DOE/NASA/3152-78/! NASA CR-135382
William- R. Martini University of Washington
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P.repared
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NATIONAL AERONAUTICS AND SPACE ADMINISTRATION Lewis Research Center Under
Grant
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NSG-3152
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U.S, DEPARTMENT OFENERGY Office of Conservation and Solar Applications Division-of Transportation Energy Conservation
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DOEINA SA13152-7811 .NASACR-i35382
STIRLING ENGINE DESIGN MANUAL
WilliamR. Martini University ofWashington JointCenterfor Graduate Study 100SproutRd. Richland,Washington 99352 April1978 Prepared for National Aeronautics and.Space Administration Lewis. Research Center Cleveland, Ohio44135 UnderGrantNSG-3152 . for U.S,DEPARTMENT OF. ENERGY Office ofConservation andSolar Applications-• Division ofTransportation Energy ConSerVation Washington, D.C... 20545 UnderInteragency Agreement EC-7?-A-31-1011
PREFACE
The author wishes to acknowledgethe aid of the followingpeople who materially assisted the productionof this manual outsideof their regularemployment. They gave informationnot generallyavailableor conferredwith the author at length or reviewedand correctedthe manuscript, or a combinationof the above. They are: W. T. Beale, R. Beiair,E. H. Cooke-Yarborough, D. A. Didion,J. Finegold,T. Finkelstein,F. E..Heffner,L. C..HOffnlan, A. Organ, B. Qvale, C. J. Rallis,G. Rice, P. A. Ribs, A. Ros_, A. SchoCk,J. R. Senft, J. L. Smith, Jr., I. Urieli,and G. Walker.
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TABLE OF CONTENTS
Figures . ..-,......................... Tables
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I. Sunlnary..... . .............................. 2 Introduction •
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2.1 WilyShould AnybodyBe InterestedIn-StiflingEngines? ..... 2.2 What Is A StiflingEngine? ........... _ ............. 2.3 Major Types Of StiflingEngines ................ 2.3.1 2.3.2 2,3,3 2.3.4 2.3.5 2.3.6
Heat Sources ' .............. _ ...... Solid-GasHeat'Transfer............... Gas Transportand Power Take-Off (Seals-),.......... Power Control .................. , .... Heat Sinking . • . ,-. .... -.... -........... WorkingGas ....................... , ....
2.4 Prese,lt And FutureApplicationAreas ................. 2.4.1 Silent Electr_cPower,, ..................... 2.4.2 ReliableElectricPower .......................... 2.4.3..Motor.. VehiclePower .-• • . . • • • • • ....... . . 2..4.4 Heat PumpingPower ................... 2.4.5 BiomedicalPower ..................... 2.4.6 Central Station Power . . , .............. 2.4.7 Power For Other Uses?. ................. 3. CurrentAutomotiveScale.Engines .................... 3.1'-Philips-FordP_ograms'
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3.1.I The 1-98 Engine (76 e) .................... 3.1.2 -The4-215 Engine (77 k, 77 aq) .............. 3.1.3 The 4-98 Engine (7.7k) .................
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3.2 United StirlingEngines (77 i, 77 j,.77.al, 77 am) ........
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3.2.1 Apl_lication Plan .... . .................... 3 2 2 Engine Design .....................
3.2.2.1 Seals 3.2.2.2 Gas Cooier ...... . ............... 3.2.2..3Gas Heater ....... .......... 3.2.2.4 Buf'ner& Air Prelleater .............. 3.2.2.5 Power Control .......... ......... 3.2.3 Engine-Per.forn_nce ...................
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3.3 GeneralMotors Engine ......................... 3.3.1 History . • ' " ' ti.................... 3.3.2 NASA-LewisTes ng ..................... • 3• 3• 3 Eng,ne Measuveuz_nts (7lbd) . .............
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3,4 FFV Engine ................................ 4. Review Of Engine DesignMethods ...........
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¢,I StirlingEngine Cycle Analysis .................
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4.1.1 StirlingCycle, Zero Dead Volume, PerfectRegeneration 4.1.2 StirlingCycle, Zero Dead Volun_e,Imper.fect Regeneration 4.1.3 Otto Cycle, Zero Dead Volume,Perfector Imperfect Regeneration ........ 4.1.4 StiflingCycle_ Variabie'DeadVolume,Perfector i ImperfectRegeneration ............. 4.1.5 CombinedStiflingand Otto Cycle Variable Dead"Volume, Perfector ImperfectRegeneration...... . . .. . . .......... 4.1.6 Conclusionsfroiil Cycle Analysis ..... . .......
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4.2 Eirst Order _sign Methods......................
65 68 72
4.2,1oi Engine Definition . ................. 4.2.1.2 Sample Engine Specifications.............. 4.2.1.3 NumericalAnalysis ................... 4,2,1,4. SchmidtEquations , ................ .....
4,2,2,1..... Engine Definitionand SanipleEngine Specifications.................... 4.2.2.2 NumericalAnalysis ................ 4,2.2,3 SchmidtEquations .............. 4.?..3 ExperienceFactors ..................... 4,2,3,1 EfficiencyExperienceFactors ......... 4.2.3.2 Power ExperienceFactors............ 4.2.4 First Order Design Procedure ............... 4.2.5 Cnnc.lusions on First Order Design Methods.......... 4.3 SecondOrder DesignMethods .............
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4.2,]..Piston- DisplacerEngines . . ............
4,2.,2 Dual Piston Engines ..............
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4.3.1 CapitalLetter Nomenclaturefor Section4.3 ....... 4.3.2 Basic Power Output .......................
72 75 75 78 82 82 82 85 89, 90 lO0 I00 lOl lOl I02 lOB
4.3.2.1 SchmidtEquations- Sihusoidal- Isothenllal. .
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4.3.2.1.I Alpha, Dual Piston Fot_nof Schmidt Equation ............ 4.3.2.!.2 Beta Engine Fo_'mSchmidt Equation . . 4.3.2.1.3 Gamma Engine Form Schmidt Equation
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4,3.2.2 Basic Power AssumingSinusoidal,NonIsothen]]al Processes........... 4.3.2.3 Non-Sinusoidal,Isotheriilai ........... 4.3.2,3.1 Rho,_)ic-Beta (PhilipsEngines) . . . 4.3.2.3.2 Crank Drive-AlphaEngine ....... 4.3.2.4 Non-Sinusoldal,Non-lsothe_lal.........
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Loss ...................
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Screens ................ Slots .................
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4.3.5 Basic Heat Input , .... ....... 4,3,6 Reheat Loss ......................... 4.3.7 ShuttleConduction ....................
121 122 129
4.3.8.1 ConstantArea Conduction........... VariableArea, VariableThermal'Conductivity . , 4.3.8 4,3,8.2 Gas and Solid Conduction .................
134 134 133
4.3.8,4 -RadiationAlong a Cy.linder with Radiation 4.3.8,3 ConductionThroughRegeneratorMatrices .... Shields ..... •...............
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4..3.9 PumpingLoss ............................ 4.3.10 TemperatureSwing Loss . .................... 4.3,11 InternalTemperatureSwing Loss ............ 4,3,12 First Round Engine.PerformanceSunm_ary .... ' .... 4.3.13 Heat ExchangerEvaluation.................. _q,
I17 117 120
4.3.3.3 Heaterand Cooler PressureDrop - Interleaving 4.3.3.2 Heater Fins , and Cooler PressureDrop Tubular . . , 4,3,3.4 Heater, o e n Regenerator i d g o . ..
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Regenerator Pressure Drop 4.3.3.1,I 4,3,3,1,2
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Fluid Friction
4.3.13.1 TubularHeat Exchangers.............. 4.3,13,2 AnnularGap Heat Exchangers, ......... 4.3.13.3 Isothermalizer Heat Exchangers .......
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4.4.1 •BasicDesignMethod .... .............. 4.4.2 Funda_ntal Differential u tions . .......... 4.4,2.1 COntinuityEquation .. , , .......... 4 4 2 2 Momentum Equation 4.4.2.3 Energy Equation ..................... 4 4 2 4 Equationof State
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4..4.3 Comparisonof Third Order Design Methods....... 4.4.3.1 Urieli .................. ...... 4,4,3,2 Schock .................... • . ,. 4.4.3,3 Vanderbrug................... 4.4..3,4Finkelstein ........... 4,4.3,5 Lewis ResearchCenter ( e ............ ...
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4.3.14 Iterationto Find EffectiveGas Temperature .......... 4.3....... 14.1 Flow Heat Exchangers ..... . 4.3.14.2 Isotherm_l izer Heat Exchangers ........
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4.3.15 Coi_clusions or_Second Order Design Methods ....... . . . . 4.4 Third Order DesignHethods , ........ ............
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4.4.4 Conclusionson Third Order Design Methods ............. omparisonOf Theory With Experin_n£..................
5" "5.25.3 _'1 MITThe. Allis°n GPu.3Coollng Engine EngineFnglne.......... ......................... , , , , , ........... _......... ..............
152 153
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7. Sample Design Procedure ......... 167 6. Auxilia.7StirllngEngine Design Problems" .................. .-. ............... 366. 7.1 StirlingEngine Design Form --W. R. Martini,October, 1977..... 168 7.2 Sample Design Calculation.......... , ........... . . . 219 248 8. References ........ . ......................... 9.
Directory
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Api_endix A ............................. •
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F!GURES 2-I
Common Process for all Heat Engines .....
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2-3 Example of Closed Cycle Gas TurbineEn,qine ............. 6 2-4 EssentialCharacterof a Stlrling Engine . , , . , ........ 7 2-5 StiflingEngine DeSign Option Block Diagram ............ 8 2-6 Main Types of StirlingEngine Arrangements ............. lO 2-7 RiniaArrangement ...... , , .................. il 2-8 PhilIps Double-ActingSwashplateEngine .............. li 3-I Philips 1-98 Engine on a Test Bench ................. Ig .......... 2-2 Exampleof Internal Combustion Engine ................. 6 3-2 Cross Section Of a Rhombic Drive Engine .... , ......... i9 3-3a Phllips-Ford2-215 Engine Cross Section .......... , . . . . 21 3-3b. Philips-FOrd2,215 Engine Assembled .................... Zi 3-4 Stirling Engine Fuel Econon_,v ...................... 22 • 3-6 3-5 3-7 3-8
Stiriing Emissions............ The 4-g8 Engine PartialDe,cription....
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Engine PerformanceMap for the Ford ........... Pino Packagingof the Ford 4-98 Engine in4-g8 a lg76 t ,
Rear Wheel Drive . -68"Eng ,n; 3-g Packaging ofthe Ford in'a
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V4X35 Engine Air-Fuel ...... , . .... , . 36 Temperatureand Contro 1 .............. .......... 37 Cold StartingSequencefor the United Stiriing ............. 35 Speed and PressureResponsefor the united.S:tirli_g V4X35 Engine .... ............. ....... 39 3-20 Cross Sectionof Double-ActingV8 PlSO"Engine ........... Oeveloping140 KW at 2400 rpm ................ 40 3-17 3-i6 3-19
3-24 3-25 3-26 3-27 3-2B
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Measured GroundSpecificFuel Power Unit for Consumptionfor )learSilentOperation the GPU-3"Eng ine ' ..... : .... 43 42 Measured Engine Horsepowerfor the GPU-3 . ..-..... • . . . 43 Schematicof Single CylinderStirling Ehgine'with Rhombic Drive ................. 48 Schematicof WorkingSpace • : : : : : : : : : : : 49 SchematicShowing Dlm_nslonsNeedecLforCalculating Heat Conductlon ........... . • . • 50 ..........
3-23
PerformanceResults PlSO V4 Engine Module for with PlSO AuxillarleS'o.'f V4 Module _.... 1SO Engine ShowingPresent DeveioI_me.nt Status (UnitedStirling)........... The General Motors GPU-3-2 StirlingElectric
3-29 Schematic Showing Arrangement of'Regener;tor'Cooier Unit Around Cylinder .................... , ......... '.
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FrontWheel Drive.. , . ... , ...... . . .......... 3-i0 united StirllngAppllcationPlan . . ............... 3-11.... United Stirling P-150Engine in a Truck .............. 3-12 Conceptfor United StiflingProductionEngines ............ 3-13 The Urdted StirlingRod Seal ....................... 3-14 United Stirling InvoluteHeate'r............... .... 3-15 United StirlingBurner and Air Preheater
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List of Figures Page 2 3-30 4-1 4-2 4-3
Rhombtc Drive Scllen_ttc , . , , , , . , . , , , ......... Theo_ttcal SttPltng: Ericsson at_dOtto Cycles ......... rt_eorettcel Cycles , , ...... , ............ Simple 5ttrll_9 Engle_ewtttl Annular" Gap Re,qenerator i .......
4-4 •_-5
Effect. of Regenerator EFt'ect_veness on Eff!¢tency ........ 59 EffeCt of Dead Volu_mzo_ worl< per Cycle fat _ Isothermal Spaces ai_d Constaf_t Average Pressu_e ....... Comparison of Adiabatic ae_dIsothermal Hot end'Cold ..... _'......_4 Gas Spaces fop 33_, Dead Voluz_. , ........ 71 Pt_ton Displacer Et_gtz_eN_en_lOtu_e_ ............... 73 Phasing9of Displacer and Powe_'Plstow .............. )_ Flow Otogra_ fo_' Wbrk h_tegr_l Analysis , , , , , , , , ,, , , , 77 I)ual Ptston Engt_e NOi_._cia_,',',_and Assumpttohs fo_' Sa e cse , , ,- .......... o ..... Work D_ag_am t'otDual Plsto_)Sample Cas_.. ,., , , , ,% Engine ExperienceFactor No_nclatu_ ................. 91 IndlcatedEfficlencles .................. 91 O_IculatedIndicatedEfficlehclesi'oC"Optimized-. Phfllps1-98 Engi_w_s................ 9:1
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44 5,t 55 5tl
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4-7 4-8 4-9 4-10 4-II 4-12 4-13 4-14 4-I_ 4-17
GeneralizedRhon_HcDrive at Zero a_Idat Maxt_,,u_ VIILX...... II_ One EIe_i_Lof RinlaArrang_w_nt,, Stlrlln9Englnu Craz_kL1ri ve .... 114 4-1_ _1_ through an infinite Ra,,don,ly St;cke;t ._love;,-ScC'een Matrix, Flow FrictionCliaracterlstlcs, ............ 11,_ 4-19 Gas Flow InsideC1t"cular Tubes with Abrubt ConteactionEntrances .................. . , , , I;TO 4-;]0 Reheat Loss .......................... , , , . 4-_I Gas Fiow Througl_ an l.,._fi_ite Rando_lyStackedWoven$creet_HaLfix, Heat Transfer CharacteHstlcs ........... I.?_; 4-22 $1_uttleConduction . , , ............... 130 4-,3 Tl_et_w11 Coliductlvltl S Of 1'b ble C _itructlon MaterlalsforStirlin)! Engines ................. 4- ;24 Co_ n , _ -Wa1 1 Condu_"_m .......... " i_putatioof Tapered (yll_de_" t_ 4.,_r. l'hi_'d Order'Do.slgnMethods ........ . ...............
I,_ 1-37 14_i
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UP|eli El_gtne Hodol ................. s-1......He t .put Wo 'kO tput
ForAlitso. nD'- TA:
Stlrlin9Ei_giz_e ........ , ....... , ...........15!, InternalEt'i'Iclency Lkltafor Allison PD-I_7A St|l'l-Jng I!Itui_iP , . . 1._i_6 L1imenslo_less Cold Work, Wa_i_Work, and P;_,ssm'_) Ratio {16'_ I(;I rVT " , ,-_, .............................. 5.-.4 .Dlmei_slontess Cold Work, Wa_ W_'k, _d Press_,re Ratio rV1 , l.t_l........................ I{',1 5-2 5-3
5-5
Dh_}_isl_mless Cold Work_ Wai_;W_'k_ ai_dPressure Ra-t!OJ'Vl " 0,9; ...........................
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_. Comparison of Pressure Drop Losses .................
7-1 ......Mass Flow Approximation
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3-1 3-2 3-3 3-4
TABLES Major Innovationsin the 4-215 Engine .................. 22 Other Test Results ............... 23 Phase I FunctionalStatus vs. Objectives ....... , .......... Major T_chnlcaiProblemsEncountered .............. " 25
3-5 3-6
PrOblems EncounteredYet To Be Resolved PerformanceTargets for United Stifling r d c p
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3-8 3-7 4-1
Test Points for GPU-3 .......... 47_._ GPU-3-2 Dimensions .andParameters.. ............. 45 Effect ofEngine Adiabatic Spaces'on a Di;crete .Stir]ing Cycle with Dead-Volume .............. 69 ........ 4-2 IndicatedEfficienciesof a i-68'Rhombic'Drive PhllIps Engine ....... 92 4-3 B_ake (Shaft)Efficienclesfor a l'-g8-1_homblc Dr(ve ...... PhlllpsEngine Optlmized-forEach OperatingPoint , , 94 4-4 _ MaximumBrake Efficlenciesfor VariousStirling Engines . . [ _.i .95 4-5 Maximum Brake Efficienciesfor Three Stirling Engines . . . 96 ' 4-6 MaximumNet Brake Efficienciesfor VariousStirlingEnGines.... 98 4-7 4-8 4-g 4-I0 4-11
5-2
viscosit_f WorkingGases. mass/cm sRc a.t_PAV.G = TO.MPa ..... Heat Capacitiesfor Workingg Gases, j/g_K ......... Flow.Diagramfor Work Integral.Analysis............. Coefficientfor Shuttle Heat ConductionEquation ....... . . TypicalTemperatureWave Length,LT, at Room TemperatureCondition .................. ... Breakdownof Losses and Pffwers. for the Allison'Model PD-67A Enginew_th I18_ Phase..Angle............. • Summaryof RioS's Data (69 ar) ...................
5-3 5-4 5-5
PressureDrop ......................... LERC GPU ModelLoss Predictions , , ..... , Coinputed Performafice i_orGPU,3 Test Points
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(Martirii, 2nd Order) ......... P n ....... Engine CalculationsUsing An Analytical/_proximat(o of the EffectiveMass Flow Rate (A) and a Numerical ApproxiniatiOn (N) ............... 8-I. StiflingEngine ReferencesOrganized'byYear'of Publication ................. 8-2 PersonalAuthor index to Refer_.hces ............... 8-3:.._CorporateAuthor Index .................. , ....
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B-4....Paper Classlfication of StlrlingEngine References " Su"j" b ec" t ...... 8-5 NumbersRelatedto Each StirlingEngine
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Classification.......................................
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l. SUM_IARY
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hlterestin tileapplicatlo,of Stiflingem.lit_es to serve a varietyof pokier produclnqneeds has i.creasedconsldevably ' • over the past severalyears, lhis interesthas been gev_eratcd principallyby the potentialsfor hi,:th efficie.cy and low emissionsofferedby the Stirlingengine coupledwith its i.herev_t quietnessand capabilityto ope-rate with a varietyof fuels or using a variety of heat;sources.
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The DOE Office of Conserw_tio.,Divisionof Tra,_sportation Ener_v Co_servation, has establisheda nut,_erof broad programsaiti_ed at reducinghigh_Yay vehicle
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fuelsuch consumption. The DOE StirlingEngine High,my Programis one peo.qram.This program is directedat the Vehlc!eSystems develop_}_nt of the Stirlin9 engi.e as a possiblealte_ative to the spark-ignitionengine. Project _lallagetl_tlt responsibilityfor this ptR
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Office, was pv'ovided by__ g_rantfrom the Lewis ResearchCenter Stirlin9 Engine Project For Stirlin.q enqlt_esto enjoy widespreadapplicationand acceptance .notonl.v must the fundat_vental operationof such engines be widely understood,but the
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requisiteanalytic formust the simulation,, .design,ew_luationa.d optimization of Stirli,.q engi.e tools harchvare be readilyavailable. At the presentti_, the
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t_msthighly developed-andverifiedanalyticp_grams are proprietaryto-specific corporati.ons .....
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The purposeof this design t_nual is to providean introductionto stirlim!cycle ! '_ heat et_gines,to organizeat_didentify the availableStiflinge.gine literatu,_e.. ............ i..._ and to identify,organize,evaluate and, in so far as possible,comparenon--I _,_ pvx)prletary Stiflingengine design n_thedologies, As such. the inanual then _. represet_ts a first step in the ,longpvx_cessof making availablece_orehe_isive,... _ ,
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The basic principlesof heat em.li.es at_eexplained.... A Stirlingem]ii_eis defi.ed as a heat e,gine tliat,_ovesa body of gas around i. such a way as t,ocempv_.ss the gas principallyin the cold part of the e.gine and expahd it priv_cipally i. the liotpart of the engi.e. _lleatis supplieda.d re,_vedthro.qhtl}e walls of • . . the et_glno, In ItltroducIiii.!Stirlln_.! etl_,lltle$_tile variety
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of
Stil'ling
eil_,litle t.vpes atld theil"
utilityit}compariso,to other machines at_ discussed, tlsetulStirlim]cmlines are or cat,be built from an output of a.fe_ watts to a ,_.gawatt., Pokierdensity -- is usually as hlgllas a diesel engit_eand can approacha 9asoli.ea,tomobile engi,e. Efficiencles30%higher t.hat_ an aoto_bile engine aix,p|x
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The theory of Stirlingengine is presentedstarting from simple cycle analysis. Importantconclusionsfrom cycle analysisare: I) Comparedto an engine with zero unsweptgas volun_ (deadvo!un_)., the power availablefrom an engine with .... dead volun_ is reducedproportionalto the ratio of t)',e dead volunw_to the maximumgas volul_,and 2) At the usual dead volun_ ratios of greater than 50.,'; used in Stiflingengines the error in computingthe work per cycle using _ne easy to compute isothermalspaces insteadof the more realisticbut more difficult to computeadiabaticspacE, s is -Ito .2%.
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Engine design n_thodsare organizedas first order, second order and third order
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with increasedorder nunber indicating_increased complexity..
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First order design l_thods empl.oythe classicalSchmidtequation and ape principally useful in preliminary.systems studiesto.evaluate how well-optimizedengines
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may performin a given heat engine application.. Secondorder design n_thodsalso utilizethe Schmidtequation,but, in addition, incorporateengine loss relationshipsthat apply generallyfor the fuil engine cycle. This n_thod assunes that the different rprocessesgoing on .it, the engine interactvery little. The author'ssecond order _thods are given for.. several_ differenttypes of Stirlingengines, These n_thods ape presentedin detailby usingwork sheets that.need only be filled out for the.specificca_e. One sample _roblem i.Rpresented_usingtheseworJcsheets. The literatureor_third order nw_thodsis quite extensive..This n_thod solves the equationsexpressingthe conservationof energy, mass and mon_ntum using nunw_rical n_thods, The engine is divided into many nodes and short ti_ steps are requiredfor a stable solution, So,_ thirdorder methodsassun_ that at each instantin time the pressure is unifonlh This assumptiongreatly reduces computationti_. If press_re is not assun_dunifonlhthen the.tin_ step can be no longer than the tin_ it takes for sound to travel from one node to the next. Third order design n_thodscompute the engine perfon_lance with much fewer assumptionsbut require thousandsof tin_s longer, computationtin_. Both second and third order m_thodsmust be validatedby ag_en_nt with n_asut-ement of the perfo_nce of an actual engine. The developnmntand .testingprograms for engines g_ater than a few horsepower ate sunm_arized.Curpentenginesby Philips,Ford and LlnitedStirlingar_ described, A I0 year old engine, the GPU-3 built,by.GeneralMotors for the U.S. AridLY andnow under test at NASA.-Lewi_, is describedin enough detail so that predictionscan be made about its indicatedpower output and-efficiency,
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All the literaturenow availablethat comparesengine n_asurementswith calculated perfon_nce is presented. Qvale gives a partialdescriptionof a Stirlingengine built by Alli.son and claims good agreen_nt. Rios built and fully describeda Stirlingcooli,gmach.ineand shows that his computationn_thod agreeswith his li_asur_,ents-. The performanceof [l_eGPU-3 engine p_sently under test at NASA-Lewiswas to have been ppesentedfor.certainag_ed upon test points. Unfortunately,ti,edata a_ as yet unavailable, The predictionsof the indicated output power and efficiencyhave been made for these testl_ointsusing both the second order analysisof Martiniand thethird order analysisof NASA-Lewisand are p_sented and compa_d.
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The tasks undertakenin this grant proved larger than anticipated. The original objectiveof identifyingand organizingall availableinformationon Stirling engines has been met, Over 800 publiclyavailablereferenceson Stirlingengines are-givenaccordingto year of publication,personalauthor, corporateauthor and subject..However,a thoroughevaluationof all availableanalysismethods could not be accomplishedwithin the allottedresources. Nevertheless,it is felt that there is benefit to be gained by making availablethe progressto date. At _his point, most of the design methods that are describedin the literature in enough dete.ilso that others may use them are given in this manual so tilat the r_ader can use them. All of the simple methods are given. For these methods to be of kuown utility,they must be comparedwith reliable, engine test data over a range of operatingconditions. This comparisonhas not been done because the data are not availableat this time. Such data are being generatedat at least two governmentlaboratories. Futuresupport, if forthcomingwill enable incorporationof such data, completionof the design methodsevaluationprocess and productionof a more comprehensivedesign manual.
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2. INTRODUCTION 2.1
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Why Should Anybody Be Interested
In Stir.ling
Engines?
1
For many years during the last century, Stirling engines occupied a.. ....... relatively unimportant role among the kinds of_ngines used during that period. They were generally called air engines and were characterized by
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high reliability and safety, but.low specific power. They lost out in the dollars-per-horsepower race with other competingmachines. In the 1930's some researchers employed by the Philips Company, in Holland, recognized some.possibilities.in this old engine,providedmodern engineeringtechniques could be applied.. Since then, this company has invested millions of dollars
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and has created a very commandingposition St_rl.ing engine technology. Their developmentshave lead to smooth_andin quiet-running demonstration
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engineswhich.havevery high efficiencyand can use any source of heat. They may be used for vehicle.propulsion to producea zero.or low level of pollution. A great.variety of experimental Stirling engines have been. --built from the same general principles to directly pump blood, generate
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electYicity, or directly generate hydraulic..power.. Many.are used as heat pumps and some can be used as both heat pumps and heat engines depending upon the adjustment. With a.few.notableexceptionsof independentindividuals " who have done very good work, most of the work on StiFlingengines has been done by teams of engineersfunded by the giant companiesof the world• Thevital detailsof this work are generallynot available• The United States governmentis beginningto sponsorthe developmentof an open technology on Stirlingenginesand is beginningto.spend large sums of money in this area, DOEcontractedwith the Ford Motor Company to spend 160 million dollars over the next 8 years to bring about a commercialStirling engine (77 ap)*• DOE will supply llO million of this sum. About 4 million dollarswill be
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conventionalengine gas mileage can be.obtainedwith the Ford-PhiiipsStirling engine. DOE has announcedthat a second team composedof Mechanical spent in Also the firstyear-to, better,assure both parties that 30% better than. TechnologyIncorpOrated,Latham,New York; United Stirlingof Malmo, Sweden, and American Motors will be negotiatedwith to help "establishthe development base of component,subsystemand system deSigns., fabricationtechnoiogy test experienceand assessmentof cost and market ability necessaryto support a decisionby 1984 by the U.S. automobile_.ndustry t? establisha production engineeringprogram ,or the $tirlingengine- (77 a_), Since for many engineers
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interestmust followmoney, now for the first time-a reason for beginning, to become familiarwith the interestingand varied propertiesof this class of thermalmachinesexists for a-much larger group of engineers.
