along the economizer portion, and therefore, we have:

-

v0 + v'

2

{11.5)

-

In the evaporating portion, the unit volume of water changes sharply, and it is reasonable to take its mean value in calculations. For tubes that are heated uniformly along their le ngth, quite accurate results are obtained by assuming a linear law of variation of the steam content in the flow, and therefore:

-Veo = V '+

z(v· - rl) 2

{11.6)

With uniform heating, the heating load per m e tre of tube length, q 1 = = Qll, is constant. The length of the economizer portion will then be found as lee =

(i' - io)

QG l =

lH,ub (wp) f

(11. 7)

ql

and the length of the evapora ting portion: (11.8) Subs tituting Vee • z•• , Veo • and z•• into equation {11.4) and arranging the terms according to the powers of (wp), we obtain the cubic equation:

D. p = A (wp) 3

-

B {wp)2

+ C {wp) {11.9)

127

where

A=

~ (v" - v')

t.t!ubf

4dqt r

B = ifr[t.i~ub (v• - v')-v']

(11.10} (11.11)

and

C=

~ (v• -v') l2ql

4jdr

(11.12)

If there is no water subcooling at the inle t of an evaporating tube, !::,.i,ub = i' - i 0 = 0 and the coefficient A turns to zero and B changes. s ign. Equation (11.9) then takes the f o m: !::,.p = B {wp) 2 C {wp) {11.13)

+

i.e. it is a quadratic equation which expresses unambiguously tho hydraulic characteristic. Equa tion (11.9) is the equation of the hydraulic cha racteris tic of a n evaporating tube at !::,.i•ub > 0, i.e. in the presence of economizer portion. In this case, the h yd ra ulic charac teristic is described by a cubic equation whose solution can have either one· real and two imagin ary roots , or all three real roots. I n the former case, th e characteristic !::,.p = f (wp) has neither extrema nor common points with a h or izontal tangent {curve 1 in F ig. 11 .2) and is unambiguous, since any value of pressure gradient !::,.p has only one corresponding flow rate of the working fluid, wp. In the latter case, the characteris tic has an inflec-· tion point a nd two extrema; it is ambiguous, since any value of pressure gradient !::,.p has three corresponding different flow rates {curve 2). Ambiguity of the hydraulic characteristic will become clear from the following r easoning. For the same h eatrelease rate, as the flow rate of water s ubcooled ur1der the saturation point increas es, the volume v elocity of the mixture is not increased, but decreased . An increased flow rate of subcooled water leads to an increase in the le ngth of the economizer portion and in the quantity of heat spent for b eating the water to boiling . Accor-

128

11.2. H11d rodynamlc Stability of Flow in 1/orlzontal 1'ubcs

Ch. 11. Hydrodynamics of Open Hydraulic Systems

JJp

129

4p

IU')'

4

Fig. H .5. Region of the hydraulic characteristics of a tube producing steam-water mixture

lt!Cf

l

Fig. 11.4 . Effect of the flow rate of subGOo led water in a steam-generating tube on flow velocity at tube outlet 1-11- wnter now rates

I

0~------------~~

0

dingly, the re remains less h eat available for evaporation, and therefore, tho velocity at tho outlet decreases s ubs tantia lly {Fig. 11.4). This continues until the evaporating portion disappears in the tube. As soon as steam generation is interrupted, a further increase in the flow rate of water causes a proportional rise of the velocity along the whole length of the tube, and therefore, a change in the hydra ulic resis tance of the path. As the w a ter flow ra te increases, t he hydraulic resis tance of the economizer portion, !:.Pee• increases while that of the evaporating portion , t:.p •• , decreas es . Depending on t he ratio between !:.Pee and t:.p •• , t ho to tal hydraulic resistance of the path may either increase or d ecreas e with an inc rease of the load in a pa r t icular ra nge of flow rates , resulting in t he hydraulic characteris tic being either unambiguous (steady-s tate) or ambig uous (uns teady-state). L et us consider the hydraulic c haracteristic of a once- through element, which bas three real roots by equation (11.9), see Fig. 11.5. At v ery low flow rates of water, (wp) < (wp), and s uperheated s team will form at a g iven heat release rate , since the path

has neither an economizer nor evaporating portion, bu t is essentially a superheater along its whole length. At very high flow rates of water, (ri.lp) > (wp)w, the available heat is insufficient to heat the water to the s aturation point , there is no s team generation , and t he whole pa th is essentially an economize r which d elivers w a ter. For those extre me cases, the hydra ulic ch arac te ristic is described by the p arabolic equation:

b.p =

S (wp)2 2

l)

(11 14)

As follows fr om this equa tion, with the same mass v elocity o'f the flow , the resistance to the motion of ·steam is greater thari tha t to tho motion of water, Since V 1 is greater than V w • If a s team-water mixture forms in the path [the range of flow rates (wp). < (wp) < (wp)wl. the characteristic may become uns table and the flow rates ma y v ar y, so that a steam~ water mixture with widely different s team contents will be delivered periodicall y . S ome of t hese steam contents m ay turn out to be excessive for the give n heat release rate, meaning that the cooling of the tubes will become unreliab le. An unstable h ydr aulic charac teristic can result in differe nt flow rates through individual parallel tubes that are connected to a com mo n heade r. A m ore dangerous s i tua t i on , however, r~sults when the flow r a te through a tube c ha nges. For th e same heat re-

Fig. 11 .(). Effect o[ pressure on tll'e sta bility of hydra ulic charac teristic {P1 < P 2 < P 3 )

lease r a te, t his can cause t emperature varia tions in the tube wall and the a ppearance of critical fa tig ue s t resses and , eventuall y, d amage of the evapora ti ng tubes . Sin ce t he ambiguous hydraulic characte ris tic is mainly due to a l a rge d ifroronce between the u nit volumes of wntor a nd steam, a n incr·ease in pressuro can ma ke th e ch a rac teris ti c more s ta ble and tho motion of the wo rking fl uid more stead y-s late {F ig. 11. 6). As noted earlier, i nstability of t he hydL·a ulic characteris ti c is associated with the presence of an economizer po r·l ion in a tube. F or this reason , wi th a hig her degree of water s ubcooling a t t ile tube inle t , the ch aracteris tic is less s ta ble (Fig. 11.7). On th e o the r ha nd, if s t:ilicooling is decreased by rais ing the in le t te mpe rature c lose to . t', another proble m ma v result: as tho s team-water mix t.m·e enters the inle t header of a bank of evapora ting t ubes, i t will be separated into steam .tlp

~ig.

11 .7 . Elfcct of water 6ubcooling a t the •!llct of a steam-generating tu be on the slabilt ly or hydrauli c characteristic (p ~ consla nt) 9- 0 1524

Fig. 11.8. Tra nsfo rma t ion of an unsta ble hydraulic charac terist ic into stabl e by throttling subcoolcd water fl ow

a nd wa ter in t he header , so that some tubes will rece iv e more wa ter and less steam than othe rs, i.e. the flow r ates of water and s team in them will be sharply different and uncontrolla ble; this can lead to overheating, and even bur:n-throng h of tho ev apera ting tubes whic h a rc hea ted q uite intensively i n t he boiler furnaces. For the a bove reasons, once-through boilers are made with a non- boiling economizer section. N o-boiling conditio ns m ust be ensured no t onl y a t the r a ted load, but also in ope ration under nny load and with any kind of fu el for which the boiler has been designed. An unstable hyd raulic characteristic can be stabilized by introducing a n addition al res is ta nce in tho economizer portio n of the hydraulic s ystem, which will va ry by a parabolic law depend ing on the flow r ate of t he wo rking fl uid . As s hown in F ig. 11.8 , tho initial a nd the addi.tion al charact.e ri s ~i c a1·e added graphically so that t he resul Ling characteristic is stable. T he hydra\Jlic resistance of t he econom izer portio n is us ually increased by two me thods: by increas ing its resistance locally (moun t ing a n orifice plate) or at a n app reciable l en ~th (providing a s tepped tube) . "' Orifice pla tes. Orifi ce plates produce a pressure g radien t proport ional to the sq uaro of the flow r ate of t he s ingle-phase fl uid tha t passes t hroug h

Cll . 11. llydrodyllllmtcs of Open Hydraulic Systems

132 '-int

dp

1

u

'f.dphr

-tJ i

4i

\.

2

' In

obtain the hydrostatic head 'Ztlp 1, in a IT-sh aped section. The total hydraulic characteristic of a n-shaped section 'Ztlp = 'l:, tlphr + Li:!.ph {1'1.19}

ItJp "' rtJPnr ' '£Lip11

2 ioul

0 (a)

LJpf"

- 4p

u (6)

---- - ,v;o

l in

Fig. 11.1 3. Hydraulic cliamctcri s ti c of a ll-sbaped heated tube ~ i - J u• n t

:.hsorrltio n hy the tul>P

elemcn~

'I

I

in which enth alpy i 1n 1 var ies according to tho flow rate at a given heat release. With a smaller ~low. rate of the '~orking fluid, itnt 1s h•gher (curve I m F ig. 11.13b), so that the enthalpy of the working fluid sharply increases in th e descending element of the tube (curve II), especially in the outlet portion. With a decrease in the flow rate, this results in an essential decrease in the flow density and, accordingly, in the hydrostatic component tlp~"' . ·, ·; Adding together the h ydrostatic components fo r the ascending an d deseending element, tlp/!" and 6.1."' , we •

4p

t

llmhi!J.UOUS

lin lout

reg1011

o~~~=====~wp ~ r.tJp, - 4p

------~Lipf"

l:i g . 11.11t . H ydrau lic chamclerislic U-shaped heated tube

of

11

may be ambiguous in a wide range of flow ruLes of the working flu id {Fig. 11.13a). F ig ure 11.14. shows the total hydr aulic characteristic and its components for a U-shaped section, which has been constructed according to the method discussed above. Tho hydraulic resistances in tho ascending and descending branches arc positive aHd are thus added together ('l:,tlph,)· T he hydrostatic component in the descending branch, 6p1.''", is negative and tho enthalpy of flu id at the inlet to this hranch, i in, is assumed to be constant and independent of the flow rate . The beginning of th e ascendincr motion coincides with tho end of th~ descending motion. The hvdrostatic componen t of tho asccndin.g moti on is positive, but the en thalpy at the inlet to the ascending portion (in the point of transition from descending to ascending flow), i 1n, is dependent on the flow rate. A t low flow rates ' i ;n t is high and the density of th o fluid is low, which l1 as a retarding effect on the rise of the hydrostatic head with the increasing flow rate, in t h at zone. Only in the zone of large flow rates at which tho quantit y of heat por unit flow rate of the wot·king fluid is not as substantial, i. 1111 becomes lower and the hydrosta ti c head tlp;:• becomes much larger. Tho resulting curve of hydrost atic heads is denoted as L.tlph in the fi gure. As may be seen , the total hydraulic characteristic of a U-sh aped section is ambig uous in a w ide t·auge of flow r ates of the working fluid. Hydrau li c characteris tics of N-sh aped aod more complicated multi-pass systems can be obtained in a similar manner. As follows from tho above analys is, the hydrostatic pressure gradi ent improves the hydraulic characteristic of nn ascending flow and ad-

133

11.3. Hydrodynam ic Stability of Flow in Ve rtical Tubes .t.lp

tlp

3

6

J

- ..' ~ . '

4 I

0

1

wp (a}

4

0

{D)

Fig. 11.15. Ambiguous hydraul ic cha rac tcri~ti cs (a) o f·(l sing le lube: (b)

vorsoly affects that of a descending fl o.w . _In this respect, a U -sltapoc.l circu •L IS better than a fl-sbapcd, since t~o working . fluid in its outlet port•on, where •t has a high steam cont ent, and therefore, lower density moves upwards and the effect of th~ hy drostatic bond is positive. The hyd raulic characteristic is improved evcu more iu a u N -shaped system wi Lh an inlet header arr anged at the top and an outlot header at the bottom . In additi ou , this system has two ascending portions per one descending . I n general , tube sections w it h a low number or passes have either an ambiguous or insuHicien tl y stable hydraulic characteristic . With an increasing number of p asses in a h yd rau I ic system , tho effect of hydrostatic component on the total pressur e gradient d iminishes, but the role of hydraul ic resistance becomes more s_ignificant. When tho number of passes is greater than 8-10, the h ydraulic characteristic o[ a multipass s ystem approaches that of the horizon tal evaporating tubes. An unstable h ydraulic characteristic of a single tube (channel) with ascending or descending motion of the working fluid under the action of l1 ydrostatic head is realized in tho w hole region of ambiguity (curve 2-3-4-5 in Fig. 11.15a), s ince the flow rate is determined by external conditions, i.e. by pump capacity. R eal heating surfaces consist o[ a large number of pnm ll ol tubes. I n multi/.t.J,be systems, the total flow rate of the fluid is also determ ined by pump

or~

lube S)"Slem

capacity, but t he flow rates through individual tubes may tum out to be different. As has bo~n established by e~pcriment and confirmed by cxpen encc, hydraulic characteristics in such systems are r ealized only in ascend iug port ious (the leftmost curve 1-2-3 and tho righ trnost Clln·o tJ.-5-f} in Fig . 11.15b) . A decrease in t.he flow rate iu a tube uear a m iuimum of the h~draulic chnractoristic (at point 4) will cause a sudd en drop in the flow rate and a chango in the co nditions described by point 2 . A rise in !,he fl ow nlLe at a max imum o[ the eharacteristic (near po int 3) can load to a sudden increase in the fl ow rate in som o tubes of tho circuit and a ch ango in the conditions of point 5 . The descending brunch of the characteristic (portion 3-4) is no t realized, except for cases where the system docs not have many tubes (throe or four). rn th is region of flow rates. unambiguous motion cannot be ensured with the r esult that t he flow rotc either jumps into the region of lower values (left-hand branch) or inlo t hat of !1igher values (rigbt-hand branclt), while the to tal flow r ate of tbe working fluid remains unchanged. Operation on the left-hand branch of .the characted stic usual! y cannot malllLain tho required tompemturo cond it ions of inten sively heated eYaporating tubes. Tho sole real region of' operation of a once-throucrh circuit is tho right-hand branch of the clwracLeristic which inc] udes ambiguous and unombiguous por·tions. In the •u•ambiguous portion 5-{j of Lhal branch ..

134

Ch. 11. /Jydrodynamics of Open Hydraulic Systems

Ap

11.3. II ydrodynamic Stability of Flow in V ertical Tu bes

tlp 2

.

'

r

2'

0

(IU'J'Jwz

(a)

Fig. 11.16. EHccl of maldistribution on the workin~ fluid flow rate in pa rallel tubes with slnblc hydraulic characteristi cs 1- hydrnulic chnnH;I,I•ristic or un C h;Jlll'll t~ 2 -

hyrlra ullr. t' llru·aclf'rl~l ir of a m tlltuncLionlu g: lube

the v elocity of the working fluid is so high that iL often turns out to bo unfeas ible. Thus, one must opera te on the ambiguous portion 4-5 for which lhe bound:-.ries of reliability should be determined. In circuits co mposed of parallel tubes of the snme design and heated identicall y, st abil ity in the -region of an ambiguous hydraulic characterist ic can be ensw·ed for t he -entire external (ascending) branch of t he characteristic (portion 4-5 in Fig. ·1 1.15b). In a system of parallel tubes, heat -absorption is always different in view -of j the structural and hydraulic noni·dentity of the tubes (see Soc. 11.4). Therefore, somo tubes whose operating condi tions deviate from the average values for the syst em (malfunctioning tnbes) have a different hydraulic characteristic than is average for the system. As seen from F ig. 11.16, oven with an unambiguous ch aracteristic of' the system, differ on t (but s table) flow rates of the working fluid may appear in a reference tube and n malhmctioning tube. Vlith parallel operation of a system of tubes with different ambiguous characteristics, three cases arc possible: lhe pressure grad ient between the heAder of the system at the minimum of the hydraulic characteristic for a malfunctioning Lube can be e ithe r (a) sma ller than the pressure g radient in t.hc c.ircuil (Fig. 11 : 17a),

fw;p)wr

( 1/.J'f'Jmr

.dp

0

2 -~

~ ~

"" ""

on tho characteristic of the malfunctiGn ing tube). Points and 2" on the descending branches of the character istics cannot be realized (see Fig . 11.15b). Points 1' and 2' on the lefthand ascend irlg branch of the characteris tic are also not realizable as long as the condition t:..pw > llPmtn is satisfied. This means that unfavourabl e conditions in an element with a low flow rate of the worl~j.ng fluid can be prevented by providing a flow rate at wh ich the pressure gradient in the characteristic of the main number of tubes will be h igher than the pressure gr adient at the minimum of the hydraulic characteristic of a malfunctioning tube, (wp)101 > (wp)mf · With tlpw < LlPmtu• the1·e are no working points on the descending and right-band ascending branches of the characteristic of a malfunctioning tube. Under such conditions , tho only remaiuing points which correspond to the two different flow rates of the working fluid are 2' and r. At one of them (point 1"'), a high flow rate is establish ed, which ensures stable operation of the m ajority of the tubes in the circuit. At point 2', the flow rato is too low for proper cooling of the worst malfunctioning tube, with the result that the tube system will be unreliable. With tlp,0 = tlpm 111 , t he flow rate at the minimum of the characteristic of a malfunctioning tube is unstable. In this case , a pressure gradient in the tube system has two different corresponding flow rates. One of them, in the malfunctioning tube, has a low value , 2', which cannot ensure proper cooling conditions. The other flow r ate, 1"' on the characteristic of t he majority of the tubes, ensures proper cooling of these tubes. The flow rates in points 1' and 1" for an average element are unr eal for t he reasons given earlier. The condition tlpw = tlPmrn determines the boundary of stability of a malfunctioning tube, i.e. the extreme st ate up to which the operation of l,he wh ole circuit can be stable.

IUJ'

u (6)

(tu,DJ,,

Llp

(C)

Fig. 11.17. Hydraulic characteristi cs o f ITshaped circuits 1- element ; t-maltunclloning tube

(b) greater than that pressure gradient, (Fig. 11.17b), or (c) equal to tho pressure gradient in th e circuit. T hese cases are analysed with a gradually decreasing total fl.ow r ate of the working fluid, and therefore, a decreasing pressure gradient between the headers of tho hydraulic system. In th e first case, when the pressure gradient in the system exceeds the pressure gradient at the minimum of the characteristic of the worst malfunctioning tube, !J.p.., > llPmtn, i.e. of the malfunc tioning tube whose minimum of the characteristic is higher than the minimum of the characteristic of the main number of tubes , three operating poin ts are p ossible on each of tho curves (1', 1" and 1'" on the genera l charnct.cristic of the ma iu number of Lubes and 2', 2" and 2··

135

As regards the stability conditions, the lowest mass velocity allowed in a system is expressed by the inequality (wp)w ~ m (wp)m/ (11. 20) where (wp)m/ i.s the mass velocity in a system of tubes (channels) on an external branch of its hydraulic characteristic in the point corresponding to the minimum of the hydraulic characteristic of a malfunctioning Lube, (wp)w is the m ass velocity in the system, and m is Lhe reserve factor, whicl1 is assumed to be equal to 1.5. Stable opemtion in the region of ambiguous hydraulic characteristics can be ensured by throttling the flow bv means of orifice plates or stepped t ubes . Another method is to carefully select the mass velocity wp of the working fluid at the rated heating load of a particular water-wall section so as to ensure reliable cooling of the tubes at a given mini mal heating load in vi ew of their thet·mal and str uctural non-identity, Lhal is, to run the circuit on an external ascending branch of its hydraulic characteristic, d (t:..p)/d (wp) > 0. Tho latter method is preferabl e, since it does not require tube throttling. In most cases, orifice plates are employed when it is necessary to equalize the flo w rates of the fluid through parallel hydraulic elements, such as sections of furn ace water walls. In some cases, flow stability can be achieved more efficiently by changing over to another scheme of tube connection which bas no downtake tubes. The stabi liLy of the hydraulic characteristic call be affected not only by h eated (evaporating) tube sections, but also by unheated steam-circulating tubes. For instance, Fig. 11.18 shows an \lnlucky arrangement with external unheated steam-circulating tubes connected t o a lower header. The hydrostatic head in the tubes is negative and the circuit is essentially a IT-shaped system with an ambiguous hydraulic charact eristic . With hydraulic maldistribution and too low worki ng fluid veloci ties (due to a low

-

136

Ch. 11. Jlydrody11amlcs of Ope11 Hydraulic Systems

I f

I

2

Fig. 11.18. n-shaped circuit wit h un heated downtake Lubes (a) nnd its hydraulic characler isl ics (b)

dp

1-J-J'AI'IIIh•l heated wnlcr wn ll.• nnd lhciJ· n!spcct i vc h)'di'Clulic c h aract~rit-~Hcs: 4 unhcn lcd downtak•.. lubes; S- Uf•llt.'J' mixing

.i

h e aUt~r

31

\![ dp

(a)

gradient /::,.p1 ), ambiguity of tho characteristic may result in section 2 malfunctioning and havi ng a low flow rate on the lcfL-hand branch 2' of the characteristic. Thus, under completely favourable operating conditions in sections 1 and 3 (the corresponding fl ow r ates arc denoted as 1' and 3'), secti on 2 will operate unreliab ly. Reliable opemtion in the circui I, can be achieved by providing a pressu re gradient /::,.p 2 at which the working points will be on the extreme branches of the characteristics of all the sections and will have close velocit y values. It is also possible lo elim inate ambigu i ty of the hydraulic characteristics of the sections by providing a mixing header at the ir top. The operation of complex circu its with a number of once-through elements is analysed by using their r esulting hydraulic characteristics. Those are obtained graphically by adding the characteristics of individual elements together, taking account of the scheme of th eir connection. If some elements are connected in series, the flow r ate of the working fluid is the same in all of them. For this reason, the resulting characteristic is const-

ructed by ad ding together the chaL'acteristics o[ t he elements at the same flow rate of tho working fluid (Fig. 11.19a). Tho hydr aulic resistance of such a system is higher than the resistance of anyone of its clements. In complex once-tluough circuits composed of a number of elements corlnected in para llel, the hydraulic resistances of the elements are constant. The general char acteristic of the system is obtained by addi.ng together the characteristics of the elements taken at the same pressure gradient in the circuit (Fig. 11.19b) . In such oJ case, the hydraulic resis t ance of tho ci rcui t is smaller than that of anyone of its cleme nts. t 1.4. l\laldis tri bution of Heat

For reli able operation of a heating , surface (section), i t is extremel y important that all its parall el tubes oper ate und er roted (average) conditions. Jn practice, however, one has to b ear i n mi nd that the tubes of a section may have differen I. hydraulic characteris tics (d ue to Yllrialions in thei r diameter, length, surface roughness, effect of headers, or effect

dp. 2 I

0

WJ' (a)

1+2

0 (!>)

Fig. 11.19. S ummutiou or hydrauli c chamclcristics for series co nnec tion of once-through clements (a) and £o1· th eir parallel conn ection (b)

13T

11.4. M aldistrlbutioll of lleat

o( instability in opor·alion of evaporating tubes) and differe nt thermal cluwacteris tics (different heat absorp\.ion due to their dirforcnl. arrangement rei aU ve to the flow or combustion produels, uneven slagging. fouling, etc.). Differences in tho hyd r aulic and thermal charactel'istics of tuhes are especially evident in high-capacity plants with developed heating s urfaces where deviation of some ·..Plements from the rated conditions are· more probable. Undor s uch condi t ions, the working fluid m ay be distribu ted unevenly between the tubes, and thorofore its uni t enthalpy at the outlet or s~me tubes mny differ s ubstan tially from the average value. In some malfunction ing tubes , d angcrous \.em perat ure conditions m ay a ppear. T h e reliable operation of a oncethrough element can bo characterized by two groups of factors: (a) paramcl ors of an element tba t operates under average condi tions in the system: t~/' , !::,.i. 1,

0 . 11 q.z. z. 1, H e1

(b) parameters of a maHunctiouing tube (or channel) : t~~' /::,.iml• Gml• qml• Zmf• H m/ where G is the flow rate of the working fluid in an element, q is t~o quantity of beat transferred to 1t , /::,.i is the beat absorbed by an eleme nt , H is the area of a heating s urfa ce, z 1s the coeffi cient. of hydraulic resistance, and t"" is the temperature of the working fluid al. the outlet from parallel tubes; the s ubscrip ts 'el' and ·mf' s tand respccti vel y for an elemen t under average cond itions and a malfun ctioning tube. Let us i ntroduce some additiona l des ignations: p11 = Gm 11G. 1 (11.21) is the coeffi cient of hydraulic maldistri bution; p 9 = /::,.im / f>iel (11.22)

is the coefficient of maldistribution of h oa 1.; (11. 23)

is the coefficient of non-uniform heat absor ption ; (11 .24) is the coeffi cient of hydraulic nonun i rormity; (11.25)

is the coefficient of structuroJl nonidentity. . Taking the coefficient of maid is tribution of h eat. as a basis, we ca n establish the relations hip between the coc[ficients indicated: =

pq

tli,,J = t!.ier

qm!Hm/: qezffez

Gmf

(11 .26)

Gel

or, on substilu Ling Ll1e corresponding values from (11. 21), ~('11. 23) and (11 . 25): pq =

I] II a 1]< t r

p,

(11.27)

The coefficient of structura l nonident i ty 'll•tr is not associnlcd with tho processes wh ich occur in a I u be system ; it is usually estimated as l')•t r = 0.95-1. . The coefficients oi thermal and hydra ulic m aldistr ibut ion are in lorrelated as foll ows: (11 .28) Pq = 1l ha1Ph Maldistribution of heat m ay be· caused by different thermal characteristics of parallel tubes, while llydrau1ic rnaldistributioo is due to differences in their hydraulic characteristics. As follows from equation (11 . 28) , maldistribution of heat can be caused either by different beat absorption, by hydraulic maldistribution, or by both. Maldislribution of beat depends not only on the extent of thermal nonuniformity and hydraulic maldistribution, but al so on a particular combination of these t.wo fact ors. Tubes wbich are h ealed the most intensively and, on the other hand, with Lhe lowest flow rates tluough them , turn out to be operating under the most dangerous conditions. If the grealest d ifferences of various kinds (in h eat a bsorption, flow rnte, structura l d ifferences, etc.) arc found not in a s iugle·

•138

Ch. 11. Hydrodyn amics of Open Hydrau lic S y&te ms

tube, but in various t ubes, t hey a ll s hould be checked separately .for mal·dis tribul.ion of heat. Those with the worst mal d is tribution of heat should be checked additionally for l ongterm streng th and scaling con di t io ns . H ydraulic maldistribution. In a sys te m of parallel t ubes conn ected t o head ers at the inlet and outl et and with forced motion of the work i ng fluid, m easures s hould be take n to -distribute tho fluid evenly between the tubes. Unde r practical cond iUons, the distri bution of flow rates is alwa ys m ore o r l ess uneven, i.e. h ydraulic m aldist ri bution occurs [s ec formul a (11.21) 1. Hyd ra ulic mald ist ri bution m ay appear due t o h yd t·aulic non-i d enti ty of the parallel tub es, which may be caused by differences in their hydra ulic resis tance, due to th o h eader effect, o r through pressure variation a long the length of tho h eader (see Sec. 11 .5). T his ki nd of mal dis tribution appea rs mainl y i n the heating ·s urfaces of s uper heaLers a nd , to a lesser extent, in economizers. T o d eri ve t ho equation for hydraulic m aldis tribution, l et us write the ·equation for total pressure g t·adient in an element:

nec ted in pa ra llel in the system , it can be wl'itten that 6prn/ = 6 pel· Solving s imultaneous ly equations (11.29) and (11.30), we obtain the expression for hydraulic mald istribution:

_

(wP)mf (WPJel

Ph -

-=--+-2-(---:;·1--=-tt• )- ~

V. -

=

•ctVct

uin

Uf -

· mt'lrnt + 2(V_;m/ -

m/) V;n

•

(11.31)

X (1-

where ot..p,,cad = tlp'hfnd - tlp~1tad is the d ifference of pressure g rad i ents in the heade rs between t ho sections wi t h a m a lfunctioning tube a nd an ol em en t, Mp 11 = t..p;:•t - tlp•J. is the d i Herenee of h ydros ta tic h eads in the malfunc tio ning tube and el em ent, tlp 1" and tlp 0 0 nre ta ken for t ho c leme nt. H ydraulic maldistribution in s uperhealers a nd non-boiling economi ze rs. T he form ul a for the coeffici ent of hydra ulic maldistribu tion ac quires t he simplest for m for non- bo iling economizers in w hich the working fluid in a hori zonta l or ascending motion, has a n ampl e reserve of subcooli ng. In this cas e: 1 ~ ve 1 = cons tant; Vel ~ vm/; t he difference of h ydrostatic hea ds between a malfunctioning tube a nd cl em ent and the resistan ce due to fl ow acceleration a re neglig ible: Otlpll ~ 0, flPac ~ 0. With a uniform wa ter s uppl y to and removal from the head ers, the coeffici ent of hydra ulic mai d istributio n for these co nd itions is d etermined by tho ratio of the coefficients of hydrau l ic res istance:

ve

+ ll Pi/,ad + t..p~1

.I '

(H .29)

:and simil a rly for a malfun ctioning -tube (wp);nl -

A

-U PmJ = Zmj - -

2-

+ (wo) • m 1 (v"'' 2

1

Vm t

v~"') ' t.. prni 1n -r ltt ad

+

A

u

pmf II

(11.30) When thoro is a large n um ber of p a rall el tubes, the effect of a ch a nge in heal. absorption in a malfun ctioning tube on the total pressure g ra·dien t can be neg l ected , and t he re fore, tlpct = cons tan t . S ince the prcss ut·e gmdien t between the inl et sec tio n of the supply header and the outle t sect ion of t he d is charge head er is t he ·same for a ll t ho tubes whic h are co n-

p,, = 1./ v

Zet Zmf

= -_ ~ ( 'L1. 32)

,r,,,,

With t he workin g fluid s u pplied to and re mo ved fro m a head er t hro ugh its end faces, the head er effect is s ubstantial and the formula for h ydra ulic m aid is tri butio n t akes the form: Ph

=

V _1_ ( 1 l'JI,

139

11.4. Maldtstrlb ution of Heat

{jf:o.pr,.ad ) t!.f'ttr

( 11 .:!3)

ln non-boil i ng con vecti ve economize rs with hori zo nta l t ube coils , tho <:.oeffi c ion t of hyd rau I ic maid is tri bulion us ually does not exceed 0.9 . If d o wntake mo tio n t ak es place in a non-boiling econo m izor a nd the hydra ul ic characteristic m ay be ambiguous, t he hyd rostati c co mponent sh ould be t aken in t o acco un t; t his is a lso neccs~ a r y for all b oiling econom izers. Ilydraulic m a ldis tribution-jn superh eaters h eavily de pends on amorc nces in t h e total coeffi c ients of tube resis ta nce, and in the ir heat absorption , a ud o n pressure changes along t he 1tcade rs. Negl ecting I he pressure varial io n c aused by s tea m fl ow accel e ratio n , we got : ,.