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Like any.heatengine, the Stirlingengine goes throughthe four basic processesof compression,_heating, expansion,andcooiing (See Figure 2-I). A couple of examples from every day life may make this clearer. For instance, Figure 2-2 shows how an automobileinternalcombustionengineworks. In this engine a gas-airmixture is compressedusing work stored in tI_emechanical
_'
flywheelfrom a previouscycle. Then the gas mixture is heated it and allowinqit to burn• The higherpressure gas mixture nowby isigniting expanded * See referencesin Section.8 --
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Figure 2-I. ComnlonProcessfor all Heat Engines. l
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whichdoes more work than was requiredfor the compressionand results in net work output. In this particularengine, the gas mixture is cooledvery little. Nevertheless,the exhaust is discardedand a cool gas mixture is.
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brought-inthroughthe carburetor_ Anotherexample of the generalproces_ shown in Figure 2-1 iS the closed cycle gas turbineengine (See Figure 2-3). The working gas is compressed, then.itpasses througha steady-flowregenerativeheat exchangerto exchange heat with the hot expandedgases. More heat is added in the gas heater. The
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by the compressorand createsnet work. To complete the cycle, the expanded gas is cooled first by the steadyflow regenerativeheat exchangerand then hot is expandedwhich generate_more energy than is required the compressedgas additionalcooling to_the heat.sink.
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. In the first example (Figure2-2), the_Processesoccur essentially_ in oneplace, one after the other in time, In the second example (Figur=2.-3), these four processesall occur simultaneouslyin differentparts of the.machine. In the Stirling_acliine,the processesoccur sequentiallybut partiallyoverlappingin time. Also the processesoccur in differentparts of the machine but the boundariesare blurred. One of the problemswhich has delayed the realizationof the potentialof this kind of thermalmachine is the difficulty in calculatingwith any real degree of confidencethe complex processesWhich go on inside of a practicalStl_lingengine. The _uthor has the assignment to presentas much help on this subjectas is presentlyfreely available,
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Q VOLUME.
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Essential Character nf a Stlrlinq Engine. i
A heat enoihe is a Stlriing engine for the purpos.eof this book wl_en: I.
The working fluid is contained in one body at nearly a coi1_non pressure at each -lhstantdueing the cycle.
2.- -The working fluld is manipulated so that it is genet'ally conipressedin tliecolder portion of the engine and expanded generally in tliehot portion of Uie engine. 3.
Tralisferof the compf-essedgas from the cold tc the hot portion of tliOengine Is dogie.bymanipulating the.fluld boundaries without valves or real pumps. Transfer of the expanded hot gas back-to the cold portlon--ofthe engine is done the same way.
4.
A reversing flow regenerator (regenerative heat exchanger) may be-used to increase efficle_}cy.
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compressedin the cold space, transferredas a compressedfluid into the.hot spacewhere it is expandedagain, and then transferredback again to the cold. space. Net work is generatedduring each cycle equal to.the area of the enclosedCurve. 2.3 Major Types Of Stirling Engines
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In this publicationthe author would like to considerthe classification of Stirlingenginesfrom a more basic standpoint. Figure 2-5 shows the.various
. -
The generalprocessshown in .Figure2-I converts heat into mechanical energy. The reverse of this processcan take place in which mechanicalenergy is convertedinto heata pumping, Figure 2-4shows ger_eralized Stirlingengine machine as describedabove. That is, a.hot and.a coldgas space is connectedby a gas heater and cooler-and regenerator. As the process proceeds to producepower, the working fluid is
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emerges. First SO,hetype of external heat sourcemust be determined, Heat must then be transferredthrougha into a working fluid. There must be design.area-_ that..must beaddressedsolid before a particularkindof Stifling engine -.-a means of transportingthis gas between the hot and cold portionofthe engine and of compressingand expanding, it. A regeneratoris needed to improve workinggas from the environment. Expansionand the-gascreates efficiency, net indicatedpowerwhich Power control must is obviouslyneeded be transformedby ascompressionof some are type seals, of tolinkage separatethe to create
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useful sink. power. Also the waste heat from the engine must be rejectedto a suitable
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A wide varietyof"Stirli,gengineshave been manufactured. These old engines _,., "::: are describedvery well by Finkelstein(59 c) and W_lker (73 j). Usually these .::_ "-
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involvethree basic typesof Stirli,_g en,i,les,(l,le, the alpha type, u._estwo pistons (See.Figure 2-4 and 2-6), These pistonsmutually co{npress the workin_.I gas in the cold space, move it to the hot spacewhere it is expandedalldtheli
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the hot and cold gas. spaces. Tile other two arrangements use a piston and "_ """1 ' displacer, Tile pistoh does the compressingand expanding,and the displacer ."._. does tilegas transferf}"o_1 hot to cold space, The displacerm'ran(.lement with ............ !_T:;,_ the displacerand the power piston in line is called the l_eta-arranqe_)_,nt., :i ,
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and tl_episton offset from the displacer,to allewa s_mplm,_:,,chanical.. arrange_1_ent, is called tile.qan__a-arrangement, llowever these arranqements concent:rate on only one of !:hevital design clioices which face a creative designerof Stirlingengines. The.otherdesign choices under tilecateqories sl_ownin Figure 2-5 will now be enuu_erat_d to indicatetl_ebreadthof possible
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Stiflingengines.
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2,3,1 Heat Sources i !
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Since heat is supplied to the outside.ofthe Stiflingengine, _k_n¥kinds of heat sourcescan be incorporated. Almost all work so far.has been t.m_ard the developmentof a liquid fuel burner which requiresan air pre-heater:to work effectively. Virtuallyallytype of liquid-fuelcan be used. Som(_wm'k .....is now being start, ed using solid fuel burnerswhich are mostly fluidi;:ed bed coal burningexperin_ntsin which a heat pipe transportsthe heat trom the
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burningcoal to the engine (76 f). For underseaapplicationa system h,_sbeen developedto react-lit:hi_m with SI:6and transportheat to tlieengim, with a
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energy storageunits coupledwith Stiflingenginesmight,be better for electric
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vehicles, than even the most advanced type oi'electrochemical b,ltteries coupled with electricmotors (76..c).Relatiw, ly snlall mirrorsor lenses t'ecuslng on -
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a smal.l-Stlrling engine.arebeln(:l consideredas potentialpower sourcesfro"the ! future (77 ac), Tlieconclusionhere is.that there are manyways of usin(,l ;, Stlrlingengineswith less co_l_ton heat sourceswhich haw_,definite possibiliti_'_ : for tllefuture.
'
2.3.2 Solid-(,as
E
The technologyof how to add and.remove hl_atfrom the wm'kin!lfluid in the Stiflingeraline is tilemost crucialof the entire Stirlihq l, ilqil}e desiqn. There are two essentialreasons for t_'ansfe_'i"ing lieatint, o and out of tlieqos. The first is to supply the heat-ofexpansioil (heater)and remove-tl_e hL,_li, of cenll;re_. s.ton (cooler). The second is to supply ahd remove the sensible heat ,l:: the working fluid osci_latesbetween tliehot and cold part:of the engine (regenerator). It is qulte.-cleai' f|'oii_ l.iqure 2-3 that the closed cycle _!asturbine(l_rayton Cycle) also-sharesthese essentialreguirements, lor both the lh'aytonCycle as well as the StlrllngCycle e.ilgilie frictiohallosseslllust hi'lllin|illi_:t,d, llowew, r, in tileBraytonCycle making t:lie heat Oxcllan,qet_slaf'geto reduce frictionhas no effect on the capacityof tilt' comF:'esso_'-OXl_,mder-, Ilowever., the.price that the
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Stirling
em.ltne pays for nl_t having t.e have the cost and proble_l_s of clx_llq'essm's needed ill tile Brayton Cycle is the Ilt_vessity of kl'el)tllg ttle undisplaced or dead volunw_to a-mtnlmu_li.for the h_iat exchangers and assoc-i,lteJ
..............and expanders
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Heat Transfer
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R_
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= = = = =
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6 ALPHA-TYPE HEATER REGENERATOR COOLER EXPANSIONSPACE COMPRESSIONSPACE
BETA-TYPE
GAMMA-TYPE
Figure 2-6. Main Types of Stirling EngineArrangements...... i
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ducts. Typicallyhalf of the engine volume is in the heat exchangersand ducts and this reducesthe power output to about haLf of what it theoretically_ could be with-no3ead volume. A number of earlyair engines (59 c) used a positivedisplacementcompressor and expander. In these, dead volumewas no problem but valvingwas. The Valved hot gas engine at MIT (72 ar, 73 ay, 75 bf) is being used_toinvestigatethis alternativewith modern.engineering, Typicallyin a Stiflingenginethe working fluid passes,as it goes from the cold space to the hot space, first, througha gas cooler made of many parallel small diatneter tubes with the gas insidethe tubes (See Figure _-6), Second, througha regeneratormade of stacked finemesh screens,and third, througha tubulargas heater like the cooler; Combining the heat exchangerswith the variablevolume spaces is theoreticallya good way to greatlyreduCe dead volume. This is an old idea (1854b) but has recentlyreceivedrehewedattentionunde_ the name thermalizers(73 p) or isothermalizers(77 h).. One of the chief design challengesis to build efficient,low dead volume heat exchangersat a reasonable cost. Very high gas pressures-are-used becausepower density is proportional to averagegas pressure. Losses increaseonly slowly with gas pressure. High qualityceramicsare being consideredbecausehigher temperatureand niore complicatedshapesmight become economiccompared to brazed,super-alloytubular h_at exchangers. Higher temperaturealso greatly increasespower densityand ....... 2.3.3. Gas Transportand Power Take-Off (S_ Stirlingengine gas transportis always positivedisplacementof some sort. Pistonsare the usual The engine the most attentionis |
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Figure 2-8.
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Phtltps Double-Acting Swashplate Engine.
combination of 4, 2p_ston machines. Itowew_r, since each piston is double acting, .... ohly four pistonsare needed to implementthe cycle. This is called t.ho.-Rini_ arrangen_i_t (See Figul-e2-7)(46d). Power take-offcan be with a swashplate (See Figure 2-8)(69f) or with a conve|}tional crank ,indcross head-(69 f) or with a hypocycloidcrank (76 c). Piston seals,c_nnotbe oi'Ilubricatedsin_e tlie. oil will foul the heat excha_gersquickly. Filled-Teflonpist._nl'Ingsare usuallyused, The volume of gas insidethe St, irling engine is very sma|l so that any leakagegreatly.reducespower. Speciallydesignedmech_micalseals m' II
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.... reinforcedr(}llsock seals ar.ealso.a possibility(76 c), _.uthave not received much testing.• In some low power systems,leakage,sliding frictionand mechanical.w_ar byalmost using diaphrams (75 l) or bellows -,t i ' oil backed roll have sock been-eliminated seals are used to eliminateleakage. Fabric (71 ao) l( insteadof pistons. Finally,the free suri_ace of a water column has been used ;i to el.iminate leakageand friction. ii'!'''l -if! 1 as a power piston in somelower experimental water pumps (76 k)and heat pumps (75 g) -<'!iiIii!J Rotaryand shaft seals have been eliminated.fora number of developments, =_:_!il!!!Water pumping (71 g,.7l ap) oil pumping (77 x) and electric power output using pumping (77 a, 77 bn, 73 b)are°.nowbeing developed
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In .thewater, gas alldheat punlping cases, pressurechange may and be due only _Li!ii_i a linearelectric.generator.C75 n, 74 f), and gas pumping C76 al)., heat to the transportof gas _rom the co_d to the hot side of the displacer. If it -_<."_,_ pumps gas or liquid it is called,a thermocol_pressor (69 x). This is equivalent _i:-!:>iii) to an internalcombustionengine,withoutcompressionbefore ignitionof the gas mixture. Power is low but it is attractivebecauseof its simplicity. If
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_:]!!_'! pressuresurges are createdby.a singledisplaceroperatingbetweena hot and a warmpatented zone, then a Vuilleumiercycle cooler isrealized. This type of machine was by Rudolf Vuilleumier(18 a)-and has recentlyreceiveda lot of goverm_entdevelopmentto produce.reliablecoolers for infraredsensorswhich i must operate in the-20 K range.
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by an electricmotor (76 __, and by a crank and flywheeldriven by adisplacer _ drive,piston (74 n). A plug-in-orificedrive for the displacerhas also been demonstrated(70 v). Latchingelectric solenoidscan.be made efficientand These displacer-onlytype machine, s have.beenoperatedwith a crank driven springshave been evaluatedfor this purpose...
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All the displacer-onlymachines have their counterpcrtin a machinewith a ....... could power piston. be also used For instance,if for the purposeof the liquid driving orgas the pun_p displacer. has some Also, inertiaadded,.. overcenter theftthe mass-spring-damper system can be designedwith a resonantfrequency efficientlyattainableby the Stiriing e_gine displacer. A much larger displacemenl_wouldthen be PoSsiblefor the same amount of gas processedby the displacer and regenerator. Therefore,more powerwould be generatedwithout increasing losses, An .oilpumper using a metallic inertiameii_ber and a bellows-seaied drive piston has been demonstratedto be self starting.(77 x),. Heat pumping using a flu__ f__f__yl wheel between two beta type Stirl-ing engines is under development (77 h). Finally,displacer-piston machinescan act as thermallypoweredmechanical amplifiers. A small amount ol_ power moving the displacercan controla large amount of power at l:hepower piston. This could create a push or pull. In a multipistonengine a very even torque and a speedexactlymatching the excitation. frequencywould be realized.
............ 2,3.4. Power Control The Stirlingenginesof the last centurywere controlledby heat inputand by a hand operatedwrit valve-(Sgc). Heat was appliedthrough burnim3wood 12
or coal, usually. When hot the engine was turned over once by hand and started. Water pumpingwas usually the task, so rapid controlwas not required. Modern enginesare being used to gelterate electricityor operate vehicles. In both cases higIilyresponsivespeed control is needed. The standardmethodhas been to rapidlyadd or remow: working fluid (71 i). Other ,_thods have been consideredlike varying tilestroIceof the-powerpistons (possiblein the Philips swashplateengine (74 c)). Temporarilyconnectingthe working gas space to tile buffer space during a controlledpart of each stroke also is shown to control powee (73 v). Chanqinqthe pI1aseanqle between the piston and displacerduring Operationhas been den_nstrated(76 c), With this type of power control one .can change during operationfrom positive torque to negative torque for regenerative braking and heat reclamation. For"maximumefficiencyat.a particularspeed and torque requireiilenlz one can arrange to change the stroke of the displacerat _.90° phase angle (76 c). It is also tI1eor_tically, possibleto do the same thii_g with a Rinia swasIiplate macIHne by tiltingthe swashplateover center, In a displacer-powerpiston lhachine(Bet_or Ganglia type) the displacer requiresonly a small fractionof the engine power output. Up.until now.we have talked about obtainingthis power by mechanical, linkage_rom the power piston througha crank mecIia_iism which may be fixed or variable in phase angle and stroke. Englheshave been built in which the displa{:er is driven by part of the prJessure-volu,_ energy generatedby the engine but applied to the displacerdr'_ve, piston insteadof the power piston (72 j). Some of these engines_re controilableby spoilinq througha _valvepart of the energy applied to the displacerdrive piston (77 x). Di:;placerscan be driven.byelectric,pneumaticor hydraulicn_ans_entir._ly independentof what happensat-the power piston. A class of thermallypov_ere,! actuatorscould be created. Also speed controlledengines analag(_us to asynchronouselectric,_tor could be dcveloped. That is, the engin_ _ould _ct. as a lleatengine or as a heat.pump dependingon whether-theengi.neis d,_ving tlieload or the load is driving the engine at the excitationfrequencj. One can conclude that there are many usefulways of controlli_xg. Stifling engines some of which may be cheaperor _re .energyefficienttllatthose now considoted.standard.
.3.5
at_.StD.n t.t
Coniparedto interi_al combustionengines,Stirlihgengines rr,,luire a larger radiator, Comparedto a Diesel engine, three times,_)reheat must be dissipated....... .tlirough the radiator (75 w). A specialt!_ihcorrugatedradiatorhas been developedto allow a more powerful radiatorto be installedin the same voiu_w_ (74 c). Tllestandard,_thod is a pumped coolant loop and a heat exchangerto. the air.. Not much has been done with heat pipes,•boilingcondensingsystel_s oi-fins. Possibly the cold space can be shaped,wi_h a large surfacearea .so tllat-direct cooling to the air through fins is a possibility, In the lieatsink area one differencebetween interi_(_l combustionmachii_es and .Stlrllng enginesshould not be overlooked. In an internalcombustionehg_ne the engine has to•be kept warm to work well, In a Stlrlingengine the coldP_" tlleheat sink the better tlieengine works. Anotherbig advantageof a Sti,,'.ling engin6 is that it can operateover ti_eenti_ availabletemperaturedifference providingmaterialsof constructioncan be found. Nol_odyhas seriouslylooked at enginesdesighed to operatebetween ?,DO0 C _nd-amb_e_ttemperature.
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2.3,6 WorkiI_Gas
,,_
Aln_st all the ea_'lyStlrlin.q enginesused air at a minimum pressure of one atn_)sphere (59 c), As early as 1827 engines built by the Stirlingbrothers used pressurizedal_ .(59c), but tileideadid not.catch on, The first _nglnes built by Philips used pressurizedair ,froma built,inair compresser(46 a). An analysisof all possiblegases will show that hydrogen and helium are much better tlianany other gas. Hydrogen is best because it has tilehighestthermal conductivity,the.lowestviscos-ity and a low heat capacity, on a volun_ basis, Caly a small anx)untof heat is needed to.-change its temperature, However, hydrogenpe_ates throughn_tals,and no containeris completelyimpern_able, Hydrogenis also flammable, but the anw)untof gas employedis quite small, Also sonw_nw_taisare embrlttledby i_ydrogen,On tileother hand, helium is inert and can be permanentlycontainedin _l_ta.l,. It h_s an even lower volun_trlc heat:capacitythan hydrogenand ali_st.asgood a thermalconductivity,but the viscosityis twice that of hydrogen, Micliels(76 e) showed that a Stirling
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engine can be designedto.use either hydrogen,helium orheater,cooler nitrogen all with salneefficiencyfor the sa_l_temperature, However,the and tile regeneratorof-eachenqine would be designed quite differently, Helium and. hydrogencan attain the san_ power density, However,an engine designedto run .-. with hydrogenwill run poorly with helium, Hydrogenhas a broader range of higll efficiencyoperationthan does helium, A Stirlingengine runningon nitrogen or air appearsto be limitedto 20 to 25_ of the power of a helium or hydrogen filled engine of tilesan_ displacen_nt(76 e), ....... Dissociablegases like nitric oxide (67 h) have been proposedbut there seems to have been no appreciationof the need for good heat transferproperties, Liquidslike-waterhave been used (31 a), Water-hydro_qen has also been proposed . for use in a Stirlinqenqine (74 ao),. The additionof water to the gas improves the power density. However,tilewater vaporizesat a.high temperatureand condensesat a low temperature, Little regenerationis possiblefor-thewater componentof tileworking fluid, However,at n_derateheat source temperatures, the simple Rankinecycle has a good efficienc,y comparedto the maximum.possible, Much n_re heat must be transferredthrough., about the sag_earea and thicknessof gas film, A better solution} probably is to eliminatethe permanentgas entirely to attain higllrates of heat transfer. A successfuldisplacer-powerpiston typeStirllnqenqine uslnq qas-free_ater-steamwas demonstratedin the-artificial heart program (.76bc) "
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_.._
"-"_'_
2.4 Presentand Future ApplicationAreas
_,
At tilepresent,the only Stirlinqengines that can be purcllased on the open market deil_onstrate tl_eprinclplebut do not denK)nstrate the power densityand efficiencypossiblewltl_n_dern technology, However,tilefollowingare considea_ed
i_'_ .;',' ::_,
to be the future applicationareas,
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2.4.i Silei]tElectricPower
[
ll tilelaboratorythe applicationthat has receivedthe eal'llestattention by PMIIIps (47 b) is tilecouplingof a Stirlingengine to an electric generator to achievea near silent electric power source, It appearsthat an engine made. by FFV of Sweden will be i_k_rketed ill .I97gin tileLlnitedStates Just_for that 14
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purpose. StirlingPower Systemsowned by ThetfordCorp., Ann Arbor, Michigan, and FFV will be the marketingorganization. Presentsmall portable generators are unreliableand noisy. A premiumpriced Stirlingengine machine may enjt)y a good market among owners of yachts and large self-containedmotor homes. Relativelysmall solar heated electricgenerators, are being studiedwith the idea of demonsLratingtheir usefulnesson a small scale (77"ac). 2.4.2 ReliableElectricPower Super-reliablethermo-mechanicalgeneratorsusinga diaphram5tirling engine and an oscillatinge]ectric_alternator are beginningto supplant thermoelectricgeneratorsin remote power source applications(77 t, 75 z). DOE is sponsoringtwo differentdevelopmentsfor isotopepoweredelectric power generationin remote locations. One uses the PhilipsStiflingengine _. (71 aj, 76 j).. The other uses a free-pistonengine and linear electric generator(76 az, 77 m). It appearsquite certainthat s.uper_reliable types of Stirlingengines and electricgeneratorswill take the-placeof flameheated or radioi_otopeheated thermoelectricgeneratorsbecausethey will be both cheaper to build and much more efficientand thereforecheaperto operateand have been demonstratedto be more durablewith no degradationin efficiencythat is always experienced with thermoelectricgenerators(77 t). 2.4.3 Motor Vehicle Power Applicationof the Stirlingengine to motor vehicleshas to date received the most attention. A number of demonstrationvehicleshave been built and are in the processof being tested (77 am, 77 i, 77 aq). A Stirlingengine is probablya better engine for automobilesand trucks as far as noise, performance and fuel economy is concerned. But, can the cost of the Stirlingengine be .. reducedsufficientlyto allow a saleableproduct to be offeredat the auto showroomfloor? As explainedin Section2_I, Ford Motor Co., Phil.ips, MTI, United Stl_lingand An_ricanMotors are__nvolvedin development.ofthe Stir'_ing engine for motor vehicles. A nunber of studiesand proposalshaveshown that stored thermalenergy coupledto a Stirlingengine makes reasonablesense for vehiclepropul.sion (76 c, 74 c, 77 y). Using performancenumbersfrom the 1975 and 1976 IECEC Records,theauthor performeda preliminarystudy of how a future propulsion system using thermalenergy storageand a controlledStirlingengine_ould comparewith future battery-electric motor propulsio_systems. The tablebelow, shows the results. P_opulslon System
ProjectedBOO C LiF ThermalEnergy Storage + ControlledSti.rling Engine
_)_
] Calculated SpecificEnergy WHR(m)/Kgof System at 20 W(m)/Kg System
l)O
Calculated Efficiency WHRun)de_!ivered WHR(e)s_pplied
0,35 to 0.45
t5
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System Propulsion
_ ' •
1
_
SpecificEnergy WHR(m)/Kgof Systeln Calculated at 20 W(m)/KgSystem
Projected500 C Lithium-
Efficiency WHR(m)delivered Calculated _[4R(eYsup'plied 0.46
. i _
Controls+ ElectricMotor Iron SulfideBattery+ ProjectedZinc-Nickel
50
I;
Oxide Battery+ Controls+
30
0.38.,.
, _:!_,I_.
ElectricMotor TractionBattery+ I0 0.26 : _" Controls+ Electric .... Motor i'i;, CurrentLead Acid il The Stirlingsystem is expected to,be lighterand about as efficientas the • !'_ advanced batterypropulsion-systems°In add,ition, if a.practicalway of •i_ rapidlytransferringheat into the thermalstorage can be developed, then
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energy.Cheapers°urces solarcould be employed. of heat from burning..coal orwood or fronlconcentrating noise, reasonablepower densityand to the low heat A Stiflingengine should be goodthe.higherperformancedue for si_ipand boat propulsion. Tlle _ow sink temperatureand especiallyits reliabilityshould all be advan.tages to outweighthe probablehigher cost. A good, reliableStirlingengine outboard
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should-sellvery well. 2 4 4 Heat PumpingPower
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Stirlingengines in reverse,heat pumps, have enjoyed a good market in the cryogenicindustryto produce...liquified gases.andto-cool infrared sensorsand the like (77 ax). Stirlingengines have also been tested to take the place of the electric
i ! _: I •
motor in a commonRankinecycle heat pump for air conditioning(77 ad). One free-plstonengine•pump is being developedfor this purpose (77 w), Engine driven heat pumps have the advantageof heatingthe buildingwith both the _ waste heat from the engine and the productof the heat pump (77 j). Also being __ consideredand undergoingpreliminarytestingare Stirlingheat engine heat umps. These could be two conventionalStirlingenginesconnected together 73 x) or free-pistonmachineswhich eliminatemuch of the machlneryand the .... seals (69 h). Using machines of this•type it appears possible that the primary_ fuel needed to heat out"buildingscan be greatlyreduced, to less than 25,1, of _'_ that Row being used (77 h). With this type of incentiveStirlingengines for house heatingand coolingmay be very big in the future, j
16
.........
-_' " .
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....
' 4
2.4.5 BiomedicalPower MiniatureStirlingenginesare now being developedto power an artificial heart (72.ak). Indeed this engine appearsuniquelysuited for this application since it is very reliableand can be made efficientin small sizes. One engine
,
....
•
I
of this size has run continuouslyfor 3.25 years and is still going (77 x). Once the blood pump compatibilitywith the body is improvedto the order of years fromthe present six months then this applicationarea will open up. Between the tens to hundredsof horsepowerrequiredfor automobilesand the few watts requiredfor artificialheartsmay be many other applications. For instance,poweredwheel chairs now use a cumbersomelead-acidbatter%and controlbox betweenthe wheels and an electricmotor belt driving each large wheel. With a Stirling engine and thermalenergy storage the same performance might be obtained,using a TES-Stirlingengine, belt drivingeach wheel with the speed controlledelectrically. The large batterybox and controlscould be dispensedwith and_the chair could become truly portableby being collapsible like an unpoweredwheel chair. There may be many specializedapplications like this.
:I _, i:
._
2.4.6.... CentralStation Power
._ •
•
Many people have asked if Stirlingenginesare useful in the field of centralstationelectric _ower. Very little has been publishedattemptingto answer this question (68 k). R. J. Meijer (77 bc) calculatesthat Stirling enginescan be made up-to a capacit¥of 3,000 HP/cylinderand 500 HP/cylinder Stirlingengineshave been checkedexperimentallyusing part engine experiments (77 bc). Many simple but efficientmachines could be used to convert heat to say hydraulicpower. Then one large hydraulicmotor and electric generator could producethe power, in the fieldof advancedelectric power generation it should be emphasizedthat the Stiflingengine can operatemost efficiently over the entire temperaturerange availableand could supplantmany more complicatedschemes fer increasingthe efficiencyof electricpower generation. 2.4.7 Power For Other Uses?