,fl /, -=-

lI

-

VcJ 1 ·( l] 11. ''mI ·1

+

66Pil earl Ot!. p,, ) L\ Pil r

( 11.:-l4) The head er e ffect s hould be consid e red when ot..p,.eodi tlp ,, 0.05. The hyd rostatic co mponent of t h e total pressure g r ad ieut is s u bst an tia l o1d y in s ing l e- pass s uperheaters a l ?Jtlp,,! flphr 0.05. llydraulic maldis tribution in the zones o[ sudden c hanges in the uni t vol ume of the work ing fluid. In mode r n -once- thro ug h boi lers. stea m-ge ne rati ng ~l em en ts are usually arranged i n t he l ower rad i a tion section which is heal ed th e most iutcnsiv el y. The -combin a tion of a subs tantial hy draulic mald is tribution and_ inten·s ive hea ting can , uud er cert am cond il ions, resul t i n H s ha rp rise i n tempe rature and unit vol ume of t he working flu id in a malfuncti oning tu~e , reduct ion in the fl ow rate through 1L, and o verheati ug of t he tube m etal u ut i l bum-o ut occurs 1351. Hydra ulic mal d istri butio n in s uch tubes m uy nppear on nn a pprecia ble change iu ~h e uni t vo lume of tho hea ted wod(ln g fluid . It a ppears m a inly in tho h ea l,ing s urfaces of t he high-heat capac il y 1.oncs of su porc ri 1leal- pressure boi I ers , iu 1 he e \'nporat ing surfaces of s ub-cri t ic a l- press ure boil ers, and in boi J ing econo mize rs.

>-

>-

rn

some cases, t h e hydraulic c haracteristic is s t ab ilized by moun t ing orifice plates ut the entry to tubes. In steam genera tion zones , the press ure l osses 6Pa c a nd tlp,,cad are us ually negl ected . For s uch conditions, and no ting t he assumptions made earli er, formul a (11.31.) takes t he for m :

_ \

p,, --

, /

-

~ el

el

ZefVcl + 'oorVor . ( 1 _ Mpt. ) - .J. ~ '"'v"' ! t.p,, Zm jU ru j 1 'bor or

t11. 35) 1 ~ "' ' , v" l 1ere e-' ';:)on ~or or' v"' or cai·e tl1ecoeffi c icnts of resistance of t he o rifice plates a nd un it vol umes of the flu i d flow ing t h rough the orifice plates mounted in a n el ement and malfunct ion ing tube. The difference in hydros tatic heads be tween a mnl fun c tioning tube a nd an clement can be writte n in l,he foil owing for m: v..r

Mph= t..p;~ 1 - D.pf.' = -

:1 - z (l~;;r:o:., I

tl

-

- [ ~ (hp)~ . - Z (hp)fl-.1} g 1

- "' = {[l:" (hp) 01

-

"' "-'

(I~p )
- l ~ (hp)d:,~ - Z (hp)~}.. J} g

(11.36 )

W ater walls of st.carn bo ilers in high-capaci t y monobloc uni t;> are mad_e in t he form of ver tical sections , hon zontally coiled sections, U- and_ Nsh a ped sections , multi-p ass sect 1 o~s with horizonta l tubes , etc . H y dra ullc rnaldistribution in s ome of these types will b e discussed below. Horizontal circuit. In horizonta l tubes t here is no h y drosta tic head, an d therefore, the for mul a of hydraulic mal distribution with throttling t a kes the form:

(11.'37) If there is no t hrottling, t he fo r mula is s i mplified:

Ph -=

II

:dVe/ = =mJUmf

v

-

1 ll h

~cl Vmf

('11. 38)

140

Ch. JJ. ll ydrody na m ics o f Op e n /J ydrcwlic Syst ems

V cr t ical ci rcuil. I n ver tical c ircuits the hyd rostatic head h as a vital effect on hyd r a ulic m a ldist ribut ion. In some P.articu!ar cases, and t a ki ng into co.ns JdcratiOn th o cHect of va ri ous factors [in form u la (11.36)1, the eq uation for hydraulic maldislribulion (11.35) lakes tho form: s ing le-pass ascend ing section:

- ..VI r1 ;C/ _ _ . . :;. :_ lh "mf ., ZefVe / (u:p); l

..

I_..!_

v

lJ/1

2gh (Pel-

(1Ul0)

Umj

Pm f)

( 11.40)

'lh

;-

J If '

500 400

v

i

/

I

I I

I

I

/'It

-\ ! "'

)~

\

0.0

~

I I

r--......

T'0

I

0.8

I

\

T

l2

I

i\ •I

I

f.O

r

\

I

,3 0.5

~

t4

1\J 'It><

1.5

t.8

~~cl

ll.ae/• kJ/ kg : J-4 00; !!- GOO; J - 1

llm.f

'"'·' -

~· -

zo

Fig. 11.:1.0. Ma ldisl.ri bu tiou characteristics of a o ncc-tlu·oug h elemen t a t p = 24 J\1 Pa· . and iin = I 200 kJ / kg

-----~2g-,~.~ , (~-p7l,,,--= p'~'~)--~ (-~"~'/,-~fl p -~.",'.~'>-J

X \

/ 1-

_1_

~

-

0.5

t ,,·o- pass U-s h oped sect ion :

-11

500

lat

0. 7

_-;,r/

=et~e/ (wp); l

Pll

J

700

f.O

s ing le-pass descending sect i on:

Ph -

tu

300

P'' -

2gh (Pel - Pm/)

•c

~.•·•

ZeWe / (wp)~l

(11.41) As fol.l~ws from formu la (11.38), t he coefftcJen t o f hyd r a uli c maldistribu t ion .in h oriz onta l t ubes d e pends on th o r a t1 o be tween the the rm a l a nd t ho hydrau lic ch aracteristics i n a n cl emcnt and. a m a lfu ncti on ing t u be. I n vert1cal t ubes, h yd r aulic mal d isLdbuLion. also d e pends h eavily on the h yd rost.at1c com ponent and i ts con tr ibu I ion to t h e total pressure gradient betwee~ the dischnrgc and su pply headers, I.e. the r atio bot ween t.p and b Pirr· '' O n t.he o ther h and, the rel atio n be tween the increments of enth al pies in a malfunctioning lube and an aver age. e~ement is charactet·ized by the coefftc tent of mnl d is tr ib ution of hea t p , [see f ormuln (1 1.22)1. Assu m ing a nu mber of va lues of Pq = 6i m 1t U"i e /r , one ~a n d et~rm ~ ne the coefficient of hyd r au h c mal distnbution P~t=(wp)m tf(wp)c~

141

l1 .5. Distribution of Worlclng Fluid Be t ween T ubes

oou

and, f m m ?xpression p, = 1) 110 /p , th~ corres pondw g coe ff ici ents· of q nonuniform heat . a bsorp t io n 1l t.u· With the k ~1own values D.irnf and i 111 • we can futd the un it enthalpy of the ~vork ing fl ui d at the exit from a mal Iun ctioning tube, a nd the r efore, i ts tem per ature t~':J. Using these d a t a, we can construct maldistribution characteristics which show varialio ns in the coeffi c ien t of hydraulic mald is tri~ u ~ion a nd lem~ er a ture of the w orking n .Uld at t he e xt t from a m a lfu nctiolllng tube de pend ing on t h e coeffi cient of non- uniform h eat. absorption, i.e. Pt! = I (11110) and 1,:;1 = f (1lh 0 ), see F 1g. 11 .20. The mHI d istrib u ti o n ch a r acteristic:; o f mo re heavily heated Lubes (TJtra > 1) for Ph aro ~ailing a.nd for tex arc ris ing. In a part1cu l:u· porti011, curves of Ph fall off steeply t o a c l'i lical sLate wh en a slig ht i ncr ease o f 1'11," c an lead to a s h arp drop in the fl ow rate and an iucr e asl! in t ex· This is ass ociated with the fac t l h nt in the 1·egion of high

h ea t. capacit ies evcu a slight increase in the unit enthalpy. which can always occur in s ome t ubes, can cause a sh nr p i ncrease in the unit volu me of flui d, v, a nd t. h c1·e foro, in h y dr a ulic resis tnnce. T his i11 tu r n l eads to a l ower flow rate through the tube, i. e. mn l dislribution in the tube is aggrnvatccl furth e r , whil e the un i t h eal absorpti on 6i. inc reases al ong with the volu me of fl u id in il, IJ. The pro-cess c onti nues unti l a flow ···rate is -established which has a correspond i ng stat e of mal dislrihu tion of heal a t. a gi v on h e aling l oad. l n some cases, this m ay l ead t o emergen cy s ituations . T he a ll owabl e heat ing lond is established for the particular opornting cond itions of a heating s urface. For steam s upe rh eat ers in whic h the outlet port i ons o f tubes o per a te u n der almos t -ext re m e temperatu re condiUons, th e a ll owabl e h ealing load sh ould not -exceed '15% of the to t a l hcnl abso r pti on h y the s u perh eat er. F'or bett er rel i ability, tl1 e tube system of steam s u pcrh en ters is sect ion llli 7.od i n l.hc steam path. Eco u omizers arc mounted in r eg ions o[ m od er a t o h e at ing r ates, a nd wa t e r in them h as a r ei ali voly low t emperature. For econ omizers, thormal m aldistri bu t ion of 50% or more is allowabl e. F or this r eason, it is not n ecessary to sect io nalizc t h o econ om izers in tho wa t er path . I n ev!l porating t ubes, temper at ure is rel ativel y low (boiling point). there are no fl ow distu rbances, and th er efore, h eal is r emoved pro perly, the tem per ature of the l.u bc wa l Is usu a ll y exceeds t h at of t he worki ng

rr

flu id by only 20-30°C. An a pprocinb le maldis trihuLion o [ heat m ight be a llowed here, but adverso temperature condi tio ns are l ikel y to occu r in evaporating tubes, es pecially at hig h heating intensities. For this r eason, mu ld istribution of heat in evaporating 1uhes s hould be not more than 20-'tO%. In su percri lical -prcssure boi lers, t.he zo ne of high h eat. ca pacities is m ost sens i tiv e t o va ri a tions in h eat absor ption. In t his zone, tho ther m ophysic al proper ties of the wo rki ng flu id vary roost significantly w i th v ari a tions in enth alpy. T h er e for e, i t is es pecia ll y i rn por t a n l I o cons t r u c t t h e charuclcl'is lic t<;;;, = I (1l tra) for this zone.

11.5. E ffect of H eade rs o n t he Distribut ion ol' Wo rking fluid B elween T ubes There arc three main types of h eaders (Fig. '11.21): (a) sttpply, or distributin g, headers, l , whi ch d istrib utc 1he wo rking fJ u id between pa r allel tubes connected to thoro; (b) disc/wrge headers, 2, which rec eive fl uid from a number o £ paralle l t u bes; a n d (c) intermediate, or m ixing , hea.der.~, 3 , w hich are used t o equ a li ze n on - id entity i n tube oper ation. Mixing headers arc m ost effic ient when th o flow is single- phase (either steam or water). They nre ofte n em ployed to equa lize non- id entic al operation of tube coils in su perbeaters. Suppl y a nd d ischarge h eaders have d i£fercnt effects on the oper ation of h eat i ng s urfaces . 1 n s t eam s u perheaters, the ir effect d e pe nds h eav il y on I

I"'

J

3....._

l sl

section

'\-

Fig. '1 1.21. H eaders and the ir connect ion wit.h th e tube s ystem of h e.a Ling surfaces (u) lin~ar connection ; (b) Clow t mnst cr 1hrough mix in~ head~•..: (c) Cl ow transrcr :.hrou~ h t"rosso\'er t•a\}(·~

Zntl

X

1 I I I

'

.

section

2 (a)

2 (h)

(C)

•

142

11.6. Flow Pulsations

Ch. 11. Hydrodynamics oj Open Hydraulic Systems

~

.tfp[n

Steam inlef

I~-..,

IIJtn

% ...

·-"'~

":;

•

...

~

I ~ ~

0

~

I

11Pcotl Steam

outlet

0

we,

I

I

i!l l l l lll

I

I

i lli'l l ll

I

~· 0

, I

•

0

I

IITu I

0

0

'I (a)

Win

11111111111

111 11111111I

I

I

I

illiilnMrnl

(6}

••

Ill Uit n

~

I

111111111 11

1111111111 1 Ill

••

~

,,,

I

{d)

(C)

llp f,r

Fig. I 1.22. Hydraulic cbaructoristics of a Z-shnped superheater circuit (a) distribution or velocity nnd velocity head: (II) prORSUI'C dls trlbUtiOil

how sl,earn is su ppliod to, or t·emoved from, a header. ln some plants, headers were used in which steam was admiLLed and discharged as a concentrated jet through the end faces. For instance, in a Z-shapod superh eater circuit (Fig. 11. 22), as steam is distributed between the coils, its axial velocity in the supply header, w 1n, decreases, and accordingly, the pressure head wr.p/2 decr eases and changes to static pressure t.p;l' (Fig. 11. 22a). In con I rast to this, the static pressure at the outlet from the discharge header, t.p~~, decreases. As foll ows from Fig . 11.22/J, the leftmost coils of the superheater operate at a pressure grad ient 6P coii t.p!~' t.p~, which is higher than the pressure gradient 6P co il in the rightmost coils. The difference between the pressure heads in the coils is equal to the sum of static heads in the supply and discharge header, i.e. 6p!~1 t.p~~. The difference in pressure gradients appears not on ly between the extreme coils, but also between any two sections along tho l1oader length and is determined as t ho sum of the respective values of 6p $1 '1~ and t.pex for these , , sections. In other circui ts with concentrated supply and removal of steam through

+

+

+

+

~

Fig. H. 23. Pressure di s tribution in a nshapod hydraulic circuit containing a singlephose fluid

the header end faces, more favourable conditions can form, though the operation of parallel tubes in the sysLem may be substantia] ly non-identical. For instance, with concentrnted supply and removal of steam through the header end faces in a IT-shaped circuit (Fig. 11.23), the conditions of steam admission are similar to those of a Z-shaped circuit, so that the pattern of static pressure distribution a long the supply h eader remains essentially the same, i.e. pressure increases along the motion of fluid. ln the discharge header, static pressure decreases towards its outlet. As follows from Fig . 11 .23, the leftmost coils are at a pressure gradient 6p~~ 6P coil and the rightmost ones at 6Pcoil + t.p~~ . Tbe difference in the pressure gradients b etween them is determined by the difference in the static heads in the supply and discharge beadm·, t.p!? - t.p~"f. Since the unit volume of th e fluid in the coils is higher upon heating than before heating, the effect of the discharge headers on fluid distribution between parall el coils in any hydrau lic system is more substantial than the effect o£ supply headers. The header effect can be d ecreased either by increasing 6Pcoll or by decreasing t.p. 1 in the headers . Both measures are ineffi cient, however , sin-

+

Fig. 11.24. Static pressure di stributi on along the leng th of a header depending on the method', of supply and di scharge o£ a single-phase flow

ce the former requires a higher pres- multiple forced circulation boilers, sure in the boilet· and a higher auxi- tho resistance of evaporaLing tube liary flow rate, while the latter re- coils is high, so that the effect of presquires larger headers, and l,herefore, sure variations along the length of headers may be neglected. more metal. The effect of velocity head can be diminished if steam is introduced and 11.6. Flow Pulsations removed nol, through the end faces of Tho steady-state operating condia header (as in Fig . 11.24a and b), but from its middle (Fig. 11.24c). tions of a boiler may be disturbed by In this case the axial veloci ty of steam various factors, l eading to pulsations. decreases by 50% and the velocity in the working fluid flow. The disturhead by 75%. Still better r esults can bing factors are variations in the heabe obtained by distributed steam ad - ting intensity pressure, now rate and mission to a supply header and dis t- temperature of feed water. There aret•ibuted removal from a discharge hea- two main t ypes of flow pulsations: der. With two supply or discharge tu- boiler pulsations and intercoil pulsabes provided in a header (Fig. '11. 24d), tions . Boiler pulsations are oscillations in the a.xial velocity and velocity head can be diminished respectively to 1/4 tho £low rate of the working fluid in and 1/16 of th eir values in a header individual elements, circuits or the with a single tube. In modern boiler whole plant. They may be caused by plants, fresh steam sup01·hoaters are sharp variations in the indicated paraconnected to a number of supply and motet'S. In similar sections of parallel discharge tubes, so that headers have tubes, flow parameters vary synchonly a slight effect on steam d is tribu- ronously. Boiler pulsations are aLLetion. In reheaters, where the t·esi- nuating (Fig. 11.25a); they disappeat· stance o£ tube coils is relatively Jow as soon as the disturbance is elimiand the resistance of h eaders is high nated. Flow rate pulsations can attain a· (because of high steam velocities), the effect of headers can b e substantial. level characteristic for the gi von conIn economizers, where the unit volume ditions, after which they do not. disof water is naturally low and tho axial appear s pontaneously (Fig . 11.25b). velocity in headers inossen tiul, the This means that the flow rate of effect of velocity head presents no water (wp)w through some l.ubes firs!. problem. fn once-through bo il ers and increases to a maximum, then decrcaI

jft4

i

'

I

Ch. 11. llydrod!lnamics of Open Hydraulic Systems

upper surface of the tubes and forming fatigue cr acks. Intercoil pulsations can be characterized by the pulsation period -r and amplitude (see Fig. 11 .25). As has been established, intercoi I pulsations obey the follow ing regu(11) larities: (a) the~' can appear in some tubes (ruj')w.fu;pJs. r1 of an evapontliug section even under lt steady-state l1eating and hydraulic ~ conditions in a boiler; I :-_ I (b) pulsations of the flow rate of the fluid in pat·allel Lubes of a section are shifted in phase so that the total flow ra te and other· parameters of the fluid at the outlet from the heating sect ion remain cons tant; (c) the amplitude of flow rate pul'Fi g . 11.25. Pattern of attenuating oscilla- sations at the inlet of a tube is much tions (n) and sclf-s ustu ined osci llul.ions (b) higher than the amplitude at: its out·in 11 s ingle tube of a once-th rough element let, while tlto pu lsation period is the same; (d) the hig hest flow rate of water ses, passes llu-ough the average value. at the inlet corresponds to the lowest drops to a minimum (sometimes nega- steam fl ow rate at the outlet , i.e. tive), and then increases again. This the phases are d isplaced by 180°; (e) in intercoil pulsation, the presprocess may be repeated more than once. In this case, tho flow rate of sure in evapot·ating tubes oscillates water in other evaporating tubes also with a period equal to the period of pulsates, but the process is shifted in pulsation of the fluid flow rate. phase. Therefore, the flow rate of Since intercoil pulsations are caused wat or through some t.u bes i ncreascs primarily by variations in the phyperiodically while at tho same time s ical properLios of t;he working fluid docreasi ng in other tubes , wi Lh the in t.he zone where eva porat ion begins, total pressure gradient between the the probability of their appearance headers of these tubes remaining the decreases inversely with pressure. At same. This phenomenon, called in- supercrilical pressures, pulsations are tercoil pulsation, can occur ovoo at a less common and have a lower ampli·constant total flow rate through the tude, but the pattern of flow rate parallel tubes of a section. pulsations at su bcritical and supercriThe pulsation period in once-tluough tical pressure is essentially the same. boilers may sometim es be as long as Flow rate pu lsaLious diminish with fra<:l ious of a minute or a few minu- an increase in the muss velocity, owing t.es . With a high amplitude of flow to the resulting i ncroase in hydraulic rate pulsations, this may be harmful resistance in the econom izer porlion to evaporating tubes, since heat trans- of the tubes. The boundary mass velofer is impaired during tl1o periods of ci Ly in horizontal l.ubes at which pullow flow rate, resulting in tempera- sations can occur depends on pressure ture variations in t.he tube walls p, heating load q, length of the heated (curve t,) and fatigu e stresses in the portion l, and inner diameter of lumetal. In horizontal tubes, phase se- bes d: paration of t he flow may take pl ace . (11.42) -<·n·a t iug the risk of ovcd1oaLing the

12.1. Laws of Free Clrculatton

Ascending-Jl1Scending and slightly inclined tube elements in which fl.ph does not exceed 10% are calculated as are horizontal tubes, with (wph increased by 20% . With a higher contribut ion from tho hydrostatic component, the calculation is done as for vertical channels . Tho actual mass velocity should always be greater than tho boundary value: {wp)w > {wp)b. If this condition is not satisfied, the hydraulic resistance of the economizer porlion of tubes can be increased by mounling orifice plates. These are arranged at the inlet of tho tubes. For once-through boilers, throttling conditions to avoid pulsations should be calcul ated for the lowest value of (wp)g . mass velocity wp. The degree of throttC= I = f(l:!.tltlt p) ling required to prevent intercoil pul(wp)b sations also elim inates instability in where 6.iin i.s the degree of subcooling of the working fluid a t. tho inlet and p the hydraulic characteristic of the coils. is pressure.

where (wp} 0 is the boundary mass velocity at a pressure 10 MP.a which can be found on curves plotted for the given conditions of inlet throttling and subcooling, and kp is a correction factot· for the given pressure. In vertical tubes (coils), the hydrostatic componon t of the pressure gradient, 6.p 1., decreases the probabil ity of the appearance o[ pulsations, and therefore, decreases (wp) 1,: (wp)g = c (wp)~ · {11.43) where (wp)~ is the boundary mass velocity for a similar horizontal tube, Isee formula ('l1.'12) I and c is the coe£ficient for vertical tubes which can be found on curves:

HYDRODYNAMICS OF CLOSED HYDRAULIC SYSTEMS 12.1. Laws of F ree Circulation Free-circulation boilers usually have a circulation circuit of evaporating tubes arranged in the boiler furnace. Continuous motion of water and steamwater mixture {circulation) is organized in the circuit, which ensures continuous and ef£i.cient removal of heat from the heating surfaces. Tl1is makes it possible to maintain the temperature of the tube metal at a tolerable l evel and thus ensure the reliable and long operation of the circul ation circuit. Free circulation is produced by the driving circulating head S dr which 10 - 0 1524

appears from heating the vertical uptake lubes !see formula (1.1)1. Let us write Bernoulli's equation fot each section of the circulation circuit. I t is assumed (Fig. 12.1) that a steamwater mixture of density Pa moves in section 3-4, and, at the pressure in the drum, wal.er of density p' moves in the remaining path, i.e. in sections 4-1-2-3. The reference pl ane is taken at the header level (2-3). For section 1-2 (downtake tubes) we have: (H - h) p'g + p,

+ U~j• p' (12.1)

146

Ch. 12. Hydrodynamtcs of Closed Hydraulic Systems

. The ~ ifference b &tween the driving crrculatmg head and the resistance of ascending tubes is called the useful circulating head:

r''"~:

"

-7 f

Su, = Sdr - b.p 0

8

,.---'-----.,

Su 8 = 6-pdtu 2

J

Fig. 12.1 . To derivation of the principal equation of circulation

Similarly, for sections 2-3 (lower hendor), 3-4 (uptak e tubes), and 4-1 (water space of the drum) it can be written:

W:i•

,

Pl + TP =Hpag + p, '

•

A •TPo + uPJ-4

tr

1

IDe

(12.3)

w•

l.:.p g+ P4 +-f Pa = (H - h) pig + p1 (12.4)

Adding together the pressure gradients in the sections of the circulation circui t and noting formula (1.1), we obtain:

H (pi -

p~)

Sus

(12.7}

Comparing formul ae (12.6) and (12. 7), we fi pd the principal equation of circulation:

H

g = 'Lb.Phr = Sd, (12.5)

With steady-state motion, tho pressure difference between the water columns in the downtake t ubes and the columns of the steam-water m ixture in the uptake tubes is counterbalanced by the sum of hydraulic resistances to the motion of the working fluid in the circuit. Having related all resistances to the down take and up take tubes , we get : (12 .6)

147

12.1. Laws of Free Circulation

O L---------~-------~ ~0~

(12.8)

i.e. the useful circulating head is s pent to overcome the resistance of the descending sections . The driving circulating head, and therefore, the useful circulating head depend heavily on tho relative velocity of steam (w,) in the ascending tubes . With the same mass flow rate of the fluid, as the relative velocity of steam increases, the fraction of the tube cross section occupied by steam, ), increases; thus , the densit~ of the steam-water mi x ture in the ascend ing tu bes increases . In turn, the relative velocity of st eam, and therefore,
w;,

Pm = f (wo, w~, p, d) = f (w 0 , w~, p, d)

s...

These relationships aro rather complicated and hove not yet been solved anal ytically. Their graphical solution is also impossible in view of the large number of the parameters involved. For this reason , S,. , is usually represented graphically as a function of w 0 at various values of w~ and constant v~ues of the other parameters (p, d). Figure 12.2 sl'IOWS w 0 -Su. curves obtained at various values of resolved steam velocity w~. For the same calculation velocity w 0 , as the heating rate. is increased I (w~) 2 > (w;)1 l, the denstty o[ the steam-water mixture in ascending tubes decreases and Su, increases . Under identical condi t ions, the useful circul ati ng head depends on th e

Fig. 12.2. Effect of circula tion v
< (roOlt

pressur~

•

m the circuit (Fig. 12.3). At a h1gher pressure, the density of the steam-water mixture in ascending tubes is higher, and therefore, s~~. . is lower. As pressure approach es the critical value, s,.. decreases to a r elatively low value, so that free circul ation becomes ineffective. The ul timate pressure at which reliable free circul ation is still possible in boilers is equal to 18-19 MPa . On the other h and, even at supercritical pressures, but at low fri ction losses in the circuit of once-through boilers , free circulation turns out to be sufficient to fire the boiler at a water How rate that is reduced by 50% and wi th the recirculation pump switched off. The effect of relative steam v elocity depends on pressure in the circuit. At a low pressure, large formations of steam are possible in a tube (slug flow), and the relative s team velocity

f

is rather high. As the pressure and saturation tempernture increase sur~ace te~sion decreases and 'slugs' break mto fm ~r bubbles , thus decreasing th e rela ttve steam velocity. At piPer> > 0.7 (see Fig. 12.3), the effect of relative steam velocity can be neglect ed. Let us recall that the actual dens ity of \.he s team-water mixture p4 depends on \.he actual volume steam con te~t q> [see formula (9.40)1. Using equat ton (12.5), we obtain a convenient formula for th e driving ctrculaLing head: 1

Sdr = H (p = H

-

Pa )g p *) g

(12. 9)

Formula (12.9) h as been derived under the assumption that the ascending tubes of a circulation circuit con lain a steam-water mixture al ong their whole h eight. Actually, developed boiling b egins in the ascending tubes at a certain distance above the inlet and accordingly, the whole length of th~ tubes should be divided into an economizer portion H e c and evaporating portion H . 0 • Tho section in which developed boil.ing begin ~ . is called the boiling sectwn (or bo£lmg point). The height of the evaporating portion in ascending tubes can be found by the formula He o = H - flee (12.1 0) a nd subst!luted into formula (12.9) to determ1ne the driv ing circulating head. With a non-boiling economizer, tho water enthalpy at its outlet, i:C, is less than i and therefore, tho temperature of water in the boiler drum i~ b elow tl.1~ boiliog point. The quanttly of hodlfJg water that enters the rlrum is greater th an the quantity of feed water by the magnitude determil;led by tho cir culation ratio K, so that the degree of water subcooling in the drum can be found as 1

,

I

p

O.lJicr Per

Fig. 12.3. Effect of pressure on the useful circulating head 1-w, neglected; 1- w, considered

to•

(12.11)

148

Ch. 12. Hydrodynamics of Closed Hydraulic S ystems

149

12.2. Calculation of Circ ulation Circuits

Therefore, in the general case, water at tho inlet to the d escend ing tubes i s s ubcooled*. The degr ee of su bcooling increases as water moves in th o descend ing tubes, which i s du o to an increase in its hyd rostatic pressu re, and nllains a m aximum in the lower h eader of the circulation circuit:

+

lii' flp

P'g

(H _ flPde•) p'g d~·

(12. 12)

where Qc is the hea L absorption o f the c irc uit, kJ/h , and H e is lhe heated h eight or the c ircu i t, m. The height o[ the economizct· portion can be found [rom t h e IJal ance o£ heat fo r tha t portion, i.e. the quantity of heat that s hou ld be transferred t o w ater per unit time to preheat i t to boiliug in the economizer portion [formula (1.2.1 5)1 a ud the quautity of heat a bsorb ed for the same Lime by the ccouom izer portion from the furnace [formula (12.16)1. H ence we have:

flp

A •

Ll ~ce

H

=

•

61'

ecP g flp

(12.13)

Therefore, the degree of water subcooling per uni t flow rate (1 kg) up to t he boiling section is A .

Ll~c/

+

6i'

'

(H

P IJ1 des H , flt' ccP g t:.p

t:.p

t:.Prles \ p' g J

(12.14)

or for the total flow rate of c irculating water, G, kg/ h:

. + [ 6 ~d

l!.i' flp

,

Pg

H ec =

JG

(12.15)

Hc

• When all feed water is fed to a bubbleca p steam washer (see Sec. 15A), subcooli ng is climina led by Lhe partial condensa li on of bubbling steam.

6 i' ' flp p g

I

11 cG

(12:l 7)

12.2. Cnlculat ion of Cir cula tion Circu its Free-circulation circu i ts may be either s imple or compl ex. In a simple circuit (Fig. 12.4a a nd b), all ascendi ng tubes h ave the same geometrical characteristics (diameter, l ength and shape) and arc heated under identical conditio ns. Simple circuits have no common olements with other cir cuits. An example of such a circuit is the water walls of boiler furnaces. Complex circuits (F ig. 12.4c) may have different geometrica l characteris tics and different heating cond i tions . They 1

1•

1

5

5 2/

-2

4

/

tJ

4

Assumi ng tha t heat absorption a long tho height of the cir cuit considered is constant, t h e h eat abs 01:bed for tho sam e time in the economizer portion is: _ HecOc (12.1G)

Qee -

Oc

(H des _ flPc te.• ) p' g .

-H,.p ' g tJ.t' flp

·(a) with stcam-f:Cncrntlng tubes connected direc tly to the drum; (b) with stcnmclrcul nl.l ng lube•; A- working point; 1o~r-nctuu t

circul ation \'el oci ty (wntt.:l' rlow rnle)

(0)

(b)

t:.i' , ( t:.Pde• ) flid+ L\1) P g fides- P'll

where -t:.!' p' g is the change of wate r enthalpy p er unit height, k J /(kg m) , and !J.Pdes is the h ydraulic resistance of Lhe descending tubes, Pa. Tbis is the degree of subcooling th a t. water h as at the entry to the ascending tubes. As it moves there to the boiling secti on, the hydrostatic pressure decreases and subcoo ling diminish es by the magnitud e:

Fig. i 2.5. Circulation diagrams of simple circui ts

t 2t t

- {/

(a)

J

0

(h)

J

J (C)

Fig. 12A. Diagrams or (a, b) sirnrle and (c) corn pl ex cir·cula Lion ci rcui ls J- drum; ! - up take tub<•• (water wall•); J- hender;

4-downtnkc

tubes;

s -stcam~i rculating

lubes

may h ave commo n elements, such as descending tubes whi ch supply the working fl uid to the ascending elem e n ts of all sections w hi ch form a complex circulation circuit [22 1. S imple circulation c ircuits . The principa l circulation equation (12.8) is solved g raphoanalytically. Both s ides of t h o eq uatio n depend on the water flow rate (circulation velocity), i.e . S 11 , = I (w 0 ) a nd IJ.fJdes = I (w 0 ). With an incr ease in w 0 , the useful circulating h ead decreases (see Fig. 12.2), while the hydrau lic resista nce of tho descend ing elements of the circu it increases i n proportion to the square of the flow r ate. Intersection of the curves Su s a nd !J.pde• determines the worki ng point A of the circul a tion diagram (Fig. 12.5a) whose coordin ates satisfy the circulatio n equation (12.8 ). Three different values of circulation v elocit y w0 1, w 02 , and w 03 are given for cons tructing tho circul ation diagram . Tho ca lculation d etermines successively: the hydrau I i c resistance of tho descending tubes in which water flows ls ee formulae (9.43) and (9.50)1; the r es pect ive he ights of the econ o mizer portion (12.17) and th e evaporating portion (12.10); t he r elative cross-secti on al a r ea occupied by steam (9.34); the driving circulating h ead (12.9); the resistance of th e ascending portion in whi ch the s t eam water mixture moves (9.49); and t he useful c irc ulation head, (12.7). The r es ults obtained arc used t o

construct the -circula lion diagram (Fig. 12.5a), i.e. the curves S"• = = f (w0 ) a nd !J.Pdu = f (wo). Then the act u a l circulati o n velocity W:: is found for the working point o[ the diagram; toge ther wil,h the qu a ntity of steam formed in the cir cu it, G,, it makes it possible to det ermine t he circu latio u r atio K. In moder n steam boilers , primarily simple ci rc u lation c irc uits are em ployed in the form of water-wall sect io ns connected to s t eam-circulating tubes (Fig. 12.4b). In s uch c ircui ts, the d riving head a ppears both i n heated water-wall tubes and unhea t ed steam-cir culati ng tubes, since t hese are also filled with the steam-water mixture (Fig. 12.5b) . · The corresponding usefu l heads are: S;:'~ in h eated water-wall tubes and s~~ in unheated steam-circulating tubes. The total usefu l h ead of the c = ClrCUlt, ... U& u•' IS s pen t to overcom e the hydraulic res is tance of th e d escending tubes !J.Pdc•· The coord inatos of point A at th o intersectio n of the curves det er mine the actual water flow r a te in the cir cuit, G~, and us eful h ead S~•. T h e actual useful h eads of the water-wall and steam-circulating tu bes are de termined by the ordinates of corresponding points on the curves a t G~ . T he total cross-sectional aroa of steam-circulating tulles is s rn a ll.er than that of watcr- wnll tubes, and therefore, at high fl ow rates (G > Gcr), their resistance m;1y lurn 011t to be higher than

. . s

sww + sse

.

150

lJ

Fig. 12.6. Circulation diagram of a complex circuit

the useful head produced in them, that is, the useful head of water-wall tubes S::';" will be partially spent to overcome their resistance. Complex circulation circuits. For a complex circulation circuit with a common downtake system (Fig. 12.4c), the curves of useful head are constructed in the recommended seq ueace I or each ascending section: Su.r =

+

+

= (S";.~ S~~)r. Su.u = (S::'!" s.:~)n, Su,m = (S::'!" S~)m (see Fig.12.6).

+

Since all the sections of a complex circuit operate in parallel at the same pressure gradient, their circulation characteristics are summed up by adding together the water flow rates at the same values of useful heads (by the abscissae) to obtain the total characteristic DB. Additionally, a curve of resistance of the downtake (water-feeding) section of the circuit, which is common for all ascending sections, is constructed (curve OC) . T he intersection of curves DB and OC gives the working point A of t he circulation diagram, by which one can find the total water flow rate in the complex circuit, l:.G, nod the useful head Sua· Water flow rates in the sections are found by drawing the horizontal through the working point up to the intersection with the curves of useful circulating head for each section. When the water flow rate and quantity of steam produced in each section are known, one can determine the actual values of w0 and K and calculate w4 .,. and the total circulation ratio for tho complex circuit.

151

12.3. General Hydraulic Charact eristic of Evaporating

Ch. 12. Hydrodynamics of Closed Hydraulic Systems

Nowadays, circulation circuits are calculated by means of electronic computers. This makes it possible, without spending much time, to calculate various variants for various designs and operating parameters of a boiler plant. Steam generators employed at nuclear power stations with water-cooled water-modern ted reactors may be either vertical or horizontal in design (sec Sec. 24.2). In both types, the evaporating heating surfaces are formed by tube banks immersed into a large volume of boiling water. The mecha nism and hydrodynamics of such systems differ from those of the circulation systems of conventional steam boil ers (where boiling water moves in tubes) and have not been yet studied properly. There are no reliable data for the circulation of the driving and useful circulating head nor reliable models of tho mechanism of water circulation through tube banks. Furthermore, ascending and descending elements of water flow cannot be distinguished clearly. On the other hand, water circulation in intertubular spaces is employed widely in the horizontal and vertical steam generators of nuclear power stations in the USSR and other countries. In vertical steam generators, a tube bank is surrounded by a shell, so that it is possible, with certain assumptions, to single out the ascending and descending portion of the circulation circuit. Calculating the circulation circuit is not very difficult and can be made by the standard method of calculating circulation in steam boilers discussed earlier. In horizontal steam generators, the ascending and descending portions of the circulation circuit are not separated structurally. Circulution takes place in a large volume with a tube bank immersed into H. For this reason, the patlern of water motion through freely immersed tube banks should be analysed before selecting the configuration of the circuit for c-alculation. 4

12.3. General Hydraulic Characteristic (){ Evaporating Tubes and Its Role in Eslimating the Reliability 11£ Circulation The general hydraulic characteristic <>f an evaporating tuhe relates the useful circulating head to flow rate and includes the ascending or descending motion of the working fluid. Before constructing the characteristics, let us consider the ··laws of distribution of density of a steamwater mixture in an evaporating tube as a function of circulation velocity at a constant heating intensity. As seen in Fig. 12.7, if we neglect the relative velocity of steam Wr (q> = ~) and frict ion in tubes 6p1,, the curve p, will be symmetrical and have a peak in a point corresponding to the zero circulation velocity w 0 = 0 and boundary density p •. In other words, with a zero flow rate of water, the tube will be filled only with steam. An increase in the water flow r ate at a given heat release results in a denser steam-water mixture which at high values of w 0 is asymptotic to its extreme value p'. The general hydraulic characteristic of an evaporating tube in a circulation circuit for Lhe given conditions (w, = 0 and 6p1, = 0) is a mirror image of the curve Pm (curve 1 in Fig. 12.8). For these conditions, q> = ~As t~e circulation velocity w 0 decreases, the useful circulating head increases symmetrically and in the limitapproaches its maximum: s~;x = II (p' - p") g (12 .18)

t .

0

Fig. 1.2.8. Ef£cct o[ the steam slippage nnd friction on the total hydraulic characteristic of a steam-generating tube J-lbcoretlcn l clrculallnc bead (neglecting steam slippage and friction) ; .!!-steam slippage conside· red: 3-,•~am s llppogc and friction consldert>d

The useful circulating head depends substantially on the relative velocity of steam, this effect being different depending on the direction of motion. In ascending motion, w, decreases

and decreases p"" and therefore, Sua is increased (curve 2) . As, however, the circulation velocity approaches zero, the highest useful circulating head will be lower than that found by formula (12.18). Friction forces are always directed opposite to the motion of fluid, and therefore, decrease Sua in ascending tubes and in.crease it in descending ones (curve 3). The concept of zero circulation velocity is conditional, since an ascending tube is heated and thus generates steam in an amount corresponding to tho absorbed heat. To generate steam, the tube must be fed with water. When there is no circulation through an evaporating tube, water should be supplied at such a rate as ,o' to compensate for the quantity of steam generated in the tube; this is called the make-up velocity Wmu. The term implies, firstly, that the quan,o" tity o[ water supplied to a tube is ·wo------ - - - - -- ·% low and, secondly, that water can 0 enter the tube from the bottom as well as from the top, i.e. either ascenFig. 12.7. Variations of density p111 o[ steam· ding or descending motion is possible "'" ler mixture as a function of w0 in ascend· in the tube. The region of very low ing and descending motion

"- B,!~

.... ..• , "'

\c

0' 0 0

Fig. '1 2.9. Effect o[ pressure on the total hydraulic charact eri sti c or a steam-genera ling tu be

s," c

SuJ

['..A

"...... If"- £ _,

lllmu

A

.

".. OJ "'-, , -~

!:"

"'

">

A

(II)

bl gbcr pressure

Fig. 12.11. Non-uniform hea t absorption by parallel tubes in the wa ter walls of boiler furnaces (a) acros.' the furnace width; (b) nlon~ the height where some tubes arc shaded T

f' E

(D) positive and negalive circu lation velocities (hatched area in Fig. 12 .8) is usually excluded from analysis. The right-ha nd branch of the general hydraulic characteristic corresponds to tho ascending motion of fluid, and the left-hand one to the descending (reverse) motion. Th e relative position of the branches depends on the pressure in the circuit. At a low pressure, the effect of relative steam velocity is high , and therefore, the left-hand branch passes higher than any point on tho right-hand branch (Fig. 12.9a). In contrast to this, at a high pressure, the steam velocity and hydraulic resistance are low, and therefore, an appreciable portion of the left-hand branch lies lower than the portion of the right-hand branch in the region of low circulation velocities (Fig. 12.9b). In the right-hand branch , we can find point C which determines tho flow rate of water at the make-up velocity, (wp)mu· The ordinate of that point gives us the useful head of stagnation S~'., i.e. the head at which the working fluid virtually ceases to move, resulting in the phenomenon of circulation stagnation. With circulation stagnation, water in a heated tube moves very slowly upwards or downwards, while steam moves only upwards a nd bubbles through the column of water in the tube. Circulation stagnation may

III

l I

I

appear in circui ts with 0\' aporaling tubes connected to the water space of the drum, i.e. below the water level in the drum (Fig. 12.10a). With tubes connected to the steam s pace of the drum (Fig. 12.10b} , the useful head of water, which moves very slowly, is insufficient to overcome tho resistance of the down take tu bos and to raise the working fluid to th o topmost level in t.he uptake tubes or the circuit. Thus, a free water level can form under such co nditions. The leHhand branch of ·the characteristic, which describes steady-state descending motion , has a minimum io point 8 (see Fig. 12.9). The transiti on from ascending to descending motion passes through the zero velocity and is called circulation reversal. Tho ordinate of point B gives us the useful head of reversal, sr::: ' i.e. a head at which a chango from ascending to descending motion occurs in an evaporating tube. The distance between the horizontal line DE (Fig. 12 .9) and the axis of abscissae is the pressur e gradient in downtake tubes llPdeo = which, according to equation (12 .8}, determines the working point A in the circulation diagram. As this pressure gradient increases (line D'E' in Fig. 12.9), the water now rate decreases, but at low pressures the head of stagnation is achieved earlier, a nd

s:,

(a)

Co) Into tbc water space; (b) Into the steam spncc

tIH+--'

-

.

~ ~\

~

. ). /,

'

••

therefore, circulation stagnation is more probable (Fig. 12.9a); at a high pressure, the head of r eversal is ach ieved earlier and circulation reversal is more likely to occur (Fig. 12.9b). Circulation circuits are systems of tubes connected in parallel which may be heated differently under actual conditions in a boiler. Non-uniform heating of some tubes may b e caused by structural factors in the system or by operating conditions. Fot· instance, tubes in the middle of a furnace wall usual1y obtain a quantity of heat roughly twice that absorbed by corner tubes (Fig. 12.1.1a). Tubes around burner ports and at a certain height above the port turn out to be shaded, i.e. they are not dir ectly exposed to the r ad iant h eat of flame (Fig. 12 .1.1b). In the operation of solid fuel-fired boilers, especially when the combustion conditions are disturbed, some water wall tubes may be clinker ed by slag across their ·width or.along the height (Fig. 12.12a). Since slag has a low h eat conductivi-

(a)

Fig. iZ.iO. Connections of evaporating lubes to the drum

I ··~~

:;

.....

(a)

'

I

::-

fVmlt

.

.

to form a burner port

E'

:'--.... A

ll 0

(a) lower pressure;

153

12.3. General llydraul!c Cltaractcrlsllc of Evaporating

Cit. 12. llydrodynamics of Closed Jlydraulic Systems

152

Fig. 12.12. Non-uniform heat absorption by lu bes of water walls (a) due lo cli nkering; (b) du e to misalignment of so me lubes

ty, its layer will transmit substa ntially less heat. In som e cases, say, if tube fastenings arc loosened , some tubes may protrude from a tube row (off-rank tubes) , Fig. ~ 2.12~, a nd will obtain more heat, whlle adJacent tubes will be shaded by them a nd r eceive Jess heat. Figure t 2.13a shows a system o[ parallel ascending lubes in a circulation circuit which have identical goometrical and structural char acteristics. Sl!ppose that some of them are eli nJ<ered. Unclinkered {clean) tubes (say, tube 1) will operate und er the rated conditions, i.e. they receive the specified quantity of heat and deliver the specified quantity of steam D. L et tube 2 be clinker ed in the top half only so that no steam forms in that portion; the lower half will then absorb half the specified heat, so that the whole tube will produce D/2 of steam. Let tube 3 generate steam in a quantity D/2, but in contrast to tube 2, be clinkered in its lower half only. Let tube 4 be clinkered uniformly along its whole length to such an extent that it delivers steam in the same quantity D/2 . Finally, tube 5 is supposed to be clinkered along tho whole h eight to such a degree that it docs not r eceive heat at all, and therefore, produces no steam (D = 0). Assuming that all the tubes are hea ted u niformly along their height, it may bo taken that the quantity of steam in Lhem increases linearly (Fig.12.13b}. As may bo seen from the figure, differently heated tubes prodliCe different quantities of steam, and thereforo, develop different driving circu-

.• 154

Ch. 12. Hydrodynamics. of Closed Hydraulic System•

0 0/2 D/2 0/2 0 • 0

0=0

.D Fig. 12.13. Effect of clinkering of stez.m-genera ti ng tubes on the quantity of generated steam

D/2

f

..... .-

..., (a) 1

2

J

4

I

5

laling heads ; clean tubes deliver the specified quantity of steam and develop the highest driving head: sdr = = If 8 QJ (p' - p ") g. On the other hand, the cliukered t.ul>es which obtain the sa me qu antity of heat and thus deliver the sarno quantity of steam JJ/2, are slnggod d ifforontly and will develop differcut drivi ng heads (always lower than that in tho clean tubes), since, at the given hent absorption and th e corresponding p0 , s team fill s them to a different height: in tube 3, steam form s only in the top half, H/2; in tube 4, i l I ills the whole tube height; in tube 2 , it also fills the whole tube height, but has a lower density. Figure 12.14 shows curves of useful circulating h eads for a system with non-uniformly healed tubes . As has been demonstrated, tho driving cir culating heads in the tubes are different. I n such a system, all the ascending tubes are connected to com-

1

moo headers and operate under the same forced pressure gradient D.p which is equal to Su, [see formula (12.8)1. Hence, the useful circulating h ead should be the same for all the tubes in the circuit. Owing to non-uniform heating, however, this useful h ead, which is common for all tho tubes , corresponds to diHerent flow rates of the water that circulates in th em. With generally favourable temperature conditions for the main number of tubes, uneven heating may result in that little water will pass through some of the tubes. Thus, circu lation disturbances, such as stagnation or even circulation reversal, are likely to occur in these Lubes . Circul ation circuits are checked for circulation reliability, i.e. for the absence of circulation disturbances, by using the reliability criteria given below. The checking is done for the least heated tubes (with 10 % reserve). The crit~rion of stagnation is: (12.19) the criterion of circulation reversal is srcv;sc > 1.1 (12.20) U3 U8 and the criterion of free water leve l is (S ~,'.- 6Pwt)IS~, > 1.1 (1.2.2 1)

l'

Fig. 12.14. Effect of non-uniform h ea ting of parallel evaporating tubes in a circulation ci rcuit on the direction and velocity of circu Ia tion J-s". or strongly hcnlcd tubes (most lubes in Lhc c lrcuiL) ; 2- S u• or poorly heaLed tubes (some tubes In the circuit); 3-S u• of the worst hea t ed tubes (a few Lubes In the c ircuit)

whore D.pwt is tho pr c~sure loss fo r raising the mixture a·bovo tho water level in the dru m, hwt (sco F ig. 12.10). The phenomena discussed arc extremely dangerous, since circulation stagnation or the appearance of free water level can interrupt the motion of walor in the cirCillalion circuit, while cir-

155

12.4. Hydrodynamic• of Derc• nJing Tubes

culation reversal involves a chango from ascending to descending motion, i.e. the passage of velocities through zero . All these regimes can disturb heat removal from the internal surface of evaporating tubes and lead to i)verheating an d even burn-out of tho tubes. Circuits operating at pressures p above 11 MPa or with local heat absorp t ion r ates q above 400 kW/ m 2 are additionally checked for ·'tho probability of heat transfer impairment (burn-out conditions), soc Sec. 10.3. 12.4. Hydrodynamics of Descending Tubes and I ts Effect on the Reliability of Circulation

0 tif

a

~i~7 ~ c

i:'.t' "'

"6

a'

c' ~h'

~d

~ d'

t:

I I

= ~

=

I

I

r

X

..

m

"'

m'

)rn

n'

I I I I

'

( )

J

1\

I I

~

{If)

Heliable operation of ascending tubes in circulation circuits is ensured by a continuous supply of the required amount of water. A decrease in the water supply through descending tubes to intensively heated ascending tubes can lead to insufficient cooling and, furthermore, to overheating of the tubes. The situation is dangerous and most often results in burn-out of the heated evaporating tubes. If water supply is fully stopped, the temperature of the walls of h eated tubes may rise at a rate of u p to 20-25° C/s, meaning that 10-15 seconds are sufficient to got t he plant out of order. Descending tubes of a circuit may turn out to have a water flow rate too low to ensure proper temperature conditions in evaporating tubes if they have an excessive hydraulic resistance or if steam is entra ined from the drum into them. H ydraulic r esistance of descending tubes. Vlhen analysing the operation of descendi ng tubes, we should distinguish between two cases: ~a) w~ ter supplied from the econom1zor 1n to the boiler drum at the saturation temperature (boiling economizer, t;. = = t') and (b) water fed at a temperature below the saturat ion p oint (nonboiling economizer. t;. < t').