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Who is to say whether the above llst of uses is complete. As these machinescome inte use and many people become involvedin perfectingthem for their own purposes,many presentlyunforseenuses may develop. A silent airplaneengine may even be possiblefor small airplanes. The Stirlingengine is still a heat engine and is limitedto the Carnot efficiencyas other heat enginesare, but it appearsto be able to approach it more closely than the others. Also the machine is inherentlysilentand uses fewer movinq parts than most other engines. What more will inventivehumans do with such a machine? Only the future can tell.
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CURRENT LARGEENGINES
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The history of Stirling engines is fascinating. The reader is referred to Walker-(73 j) or Finkelstein (59 c) for this type of information. In this section those current engines with power greater than I horsepower will be described, This selectionleavesout model engines,and small free piston machines for pumping, refrigerantor blood or for producingelectricity, The enginesto be discussedare:
il i ;.! ii
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N. V, PhilipsCo. (Netherlands)
'_
1-98 4-215 (Fordtesting& modifying)
_:
Ford Motor Company 4-98 Double Acting Swashplate. United Stirlingof Sweden (USS)
-
P-40 P-75 P-150 GeneralMotors (NASA-LewisTesting) GPU-3
;. _ •.
:.
FFV (A Swedish GovernmentOwned IndustrialGroup) AuxiliaryPower Unit Engine 3,1 Philips-FordPrograms -w
CurrentPhilipsengines use tubulargas heatersand gas coolers. The coolersare water cooled and the heatersmay be heated by a flame or a heat pipe. Stackedscreenswith very fine wire meshare used for the regenerator,
i
engine)and the 4 cylinder• double acting Rinia configurationwith a swashCurrent, types use(4-215 rhombicdrive power piston (.the 1-98 plate crank case and the with 4-98 displacerand engine). Power control is by adding and removing gas. •The engines must be preheatedand then crankedto sty,
i:
3.1.i The 1-98 Engine (76 e)
i
About 30 of thes_ engineswere buil,t. It has one cylinderand a piston swept volume of 98 cm_, Figure 3-I shows one of those engines On test. Figure 3-2 showsa cross sectionof this type of Rhombicdrive engine. The engine operateswith a heater temperaturefrom 250 C to 850 C and produces as much as 20 KW at reasonableefficiency, It is capableof deliveringabout 15 KW at 3,000 rpm and 220 arm gas pressure. With hydrogenworking gas, with properly optimizedheat exchangersand with a heater temperatureof BSO C and a cooler temperatureof 0 C, this engine will produce lO KW at a shaft efficiencyof about 43%. This does not includethe heater efficiency(76 e).
18
N
0
Figure 3-i. Phi]Jps!-98 Engine on a Test Bench.
Figure 3-2. Cross Sectionof a Rhombic Drive Engine, J ....
REPI_ODUCIUI', I'I'Y Of,' "1'11_ •
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3.1.2 The 4-215 Englne C77 k. 7./. aq) ij :j I
The developmentof the 4-215 engine started at PbIlips, Ei-ndhoven, in mid 1972, Figure 3-3 shows a cross section.anda_picture.ofthis engine. It uses the Rinia arrangementwith 4 double-actingpistonswith a swashplate
i i! •
swashplateenginesare shown in Table 3-I. This engine was installedin a drive, The major innovations incorporated 4-215. engine over Ford Torino 4500 Ib inertiaweight vehicle.into The the best fuel-economy in previous the vehiclewas found to be 12,6 MPG on the Metro_Highwaydrivingcycle (See Figure 3-4). This is significantlyless than the 15,5 MPG that the conventional vehiclewouldget with emissioncontrols Ford has alreadymade improvements in the engine and _ynamOmetertests have_resuited;in a simulated14.4 MPG. Ford believesthat with additionalimprovementsnow underway the objectiveOf 15.7 MPG by October, 1978 will be reached. Ford has identifieda series of_modificationsto the presentenginewhich should realize a 30% improvement in gas mileage tO 20.2 MPG by the end of the 160 milli.ondollar programwith DOE in i985. Furtherout is the expectationthat•if ceramics like silicon carbideand siliconnitride can be substitutedfor the expensivenickel.alloy
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more enginescould be made with the available-resources.Stephens,et al hot (77 at) ends, calculatethat-300,O00 that the.MPG would goengines, to 23,2, would the consumeas engine costs much would cobalt dropasail and many. the United States used in 1976. Scarce materialslike cobalt and nickel and chromiummust be used sparingly. One of the big reasonsDOE is interestedin Stirling engines is that it can have high fuel economyand low pollutionand low noise. Figure 3-5 shows that Ford has not been able_ meet emissions-'s_andards with the vehicle e_Igine, Previouslyconductedcombusterrig tests at steady operatingpoints showed very low pollutionlevels. Ford expectswith.furtherdevelopmentto meet.emissionstandards.
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The.reSultsof other tests (Table3-2)show that the engine is about 50 Ibs over weight objective. The slower start-upand accelerationis attributedto a higher pressuredrop throughthe combustionsrideof the en_e than was anticipared, Table 3-3 shows the present status and the objectivesof the eight year Ford/NASA/DOEdeveiopmentprogram. Improvementsin a numberof categorie_
__ i .,;, .._" ii-_, '-':" .-.:
are.anticipated. to be successfulthe development has to be to However,for lower cost, the Thisprogram aSpecthas been Ford's main big concernfrom the beginning, Although nothinghas been publishedon this most vital-aSpect, Ford must see a way to.make Stirlingengineseconomicallyattractiveorlthey would not continuethe program.•Like any other developmentprogram, Ford has encounteredquite a number of problems. Table 3-4 shows the major technical problemsthey have encounteredand resolVed. Table 3-5 shows the major technicalproblemsbut not yet resolved. These certainlyare major problems. but there is nothingof a basic nature. During this developmentprogram, Ford intendsto utilize the same basic engine conCept but with improve_nents in components,auxiliaries,and drive to achievethe stated objectives.
i_ :,._ !_ '__,_ _
3.1.3 The 4-98 En_ine C77 k)
_':_
The 4-98.Stirlingengine is so far a design study Of a down-sizedversion
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4-215 170 H.P. ENGINE
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• • • • •
LENGTH-- 36.5 INCHES WIDTH (MAX) -- 26.0 INCHES HEIGHT (MAX)--2"/.3 INCHI_S WEIGHT (LBS)-- 713 DISPLACEMENT (PER CYLINDER)-- 2i5 CC • DESIGN SPEED-- 4500 RPM (MAX) •
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a. Cross Section
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Assembled
Figure 3-3. Philips-Ford2-215 Engine
ORIGINAL PAGB IS POOI_
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7 Major Innovationsin the 4,215 Engine (Reference77 aq) .......
;. .,I
" 200 atmospheresworking gas pressurevs. 150 atmospheresfor previousengines.
.... :_
• Firstengine with rotary,ceramicpreheatersystem...
......
]
, New air/fuelcontrolsystem to satisfydynamicrequirements.
_,!
, New power control system for automobiledemands. , Three tinleslarger'than previousswash plate engines.
'•!;I _
Half the specificweight of previousStiriing engines,
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• Packageablewithin existingengine compartments.
,•i
, 4000 rpm capabilityvs. 2000-3000rpm of rhombi.c drives,
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• First engine,with exhaust gas recircuiation.
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• Unique coolantflow throughcoolingunits, • New lubricationsystem.
i•.11
-First engine designedto.drivefull range of automotivetype accessories. .....
"_ ,
20 I0 0 I0 20 30 40 50 60 I. , I i I , I l I , I , I _ I: ._..J '. WORSE - BETTER THAN BASELINE
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•
ERDA CONI RACT ',4TH GENERATION_ OBJECTIVES
.'
....... 11202 MPG
.
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PHASE I OBJECTIVES •
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BEST .... DYNAMOMETER
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TF:ST T.ODA_i
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1_) 15 METRO HI£3I_WAY FUEL ECON. OMY IMPG)
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Figure 3-4. StirlingEngine Fuel Economy. ,-I
22
,
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HYDROCARBONS --GR/MI
o
05 .-J,
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1o
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(0 58) VEHICLE TEST
[ (o.1o) COMBUSTOB RaG TEST
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_ARBONrMONO×IDE2
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COMBUSTOR RIG TEST "_.......
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OXIDES OF NITROGEN-GR/MI 0.5
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LOW MILEAGE OBJECTIVE 50 K MILE OBJECTIVE (CLEAN AIR ACT AMENDMENT OF '!,970)
Figure3-5. StiflingEngine Emissions.
Table 3-2,.
Other Ford VehicleTest Results (Reference77 aq) ............................... Acceleratioh(0-60MPH Time) DynamometerTest = i6.0 Sec. Objectives ,_ = 12.7 Sec. VehicleWeight (Curb) Measured = 106 Ibs. over baseline ObjeCtives= 50 Ibs. over baseline ....... Start up Time (Key-onTo Driveaway) Measured = 24 Sec. Objectives= 15 Sec. 23
):ii I,
Table 3-4
'_
Major Technical Probietns Encountered and Resolved on Phiiips-Ford Program (Reference77 aq) . ..... ' Swashplate surface galling. ............... • Drive system noise due to non-conCentricCrossheads, , Regeneratorend-platebending_ • CrankcaSefaiiure. • Engine out of balance. ' Pistonattachmentfailure. • InSufficientexhaustgas recirculation. .,Unstableair/fuel controlsystem. • Power controlcontamination ....
Table 3-5 ProblemsEncounteredYet To Be Resolved on PhiIips-Ford Progr'ain (Reference77 aq) , Roll sock seal systefni_ailUre. • Preheaterleakage. • Preheaterbinding. , Fuel burningon preheatercore. • Heaterheadtemperaturedistribution. • Excessivewarm-up time. • Insufficientbu)_nerair supJ)iy. • POwer controlinstability. • Heaterhead cracking.
25
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of the 4-215 engine to be used for smaller cars which will be more common in the future. Figure 3-6 shows a sectionof this engine and gives some pertinent parameters, Other dimensionslike the number and size of theheater head tubes, ...... the number and size of the cooler tubes, piston diameter,regeneratorwlre • diameters,etc., were also chosen, Many cases were evaluatedto select an optimum design, The calculatedperformanceof this optimumdesign.isshown in Figure 3-7. Note that althoughthe.deslghpoint is at 5,400 rpm the best torque and efficiencyis at 2,000 rpm. Note that the torque is exactly proportionalto mean pressure. This engine performancemap is used along with the characteristicsOf the vehicleand the requirementsof the particular drivingcycle to compute the vehiclel}erforma_ce characteristicslike fuel econO_y, rate of acceleration,etC, A new engine must usually fit into the engine compartmentof the existing .....vehicle, Figure 3_8 shows the result of a ,_esignstudy by _Ord on how the 4-98 enginewould fit-in a 1976 Pinto. This engine !n this arrangementrequired that the car be lengthened3.2 ihches tO accomodateit, Therefore,a front wheel drive arrangementwas studied. Figure 3-9 Shows that this way the engine fits well underpowered the hood andPinto..The permitsa shorter front_endarrangementis overhangthan the conventionally 1976 accessorydrive somewhat more complex, however,due to the fact that neither the fan nor the Preheater drive shaft is parallelto the engine crank axis, 3,2 United St.irling.Englne. s (.77. i, 77 J, 77ai, 7_7am) KB United Stirling (Sweden)AB & Co., was organizedin.1968as a research and developmentcompanyjointly owned by Kockumsand FF.V. Kockumsis a publ.icly owned companyhaving its main business in shipbuilding.andlumber industry. F_V is a government-ownedindustrialgroup, United Stirling is a licenseeof NV Philips Company. United Stivling startedby building rhombic drive machines. They then startedon Rinia arrangementmachines but have not used the swashp!ateof Philipsbut have used more nearly conventionalcrank drives. They also do not now use the roil-sockseal.thatPhilipsemI_loysbut have.developedtheir Own mechaniCalseal,
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3.2.1 ApplicationPlan United Stirling is planninga productline of 3 engines (See Table 3-6). All three enginesare intendedto be availableas direct flame heated versions... as well as heat pipe heated versions. United Stifling has evaluatedthe market for Stirling engines, They feel
_..,i.
that the be i_enetrated startingfrom thein upper left hand cornerNote of Figure 3 market lO and will proceedingthrOUghthe applications "wavesofattack". that in this plan Taxis and Cars would be the last apl_lication,However, if a large amount ef assistanceis forthcomingfrom DOE based upon applicationof the United Stirlingengine to cars, thls segment of the market will obviously .... receiveearly attenti_)n. United Stirlingpublicationsindicatethat field testingof preproductlon ,.# prototypeswill start in Ig7g wlth mine vehicles in a SWedish iron ore mine.................. " Figure 3-II shows how their P-150 enginewill occupy essentiallythe same .. space as the Diesel engine it replaces. UfiitedStirling plans to give high priorityto total energy systemswhich use 40-140 KW Stlrlingengines to power ' 26
4-98 84 H.P. ENGINEI_ e LENGTH-- 25.5 INCHES • WIDTH (MAX)--20.6 INCHES • HEIGHT (MAX)-- 23.0 INCHES • WEIGHT (LB_)-- 374 • DISPLACEMENT (PER CYLINDER)-- 98 _C • DESIGN SPEED-- 5400 RPM (MAX)
MAJORCYCLE& COMPONENT DESIGN PARAMETERS FOR.THE4.,98 STIRLINGENGINE-CYCLE PARAMETERS I • MAX MEAN PRESSURE--200
ATM
e_WORKING GAS-- HYDROGEN e HEATER INSIDE WALL TEMP.--1023 • COOLER INSIDE WALL TEMP.--353 • MAX. ENGINE SPEED--5400
K (1382 F) K (176 F)
RPM
r
[ CoMpONENT PARAMETERS ' I • NUMBER OF CYLINDERS
4
• SWASHPLATEANGLE-- 18 • SWEPT VOLUME/CYLINDER-- 98 CM3 ..... • VOLUMETRIC RATIO OF EXPANSION-- COMPRESSION-- I.lO • REGENERATORFILLING FACTOR-.- 38%
Figure3.6, The 4-98 EnginePartialDescription
27
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, i
4-98 STIRLIN(_ ENGINE
_
_
NE'fTORQUE @ _ j_b Figure3-7. _40
,'_
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_
ENGINE SPEED
_
POINT
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DESIGN -.
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ENGINE
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SPEEO
(RPM)
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40 _0
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1000
2000
,
3000
4000
I
1 l
5000
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FigUre3-8. Packagingof the Ford4-98enqinein a 1976Pinto,RearWheelDrive. l) BasicEngine,2) Blower,3) Radiatorand Fan,4) Air Conditioning Compressor/Optional, 5) Alternator, 6) WaterPump,7) PowerSteering Pump,8) HydrogenStorageBottle,9) Starter/Blower Motor,lO) ExhaustSystem,II) SteeringSystem,12) Air Cleaner,13) Air AtomizingCompressor.
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Figure 3-9, Packagingof theFord 4-98 Engine in a 1976 Plnto,...E_ont Wheel Drive;,
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1
Table 3-6. PerformanceTargets for United :
"
I
Stirling ProductLine -:.
EnflineNumber Power -,
RPM Number of cyl.
.P4._.O0 40 KW
Welght (withauxillaries)
150 KW
4000
2400
2400
4
4
8
Max efficiency (installedin vehicles) _35% •
75 KW
180 kg
I 37% 350 kg
37',f, 650 kg
29
i
-I
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Figure 3-10. United StirlingApplicationPlan,
........
electric generatorsandheat pumps, These.,,would be used in shoppingcentersor apartme,thouses, United Stirlin_expects to realizea 45% fuel saving compared to a conventionalfurnace, _,fterthis, Unit, ed Stiflingsees the next importantapplicationwill be the city bus. Traffic authoritiesin many metropolitanareas are reportedlyinterested in obtainingengines for testing as soon as possible, United Stirling'splans would allow ,_histo happen in 1979. At present,United Stiflinghas four P75 enginesof the V type on test in their laboratory. They have their V4X35 experimental engine installedin a Ford Taunus.stationwagon for the purposeo_ testing engine control. -...... 3,2.2 Engihe Design United Stirling'sproductionengines are now expected to look like Figure 3-12. The P-40 and P-75 will have two cranks on each of two crankshaftsgeared to a co_mmn drive shaft, The P-150 will be two P-75's co,_inedjr, to one block. _Thefour connectingrods driw; the four double-actingpistons throughcross heads to take the side thrust. An oll pump pressut_ lubricatestheseworking parts. -. The differentcomporentsof the engine designwill now be discussedstarting with the seal which is the principledesign problem.
COMBUSTOR BLOWER AND AIR FILTER
,--
EXHAUST PIPE
FAN .o
RADIATOR
/ P-150 _
ORIGINAL DIESEL ENGINE
,, COMBUSTOR BLOWER AND AIR FILTER
Figure 3-11. United Stirli_gP-150 Englr_ein a Truck.
Figure 3-12. Conceptfor United StirlingProductionEngines. _2
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v
...
PISTON CYLINDER
_
v
PRESSURE
,%_
,
/:
MIN
,_.,,.,t
I_.
::::
"-
T,ME' .
-.;'::
:
_";'"
:_..... "_"
,.,;,,_:_:,:
:2
_
"':"I
_
::"
_
. '_
,_.
i
...,,, "-
MIN.PRESSURE ..-ROD _" SCRAPER
',_ I
'_"
_._ HYDROGENSEAL I
':':
:.. ii':!" _i_
"_" "
_';..
FILTER
_':
,.._
._ ,_..
i_., -
OIL DI_AIN
Figure. 3-13• The UnitedStirlingRod Seal,
..................
'_
_ '_eTA
: 3,2.2,1 Seals ':i:_:... The sealfor thisenginei_ presentedin Figure3=13• UnitedStifling -:;:!:_ reportsthatthis sealhas been testedfor severalthousandhoursin component , , and in enginetest rigsand has goadually been developedtoits presentsatis;,:.:i_aotory State, The threeelementsof the seal are: ,,.. I. The top sealelement, This seal is dry. The shaft . passingthroughthe Sealhasnot.beenwet with oil. .:: The seal sealsbetweena varyingenginepressureand :_ the minimumenginepressurebelowthe seal This minimum _-," cyclepressureis maintained by a checkvalvethatalso _ b"i_gs leakingworkinggas back into the Cycle• 2. The SCraperring. This elementrefnoveS the excess " lubricating oil fromthe pistonrod. Oil scrapedaway _; drainsto an Oil-gasseparatorand thenceback to the. crankcase. •
: ,i'_'_ ..... •
3. The Hydrogensea-1.This elementmaintainsthe pressure difference betweenminimumcyclepressureof the wo_'king gas and atmospheric pressureair and lubricating oil in the crankCe.se.
.::'
•"
33
._
,. _ :::: :x_ ,,, ._ _,; ._ ., ,j
%'.
-,_ :; _
_Figure 3-I4. United stiflingInvoluteHeater. ,'"
_
w, .....
|
....
Nothingis said about the piston seais but they are probablyfilled Teflon piston rings Since these have worked well for others particularly_.when the i_iston liner is cast iron. 3.2,2.2
Gas Cooler
The gas cooler Consistsof many small tubes the sa}_eas the Philips engineS• The regeneratoris a porousmass pf'obably also the saineas in the Philipsengine. These parts have to transferthe heat with little flow frictiona_d little dead volume. An Optimum design is very importantto engine _erformanceas well as cost. 3.2,2.3
Gas Heater
The gas heater to be used on United Stifling productionengines is of the involutetype (See Figure3-12 and 3-14). Each of the V tubes in the ring is the same. Its inner leg is bare and straightup. Its Outer leg is finned,slantedand curved so that the tubesmaintain an even spacing. This gas heaterwas _onsideredthe best by uss from the standpointof performahc_ and productioncost.
34
i
i
Airflow Figure 3-15,
in a Stirling engine. Temp (C °) Untted Stirltng
Burlier and Atr Preheater,
..
3.2.2,4 Burner and Air Preheater The burner and alr preheateris differentthan the PhilliPs engine previouslydescmbed. This air '}reheater is the counterflowtype (See Figure 3-15), This substitu;1oneliminatesthe machineryneeded to r'otate the reversingflow matrix and seal the matrix as it rotatesas done in the Ford-Philipsdesign. 0i]the other hand, it is difficu.it to pack in asmuch surfacearea for l_eatt_a_1$ferin the limitedspace availabieusing the counterflow heat excllanger.No real infot_atlonis yet availableon the.. United Stirlingair preheater. The burner burns atolfHzed fuel with swirlingprel_eated air. Possibly secondaryair is added. Figure 3-,15shows that the hot gases from the burner enter the gas heater at 2,000 C and leave at 750 C. This exhaust leaves the air preheatedat 190 C. This drop from 750 C to 190 C raises incoming ce_ibustion air fro_i50 C to 680 C. 1"hisburner system can get the en.q_nestartedrapidly froi1_ a cold start. Figure 3-16 shoeshow this is done. "Theheater tubes in a Stirlingengine must be heated up before tllestarter, motor is engaged. The burner blower, non_ially driven by the enqine, is driven by a separateelectricmotor during the heatin.q-up period. When the l}eatertube tei_perature has reached400-
.
,,,,
i_
. ..........,
.........
.
_:'_"' i._:_J ->_",_.!_...._.L,_, .... x.,,. .
_
...._;,.,
..... i". '_,'__.-_'_
,I speed rpm,
ti!,.
. Starter engaged
Heatertube temperature.
,ooo '1ooo
'"
250
: l;t•"
500
J
0
',_
0
•
;
,
,
,
,'
10
20
30
40
50
60
0
3
_i.I!i ':4-1 " • . : i;I i.l i.
Figure 3-16.
Cold Start'ng
Sequence for the United Stifling
V4X35 Engine.
300 C, the starter is engaged. According to Figure 3-16, after 12 seconds .... of heating-up, the starter is engaged for about 2 seconds. The engine now runs at idle speed and a driver would,havebeen able.to drive away, After and the engine can deliver-fullpower. This start represents20 C ambient temperature. Tests at--32 C have been made with a slight increasein cranking timeadditional30 due to hlghersecondsthe hydrodynamiclosses inthe drive, mechanlSm."(77 i), level and heater temperature has-reachedits normal The bUrner System must supply heat rapidlyas is seen, but it also must not overheat the working gas heater. A contr.OlSystem todo this is shown irLFigure 3-17,. An explanationfrom reference77 i iS given below. .-
=
""I .I
With varying demand for heat in the working cycle of the engine,the air/fuelflow is controlledin such a Way that heater _emperatureis kept constant. Thus the air/i_uel control is indirectlygovernedby the po_er control, in addition the air/fuelratio is controlledwith regard to emissions. Figure 3-17 shows a system,where a Bosch K-Jetronicunit is used. The temperatureof the heater tube is measured by a therm(_cOuple i. The signal of the thermOcoup!eis amplli_ied and convertedin the electroniccontrol unit 2 to a signal cm_i.rolling the positionof the air throttle3, Thus the rightamount of air is deliveredtO the combustervia the burner air blower 4, In a slightlymodified Bosch K-JetronIcunl_. a sensorplate 6 instaliedi_sidea conical air
141 ,i:iI :._
'.:, ";-_-! '
•
36
i! 'i
....
i
2
_
i _err_x:_ 2 3 4 5
E_ct_hiC corit_ uhit Air throttle Burrer air bk'w_r _el tank
K-_tronicunit
6 _ 7 8 9 10 1i 12
p_te
F_I _Jter ,_iaf _I_ Ru_er _fferential pressure_ Pressure teguiati_ _
Figure 3-i7. Tempei_ature and Air-Fuel Control. ii i
....................... I_
........
3.2.2.5 P_r
passageprovidesa positionindicationof air _ow Pate. The fuel from the tank 5 passes an electric pump 7 and a filter 8. The rue1 pressure is heid Constant by a relief valve 9_ The positionof the sensor plate controlsvia a plunger10 the amount by which a fuel meteringport is opened. The differehtialpressureacross the meteringport is maintainedat a ConStantValue by a valve 11 So that the fuel flow tO the atomizerdepends upon the amouhtthu port is opened Only. The air/fuel ratio dependsupon the hydrauiic counterpressurecontrolled.bya pressureregulating__ valve 12. AdjustmentOf the ratioover the load range can be achievedby a-mOdificationof the shape of _e conical a_r passage...........
.-
Control
Power controlof theengine is now done by changingthe averagegas pressurein the engine. This is the same way Philipsdoes it althoughUnited Stlrlinghad used dead Volume controlon their engin_ they put into a Pinto for Ford. United Stirlinguses one hydrogengas compressoroperatingas an auxiiiaw, and Philipsuses two pistonson each of the four power pistons as part of an internalgas compressor. Othe_ise the processis ve_ similar. Quotingagain from reference77 i: 37
=,, ....
_ ..........
i_:Ni_ :_'_"_
_w'"_" '_'::_"'_ .'_. _'_
"'I_" ....I
";I "_ I
"I ¸_
' I"'_ J_'_'_':'_.'_ .._::_'_':__:"_-I,._ _ !_:_ | _T';_:_"._t_.,, _ _"'L_':'_'_:I' .:.'_ _FI_
' !
,21 , ,
" !
orcu_tihg
-'2
''_
i. 1,"L" • -i
1 2 3 4
Figure 3-18. •
I'
Ul
Simplified "
I
i .....
Hydrogen Storagevessel H_fogen compressor_ Control valv_ Comp_'eSsor short, circUiting valve •
'.'_
-:;. : _:i '.' _,.>:.:: ,:__, :, '.
Diagram of the Power Control System... F ................
_'
1..........................
I..... r............
A sin_plified diagram of ti_epower controlsystem is shown in Figure 3-18. Main parts Oi_ the system are hydrogen. storagevessel.,hydrogencompressor,controlvalve block and a servo-system(not shown) which contrOlSthe position of the control valve. To increasepower, the controlvalve slide in Figure 3-18 is moved to the right, Thereby hydrogenflows from the high pressurestorageVessel via the Controlvalve to a timed supply system built into the engine. Thi_ timed supply system mainly supplieshydrogen into the cylinderswhen the cycle pressure is near its maximum value. A gas flow into the cylinderswithout the timed supply SyStem results in an undesirabletorque drop during ...... increaseof pressure. To decreasepower the slide is moved to the left. During the first part of the movement dumpingof hydrogen f_om the engine via the compressorto the storagevessel --
'i
". ,, .I '_' . i', :; I
lowers the power output, At the second part _hort cir.... cuitingof hydrogenbetweenthe cylindersis added, thus giving a quick decrease ol_ power, . , The link betweenacceleratorpedal and controlvalve is a servosystemwhich for differentacceleratorlevels moves the controlvalve slide in such a way that an engine pressurecorrespondingto desiredpower output will be reachedand maintained. Low Idling speed is maintainedby controlof appropriateworking pressure,using a speed sensor and the short circuitingvalve. The hydrogencomp_sson._s.an.o_.-i-i_ree, single
I: ":.
..... ;_I:_ :::::] ..;_. _ i,. .: " ," _ "'. " *} .:
"'I " _ -:I. . I :]_,._ -
•_38-, [
........
!
......
Engine
Engine sl_eed rp_
j i ,,! .
pri_ssu_e
.. C!
uar
3000
'
-i
I
_
150
•/ i
2SO0 Engtne pressure ......