I'd

/Pd-.....,

o'

I

pf

k

e

[b)

k'

p' (c)

Fig. i 2.15. Distribution of pressures and the corresponding entbalpics of water a t the saturation line along the height of down take tubes

With a boiling economizer, water temperature at the inlet to the descendin!; tubes is tin= t' {Fig. 12. 15a) . As water moves through the drum to the inlet of the descending tubes, its velocity is negligible, so t hat the velocity head due to the non-parallel drum walls can be neglected. Pressure changes can only occur due to a rise in the hydrostatic pressure by a linear Jaw (line ab in Fig. 12.15b). The pressure at the inlet to the descending tubes is higher than that at the water level in the drum by the magnitude (section be): D.p~ = h;,p' g

(12.22)

Upon entry into descending tubes, water velocity increases substantially, since t he hydrostatic pressure decreases because of the appearance of velocity h ead and inevitable energy losses on local resistances. Thus, tho pressui·o at the inlet to the descending t ubes decreases (section bd) by: (12.23)

156

With furth er motion of wnLor in ~he descending tubes, press ure ngui n mcroases, due to an increase in Lhe hydrostatic pressure of tho water column a long line de by tho leng t h of section ef:

(12.24) or, i[ we additionally consider the pressure Joss by fri ction and on loca l resistances flPa e• = [Ila e• X ( ':

w;i-. 2g

+ l:£ )] p'g

(12.25)

where

Re[el'l'ing to Fig. 12.15, as water moves in the descending tubes, iLs pressure increases continuously, except for the t ube in let prop or , where it docrouses somewhat. If, however, assume that flp~ > tlp 1n, i.e.

h In >(i + 'oln t )

w2

dt~ g

2

(12.26)

to or. greater than tlp~, the pressure of water at the in let to the descenrl i ng tubes will drop to s uch a level that the water will turn out to be su perheated at the drum pressure or will boil in the zone of reduced pressure. Stearn bubulcs thus formed will be entrained uy circulating water into the desce nding Lubes where th e prossure is higher; Lhus, water wil l turn out to bo subcooled there and s tea m bubbles will condense. Complete condensation of steam requires a certa i o ti me. As a result, steam bubbles wi'll be curried by the water flow an appreciable distance in tl te descendin
it will follow from Fig. 12.15b that t he water pressure in any point of the descending system exceeds its pressure at the water level in the drum Pa· The enthalpy of boiling water is distributed according to the increasing pressure (a'b'd'k' in Fig. 12.15c) . The actual enthalpy of water i.n any section of the descending tubes IS equal to id; it corresponds to tho pressure at the water level in the drum Pd and is constant if there is no heating of tho descending tubes (line a' p'). The horizontal sections between these lines determine the degree of wa tor s uucooling in the respective s~cti o n s of the descending tubes; .for 1nsLance, the subcooling ill SeCtiOn X- X is determined by tho section m'-n'. Therefore if conditio n (1 2.26) is observed, 'boiling and steam generation in unheated descending tubes is impossible. * Steam can also form in descending If the pressure drop at the inlet tubes on a sudden pressure drop in tb c to the descending tubes tlp 1n is equal boiler.

:1.

13.1. Laws of Bubbling

Ch. 12. Hydrodynamics of Closed 1/ydrau/ic Systems

Fig. 12.16. Determination of tbe minimal wa tcr level above the inlet to down take tubes

both free and forced circulation. Their formation can be prevented by ma intaining the wate r level in the drum at a safe height above the inl ets to the desce nding tubes. The probabi lity <>f formnlion of steam cones increases with au increase in the diameter of the descending tubes. As recommended by the standard method of hydraulic calculation of steam boilers 122 1, the ratio of the minimal water level h to the diameter of descending tubes dde. should be chosen by tho curves given in Fig. 12.16. With a non-boiling economizer, the temperature of feed water supplied to the drum is below the saturation point. This water is mixed with boiler water . and forms a mixture whose temperature is below the 'saturation point under pressure at tho water level in· the drum, tin < t'. Water at this temperature enters the des-

157

cend i ng tubes. This degree of s ubcooling is equivalent to the degree of subcooling provided by forming a proper water level in the drum. Water subcooling in the drum is no t a useful means of ensuring the stahlo operation of descending tubes in view of the comp lexity and inconvenience of this method. As with a boiling economizer (t 1n = t'), t ho stable operation of descending tuLles in a circuit with non-boiling economizer (t 1n < t') is achieved by preve nting the formation of steam cones above the entry to the descending tubes. Subcooling of water at the i.nlet to descending tubes at tin < t' me re ly e ns ures a certain reserve of reliability. Entrainment of s team from the water space of drum. The normal supply of water to the descending tubes can be disturbed if steam uubbles in the water space of the drum are entraine d by water and carried into tho descending tubes. When velocity of water flows in the drum is substantial, steam bubbles below the water s urface have no time to separate and are thus entrained by the water into the d escendi ng tubes. Such conditions may appear, for instance, when the ends of the evaporating tubes in the drum are arranged too close to the inlets of Lhe descending tubes. The entrainment of steam into the descending tubes is prevented by properly organizing the water flows, for instance, by arranging partitions or by separating the steam-water mixture in cyclones.

HYDRODYNAMICS OF BUBBLING SYSTEMS 13. I. Laws of Bubbling In free-circulation boilers, Lh e working fluid moves as it is hcnted in ascending tubes; in once-th roug h and

mt)ltiple forced circulation boilers , its motion is caused by the pressure head developed by the feed pump. In ei Lhet• case, the fluid in evaporating tubes is two-phase and its motion is

I

! 1I

158

Ch. 13. Hydrodynamics of Bubbltng Syst ems

5

5

-- - - -- - ------: --:.......---

13.1. Laws of Bu bbli_n_,g'---- - - -- -- -- -1...:..;. 59

.

r

-

1f

~~

2 (!J)

.

-,--1-

/

.

~

-<::

"" - -1-

--

'//

(a)

1 f- •

."\.

-

- 1-

12

Steam

(C)

8 9

Fig. 13.1. Devices !or steam bubbling through water layO!r (a) In boUer drum; (b) In separating drum or c hannel-type; boiling reac~or; (c) In s t::am washer; 1- downtal<e tubes; Z-dlstrlbutlon plate; J-drum; 4-stenm-clrculating tubes; ~-steam-generating tubes; 6- GCparatlng drum; 7- steam·wnter mixture from process channels; a-steam box; 9-feed water he ader; 10- dlstributlng perlorated tubes; 1 J-feed water (wash water); Jt- wasb water drainage

essentially the combined the two components, water which may have different Three principal cases are sible:

w. w.

>

motion of and steam, velocities. then pos-

0, ww > 0-ascending motion; 0, W w < 0-flow reversal, and 0, ww < 0-descending motion.

> w. <

In contrast to these cases, in which both phases are in motion, there may be a special case when only the lighter phase (steam) is moving, while the heavier phase (water) is stagnant, i.e. it has a zero average velocity: w. > 0, Wr.o = 0. This is known as the process of steam bubbling through liquid. Steam bubbling is a specific kind of motion of a two-phase mixture in which bubbles of the lighter phase (steam) rise through the bulk of the I

heavier phase (water). Bubbling occurs in the drums of boilers ami steam generators when the steam-water mixture is introduced below the water level, in the separating drums of channel-type boiling reactors, in s team washers, etc. (Fig. 13.1). It ca n also occur in evaporating tubes on certain hydrodynamic disturbances of flow, such as the formation of a free water level or circulation stagnation (see Sec. 12.3). The layer of the s teamwater mixture in which steam bubbling takes place is called the dynamic (movable) two-phase layer. Bubbling is usually effected by feeding steam under a perforated distribution plate (Fig. 13.2). As steam moves through holes in the plate, its jets break into separate bubbles which rise through tho bulk of water above the plate to the

llil

-

-·

~

~

~

--

-

0

0

0

0

(j

0

0

0

0

-o-.

A/

-0

0

0 0

--

o:o-

'o • o 0 0

.--~~.L., /,'.::.71 .--.

-· .... . .. - - -- i

'f''

n 0

- z(a)

I I I

I

I

I

6:16

,

J ... ..... .. .•... .... .

v·t

rrf

"'

'I•''

'"'

'fap

....

l I

'f

0

I

i I

~ · A f.lr.JI f.)!. o o -..- if.•~ ~"-' _; i~~ -. . . .. _.._._,...., ~,~ - • ..- ••- • ., - • - , r '"":' ' ,-. • • ...- • f

~

-

"'

, 'f.... {6)

I •

-.. -· .-·-· -· ·-

~

·-~

•

_.

A

' 0 ' .- '.-' '~ L. _, '· -··-··~ v 1

,- --- ] ~ ,-.·.-:: .!. •--~41 • ._ -

.-

. ... . - - Lo

'

- · -•'-=

2

Fig. 13.2 Analysis o[ the bubbling process and steam content distribution along the heigh t of apparatus . (a) at low

0; (b) nl 111gb to0; I-IIJ-zoncs

to

or dynamic two-phase layer; 1-ateam cushion; .e- nonle

separating surface between the phases (which is usually called the disengagement surface). The disengagement surface is not smooth but seething, or turbulent, with high splashes being formed continuously by steam bubbles which rise to the surface. In the course of bubbling, steam bubbles entrain wa ter which then moves downwar d at the walls and in the spaces between bubble chains and is thus forced into circulation. As a result, a zoro··average flow rate of water (i'Vw = 0) and a positive flow rate of steam (w, > 0) are established in bubbling. Bubbling is eUected in a bubbling apparatus, such as a vertical column (Fig. 13.2). The water level indicated by the water-level gauge glass at the column is lower th an that in the colu mn proper, since water in the apparatus is at the boiling point and, besides, is saturated with steam bubbles and forms a steam-water mixture of a density Pbu b · Water in the gauge glass is subcooled below the saturation temperature at the pressure of ·bubbling and its density is Pe· Since the pressure at the bottom of two communicating vessels (point A) should be the same, we have: hphf>bubg =

(hr.oetPg

+ D.hp.) g

{13.1)

Noting that the density of steam p. is much lower than that of water in the gauge glass, Pe• we obtain: hplrf>bu b =

hweiPg

(13.2)

Since Pbub is smaller than Pe• the physical level hph es tablished in the column is higher than the weight level h r.o ei observed in the gauge glass by the magnitude D.h. The physical level in the apparatus is essentially tho level of tho working fluid at a steam content q> close to unity. Tho difference D.h is called the water swell. The supplied steam is distributed over t he column cross section according to the hydraulic resistance of the wat er layer; with a concentrated steam s upply, this resistance may be dif-

(erent in various points of the cross section. A uniform distribution of steam can be attained by mounting a perforated steam-distribution plate in the water space. The hydraulic resistance of the pluto is much higher than that of the free cross section of t he column and is thus a decisive factor in steam distribution. The plate is perforated evenly, and there(ore, steam is distributed uniformly ovet· the cross section. A gap is left. botween the plate and column walls to perm it return flow of the water. The edges of the plate are bent downward to prevent a sudden outburst of steam at the walls and to form a steam cushion beneath the plate. A steam cushion is essential for normal operation o[ the steam-dislr:ibution plate in which steam bubbles flow continuously tluough its holes. At the moment of formation of a steam cushion, steam bas a definite (minimal) velocity wm"1n in the perforations of the plate. For the stable existence of the steam cushion, the actual velocity of steam flow through the perforations must be higher than the minimal value, i.e. w" > w m"in· This is easily accomplished if perforations have a diameter d 1 = 2-3 mm, i.e. smaller than the break-off diameter of steam bubbles. In the steam boilers of thermal power stations and the steam generators of nuclear power stations, submerged distribution plates have larger holes of a diameter of 8-12 mm or even more. Under such conditions, a steam cushion can form if steam passes through the boles in con tinuous jets. Steam jels can entrain a slight quantity of water droplets from the water space of the apparatus, hut this has no substantial effect on the hydrodynamics of the d istribution plate. The hydrostatic head needed to form a stable steam cushion is determitred by the difference in the masses of water and s team columns of a heigh ~ equal to the thickness of cushion o: D.p = 0 (p' -

p") g

(1:-1. 3)

160

Ch . 19. llydrodynamlcs of Bubbling S yst em s

18.1. Laws of Bubbling

Fig. 13.3. Analysis of operation o£ a submerged di stribution pi n le

- - - •a 7/: -- --- - ----. -

-n -

~-

o- - o ~/ ~--·

-

-

['60 -

-

-

""'"" d 1• 2R1 --I

interval: from the value corresponding to the s team flow rate immediately above the distribution plate up to almost unity in the steam cushion and in the steam space. Tho distribution of CJ>bub along the height depends mainly on the steam flow rate or, what is the same, on tho resolved steam velocity w~. For a particular value of one can distinguish between three zones in the dynamic two-phase layer' above the distribution plate (Fig. 13.2). With an ample steam supply, this layer is filled with steam, and therefore, CJ>oub = 1. The first zone o.f the two-phase dynamic layer is immediately above the plate. In this zone, the steam flow is sta bilized: the larger bubbles break down into finer bubbles, while fine bubbles combine to form larger bubbles , i.e. all bubbles are essen t ially transformed i nto the same stable size. The s team content CJ>bub changes from the value corresponding to the relative free cross-sectional area of the plate q>p 1 to a certain constant value !J>bub whlch is determined by the particular conditions of bubbling: steam flow rate and pressure. The initial zone of the dynamic layer has a limited height, usually of a few centimetres. The second zone is characterized by a constant value q>~~b = constant which has been attained due to stabilization at the exit from the first zone. The bubbling process in the stabilized zone is described most accurately by tho generalized formula proposed by M.A. St yrikovich and S. S. Kutateladze [31]:

.

A

t:

l..l P = '<>peri

(w") • • 2 P

+ 2o R,

(13.4)

T he combined solution or equations (1 3.3) and (1 3.4) gives the minim al thickness o[ n stable stouro cushion: _ 2a 0 mi n - R,(p' - p") g p" (w")l +S perl 2g (p' -p")

(13.5)

where a is the surface tension, Sperl is the coefficient of resis tance of the s team-distri bution plat.e which is det ermined by the free cross-sectional area of its perforations; R 1 = d 1/2. A steam-distribution p late vvith perforation holes can operate efficiently, with a stable cushion, only in a narrow range of heating loads near t he rated boiler load. With an increase in the steam-generating load, the h eight of the steam cushion increases in proportion to the square of the ratio of loads (D:r!D,)Z, and may rosu lt in tho hreak-th:rough of steam at the plato edges. At lower loads, steam is distributed unevenly over the cross section. A new ty-pe of steam-dis tribution plate has been developed at tho Krzhizhanovs ky power engineering institute: it has numerous pipes per[or ated along their whole length a nd

closed nt Lhe bottom ends, which nrc mounted in the holes of n distribution plate (Fig. 13.4). The number a nd arrangement of pipes and the number of perforaLions in them are determined by the desired range of varialion of the steam-generating load. Steam accumul ates in the water spnce under the plate and forms a steam cushion of 11 height up to tho length of the perforated pipes . [ t flows through their perforations into the water layer above the distribution pl ate. At a chaugo in tho steamgenerating load, tho number o[ 'active' perforations is self-regulated by a change in the height of tho steam cushion. This ensures uniform bubbling and uniform load on the disengagement surface in a wide range of steam-generating loads. As in [orced motion, the principal characteris tic of bubbling is the relative cross-sectional area occupied by steam, CPtmb· The distribution of steam and water along the height of a bubbl ing apparatus is different, and therefore, CJ>bu b can vary within u wide Steam ou/let

t UnilA

-

t I l.tJ "IT . -- -- -1-::-- • .... -- - -··-

. - - - -- ---- - - -

q> ~~b ::::::

0 ·4 (

1- perlorn lcd steam-dis tribution plate; ll-perforated lubes; J- stcam cus bion; 4- slcnm-llcncra ting healing surface

p•

(w•o V4t !:.,_ p'-p")0. 7 a"'" g c.. (13.6)

·-::~

Fig. 1.3.4. Steam distributor

p• )O. H

Tho formula is applicable at steam content q>~1ub::;:;;; 0.7. In the third zone (transient zone}, CJ>bub increases continuously from the stabilized value q>&~b t o q> = 1, w hich exists above the two-phase dynamic layer. The height of the third zone 11 - 0 15 2i

•

h

h;s h2

h,

I

p /f

f

I

/'

w;,

This head is spent to overcome the hydraulic resistance of perforations and to form an excessive pressure r equired to break through the water film at tho exit of steam into the water space a bove the plate (Fig. 13.3). A wa ter [ilm can be broken through by a force 2nR 1a which develops a pressure 2nH 1a/nRi = 2a!R,. Then we have:

1.61.

~ c::;

~

~~

~

I I I

~~

~

lf 0 ~dp

.i

Fig. 13.5. Effect of resolved steam velocity on the distribution of q> along the height of apparatus w01 < w02 < w03; h,, h,, h,- rcspcclivc heig hts oI steam sf)ncc

depends on w~ . At a low w~, individual r ising bubbles are distributed in a relatively large water volume and therefore cannot influence one another. Rising bubbles only slightly deform the disengagement surface, so that there is a distinct boundary between the second an d third zones and the lat ter has a low height (curve w;, in Fig. 13.5). W ith an increase of w~. the quantity of bubbling steam increases, bubble chains move in the water and combine into steam jets, and a return circulat ion of water appears in the apparatus. The number of steam jets then incr eases and impedes the return circul ation of water , i.e. water entrained by the rising steam cannot flow back as easily and is retained for a longer time in' the · upper portions of the dynamic layer, thus leading to water swell. The phaseseparating surface becomes less distinct, the transition zone of the dynamic l ayer increases in heigbt, and the height h of the steam space in the apparatus diminishes accordingly (curve 1 in Fig. 13.5). The hydrodyna· mics of bubbling depends substantially on pressure. With ao increase in pressure, steam density increases, so that steam bubbles rise in water more

.w;

13.3. Effect of Non-untform Heat Release and Impurities

Ch. 13. Hydrodynamics of Bubbling Systems

162

slowly and are retained in the water space for a longer time. This increases IJ>bub' and therefore, causes water swell and an increase in the height of the stabilized and transient zones. Thus, an increase in pressure is qualitatively equivalent to an increase in w~. For a given weight level, the height of the transient zone, h 1r, depends on the fraction of the crosssectional area occupied by steam. The height of the transient zone has a direct effect on tho moisture content of tho steam supplied from the apparatus into a steam separator. With a higher h 1 n the height of the steam space is lower (see Fig. 13.5) and the moisture content of the steam is higher.

and by the force due to surface tension: (13.9) F 0 = :rt da that is Ft.p=Fc+Fa (13.10) Substituting from formulae (13.7) to (13.9) into (13.10), we obtain the formula for steam velocity w" in the boles of a perforated plate, that enables the water layer to be 1·etained on the plate:

,

, I

v

w = .

2gp' ~. ..P

in which ~ is the r esolved coefficient of resistance of the bubbling device:

s=spert+swf 13.2. Dynamic Layer in Steam Washers The washing of steam by pure water is a widely employed method for improving steam quality (see Sec. 15.4). It is commonly effected by passing the steam through a water layer that is retained on a perforated plate. Water overflows the peripheral enclosure of the plate, whose height is chosen so as to obtain the desired water level (Fig. 13.1c), but cannot flow through the holes, since the water column above a hole is acted upon by a force F 6.p which appears due to the difference of steam pressure below the plate and above the water level. This force is equal to the hydraulic resistance for the passage of steam through the perforated holes and through the water layer above them:

1_1:

-, _...,

(w") 2 1

2· J

p

•

FI rnt2 d

4

(13. 7)

Up to the moment the steam breaks through a hole, this force is counterbalanced by the gravity force of the mass of the water column:

Fl!.=

(13.8)

(13.11)

(13.12)

In formulae (13.7) to (13.11), d is the diameter of holes in a perforated plate, hw is the level of water above the plate, H is the actual height of the bubbling layer, and ~JJcr/ and ~w are the coefficients of resistance to the steam flow in a bole and in the wash water layer. The height of the steam-washing layer of water is usually not high (50-70 rom) and its resistance is low compared with that . of perforated holes, i.e. Sw <~per/· Therefore, it may be assumed in formula (13.11) that £ = Sperl· Formula (13.11) gives a certain reserve of the velocity of steam flow through perforated holes since the actual velocity of steam is higher and is certainly sufficient to ensure the hydrodynamic stability of steam washing by bubbling. 13.3. Effect of Non-uniform Heat Release and Impurities on the Dynamic Two-phase Layer

Boiler water may contain surfaceactive substances which are concentrated mainly at the boundaries between phases. This increases the strength of water films which envelop and diminish steam bubbles. Finer

h

c, ~ !----_J__ __ l __ 0 1 1

__;Cfl~ 1

·' height Fig. 13.6. Distribution of q> along' the of apparatus at different concentrations (c1 < c 2 < c3 ) and constant weight level bubbles rise more slowly in water. Stronger water films are broken with a certain time delay, so that the process of passage of steam bubbles into the steam space is retarded. Under such conditions, the dynamic two-phase layer is satmated with a greater amount of steam, thus leading to water swell and an increase in the height of the layer. The general distribution pattern of steam content along the height of the dynamic two-phase layer at a constant steam flow r ate and various concentrations of impurities in water is shown in Fig. 13.6. As may be seen, the steam content q> at a given concentration of impurities increases along the layer height. At a low concentration of impurities the steam content at the exit from a steamdistribution plate is not high. It remains almost constant to an appreciable heigllt (q> increases slowly), increases rapidly in the transient zone, which has a low l1eight, and attains a value q> ~ 1 above the physical water level. With an increase in the concentration of impurities in water, the steam content at the exit from the plate increases and the length of the zone where q> is almost stabilized becomes smaller (or even completely disappears at a high concentration). In contrast to this, the height of the transient zone in creases substantially. In steam-generating plants, the generation of steam may be substantially non-uniform across the cross-secI 1*

163

tion of an apparatus. This is mainly due to a non-uniform heating intensity which, for instance, in the highcapacity horizontal-type steam generators of nuclear power stations may vary along the length of evaporating elements by a factor of two or three (Fig. 13 .7). The heating intensity can be equalized either naturally, under the effect of a water layer for steam bubbling, or by means of various devices, such as a submerged steam-distribution plate. Figure 13.8 shows the curves of steam content q> at various levels along the height of a bubbling layer with a symmetrical (steam is supplied at the centre of the cross section) or asymmetrical initial non-uniformity in a vertical column without a perforated plate, where steam content is equalized naturally. As may be seen, the steam content at the entry to the two-phase layer is distinctly nonuniform, but is equalized along the height dlle to bubbling in a free volume of water. A non-uniform steam content leads to the appearance of transverse gradients of density in the steam-water mixture that fills in the apparatus. In turn, these gradients lead to oriented convective currents which equalize the steam content and density. Figure 13 .8 shows curves of q> for four sections at various heights in the bubbling layer. As may be seen, nonuniformity decreases along the height due to steam redistribution, tlwugh complete equalization is not achieved

Fig . 13.7. Zone of different steam-generating intensity in the steam generator of a water-cooled water-moderated power reactor (horizontal section) J- housl ng; 2- cooln nt in: 3- coolan t out; 4-

zonc or lnl en•h·c steam gener ation: s- zone or modcrule stcnm ceneralton

·I I

164

Ch. 13. Hydrodynamics of Babbling Systems

I

165

14.1. lmpzlrttles In Peed Water

h •

•

3

PHYSI CO-CHEMICAL PRINCIPLES OF BE~VIOUR OF IMPURITIES I N WORKING FLUID Fig. 13.9. Effect of resolved steam velocity w;; on the height at which cp is equalized

-..

0

0

(a)

h

R

tSteam

~--+--

1

tstea~ ~ {D)

•

Fig. 13.8. Curves of steam content at various [cve!s (1, 2, 3, 4) ~ong the height of a layer wtth {a) symmetncal and (b) asym. metrical initial non-uniformity { ~j.p.ce

the water entrained by bubbling steam flows down mainly along the walls. In columns of a large diameter, the effect of walls is smaller, so that ascending and descending currents, a,nd therefore, thelsteam content, are distributed more ·· evenly over the cross section. ' .• • •

·I~~~

14.1. Impurities in Feed Water and Their Efrect on Equipment

w;

..J.The effoctRof on tho height at which flow equalization is achieved is shown clearly in Fig. 13.9. The left-hand portion of the curve relates to the low values of w~, and consequently, low density gradients, so that flow equalization' occurs at a great er height. At a higher steam-generating intensity, flow equalization occurs more quickly, notwithstanding the higher initial non-uniformity. Therefore, the height of s tabilization is lower. It might be expected that t h is trend would continue with a further increase in w~ which leads to an increase in the density gradient. Actually, however, at very high flow rates of steam, the axial compon ent of the velocity of the steam-wat er mixture increases sharply and the process is extended along a greater height in the layer. I n a certain range of high values of w;, t he effect of velocity is predominant and the height of the equalization layer continues to increase. Finally, at very high flow rates of steam (w~), it begins to carry off much moisture from the layer . Extrapolation of the curve to · its intersection with the axis of abscissae will give a poio t at which water will be completely carried off from the apparatus, i.e. the process of steam bubbling will change to the forced motion of the steam-water mixture.

During tho operation of any lype of boiler-turbine installation the W<Jrking fluid becomes contaminated with impurities. The quantity and composition of impurities depend on th e t ype of plant, composition of str11 ctural materials, and operating conditions. The principal sources and compositions of impurities in lhe aqueous

heat carrier of thermal power stations are given in Table 14.1. Impurities may be present in boiler water in either a dissolved or a suspended state. Under particular conditions, they can precipitate from water and form deposits on the heating surfaces, thus impairing h eat transfer and raising the t emperature of tube walls. Deposits are especially dangerous in intensive l1eating zones (water walls in boiler furnaces and fuel elements

Table 14.1. Principal Sources and Compos itions of I mpu rities in an Aqueous Hea t Carrier Sources

•

In leakages: in condensers

in feed water and tap water hoators

.

Principal lmpu rllies

Salts (chlorides, sulphates and bicarbonates of calcium, magnesium and sodium), colloidal impurities (organic matter, silicic acid), suspen· dcd matter and gases (02. COt, N2) Salls (calcium, magnesium and sodium chlorides, su lphatos and bicarbonates), silicic acid, and gases

.

Make-up water (demi nera 1izcd, cl i- Sodium compounds, pro- Gases: 0 1 (in dcminernducts or metal corrosion lized water); COz (in stilled) distillate) Softened water

Sodium com pounds, silicic acid, gases (tho composi lion or gaseous impurities depends on tho water treatment method)

Products of corrosion of structura l materials

Oxides of Fo, Cu, Cr, Ni , Zn, Co, Al, etc.

Products of radio lysis nncl othcz· iJroccsscs und er the effect of neutron luxes

Hod ioactivo products o[ corrosion of metals: Fe, Mn, Qo, AI, Zr, etc.; gase~: N2, 02, Xe, Kr, etc.