2000
Engihe speed
100
.................... 1500
Max I I
1000
I
'",' ;' i
AcCelerator ___-,R-ositioh -
.i
...... .......
50
500 0
._0.5
1,p
1.5
lO
T}me sec
' F.igure..3_19, .Speed and pressureRespOns.e,..for the United Stlrlin_V4X35 .Engine._. •
stage,dOuble-actlngcompressorwith piston rings acting as suctionvalves. The displacementis lO cubic cm and the pressureratio is i:i0. To unload the Compressorduring increaseoi_ power and steady state conditions,the suctionand pressure _ideS Of the compressorare connectedto each other by a compressorshort Ci.rCuitlng valve.
To lllust, rate how.rapidly this power controlsystem operated,...the V4X35 engine,equippedwith all auxiliaries,was disengagedfrom the dynamometerand speed increaseand pressuret'espOnse were measured, Figure 3-19 Show_ Speed and pres)ure Increase-versustime for the free runningV4X35 engine when the acceleratoriS suddenlydepressed.. (Note: A slight short circuitingeffect is maintalned at low idling, DepressingLhe acceleratorwill close the short circuitin.q valve and start engine accelerationbefore pressure increases,see Figure 3-1g,) The tests show that the powercontrol system acts fast and accurately_ NO torquedrop could be measured and the lag time betweenacceleratorde_reSslohand valve responsewas short." (from77 I)
39
,_.
}_'
, :" •. :_:_:i I
Figure 3-20. Cross Sectionof DOuble-ActingV8 Pi50 Engine Developing150 KW .. :. at 2400 rpm.... . , 3.2.3 Engine Performance Finall_some performancemeasurementshave been publishedfor the PiSOV4 engine which is also Sometimescalled the P75 engine since it is half the PISOV8 engine. Figure 3-20 shows a cross sectionof this engine and Figure 3-21 shows this engine with its auxiliariesattached, Figure3-22 Shows the measured and calculatedpower output and efficiencyfor two _ifferentmean pressurelevels. Note that the calculatedand measured values agree closely. The maximumefficiencyis 32%-at 70 Ccoolingwater. * If the ambient temperature is 30 C then a 0,8 m2 area radiatorwould be needed (77 i). If it is used as a marine engine,efficiencyincreasesto 36% at 20 c coolingwater.
""
3.3 GeneralMotOrsEngine
_!.
3.3,1 _Histor_
t_: _'_; ,,. ;:: '*'
GeneralMotors starteda cooperativeeffort with N.V. Phiiips in 1958. In 1965, GM was able tO state that "The AllisonDivision,the Eieotro-Motive DivisiOnand the ResearchLaboratorieshave operatedfull-size,modern, practicalStlrlingengines for a total of 6500 ho_r_," (65 t). Eventt_ally, about 3],000 hours of operatingtime were acCumulated(74 bc). The last
I./.
paper from GM (69 f) talked abouta 4 cylinder inline Rinia type engine and reportedOn the initialswashplatedrive te_ts. About this time the GM program
I.,L
was be revivedafter reportedly, of $13 million_ fromcancellednever GM. From aboutto 1960 to about 1966 an GM expenditure, Researchconducteda programfor the
_"
U.S. Army to produce a silent electricpower source. This Ground Power.Unit_ (GPU)developmentwent•throughthree differentmodels. 40
IW_______---
• I
....
',f,
:_>1
-L
Figure 3-21. PI50 V4 Engine Mod_ulewith Auxiliari_e..s_. ......
:
pO'fll_.R kW _'7, EFFECTIVE EFFICIENCY
3o.'/
__. ....._'-
To-I
__
7_PJI _o -I- 2o
_--_' "
E_FICI_NCv _.
,.
./ /...
.]
.....
COOLING WATER TEMPERATURE 70 C
":,
/"'-
PO'WER
",
•
ALUES _
,o,k_:,1_'_...<
I
I
I000
I
I
i5110
200()
'''1
;500
ENGINE ,3PEED RPkL
_=4--r_3-22. Peri_orfnance _,_, Results i_orP150 V4 Module of PlSO Engine ShoWing PresentDevelopmentStatus (Unit.ed. Stirling). L"
•
li_liODUCi_ii, iTyOF TI_ O_,I_I_AI,__I)AG_ IS POOR ,
4_
m
iil
,
_l' _"._,,,_ ..._..,.,_ _ .._L-.,,,,._.._1! _
3.3.2 NASA-LewisTesting Two of the last model GPU-3were preservedand are now being used by NASAengine. The first report on this effort (77 av) indicatesthat the machin-_is • almost ready for detailedtesting. Figure 3-23 shows the GPU-2. Tests have -_hownthat the brake specific fuel consumptionis about the same as that obtained by theto Army in their acceptancetesting Figure3-24). However, engine. Lewis obtain reliablemeasurements of (See a more or less modern type ofthe Stirling output falls short of that originallyobtaine¢1by the Army (See Figure 3-25). The differenceis suspectedto be due to excessiveleakageof gas past the power piston. This leak is being fixed and with minor repairsand additionalinstrumentationit will soon be ready for:detailedtesting (as of December 1977).
ii:
! i_;'_" '_ _T'i} l _._ ,.. _ ,!
,,_:,_1
,
Figure 3-23. The GeneralMotors GPU-3-2Stirling ElectricGround Power Unit for Hear Silent Operation(ref. 68 p) PictureCourtesyGeneral Motors Research,
L
42
I..:!
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l.
,
'
' _',_
i
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,
"]
'
i. _I
""
LI
....
_'; "'
)
MEASURED SPECIFIC FUEL CONSUMPTION
-- NASA LeRC
BSFC, ....... Iblbhp-hr
b_. HELIUMDATA. _--NASA LeRC _]_ HYDROGEN DATA
"ii.l ' ==-: !.J -'}
_(_f,T/_)b._ rRANGE OF U.S.ARMY
0
Figure.3-24,
1
I
I
2 .... 3 4 .. ENGINEOUTPUT,hp
l
1
I
]
k
6
Measured Specific Fuel Consumption for the GPU-3 Engine. MEASURED ENGINE HORSEPOWER..
Figure 3-25,
i"_i
Measured Engine Horsepower for the GPU-3.
Ir : '+. :
.... 3.3.3 -+i I
I:" ,..:" + :
Engine Mea$urements (77__b_d)
;I !
:/_ ! i
Presently available physical characteristics _f the GPU are given in Table 3-7.
i i :
volume by about 20 percent. Table 3-8 gives the test points that NASA-Lewis intends to use to compare with various analytical The heater temperature is meaVolun_ displacement tests at LeRC indicatemodels. that max. gas volume exceeds calculated sured by thermocouples in the working .gas stream half way through.the gas heater,
! il ,) :.
It is considered to be a gas temperature rather than-a metal temperature.
Note that
i:_-.'.
will be provided in an addendum,to and/or a second.edition of this manual along with updated engine dimensions, temperature is as close as they can get. The experimental data, when available, 3,4 FFV Engine ther_ is no good way of measuring the cooler metal temperature and tileinlet water
y_,_:.. :_i_,_ _',_ _!._i_: _ : r
I
_i_i
ii,_i ._ )
k
if' .'
,+i
FFV is a Swedish government owned industrial group which is 50% owner of ! -iI i !
'
i"t
:....
United Stifling. They have produced anapplications. engine to power an auxiliary electric power unit for conm_:.rcial and military A nun_er of these engine-
: "'.
generators are built,and are being demonstrated. The engine will be marketed in the United.States by Stirling Power Systems of Ann-Arbor, Michigan. This company is owned by FFV (80.5%) and Thetford Co., (19.5%), a recreational vei_icle
_'+I ' !i l
machine will be in late 1978,Arbor, and the enqine qenerator istechnical planned to be for sa_ equipn_nt supply fimofAnn Michigan. The first paperon th_s to the genera] public in 1979. " "
1_?: ._ ! _, :._
i
ECCENTRICIT..Y (0:813 in)
_ ]
I.
t
I
I I I
IPONER P:STO_ Y(_,_E
I
,,.... ,'_ ,|
It
........................
i
CRANK RAt}It,S
I,
(n.55 i.)
!I i
CONNECTING ROD LENGIH (1i,'_ l_ in) I
I_
\
I i;
_ .....
• , Itlkt DI.gpI_ALtl, Figure 3-30_
RholnbicDrive Schematic.
tl.
I 44
'
i
,
i
Table 3-7 GPU 3-2 Engine Dimensionsand Paran_ters
! _, i .... i __' I 1 I I ?_ _,
(SeeFigure 3-26 for Overall Engine Schematic) Ng. of Cylinders Type Drive Working Fluid Design Speed Design PressureDesign Output Design Efficiency Bore Stroke Displacement
Cooler (See Figure 3-29) Tube Length Heat TransferLength_ Tube I.D. Tube O.D. No of Tubes/Cylinder DesignWater Flow Design Water InletTemp.
i
I Displacer Rhombic H2 3000 RPM 1000 PSIA 8.0 Net Brake HP 26.5% 2.75 in. 1.208 in. 7.175 in.3
OLD NEW COOLERS* 1.76 in 1.813 1.37 in 1.408 0.040 in .0425 0.060 in .0625 312 (or 39 tubes/regenerator) lO.GPM/Cylinder . lOOVF
Heater Tube Length
9.539 in.
Heat TransferLength
6.12 in.
Tube I.D. Tube O.D. No. of tubes/cylinder Design insidewall temp.
*
'
, [
l
_ "i.321 in. (completely insulated) betweenI and.2 ** 3.06 in. from 2 up to 3 |3.06 in. from 3 down to 2 _2.098 (completelyinsulated) from 2in. down to 4
.i19 in. .19 in. 40 (or 5 tubes/regenerator) 1400°F
_: ' ,i_
_ i
New coolerswill be used in the baseline tests providedthey are completedin time.
I; ii
** See heater tubes in Figure 3-27 for definitionof locationsI--4-4
' !I
i, i
I 45
i , i
!'
.... I!i .... I I
"_
i
Cold End ConnectingDLc_s (See Figure 3-27) Length Duct I,D. No. of ducts/cylinder
.625 in. .235 in. 8
4-'
_ _N plus .0170 in,3 in cooler end cap.
[ _-";k : i_,_ ,i_i 'l' :'." _; -_
Regenerators (See Figure 3-28) _._
! '_'_
t:_ngth (inside)
0.89, in,
::.'_
Diameter (inside)
0.89 in.
.d,:
Material No, per cylinder
304 Stainless Steel Wire Cloth 8 (308 Layers of 213 x 213 wires/inchX..0016 in. diametermesh) 28.6
Filler Factor
Drive (See Figure 3-30)
I
''
I • _,:._ . ,.I
I :;,l
j-_ c ConnectingRod Length Crank - Radius .. Eccentricity
1.812 in. 0.55 in. O,813 in,
i,.: { _ ".. ;-_._
Miscel 1aneou s
...." • 1
Displacerrod diameter 0.375 in. Piston rod diameter 0.875 in. Pistondiameter 2.740 in. buffer side, 2.748 in.: comp. side Displacerdiameter 2.740 in. ExpansionSpace ClearanceVolume 0.252 in.3 CompressionSpace ClearanceVuiume 0.353 in.3* Buffer SpaceMinimumVolume . 17.0 in.3 TransferRing Dead Volume 0,405 in,3 Dead Volume Due to Dri1I,Holes at top _f EnginesCylinder 0.099 in.3
i "},,{ ,,j.._ 1 1 1 _,,_ .::,4 ,;_]
.i_I, .,:_. :5_,
• This is total volume of cold end connectingduets. No clearance volume is assumedbetween the displacerand the power piston_
-t.], -',
.I
, '.ii
d
46
!
I I
Table 3-8 Test Points for (IPU-3for Comparisonto Various AnalyticalMo_els
Working Fluid: H2 Engine Speed (rpm).
Test Point
.....
Mean Pressure (psi)
Heater Temp.** (F)
Coo1er Temp.* " (F)
Cooler Water Flow CGPM)
l
1500
300
1300 .
70
6
2
2000
300
1300_
70
6
3
2500
300
...... 1300
70
4
3000
300
1300
70
.---
6 6
Working Fluid: He Test Point
£ngine Speed (rpm)
Mean Pressure (psi)
5
3000
600
1300
70 .........6.
6
1500
600
1300
70
6.
7"
3000
400
1300..
70
6
8
1500
400
1300
70
6
*
Heater Temp.** (F)
Cooler Temp.* (F)
Cooler Water Flow (GPM)
CoollngWater llilet..Temp. - Is Not Controlled- Will Be At " Ambient Temp.
** TemperatUreof the worRing gas stream at Point 5 in P#gure-3-27.
47
Q
TRANSFERRING "
QHEATER TEMP., FORBASELINE _ TESTS
).12B"-
I
HEATER
O000 0 0
0 0,_
(P. SPC.
k
® i
REGEN.
COOLING WATER IN COOLER I.D. 0.0170IN3
COMP,SPC, I i
l I
Figure3-27. Schematic of Worklng Space. (Indicates DifferentRegionsof HeaterTubes,Compression SpaceClearanceVolumeand Locationof HeaterTemp.Measurement for BaselineTests.) 49
I HEATER
00.518"
¢_o.518"
O00q)t 0 0
@0.44B"
0 C)% EXP. SPC.
• 56"
0,47"
1
'
I
0
2
"
0
O,40" 1
REGEN,
• 54" ,370"_
1.716" END PLATE IS 1/32"THICK
I.300"
Figure 3-28. SchematicShowingDimensionsNeeded for CalculatingHeat Conduction. (Black Dots on Regeneratorand Cylinder Indicate Where Temperatureswill be Measured.) so
39 COOLER TUBEI PER.REGENERATC CAL REGENERATOR
• _
Figure 3-29. SchematicShowingArrangementof Regenerator-Cooler Unit Around.Cylinder, (Also IndiCatesPath of Cooling Water.Flow and Number of Heater and Cooler Tubes PerRegenerator,)
51
4.
'.., .._ ..i
REVIEWOF ENGINE DESIGNMETHODS
The main purpose of this publicationis to teach an understandingof Stir.ling engines and compare and presentin understandableform the availableways for designingStirling engines,.First, in cycle analysis the basic thermodynamics of the Stirlingengine will b¢ _xplainedand the effect of importantdesign parameterswill be discussedusing a theoreticalstepwiseengine model, Next, the methodsof calculatingloss-freeengine Output powerwhen the engine i_,. crank operatedwill be presentedand compared. These methodsare usually. called the Schmldtanalysis, This analysiswhen combinedwlth experience factors is definedherein as firstorder analysis.
i
I_(
• ]
Next, second Orderengine analysesfrom a number of differentsourceswill be presentedand Compared. SeCond order analysisStarts with the Schmidtanalysis or somethingsimilar. Variouspower losses are Calculatedand deductedfrom the SchmidtpOwer. Variousheat losses are calculatedand added to the Schmidt ..... heat. Al.lthese engine processesare assumed to proceed in paralleland independentof each other,
ii i ! !
Finally,third order analyseswill be presented, These analysesdivide the engine into a number of nodesand solve the basic differentialequations that govern this engine by numericalmethods. Third order methodsare much more labOrous,but since fewer assumptionsare made, predictionof engine peri_orma_ce is expected to be mOre accurate..
'i l!
The task undertakenin this grant proved larger than anticipated. A thorough evaluationof all availab]eanalysismethodscould-notbe accomplishedwithln the scheduledresourcesand time allotments. However there is benefitto be ...... gained by making availablethe progressto date, incompleteas it is. It is expectedthat future supportwill enable all availabieanalyticalmethodsto be described. It is also expectedthat performancemeasurementsof a number of fully describedengineswill also be available. With all the analytical methodsavailableand with reliableengine measurements-to, cot_pare them against also available,the designerwill finallybe able to choose with confidencethe
,_ ,_ .. =
design method that meets his requirements. 4.1 Stirlini_ Engine C},cleAnalySis ",i,, _,
in this.seCtionon cycle analysis the basic thermOdynamicsof a StIPlingengine will be explained and the effect of some necessarycomplicationswill be assessed. The thermodynamicdefinitionof a Stlrlingcycle is isothermalcompressionand expansionand constantVolume heatingand cooling,I, 2, 3, 4, I n Figure4-I. Tl_ethermodynamicdefinitionof an EricSsoncycle is.isothermalcompressionand expansionand constantpressureheating _nd cooling, i, 2!, 3, 4', 1.in Figure 4-I. This Ericssoncycle encompassesmore area than the Stirlingcycle and therefore,producesmore work. :'owever,the volumeti'ic displacementis larger, ..... the_ tileengine is larger. There is a modern pumpingengine concept 52
.......
which approximatesthis cycle (73 p). The early machines built by John Ericsson used valving to attain constantpressure heatingand cooling (Sg c), thus.the cycle name. The thermodynamicdefinitionof the Otto cycle is adiabaticcompressionand expansionand constantvolume heatingand cooling, i, 2", 3, 4", l in Figure 4-I, The reason this cYCle is mentionedis that the variablevolume spaces in a Stirlingengine are usuallyof such size that their compressionandexpansion is essentiallyadiabaticsince little heatcan be transferredto the walls during the proCeSsof compressionor expansion. An internal, combustion:engine approximatesthe Otto cycle. In real StirIInqmachines,a large portionof the gas is in the dead volume which is compressednearly i_othermallyso the loss of work per cycle is not as great as shown.
L_J
==
" :_
_
H
L,IJ
aQ _0\
_"
.=
TC 4' .....
TOTAL VOLUME .__
':"
Figure 4-1. TheoreticalStirllng,Ericssonand Otto Cycles.
In Section 4_I, discreteprocessesof compression,heatihg,expansionand coolingwill always be employed. Numeeicalexampleswill be used to make the processesclearer. The sectionstarts with the simplest case and proceeds throughsome of the more complicatedcases. The conclusionsfrom this section carry over into the next sectionwhere the volume o_f__the variable volume spaces change sinusoidaiiy_ ...... 53
I ,I '-"I
4,l.i Sti_iingCycle,Zero Dead Volume PerfectRegeneration .... I, " _
The Stirlingcycle is definedas a heat power cycle using isothermal compressionand expansionand constantvolume heatingand cooling. Figure 4-2 shows such a process. Specificnumbersare being explanations easier to follow and allow the reader to used checkto tomake see the if he is really g_ttingthe idea. Let us take 100 cm_ of hydrogenat 10 MPa (_I00 atm) and compress it Isothermal!yto 50 cm). The path.taken by the compressionis . easily plottedbecausePV is a constant. Thus, at 50 cm3 the pressure is 20 MPa.(_ZOO.a_m),.The area under this curve is, the work the gas.and it is also the heat output.fromt_e gas for therequiredto cycle. I_ compress the pressureis expressedin P_sGals (Newton/sq.meter)(1 atm_ lOSN/m 2 ) and if the volume is expressedin m_, then the u;litsof work are(N/m2)(m_) = N-m = Joules= watt seconds,FOr convenience,megapascals(MPa_ and,cm3 w.ilibe used tO avoid very largeand very small numbers.,
1 i ! i i 1 _ i
The equationof the lineis PV = I00 x lOSpa(lO0 x i0"_m3),=I000 Joules = IOMPa (lO0 cm)) =lO00 Joules
i
The work incrementis dw = PdV = lO00 dV
(4-I
Integratin_ V2 w_
lO00 _ I dV V2v= lO00 _n V] VI = lOOO l_ : •VI_T )
(4-2
Thu_ w = I000 in _
=
-693,14Joules
The answer is negativebecausework is being supplied. Also by the perfect -gas law, ----_PV = nRTc where
P = gas pressure,N/m2 or MPa V = gas volume,m) or cm3 n = number of moles of hydrogen,g mol
54
"
i'
'_'"l
I
•
I'_
t
--i'
i I
/ , ,";
Ill
;
60"
3
HYDROGENWORKINGFLUID m--'STIRLING CYCLE, NO DEAD VOLUME, ISOTHERMALCOMPRES"
55 " •
50
.
SION AND ,EXPANSION _ --. mSTIRLING CYCLE, 33'.. DEAD VOLUME, ISOTHERMALCOMPRES,
/
SiON AND EXPANSION • OTTO CYCLE, NO DEAD VOLUME, ADIABATICCOMPRESSIONAND. EXPANSION
i _ i 'li
_
\ \\
! i i
'
-!
_ '_._._
'/ ,
900 K
.... !
_35-
_
:.
! _'
, ,...
3' b I _ 40
i L,'j
, . !, :_ _,_ '
900 K
I.
_'N
30-
/' _
'
t / 25--
2" , 2'
%
ADIABATIC
_
_
i •
L_u
20-
2
%
._
15--
"_'_' 300 K
300 K 10-
I
I
50
60
,._
,I
I
70 ....80
I 90
I'
-
// '_
I
-
i,
I 100
GAS VOLUME,cm3
Figure 4-2. TheoreticalCycles....... 55
++,i.'_t, _ 'I'T+_,: ++'lJA+'_'*:_I+'..: .,i I --
++ "
:I
_
_,+: I :+'_++t./'+'_:_'+x + .+..... """ .... +'";++"'; +;:?
.......
:. •ul+ +t . I _I.7_ ., + , ++;+;m_+_+..+ ,+ ,,:._:+,,.j+ ....I...... +#, .... ++r a,+"<++t++++:,++_+ + ++':.++; _t+++:+ _' _++,+ ++%_ + 'q ?'7;_I+"_+! +'l " :'!:'++i_! :'J+ :,.._/,:, ++;:,t"_r+_,l+t,'_ :'..... ,-,- ,++,,, _ +
. _,+
'
+
......
_+_
.1+1+._
+
1'
+_+_+t
m
_
+'
+
'_"
'+"
+'
++
'
+
+
'
+'
+
:_
+'+
_
++'++
'
•:I +:I+A--+++# • ....t +--__+
'
,+ t +.+._++
+
+" "+
'
.+ .
._
+
t
!+ i R = universalgas constant !:
--8.134 Joule/K (g mol)
Thus
i +'i..i+ ! "
r
' +
+
(I0 MPa)(iO0 cm3) - n (8.3i4)(300) Tc = cold s_de temperature, n = 0.4009 gKmol
Therefore,the formulafor work nortllally given in text books is nRTc ]n+/V'_\. This quantity is also the negativeof heat of the compressionof the gas or the heat removedfrom the cycle,
I
':_ _, ._
Next from state 2 to 3 the gas is heated at constantvolume fr.om300 to,say, 900 K. Assume for the moment that the regeneratorthat suppliesthis heat has no dead volume and is I00% effective. The heat that must be supplied to the gas by the regeneratormatrix is:
'
q(r) = nCv (TH - Tc)......
(4-4
..=,
.... I"
i;
F
where Cv = Heat capacityof hydrogenat constantvolume, J/K (g mol) = 21.030 at 600 K average temperature
•
I i ,!
Thereforeq(r) = 0.4009 (21.030)(900-300)
I
= 5059 joules
! { i i L
Note that the heat transferrequired in the regeneratoris 7.3 timesmore than the heat rejected-asthe gas is compressed. The pressureat state 3 after all gas has attained900 Kis: P"-
I
._
RTH/V2
11
= 0.4009 (8.314)(900)/50 = 60 MP,_
+
f I I
isothermalexpar_sion of the gas from state 3 to state 4 (Figure4-I) is governed by the same laws as the compression. 4,
I"
56
==
'_
_'_."I __l
[
,,,'., i '
-_d_
.....
.:'" G:\._,
: _ o,,,_'_ ,, ,s" ,--_z _' _ .
!:
w(out) : nRTH In _ lO0 = .4009 (8.314)(900)In -_ =
,I -I [
_
<'; 2079.4 Joules
This quantity is also the heat input to the engine. Theexpansion.line is easily plottedwhen it is noted-thatPV = (60MPa)(50 cm3) .................
Finally the return of the expandedgas from state 4 to state l back through the.regeneratorfinishes the cycle..The=same formulaappliesas for heating. 3000_0.Joules
= .4009 (21.030)(900-300) Joules = 5059 Joules
.......... --
The net work generatedper cycle is w(net) = w(in)+ w(ou_) = -693.14-_2079.4 = 1386.3 joules The efficiencyof the cycle thereforeis n = _ " .1386.3 , 0.6667 q L]_L_ 2079.4 =
-
In.generalthe efficiencyis V2 n
w(in) + w_out) q(.in)
..... n =
n RTc In _
V + nRTH In _
nRTH In
(4-5
V2
TH " Tc = 900 - 300 0.6667 TH 900 =
(4-6
This efficiencyformula is recognizedas the Carnot efficiencyformula. Therefore,the limitingefficiencyof the St.irling cycle is as high as is _,possible. 4.1.2 StirringC_cle, Zero Dead Volume_ ImperfectRegenerator )
I
• '
I
One of the chief engine inefficienciesis the regenerator. Consideran annular gap around.thedisplacerwhich acts as gas heater,regeneratorand cooler. (See Figure 4-3_ Assume that thisengine operates in a stepwisemanner and that this annulargap has negligibledead volume. Let E be the regenerator effectivenessduring the transfer. For the-transferfrom cold space to hot space:_ 57
. _!
...... I !ilL!
iL...... ,%_ "I
-
i |JJ
i tll
.............
"
SPACE HO_
-....
,
.,l
ii i
_"'"_"
.
R
HEATER
H
}'
SPACE
, DISPLACER, ,II
J
....
,_!._
COLD _
I
ATOR
_ , ............ . ...... ........ '.*:i
j
REGENERATOR
COOLER
TH
TC
,.,
i1 Figure4-3. Simple StirlingEnginewith AnnularGap Regenerator. i|,
,,i
{ TR " Tc _ E = TH Tc Now during
transfer
the. heat
i (4-7 from the regenerator
q(r) = nCv (TR - Tc)
i:;: (4-8
l
and the heat from the gas heater is: q(b) = nCv (TH - TR)
_ .!
"_ (4-9 ,: 1
Therefore,the efficiencybecomes: V_ Vz
I *
nRTH In _-_.- nRTc In _
I ".,! .i
nRTH In._-_.+ nCv (TH - TR) Which reduces
,.._
to: TH - Tc
n =
Cv (TH TH +'R
"Tc)(1 " E) V_
(4-11
V_
,,
58
.!
-,
t !
For the numericalexamplebeing used here:
9oo-3a," n = 900 + "_I"-'03_-(9-00"300)' (l - E) 8.314 In ]-_
_
600 900 + 2189.5 '(I - E)
Figure4-4 shows-howthe engine efficiencyis affectedby regeneratoreffectiveness for this numericalexample. Some of the early Stirlingenginesworked with the regeneratorremoved. Figure4-4 shows that at low regenerator effectivenessthe efficiencyis still reasonable-.How close it pays to approach 100% effectivenessdependson a trade-offwhich will be discussedunder Section 4.3.
Rallis (77 ay) has worked out a generalizedcycle analysisin which the compression and expansionis isothermalbut the heating and coolingcan be at constant volume or at constantpressureor a combination. The heating processdoes not need to be the same as the coolingprocess• He assumesno dead volume,but allows for imperfectregeneration. For a Stirling cycle he derives the fo_lula:
•
'
I
[i!?
!
i
...i
'I
n : (l
( '
+ T(y - I) In v
,i".'J c,+,,
where
,
."._
-:s_
:i'_I
n : cycle efficiency
i
:I
'/= CplCv - TH/Tc
il;_:_ I.-i; .:_,,
v = Vl/v2
',
c.--E
,.
I
;".ifI •:I I .... • I ) ! i I
EquatiOns4-12 and 4-i1 are the same, just differentnomenclature. Note that for c : E = l both Equation4-11 and 4-12 reduce to .tbe_Carnot equation,
...!.
Equation4-6, Rallis (77 ay) also deriveda formula for the Ericssoncycle efficiency:
.>.. '_':"_
[
i ""
,)
." :-" I
n = y(l -._)
-
In v -l) l,nv
(4-13
'i. i •
Equation4-13 also reducesto Equation4-6 when c = l, that is for perfect regeneration. To attain Carnot efficiency,the compressionand expansion ratiomust be the same. Rallis shows this using cycleswhich will not be
"I I
treatedhere.._:. Railis also gives a useful formulafor the net work per cycle for the Stirlingcycle: _ W
.
: v(_(V-l)l_n v
(4-14
For instance,for the numericalexample being used here: ..}' I
I
"
'
.
i _,
W : (50_cc)(I0MPa) 2 (3-I) In 21(2-i)
) .
_..
= 1386.3 doules
_'>
which is the same as obtained previously,
I
i' I
4.i.3 Otto Cycle, Zero Dead Volume_ Perfector ImperfectRegeneration that there The variablevolume spaces in Stirlingenginesare usuallyshaped so is little heat transferpossiblebetweenthe gas and the walls during the time the gas is expanded or compress_, i. Analyseshave been made by Railis (77 az) _nd also by Martini (69 a) whirh assume adiabaticcompressionand.expansioh With the startingpoints being ";,he same as for the Stirlingcycle. For ins.tance for the numericalexample in Figure4-2, compressiongoes from l to 2" instead of from 1 to 2. Expansiongoes from 3 to 4" instead
_
60
I F_
i
I IL! i I 1 ili ,,, ; ! .... ... ,,I i
)
I
of from to 4. cycle is3lost,
_I . _:_ _.-,
It appearsthat considerablearea and thereforework per
the same as for the isol_hermal case. For the numerical exampleafter compression to point 2" the pressureof the gas is 26.39 MPa and the gas temperature is 396 K, As this gas moves into the hot space througha cooler,regenerator and heater all of negligibledead volume,it is cooled to 300 K in the cooler, heated to gO0 K in the heater. As the gas is transferredat zero total volume However,this processis not thepressurerises. pressure at point 3 is not change from the cold space tocorrectbecause the hot space the This pressure rise results"'_a temperatureincreasein the gas due to adiabaticcompression. Therefore,at _he end of the transferprocessthe mixedmean gas temperature in the hOt space will be higher than gO0 K. Point.3 is calculatedfor all the gas to be exactly 900 K. Adiabaticexpansionthen takesplace. Then by the same processas just.described,the transferof the expandedgas back into the cold space resultsin a lower gas temperaturethan 300 K at the end of this Stroke. The computationalprocessmust be carried, throughfor a few cycles until this processrepeatsaccuratelyenOugh. One way of computingthis processwill be described in SectiOn4.1,5 when the effect of dead volume, will also be considered.
•,
ii
4.1.4 Stirling Cycle, Va.riable Dead .Volume,Perfector imperfectRegeneration
.-'I.
An i.nefficient regeneratorbacked up.by an adequategas heater and gas cooler
i.
presentin any real engine decreasesthe work availableper cycle. per cycle. It will shown that cycle additionof dead volume which mus.t be will not change the now workbe realizedper but will increase the heat required Assume that the annulusbetweendisplacerand cylinderwall (see Figure4-3)
( .
the displacerto the other is uniformand that the pressure is essentially constant. The gas containedin this annulus is: has a dead volume of 50 cm3_ that the temperaturegradient from one end of x=X n = "Er
dv
.
iil ! ..
(4-15
X=0 where i .,
v = dv = A = x = X =
_,:
• :.i
-
"
total volume of annulus Adx --dii_ferential volume of the annulus flow area of annulus distance along annulus total length ol_ annulus
61
TX = TH - _
(TH - Tc)
(4-]6
By...substituting and integratingone obtainS: PV ]n (TH/Tc) n =
......
I' (4-17
R (TH - Tc)
_,
L:
Thus the effectivegas temperatureof the regeneratordead .volumeis
.....T R = (TH " Tc I/ ln(TH/Tc)
(4-18
,:
which,is the log mean temperature. Thus for the numericalexample:
go0- 300 TR "-" in 9_
= 546.1K
Quite often it is assumed-thatTR =
TH.+ Tc gO0 + 300 = 600 K. "2 '.,_=_L.. 2
For the largedead volumeswhich will almost always result_ it.is importantto have.therJgLhtgastemperatures for the regeneratorand heat exchangers. Assume for.themo,._ntthat the hot and-coldgas spaces can be maintainedat 900 K and 300 K and that the pressureat the end of the expansionstr'.,ke, 30 MPa (_300atm)is maintained. It is sometimesconcludedthat one should compareengine cycles that have.thesame peak pressurebecause this pressure is used to size the enginewall thickness, However,the wall thicknessshould be sized on the basis of creep. The time averagedpressUrewould be more appropriate. Thus, the above assumption, The gas inventorynow is:
n-
R
+
n =8._
(4-1g
i I i
'i
,-
"
+
t
= '0,7313g nlol. The equation, for the gas expansioni_: p = n R _. (0.7313)(8..314) VH VR ' VH . 50
. P
A +V_H
(4-20
. where A = 5472.
B = 82.4
F
The work output by expandingfrom VHI = 50 cm3 to VH2 = lO0 cm_
is:
fVH2 W(out) =j VHIP dVH =
;H2
A dVH VH + B
(4-21
VH1
VH1 + B = 5472 In (_) = 1753 Joules The equation for gas compressionis n R P = Vc
C
{0.7313) (8.314} VR
Vc
50
- where C = 1824.02,D = 27.4
Analogouslythe work of compressionis Vc w(in) = C in 2 • (+D) Vcl + D = 1824.02In _ .50 + 27.4_
\ 100+ 27.41 = - 908.37 joules ....
Thereforethe net work is w(net) = w(out) + w(in) = 1753.08- 908.37 = 844.71 Joules
b3
,
.,
.
:_J___L_j ,,t,,..... J
l
f [!
Fr ...... r....
_ __.-._---------
....
---"--.---.
,
-
' I
Figure 4.5 shows how dead volume as % of maximum total gas volume effects .the work per cycle. For more generality the work per cycle is expressed as a %..... of the work per cycle at zero dead volume. Note that the relationship is _i :-! _( ).i F.Ii
almOst linear. This curve differs from that published by Martini (77 h) in that in Figure 4-5 the pressure at the end of the.expansion stroke was made
._ -.:_i : i ,. ' ' }"I . ,
..... the minimum.pressure was made the same, This caused the average ._ressure to decrease more rapidly as d_ad volume increased Figure 4-5 is mor.etruly representative,of effect ofdead..volume on.Figure.2 work perof cycle. the same.(average the pressure), in the previous reference.7? h,
...i
i"
i. ,.. , "I £I
100
' '
!
!
,
i
I J
L_
J
:;'::i
_ 80
i
l,i
"
'i
-"2
0
c_ i
_
i
'
EXAMPLE PRESENTED "*"
,_-i
1 ! I
=
i!
IX
"'
I
N-
i... I
d
_
ee.
0v
:z
20
I
.
I
I
0
0
.
20
1
40
60
80
I00
DEAD VOLUME, % OF TOTAL MAXIMUM VOLUME Figure 4-5.
!
"
t"
!.l
ii, I.
-
! i
Effect of Dead Volume on Work Per_. Cycle i_orIsothermal Spaces
af_dConstant Average Pressure.
......
,'
_......................
• :71 i
64
I' I,
t
.l
4.1.5 CombinedStirlin_ and Otto Cycle VariableDead Volume_ Perfector ',Imperfect Regeneration "_
_, _:_ ,_
If the hotand cold spaces of the Stirling engine are free-ofheat exchange surfaceas they usuallyare, then compressionand expansionin these spaces takes place essentiallyadiabatically. Assume that the heat exchangersand regeneratorare placed, as shown in Figure 4,3 so that gas entering the hot space is at hot space temperature. Assume further that: 1) the gas in the heater is at heat source temperature,2) the gas in the cooler is at heat sink temperatureand the gas in the regeneratoris at the l._c) mean Cemperature between these two,.....Assume that the dead volume is distributedas follows: heater regenerator cooler Total
l0 cm3 30 cm3
i _+
(
Assume as before that the cold space is compressedfrom lO0 cm3 to 50 cm3 while the hot space is zero. Transfer takes place to the hot spacewith the total Volume held at 100 cm3. Expansiontakesplace In the hot space from 50 to 100 cm3. Finally,transferoccurs back to the cold space with the totalvolume held at 150 cm3. We will now follow throughthinscycle and keep track of pressures. Using a gas inventoryof 0.7313 g mol),as before, the initial common pressure is: nR
!
VHs VH VR' Vc Vcs
(4-22
h
assume:
_
3 (8.31,4} 900
546.1
3OU
Therefore.... Pz = 14.051 MPa Now let VCS go from 100 to 50 cc, VT from 150 to 100 cc. During the compressionstroke the gas In the cold space is compressedadiabaticallyand the gas in the heater,-regenerator and cooler is compressed isothermally. Thus: __
P2 " _0 Also-the
J
+_+_ +0'7313(8"31-4)
adiabatic
+ _SO
(4-23
cohipression law applies to__the cold space. 65
_i ,..
;_
' I_!__I_,_iy _i"_ !_,_ rl!i _i __i
...... I ......... i .............. ! •
I
k-_
I :i_!
!
where k = 1.40 = Cp/Cv for hydrogen. These two equations in two unknownsare Solved. Equation 4-24 is solved for TC5 and Sub._tltuted in Equation 4-23. Then
(iL:_ ;;''_ I: ,_,_
:: I
P2
1_ ,;, ' t i,,
::_ll :i_, I
calculator. Thus: TCS,= 354.92 K, P2 = 25.31 MPa
' ,
From state 2 to 3 (see Figure4-2) gas is transferredat no change in overall volume,.The gas from the cold space is cooled down tO 300 K as itenters the heat exchanger. It heats to 900 K in the regeneratorand gas heater and enters the hot space at go0 K, AS elementsof gas enter the hot space,pressure increases. This pressure-increase Causes the fir:t elements to attaln a temperature higher than•theheat source te_perature. Assume that the gas in the hot space is thoroughlymixed at each stage. Assume that 5steps are accurat_ enough to define the process. ThiS wili_be checked later. By the gas law:
_:_ _., :I _ I :_
is determined
!1
by a secant method of approximation using a programmable
0.7313 1_) _' 30(8.314) +
P2.2 =
10
+
=
10
6.08003 + 0.09938 +
_1 _
I_i,._-! : :,.,.
lO
+
40
(4-.25
1% I .,:
i .:._ !_;_,
,": _ •: I :,,C i -"L; .:_ I ':;t_*_ _':_'
:i_ _,
40
,,,'
:_
also by the adiabaticcompr,-=sstonlaw
THS2
= •900
"'_
I
I
comblnlng
.... 6.08003
,t ,: i_l
P2.2 = 900(_)
i0
0,,'_"_'_'+ O.09938 +
n'_nAv.,..,,,
40 354.92
P
"
_.,-_, 'i
i
- :
,
_
-- I
Soiving as before: P2.2 = 27.62 MPa THS2.2 = 922.73 K TCS2.2 =.363.88 K Then during the next increment the next 10 cc starts into the hot space at 900 K and the first 10 cc continues on frOm 922.73 K. Thus:
P2.4 -
lO
6.08003
t(_
o.286 *
g22.73(..P2.,_4'_
+
0.09938
900 [ P2,4'_ 0.286
30
+
P2.4 = 30.23
TH$2.4 = 947.06 _K
THS2.4 = 923.73 K
TCS2.4 = 373.40 K The two parts of gas in the hot space have different temperatures. temperature is found by adding the masses and finding the effective Thus:
v1
v2
_'1 + _2
o
T. 3 =
v1 + V2 =
A mean temperature..
(4-27
T3
•
THSM2,4 =
20
935.25 K
67
i I! II 11 1 i i-!_1 iii i:! i_ ) i:)_ i_ • _I I! _ iILI i_ i: , _(!
i _i.I !;ii! !iI _I ;:I i:i_[)
j
, I ( !1
.......... A computerprogramwas wrltten to do the above calculationnearly automatically. The resultsare given in Table 4-I. The work diagram for this specificexample is plotted in Figure 4,6. The work diagram is comparedwith the same engine cycleand gas inventory only assumingthe hot and cold gas spaces are isothermal at the heat source and hearsink temperature, For 33.3% dead volumelassumed here the effect of having adiabaticgas Spaces insteadOf isothermalcreates 10% more pressureswing but only 2.7% more work per cycle, Current practice Therefore,the error in assuming isothermalvariable volume spaceslinstead of the more realisticadiabaticvariablevolume spaces would be less than 2,7% when the work per cycle is computed, It is not expected that this conclusion will change when crank operatedengines are considered. Therefore,it is concludedthat figuringthe variable volume gas spaces as isothermalat the heat source and heat sink temperature will give the right cycle within in Stiflingengine design is to have about 58% dead volumework (seeper Section7), one or two percent for practicalengines. The isothermalassumptiongreatly reduces the laborof computation.
. _). _ I_,
Other formulationsare given in the literaturefor solvingthe above problem. Hoffman (77 be) and Rios (69 o, 69 ar)present equationswhich probably get
ii i.i_iI I if _ ., _
understandand comparetheir_ethods with that giVen above. However, it is to thethat samethe endRios point a differentway. The author working has not been able toincrefully known method uses a computerprogram on 720 time ments per revolution, However this is not mandatorybut the effect of reducing the number is not known. Rios did not actuallyuse such fine divisions.
:_ _
4.1.6 Conclusionsfrom C_,cleAnalysis I. Stirlingand Ericsson-cycleshave the same limitingefficiencyas the well known Carnot cycle. ,_
2. A good regeneratoris needed to attain high efficiencybut the cyclehas some efficiencywithout one. 3. An inefficientregeneratorbackea up by an adequategas heater and gas cooler will not affect the work realizedper cycle but will add to the heat requiredper cycle., 4. Dead volume has an almost linear effect on work availableper cycle. That is, iI_ half the maximum gas volume in the engine is dead volume, about half the workper cyclewould bc realizedcomparedto the.same displacements and average pressurewith no dead volume. Some dead volume is inescapable, 5. The most correcteffectivete(iiperature for the regeneratoris the log mean teml)erature.
,:
6. At the Usual dead volume ratios used in Stirlingengines the error in computingthe WOrk per cycle using isothermalspaces insteadof the more realisticadiabaticspaces.isi or 2%.
60
:i
•
!I
'i °.......
Effect of AdiabaticSpaces on a Discrete StlrlingCycle with Dead Volume VHD_ lO cm3, VRD = 30 cm3, VCD = I0 cm_ TH = 900 K, TR = 546.1 K, TC = 300 K
`-I___:_ II i :
I
"1
©
_"
"
l
VHL
VCL
P
0 0 lO 20 30 40 50 5 cm_ I0
I00 50 40 30 20 10 0 45 cms 40_
14.051 25,31 27,6] 30.22 33.2i 36,57 40;38 26.41 MPa 27.60
20 25 15
30 25 35
30.20 31.62 28.86
35 40 45 30 50 55 60 65 70 75 80 85 90 95 i00 100 95 90 85 80 75 70 65 60 55 50 45 40
15 I0 5 20 0 0 0 0 0 0 0 0 0 0 0 0 5 10 15 20 25 30 35 40 45 50 55 60
34.76 36.48 38.31 33.14 40.27 38,68 37.20 35.81 34.52 33.31 32.18 31.12 30.1i 29.17 28.28 28.28 26.66 25,23 23.94 22.78 2i.73 20.77 19.90 19,10 18.36 17.68 _ 17.06 16.47
Table 4-I THS 900 1064 923 936 949 962, 975 911 K 917 .....
TCS .... Comment 300 355 364 374 384 395| 406 359 K I 364
InitialConditions First COmpression Gas Transfer to Hot Space at AV = 10 cm3
929 935 923
373 379 368
fer to Hot S_ace at AV = 5 cm_. DuplicateGasTrans-
948 955 962 942 969 951. 936 924 912 902 893 885 878 871 865 865 85i 838 825 814 803 793 783 774 766 758 750 743
388 394 399 383 405 400 396 392 388 384 380 376 373 370 366 366 295 293 291 289 287 286 284_ 283 281 280 279. 278
P by using AV = I0 cm3 which is acceptable. Only 0.3% error in
Expansion in the Hot Space AV = 5 cm3.
Transfer to Cold Space AV = 5 cma.
,?.'L _._ ,_
Table .4-1, Page 2
,,",;;!,_;_
VHL
VGL
P
THS
TCS
; "r , ,,._, :,.;.!
cm3
cm}:
MPa
K
K
35 30
65 70
15, 93 15.42
736 729
277 276
20
80
14.50
717
274
Transfer to Cold
_!" :
75 85 90 95 lO0 90
14.95 14,09 13.69 13.32 12.98 14.42
723 71l 705 700 695 716
275 273 272 272 271 279 1
Space aV = 5 cm3.
i){., .=I .L_I
298 310 288 323.I 332 34l 342 363 375-,-367
Cold Space AV = lO cm3. Compressionin
359 352 345 339 _
Expansionin Hot
25 15 lO 5 .... 0 0 0 0 0 l0 20 30 40 50 60
70. 60 80 50 40 30 20 l0 0 0
18.21 20,75 16.13 23.91 26.35 29.15 32.40 36.15 40.52 37.39
70 80 90 lO0
0 0 0 0
34.68 32.31 30.22 28.37
........ 765 794 739 827 925 939 954 970 g8" 9_g 922 901 884 870
Comment
;' I ii,,
Transfer to Hot Space AV = lO cm3. 0.6% error inclosure of P at this point. Space AV = lO cm3. 0.3% error in closureof P at this point. Satisfactory.
i' 7O
i
..... 40
ISOTHERMALTHS, TCS, §PdV : 792J ADIABATICTHS, TCS, §PdV = 812J
_
35
_ 25
'-.._
_
20
....
/ 4
15 I 100
I II0
I 120
I 130_
TOTAL GAS VOLUME,crh 3
I 140---
150 .....
Figure 4-6. Comparisonof Adiabatic.andIsothermalHot and Cold Ga._Spaces for 33% Dead Volume.
71
',
i !!
! ,!
4_2 First Order Design Methods effectof dead volume, regeneratorefficiencyand adiabaticversus isothermal In the preceedingsection the thermodynamicprincipleswere explainedand the
i ] i I • ! I
--
variablevolume spaceswere discussedusing a Stiflingengine modelentirely in which the 4 processesof compresslon, heating,expansionand coolingare separated. In almost all Stirling enginesthe displacerand the power piston or the two power pistonsare moved with a crank. Therefore,the four processesoverlap. The heart of the first order design method is the computationof the output There are basicallytwo ways to attack this problem,numericallyand analytically. In the numericalmethod the hot and cold volumesof the engine under considerapowerwhen the parts sinusoidally. tion arecomputed formove a number of times.... during the cycle - say every 30_ of crank angle. The dead volume isalso computed. The effectivetemperaturesof the hot, cold and dead volume spaces are specified. Also the gas inventory is specified. It is assumedthat at each crank angle the pressurethrough-
1
._.
out the engine is common the same. Since the temperature andis volume of each gas space is specified,the pressureat each crank angle calculatedusing the perfectgas law. The gas pressure is then plotted againstthe total gas volume and the area of the closed curve is measured to give work output per cycle. The maximumand minimumpressuresare also no_cd,
'
,
i! !-
_ i,_
In the analyticalmethod the movementof the machine parts are specified sinusoidalwith a specifiedphase angle differencebetween them. In the same way as in the numericalmethod, gas temperaturesin the differentparts of the engine are specifiedand are assumed to be constant. Thenusing the methods of calculus the pressure-volumediagram for the engine is integratedfor the generalcase. Gustaf Schmidt (1871a) was the first to do this and publish his results. Since then, a number of authorshave presentedformulasbased upon the Schmidtanalysis. In this section the analysiswill be dividedinto piston-displacer engines and dual piston enginessince some formulaswork for one type and some for the other. Within each subdivis.io_ the numericalmethod will be explainedand a sample problemwill be worked out showingthe work diagramand an approximation of the integral. Next the analyticalequationswill be presentedand the same engineswill be calculatedusing these equations. If the equation is valid the same numericalresult should be obtained. Finally., a survey will be presentedof publishedcommentswhich relate the Carnot efficiencyto the actual efficiency of real enginesand.whichrelate the indicatedpower output to the power calculatedby the Schmidt analysis,
ii
4.2.1 Piston - DisplacerEngines
I_
4.2.1.I Engine Definition The nomenclaturefor engine internalvolumes and motions is describedin Fig,re4-7 and 4-8. 72
_i
r
i!
i ,. :
_
--
-
!
_
i
!L l
,
!
:
"
,
vHo 4 _v,,o vco k_-_-::==:=_---_-_::__:==----_. r " oR,vE "-
i,_IF
I_---ST
AHD
I
Z
' II
'"
DISPLACER
II HEATER
,'
REGENERATOR
,
i
I _
I
i
__VPL _
i
, I
'
COOLER
MIDPOINT OF DISPLACER TRAVEL
'
i
_ MIDPOINT
i
_, _
OF POWERPISTON TRAVEL
"
I _
' I
,)
AHD = VHD = STD : VRD = VCD : ACD = VPL TH = TR = TC = M : R :
area of hot face of displacer, cm_. hot dead volume, cm3. stroke of displacer, cm. regenerator dead volume, cm_. cold dead volume, cm3. area of cold face of displacer cm"_ power piston live volume, cm_.' ' effective hot gas temperature, K effective regenerator gas temperature, K effective _old gas temperature, K engine gas inventory, g mol. universal gas constant, 8.314 J/g mol'K
1
3
P : common gas pressure, MPa. PHI = crank angle, degrees. ALPH : phase angle, degrees.
i !
! Figure 4-7.
Piston Displacer Engine Nomer, clature,
i
VHL : AHD(STD)
(4-28
/,
VCL : ACD(STD)
(4-29
_' !
r-
Hot volume,
VH =
VHL
2
-1
i
Ii _ cos(PHl) I + VHD
L
(4-30
-_
Cold volume, VC=
i !
VCL 2
+ cos(PHI
[1)]
•
_
+ VCD + _ 2
VRL
cos
_.
-
(PHI
ALPH)] (4-3l
73
II
I
'_
Figure 4-8.
Phasing of Displacer and Power Piston.
Total volume VT = VH + VC + VRD
(4-32
Engine pressure
p : M(R)
VH + VC TH-- _
74
(4-33 VRD + T_
°
..,! l_......i : ,
__,i |_ |_I |'_i;i '],_['i | _!I "-| :'_i 'IIi i:. i
........ "
¢ r:!
....
t
I
I1 l_."1 ,_._
/
i
t
_1
Fr _ { j
,
T
...... r-r
:..i. "
., I i
"......
'"
[. ! l
, f ,
VCD includesthe dead volume in the cooler as well as the dead volumebetween ---the strokesof the displacerand the-powerpiston. Accordingto the classificationof engines given in Fi.qure 2-6, the gamma type machinemust have some volume between the strokes to allow for clearanceand the flow passagesbetween. In the beta type engine the strokesr,fthe displacer and the power piston overlap so that they almost touch at one point In the cycle. This overlap volume is subtractedfrom the dead volume in the cold heat exchanger. For a beta type enginewith this type of stroke overlapand ALPH = 90u and VCL = VPLL then VCD = VCDHX- _
(2-V_)-
VCDHX,- _PL (I-_/_) where VCDHX = cold
J-.-':'-i
dead volume in heat exchanger.
I L'"_! ,.!, _! _I
4.2,1.? Sample En_ineSpecifications In order to checkequations which look quite different,it was decided to specify a particularengine and then determineif thework integralchecks. The specificationdecided upon was:
_i _i _i
L•=_i ',,i
[._;
M(R) = I0,518 J/K TH =_600 K TC== 300K VHL VCL = VPL = VRD = 40 cm3.
VHD = vco=o
ALPH = 900
TR is defined.anumber of ways, dependinghow.it is definedin the analytical equation that is being checked..It may be: (1) Arithmeticmean (Walker) TR - (TH
= 450 K
(2) Log mean, most realistic TR = (TH - TC)/In(TH/TC)= 432.8 K (3) Half volume hot, half volumecold (Mayer) l l l
r_: _(TH-_)+ TR = 400 K The above sample engine specificationis for a gamma engine. For a beta engine assume in addi'_ionthat VCDHX = 0 then: VCD = O.-.40 (I -_/_) = - II.7i5 cm3 4.2.1,3 NumericalAnalysis " '_¢
Using the numbersgiven in Section4.2.1.2,Equations4-28 4-33 can be ovaluatedfor PH_ : O, 30, 60, . .., 360, P carlbe plottedto againstVT and the result closed curve can be integratedgraphicallyand the maximum and minT5
_
T !
!II
i .,i
1
o
1 I
differentexamplesglvP.s resultwhich is 4.5% lo_ when comparedwith valid imun gas pressurecan be a noted. The author'sexperiencewith a number of analyticalequationsand with numericalcalculationswith _ery small crank angle increments. If the investigatorhas access to a programmablecalculator ora computerthen the computationcan be made with any degree of precision desired, _ Figure4-9 shows the flow diagramwhich was used for programming. The author has used both an HP-65 and an HP-67 for this purpose. He has also used this method as part of a larger second order calculationwritten"in FORTR/_N. Using the 400 K effectiveregeneratortemperaturethe followingresultswere obtained for the numericalexample.
r • •: i .
DELPHI 300 20 l0 5 O.25 Mayer equation
_Pdv 314.36 Joules 322.56 327.53 328.78 329.1994570 329.2005026
% Error 4.5 2.0 O.50 O.13 0.0003 0
The Mayer equationwill be given in.Section4,2.1.4 and discussedmore fully there. It uses the same assumptionsas were employed in the numericalanalysis. One can see from the above table that the result by numericalanalysisapproaches the Mayer equation resultas DELPHI approacheszero. .Thetwo check. If the arithmeticaverageis used TR = 450 K ther,. ' DELPHI _Pdv Pmax lo
360.45
1 PHI for Pmax
58.l0 MPa
I170
If the log mean avera._e is used TR = 432.8 K then: DELPHI
, _ Pav
l°.
350.04
Pmax 56.99 MPa
PHI for Pmax
I
If7°
!
I
For the case of the Beta engine with essentiallytouchingdisplacerand power piston at one point in the cycle VCD = -11.715cm3. For the arithmeticaverage au:d volume temperatureTR = 450 K. Then: PHI for DELPHI Io
_ Pdv
Pmax
516.32
Pmax
74.0862
117°
Precisionin calculatingthis work ir_qral is mainly of academicinterest because the result will be multipli_.d it_first order analysisby an experience facto_ like 0.5 oP 0.6 (one figure precision). Even in seco_Idor third order analysis no more than two figure accuracyin the finBi power output and
..
•
.....
...2£2_.