Water additives

Phosphoric salts, ammonia, hydrazine, chclntos

•

166

I '

Ch. U. Behaviour of lmpurltlel In Working Fluid

in nuclear reactors). At nuclear power stations, radioactive deposits can char acterize the radiation situation of the equipment. Impurities can partially pass from water to steam and form deposits in superheaters and in tho steam path of turbines. Deposits in superheaters are intolerable since the outlet portions of their coils even at rated heating loads operate at the upper admissible temperature limit of the tube metal. Even a slight layer of deposits can then raise the metal temperature to an inadmissible level and promote creep phenomena and scale formation. Deposits in the steam path of turbine are also extremely undesirable. They increase the roughness of the blades and friction losses and thorofot·e diminish turbine efficiency. Heavy deposits in the steam path of turbine can cause additional axial pressure, requiring a decrease in the turbine power. The effect of deposits is especially perceptible in high-pressure turbines where the unit volume of steam is lower and the high-pressure section is accordingly smaller in size. Methods have been developed to minimize the passage of impurities into water with inleakages in condensers and with make-up water. It is much more difficult to prevent water contamination with tho products of corrosion of structural materials, especially in plants operating at nearly critical or supercr itical pressures. I n operation, feed water is allowed to have a certain composition and concentration of impurities depending on tho type of plant and iLs water balance: hundredths of a milligram per kilogram for once-through boilers and a few tens of milligrams per kilogram for drum-type boilers. 14.2. Solubility of Impurities in an Aqueous Heat-transfer Agent and Formation of Deposits I n a sufficiently wide range of high and supercritical parameters of a homogeneous aqueous heat-transfer agent

(steam and water), the thermodynamic solubility of low-volatile inorganic substances as a function of the properties of the solvent is determined by two parameters: density and temperature. Solubility can be described by the equation proposed by Prof. 0. I. Martynova: ' l n C = rn ln p -

167

U.2 . Solubtllty ofl mpurltles in Heat-transfer Agent

tJ.H RT

tJ.S~

+n

mg/kg 120 100 80 C aS04

(14.1) 60

where C is the solubility of a substance in an aqueous heat-transfer agent, p is the density of H 2 0 at the given parameters of the process, I::I.H is the thermal effect of dissolution, R is the universal gas constant, T is the temperature, t.S is the entropy of dissolution of the substance, and m is the coordination number (hydration characteristic). Calculations of the solubility of substances in an aqueous heat-transfer agent by formu la (14.1) are possible if tl1ere are reliable data on tho threo parameters which characterize the dissolution process : t.EI, !::IS, and m. T hese data are only available for certain impurities and for a limited range of parameters. For this r eason, laws of dissolution of various impurities in water and steam are mainly studied experimentally. Tho general laws of dissolution will be discussed below. Dissolution of impurities in water and laws of format ion of deposits. All substances present in boiler water can be divided into two groups: slightly soluble and readily soluble. Tho former group includes calcium and magnesium salts and hydroxides and oxides of structura l materia ls with which the aqueous heat-transfer agent may have contact. Solubility curves of selected slightly soluble impurities in hot water are shown in Figs. 14.1 through 14.3. The group of readily soluble impurities which are found in t he water of steam- turbine plants includes sodium salts and sodium hydroxide. Their solubility curves are shown in Fig. 14.4. As seen from the figures, the solubility of some substances

0

\

0

cacoA 20

.._ ~

-....; ::-

Mg ( OH) 2 •

0

l

0

•c

350

250

150

t ~5L0~~20L.0~~25~0~-J~O~O~~

Fig. ilo.L Solubility of prin cipal scale-formers in water

1' 2 E· ffcc t of tcmpPrature on the so. F tg ... · T tcr at lubllity o[ m ag neti t l! in bot t ng wu va rious va l ues o[ p Ho -

- - reducing

__ -

m••dlll ul.

oxi di zing

JJlt~ d IU Ill

pg/kif

c 6, 10~

/ l/

tO J

i--2

17

to

~

/

I ~ l\

10

{

80

1/

60

f

.........

:.-

s~

"

j0

20

4

10

4

8

~Na.OH

ll

40

~ t.....

00

/

70

3

~ !-...

J

v

50

1'\.

'1\

I

90

)

I

2

oj.

8

Fig. 14 .3 . Solubility of m e ta l

P.Ho 10 oxides

boiling water (p = 7 MPa)

0 in

(o"ldldng med ium); 2 - Fe (reduc ing me1 - Pe dlum); 3- cu; 4-Zn; s - N I; 6- AI

V\_Nopo4

-

JO.zS04

\

i\

\~

{

100 200 300 400 °C

Fig. V..4.. Solubility o[ readily soluble compounds in water

I

i68

•

I !

Ia

14.2. Solubllltv of Impurities In Heat-transfer Agent

C". 14. Be,.avtour of lmpurltlu In Working Fluid

increases with temperature while that of others decreases. '· · Sli'ghtly soluble impuri'ti.es. Calcium and magnesium compounds and metal o~i des which be.long to the group of shghtly soluble Impurities, come into the steam-water path of steam-tu rbine plants from different sources and what is most important, behave dif~ ferentl y in an aqueous heat-transfer a?ent. For this r eason, they will he discussed separately. In normal operation of boilers the concentrations of slightly solubl ~ impurities in feed· water, mainly of calcium and magnesium salts, are low. They may inc!ease on certai n disturbances in the system of condensate cleaning and water treatment or due to excessive inleakages in condensers. In any electrolytic solution, a dissolved substance partly dissociates into ions (cations Mcm+ and anions Ac"-) and partly remains in the form o.f mo~ecules . The degree of dissociatiOn, 1.e. the fraction of dissocia ted molecules, depends on the properties of the solute and t emperature. For a saturated solution at a given t emperature, the product of active concentrations of ions a~rem + · aAcn:Vhich is calle.d the solubility product, Is constant, I.e.

of them can crys tallize on heating surfaces and form scale; these are ~alled scale formers. Others crystallize m the hulk of the solution and form sludge and are thus called sludge formers. Rough elements (protrusions and rocesses) on solid heating surfaces can sorv,e as centres of scale format~on, and disperse and colloidal particles and gas bubbles susp ended in water can serve as centres of sludge formation. The conditions required to avoid scale formation from Ca and Mg cations and so;- anions present in water can be written in the following form:

< SP aMs2+ . a,so:-< SP aca2+ . asoi-

}

(14 .3)

In order to de term ino the allowable concontraLions of Ca (or 1\Ig) and scalo-f_?rm ing anions in water, it is essent1al to know the solubilities in water of all the substances which may form under particular conditions and their dependence on temperature. Such data for the principal scale formers are given in Fig. 14.1. As may be seen, they have n egative temperature coefficients of solubility, so their solubility in water at high temperatur~s is only a few mg/kg, i.e. threen m Sp -aM m+ ·a n(14.2) five orders of magnitude lower than e AC that of easily soluble salts. When the where n and m are stoichiometric solubility of a p articular impurity, coeUicients. say, of CaS0 4 , at a given temperature For substances with a positive tem- is known, one can determine the perature coefficient of solubility, active concentrations of respective d (SP)Idt > 0 and for those having ions Ca2 + and so;- and then calcula te a negativ~ coefficient , d (SP)Idt < 0. the solubility product from formuDependwg on the composition of la (14.2). feed water, boiler water may contain Products of corrosion of structural c a2+ and Mg2+ and anions materials . ca t Ions . Feed water can bring into 3 2SO'Sio~P0 C0 d Cl4 , a , • , an . the steam-water p ath of boilers the 3 , As evaporation proceeds the con- corrosion products of a number of centrations of all ions u;_crease and structural materials, such as ir on , approach the solubili ty limits of the copper, zinc, cobalt, aluminium, etc. substances involved. Their compounds can form deposits Dissolved substances can crystallize on boiler surfaces which are determifrom water. Those which have the ned by their solubility in the aqueous lowest sol~b_ility product under parti- medium under the process conditions. cular conditiOns crystallize first. Some The solubility of most corrosion pro-

ducts does not exceed a few hundredths of a gram per kilogram* (Fig. 14.3). The highest quantity of corrosion products enters the steam-water path in the form of oxides of iron which is the main structural material of boiler plants of any pressure. Iron combines with oxygen into a number of oxides, two of them, hematite Fe 2 0 3 and magnetite F e30 ,, being the most important in steam-generating plants. Of h ighest interest are tho. properties, solubility in particular, of magnetite as it is the main oxide of iron that can form a t temperatures below 5505700C, i.e. at the operating temperatures in high-pressure and supercritical-pressure plants. The solubility of magnetite in hightemperature water depends substanti ally on the pH index of the medium. The solubility curves of magnetite in boiling water depending on temperature and at various values of pH (in oxidizing and reducing media) are illustrated in Fig. 14.2. As may he seen , in a wide r ange of high t emperatures 250-350°C (4-18 MPa) and pH= 69, the solubility of magnetite in reducing media does not exceed 4050 J.l.g/kg, in oxidizing media it does not exceed 20-30 1.1glkg. The actual concentrations of this subst ance in water are much higher, which means that water contains colloidal and disperse particles of iron oxide, as well as dissolved iron oxides. Suspended (colloidal and disperse) iron-oxide particles, irrespective of their size, can form deposits on heating surfaces. The heav iest deposits (a few hundred grams per m 2 in a year of oper ation) can form on the elements of the steamwater path which are heated most intensively. 70-90% of these deposits are iron oxides . Deposits of corrosion products of iron usually have two layers possessing different physico-chemical properties. The interval layer is dense and bonded • At typi cal pH values of boiler water at thermal a nd nuclear power stations (sec Ch. 15).

169

1

t t t t t tr Fig. 14.5. Diagram of circulation in a deposited iron oxide layer J - wa tcr Claw; 2-lhlckness or deposited Ioyer; J - cupllla rles; 4-stenm ou tlet from n 's t.cam pipe• at pressure p 8 ; 1' w Is the pressure or wat.cr

firmly to the metal ; it forms through corrosion on the metal sur face . Tho external layer is loose and porous a.nd only weakly bon ded to the surface. The internal layer is not dangerousto operation of the metal and is even desirable, since the dense fi rm oxide film pr otects the metal from further corrosion. On the contrary, tho loose porous external layer (which forms mainly from colloidal and disperseparticles) has a low conductivity and thus impairs heat removal from themetal surface. In addition to the above, bubbleboiling can l ead to the 'wick effect' in porous iron-oxide deposits: water· is sucked in through numerous capillary pores in a layer to the h eatingsurface where it. evaporates. Stonm isthen ejected back through a widechannel, or 'steam pipe' (Fig. 14.5). With such local circulation and evaporation of water, impurities (including corrosion-active impurities, such as alkalies, chlorides, etc.) are concentrated at the metal surface and can enhance corrosion. In porous deposits, an appreciableportion of h eat is removed due to th&. ev aporating effect. This determines. a high ' effective beat conductivity' of deposits, which includes heat conductivity as a physical costant and h eat transfer from the wall to the· working fluid. For this reason, the· temperature of the metal in 'wick

I

I

170

boiling' increases by not more than 10-20 dog C even under substa ntially thick deposited layers (afew hundredths ()r even tenths of a millimetre). Heat transfer may be sharply impaired if ~apillary pores are clogged due to d eposition of other impurities present in water. Since porous deposits h ave a rough surface and an appreciable thickness, they can d imin ish the free crosssectional area of tubes and increase their hydraulic res istance, which lowers the working pressure. We can divide the formation of the . ~xternal layer of iron-oxide deposits into three stages: t h e transport of suspended particles from the flow core into the I ayer at the wall ; the motion {)f particles in that layer; and their .attachment to tho surface. At the first -stage, tho lal'gest contribution is ft·om hydrodyn amic forces. At tho second and third stages, depending on parti~ular condi tions of the process, forces {)f electrochemical nature may be .active in addi tion to hydrodynamic .and intermolecular forces. E lectrochemical forces cause motion of the ~barged particles of corrosion products in the electromagne tic f ield which appears in the heated layer of the .heat-transfer agent just at the wall under the ac tion of a thermo-e.m.f. The t hermo-e.m.f. appears in the drcuit consisting of the heating surface (first-order conductor) and aq u-eous heat agent (second- order conduc-tor) at a temperature difference existing between its portions. Due to -these processes, the corrosion products suspended in water are de posited on the heating surfaces; at the same time they may be partially washed off from these s urfaces by t he working iluid. The rate of formation of deposits is :an important characteris tic which det ermines the possibility of long uninterrup ted operation of steam-generat ing plants. As applied to iron-oxide .dep osits, tho rate of their formation .depends on a large number of process :parame ters: mass velocity, h.eating

I

plfg

'

oL---------~~------~~ appro~.

171

14.2. Solubility of I mpuritles In Heat-transfer A ge nt

Ch. 14. Behaviour of Impurities In W ork ing Fluid

7

Fig. 14.6. EHccL of pH 0 on the rate of deposition of iron oxides

load, boiling condi t ions, pH of aqueous heat agent, particle size and dispers ity, etc. In v iew of the complexi ty of t he process of iron-oxide de pos ition and its dependence on many factors , there is still no physical model which embraces t he effects of all the parameters indicated. The effect of the pH index of heat agent on the r ate of deposition of the ironoxide external layer at subcritical pressures and 0 2 concen tra Lion at a level of 0.4 mg/kg is s hown in Fig. 14.6. As may be seen, tho lowest rate of depos ition is at the pH value corresponding to the isoelectric point of corrosion products. As n oted earlier, as suspended corros ion products are deposi ted on heating surfaces, t hey are partially washed off by the working fluid. At the beginning of the process, when the surface is free from deposits , the direct process prevails and th.e rate of depos ition is at a maximum (Fig. 14.7). As a layer is accumulated on the surface, it is washed off more intensively. I n the course of time, and

o~--------------~

Fig. 14.7. VnriaLion of the rate of form ation of iron-oxide deposits

•

d epending on tho particular conditions, a balance is establish ed between d eposition and wash. ing-·off, and therefore, a particular rate of deposition. Products wash ed off from some portions of th& surface can be deposited ()n other port ions. Th.is property of deposits has an adverse effect on the ()peration of circuits in nuclear power stations since it is o ne of the causes of radioactivity transfer along a c ir<mit. ,'.> Easily soluble substances. Figure 14.4 shows the solubility characteristics of easily soluble impurities. The temperature coefficients of solubility i n t he region of intorost for steam boilers and steam generators (above 200°C) are positive for some of them (NaOH) and negative for others (Na 2 SO,, Na 3 P04) . When hydrodyn amic and heat-transfer processes occur properly and ensure r eliable temperature conditions on the h eating surfaces, the concentration of each of the substances in the water of b oiler drums is only a small fraction (){ the allowable value. For ins t ance, at a water t emperature of 343°C (p = = 15 .5 MPa}, tho solubility of N a 2 SO , is roughly 10 g/kg water, i.e. five t imes the concentration allowed i n b oiler water to produce clean steam (2 g/ kg). This example shows that t he precipitation of a solid phase from a solution is only possible at a very high degree of vaporization of t~e s olution in a boundary layer of botling liquid , which is never achiev ed under normal hydrodynamic condit ions in drum-type boilers. Therefore, under such conditions, easily soluble salts in water present no danger of de pos it formation on the heating surfaces. Sol ubility of i mpuri ties in working fluid a t s upercritical pressures and fo rmation of deposits. The temperature of a process has an essential effect ()n the solubility of substances in H20 at supercritical pressures, especially i n the region of high heat capacities. Data obtained at a pressure of 25 MPa are illus trated in Fig. 14.8.

pg/kg '{:(Mf

v

1\

J siOr 1

J

. 1-.

/

If\

'

I\

/0 ' c-Fe3(4

10 10

Q

f

250

oP ,

CISI4 350

coPY ./~ I

'- ../

l,h

HO

0

550 C

Fig. 14.8. Iso bars of tbc solubility of selected substances in Il 2 0 at supercriticul pressure (25 MPa)

By comparing the solubility curves with some thermophysical parameters of aqueous boat agent, say, density p or dielectric permittivity e at supercritical pressures (see Fig. 9.6), it can he seen thai they have essentially the same pattern. Like density or dielectric permittivity, the solubility of mos t impurities decreases inversely with the temperature in t he whole temperature range of interest. These r egularities suggest t hat most of the impurities present in the working- fluid of s team boilers at supercritical pressures can precipit ate only in a rather narrow range of varia tions of thermophysical parameters, namely, in tho r egion of high heat capacities (see Sec. 9.5) . An excep tio n to this r ule is the solubility of t he corrosion products of iron, mainly of magnetite Fe 3 0 ,, whir.h varies only slightly with temperature (Fig. 14.8). Besides, it is only s lightly dependent on the density of the heat agent, and therefore, on the state of the working fluid . For this reason, iron corrosion products tend to 'spread' along the whole steam-water path of the boiler and turbine. On t he other hand, the thickness of iron- oxide de pos its de-

172

Ch. U.. Behaviour of /mpurltle1 In Working Fluid

mgjkg 50

r.,"V

40

\

JO

20

p=fBMPa

i'-.

["'-

10

'

"

p:f4MPa I I

p =JMPa

0 MO

.

450

v

~

500

•c

Fig. 14 .9. Solubility of NaCI in superheated st.eam at subcri tical pressures

•

I•

!II

pends substan tially on th e intensity of b eating, so that the surfaces heated more intensively (such as the lower radiation sections of once-through boilers) are fo\1l ed with iron-oxide deposits much more substantially than tl10se operating at lower b eating rates. Solubility of impurities in superheated steam of subcritical pressures and the formation of deposits. The solubility of substances in superheated steam of subcritical pressures is determined by the properties of the solven t (superheated steam) and the properties of the solid impurity with which steam is in contact, with both being dependent on the process parameters, i.e. pressure and temperatu.re. The strength of the bonds between ions, molecules or atoms of a solid impurity depends substantially on temperature. With an increase in t emperature, these bonds are weakened and the solid phase can pass over in to steam. Pressure variations in th e r ange of operating pressures in steam boilers have little effect on the behaviour of the solid phase. Temperature and pressure which determine the density of superheated steam, have a strong effect on its ability to dissolve solid impurities. At a constant pressure as the temperature of superheat incr eases, the steam d ensity decreases, resulting in a dec-

rease in the dielectric permittiv ity of H 2 0 and a lower polarity of water molecules . As a r esult, the dissolving power of superheated steam first decreases with increasing temperature due to a decrease in its density. With a further increase in t emperature at a constant pressure, however, although the steam density continues to decrease, the crystalline bonds in the solid are weakened and th e solubility of t he substance respectively increases. Figure 14.9 shows isobaric (constantpressure) curves o( the solubility of N aCl depending on temperature. As. may be seen, the effect of both factors (pressure and temperature) at the minimum of solubility is roughly the same . In the left-hand branches of the curves, the effect of t emperature variations in density is predominant, while the pattern of the right-hand branches is determined by bond forces in the cryst alline lattice. The pressure of superheated steam also has a strong effect on its dissolving power. At higher pressures, steam has a higher density, and therefore, a higher dissolving power, but the effect of pressure lessens with an increase in the temperature of superheating. The isobaric solubility curves of other compounds, say, Na 2 SO, or CaSO, , have essentially the same pattern, but the quantitative relationships are different. Tho practical significance of the solubilit y of subst ances in superheated steam consist s in the following: · if the concentration of an impurity in steam is lower than its isobaric solubility, it will be dissolved and carried off by steam and will usually form deposits in the turbine. rr' however, its concentration is higher than the isobaric solubility, the excess will be deposited in the superheater path and the r emainder in the turbine. 14.3. P assage of Impurities from Water to Saturated Steam There are two kn own ways for impurities to pass from wat er to steam: they can be carried off as droplets of

173

14.3. Passage of lmpurutes from W ater to Steam

boiling water or by dissolution in steam. The concentration of impurities in saturated steam can be charact erized by the total curry-off coefficient I 01. k C.Ot 70•

k~o =ro+kd=

g:

-·--·_-.: -~o "'--- ----------

~----0 ----- - -- -__n,_ -------- - - - - -- - -(h)- --

:-_0- (a)

- - --·

-(c) -

(14.4)

where (J) is the water content of steam, %, which characterizes the concentration of impurities which can p ass int o saturated steam with water droplets, kd is the distribution coefficient, %, which characterizes the concentration of impurities due to the dissolving power of steam. Tho relative role of the components in the carry-off coefficient depends on a number of factors , primaril y on pressure. For instance, at low pressures, the dissolving power of steam for most non-volatile impurities present in water is n egligible (kd ~ w) , and therefore, kc~ ~ ro. With an increase in pressure, t he dissolving power of steam increases, r esulting in a h igher contribution by the distribution coefficient, so t hat it may turn out a t a sufficiently high pressure that led ~ ~ ro and kc~ ~ led. The mechanism and laws of water carry-off by steam. Tho mechanism of the formation of water droplets in the steam space of a boiler drum may be different depending on the scheme of steam supply. If steamwater jets are ejected below the water level into the drum, steam bubbles riso to the disengagement surface and form a two-phase dyn amic layer (Fig. 14.10a and b). A steam bubble is acted upon by two forces: the force of internal pressure which tends to rupture the wat er film that envelops the bubble and the force of surface t ension of that film which resists the rupturing force . In pure water, water flows down from the upper spherical surface of the film which consequently becomes thinner (Fig. 14.10c). A hole forms in the top of the sphere, which is widened by the forces of surface t ension. The fil m is retracted into

(d)

(e)

Fig. 1.4.1.0. Formation o( condensed moisture in the steam space of a drum with evaporating tubes ent.ering the water space (a) ris ing stcnm bubble: (b) bubble at the discnga·


the bulk of the water, and the steam bubble is freed and enters the steam space. As an annular \vave forms in the process, water droplets break off from its edge and are ejected into the steam space (Fig. 14. 10d). Water tends to fill iu the newly formed crater and water currents collide with one another in the centre and rise forming a vertical column from which water droplets can also break off (Fig. 14.10e). In steam bubbling through a layer of low-mineralized water, water films whicb envelop steam bubbles may have different thickness, and therefore, form water droplets of various sizes . When steam enters the drum above the disengagement surface, water droplets can appear in the steam space due to disintegration of the moisture that is carried by the steam supplied from evaporating tubes (Fig . 14.11). The degree of water atomization depends on tho kinetic energy of s~.~am-water jets. At high heating loads, and therefore, a high velocity of exit of the steam-water jets into the drum, they possess a high kinetic energy and can atomize water into finer droplets, resulting in a more intensive water carry-off. A dynamic equilibrium is established in the steam space between the water droplets which enter the steam space and those which

174

14.3. Pauage of-Impurities from Water to Steam

w .

h.m 0.8

Fig. 14.11. Formation of condensed moisture in a drum with steam-water mixture entering the steam space

settle in the water. Tho concentration of water droplets is the highest just at the disengagement surface and decreases the farther it moves from that surface. The largest droplets can be ejected to a height of 600-700 mm. If the rising velocity of steam is low, it can entrain only the finest water droplets. With an increase in the flow rate of st eam, the larger droplets can be entrained. For this reason, the water content of produced steam turns out to be higher at higher beating loads (see Fig. 14.12). The water content c.> of steam is determined by t he beating load D: c.> = ADn (14.5) I

I

i

J

Ch. U. Behaviour of Impurities In Working Fluid

where A and n depend on the design of the drum, pressure, and the concon tration and ionic composition of impurities in the water. The exponent n changes substantially with the heating load. The dependence of the water content of steam on the beating load is approximated in logarithmic coor-

I

I

' I

,/

•

n=flo2

log O{log w;}

Fig. 11,.12. Effect of the heating intensity on the water content of steam

• 1 11

Fig. 14.13. Effect of th e height of steam space on the water content of steam

dinates by broken straight lines expressed as power functions (14.5). Ther& are three such straight sections. (Fig. 14.12). For loads characterized by a very low water content of steam ((I.) < 0.01 %), n = 1-2; for loads at. which c.> = 0.01-0.1%, n = 3-4; and for higher loads witl• w>0.2%, n. ;;:;;:: 10. For drum-type boilers of thermal power stations, operation at. the beginning of the second section is typical, for which n. = 3-4. Steam velocity is proportional to its flow rate D. The average flow rate of steam related per m 2 of the disengagement surface is called the rate of evaporation per m2 of water surface:

RF = DIF (14.6) The average velocity of steam related to m 3 of tl10 steam space is called the rate of eL·a.poration per m3 of steam. space: Rv = DIV (14.7) The height of the steam space has a vital effect on the water content of produced steam. At RF = constant, with a smaller height of the steam space, larger droplets can reach tho region of high steam velocities at the inlet to steam-circulating tubes, and therefore, steam will contain more moisture. In the steam space of a larger height, the largo droplets cannot r each the steam-circulatingtubes as easily and the water content of produced stoam will be lower (Fig. 14.13). Beginning from a certain height (roughly 0.8 m) which is

unattainable even for the most farreaching large droplets with the highest kinetic energy, any further increase in the height of steam space cannot significantly decrease the water content of steam. Under such conditions, steam carries off only fine droplets whose souring velocity W 80 is smaller than the rising velocity of steam w;', at RF = constant. Fine droplets are transported by the steam flow irrespective of the height of steam space. The soaring velocity of water droplets is understood as the relative velocity of a droplet at which its mass is counterbalanced by the force of resistance in steam flow. For these conditions, it may be written : nd~r

6

2

••

n durP w;o (p' -p") g = ~ 8

whereby W 10

= 1.155

V dt ( ~:

- 1) g (14. 8)

where ddr is the diameter of droplet and 6 is the coefficient of resistance. With an increase in pressure, the density of steam increases and offers a greater resistance to rising droplets. On the other hand, as the difference in the densities of water and steam decreases, the transporting ability of steam is. enhanced. This is also due to the fact that an increase in pr essure decreases surface tension , so that the size of the water droplets decr eases and they can be more easily carried off by steam. S ince, however, pressure has a stronger effect on the transporting ability of steam tl•an on its resistance, an increase in pressure results in a higher water content of steam. We have discussed tho Jaws which govern the carry-off of droplets of pure or low-mineralized water. These laws hold true for a rather wide range of concentrations. All other conditions being identical, the water content of steam in this range is constant. Begin-

175

w

Cs

Fig. 14.H. Effect of salt content of water on water content of steam

ning from a certain concentr ation typical of a particular substance, the size of steam bubbles in water diminishes, and therefore, the velocity of their rise decreases and cpbub increases. This results in the water swell in tho drum and the ejection into the steam space of a large number of water droplets witl1 a high concentration oi the impurity, which critically impa irs the steam quality (Fig. 14.14). The concentration of substances in water at which tho water level suddenly swells up and increases the carry-off of moisture by steam is called the critical concentration. P hysico-cbcmical principles of U1e distrihution of impurities between water and saturated steam in equilibrium. A two-phase single-component system may be, depending on the relative concentration of the phases, in the> form of boiling water containing steam bubbles, or wot steam containingwater droplets, or boiling water in contact with saturated steam. I rrespective of the structure of the twophase system, water and steam are essentially two solvents of the samechemical nature but different density and dielectric properties (see Soc. 9.5) which determine their ability to dissolve inorganic substances. If the two-phase system is in thermodynamic equilibr ium, the non-volatile impurities present in it are distributed between the phases accordingto 'the law of distribution of solutes in immiscible solvents. This equilibrium can be characterized quantitatively by the distribution coefficient kd which is expressed in terms of the activity

176

14.3. Passage of I n ~rities from Water to Stea m

Ch. U. Bchaulour oflmpurtuu In Working Fluid

of the solute in steam, a., and in

coefficient kdn . 1 , is as follows:

,_m

(14.9)

l
k"'

P.

d .trP

(14.12)

Similarly, for the ionic form: For dilute solutions (which are ty-pical for the conditions of steam generation at thermal and atomic power stations), the activities cart be replaced by the concentrations of l:he solut e, i.e. (14.10)

l •

.

I

I I

•

I

.I

II

I

I

The distribution coefficient depends on the form in which substances are present in an aqueous solution. Substances present in water in a molecular form have the highest capacity for passage from water to steam. Those which are present in an ionic form, will dissolve in steam much loss readily. The law of distri!Ju Lion holds true for substances which arc present in both solvents (steam and water) in one and the same form, either molecular or ionic. The distribution coefficients k::' and k~ corresponding to this condition are thermodynamically true and written as:

c!

t and k d.tr = ct

(14.11)

w

At a constant temperature, the true distribution coefficient of a s ubstance is constant and independent of the initial concentration of the substance in one of the phases. Determining the tr ue distribution coefficients involves appreciable difficulties, since it is practically impossible to find separately the concentrations of substances in the molecular and ionic form. For this reason, tho distribution coefficient is usually determined through the total concentrations of a substance without taking acco unt of the forms of its existence in sol vents, i.e. the appa.rent distribution coefficient is determined. The correlation between the apparent molecular coefficient of distribution k;F.ap and the true distribution

k~.ap =

!cL,

~}

(1 -

(14.13)

where~ is•the fraction of the molecular

form in the total concentration of a substance in the solution (~ depends on pH and temperature) and (1 - ~) is the fraction o[ the ionic form. The total apparent distribution coefficient is the sum of the molecular and ionic apparent distribution coefficients. According to the law of distribution between two immiscible solvents, the passage of substances from water to steam takes place under adiabatic conditions at a constant saturation temperature and particular pressure {density). On the other hand, as follows from Fig. 9.8, the density lines of water and steam at any temperature (pressure) have no real regions of gradual passage of substances from water to steam. This passage from water to saturated steam at equilibrium takes place not gradually, but suddenly, as follows from the distribution law. As pressure approaches the critical value, i.e. as p"/p' tends to unity, this "jump" declines and only at p =Per can the substances dissolved in water p ass over smoothly into saturated steam in equilibrium with water. At low concentrations of substances in aqueous solut ion, the e£fect of process parameters on the coefficient of distribuiton between water and dry saturated steam in contact with it (w = 0) can be described by the equation proposed by Acad. M.A. Styrikovich: led =

p• ( p'

177

------------~~~~~

)n

(14.14)

which holds true for conditions when the solute is present in water and in steam in equilibrium with water in the same form (either molecular or ionic).