INPUT DIMENSIONS
[
I
CALCULATEEQUATIONCONSTANTS I
I ,N,T,A_,_ _TO_AO_ _,_T_I
..........
_,r
i...Ll
-I
I
DISPLAY PHI(OPTIONAL) . I
I CALCULATEAND STOREVC, VH, VT i
i
.
PUT.VT AND
_
[
DISPLAY VT (OPTIONAL)-
P IN SECOND REGISTERS STORAGE
,,
,
I
I i
CALCULATE AND STORE P
i
DISPLAY P (OPTIONAL)
I ]
i
l
k
½ I
......
PHI : PHI + DELPHI
YES ._,_, _,
,..,_,,,_.NO
i' [
...............
t PHI PMAXAND AT PMAX FIND
i
I ¢
YES
i Figure 4-9.
!.
!
PMAXAND PHI AT PMAX ,
Flow Diagram for Work Integral Analysis.
77
r
!
'
5,-,
efficiencyshould ever beexpected. Thus errors less than 1% should be consideredinsignificant. Therefore, DELPHI = 15o would be adequate for all practicalpurposes. 4.2.1.4 SchmidtEguations At McbonnellDouglas,Mort Mayer reduced the Schmidt Equationtothe following relativelysimple form (68 c).
W = M(R)(TC)(2_)B(VP B2 + C2 ) [ (A2 - B2 A - C2)½
-l]
where: t
.
_
I_
W = work per cycle, J M = gas inventory,g mol
_l .I ii
R = gas constant= 8.314 J/g mol • K TC gastemperature,K temperature,K TH = = effectivecold effectivehot gas A = VCO + -_ (VHO) VCO =Y_iil"
+ VDC + V__+ VRD2
VHO = VHD
L_
,_:
W
2
Y_-
= VPL/2
,C
B = Y-_I - _HC)sin(ALPH) C = [VPL - VHL(I - _)cos(ALPH)]/2 ALPH = phase angle between'" displacerand power piston,normally 90° From the sample engine specifications: VCO =
+ 0__
+ _-
60 cm = 60 x 10 m = 40 x 10" m
300 ,., . s 3 A = 60 x 10"_ _-O_(_ux I0"6) = 8 x I0" m 6
B = 40 x 10" 300_ .s 3 2 (i -_-_, = i x 10 m 6 C = 40 x 10" ._3 2 =2x10"m Using these inputs the Mayer equation gives: W = 329.2005026JOules
78
......
r,.
(4-34
The Mayer equationevaluatesthe integralexactly given the _ssumptionsthat were used in its de_ivation_like sinusoidalmotion and half the dead space at hot temperatureand half at cold temperature.•The.numericalmethod (_ection 4.3.1.3) approachesthis same value as the angle incrementapproacheszero. The Mayer equationmust have VHL = VCL. That is, itcannot consider the effect of the displacerdrive rod. J. R. Senft (76 n) presentsa Schmidtequationfor finding the energy generated per cycle. His assump_ons are the same as have been made so far with the temperatureof the_deadspace gas having the arithmeticmean betweenthe hot and cold gas spaces. This equationis for a beta _pe engine with the displacer and power piston essentiallytouchingat one point during the _cle. His eq_ti on is :
W=
_(I" ]y+ (y2. T) Pmax X2)' Vdk sin a [
Y"+ X Y
(4-3!
where X
=
[(T
-
1)2
+ 2(T- I) k cosa + k 2],
Y = _ + 4X_/(I _)+
D
2
D = (I + k - 2 k cos_)½ In order to illustrateand check this equation it is evaluatedfor a specific case previouslycomputedby numbericalmethods. (See Section4.2.1.3 for TR = 450 K and VCD = -11.715cm3,) TC 300 _ 0.5 = T-H= 6-_0 _ " Vd = vo'lumeswept by displacer= VHL = VCL = 40 cm_ Vp = volume swept by piston = VPL = 40 cm3 VD = volume of all dead space =VRD + VHD + VCD = 40 cm_ X = VD/Vd = 40/40 = l k = Vp/Vd = 40/40 = l = phase angle = ALPH = go° P.nax= maximum pressure.attainedduring each cycle = 74.0862MPa D = (I + i - 2(1)cosgo°)½ -_7_ Y = 0.5 + 4(i)(0.5)+ X/_-= 3.247547
(1.5)
X :
[(0.5- I)2 + 2(0.5 - 1)(1)(cos90o) + 1]
_ = 1.118034 79
y •+ (y2 . X2)%= 6.296573
'. :_,_(
This answer agrees very weil with results obtained by numerical ,methods Of 516,32joules. Senft (77 ak) also has adaptedh_s equationfora gamma type englne-(withoutstroke overlap). In this case the equationsfor W and X are the same and the equation forY is: 4×T Y = (l+ _)+ l + • + k
(4-36
Therefore:
+1--3.833333.
Y=.0,740513
y + (y2 . X2))_= 7.50000 To agree with the numericalanalysisof Sectlon4.2.1.3for TR = 450 K, Pmax = 58.10 MPa. Thus. '
W = _(I - 0.5)(58.10)(40)sing0°(0.740513) 7.50000 W = 360,45 Joules This .resultagrees exactly with the numericalanalysis for DELPHI = l°, TD = 450 K and Pmax = 58.10 MPa. (See Section4.2.i.3.) This new Senft equation is also correct° Cooke-YarbOrough(74 i) has publisheda simplifiedexpressionfor power output which makes the approximationthat not only the volume changesbut also the pressureChangesare sinusoidal. The regeneratoris treatedas being half at the hot volume temperatureand half at the cold volume temperature. His equationis: VEVo - AT sin VC Output Power= _-_ TM
80
• '.,c
i_!
+I+ _--_}
._ ::, _*
TC+ _M AT
(4-37
...... r.___
1¸
: ,! _ i_ :i
:_:,
! • :_ ,II
"!I
where: =
'
on"stmean pi of working gas, approximations or pressure with boththese displacer and .power atpressure mid-stroke. (Withthe used, two pressures can be regardedas identical.) If the mean pressure is known, it can be ..... used directlyin Equation (4-37). 0the_rwise the mid-strokepressure can be calculatedas follows:
_ =
vRD'M_
_
_
.,_i +_.20
"i
= 40.59 MPA = operating frequency,radians/sec = 2_ sO that output power in watts is numericallyequal to power per cycle, Joules VE = VHL =.40:crn 3,
j .i : "
V0 = VPL = 40 ,cm3 VM = total gas volume of system when output piston is at midstroke " VPL = VRD = VHL 40 ++40 _ +T 20 = 100 cm3
+
+ . = 60 cm3
",
:._
i i..
,_T = TE - Tc = 600 - 300 =300 K e = phase angle = a = 90° Vc = cold gas volumewith both piston and displacerat midstroke and regeneratorvolume split betweenhot and cold volumes
=
.)
":i'
i0.518 = 60-'-ff 20+. _+40
•
.I I
.ii:
(3uo)i
_j
output power= 4,0'59 I'_) _ 300+ i-_ (300) = 318.79 Joules/cycle
, ,...,I , :".I
/
B1
.................
.l .i ....... 4.:..... ,' ..... ).
• ._,:.,.,.._
.
_4 _ ._..,_4J_±___ _" _
Becauseof how V is determinedthls result should be compared to the.Mayer equation,that i_, to 329.20 joules. Therefore,the Cooke-Yarborough equation . , appearsto be a reasonablygood approximation(3,2%error). The accuracy improvesas.the dead volume is increased,because the pressurewaveform.is.then more nearly sinusOidal.
I
_
i' ;N " ,:_ :i
'i ','_
4,2-,2 Dual Pisi:onEnBine_Es
. _
4,2.2,1 Engine Definitionand Samlep__;_ineSpecifications
.. :,:
The nomenclaturefor engine internalvolumesand motions are describedin FigUre 4-I0, Also given in Figure4-I0 are the assumedvalues for-thesample case. The followingequationsdescribe the volumesand pressures.
:.' _".
Hot Volume
:'_
VH =Y_-[I Cold Volume
-
VC= _[I Total Volume
- sin(PHI- ALPH)] + VCD
sin(PHI)_
+ VHD
VT = VH + VC + VRD
(4-38
,. "" ,-
(4-39
" .
(4-40
Engine Pressure p =..
"'_
M(R)
+
(4-41
+ VRD TT
.-I
)
4,2,2.2 NumericalAnalysis
_ '_._
Using the assumedvalues given in Figure 4-I0, Equations4-38 to 4-41 were evaluatedfor PHI = O, 30, 60, . . . 360. The results_ere:
i: ._.
,. '|
I .
)
I! m
......
'
I
VHD
I-
........
.....
VHL "_\_'"_'_\'
-T VCL
VH _= 40 G
20 PHI 90
Symbol, VHD VRD VCD VHL VCL TH TC TR M R M(R) P PHi DELPHI ALPH
180.
270
360
Definitionhot dead volume regenerator dead volume cold dead volume hotpiston live volume• cold piston live volume, effectivehot gas temp. effectivecold gas temp, effectiveregeneratorg.t. engine gas inventory gas .constant cofnmongas pressure crank angles crank,angle increment phase angle
I_- ALPH-_
Units cm3 cm3 cm3 cm3 cm3 K K K g mol J/g mol.K J/K MPa degrees degrees degrees
AssumedValue 0 40 0 40 40 600 300 450_ 1.265 ....8.314 10.518 to be calculated (DELPHi)N: 360 N = interger
FigureA-lO, Dual Piston EngineNomenclatureand Assumptionsfor Sample Case,
•i
":,y] ,,(
-_,
PHI
VT
P
Degrees
cm3
MPa
0
)
.... -
100.0
30
-
:i
--41.2•
87.3
4s.;,
'_:i;
60 go 120
72.7 60.0 52.7
54.4 67.6 83.0
]
150
52.7
91.9
'
I
180
60.0
86.1 •
i
240
87.3
57.0
_
_:
i ] ,._ +'
_:'
_1
270
100.0
47.3
_
300
107.3
4i. 9
i
330
107.3
39.9
_;
360......
100.0
41,2
:,
This data is graphedin Figure 4-II and graphicallyintegrated. A value of 695.3 j was obtained. As before,a numericalintegrationwas carried along indicatesthe accuracy of the graphicalintegrationprocedure. To approach as the pointswere calculated. This was 668.8 joules,a 3.8% errorwhich the answerthat should be obtainedby valid Schmidtequations,DELPHI should be reducedtoward zero. The results obtainedwere:
1 :l
i"
•
i+) !_
,i II ,, i
I DELPHI
_VdP _Toui es
Pmax
TR K
% Due toError DELPHI
;]
_Li 30 10
668.8 696.8
91.87
450 450
4.5 O.5
I
700.324
91.98
450
0
30 1
641.284 671. 517
89.121 89. 220
43•2.8 432.8
4.5 0
30
587.9
400
4.5
400
0
1
|
.... I
(.
.........
84
,-
615.-619
83.831
":"
i
Note the differencein the result dependingcn what is used for the effective temperatureof the gas in the regenerator. If the regeneratorhas a uniform temperaturegradientfrom hot to cold, which it usuallydoes, then the log mean temperature(TR = 432.8 K) is correct. Thearithmetic mean (TR-= 450 K) gives a result for this numericalexample4,3% high, The assumptionthat the regeneratoris half hot and half cold (TR = 400 K) gives a result 9.1% low.
1.00
9C
80
70
60
695.3J
i L
50
----
-)
40 50
60
I
l
70
8_
I
90 ..... 100
110
VOLUME,cm3 •
Figure4-11. Work Diagramfor Dual Piston Sample Case (DELPHI= 30°).
!
::
4.2.2.3 Schmidt Equations Walker (73 J) gives a Schmidt equationmost adaptableto the two piston engine. Using his nomenclatureit is: ---
85
\(I +=)/ I + where
1 P = work per cycle,
Joules
Pmax= maximumpressure during cycle,
MPa
VT = VE + Vc = (I + _)VE VE = swept volume in expansionspace = VHL •
Vc = swept volume in compressionspace= VCL = Vc/VE, swept volume ratio = TcITE Tc = compressionspace gas.. temperature= TC TE = expansionspace gas temperature= TH TD = dead space gas temperature= TR (Tc + TE)/2 6 = (_2 + 2_K COSa +_2)½/(T + K + 2S) a = angle by which volume_variations in expansionspace lead those in compressionspace, degrees S 2XT/(_ + 1) (Thisis where the arithmeticaverage temperature for the regeneratorenters.)
)i i
i
_i
i,
X = VD/VE, dead volume ratio VD = total dead volume,cm3 = VHD + VRD + VCD e = tan"l (Ksin a/(_ + _cos a)) (Note that e defined incorrectly in Walker'stable of nomenclatureand on page 36, but is right on page 28 of reference73j) Now in order to check this equationagainst numericalanalysisit should give a work per cycle of slightlygreaterthan 700.324Joules when 91.98 MPa is used as the maximumpressure. TD = 450 K is the same assumptionfor both. (See Section4.2.2.2.)
i
Therefore: VT : 40 + 40 = 80 cm3 : Vc/VE : 40/40 =.l Pmax = 91.98 MPa = Tc/TE = 300/600: 0.5 X = VD/VE = 40/40 = l '.; = 2(I)(0.5)/(0.5+ l)..:2/3
_'
= (0.52+ 12)½/(0.5+ l + 2(2/3))= 0.39460 e = tar,'1(I/0.5) = 63.430
i_'i
P = -700.37joules
I
Thus the formula checks to 4 figure accuracyexceptfor the si,.. Walker obtained the above equationalong with most of the nomenclaturefrom the publishedPhilipsliterature. MeiJer's thesis (60 c) containsthe same formulaon page 12 of reference60 c, except he uses (I- _) insteadof (_ - i) and a positiveresultwould thereforebe obtained,
_.
.-
In Meijer's thesis (60 c), the quantityS is definedso that dead spaces in heaters,regeneratorand coolersand clearancespaces•in the compressionand expansionspaces, all of which have differenttemperaturesassociatedwith them, can be accommodated.
:4
Thus:
:i
s-n
s: s=l
Vs Tc
(4-43
where Vs and l" s are the volumesand absolutetemperaturesof the dead spaces• Using tBis formula it would be possibleto use the more correct log mean temperaturefor the regenerator. Thus:
i ':_ _i
i_
i! The above equationthen-evaluatesto' •
_'_ _ °-_
P = 671.537Joules This is within 0.003% of the value of 671.517 computednumericallyfor i degree increments(see Section4.2.2.2). Finkelstein(60 v) independentlyof Meijer derived the followingformula for the work per cycle: + n + _
WRTfw(p)
(4-44 87
_( < ._ ':i -_
V,
i
I
,
.,
./
where "i
I From his derivation it is apparent that used by Walker. Thus: .....
1i
and V : VE also Finkelstein's
f
analysis, _
P:
WRis equivalent
I {
When these transformations are made: 2_(I - T)(sin_)M(R)T c . (T + _ + 2S)2_(I + V_-_-_)
I
This compares to 671.537 by the Meijer I '
(4-45
K :l _ : 900 M(R)Tc = 10.518(300) = 3155.4 a :I(1.5 + 2s): 0.38735 P :-671,55
! i I
I
_e M(R) used in the numerical
Using the last numerical example: S : 40C300) : 0.693 40(_32.8)
I' ,
i :
to that
n : K, _ = T, _ = _, v = X, _ : 2S, p : _, T = Tc
I
I i ...... +
his nomenclature runs parallel
,
:-
"t ,
_, •
formula and to 671.517 by numerical
analysiswith I degreeincrements. Therefore,the above formulaalso is useful in ccmputingthe work output per cycle. Note that this formulaemp_,oys the gas inwntory instead oi_-the maximumpressure. ,Zarinchang(75 d) presentsa formula.forthe work output per cycle of a dual
i piston It bears a superficialresemblance• tonow thebe Walker equationbut is not engi_e_ identicalur easily convertedto it. ,Itwill evaluatednumerically .......... to determineif..itgives the right answer, xk(l t) Vl v_i-_-_-_..s in_ W _=_ " Pmax ,max (t + k + S)-_/(l + F) (l +_
'_ where
:,.
'
I:
W =-work output per cycle, joules k : ratio of swept volume of compression space to expansion space, _ 1 for the sample problembeing used. t = temperatureratio 300/600= 0.5 Pmax = maximumpressure = 91.98 MPa VI,max
(4-46
= assumedto be swept volume of expansionspace,not defined in reference75 d : 40 cm_
• IrI ,
I
' ,
'
ii ,:
F ._ t:L 4 k._ +k2tk .....(%
" : : ., : i
"i , ,!
,_ =-_phase lag oi" the crank for the compression space piston ...... behind the crank For the expansion space piston = 90°. .-S - proportional dead space referring to swept volume of the expansion and reduction to lower temperature = 4xt/(l + t) Arithmatic mean temp. for regeneratorx = ratio oftotal deaJ volume--toswept volume of expansion space = 40/40
'
., 1
= 1.
Evaluating:
ill
,i
s -- 4(I)(.5)/1.5 = 413 0.25 + 1 + 2(.5)L1)T(O__. F = ---[7.5--$- I--4--4-/-3-)- ..... O. 441 W = 669.408 Joules - 4.4% low compared to the Walker numerical analysis
_ I !
cos,_ -S) .....
',
formula
and to
However, if F is.defined the same as ,_of the Walker formula, that is,...put a square root sign over"the entire numerator, then F = 0.39460 and W = 700.37, exactly the same magnitude as obtained with the Walker formula. Thus it is concluded that the Zarinchang formula is also valid after it is corrected as shown above.
: ,
I
!,
I
i ,y!
4,2.3
,_ ,. i-',_.
Experience
Factors
I
Once the Schmidtand the Carnot equations have been eva-luatedfor an.engine, a rough estimate of its power output and efficiency can be made if it is designed
.:_..< |_!
t
;
,
simi-lar..-to an engine-for which test data exists. Figure 4-12 shows how.experience factors can be applied after relatively simple calculations to obtain ball park estimates of the size, weight, and efficiency... for a particular output power level desired.
'' ,
_._ _-.:!
To illustrate, assume one has an engine for'which you know the d.in_nsion,the speed of operation, average operating pressure, type of engine (,_,_ or y) a_id input and output metal temperature. From this-inforillation one can calculate using the appropriate Schmidt equation from the preceeding sections the calculated,power output, W . If the engine were.perfect with no losses then the Carnot equation wouldCapply: Tc Wc _c = I - y_
i
Qc
where Qc = bas.icheat required before losses a_e added.
._ -- _'
By measuring instantaneous values of engine pressure a.d power piston displacemerit,one can plot a work diagram. The area of this diagra,ltimes engine speed is the measured indicated _ower, Wr. The heat input to the engine, Q, .-. can be nw_st,onveniently measure_iby addlng the lieatabsorbed by the cooling water to the power output. Q is considerably greater than Qr' The indicated
-!
i
_
' _,Immd
efficiency, I
q, is W_/Q,
Some of the measured indicated
power is
absorbed
by
friction tile s_a,ls on andtilecranks the engine. L_rc_kepo_,;er, Wi_, is the power-. that can in be measured output of shaft by measut_ing the braking torque and..
_
....,_
I •'--"_ 1
wla = Wn/Q. To operate independep.tly..most _nglnes require auxillaries. For a typica_ Stirling engine a fuel pump,a combustion air blower, a water punlp,a the-speed. The mechanical efficiency is WI_/WI. The.brake ufficiency is cooling air fan and aworking fluid pump and-a generator would all draw power ....from the engine. The net brake power, WNB,-is what is left. Net brake efficiency is nNB = WNB/Q.
_
The efficiency experience factor is of three kinds: I, indicated_ nln c
, .....
2.
brake_
3.
net
TiB/_lc
brake,
_NB/_c
Th_se efficiency factors are_xpressed of Carnot efficiency.
....
i
'4......
in the following tables as a percent ....
'
Power efficiency factors relate the power realized to that calculated by a Schmidt equation..orequivalent. .......................
_. !
All available information that would allow this efficiency and power experience factors to be calculated will now be given,
t 4.2.3.1
Efficiency
Experience
Factors
The most extensive .informatioli is available from publications authorized by N.V. Philips Co., and their licensees which generally give efficiencyas, a
: i , "'i
/:_
i "_
function,.ofoutput power given displacement engine, For each point curves given the size of for the a gas heater, regenerator, gas cooler, the gas.on the pressure and engine speed are chosen to give the best efficiency for the desired.-_ power. No dimensions except for the disglacement are usually given but this infor_ilation indicates what a well designed engine can do. Table 4-2 shows
"
indicated efficiencies calculated by,Michels_ for a 1-98 rhombic drive Stirling engine. The 1-98 has a 98 cc displacement disp'iacerand power piston.
i_
Michels shows that for optimized engines the indicatedefficiency depends upon
_'
heater temperature and cooler temperature and not upon the working gas used, Figure 4-1-3shows Michels' curve correctly labeled.
i. I
i_ f_
k'
"i 'i
__z:",
JWI
I
I
i
i
,
i
i
Table 4-2 IndicatedEfficienciesof a (Reference 76 e) I
1-98 Rhombic Drive Philips Working ,
I
Fluid
Heater
Cooler
Engine
Indicated
Indicated.
Percentof ....
Maximunl Temp. C ............... Temp. C . Power at
% Efficiency
Effi ciency........ Carnot
I
Efficiency .Kilowatts
-I
', ' :i _' ii '.i
i
H2
850
lO0
.....H2
400
1O0
H2
250
I00
He He
850 400
I00 I00
He
250
100,
N2
850
"2
400
N2
250
lO0
H2
850
0
H2
400
0
H2 He He
250 850 400
0 0 0
He
250
N2
..i O0
"
.......... 850
8
50
75
32
72
18..
63
i
50 30
75 67
!. i ,.
17
59
::._.k
49
73
.:
.3s
31
7o
Negative
....
---------_ .....
.6 1 : .18 -I,5
lO
75
2,8
45
76
,
1 8 2
34: 58 42
71 77 71
! I
32
67
55
73
.7 2
N2
400
0
.48 -.
42
71
N2
250
0
.18
33
69
Anotherway of correlatingthe calculationsis to relate,the indicatedefficiency to the Carnot efficiencyfor the particularheater and cooler te_Iperature employed. Figure-4-14sllows _F,i_indicatedefficiencyfactor, (n/n_). Note that it goes i_rom65 + 6% at 250 C heat temperatureto 75 + 2% at 800_C. Based upon much experimentaldata, Michels calculatesthe brake efficiencyfactor, n-/q_, for a an engine without poweringnecessaryauxiliaries. .Table4-3.showst_e.-h_aximum i
L
,
)l
57
0 0
35
•
:
: "_i
I i i
I
L
!
""
Table 4-3
_,
Computed
Brake
(Shaft)
Efficiencles
for"
Engine aOptimi:ed 1-98 Rhombi.c for Drive Each Operating Phi I i ps (Reference 76 e)
"_ Working _t
Fluid
Heater
Cooler
Shaft
Power
Temp. ¢
Temp. C
at-Max, K, wattEff.
Brake Eff. WB
'_
H2 .
,,_, ,.
,_
of %
Mechanical
Carnot Et'f.
Efficiency WB
i
IIc
l-J, _,!
Point
H2
,850
1O0
4
40
60
O.80
i_
4oo
1oo
o.8
25
56
o. 78,
f
_JO'_r"
I00
O. 12
12
42
0.67
I}i
' i
,' _ i
He
.... 850
1O0
4
40
60
O. 80
!
'_/
,[ '. ,
,_i
He
400
100-
O. 4
24
54
O, bO'
!
:
lle
250
I00
0, I
12
42
0,71
N2
850
I00
1 0
43
64
_
N.2
400
1O0
O. 2
26
58
O. 84
,_ _! =} ._i
N,_
250
1O0
Negati ve
....
H., _
850
0
6
47
62
0 . 82
_.
21
H,
400
0
1.8
36
61
0 80
,i )¢;i
H_ _.
250
0
0,7
26
54
0 76
I[;:,
He
850
0
5
46_
61 "
0.79
_!--_
He
,ILl{.)
0
1",_-
36
61
0.86
_
He
250
0
0.4
27.
56
0.84
N..
850
o
N,,"
400
0
(I. 'I
38
64
N,1
"_|'1 _,_tl
0
0 17 ......
29
61
; ,
•
,
\-.
! [r_
rill}"
.._
"
.
,-
_--
-
.......
0.88
;_
/
-_
I_
,
o.8: _0
.. aO
0.88
,
t I
brake efficiency points for these calculations. Figure 4-14 shoi,'s how the brake efficiency factor depends on heater temperature. The mechanical effi-ciency for this machine is generally about 80% (see Table 4-3). _ ' .... i i i I
The-size, weight, power and efficiency for a number oi:other engines mentioned in the literature are presented in Tables 4-4 and 4-5. It should be emphasized that the powers given are for the maximunlefficiency operating point,not the nlaximumpower point. Note that tliebrake-efficiencies range froni4_,to 69% of Carnot.
o I iI ..... _ i
Finego]dand Vanderbrug (77 ae) using data from the Philips-Ford 4-215 engine conclude that the maximum brake efficiency is 52% of the Carnot efficiency. This factor"is_based upon 1975 data. Improvements have..beenmade since then..
•.!. _,_ _.
Net Brake Efficiency Tileinformation presented in .,Tables4.-3to 4-5 is for engines without auxil_iaries. In Table 4-6 performance and.efficiencies are given for---th--e--e'ngine powering all auxi.liariesneeded ,to.have the engine stand alone, This includes the cooling fan, the blower and atomizer and fuel pump for the burner, and the water pump for the radiator-, Table 4-6 shows that tilemaximum net brake efficiency., is from 38 to..65%of.ideal.
......
.....
,! I
Carlqvist, et. al (77 a.l)give the following formula,for well optimized engines .
operating on hydrogen at_their maximum efficiency points.
'
Pnet...... neff '
T. ' EF
TC (I
- y-_-H ) "C
. ' nH
'..
. nbl
i fA
where
(4-47
] ._
)
neff = overall thermal or effective efficiency.........
Pnet= net shaft power with all auxiliaries .driven................................... !:1 ..... EF : fuel energy fl>_w ii
:/
TC, TH = compression _-expansion gas tempe,_ature,K C = Carnot efficiency ratio of indicated efficiency to Carnot efficiency, normally from 0.65 to 0.75. Under special conditions 0.80 can be reached. nH = heater efficiency, ratio between the energy flow to the heater and tllefuel energy flow.. Normally between 0.85 and 0.90. nbl= mechanical efficiency, ratio of indicated to brake power. Now about 0.85 should go to 0.90. fA = auxiliary ratio, At maximunl, efficiency point fA = 0.95. Thus the most optimistic figures: TC TC llef f --(I -_-) 0,75(.90)(.90)(.95) = (l -_)(0.-5'_) H "H
I....
•
• '
,'
I
,
1
I
i
!
i :
I F,
,
4.2.3.2 Power ExperienceFactol'_s Experiencer.ctorsbased upon the SchmidtEquation - Only a very few references give numbersrelatingthe output brake power to that predictedby applicationof the Schmidtequation. The availabledata are:
' "'
Author i *
Urieii Zarinchang Finegold & Vanderbrug Martini (calc)
.__ -_J_ i_i, "; ! i_---_ i _il _r _ _ _-'
Reference
WB/Wc*
1977 af 1975 d ].977 ae
0.3 to 0.4• 0.3 to 0.4 0.32
Table 5.5 0.6 this report *See Figure4-12 for nomenclature,at maximumefficiencypoint. This power experience factor is the product of two factors. One factor of about 0.8 is the_mechanicalefficiencyfor the machine. The other factor expressesthe fractionof the basic powerremainingafter internalflow friction is deducted. This second factor is larger at the maximumefficiency ....... point than it is at the maximumpower point. Until more is known about this factor,it should be used as.a very rough guide. 4.2.4 First Order Desi._n. Procedure
,_
In a first order design procedurethe followingsteps are used:_ .q
i. EstablishTH and Tc. 2. Calculatenc. 3. Determine,indicated,brake and.netbrake efficienciLes using efficiencyexperiencefactors. 4. Establishtype of eF.gine,pistondisplacementand fraction dead volume and speed. (See Section3.3.3 for description of-a typicalen_;ine.) 5. ComputeWc wit*_appropriateScI_midt equation. 6. - Predictbrake power using the powerexperiencefactor,
!
1
i I4 i
As a sample of this procedurethe followingproblemand solutionis offered,
i 'I
Problem: Your lab reportsa new materialhas been discoveredwhich will allow an engine like the GPU-3 (see Section3.3) to operateat a 1500 C. Estimate poweroutput and efficiencybased upon first order methods. Ii
Solution: i) TH = 1500 + 273 = 1773K Tc = 20 + 273 = 293 K Tc = 293 2) nc : I - _ I .... -_ : 0.835
4
i &
| l ! il i
i
{! • _l
I
,
3) From extrapolation of tilebrake is 0.65., Tlierefore nBFigure4-14 = 0.65(0.835)= 0.54 efficiencyf_actor 4) Use the Cooke-Yarborough Equation (4-37)and furtherestablish that: " " _, = 4.137 MPa (600 psia) ...... ' = i00',(50 Hz) VE (7.01)2(',_/4)(3.068) Vo : 118.4 cm 3
: 118.4 cm3
VM _ VHD + VRD + VCD + 0.854Vp+ 0.354Vo (See Section7.2 for values of VHD, VRD ahd VCD,) VM z 81.8 + 51.8 + 17.2 + 101._i__+ 41.9 = 293.8 cm3 A? = 1773 - 293 = 1480 K O : 900
'
Vc = Y-_ + VCD + (Vo + VE)(0.354) b
+ 17,2 + (118.4+118,4)(,354) = 126,9 cm3 _m VEVo AT tin _-
_
5) Calculatedoutput power, Wc = --8-VM
Vc Tc + _
Wc_ 4.135(I00_)(118.4)(118.4) 8 293.8 = 12.3KW
-_
AT
(.1480)(sin 90°) ZBLI--+ _126'9_,1480,)
6) Choose a power experiencefactoruf WB/Wc = 0.6 so brake power, W_ = 0.6(12.3)= 7.38 KW ! i
!
heat input,Q -_7.38/0.54--13.,7KW 4,2.5 Conclusions on First Order Design Methods., I. First order designmethods are good for preliminarysystem analysis.
_' ,i
no more than 58% of the Carnot efficiencyfiguredbetween the heater metal temperatureand the coolingwater temperature, 2. PublishedSchmidtequationsto Currentflame-heatedStiriingengines poweringall aux-iliaries can realize 3_ computebasic output power (Figure4-12)
i _ •:'
fr_omengine dimensionsare generallycorrectand can be checkedeasily 4. Reliableexperiencefactors relatingthe basic power to the brake power for a well designedStirlingengine do not exist at thistime.
i
4.3 Second Order Design Methods by numericalmethods. Second order design methods are relativelysimple computationalproceduresthat are particularlyuseful for optimizingthe design of a Stirlingengine from scratch. An equationor a brief computationalprocedureis used to determine the basic power output and heat input, l=hesethen are modified-bythe various identifiableenergy loss terms. For instance,the net output power is the
101
il ' ii
!i I ! i
1,4 _ _
I
_i
,
__j .°_-4
._. _ '_ '_ :" "'. ',
-_....._...,...,
..... _,...._.,
,
"
basic power output l_,ss fluid friction losstm and inechaiMcal Frier.ion losses. lho net heat input is the ba.._ic heat input plus reheat lo,;s, shuttle comluctlon, .qa:_aiN s_l id c_nduct.ion, pumpin_.l loss, .temperature swim] loss, internel telnp=.. eratul'e swillg 1oss, heat excham.lel, 1oss, and I11i.nus tht: l:ri cttonal heati m,) i n tht: hot end. lhen4:he net efFi_ency is the ne-t output pow{,r Cti-vided by the net heat Input.
,I
,_ .......,_
I
I tl "? " _i
"lhe methods of compui:tn_.l these basic heat inputs and power outputs and the losses are presented by-drawint.) on the-available literature, As in Sections 4.2.1.4 . .2.J, ii_"e than one e_luation or method illa,y be available. For'lack of t,ime some_oi' the more complicated methods will only be referred to in this a,,d 4 2 ............ edition. Eventually a trade-off needs to be made between cost, of computat:ion and accuracy. Howevei", many more computatiohs need to be done and much more reliable measurenlentsneed to be made m_Avell known engines before--thiskind
';
:
of judgement can be made.
-1 i
_
"
Li
<,{
l'hissection r'eviewsthe literature. Section 7.1 presents an engine design form using some of the simple-t:.-equati_ns, Section 7,2 presents a.worked out ..... example for the GPU-3 engine. This section will use an all-capital-letter nomenclature so tliat there need not be a change in nomenclature when-the
i!
equations
,_ ' :
4,3,1
'_
i
"}
i
are coded in...FORIRAN or another
Ca?ital ,.,
Letter
A:
T_
_, i,! Li ! ,.
_ -_') _:i
Nomenclature
for
machine
language,
L,
Sec.t.i-on 4.,3-
(Ecc -Re):' (se ,
AC _, Effective free flow. area For matrix .cm2 AF :-: Average free .Flow area i:hrough regenerator, till 2 AIIT= lleattransfer area Tor matrix oi"cylinder wall, cm:t AHTA = Conduction heat trar, sfer area of one regerleratol" cylinder
at level
A
,
c""_ AHTB.= Conduction i_eattransfet_-areaof one regenm;ator cylinder,at.level B, cm'.'. AIITC= Conduction heattransl*er area oil one re qenerator cylinder at cold end, c1_.' ' "
_
AHTH :;_: Phase Conduction tra)Isfe)' ALPH angle, heat degrees
...........
t_ ._
till"
Ci
B --\(LCR)"
- (ECC + RC)?
area
of one regene1'ato)'
(See Figuf'e
4-15
cylinde)"
at hot
end,
)
BEI'= BP Basic Ik, lf angle output ofpower interlea.vingcones, from Stifling end, de.qrees line b_fore losses are deducted, waits
- NX)I2 .
(for |_I,'
wires
and scr_,ens,
NX ' 0.59
and I_(M",N"')
is
1.79)
.
/
i
!,
c
\(LCR- Pa:) - O!cCj r
CP = Ileal
.; '.-'_.! : , _ r ) "_-" " ' i ,,_.
,
cl :-:A l(cv)/(cp), , (XK)(AHT)/ t(CP)(MDA)_ "
C?.L
'
.. J ". ..,
'
_I _.las at constant
pr_,ssure,
cold, .condi,_cions , C20 (XK)(AHI')I((CP)(NDA) l hot conditi_ans C3 = Geometpy cqnstant (see .
N(AF)I with
XR, NDA.and N evaluated
at
N(AF))
XK, NtlA and N ew_luat.ed
at inlet,
with
Equation
i1 =\I + Kp - 2K cos (ALPH) DC : Diameter oi: compression, cold piston, DCY : l)iameter of engine cylinder, cm IICI :._Diauleter of cone at base, cm DD :-: Diauleter oi; displacep cylinder, cm llL1R: Diameter of displacer drive-rod cm DE :_: Diameter of expansion, hot space, cm
..... t
cm
..
DEt. ,: \_I.__AU_" 4 2(.!ALI)LKAP)cos_ALPH ) +___:
................
47GP-;
4- ez)
-11
outlet,
4-130)
DELP = Pressure drop, NPa DEL.TNX= Temperature swing of Ll_e r%lenerJt.m'
' _ i . !
,1/il K
to cold o.nd of re_.le.ntwato|', Jl.q K CPN :.: Ileat capacily of I'e_.leneratop I_latpix,d/41 K CP[ el"-_.las at constanL pressure when i'lowim.l :t'OIll hol CPO ::-lleatcapacity HeaL.capacity of. 9as at constant _!t'tJ_;sul'o WhOll flowin9 lfpOlll cold end end to hot end of-re.qenerator, ,1/t.l KCt'I : tteat capacity..of piston or displacer, J/L.1 K C1'2 :.: Iteat capacity.of cylinder wall,J/.q K CV ;, tleat capacity of. qas at const.aIlt volume,J/t] K
\'
.,, _,. ' i:,: _ ! g;, _" ,g. " _'_..i ',_
capacity
matrix
material,
K (see
Equation
DELW= Work for one increment DIC _: laIside diameter of cooler tubes, cm DID = Internal diameter of displ_cev, OH1 DIH : Inside diameter of heater tubes, cm I!OC= Outside
diameter
of cooler,
tubes
cm
DP :_ Diameter of power pi.ston cylinder,.cm DR = Diameter of each regenerator, cm DOH = Outside diameter of" heater tubes, cm I1 ,: RC sin ,(PHI) ECC _ Crank eccentricity-,cm (see Figure 4-15) LT _ Re_.lene|'ator efficiency F :: F|'iction facto|' FA :: Area factor for radiant heat lransfer, Equation 4-12.2 alld 4-123 FC :: F|'action of .q/is inventory, in cold space FCblAX = hlaxiHIUIII ill t"C dtll'itltl cycle FCNIN ::Ninimum in FC durim.!cycle FCI :: Ft'actionof cycle,time for _,laS. l:lowinto hot space I.CIC, FCIH :: Effective. fraction of the total cycle time slt, ady f.low passes in direction thl'ough lhe _:ooler (llt_attw).
0i10
t, , ,,,Ill ¸.
......... ,
....
q j
I£Rt'
.
I_,llflth Ii_ll_lt'll
[C1
i 1
ol of:
}._owL_r pJ,_ton _:Olle, _'111
:
" -
t.l',!
w,lll
Li 1
,. ': ' 'i
cm i,i displacer
"l"emp.e-l_t.ur_,wave len_.Ith in cylinder
From tlot
I,nd to level
I_ (s_,e i
wir_:_ ot;--ro_enerator
wall,
m,tlerial,
wal I,
rm
i
:.(rin) tll.':ec
hot
(\
" O5 of
'
till"
1
MIL Mech,lnic,l] friction loss,watts MMX M3.,;s oi all mat."ix materi,_l • g MSII.... Mesl_si;e, wire,,4 loin MLI :: Gas vi sco.'4i ty , .q.._....¢m ..:_¢ blW i_1olectilar wel.ght o1: workiml _las, _.1_9reel' Ntllllbu_t" O1" !.'_owt;l_ IIIlJis
N. Nt'
Ntilllbor
NP NR
Net power, watts .-: Ntllllb_:l"
oi o1
N_ '.: NuIllbol,.. o1 NTt' _ Ntllllt_er oi NTtl NTIlC
!.: I i
ciil
_t - Working _.l,ls inventory. _1,lot MI1A :; Aml,_li t'ude o-l" SillkiSOi'dal Ilk_._.<\'el OCI ty at.: inlet, !'e_.leVlel',ltor,
,
'
NtllllLll_l' NuillbOl'
of of
¢OllOS
_01' tHltlilll'
_,n _i.gl'on
i'otli_llot'Jl.Ol'.g _ Cl't)Oll t'oo]ol'
i._ ._ ._'
or
Ill'l"
dl.gp],lqei
.......
l_owol ' lllli|
i !
] ,},_'t_1",_ _t_l' l't_it_llt)l%.t I O1' (.tlb_,_4 per Iool7Of tilllt.
.t
ho,llor i.lib_,._ por ioowor-tlnit t l'_tll_l'ol' tlllJls |'ot' _lJ:; coo]_'r
,_ ,4
tttAtiT) NltiH
o1" tl',illSi't'l" =' Ntllllbel' ;'.i."d:l (Wt:.'4)(t:V)
-;
tllli(.s
for
{i,ls
tlu',lt-t,l'
tlllit.,4
for
rt'{lenel',ll.or
tlllt
for
I'O_.ll_llOl'_'l 1o1" tlS ira.1 COilS
_i-c"r(-wi is_(ttV_ NILIP
NtllllL_t_i' ol'--tr,tllsfor
tlSill{l
cons.t,u]t
pressure
tic-,It
':
C,lp_iCi I)' llCAlrl)
i
tt(Altl $;'(WiiS(t,r)) NIIIV
i t ,
c,I
i
:
fl'
I
¢,1
¢111
LR -- L.onqth of roqonor,ltor, LT1 -'temperature wave lehjtll
,'
I
I'_d,
I.IIH1 ,' tk,,ated len_.lt.h of each healer t.ube • cm Lt,1X tialf thickness for _heot_ and radius for i
i
Jnq
I.It _ : hm_,it;h lotal lon_tth ot each cm h_,ator tubo, i.ll uf displ,_cer, l.lllj Len_.lt/I ol <.Vlind_,r or ro!tonerator
',
l
_'onnl,
-
Ntllllber of _'ap,lc"i I.V
t.t'_lll.,4 l't_l'
(s
t Jill
vo
lumc
tll_,ll
_
iitAtii) 'tWilStCV)_ Nil I-il!ltn<' i'l'l)qlli'lll'}', tI.', N\ : l;xt_onent ili correl,llion I' (/bit4
i
til.,,surl) : Il'Oqtlell¢.V
,it all!lle Of
Pill
CVc'll'$,/SiOt
for for
heat
bllR'l
'
I
tr,u_ft'r I
MI',I
coefficient sl,l'
Iqu,llton
t ,1.-I,_1
Ol_Ot',lltOll,
l',ldi,tll.g"'(l'<
sinusoida!
l_t'l,slttl'l , swinq_.-i_]LLl...........................................
;
i
II. .':,(NIl!XKtwIN\ t'.i_
Anlplttude
oi
(
i
,
!
:_
.i,. '. _
!
PAVG _ Time averaqed, mean pressure, MPa PC = Calculated pressure for given PAVG at given Plll - Crank angle, degrees
I
"_
. L,
'.'I .;. ":.
PMAX= Ma×imum engine pressure, MPa PMIN Minimum cycl_ pressure, PM-:-_ Mean pressure i:or cycle MPa (see Equation PR : Prandtl number KG QC : Conduction heat t_ansfer, watts QGC = Heat from gas cooler, watts QGH = Heat tO gas heater, watts-
il :i_.., +,.
QITS = Internal temperature swing loss, QN = Net heat input, watts QR : Heat transport by radiation,watts
,.{"I ,
I
- '
:
*_I ._
QRH = QS = QIS = R= =
Reheat loss, watts Static heat conduction loss, watts Temperature swing loss, watts Universal gas constant 8.314 J/g eel
_.. __ _:
RC RCD RCP RE
Crank radius, cm (See Figure 4-15.) Crank radius for displacer, cm Crank radius for power piston, cm.. Reynolds number 4(RH)G/MU Hydraulic radius,,cm AC(L)/(AHT) Mean gas density, g/cm 3
'_ -_., :
p_ 71
'"*. i 1
.,-._,_ :; c)i
MPa
I
RHOI RH02 RM ROM ROI R02 R1
=.Gas density at entrance, _/cm 3 Gas density at exit, g/cm. = Gas constant in mass units, j/g K = Density of regenerator matrix material, g/cm-_ = Density of piston or displacer wall g/cm3 = Density of cylinder wall, .q/cm3 = Thermal resistance of hot third of regenerator cylinder,..K/watt (see Equation 4-I14) R2 = Thermal resistance of middle third.of regenerator cylinder, K/watt (see Equation 4-I15) R3 = Thermal resistance of cold third of regenerator cylipder,.-K/watt (see Equation 4-I16) TC /VHD VRD s : VTfC + -'T-R + VCDI -Tt I
Reduced dead volume SC = Stroke of compression, SCL = Stroke clearance, cm SD = Stroke SI- = Stroke
of displacer, of expansion,
cold cm hot
piston,._..,;m
piston,
cm
- -C . T)-TC-FT)X rflT TR 2TCc-P2TCW-T ::5.67 x lO-_,'w/(cm.'k _)
."
I,,:
SIG
Stefan-Bol
tzman constant
!
watts
._. -,' ',": _'_ _"
: = = = = RH = = RHOM=
4-69),
an_lle PHI,.]vlI?_-..........................................
)
I
i i
I
!
i
'
if
_J .....
SP : .Streke of prover piston, cm IA ;-lemperat,ureai:lew:l A K 11_ : lemper,tlure al. lew, l B, k
,i !
';:
|
-,:
IC :_ l_ffective ietllperai:ul'e ill cold, compression space, K FeN ; Heat. sink metal temperature, K ltiS = le,lperature of cold spac:.e, K TCWI :-: lemperatui'e of cool i rig. watel' i n to eng i he,. k llll ._ lhermal di i:Fusivi ty of pis ton or displacer wall, clll;/sec K1! (( Rite1)( c'l'l )) TI12 Tht-)i_illal dilftlsi'vi tv 01: c'.vl indor...wal I, cull "Isec
i_" "_:i_. i.. i :; 4 '. *_! _i . ....... i;.:
:
]
.:_i ._ _#,_<:
t
:':'l
.:! _
-VC = VCD = Vt'.OX T2 =: VCI. Vt'LX :
.
i •_ 'i :_ ' <..t .... .q ' _ !, ,7 i
TH : Effective tlelllpu_l'attlT'e i11 hot, expal_sion, space, K TIIET tan -I(KAPsin(ALPII)/(TAU _ KAPcos(ALPII))), degrees TIIF Tlickn'ess of foil separating gaps in slot regenerator, THM _: lleat source metal temperature, K I'HS = Tenlperature of llot space, K IHT TIIW = _ THID-: TR = = T1 ::
..
i
K,!!((r to,>).
Vt/l'l of illCl'ellleilt_.¢lll / VCI2. _::Cold --. Cold live live volunle VO.ltllllO at at: begillning t'_lltt 01: iilc'.l'elllellt., CII13 Vll = lotal dead vol time, on1_ =: VItll + VRD t. VCD VII =. VHI.X + Vtlll VIII] = Itot dead volullle, c'ln,_ VltDX = [xti'a hot dead voltlllle besides that. ill qas heater, VItL = Maxinlunl hoi, liw volume till 3 "
_
i
Phase angleof between pressure and mass flow at cnl hot lhickness wir'e inscreens of regenePator, El"fecti ve enterill_,l _las te.lllpei'atu.re to) gas heater, Effective regenerator tenlperature, K (1HM - lt'l_l)/lil(l't4M,_Ttil_1) Gas t:t_,lllpet:_at.ureat inlet, hot end, of rettellel'atol', Gas temperature at outlet: cold end of reqenerator VCI.X +-VCI_ Cold dead volunle, till ;t Extl'a cold dead vol,illle besides , that-ill gas. cooler, blaXillltllll cold live voltlllle, Clll_ Cold live volulllt) at a l)artit:tildr allt.lle. P14I., till 3
.
ql-
VItLX :-" Itot live voluille ,It; a particular angle Pill VI4il = ttol live vcllUilie <1',:betlilllliil{l of illcl'elilellt, Vltl.;] --: Hot: live VOIUlllO al. e.lld of illct't_lllellt, t/Ill 3 VPI.. = Power piston live voluille, Clll 3 VRII =--.Reqellerator dead voltlllle till 3 VI-:- 1oral qas volume at allqle Ptt!
I I i I
VTI.
I '
W WCS WIIS WI' WI'I" Wt'It WI'R
,. Clll J
oily_
VIII. _ VCI Ma,,s l'ale oI tlow, _II'St'C I fl'ecliv_, flow Yale of tlas illlO cold ,,pace, {1,'.'4t't" I ltecl iw, ilow tale of !la!, iill;o hol sthICe, tl,l_,_,t" lolal WilldaHe t)ower, walt:, Gd', cooley Willda{!l, poWt,l', iv,tit,, tld), th'dll'i" Willdd_e t)tlWt,l', wall', I_,l'qiHll,l'dIOl' Willddl i' poWl,l', w,ll 1',
Cill
eild-o_ K
K K
, c'in3
Clll 3
l.'egenerator,degrees
3.
4.
Non-Sinusoidal, isolhermal 3.1 rhombic drive 3.2 douLflecrank Non-sinusoldal, adiabatic variable w_luunespaces 4.1 rhombic driw_
4.3. ;'.. l ___;Imd.d_..[.q!_U:.io.._-s!..us.o_i_]-_so._!_T_!_] 4.3.2,1.1 -,AJ.p!.b_,Pual Piston Fornl of Schmidt t-quation
:i !
Liquation4-49 be.lowis an ada!_tionof Equation 4-45 to give basic power instead of work .per cycle. It was selected because the-average pressure normally specified can be used to compute the gas inventory by assuming that the displacer and the power piston are bcth at the _iid-pointof their stroke. Tl_atis: ........ ML Thus the
PAVG
-iC ....
VHD
VHL
V
"l:_ + _-TTi+ ..... +_.-_lE ........... ET-C./-.
bas.ic power is: ........ I
L,
BP = ---NU-_2_--(-K-A-PJ--(-]" T-A_-(A-A-LPH-)]-_IJ-_ (1"ALl + KAP. + 2S)',:\ 1 (DEL) r (I +Vl Alternately pressure is
TC (EEL).-.:)..............
the basic power call be determined by first noting that r_ated to the nlean pressure by the formula (73 j):
(4-49
the nlaxinlum
,_
i;'
I
PMAX : PAVG \.'(l.-F)EL)/(I,+ DEL)
(4-50
Also.,.,it is instrucIMve to know that (73 j): 'i i:i
.
PMAX
1 + I_EL
P-h_i_ = £-" iiEC
(4-51
,,
(4-52
:.
i
Thus_Equation
(
4-42 is
transformed
to:.
I
_ I,-:'..,
BP =
N_U _!_Ay G__LV T_,,_,C]]_ TAU]_(_EH_LLT.H ET_) -
i
(KAP t_l)(l +\,"i- (DEL)2) 4.3. L'.I. 2
I I
Be.t;L E_gi!!e._.F!_'L_!.,.. Schljlj dt. Equati on
For engines in which the displacer and the power piston are in the same cyl.inder and have th_ same diameter the stroke of the displacer and tIiepower piston overlap and the displacer and power piston co,le very close at one point in the cycle. The basic power for this type of machine is _.liwmby the followin_l
i
equation: " "
i
-............
, _........... Y ._(V:' ;, Xl) '_
-+-
(4-53 f
I
! 1_'_
_-. _,_l_
i
I .
.
•
t
:; I
i 1
i
, .
.
I
i '
!
I
< J
:
i '"
,
Tl_ereis a problemhere in that Equation4-53 calls for PMAX but PAVG is usually specified. Use Equation4-50 to obtain PMAX from PAVG. Also, in,Equation4-53the dead volume is taken to have a temperaturethat 'Istilearithmeticmean of tilehot and cold volume temperaturesinsteadof the more correct log mean temperature.
,
.,,:,
4.3.2,l.3 GafITna Engine Form - Schmiflt Equat.ion Ngtc that Equation4-5.4__has the same qualificationsas Equatlon4-53. Thus: I.
":....
BP = (NU)(¢r)_]- TAU)(PMAX)(VHL) (K)sin(ALPH),, .
Z + (Za - X2)2
[Z-_X]"
4.3.2.2 Basic.PowerAssumin9 Sinusoidal,Non,lsothermalProcesses .
_, _'
,:,
(4-54
,,/ U ';2_
-
::: ,¢I
,S" 4:" '
Most Stirlingengineshave open hot and cold variablevolume spaces, These spaces have so much volume far the surroundingwall area that they act like. adiabaticspaces, E. B, Qvale (68 m, 67 n) takes pressure,temperatureand mass as independentvariables..First the basic performanceis calculated; second,the requireddisplacementsare found; and finally,the-basicperformance is correctedfor frictionalflow losses and.finiteheat transfer, rates. His basic performanceis based on adiabaticvariablevolume spaces,no.frictional
E: "-< [/': '/'i ,i I_/ , ! I/" I,/,,sl '.,:/ _:_ .,,,!i _ i.I _ ,,,..:/. V"" f} , ;.-
and in the regenerator,but with dead volume within the heat transfercomponents. Because of the has chosen the independent.vari.ables, analysisis flow losses and way no Qvale temperature difference for heat transfer in the the-heat exci,,,ngers. directly applicableto engine synthesisrather than th.e.,predictior: of,,.,the performanceof a given engine.
" [";i" .... ....
The author has diligentlystudiedthe above referencesbut he has not been.able to follow,itthroughwell enough to use ,thesereferencesor explain thenlto others. Qvale claims close agreementwith experimentalmeasur.ements on the
', I !
AllisonPD-67A Stirlingengine (see Section 4.1). Qvale assumessinusoidal .,_ variationsin mass.
i'? I
t i
4.3.2.3 Non-Sinusoid.al., Isothermal
I
PracticalStiflingenginesquite often have short cranks that lead to piston motions quite far from sinusoidal. Also, the rhombicdrive used in many Stirling engines is even mRre complicatedbecause the cranks are eccentricante-top dead center is not 180_ from bottom dead center, Means for calculatingthe basic power for two importanttypesof Stirlingengineswillbe given in this section:
I ' il i! .;
•.
' i I i I '•(
I
(>.,
I. RhombicDrive -Beta Engine (Philips) 2. Crank Drive - Alpha Engine (UnitedStirling). .................
L.__.
..
•-i,i
,_
t'i
i' q
I
Iii
!., Md_) " IR
Tt'
!
Calcul,_te
the, n_an pre.,L,_ure by:
i_'
,I'll I :.._bO_, '
•
tPH1 .:.I0 i lhe desired
bltR) to llt, et the..s_peci!"i_d
..P.A\:'.t]..J._..,!iYg...L b,_'.
Mt_! ,, I'AVG i"i,? The pi'essill'es tort>cot are
ill
t:he
dt?t(!t'llll
(,_-70
ell_lilte,
ill?d
PiT,
,It.
e,tcll
Pill
to
cause
the
s i_ocifiod
PAVtl
to
bL _
b_:
_,tPAVG_ PC .---.' \-_'M" _
t4-71
".,
VT is plotted a_3ainst Pt,. lhis I_'ol'K cul'vo is illie_ll'atod iltiniol'ic,II]._. '_o obt_lin tt_e i_oi'k Otltptlt. .1..5"t. stl_,uld be added to the calculated _oltllllO to make tip _.'or tile el'l'Ol': involved in usin9 only 12 points for intogratio!_ {see S_,ction 4..-'_. l'ltll'iil_
tile
the calculation ilt,tss distribution
aSStlPllill_l
_t qorlstJ,
of the basic power, it is also import,tnt of gas betl_eell the...hot sl,,aces., regenerator
llt
pt'eSStll't
_ _ttll'illtl
e.ach
illst_itlt
of
tilt',
c vc'.le,
..,
to calcul,_te ,tlld cold spaces
•
ll'ofll
,
'!