•

in water, for which reason their !:Oncentration in steam is usually not high. or s pecial interest is silicic acid H 2Si0 3 , a weak electrolyte which belongs lo the second group. It may be present in water in significant concentutions and possesses a high solubility in steam. Substances from the third grou p have the least solubility in steam; these mainly include salts NaCl and Na 2 S0 4 and hydroxide NaOH, which are contained in water mostly in the ionic form and are ospcci w "'I "'d.op (14 · 11) • pencil. diagram (Fig. 14.15). Pen.cils of all substances start from the ong1n wherefrom tbe total coefficient of carof coordinates which corresponds to ry-over /c~ which characterizes the ratio of total concentrations of an imthe critical pressure (for water, P er = purity in water and steam is found = 22.85 MPa) and distribution coeffrom the formula: ficient kd = 1. All substances present in water can be divided into lhr:ee groups according (14.1G) to their solubility in steam: (1) those for which n < 1; (2) those with n = As follows from equation (14.16), = 1-3; and (3) those with n > 4 . Substances in the first group possess the quality of steam depends on its the highest solubility in steam . They water content w and distribution coeinclude weak elect•·olytes - mostly fficient kJ .aP· The water content of the producls of corrosion of structural steam can be diminished by separati materials: Fe 3 0 4 , Alz0 3 , etc. that on (see Sec. 15.4). Even the compl elo may, however , have a low solubility separation or moisture, however, can-

+

12-0 1524

+

Ch. 15. Water Conditions

178

not make steam free from impurities. The distribution coefficient is a physico-chemical constant and, if water contains impurities, steam will have an equivalent quuntity of these impurities in accordance with tl1e condi-

Lions of the process. In order to cleanthe steam from impurities which have· passed into it from water due to the· distribution law, it should be washed by cleaner water than thuL from which. it has formed (see Sec. '15 .4).

Tab l e ! a. l. A llowable Contaminatio n ol I nte rnal Surlaces ol Tubes .

Conccn\ra l.ion Of impuriti es, g { m2, ut beating lOads, kWJrn2

Stnl•• o r surface

Clean

Requires cleaning

WATER CONDITIONS !5. t. RemoyaJ or I mpurities from t he Circuit The reliable operation of steamturbine plants is ensured by maintaining the proper level of cleanliness of the working fluid, i.e. by removing impurHies from the circuit in accordance with the rate of their passage to the water (see Sec. 14.1). Methods for removing impurities may vary depending on the type of boiler. Drum-type boilers operate under the principle of multiple forced or gravity circulation. The steam content of the fl uid flow in the uptake tubes of circulation circuits is limited and does not normally exceed 10-25%. Boiler water docs not evaporate deeply, and therefore, the impurities dissolved in it do not reach their extreme concentrations (to saturation) and thus cannot precipitate as a solid phase in the water bulk or on the tube walls. In order to retain the concentrations of impurities in water below the level at which they would precipitate in the solid state, part of the water is continuously r emoved from the boiler drum (blowdown water). Blowing-down as a means of removing impurities from power plants is especially efficient with those impurities which have a low coefficient of d is lri lm lion between steam

and water and for this reason are not. properly carried off by steam (sodium salts and sodium hydroxide). Blowingdown is ineffi c ient with impurities which have a high coefficient of distribution and are carried off in a I arge quantity by steam (silicic acid and' metal oxides). In once-through boilers, the evaporation process takes place with all the water being vaporized continuously. Blowing down once-through boilers is impossible, so impurities settle on the heating surfaces as deposits according to their soluhil i ty in water and steam. Eas ily soluble deposits which accumulate in particular zones of once-through boilers are partially washed off at tbe boil er starting-up and shutting-down. Slightly soluble deposits are removed periodically by chemical washing which is done after shutting down the boiler. The washing process is labour-consuming and requires much Lime and a large quantity of reagents. The continuous removal of impurities from the steamwater path of once-through boilers can be effected in a demineralizing plant arranged in the circuit downs tream of the turbine condensers . Feed water at the entt·y to the boiler conluins a noticeable quaolity of oxygen and carbon dioxide. Free oxy-

i 79

15.1. R e moval of Impurities from Circ"lt

up l O 100

100-300

300 -~ 50

25-50 200 -300

up to 25

up Lo 25

150-200

100-200

gen and carbon dioxide can cause intensive corrosion of the metal·'o[ boiler equipment. To prevent this , t.hese elements arc removed by thermal deaeration. The water conditions at nuclear power s tations are l argerl y d etermined by their operation specifics, i.e. by neutron irradiation of the heatLransfet· agent as it passes through the react or core . Further, the corrosion products of structural materials are continu ously accumulating in t.lt e circuit. I£ they are not removed in due Lime from the heat agent, th ey can form deposits on the surfaces of the circuit. These impurities are subjected to neutron irradiation in the 1·eactor and become ndioactive, thus creating a radiation hazard in the zone around the reactor equipment.. Since used water at nuclear power stations is radioactive, it cannot be blown down and discharged to escape channels, as is clone at thermal power stations. As at thermal power s l;ations, it is cleaned from impurities in ion-exchange resin water purifiers. This treatment prevents the fonnation of deposits on the working s urfaces of the circuit. The onjectives of minimizing the corrosion of structural materials and the formation of deposits and of producing steam of a high purity (and, at nuclear power stations, minimizing the radioactivity of the heat-transfer agent) are achieved by properly or ganizing tbc physico-chemical processes in the steam-water path, i.e. by providing appropriate chemical water conditions*. I t is virtually impo• In further discussion, we will rclcr Lo Lbis as wn ler co nditions.

I

above 450

up to 20

1.00-150

ssible to completely control corrosion, the activity of the working fluid and dep ositions on the work ing surfaces and produce absolutely clean steam (free from impurities). The optimal water conditions o[ a power unit should ensure the relialJle un interrupted operation of the equipment for a long time before chemical washing is required. The pl'incipal tasks are: to restrict, the fo1·mati on of internal deposit s which might cause the temperature of heating surfaces to increase intol.erably; to restrict the [ormation of deposits "·hich might d iminish the power of the unit in tho flow path of the turbine; to suppress the corrosion of structural materials in the steamwater path and l.o minimize erosion. wear. Deposits on the surface of metal areremoved by chemical cleaning o£ the· equipment. This procedure is carried out in a new boiler before starting up and then periodically during operation. A washing circuit is assembled: for this purpose, which includes washing pumps, tanks for preparation. of the reagents , connecting pipelines,. and reservoirs for the collection and neutralization of wash water. The· length of periods between chemical washing procedures depends on theoperating conditions of the boiler plant, mainly on how carefully the specified water conditions are observed. The time for a chemical washing procedure is determined by the amount o£ deposits on heated tubes and by 'the intensity of their heating. A rough estimation of the allowable contamination levels of the internal surfaces of tubes is g iven in Table.

15.1.

180

Ch. 15. Water Conditions

15.2. Water Conditions of Once-through Boilers An important factor in the organization of water conditions in oncethrough boilers is that water b lowingdown is inapplicable. For this reason, all impurities which are IJrought in with feed water and those which pass into the working £luid due to corrosion of the boiler proper and in the feed water path behind the condensate cleaners are partly deposited on the heating surfaces and partly carried off into the turbine. H should be borne in mind that only very slight dep osits are allowed in the turbine. The amount of deposits allowed in the boiler is many times that allowed in the turbine, i.e. a subcritical-prcssure boil er should be regarded as a 'trap' for impurities which prevents their passage to the turbine. Under such condit.ions, the concentration of impurities in feed wat.er can b e somewhat higher than in superheated steam, in accordance with the allowable l evel of deposits in the boiler. The allowable deposits depend on their distribution along the steam-water path, "the heating load and conductivity in places of deposit formation, and on tl1o reliability reserve of heating surfaces, i.e. how far the temperature of the metal may rise above the working temperature wi thout causing creeping and scaling. Under identical conditions, the allowable amount of deposits depends heavily on the heating l oad, which should be taken into account when selecting the zone of deposition in the gas path. The zone of deposition is usually the final sect.ion of the evaporating path and it should not be arranged in tho region of intensive heating. The length of the zone of deposition also depends on pressure. At higher pressures, the deposition zone is longer and begins · at a lower steam content of the fluid flow . In high-capacity boilers for supercriLical pressures, furnace water walls operate at substant.ially higher hca-

ting rates and are therefore much more sensitive to deposits. Since dep osits are unwanted in both the turbine and boiler, once-through boilers must be fed wit.h water that is as free as possible of impurities. In practice, this means that all tho condensate from tho turbine must be cleaned in a dem ineralizing plant. This treatment almost totally prevents l.be deposition of salts and silicic acid in t.he boiler and turbine, while the problem of preventing tho deposition of corrosion products, especially iron oxides, becomes more important. A common met.hod for increasing t.he corrosion resistance of equ ipment is to select the appropriate materials. The main structural material for making t.he heating surfaces of boilers is pearlitic steel. Pearl itic steels have many advantages (low cost, good workability, serviceability), but they possess a serious drawback: they arc sub) ect to intensive corrosion in the steam-water path of boilers. Corrosion damage is reduced by t.he application of protective coatings to the internal surfaces or tubes in the low-temperature sections of power plants. These include: the internal surfaces of atmospheric-type deaerating tanks, exhaust hoods of turbines, housings of condensers and low-pressure vacuum heaters , condensate tanks and their pipelines, and water-treatment equipment. In the high-temper ature sections of power plants, corrosion is limited by appropriat.e organization of water conditions. Hydrazine-ammonia water treatment. Thermal deaeration cannot remove oxygen and carbon dioxide completely from the turbine condensate. The concentration of residual oxygen may be as high as 10 J.Lg/kg. Residual carbon dioxide is also present in the condensate. For this reason, thermal deaeration is supplemented with the chemical treatment of feed water. Residual oxygen in feed water after thermal deaeration is bound by hydrazine N tll 4 • If water contains no other impurities, t.he reaction is as

15.2. !Vater Conditions of Once-through Boilers

follows: N2H , +O:-+ N1 +2llt0

(15.1)

Feed water always contains impurities: iron and copper oxides. In their presence, oxygen is bound by hydrazinc more quickly [381. In order to ensure tho complete removal of oxygen, hyd razino is fed at the intake to feed pumps in an amount exceeding the stoicbiom.fltric ratio from formula (15.1), i.e. an excess of hydraziDe is formed in an amount of 0.02-0.03 mg/kg. Carbon dioxide may be presen t in water in the form of either molecules C0 2 (dissolved gas) or H 2C0 3 (solution of carbonic acid): C0 2 + H 2 0

-

= If:C0:

1

(15.2}

Carbonic acid can be found by a measured quantity of ammonia added Lo feed water. Ammonia is introduced in an amount sufficient for the complete neutralization of co~ to form ammonium carbonates and to allow a slight excess of ammonium hydroxide to raise the pH index of water. Thus, hydrazine hydrate combines the residual oxygen in deaerated water, while ammonia maintains the pH index at the required level pH = 9.1 ± ± 0.1. I-lydrazine-ammonia water treatment, i.e. the chemical treatment of feed water by hydrazine hydrate and ammonia, is a conventional method and until recently was employed at almost all supercrit.ical-pressure monohi oc units. The temperature of the working fluid at the outlet of the lower radiation sections of boiler plants is usually 380-390°C. The temperature of the out.side surface of lubes in this section is roughly 100 deg rees higher, i.e. attains /l90-500°C. As established by experience, with the application of hydrazine-ammonia water treatment, the temperature of tubes in the lower radiation section of fuel oil-fired boilers increases by 10-12 deg C every month. For this reason, chemical washing should be carried out period ically in

1St

4-6 mont.hs in order to retain the tempera t.ure of tube walls below the allowable level. Neutral water conditions. All monobloc units of power stalions are provided with demineralizing plants to produce clean feed water. Upon cleaning in a demineralizing plant, turbine condensate approaches the theo-. retically pure neutral water with the electric conductivity 0.04-0.06 fLS/cm and pH index around 7. This water is practically pure and almost free of ion ogenic impurities, so that all elec.trocbemical processes in it are retarded. Oxygen in neulrnl water may produce different ef£ects on metals depending on its concentration. At low concentrations, iL can enhance metal corrosion. At elevated concentrations of oxygen, a conti nuous film of magnetite Fe 3 0 4 or hematite Fe 2 0 3 forms on the metal surface. For this reason , it has been proposed to prevent further corrosion of met.al by int.roducing oxygen into waLer in an amount (around 200 J.Lg/kg) sufficient to form a passivating continuous film of iron oxides. Under such conditions, the corrosion rate of pearlitic steel is almost as l ow as that of austenitic steel. The ability of oxygen (in elevated concentrations) to form firm protective oxide films has been utilized as the basis for tho organization of oxygenneutral water conditions in once-through boilers . For this purpose, gaseous oxygen 0 1 is added in a measured quantity to feed water. In some ca~es, hydrogen peroxide H 2 0 2 is used instead of 0 2 . To form neutral water conditions, feed water should be very pure and contain no CO~; its electric conductivity shou ld not exceed 0.2 J.lS/cm. Neutral water conditions are advanLageous in the following respecls: it can bo dispensed with expensive correction treatment of feed water uy hydrazine hydrale and ammonia; in that connection, filters of the dem i neralizing plant can operate for a longer time between regenerations; the rate of form ation or iron-oxide deposils in

--182

I

!

I •• '

Ch. 15. Water Conditions

intensively heated surfaces of tho lower radiation section is lower; and pcarlitic steels can be oruployed in heaLing surfaces. In operation with nou tral water conditions, care shou ld be taken to keep the electric co nductivity of feed water as low as possible. For this reason, the feed-water path should contain no elements made of copper or copper alloys. Neutral water conditions have been employed at a number of supercritical-pressure monobloc units for several years. Chelate treatment of water. When iron-oxide deposits form on heating surfaces, the tern perature of tho metal is determined by the heating intensity and the properties of the deposits, mainly by their thermal conductivity, which is l ower in porous deposil.s. Temperature cond i lions on healing -surfaces can be improved by two methods: by increasing the thermal conductivity of deposits or by causing the deposits to for·m primarily in the tess heated elements (say. in the economizer) , rather than in the lower ra.(liation section. The properties of iron-oxide deposits and the regularities of their formation in the steam-water path can b e changed by employing the chelate treatment of water. The method of -chelate water treatment has been pro-posed and developed by T. Kh. Margui ova et al. and consists essentially in the following. Feed water is treated with ammonia and hydrazine hydrate added in the same quantities as in the <.onventional hydrazine-ammonia method. In addition, chelates are introduced into the doaerated feed water in a quantity equh·alent to the concentration o[ iron and copper in it. Chelates aro su bstances capable of forming water-soluble compounds with various cations (Ca, Mg, Fe, Cu). Ethylene d iaminc tetraacetic acid {EDTA, dry product) is usually emp loyed for the purpose. An aqueous solution of t.he acid at a temperature of 80-90°C is prepared and mixed with an aqueous solution of ammonia: NH 3 H 2 0 = NH,.OH.

+

The ll'isubstituted ammonium salt of ethylene diamine tetraacetic acid which forms nn mixing can react with tho products or iron corrosion at temperatures of 100-200°C, with iron hydroxide F e (0li) 2 to form iron chelates. These ave readily soluble in water and dissociate at a high temperature, with a dense 1ayer of magnetite boi ng deposited on the inl.ernal su rfaces of tubes, protecting the metal against corrosion. The most intensive dissociation of iron chelates occurs at temperatures of 250-300°C which are typical for the last stages or the high-pressure water heater and economizer, so that complete thermal dissociation (thermol ysis) would be expected to take place exactly in these el ements of the steam -water path. The working fluid, however, moves in this section or the path (high-pressure water hea ter and economizer) at a noticeable velocity, 3-5 m/s and 1-2 m /s , respectively. Moreover, in su percritical-pressure boilers, the temperature of the working fluid increases quite rapidly as it moves along the path (at a rate of roughly 100°C/min). For these two reasons, the thermolysis of chelates cannot como to its end in the economizer and partially continues in the next element of the path, the lower radiation section. Therefor·e, iron-oxide deposits in su percrilical-pressure boiI ers are distributed in the following manner: around 80% settle in the economizer and 20% in the lower radiation section. On addition of the chelates, the deposits in the lower radiation section become denser and have a higher thermal conductivity, which lowers the rate at which the temperature of the wall rises in timo and makes it possib le to prolong the period between washings up to 18 months. It is advisable to automatically add the chelates according to the heating load of a monobloc unit. Ammonium sal l. of ethylene diamine totraacetic ncid and ammonia are addud to the feed water after the deaerator, and hydrazine after the demineralizing

183

15.3. Non-scaliflg Water Condilio11s of Drum-typ e Boilers

plant. The concent rat ions of additives [ n feed water in chelate .;,·ator trea tmen!. are as follows: EOTA = = 80 ~tg/k g, l\'H:1 = 700-800 11g/kg, l\ 2H 4 = 20 ~tglkg; pH= 9.1. Gaseous products formed on the thermal dissocia l io11 of tho chol ates pass together with sleam through the turbine and are removed from the -cycle as exhaust from the condenser. Chelate water treatment offers certain advantages typical for 'neutral' water con ditions (increased time between washings), but also possesses the ·drawbacks of the hydrazinc-ammonia treatment (an increased load on the demineralizing plant, since a large ~uanlity of ammonia should be removed from th e circuil, and a high use <>f rcuge~ts for filter regeneration). 15.3. Non-scaling Water Conditions of Drum-type Boilers Drum-type boilers arc often fed ·wi I h softened water, i.e. water that -contains easily soluble substances, mainly sodium salts. Owing to inleakage of the cooling >vater in condensers, calcium and magnesium salts can also get into the feed water. These salts have a very low sol ubility (milligrams and tens of milligrams per kg water), which further de<.reases with increasing temperature. During · steam generation at a high press ure, the concentrations of those ~a ll s readily rise to a value at which they can form scale. Not all calcium and magnesium compounds form scal e; some of them form sludge. Some kinds of sludge !such as Mg 3 (P04) 2 1 can stick Lo heating surfaces, which is also undesir·able. Calciu m and magneswm can form non-sticking sludge [for instance, 3Ca 3 (P0 .1 )~·Ca(OH) 2 or 3Mg0·2S i 0~ · 2 1L.!Ol which remains in th e boiler water ira a suspended state and can mostly be removed by continuous blowing-down. A small amount o[ heavier sl udge accumulate<; in the lower headers aud can ue removed by periodic blowing-down.

Ln order to correct water conditions

and transfer the hardness sa lts into non-sticking sludge, it is essential lo introduce correction additives t.o water, for instance, phosphates (such as sodium phosphate Na 3 P0 4 ) to fixed calcium . Water conditions based on tho addition of phosphates are called phosphate water conditions. For easier formation of non-slicking movable sludge, phosphates should be added to an alkaline medium. For this reason, sod ium phosphate is introduced uot into the feed water· which has a low alkalinity, but into the boiler drum where the alkalinity of the water is sufficiently high due to multiple evaporation. Thus, plwsphate-alkaline water conditions are formed. The reaction of sludge formation can be written in the rollowi ng form: 10Caso.

+ GNa

3 P0 4

= 3Cu 3 tP0 4 )2Ca(OHh

+ 2Na01l

+ ·101\n~S0 4

(15.3)

'---v--' non-sUcking movable easi ly soluble sludge sodium sulphal o

The reaction products are removed by blowing-down. For the complete removal of calcium salts, a certai n excess o[ phosphates is maintained in t.he boiler water. The excess of PO~­ for boilers witbout s tepped evaporation is 5-15 mg/kg; for those with stepped evaporation, the excess of POt- is 2-6 rog/ kg [or t.hc clean section and not more than 30-50 mg/kg for the salt section. Due to the hydrolysis o[ phosphate ions that takes place in phosphate treatment, hydroxy ions form which furth er increase the water alkalinity: PQ~- + H~O

=

HPOi- + H,O

HPOi- + OH-

=

H~PO;+OH-

}

(15 .4)

Upon phosphate-alkaline treatment, the hydrate alkalinity of water may son1etimes turn out I o be subs tan I ial (pH > 11) and cause metal corrosion. [n boilers supplied with turbine condensate wi l.h an addition of chemically puril'ied water, alkalinity is held at a moderate level b~r adding

184

Ch. 15. Water Condition$

not pure Na 2 P0 4 , but a mixture with 1'111 acid phosphate, such as Na 2HP0 4 • At power s talions fed with turbine 1·ondensate and low-mineral ized make-up water (chemical! y desalted watct· or distillate from evaporators ). water alkalinit y is controlled only by the hydrolysis of phosphates [see formulae (1 5.4)1 , i.e. by forming water conditions of pu.rely phosphate alkalinity. Phosphates a re continuously int roduced into the boiler drum by metering pumps. In recent times, the quality of feed wat,er at powor stations has improved appreciably clue to lowe r· inleakage into c ondensers, t hus resuting in a higher quality turbine cond ensate. This makes it possib le to employ water condit.ions with a lower degree of phosphate treatment. o r eYen to dispense w il h phosphate trc:1t ment a nd change to no-phos phat o non-se aling wa ter condi1 ions . 1\'o-phos phate wa ter conditions make t he boiler operat.ion l ess expen s iv e (since c.onectivc additives arc no t used), d ecrease tho salt content in boiler water, improve the quality of s team, and lower the cost of boiler equ ipment.

15.4. Methods for Generating Clean Steam

i!

I r

'

.l

i

I

The purity of s team should satisfy extremel y high requiremen ts. For instance, the total concentration of i mpurities in s uperheated steam of supercrit.ical pressure must not exceed 40-50 !lg/kg. Methods for producing clean steam vary depending on tho type of plant. In once- through boilers, the workin g fluid (water), is continuously vaporized, so that its impurities are partly deposited on heating s urfaces and partly carried off with steam. With an increase in pressure, the concentrat i on of impurities in steam increases and the quality of steam app roaches that o f feed water (Fig. 15.1). Blowingdown is inapplicable in once-throug h bo ilers. The sole way t o make cl ean steam is to impt·ove the quality of feed

15.4. Jlfethods for Generating Clean Steam

i 85

mjs

J

5vi

Fig. 15.1. Effect o£ pressure on the steam quality in a once-through boiler (Per >

>

P1

>

P2

>

P l)

water. Thus, the q ua lity of s team produ ced in once-t.hroug h boilers is controll ed by specifying the q u11lity of feed water. In drum-type boi lers, the purity of saturated steam, and therefore, of superh e ated steam is d etermin ed by the qu a lity of the wa ter from which it is prod ucod. \\' i I h a I ower concen tration of impuri t ies in boiling water (under id entical conditions). c leaner steam can be obl.nincd. mowing-down of drum- type boilers can improve the quality of circulating water, though e xcessive blowing-down can diminish the e fficiency of the steam- turbine plant owing to heat loss with b lowdown water. Separation of moisture drop lets from steam. T o produce clean steam, it is essential, first of a ll , to dry it as complete ly as possible, i.e. to separate water droplets from the steam flow. Steam-separating s ys tems should sat isfy the following main requirements: low water content in the produced steam, high unit steam-generating load, a nd low hydraulic res is tance. The s eparation of mois ture from steam is based on th e densit y difference between water and steam. A wa ter droplet in the s team s puce of a boiler drum is ac ted upon by two oppos ito fo rces: t he li fting force a nd the force due to grav ity. The relntions hip between these forces and the tim e of their action d etermine wheth er o d roplet will be c arri ed oH by s team or settle on t he water s urface. It is cl ear that a higher sepa rating effect can be

2 I

4

1\

J Crw

-

\

~-

'\.._

5

5

L _ _

7

·~

r-.....

I

f p

4

-f

'

~-

r--..... r...2 '

.........

0

-

8

12 MPa

Fig. 15.2. Effect of pressure on the steam velocity in the holes of a submerged distribution plate

Fig. 15.3. Internal cyclone steam separa tor J- hous ing; 2-l rtl<~t J)irw connt!ction: J- covcr· J- collur; j-stt>am-wn1N' mixturr in : 6- cross: pi..ce; 7- llotlom

moistening. Th is is performed iu s tea m J- mlnimal ,.c, Jnclt ~·: 2-rccomrnf·ndcd velocity separating devi ces . The principal s tMm-sepa rating deachi e ved at a lower ris ing velocity of vice in high-capac it y s te om boil ers is steam in the dru m. a cyclone separator which is nrranged Among t.hc s imples t and most effi - ins ide th e boiler drum . An internal ci ent devices for steam separa tion are cyclone separator (Fig . 15. 3) is essenperforated plates made of s teel, with tially a cylindrical ver tical housing the perforations 5-12 mm in diameter. 300-400 rnm in di a meter into which A perforated plate is mounted 100- steam-water m ixture is introduced 150 mm below the average water l e- tangentially at a s peed of 6-8 m /s . vel in the drum; it is called a submer- Upon entering tho cyclone, the s t eam ged plate (as in steam generators of flow kinetic energy produces a centrinuc lear power s tations). A nother pla- fugal effect, and the flow is whirled te is arranged in the steam s pace at at t.bo cyclone s urface. Water is presth e top of the drum (perforated baffle). sed aga ins t the walls and flows downBoth plates serve to equalize the di- ward, whi le steam flows from tho cystribution of steam over the drum cross clone uniformly nt a velocity around section ..For uniform bubbling of steam 1 m/s from beneath the cyclone cover th rough the s ubmerged plate, a into the s tea·m space of the drum (Fig . continuous steam layer (s team cushi- 15.4). A cross-piece in the cyclone boton) should be fo rm ed beneath the pla- tom stratifies the water flow which te. The condition of steam cushion sta- moves smoothly into the wa ter space bility (see Sec. 13.1) is determined by of the drum. The number of cyclones s team velocity in the perforated plate in a drum is determined by the capaho les . This veloci ty depends on pres- city of the cyclone which in turn des ure , i.e. it is lower at higher pressu- pends on its dimens ions and pressu re; the capacity of a cyclone 300 rom in res (Fig. 15.2). Tn high-capacity boilers , each eva- diameter at a pressure of 4 MPa, pora ting tu be d elivers into the drum 10 MPa and 15.5 MPa is res pec tively up to 1 000 kg/ h of steam-water mix- 4 tfh, 6 t /h and 10 t /h. internal cyclone separation is rature o n the average, some tubes d elit her effective, but increases the hydrauver up to 1 500 kg/h . These powerful fl o ws ejected in to the dru m possess a lic resis tance of t he circuit, which h ig h k ineti c e nergy which s hould be shoul d be considere d in circulation calcula tions. d a m pened in order to minimiz e steam

186

Ch. 15. Water Conditions

Fig. 15.4 . Typica l drum. internals

m/s

/ - drum; z-cvaporatln~: tubes; J- box: 4- cyclone; 5- dr:unage box; ·&-cover; 7- stenm-wnshlng perforated plate: 8 r•erforatcd steam batfle; 9- fco!d wnt•!•" dis tribution box: JO- steam..(!lrculating tubes: 1/- feed water In: J2-ho lc In a partition; I J-downtakP tube•: H - Pmcrg<>ncy water drainage

8 9

187

15.4. Method$ for Generating Clean Stearn

20

Ul '

ffj

12

2

425 mm tlia•50

8

f ..._

4

\ \

t'-.. 1'-p

-7

\,;.,_

I

• I]

_1,

External cyclones have a lso found wide application for steam separation in drum-type boilers ; they arc mount ed outsid e the boil er drum. An exter5.

-;-?

~

4/

'

3,

zt:1=~=''

~

425m.'111 tfitr. J5 '

t-

~

to- 1-

_t~ '-

L.

I 'ljf

Fig. 15.5. Typical ex ternal cyclone sepa rator ! - header: t-steam·wntcr mixture In; 3-wbirle r: 4-pe rforatcd plat.e; s-stenm-outlct pipe· 6-alr vent; 7-blow·down: 8 - dOII"ntake tubes · 9-water from drum; W- cross·piccc '

nal cyclone separato r (Fig. 15.5) is m ade in the form of a \'ertical cylinder 350-450 mm in diameter. The steamwater mixture is int1·oduced t augenti a ll y and the separation process is essentia lly the same as in an internal cyclone separator. The height of an external cyclone is determined by the sum of the requ ired heigh ts of the steam space (1.5-2.5 m) and water sp ace (2-2.5 m) to ensure efficient separation and stabilize the operation of the downtake l.u bes in the circu lation circuit which are connected to l he external cyclone. In once-through boilers , the steamwater path is provided \l'ith a stat·ting-up unit mounted b etween the furnace water walls and the s ubsequent heating surfaces. One of its principal elements is a built-in separator (for more detail see Sec. 23.4). l t has a vertical cylindrical housing with a s ingle stage of s team-separating ,·anes inside; the stea m-water mixture is introduced a t th e top (Fig. '15.6). Wa ter droplets are thrown to the wa lls by centri fugal forces, water flows through an aunulat· drainage chamber and is rem oved through a side drainage tube. D ri ed steam passes from th e separato r through the bottom chamber. This design of separator has been unified, h as standard d iJnensions and is om-

fig. 15 .6. Unifi ed built-in (s tart-up} s Lca m separa tor J- header; z - whlrl er insert; 3- whlrlcr: 4
ployed in su percritica l-pressure monobloc unils for 500,800 and 1 200MW. [[ wet steam moves in a tube at a moderate velocity, it.s moisture predpi ta tes and fl ows along the walls as a n annula r film. This process is called film separation. For effective separation of the fl ow into steam and water, the flow velocity should uot be excessively high , othenvi.se water droplets will break off from the fi Im and be carcied off ·by stenm. Th o highest allowable velocity depends on the pressure and steam content of the flow (Fig. 15. 7).

At present, turbines of nuclear po·wer stations operate mostl y on saturated steam. T herefore, to attain higher efficiency, the moisture content of steam musl be as low as possi blo, which is achieved by careful primary separation with a slight superheat before tho low-pressure cylinder of the tu rbine. The process dingram of separaliO il is dete rmined by the type of t:eactor. I n channe l type graphi le-wator reactors, saturalod steam is separated in hori1.onta l dl' l l lllS outsid e tho 1·eactor.

0

2

4

5

8

10MPo

Fig. 15.7, E ffect of pressure on the s team ,·eloci ty at which wate r d rople ts ca n be broken off from the li quid film surface

1\ powerfu l reactor mn y have a ntun-

ber of separating drums con nected in parallel. For instance, the reactor unit type RBMK-'1000 (t 000 MW) has four separating drums. The drums are mnde of carbon steel Grade 22K (0.22 C boi ler}, with the entire interna 1 surface being plated by stainless s teel. The drum is 31 m long and has a di ameter of 2.3 m. The connection di · agram for the separating drums of an RBMK-1000 reactor is illustrated in Fig. 24.13. Tho number a nd dimens ions of separating drums are not related to tho dimensions of the reactor and are chosen so as to attain tho highest degree of steam drying. Separating dmms of the desig n described can produce steam with a water co ntent of not moro than 0.1 %. In water-moder ated water-cooled tank-type reactors, st eam separation is carried out in the reactor housing (see Fig. 24. 12} . Preci pi tating separation in a small volume is insuf£icientl y effective. The steam-water mixture fonll ed in the fu el assemblies of the reactor core is fed inlo a collecting box and then through parallel vettica I tubes into axial cyclo nos. Upon separation, water is retur ned int o the water space, while steam rises through tho central portion of the cyc louos into n steam drier and thon is

188 324 mm tiin

main steam flow into a preliminary ~, drier and then into the main drim:. A steam dri er usually bas a set of vertically-arranged corrugated stain7 less-steel plates (Fig. 15.9). Each bend of plates has a welded-on corner plate which forms n vertica l pocket for tra pping and removing moisture . S team washi ng . Re-writing equation (14.4) in the form: C. = = C,Aw + kd), it may be soon that steam quality can be improved by either improving the quality of feed water (which involves extra expenditures on , _,___ 2 ,... water treatment), or decreas ing thewater content of steam (achieved by f separation of mois ture from steam flow), or by decreasing the distribution coeffici ent. The distribution coefficient is I. he constant of eq u ilibrium betweou boiling water a nd saturated steam and depends on pressure and on the physico-chemical properties of s ubstances dissolved in water. For a particular dissolved s ubstance. Fig. t5.8. Primary centrifugal separator of given pressure and given conce ntra~ ax ial type tion of the impurity, the distribution J - wbirlcr; B- CJc:ione; 3- c hanncl tor primal)' coefficient. is constant. I n t urn, kd = removal or separated mol.•turc· 4- ltow-straightcnlng vanes; 4-ch!'nnrl lot the' secondary removal = C~"/C':,:•, and therefore, cleaner or separated motsture: 6-scparatiJlg vanes In the path or secondary moisture; 7- prcdrier s team can be produced at kd = constant by decreasing the concentration of impurities in water, which again involdelivered through sloam pipelines to ves extra expenditures on water treatLho turbine. · ment. A feasi b lo version of a primary cenNoti ng, however, LhaL tho purity of trifugal separator for tank- type rea- delivered s team is determined not by ctors is shown in F ig. f 5.8. Under the the wat~r from which it is generated, ~ction ~f centrifugal forces developed hut mamly by the water with which t n a wlurler, the steam-water mixture it contacts on eutry into the s team space is separated i nto the p eripheral water of the drum, it is possib le, with feed layer which moves along the inter- water of a given quality, to s ubstantinal cylindrical wall of the cyclone, and ally reduce the concentration of imthe steam flow which moves through purities in s team by washing, i.e. the cyclone core. The main mass by passing it at the las t stage o( the of water is removed from the cyclone process through a layer of pure water , via tho primary drainage channel which say, condensate or pure feed water. is provid ed with straightening va- This is accomplis hed in bubble-cap nes to stop rotation o( tho water flow. steam washers. The remaining water is removed Steam was hing by bubbling consists through a secondary drainage channel essentially in the following (Fig. in which vanes are mounted to separate 15.10). Suppose that dry s team of a the steam which enters this channel salt concentration C is gen erated together with water. The separated fro~ boiler water wit.h31 a high conconsteam is directed together with tho tratlOn of salts C~w · In this process,

r

t

189

15.4. Methods for Generatin g Clean Steam

Ch. 15. Water Conditions

Fig. 1

and

15.9.

Saturated steam drier

Steam outLet

J - cons tant·vclaclty

~

chnnncls; 2 and 6-perfora -

ted llln t.cs; .Y-Iloritontal c hu te: 4- dralnagc pipes; 7- corr ugnted ,,tates; 8-moisturclrtiJll'ing pocket

1

..... r-

l_ A

2

A-A

v 7 :,...-

•

~

-. -

-.

•

A

·-

(j

--

5

-

~

.

•

.

7

J 4 ---

.

~ I

-

.

~

8

Steam intet 8 enLarged

7

As the new equilibrium is est ablished, the dissolved impurity in steam will partly pass over into water, since C , 2 /C1w > lc 2 , and therefore, its concentration in the steam will decrease and that in tho wash water, increase. With a good, sufficiently long contact between the two phases, C s•iCfw > lc2. Si nce both processes (steam geucrution and washi ng) occur at the same pressure, k 1 = k 2 • Furthermore, since Cbw is m uch greater than C Jw• it t ur ns out that C, 2 is much lowe r than C 11 • A strong washing effect can be achieved by passing s team in [i ne jets through a water bed, for i nstance, Crw through a perforated plate. Upou wa- - . --- ~---- ~- - 1- shing, saturated steam is subjectt:d to - - - - - -secondary separation to reduce its moisture content roughly tu its prewashing level. The sim plest steam-washing device is a perforated plate onto which wash water is poured '{Fig. -""· -- - - - - ,-15.11). For efficient operation, wa- r-- - - - - · ter sJ10uld not bo allowed to p as, tlno---- -- -- ugh the perforations, especially at low loads. This is attained by mainFig. 15.10. Principnl.diagram of steam wash- taining u definite s t oum velocity (see Sec. 13.2).

an equilibrium will be established according to the dissolving power of tho steam with respect to a given substance, which depends only on the process parameters. The equilibrium state is characterized by tho distribution coefficient k 1 = C 01 /Cbw· As steam passes further through a layer of feed water w ith a low salt concentration C1w. a now equ ilibrium s tate is established and tho steam will have another salt concentration corresponding to the distribution coefficient k 2 ..:... C. 2 1Ctw·

=------

-~

-

---

--

--

'"tt

190

Ch. 15. Water Conditions

'

_-

-- - - --....__ --:lii)-- - lJL!. -- -- -- - - ·_K -- --

~------L-------~~~

Fig. 15.11. S team washer

S team washing is carried ou t in tho s~cn m of a boiler drum (sec Fig. 15 .4). 'I he edges of tho perforated plate are be n t. up to retain the r equired la yer o[ wal~r. The dimens ions of t he washing d e v1ce are s uch that the internal dwme t er of the dru m mus t not be less t ha n 1 600-1800 mm. Feed water is used for s t eam was hing. The flow rate of wash water is determined by the s t eam-ge nera ting capaci ty. Tn mod ern s l eam boil ers, all feed wa t er is fed into a dis t.ri])ut.ing box and Lhe excess of water flows throuo-h a s lit in th e box direct ly into the ~~·aler s pace of ~h e hoi !er drum, i.e . it do cs not. partiCi pa te 111 s tea m wash ing. S tepped evaporation. The ba lance of s nits for the simp lest ve rs ion of the wa ter conditions of a drum-ty pe boil er with blow-down (Fig . 15 .1 2) is as follows :

'

Fig. 15. 13. Diagram of two-stage li on

C\' <1

para-

D_~signntlons the Stune a~ In 1;-ig. t 5. 12; adUi Uona J-

1). ni nnd "n-steam-gc·ncrating capncitics or the first an d second C\'aporatlon stages, percent o r th,. stc am-gerwratlng capac ity or tlrn pl ant

ce, t hat t he blow-down ralio p = we h a ve:

Cb•l =

cb!D =

(1+0J11) Cj w V.tl l

--

+

+

c,,.,

,_- --

'

Thus , the device shown in Fig. 15 .13 has two e vap ora tion 13t ages. Ass uming, for inst ance, t he relative s team-generating capac ity o[ the firs t s t age n 1 = 80 % and tha t of tho second s t age, n 1 t = 20% , t he concentrations of im purities in boiler water will he r es pectively as fo !lows: in the 1s t evapor atio n stage: 1 (rtt + (nll -1- fl)J Cjw Cbto =- _;__::_.:....;._:_:__:_..:...:_:_:..=__

nu -1-P -· (80 -1-20 + 1) Ctw = SC 4 20 + 1 • · fw

1%.

(15. 9) and in the 2 nd s tage:

101c fw

(1 5.8)

_ As fo llo ws from th is equ a~ ion, stea m ts ge ner a t ed u nder t he o-i ven cond itions from boiler wa ter ~-it.h th e s a lt conte nt. _exceedin g t ha t o f feed wa t er b y ~ 0'1 Lt mes. T he q uality of steam can be tmproved by more i nte ns ive blo~ving:d.own, IJu l this is economi cally tnefftct ent. Fo r co n t inuous blowin"down, the blow-down ratio is tak;n within 0.5-1.0% if the water Joss is nc. n bdcbd = (D n bd>c,ID r e plenished by dis tillate from evapo(15.5) ra tors or by d emineralized water, and Div iding both parts of equation 0.5-3% of chemically purified water is added. (1 5.5) by D and deno t ing DbdlD = = p , we obtain: A more effi cient method is that of stepped evaporation proposed by C.+ pCbd = (1 p) C1w (15.6) E. f. Romm. The boiler drum is diviwh erefrom ded b y a pa r t i t ion into t wo compar t_ (1 + p) Cjw - Cs ments (Fig. 15:13). Each of them is Cbd(15. 7) Coilllecl od to a group of c ircul a tio n p Neglecting the sail content of s loam circu its not interconnected b y t he wa(C . :=:-:: 0) and assuming, for ins tan- ter path. Tho water s paces in th e two compa rtments communicate only D Cs t!u:ough a small hole provided i n the pa rlttwn. F eed wa t er is fed into t he firs t ...., / (larger~ compa rtment and blowing- - - - --• down IS effected thro ug h t he second D•Du }-_- - OJ (smaller) compartment. Boiler wa t er I can flow throu gh the partition l1o le from the firs t int o t he s econd comparFiR. 15.12. Simplilicd diag ram of orga nizat ment, but the wal or l evel in t he lntter ti on of water conditions in a boiler drum a.lways remains below that in the forc fw• cbw • cbrl' c.- couccn tra llons or substnnces mer. Steam is removed from t he d ru m rcsprctlwly in reed waler . bofl r r walcr. blowdown water, an d strnrn only t h rough the fi rs t compa r tment.

+

i9i

15.4. .Me thods for Generating Clea n Steam

ll ebto=

(1111 +P) C~ 111 p

(20 - 1- 1) 4.8Ctw

1

= 10 1C/w

(15.10) As ma y b e seen, i 11 two-stage ev apora tion, c~to is much lower tha n Cl~, and for this re aso n the firs t compartment, where th o s alt content of water is not hig h , is called the pure compartment and th e second, whore water has a h igh salt conlont , is call ed the salt compartment. The ratio C,J~Iq 10 is ca lled the concentrat ion ratio. I n the above example, 8 0% of the total quantity of s te am are generated from wa ter h a ving a low salt concentration, and therefore, the mai n m ass of steam _produced has a hig her qua lit y than i n th o scheme with one evaporation stage, and o nly 20% of tho total quantity of steam are generated from water o f t he same quality as in the s ing le-st age method. Therefore , the qua lity or s team in two-stage evapora tion is su bstan t ially be tler than in s ing le-st age ev a porat ion. The overflow of wa ter from the pure to th o saiL compa rtment is essentia lly intern a l bl owing-down of the former. J 11 contras t. to external blowingdown, interna l b lo wing-down involves no l osses of heal, no r of t he working f luid , so t h a t tho blow-down ratio can b e chose n sol el y from considerati ons on how lo obtai n t he best q uali ty

11r

I

111T

-~

too;;.

nFf1

Cs(Cr,.-

0

Fig . 15.14. Determination of the optimal capacity of salt compartment Blow-dowu ratio: p ,

<

p,

<

p,

of s team. In turn, the bl.ow-down ratio d e t ermines the s team-geuerating capacity o f l be sa It com pn rt me nt, which ca n be ob tained from the a ppropri a t e calc ula ti o n. Assuming ,·arious values of t he steam-genoraling capa ci ty o f the salt compa rlm en l , n 11 , one c a n d ete rm ine the qu n lily of s aturated s team pr odu ced at a sel ected va lue of p of extern a l blowing-down. It is cl our tha t at n 11 = 0 a nd nn = 100% there will be no s tepped eva po ratio n and the quality of stea m in t hose extreme cases will be the same a nd corr espond to the highest contamination _ I n the w hol e r egio n of s l epped ev aporation 0 < nn < 100 % , the quality of s team will be higher (it will have a, lower content of impurities) than in a s imple s ingle-stag e sch eme (Fig.15.'14). One can calcul ate the optima l steamgenera ti ng capacity nu a t which steam will have the lowes t concentration of impurities. Each particular val ue o f p in extern a l blowing-do w n h as a co rres pond ing optimal val ue nu. With internal stepped evaporatio n in boiler drums, the difference in the· water levels in the compa rtmen ts is not large in vi ew of the limited height of the wa ter a nd steam space · of the dmm. T h is roa y cause a revers e ov erfl ow of wn l er. If this d ifferonce is inCJ'onsed by ra is ing the water level in the p u re compa r t me nt, tho heig h t of t ho s t ea m s pace will diminish, a nd therefo re, th o carry-off of wa ter droplets will i ncrease. A d ecrease in t he water

~ )

I

Ch . 16. Pro cesses on Fireside of Heating Surfaces

1.92

.... the water levels in the compartments ~

9

~

..

4

f

10

......"'~

~

---

3

~

8 .. ----

---

Clean compartment

7

6

5 Fig. 15.15. Two-sLnge evaporation circuit with an external cyclone I-drllm; 2- c vaporatlng tubes or pure COmpartment; J- feed wat er In; 4-snlt compartment

(external t.)•Cionc); .s- downlnke tube; 6- evuporaL-

tng tu!Jcs of sn it compnrl.mcnt; 7- blow-ctown: 8- rcect line or snlt compartment; !1-cross-ovcr s team tube; I O- stcam-drcu la Ling tube

level in the salt compartment may disturb tho circu lalion. With tho 11sc of extemal steamseparn ti ng cyclo nos, th e d ifference in f

\ I

2

11

___

...____:::...._::...._

fst

evaporation

stage

J

____,

..____, 2nd

evaporation

singe

8

6

7

Fig. 15.16. Threc-sLnge eva poration circuit with an external" third stage 1- drum; :. J, and 5- Is t, 2nd and 3rd evaporation stoges· 4- rced water In; 6- thlrd-stagc downtake t\lbc; '7- tbl rd-stagc evaporating lubes; a-blowdown; 9 and 10-cross-ovcr lube.~ ror water and steam; II-stcam~lrculallng tube

will be high enough to avoid a reverse overflow of water. For this reason, schemes with external cyclones are preferred, especially at a low capacity of the salt compartme nt. The effectiveness of s t opped cvnporntion increases, though not in proportion , with the number of stages. Twoan d three-stage sche mes ha ve fou nd wider application. The scconrl evaporatio n stage can be arra ngcd ei thor inside the boiler drum as in Fig. 15.13, or outside, i.e. in externa l cyclones {Fig. 15.15). In a three-stage schem e, the first and second stages are usually arranged in tho boiler dl'Um and th o third in an external cyclone {Fig. 15.1.6) I n external cyclones , the steam a nd water space may be of any height. This ensu res thoroug h drying of the steam (due to a high st.cu rn s pace) and reliable operatiou of th o circ ulotion circuits (due to a high water s pace}, and prevents water curry-o vm· from the salt to the pure com purtmcnt. Stepped evaporation makes it possible to improve the purity of steam at a given quality of feed water and given blow-down ratio. Furthermore, steam that is adequately pure can be obtained from water of a lower quality, which makes the water- treatment system simpler and less expensive. Additionally, stepped evaporation can increase the efficiency of a steam-turbine plant, since the blowdown ratio can be reduced without a significant loss in steam quality.

PROCESSES ON THE FIRESIDE OF HEATING SURFACES 16.1. Mechanis m

or Scaling

Va1·ious m ineral impurities which p ass into boiler furna ces together with the organic mass o[ solid fuels

are transformed in the hig lt-t ern perature zone: part of them are mol t.od and combined into larger parti cles which fall onto the furnace bottom as slag, while the main mass of fin e par-

193

16.1. JII ccha ntsm of Scaling

ticles of ash are carried orr [rom the furn ace by combustion products. The behaviour o[ . ash particles in th e furnace and flue duels of boi \er depends on their composition and phys ica l properti es (mel ting point , viscosity, thermal cond uctivity, et c.). The composition of ash includes a s mall quantity of low-fusible compounds, mainly chlorides and sulphates of alkali metals INaCI , Na 2S0 4 , CaCI 2 , MgCI 2 , Al 2 (S0 4 ) 3 l with a ·melting point of about 700-850°C. They arc vaporized in t.ho high-l,emperaturo zone of the flame core and then condcuse on lhe s urface of the tubes, s ince th o temperature of walls of clean l,ubes is always less than 700°C. M'edium-fusible components of ash, wilh a melting point of 900-1 100°C (PeS, Na~Si0 3 , K 2S0 4 , etc.) , ca n fot·m the primary sticky layer on waterwall and plate n tubes if the high-temperature zone is too close to the tubes owing to im proper organization of combustion (the flame touches the tubes). High-melting compounds of ash arc, as a rule, pure oxides (Si0 2 , Al 2 0 3 , CaO, MgO, Fe 2 0 3 , etc.). Their molting point (1 600-2 800°C} exceeds the highest temperature -in tho flame core, so that they pass through the combustion zone without being cha nged, i.e. they remain solid . Si nco their particles are small. these components are mainly carri e~\ off by the gas flow and constitute what is called fly ash. In the zone where the temperature of gases is stiU high (above 7008000C}, low-fusible compounds are first condensed from the gus flow on the surface of clean tubes and form the primary sticky layer on them. At tho same time, solid (high-melting) ash particles adhere to this layer. They solidify and form the primary de nse layer of slag which is firmly bonded to tho tube surface. Tho temperature on t he outside surface of the layer i nerouses and further condensation from gases is thus stopped. Tho rough outside surface of that layer retains [i uo so lid particles of high-molting ash I :1- 0 I ~24

whi ch fall on it; these form an external loose layer of deposits. Thus, depos il s on the tube surface in this region of gas temperatures most often ha\'0 two layers: a dense internal layer and a loose, or friable external layer . Ash rwrticlcs can quickly form growing doposi ts on furna ce tubes in the zones wh ere high- temperature gases co ntac t wat.or walls. Firs t, ash a nd s lag particles in a semi-liquid or softened s t a te are thrown onto tho surface of tho tubes; upon cooling, they adhere firm ly to the surface. The process is ca lled sla.gging. Slag aggregations may be qui t.e large in size and have a mass of up t.o a few tons. The presence of relatively easily fus ible particles in the combustion zo ne is determined by tho format ion of eutectics between moLa l ox.ides MeO (such as CnO, lVlgO, PeO or Fe 2 0 3 ) a nd s ilica S iO. or nl nmina minerals based on A l 2 0 3 • Tho ash o[ most solid fuels contains 5 to ''lO% of metal oxides MeO. A higher concentration of MeO lowers the soften ing temperature of ash and creates the risk of slagging. However , if ash contains more than ·ao% of Al 2 0 3 Si0 2 , its melting point rises substantially; it becomes high-molting. With an unfavourable mineral compos ition of fuel (if the content of calcium oxide CaO is mor e t han 40%), s intoring (sulphation) may start in a dopos i tod friable layer formed on the heating surfaces if S0 2 is present in the flu e gases. The process results in the growth of dense, firmly bonded slag deposits on the tube surface (Fig. 16.1). Slaggiog may occur on the tubes of water walls, platens, and sections of the convective superheater in the region 'of gas temperature up to 600-700°C. Caked deposits may overlap intertubular spacings of a width of up to 400 mm. Horizontal and slightly inclined tnbes are slagged more intf:)ns ivoly than a re vertical tubes. In zones of relatively low gas flow temperatures (less than 600-700°C) which aro typical of heating surfaces in the convective shaft, friable depo-

+

•

194

Ch. 16. Process es on Fireside of Heating Sur/a ces

ur -

18m/.~

fOTmZJ(jJ

tv • 5mjs

4.0

10

c

2.0 f.O 0

t

,,

'"e Hj) c, I

14.0

/- 7

iJ.O

t

19;)

16.1. Mechanism of S caling

I 7'

10.5

ZU

-2

f/

~ ·.;;:

J.[j f'

u

2468h

"' " '::::- "'

~ J(

4

6

8

..........

4

.......

~

w

10 tZ 14 16 mjs (h)

(a)

Fig. 16.3. Fouling coefficient for tubes depending on Lhe concentration and particle size of asb in gas Oow· (Lubes: d = 38 mm, s1/d = s 1 /d = 2) (o) depending on the lime or operation: (b) dependln~ on flow vcloclt)·: J-asb concentration 21 1:/m': 2 i glm' : J-flnc ash (mes h r~.slduc n,. = 24.5~.>: 4-coarst' ash (mesh residue n.. = 52, 5 %)

Fig. 1G.i. Ca ked deposits on the surface o[ a tube

i'

i

'

II

II.

l.

sits are more likely to form. Th ere is no dense underlayer on tlto surface of tubes, since the condensation of a lkali metal vapours h as already been fi nished before that region. Loose deposits chi efly fo•·m on tho back side of lubes rela l.ive to the direction of gas l'low, i.e. in the turbulent zone that form s behind the tube (Fig. 1.6.2) . On tho front side of t he tubes, loose deposits can only form at low velocities of the flow (less than 56 m/s) or when the flow carries very fin e fly ash . In analysing the form ation of (riahi e deposits, ash particles are divid ed into three groups according to their size [17]. Th o fit·st group includes the fin est fractions (called inertialess particles) which are so sma ll that they move along the flow lines of gases. Therefore, tho probability of tbeir settling onto the Lube surface is low. This group includ es particles of a size of up to 10 ~m. Coarse fra ctions, more than 30 ~m in s ize, are placed in the second group. Those pat·ticles possess a sufficiently high kinetic energy to destroy loose deposits on contact. The third group includes ash fra ctions of a s ize between 10 IJ.m and 30 run. When gases flow around tubes, these particles seLtle ch iefly on tube s urfaces and form a layer of depos its .

Fig. 16.2. Formation of loose deposits on tubes al various directions and velocities of gas motion

In the final resu It, the thickness of Loose deposits is determined by the dynamic equili brium bet,Yeen Lhe processes of continuous settling of medium fractions and those of destruc tion of the settled layer by coarser particles. Loose deposits o n tube s urface impair heaL transfer, which is estimated by the fouli n g coefficient: (16.1} where 6, 1 and 'A., 1 are the average thickness and conductivity of the slag layer over the lube perimeter. The foul ing coefficient E , (m~ KH)/W characterizes th e thermal t·esisLance of slag layers. The fouling of Lubes with fly ash rleposits depends only slightly on the concentration of ash in the gas flow. A d if[erence in the rate of deposition m oy be obser ved only a few hours after s Larting-u p uu til a dynam ic equili bri um is eslnblis hec:L

(Fig . 16.3a). On the other hand, t he size composition of ash has a strong effect on the formation of deposits. Finer frac tions of ash cause more intensive fouling of tubes with a thicker layer of deposits being form ed (Fig. 16.3b). The degree of tube foul ing depends substttntially on the gas flow velocity. The amount o[ medium-size particles th at settle on tubes increases rougbly in proportion to flow velocity. The destructive effect of coarse particles, on the other hand, increases in proportion to tho third power of velocity, the t.otal result being that the thickness of the deposits on tho tubes decreases with an i ncrease in gas v elocity. As demonstrated by experiments (Fig. 16.2), the intensity of tube fouling in a cross flow does not depend on tho di rection of flow. Under comparable · conditions, vertical tube coils are less s ubject to fouling. The degree of tube fouling heavily depends on tho type of tube bund les (staggered or in-line) and the longitudinal pitch s 2 of tubes in staggered bundles. Under com parable conditions (the same gas velocity and tube diameter), the fouli ng coefficient for staggered bundles turns out to be 1.73.5 times Lhat for in-line bundles (Fig. 16.4). Tube fouling increases significantly i[ the gas velocity is less than 34 m/s. For this reason, the operation o[ healing surfaces of boilers at s uch low velocities is unadvisable. Since I J*

th e load of a boiler can drop in operation by as much as 50% of the t·ated capacity, the nomina l gas velocity at the rated load should be not less than 5-6 m/s . In boiler:; fired on high-s ulphur fue l oil, both sticky deposits a ud dense glassy deposits can form on the heating s urfaces in the zones where the gas temperature is be low 600°C. Sti cky deposits on the heating s urfaces of co nvecLi ve s uperheaters and economizers· primaril y contain vanad ium compounds (mainly V 20 5 ) and sulphates. Dense deposits consist mainly of iron s ulphates and calcium and sodium oxides. Deposits that form during fuel oil burning have a tendency to grow up quickly, which may greatly impair heat transfer, increase resistance of the gas path, and shorten the campaign of the steam boiler pla nt. 10

1 2 m HjJ

9

c

\

8

:¥...., J. . i . ~.. .

7 ~2jd=JO

6 5

4 3

z

'

~ (/'~

l~d. .

l->.K ~d'
I

0

•

5

r-.....

6

7

r--.:: t'!.' oq~'- I ' ["-... t-.. ........ 1::...... ........ !-......

8

-

I", 1'-

-

9 10 11 12 IJ

IV

1~

m/S'

Fig. 16.4. Comparison of fouling coefficients for various tube bundles

I

1 !J(J

•

'

jl

r'

'

!

I: I

I

I

~I

'

!

I

I

Cit. 16. Processes

011

Ftrestde of Heating Surfaces

Since fu e l-oil ash deposits contaiu a noticeable quantity of vanadium a nd sulphur, they arc esse ntially acid. The addition of certa in substances wit.h alkaline properties to fu e l oil makes ash depos its more friable. The same e£fecl is obtained by a particular co mbustion process, for instance, al an excess air ratio c lose to unity 117]. Some methods of cleaning heating surfaces from deposits are based on the dynamic effect of jots of steam, water or air. The effectiveness of such jets is determined by their runge, i.e. by the distance at which a jet still has a s ufficient dynamic head to d estruct deposits . Water jots have the greatest •·ange and the highest thermal effect on dense deposits. Devices based on this effect are used for cleaning furnace walOL' walls. Water blowing should , h owever, be calculated carefully so 11 S to avoid s harp cooli ng of the tub e m etn l upon remova l of tho depos its. !11 ulti-jet retractable blowers have found wide app lication for cleaning radiation heating surfaces and convective superheaters. They operate on saturated or superheated steam supplied at a pressure of around 4 MPa. Platens and in-line tube banks are cleaned by vibration cleaning: highfrequency vibrations transferred to heating tubes disturb t he bond between the tube molal and deposits. Vibration cleaning is carried out by means of vibrators aLLached to water-cooled rods . Tho mos t efficient method for cleaning convective heating surfaces in the down take sbuft of boiler furnaces is shot-blasting, which utilizes the kinetic energy of flying 3-5 rnm cast-iron s hots. Shot is carded upwards in the air flow and dis tributed over the whole cross section of the shaft. The use of shot is detonnined from th e optimal intensity of sh ot-blasting, usually 150-200 kg/m 2 of a convective shaft cross section. The shot-bl asting procedure usually takes up 20-60 s. Shnt-blnsti ng is effective if it is regulal'ly carri ed out soon after boiler start-up when the heating surfaces

are still re lalivcly clean. Heco utly, the heat-wave cleaning method has found use. Jt is based on th e applicnt i on of acoustic lo\1·- frequency \1'1\\'es generated in a s pecial explosive-combustion i mpulse chnmber. R egenerath·e air heaters arranged outside th e boiler are cleaned by blo\\·ing their packing with superheated steam (at a temperature '170-200 dcgC above the satmation point). Loss frequently, water washing (water r emoves sticky deposits, but increases co t·rosion) or shock- wave cleaning and thermal cleaning arc employed. Thermal cleaning is based on pol'ioclically raising tho t.ernporaturo of tho regenerator packing up to 250-300°C by interrupting the air s upply to the apparatus. In this way, s ti cky depos its are dri ed up and s ulphul'i c ncid is vaporized.

16.2. Abras ion Wear of Convect ive Heating Surfaces The steam boiler designer shou ld pay serious attention to measu res pro· venting abrasion wear of the tubes of heating surfaces by particles of as h and unburned fu el. An improper selection of gas velocities in tho flue d ucL of the convective shaft can lead to intensive wear of Lubo metal in certain places, thinning of tho walls, and even break-through of tho tubes. The mechanism of abrasion wear is essentially as fo ll ows. Coarse particles of ash, which may be quile hard and have sharp edges, impinge on the walls of a tube and continuously cut off microscopic layers of m etal. Thus, in critical places the wall is gradually thinned. Particles of unburned fu el (in particula r , of hard er grades, such as anthracite or sernianthrucite) can also cause ab ras ion wear of the surfaces. Thus, wear of tho boi lor tubes is determined first of a ll by tho abrasiveness of ash particles, which, in turn, depends on the content of SiO. in ash and increases noticeably \\;hen Si0 2 >60% . Wear intens ity a lso de-

197

16.2. !I brasio11 Wear of Convective H eating Su rfu as

1-----=:::;!_2 J I

..

f

~

4

~ ... 1\.""-.:: .

(6) (a) fig. 16 .5. Distribution of coarse fractions of fly ash behind a turning chamber and zones o[ dangerous abras ion wear of metal of the heating surfaces pa1all~l to the p~ndicu l ar to the boiler

(o) coils

boiler lronl; (b) coils per· lront; 1- coils; t - turnlng chamber· s- distribution of coarse nsh rrncllons~ ·<~ -zone o r abrasion wear of tul:P~

ru

p ends on the total ash co ntent of cl, A w. The intensity of nbrasion \\'Oar o f h eatina su rfaces may he uno,·cn over t:> • the cross section of n g11s duct in which the heating surface is loc.atod or Mound the tuho perimeter. lt i ncrcases significantly in places where th e gas flow turns through 90°, sny, on enlry into the conveclive shaft (Fig. 1.6.5). Coarser ash particles aro thrown against the rear wall of lhe s haft, which l eads to greater wear of the tubes arranged on that wall. l n the cross flow or staggered tube huntlles, the greatest abrasion wear occurs on tho front portions of tubes alan anglo of incidence of gas flow of 30-50° (Fig. 16.6). I n in-line tube bundles, the iu lcnsily

~

..~

""~-~""'

"".....~

\

2 ~

I\1

.~

~

Fig. IG.i. Abrasion wear of a tu be . in lon g i lud inal fl ow in an air heater J - tub••;

2 - up~rr

lube plate

of wear is s nl>s tantially lower, si nce

s omo tubes are in an ae rodynam ic s hado\\' lwhind lhose in front of them. With Lhe longitudinal flow of gases in tub es (as in air heaters), abrasion wear occu rs in the inlet portion of a I nbc nL a le ngt h of 150-200 mm due to impingement of coarse particle on th e wall just after constrictio n of the gas jet (Fig. 16.7). Farther in the tube, the flow is stabilized and coar se particles move p arallel to the tube walls. Convective tube hanks should have no longitudinal gas channels in which gas velocity might increase substantially. Wear on the outer bends of a tube is especially dangerous, since the Comoustion protfucfs tub e wall in such places is thinner. The intensity of wear is determined by tho following factors: 'T 150" (1) the kinetic. energy of ash or fuel particles, which is proportional to ·~ 90m210· the square of gas velocity wJ; 180" (2) lhe number of particles (concc utration f.t 081 ,) passing along the su rface per unit time, which depends on t h e ash content oi fuel and is an incrensi ng function of w11 ; ·(3) non- uniformity of ash cont.:enlrat ions ill tho gas flow' "'""' and or gas go 180 210 J5o• 0 ve lociti es in the cross scctiou. /,·w; (It) l he density of tubes in n bn nd le, F .g. 16.6. Abrasion wear of a tuhc in cross i .e. th e rc lath·o tnhc pitch s 1 "rl. flow

Jl

19:>

Ch. 16. Proceucs on Fireside of Heating Surfaces

In the [inal resu lt, the intens ity of wear, mm/year , d e pe nds on the t.hird power of gas vel ocity:

I we = am.k ~tf.l.ash ( I•ww,) 3 ( sl$1 -d ) t.s 't

(16.2)

•

I i l

I

where Ct is the coeffic ie nt of ash a bras ivencss, mm s3 /(g h) , m is the index of wear resistance of tubes, which d epends on the steel composition, and 't is th o time of operation of a surface, h. For Llto normal operation of u tube for a t least tO years (-r = fiO 000100 000 h), the a llowabl e wear of its >val l is I we = 0 .2 mm /year. For staggered carbon-steel tube bun-dles wi t h s1 /d = 2.5.~ the a llowable gas velo citi es determined by the normal wea r by the ash of va l'ious fu els tHe as fo llows: Fue!l • . . . . . . . . . . . .w g' Eki bastuz coal . Moscow distri ct coal Chelyabinsk coal Ki zc l coal . . . . Anth racite grade ASh .' Donetsk coal grade T •

.

lll /S

7.0 9.0 10.0 10.5 11.5 12.0

To sel ec t the proper gas velocity in the gas duct of a s team bo iler, the most economi cally favourable gas veloi cty Wee (see Sec. 20.6) s hould be compared with the a llowable velocity W wc determined by lhe conditions of wear. lf i t turns out that lOwe > > w 00 , the la tter can be used in cal cu lations. Otherwise , t he velocity of gases s hould be limited by the conditions o[ wear, which necessitates a u increase in t.h e dime nsions of heali ug surfaces and fl uo duc ts. In a ny case, th e ris k of abrasion wea r s hou ld be minimized by Laking proper measures to prevent wear of Lub es. These include placing steel cu[[s o n the tube in th e p laces where inc reased wenr is most probable, such as tube bends a nd mounting cut-in inserts in the in let portions of air heater lu bes, etc. These devices are detachable and Cfl n be easily replaced when the bo i ler is shut. do1m for repairs nncl in·s pccLio n of hea ling s ul'faces.

16.3. Corrosion of H eating S urfaces Hig h -temperature corrosion. Tho term 'high-temperature corros ion' implies corrosion damage of the metal of tubes which are in contact with hig htempo•·ature combus tion products (f1·g > 700°C). It includes two kinds of corrosion which occur in various zones of the boiler and ar e of different chemical nature. One of them is tho corrosion of wat~=:r walls in the hoi lor furna ce in tho zone of the flam e Col'O, which is fos tered by Lite contact of tube meta l with s ulphuro us gases. Another kind is the corros ion of superheater tubes and their f astening el emen ts in the presence of va na dium oxi des in the gas flow. Corrosion on the fireside of water u•alls occurs in boilers fired by pulverized coals with a l ow y ie ld of volatil es (anthracites , semianthracites, l ean coals) a nd h ig h-sulphur fue l oil. T his kind of corrosion d evelops intens ively on Lubes at the level of furnace burners or s lig h t ly above it in the zones direct,l y s wept by flame. Under unfavourable conditions, the rate of corrosion wear on the front portions of tubes may be ~:~s high as 3-4 mm /year, i. e . water wall tubes in this zone get out of o L·d er in less than one y ea r (with the wall thic kness 5-6 mm). As established experimentally, the main corrosi on-active component in furnace gases is hydrogen sulphide H 2 S . Even with a s light volu me concentrati on of H 2 S at a ·s ud ace (0.040.07%), the r ate of metal corrosion increases roughly tenfold. At temperatures of 1 400-1 600°C, hydrogen su 1phide burns in the presence of oxygen a lmost instantly. Therefore, it can be present in the zone near the water wa 11 onl y iu a r educing medium where oxygen is locall y deficie nt. The primary product of t he reaction of H 2 S with tube metal is ferrous su lphide FeS which is th en changed to ferrous su lphate and fl a kes off fro m the tubes urface, thus exposing the tube m ot nl l o furth er conosio n.

199

16.3. Corrosion of Healing Surfaces

T o avoid corros ion damage Lo water wa lls fu el and a ir s hould b e d istribu' . · t ed evenly between the burners so thaL the excess ai r ratio in eac h burncr· is g reater than unity. It is advisa bl e to keep the flame from s triking tile water walls ; th is is achi eved by a rranging the extreme (corner) burners farther from the side walls or by t mning them towa rds t he furn ace cent re. Corrosion of the tubes of .convective s uperheaters h as been detected on the combustio n of fuel oils whe n tho tempera Lure of the tube walls excQeded 610-620°C. This kind of corros ion, called vanadium corrosion, is caused by the vapours of vanadium pentoxide V .0, formed in furnace gases. If fuet"oil contains sodium oxid e, tho combus tio n products will contain sodi u rn vanadates (5V 2 0 5 · Na 2 0·V 2 0
"'

rate a L relatively low temperatures of the gases a nd working fluid (a ir). The d ecisive facto r in intensive lowtemperature corros ion is the presence of sulphuric acid vapours in the flue gas flow . As the su lphur of the fuel burns in the fla m e core, it forms s ulplmrous anhydrid e S0 2 • With a certain surplus of aiL·, S0 2 is furth er oxidized to S0 3 by atomic oxygcu 0" that forms in the high-temperature zone of the flam e due to chain reactions of combustion a nd therm al dissociation. Sulphuri c anhydride can djssociate only at rather high temperatures . The res ulting reaction of forma tion and dissociat ion of S0 3 in the fl ame zone can be written as follows: Itt

80 2 +0'

~

h2

SOa --+ S02+ 1 /202 (16.3)

where /c 1 a nd k 2 a re the r eactio u ra te constants of the direct and reverse reaction, with k 1 being greater than k 2 • As a result, SO 3 ap pears in a noticea ble concentration aL the boundary o[ the flam o core , but dissociates on compl etion of combus tion. Its concentra tion then gradually decreases . As the temperature of gases in t he gas path gradually decreases, t he process of S0 3 dissoci a tion is retarded and is prac tically s topped at -Qo g = 1 2001 250°C. Thus , w i th q11icker cooling of the gases in the gas path, t he residual concentration of S0 3 will he higher. As the gases pass furth er through convective heating surfaces, the concentration of S0 3 may even rise. Depos itions on h eating surfaces, s uch as soot particles, may serve as catalysts for t he aftero xidatio n of to As a result, the concent ration of S0 3 in the gases constitutes 1-5% of the initial content of S0 2 , or 0.0020.010% of the total gas volume. I n the zones where the gas temperaLure drops down below 500°C, S0 3 begins to react with water va pours a nd forms sulphuric acid vapours which are carried by the gas flow. Tho process is complet ed a t a tempoL·a ture ncar 250°C.

so!

so3.

200

Ch. 16. Processes on Fireside of Beating Surfaces

11:..1. Corrosion of II ~ating Surfaces

Corrosion on heating surfaces may start if the tem pera tur e of the wall J K and the boundary layer at tho wall ..:_ 1.4 turns out to be bel ow the condensation_ point of water vapours or su lphuric b 1.2 : ?Cld vapours at their pa rtial pi"essures I _I 1.0 tn . the g?ses. TI1e t emperature at ' wluch motstul"e is condensed on a so0.8 lid surface is ca1led tl1 e thermodynamic t ~I dew temperature (dew point) td. 1,. For 0.5 l pure wate~ vapours at their partial pressw·e 1n combus tion products 0.4 PH,o = 0.01-0.015 MPa, td.JJ \ ~2 = 45-54°C. If sulphuric acid vapours 0.2 are present in the gas flow, tho temI\..__, I' t •. I pe~ature of condensation (sulphuric 60 80 100 120 1~ 0 •c actd dew point til.p) is Sllbs tantially higher (up to '140-160°C). Fig. 16.9. Effect of temperature ou tbe For fuel oil combustion, the dew corrosion rate i~ pncl~ i og sheets of regenerapoint can be roug hly determined from tive a 1r heu ter the formula: 1- higll excess ai r rntlo In rurnuce (a ~ I . I J:

'

-

l

:!-lowest nllowub lc excess nlr

t.~.p. = td.p. + 250 lf sro2 (16.4) wh e1·e sr = sw/Qi is lh e resol vcd sulphur content of fuel, % kg/1\U 21 (a - 1) .

'

and 0 2 = a 1s the concentration of s urplus oxygen in the gas flow I

%0 •

With a higher sulphur content of fuel and higher excess air ratio a. mor? S0 3 form s in gases, resulLing i~ a l11gher dew point. Figure 16.8 presents the diagram of ph ase equilibrium betwee n li.qui d and vapour in the two-componen t system H20-H 2S04 at various partial pressures of water vapours. The lower curves at p = constant describe t he boi ling

20

40

50

80

tOO%

Fig. 16.8. Pbase equilibrium o£ H 0 -H SO . t 2 • sys ·...:m at var•ous pressures

1.03)

\

ratio

(a 1 = 1.0 2-

I

temperature of a n 11q11cous solutio n of sulphuric acid as n Junc tion of acid co!lcentration, and the upper ones descn_be condensation te mperatu re (dew powt) of vapours. As may be seen, even a slight concentration of H 2 S0 4 vapours in flu e gases (the do tted line on the left) s ha rply i ncrcases the cond_ensation t.empcralure, and th e liquid hlm formed on the wall has a high concentra tion of s ulphuric acid. Figure 16.9 s hows two typical curves of corros ion rate at different temperatures on low- temperature heating surf~ces in contact with the flue gases obtamed on com bns tio n of high-sulphur fu el oil. As may be seen, the rate of corros ion varies non-m onotonically wi th the wall temperat ure (Fig . 16.9, curve 1). As l w decreases h·om t h e dew point (a round 145"C), corrosion first increases s harply to a maximum at tw = 105-110°C, then falls off steeply, and fin a lly, at temperatures of the wall be low 85- 90°C I there • I S a second rise in tho rate of metal corrosion. Corrosion of m e tal occurs in the presence of a condensed liquid film containing H~S0 4 on tho metal s urface. Tt can cont,in uc fur t her if new portions

of Il 2SO 4 are supplied from the gas flow. Thus, the rate of co,rrosion is propor tional to the condensation rate of H 2 S0 4 vapours. The inte nsification o[ corrosion at temperatures below 85-90°C is determined by the effect. of the so lution of s ulphurous a cid H 2S0:1 on the metal, which forms at low temperatures by t.he combination o[ H 2 0 a nd S0 2 on the liquid film su rf ace. The rate of corrosion in the temperature range of 80-120°C decreases subs tantially at a decrease in t he excess a ir ratio (curve 2 in F ig. 1G.9), which is associated "'ith a less intens ive formation of S0 3 and H 2S0 4 vapou rs in t he flue gases in that temperature range. The same effect o u th e corrosion rate is obtained wi1.11 a decrease i n the su lphur content S'" in fu el. In this cnse, the maximum of corros io n rate as n function of wall temperature lw retains i ts original pos ition. The increas ed rate of corros ion nt f w below 80°C docs not significantly depend on air conditions, since it is determined by the e£Iect of sul phurous , rather than sulphuric, acid on the metal. The flow of gases produced by the combustion of solid fu e l carries a large amo unt of fly ash, tho basic properties of which are due to th e presence of co mpounds of calc ium and other alkali metals. As fly ash reacts with su lphuric acid vapours, the concentration of sulph uric acid in the gases decreases, ·r esulting in a lower corrosion rate. To avoid low-temperature corrosi-

201:

on, it is ess ential that lw = t/ p. + +(10-15tC, i.e. the wall temperature· should be 10-15 deg C higher than the· sulphuric dew point. This is economically feasibl e on ly in the combust io n of low-sulphur fu el oils and sulphurous. solid fuels , fo r which the s ulphuric clew point t/,. docs not exceed 100-1'10°C. In other cases , th e te mperature of flue gases, which is determined by t w, will be too llig h. T he lowes t a llowab le temperature on the surfaces of a tubu lar air healer can be found from the formula: (16.5) where cx.g and a. 0 are the coefficients of heat tra ns fet· at the gas and air sides of: the heating s urface, W /(m 2 K), -o c and t,; a re tho temperatu res of the gases at the ox it a nd the ai r at the in1ol, °C. The coeffi cie nts 0.8 and 0 .95 consider respccti vely the effect of tube fouling on the gas side a nd non-uniformity of the temperat ure fi eld of gases over the cross s ection of the gas· due b. Under comparable conditions, the minimal wall t emperature of regenerative air h eaters is 10-15 deg C higl1er· than that for tubular air beaters, since for the fo 1·m er cx.g is roughly equal to CX. 0 , while for the latter, CX.a ~ ~ 1.8 ex./[. Methods fo r increasing the wall temperature l w of air heaters and reducing: the rate of met al corros ion will be dis-· cussed in Ch . 19.

:202

Ch. 17. Evaporating Heating Surface~

17.2. R eliable Designs of Water Walls

203

5

EVAPORATING HEATING SURFACES

(a)

(C)

I

Fig. 17 .2. Types of refractory-faced water walls

17 .1. Heat Absorption by Evaporating :S urfaces and T heir Layout Evaporating (s team-generating) s ur·[aces of va1·ious boilers may diffe r in ·desig n, but are al ways arranged, for th e mos t par t , in the furnace s haH and a bsorb radia nt heat. The wa ter •walls of a bo iler receive 35-4.0 % of the total heat released in the furnace. This, i n tur n, has a strong effect on the ·dis t ributio n of heat be twee n v ario us henting su rfaces (T nble 17 .1). For i nTable 17.1. lleat and Tcmperatunl Dis tributi on ll etween Roilcr Heati ng Surfaces E

-.. «:

E

Heal d lslrlbu\lon be tween healing s urraces, %

0. "''

""' -· . "' .. - _, .. ., ... .. .= u ·-""'"'_.... "... ..... .,.... -·-..... -"'"' -"'"' ., ., tc. ..... en :: •

-g ~

~:;

-o <...

c

c

C: (;

~

0:: "

0. ~ = ...

c.e " 'Vl-

-,!:: ~

> C)

"

440 540

145 215 230 230 260

62


1.0 14 14 25 .5

I i

.."' -

0

570 570/570 565/570

~

...

c. <'!

49 39 32

-

.c

.."

In hig h-pressure drum-type boilers (14 MPa or more), the fraction of heat used for evaporation is considerably lower (see Table 17.1), so that the beat tra nsferred in the furnace is sufficient to produce the required quantit y of s team and the economi zer can be of t he no n-boiling t ype. Once-through boilers are a]so provided with no n-boiling econom izers (see Sec. 11.2) from which water passes to the evaporating tubes through a dis tribution Ireader. If the header were fed wi th a steamwa t er mixture rather tha n wil h wa te r, this wo uld cause an extrem ely uneven distribution of tho mixture hot ween t.he parallel tubes. In medium- pressure drum- type boilers, additional evaporating s urfaces are formed by a boiling economizer and, sometimes, by convective eva-

c

~

0

c:

c:.

~

19 30 36 46 58

19 21 25 22 '·2

:stance, at a n average pressur e o[ 4 MPa, t he hea t absor bed by radiant h eating sm faces is ins ufficient to cov er the total heat demand for stea m ·generation (62%), so that part of the heat spent o n water evapora tion is ·transferred to the economizer. Fo r th is reason, t he economize r of m ediumpressure drum-type boilers is us ually ·of the boiling type, i. e. water is not ·only heated i11: it to the satura tio n .li ne, b ut a Iso par tially vapori zed .

(a)

(a) s mo o th-tulle YCrllc al water wall; (b) membranl!·lypc Yerll cn l water wall; (c) platen .w all ; 1-sl uds ; 2 tub•·; .1- boller cnclosur~i 4-chromll c ;Jns tc; 5- cn rborundum; c - c•·oss-p•ccc

por·ating su rfaces or convective banks. I 11 once-throug h boilers, convec tive e\'H pora ting s urfaces form a transition zoue in the COlwcctive gas duc t, which rcsem b les a t ube-coil economi zer; i L is a rra nged be t ween t he su perheater and economizer. [ n the tra ns ition zone, eva poration e nds and tho steam is slight.ly superheated (by 10-20 deg C). I n all boile r sys te ms, evaporati ng s urfaces for pressures abo ve 14 MPa a re almost oxelus ivel y arra nged in Ure furnace s haft in the fonu of water walls wbicl1 a bsorb radian t heat. \Vater walls may be either bare-tube in design , with small spacings (4.6 mm) left between pa rallel tubes (Fig. 17 .1a) , or gas-tight, made from prossed or rolled finned tubes , smooth tubes with recta ngLllar fins welded to the m o r from smooth tubes with i ntertubula r spacings filled wi th buildingup me tal (Fig . 17.1b-d). Water walls in which tubes are welded together a nd fo1'm an all-welded gas-tight s truct ure are al terna tely called membrane walls. or membranes. In boiler [urnaces which burn lowvolat.ile fuel s, th e zone of s table ignit ion and inte ns ive combus tion of the fue l is formed at the burner belt level by ma king water walls from studded tubes and coa ting them with a refract.ory material (refractory-faced water umlls, Fig . 17 .2).

17.2. Reliable Des ig ns o£ Water Walls Fig. 17.1. Types of water walls smooth (bare) tubes; (b) g ns·tlg lll with tmncd t ubes; (c) gas-ti g ht with wclilcd· on rectangu lar ti ns ; (d) gas-Ug ht wi th me tal buil ding-up belween tubes (<,>) with

/Jm ·e-tube water walls are employed in all bo il er s ys te ms with vacuum (balanced dr a £t) furnaces. In n atu rnl-

circu Ia lio n boilers, wa t er walls are almos t exclusively arra nged vertically o;· , someti m es , at a s tee p angle. In once-throug h a nd multiple forced circ ul ation boile rs , whore the mo tio n of t ho s team- water mixture can be effect ed at velocities preve nting the disturba nce of hydra u lic conditions, the evaporati ng h eating surfaces can be o r·ie nled at any a ngle, i. e. th e water " ·alls may be vertical, ho rizontal or ascendi ng- desce nd ing . Because of the di[[erences in uatural circnl alion and forced circu lntion, the r elia ble designs of wa ter wa lls for gravi t y-circ ulatio n boilers and o ncethro ugh boilers w i II be discussed separately. Methods for increas ing circulation reliability. In pro per! y des igned and manufac tured circulation circ uits operating under no rm al conditions, t here are us ually no difficulties as regards the reliability of circ ulation. L et us recall, however , th a t the drivi.ng circulati ng head decreases wi th i ncreasing press ure (s ee Soc. 12.1). An i ncrease in tl1e unit stea m-generating capacity of a boiler