{
]
the
i_el'l'oc'(
!l,lS t_.qtl,tt i on:
I
i
rL.t.'H ] P(VRm r'(V_ L) " in .... in t}ot I<e._le II01'_t to space space
the
first
and third
of
the I_las,., fl.o_' ttli'_ilqh •
these
in It_ c o ] d
fi',tctions
"
j
space.
('.lit, ri_.qellel'atot',
" , AIj, I
"
.i
,Ire evaluat_d hoa(ei'
and are u_;e,d to COl!lptltO
atl
"t
'
I i
, 'i_.. i "_
TP/_ctn'rent Untied Stifling en_iille tse.e Sect.ion 3.?.I. uses 4 doubt(,-actin,j .pistons in a linia ,lrr,tilqelllellt willl cr,tllkS using short conilOclin9 rods opol'atillg
i
e,Ichpiston. The analysis hi, low ivillbe for Olle_luarlofoi:tiletot_l Oll_lllle. Fi,lure 4-17 shows i'vh,lt is bein9 an,lly.zed For an_.:,iil_.i]{, PHI l i_o hei:lhl of the, pislOll above bottOlll dead center is:
-i !
\1
,]l__'l__ _, -"({R-_l_,"sin {rltl_," - IL'R + lit"
- _Rl'_cos ti'tiI!
(,1-'.'
,
'
i
/
I t
!
": _/1"i :,_,
Equations 4-65 to 4-71 are employed to calculate
:+_iiii}'" '_'>:) ' I
diagram same Next, way gives as wasthedone workforperthe.cycle. rhombicA drive. 12 point Aper numerical cycle integration .integration.of is 4,5% the work low. To get the power for one power unitof the four In the engine, one must multiply this integral by the engine frequency in cycles per se.cond to obtain the basic power in watts.
!,: #',,i )i, .._._
Here also the mass fractions in the hot, regenerator and cold space_ are computed by Equatlon 4-71.1. Note that these fractions depend upon the geometry-_ and the temperatures but do not change with pressure °............ ,
'_" '
4.3.2.4
_'_I:;i _i_ %,.,.:_ ._,._
After Qvale's work for Professor J. L, Smith at M.I.T. mentioned in Section 4.3.2.2,Rios (69 am, 69 o) expandedthe worJ<using the same generalassumptions. However,he is able to startwith a specificenginewith a crankconnectingrod drive mechanism. He was able to solve the differentialequa-
_iil .... "!'}i
coolingengine tionsand integratenumericallyto andwas able to closelypredict an overallsteady its performance. state. He built The author his own_ has studiedthis work at some lengthand he has a listing, of the associated ...... computerprogrambut has not yet put it into operation,
i
-
/
the work diagram in the
._i :_
Non=Sinusoidal
Non-lsothermal
An extensionof the computationalmethod describedinSection 4.1.5will now be presentedas it applies to a rhombic drive beta type engine. This calculation procedure fs not practical to compute by hand, but it can be done in a few minuteswith programmablehand,heldcalculators. The computationalproceduresgiven in Section4.3.2.3.1are followedup to_ Equation4-64. Then the pressure for M(R) = I at any angle PHI during the .... P = VHLX
•
i VRD + VCD
VHD
(4-76
.:
VCLX
wher-eTHS and TCS.are the hot space and cold space temperatures. Start at PHI : 0 with.THSl : TH and TCSI : TC. ComputeP by Equation4-76 and .,,'I,t PI. Let VHLX) and VCLX at PHI = 0 by VHLI and VCLI. At, say, FHI -:30<;ce,npure VHL2 and VCL2 using Equations4-64 and.4-58,respectively. In other words, for the first calculation:
,J .j
_i
1 VR'D-.VCD
P1 --VILLI VHD
T
+
+
VC_ _
(4-77
+T
For the second calculation:
1
Where:
l P2 = VHL2 _'H_ + K1
VC'L2
(4-78
VHD KI: _+
VCD ""_C-, '
(4-79
VRD _+
always I_.
which is
constant. Also for the adiabaticspaces:
'
115
_ _-_._
._aL,.___Jr
Jt
)-
JL_LL,____A
__'_--_-_IZ:-I
_
_,A
!
" "
!
_
,"':
'
" ,: _
THS2...... TH.......
Substituting
Equations 4-80 into P2 =
hydrogen, so E = 0 ' 286 '
4'78:
I.-
VHL2
--(4-._30• -
V'C_2-
(4-81
T
"
The only ulikllowll illEquation 4-81 is P2, A solution is made by the secant
' I ........ -I
(p2\E Pi/
_i:-
Whetm [: = k......i-_" and k = Cp/_v _ = 1.40-for
j
t'
also
Newton'smetl_od. P2, THS2.andTCS2 are calculated. Tilethird method pressurein method of approximation or some other successiveapproximation like
....:'
i i.! Iii"
the series is calculatedby: I
P3 : XH + Kl "#_X-CVHL2 + VHL3-- VHL2 ' where if VHL3XH VHL2:
i
THS2(___) •E
'_ • ! •i .! _. • _
or if
(4-82
-u/P3'E ""
VHL3 < VHL2: VHL3 XH = ....... /p3\E THS2_=Z/
In the same way, if VCL3 > VCL2: XC -
VCI.2
+ VCL3 - VCL2
TCS2IP3\E
"
TC /p31E
or if VCL3 < VCL2: !
VCL3
Now in Equation4-82, P3 is the only unknownand itis solved as before. Then the mixed mean gas temperaturesare foundby: ,-THS3-
VHL3 _-_
and
TCS3-
VCL3 _
(4-83
where XH and XC are calculatedby whicheverequationabove.applies, From incrementto incrementin PHIas ti}ecalculationprogressesthis ,m,thod takes into accountthat when gas,is leavinga variabl_a volu,iespace tiletemperaturein tliatspace simply obeys the ad1,.batlc compressionand_xpansion law. On,the other hand if gas is entering the variablevolume spacethe old gas
L
LOlilpor,l.tilr¢, cll,Ii1_leS ,Iccm'dill!I to tlm adiabatic
law from lh_ pvL,vious !lil._ i.e,ll_to [,Ill' S_IIlle-IdW [lilt |'l'OIll [he ellI:l_ri.n9 _l,lSl.eillp_,r,_tur_. 1h_,iItll_,1'_ i._,IllliXiil!l ,I[ l.h_,-plld of e,lch ill-
,
eI'_itlIl'l}, The
,... _F. )
CI'ClIICIIt tO
' _
the
Ill_x_d llk_,lllIPllIp._V_l.tlll'_ i'OI' i.h_' ll_X[; ilICI'I.HIkHII.
dtld tt_.lllp_v,ItUt'_.s sl;,Irt, to r¢_.pe_li ' with adequate accuracy. This COlllpt_iai:ional procedure is stable, at aly ,_mlle incr_ment. Smaller an_lle increIlkHIt.'" 9ive IllO1'o ,ICCLIl',l-[l' resulls, t:or ,_ p,_ri:icular c,lse the _1'1'¢_¢I. o-f Slllallo.r ,lll_.ll e i IlCl'_HlleIItS sholll d. [)t_ eV,I llltlted to d_}tot'llli II__. all: wh,./t poi lit adequa te accur,_cy ts obtained. pl'essiIves
,.: .,
,
.
-
i
_:,
'_
get
l'hiscoinplltation,llprOc_ss is cont;ima, d for two of il_recycles unt.i-l., the
-:
•
flew l.]_}stL}lllpl_l'd_iIl'e cHdIIL]es-ilccol'dlIl!l
ii" i
4.3.3
!"].u.id. F]'ict.ig..!L L.gss
..........
;i:i
The basic power is-computedas-ifthere is no fluid.friction, Energy loss due
_.i
to fluid
, A
r-_ .-.. ..,: _, ., i ' ,. ,!
...../_. _._
friction
is deducted from the basic power as a small.peS'tm'bation
the main en_,llneproc_:ss.
Ii: fluid friction cousu,k_,sa ILwqe fraction
on
of the
basic power the followin9nmthodswill not be accuratebut then one would not choose a design to be built unless the fluid frict.ion.-.we.r,e---l-ess--.-/han.IO_..the basicpower, Flui_ifrictioninside,the eth_inecan be computedby publishedcorrela.tions for fluid flow throughporousmedia and in tubes, These flow frictioncorrelations are applicabl_ _,for steady., fully-developed flow. If the fraction of the gasinventory fo.,md in tile hot spaces and in the cold sF_ces is plol-ted a_,lainst
crank anqlo, it by.(1) is ap_x_rer, t t:h,lt to a periodicflow can be ,q_pro_imat,ed s'_.eady flow, in _.lood one approximationthis direction; (.2) no flow for a period
_ '*:
of" lime (3) thensteady
, ._'_ !';'_
to completethe cycle. (See Fi_.lui'e 7-i.) The mass flow into and out of the ,'e,je,le,'ato," is. not quite in phase due to ,,ccumulatio,, ,,,ld depletion of mass i,, tile t'eqelie.vato|.'. Note thatLthe. IIklSS flow at: the cold oIld is II1UCH IIlOl'_ t}l¢tll I;}lt_ la::S flow ,IttIl_' hal:end zm_stlydue to gas densitycham.le, lhe aw_rage,_Iss flow rate and the averagefractionof the toi.alcycle i.ink: that .qasis flowiml in one-directionat the hot.endof the regeneratm'is used for the.heater flow friction,_ndhe,lttransfercalculations. _,heaverage,_ss flow rate and the ave.ragefractionof the total cycle time flowinqin one direction, at ihe cold-
._:
;'_ i.! C :,_", , .-_i_i
_lld
" ! _'!,_ _._
oi"
the
Fegellet',ttol'
is
ilsed
i'ol'
tlip.
cooler
flow
The above decisions
'_i
d_)t.Cl'lllille
how good
are t:hese
approximations.
In Ihe fuiure
,tL_pl'oXiillatiotls
,t1'_
by
COIltparill¶l
"i
[
,Ind (,l) then no flow
friction
calculations. For the reqenera.tor the mean of the above ,Ibow, two fraciions svill be used.
_'i i _"_
flow back in the othe!' direction,
i "_
and heat
iP,tIlSfP.I'
iwo flows a,d oS-.the
the auihor f,helll
with
hopes to ilklt'e
l,lbOt'OllS
but ,_we exact calculations .........
':
,l.,t.;_. I
Regenerator
}
".i.J.,!. 1.1
'}
k,lys
":"
IIl,lII'iX
and
Pressure
tlro.p
Screens london
,IS-WOII]d
(li.l
1,. p..1t)
[_l_ llsed
i'Lll'
_liw' d
Ih_'
IOl'lllllld
i'Ol"
_,l'CS-Slll'O
drop
lhl'otl_l!l
1
_t.
I'l'_.l(_llL'I'_lI:Ot':
,,
l,
I
_I'
_:
..... ..............
.........................
L_
I
t
'I
i
i
,
i
'
i
! w-J
",!
DELP = 2-_
-_i__
I +_AF: R_" "'Flow Acceleration
+ (-RH_-R-A-O-M Core Friction
(4-84
Tlleflow acceleration term can be ignored in computing windage loss for the full cycle because the flow acceleration for flow into the hot space very nearly cancels the flow acceleration for flow out of the hot space. With this simplifying assumption, the pressure drop due to regenerator friction is:
_ ' J_ '; I
,, i, I i
i
_ _ i I i . o i i,
F
L
(4-85
DEEP : 2 (GC.) RH) (RH(]M)
In tlleabove equation the friction factor F-is a function of the Reynolds number, RE : 4(RH)G/MU. Figure 4-18 shows the correlation for stacked screens usually used in Stirling engines. Note that the relationship is dependent somewhat on the porosity. Since this calculation is already an approximation it is recommended that a simpler re]ationship be used nx)readapted to use in simple computer programs. For RE < 60 let:
i ] i
log F = 1.73 - 0.93-log',RE) For 60 < RE < 1000:
(4-86
!i
log F : 0.714 - 0.365 log(RE) For RE > I000:
(4-87
_,
log F = 0.015 - 0.125 log(RE)
(4-88
'_
This relationship is shown by a dashed line in Figure 4-18,
1
I O_
, '
o, ........ o_, " '
l-I ITI o o._ " !tltl • o.,"_ I IIll " ! "_'
.
;
ot:
ttttt
_ :C"
,
• o._
i'iil ;
I
2
3
"
4
_
II
I0
:I
---:-_
'
!!' _
3
4
6
O I0 !
2
_
4
6"8
I0 _
_
3
4
_-8
I0 _
2
3
4
6
/_ t0 _
RE = 4(RII)GINLI
!i.
Figure 4-18. :: _
Flow Through an Infinite Randomly Stacked Woven-Screen Matrix, Flow Friction Characteristics; a Correlation of Exper-imental Data from Wire Screens and Crossed Rods Simulating Wire Screens. Perfect Stacking, i.e., Screens Touching, is Assumed. (64 l, p. 130)
'
',
t
v
I i
"
i
_
1
i
4.3,/,1.2
'
1
I•
i
I! 1
Slots
Besides screens, the other type of surface sometimes used is the annular gap or., i
L
,I
_i
laminar region, RE < 2000. the slot.
'-_
For,-thiscase(64
l, p. 103):
This of surface is practical at flow velocities always in (4-92 the F =type 24/_RE
4.-3.3.2 Heater and Cooler Pressure Drop - Tubular ,,
L'
Heater and cooler pressure drops are usually small in.comparison with the regenerator, Heaters and coolers are usually small diameter round tubes although an annular gap is practical for small engines (see Section 4,3.3.1.2). Pressure drop through these heaters and coolers are determined by Equation 4-85 with F determined from the fanning friction-factor plot (see Figure 4-19) and RHOMbeing evaluated at heatsource or heat sink temperature and at PAVG. The length.... to diameter ratio is usually very large so for simple programs let: For RE < 2000:
;
F = 16/RE
(4-93
For RE > 2000: log F = -1.34-
i
0.20 log(RE)
m.
?v,< 2,000 M_inli C_oltng l._ 1._
.I
11
!
0.0
0.0
(4-94
N,>IO,OQO H_tinli Cool!r_l .-¢.I0 0,0 -O,._O
--_[_
_
C)
O.O
Ii!
....
I t
:
I
!, "i
\*
i
ILIO,IO¢ i I,..t0,,,,.,
t_'t ', L/O.SO
t
....
t
i
..... i--_-'- '
i
.....
N '
o._o.,o, _.o
Figure 4-19.
"
120
.....
J
,_ z.o
, NRx lO"
,
,@ 1
3.o 4.0_o 6_ e.o,oo
......
f "-"
i
1 '
,_o-zo.o _o.o4o.o9o_
Summary of Experimental and Analytical Data. (64 l p. 123) Gasa Flow Inside Circular Tubes with Abrupt Contraction Entrances;
i
4.3.3.3
.............
Heater
and Ce.ler
l'ressur'e
DroR_,_,_!!!ter3e_)y]n]lq Fins
(see Ref.
77 11)..........
One of the advantages of this type of heat exchanger is that the gas flows into it rather than throu__L1 it. Also, it is rather complicated because the flow.. passage area changes with the stroke. Experimental data are needed. But before these can be obtained, an approximate theury is presented in the interim. One of tile. best types of interleaving fi.ns...is the nesting cone because the cone like the tube can hav_a thin wall and heat can be added and removed directly from the outside of the cone. Assume that the effective average flow rate takes place in the gap between the cone and i,ts mate at. mid-stroke at the point
"
gap up to this •point. Also assume that the friction factor is the same as for slots. where the volume of the gap beyond this point is e_ual to the volume of the 4.3.3.4 i i
Heater,
Cooler
and Regenerator
i
'_
Windage Loss
1
Since the gas flows through these parts twice per cycle, the windage-loss in the-heater, regenerator or cooler is determined, approximately from the computed. pressure drop by..theapproximate formula: ........ WP : i :"!
, ':' ! ._ . i _ 1 i i
4.3.4
(DELP.)(VHL)2(NU)
watts
(4-95
Mechanical Friction Loss1
Mechanical friction due to the seals and.the bearings is hardto compute.reliably. It essentially must be measured. However, if the engine itself were used, the losses due to mechanical friction would be combined with power required or delivered by the engine. If indicated and brake power are determined then mechanical friction loss is the difference, that is, WB - W I using the nomenclature from Figure 4-12, The friction loss should be measured directly by having the engine operate at the design average pressu_e with a very.large dead volume so that very.little engine action is possible. The engine need not be heated but the seals and bearing need to be at des-i_gn temperature.
, .;
i
•
i
'_'i i ! '
4.3.5
Basic Heat Input
The basic heat input of an engine using the second order approximations is the basic power output divided by the Carnot efficiency for the assumed gas temperatures for the heater and cooler spaces. Therefore: BHI : BP/( I - _--C H)
._
(4-96 ......
I
This basic heat input must be transferred through the gas heater of the engine. Also the heat needed to supply the reheat loss.must also be transmitted through this heater, Therefore, after the conlputational process is gone-through once there must be an adjustment downward inthe effective hot gas temperature and upward in the effective cold gas temperature to allow for some effective temperature drop in the gas heater,-andgas cooler,. These new temperatures for the hot space and cold space would change many.of the calculations performed the first time around. Particularly it would change the basic heat input because of their direct effect on the Carnot efficiency. It has been found that this procedure is rapidly convergent' I.'l
_ I
!I I
,i
'
4.3.6 ReheatLoss One-way that extra heat is required at the heat source ency of the regenerator. The regenerator-reheats .the hot space. The reheat not supplied by the regenerator heater as extra heat input. Figure. 4-20 shows how the
in the heater,, regenerator,
_,
and cooler
is due to the ineffici-gas as i.t returns to the must be suppliedby the gas temperatures vary
during flow out of the hot space as well
as flow into it. Note that atinflow the gas attains cooler temperature then is heated up in the regenerator part way. The temperature difference, A, between the heat source temperature and the gas entering from the regenerator is then multiplied by the heat capacity,., the effective flow rate, and the
I
fractionof time that this gas is flowing,to obtain the reheat loss. The methodsderived from the literatureand from the author'sown practiceare
i
given below.
The formula for reheat used by the author is:
Effective F1ow Rate
Regenerator-Ineffecti veness
QRH : FCT (WRS)(CV)(THMFraction Time F1owi ng Into. Hot
Heat Capacity
TCM)(NTUV2+ 2)
(4-97
Temp _T A
Space
!
i
REGENERATOR
.i
•
,_
HEATER
:
;
COOLER
,i i;
"'-,,'5."-, "-_"h_ _ • !
Figure4-20. Reheat Loss, I
i:_. '
_
TC
i •', ! I !
!
'
i
....
i
,,
1
"-" ...... ,, -----1
, ,.,
lacl;elemen{ in I.qti,l{inn .I..,ll is a I.ypeof an ,_pprt_xi,laI.i_,l. the iraction t_| t:iIllt' Flowi II_Ii IIItl tilt'hut !;p,lCe it_ {_i iIIldled [_y oX II'dpola tillqI.heinaxiIIIUill fl_lw into the hot spac_:.I:_ the tot.al l'l_w t_ find the fraci itlll of" the total cycle time that t.his process would occupy, if" the Flow rate were always at its mil,
',T. _,,i .; it,* _,:,_ :: 'i
pressure change durin_,l !laS rlow thl'ou_,lh the resle)_m'ator (75 a,.1, 77 bl). The rationale for usin_,l CV.in.l-lquation 4-97 is that t,he. transfer of _,las takes place when the total volume i_ relatively constant.. Itowever only a small a,_aunt of the total volume is in the re_.lenerator at. any one time. A better equat i Oil S uggested by LeRC durinq review is probably:
•'
,',.
,-
,_!,,_ -b. ," fi
QRH _:FCT {(WRS)(CP)(IHM - TCM) ....... (R-I_I3-(FC:l3/N[I (;1-971 VRD(CV)(PMAX - ........ PMIN.)]'[ IN-TUi_-% " -2 / Thi_. point deserves further study because QRH is quite,, often the ch _,_,f loss
_,.
tel'Ill.
_i ;,
The temperature ditference A in Figure 4-20 is represented by the tot:al lenlperature difference between tile hot metal and the cold metal times t.he re,qenerafor ineffectiveness. This ineffectiveness is one minus the effectivene.ss of tile regenerator material (see. Equation 4-7). This forluula for i-rmffect.iveness agrees with the simple equations in earlier st_tllddl'd references ell I'eqellel'dtoYS such as Saunders ,tlld Smoleniec (51 q).
i
:
%
_!'_: ""i :_," "! .,._.:; _,: _! "T.', ':i. :},""
Tile idea. of sep,u'atin,j powm' output and tile heat losses int:o a m,nber of superimposed processes has been used by a number of investigators of tile Vuilleumier cycle. The details of this analysis have been _,liven in"a lltllllbel' .of _,lovern,lent reports. The Mull leumier cycle is a heat operated refriqeration, m,lchine which uses helium gas and regenerators very siulilap-.to the way tile Stirliml engine is constructed, lhis super position analysis has worked well in Vbl cycle machines. In an. RCA report (69 aa, pp. 3-37) the measured cooling power using this ,lett_od ofanal,vsis..,was found to be within 8.9% of that calculated. Crouth,u,el and Shelpuk (75 ac) give the following i'ormula for the reheat: loss after it-is transla_:ed into ttle nemuenclature used in this section.
,_:,_::ii t/,I
I
",:,'..f
el ,
pdrti ctlldl' _,,, directly IIIdChjlle.
diff"erenl..
cycll, /\]St). thi s
t,'.,) (WRS) (t:I')
,1-9_ is written
Iqu,ttion
!_:
).*:,
qRtl
IlldChi lie ,lilt{ colnpdl'ed, lilt, t"lt_w l'dte
I'robablv
IIMCil{ lie
ulldel'qOes
(IHM-
]CM) (NIi.lP"-:i: 2).
in the Sdllle order tlhe hol'e first lore is t'vdludted
thi,_ can d
l'eld
needs term,
to eva ludtod is o11obequdrter, ill
be jusl.ified [.ire
thedistillCt, iOll[,l,lWeelllllt, s [d_JO Oi: ,tlld lys i S.
ldl
ly
siiIdl
lh('
Sdlllt'
W,ly.
tLelllpeYdltll't,S
ill
is
can
I'ot' dlle{ hel' specific tot tyt_t_ their i'll" but the heat c,lpacity
It, be CP in:viead I Chdlltle
pl't, SStl|'O ,llso
i
i'i _ !'<
(4-g,g
,l.-!)7 Jnd therefore
as Lquatien
,.. i} '
of CV becau,,_e dlll'i
,'el,llivcly
:i
is
tilt' Vbl
II!l i l g C>'t" le. Sllld],
,It
_j g'l
%, t 'I
.I
Y1 ..................................
:i --
_"
w !
I
i
I
i
I
..............
I
•
:
:
,'
i,
!
i
'
"
........
'r_,;
L
I
' _.i /[
Table 4-13
i
t
: ir_
Heat Capacities l'empera.ture K
HydrogenI CP CV
Hel i umI CPCV
K CP
Ai r 2
CV
298.15
14.31.-
10.18
5.20
3.12
1.0057
0.7188
(:
400
14.50
10.37
5.20
3.12
1.0140
0.7271
}_LI--
500
14.52
10.39
5.20
3.12
I.0295
O.7426
i_i_ ,'_:
600 700
14.56 14.62
10.43 10.49
5.20 5.20
3.12 3.12
1:0551 1.0752
0.7682 0.7883
_i
800
14.70
10.57
5.20
3.12 .....
1.0978
0.8109
!
_ i
1000 1200
14.99 15.43
10,86 II,30
5.20 5.20
3.12 3.12
1.1417 1.179
0.8548 0,892
,-T'
:i :
1500
16.03
11.90
5.20
3.12
1.230
0.943
I
2000
17.03
12 90
5.20
k3 12
1.338
1.051
! i
2500
17.86 .....
13.73
5.20
3.12
1.688 -
1.401
i
3000
18.40
14.27
5.20
3.12
d
:,,
I_
for Working Gases,.J/g
_
1
_;
= i
I i
.
,
,
i,
......
'
, ;
: :i
iFrom American Institute
I _ ........ _!....
2Fronl Ho_Iman,J
:: ';
P , "Heat Transfer,"
Fourth Ed , p,. 503, McGrawHill,
FCTH= (FCTI + FCT2)/2 The effective
_ :
i
of Physics Handbook, Sec, Ed., pp. 4-49.
steady mass flow rate for
1976
(4-I02.1 the heater
is:
WHS : (FHMAX - FHMIN)M(MW) FCTH/NU
'; !
(4-I02.2
The effectivefraction of the total cycle t_lhesteady flow passesin one direction throughti_ecooler is: _'i _i
FCTC= (FCT3 + FCT4)/2 The effective
e_
steady mass flow rate for
wcs....
(z$_102.3 the cooler
is:
(FCMAX - FCM_IN M___MLM__
FEFC-T J
(4-102.4
i
L!
_! :}i
Thus for the regenerator:: FCT = ( FCTH._,ECT£)/2.........................................................
"i
and
_i _. •_
WRS= (WHS+ WCS)/e
i
I
(4-i02.5
(4-102.6
The heat transfercoefficientis derivedfronlFigure 4-21. For instance,fo_ .... a porosityof (i - .286)= 0.717 the equation _s:
kL
,L
i ¸ i
,.
T
H -(_)(PR) : -0,13 - (].412log
log
(RE)
(4-I0_
....
/7
t
_
&lill
°°"
I :
f
- I _
i
t
,
:
0
.' I:
;°,t ....
TI
:oo.::liF.....
)
.oo ! ,i
+
i!
-I
...... ,+
0.001
Figure 4-2t_ .....Gas Flow Through an Infinite RandoMly Stacked Woven-Screen Matri×, Heat Transfer Characteristics; a Correlation of E×perimental Data from Wire Screens and Crossed Rods Simulating Wire Screens. Perfect Stacking, i.e., Screens Touc)ii.ng, is Assun_d (64 I, p. 129). .i ,_
.
I
'
) ......
_
!
UIL
_vllere the Reynoldsnunlber, RE, is the sa_e as that used in Section4.3.3.1,1. and the.Prandtlnumber PR : CP(MU)/KG) CP and MU have been..-qiven previously. KG and PR are given in Table 4-9. In a Stirlingengine the regeneratoris subjectedto an importantgas.pressure oscilla.tio(_ out of phase with the gas flow oscillationthat has been evaluated in the above,equations. Bjorn Qvale (69 n) has developedan*equation that takesthis p:'essure wave into ,_ccount,He assumes-thatpressureand (_assflow variationsare sinusoidal, hleassumesthat tl_ematrix temperatureis expressible by.-asecond order polynomialin X, the distancealonq the regenerator. He also concludes.that,l) fluid frictioni}asneg]igibleeffect on the state of the gas in the regenerator,2) ti_egas and nlatrixtei_Iperatures at-one location are practicallyconstantwith time,.3) the-differencebetweent)}egas,-ai_d matrix temperatureis small comparedto the longitudinaltemperaturechaI_ge and, 4) tlleeffect of longit_zii_lal conductionis negligibleon tl_eheat. transfei' process. He startsout with equationsrepresentingconservatio_of mome_tuni, mass-and energy and the equationof state. He conclud_,s that:
|
L
..... l..........
i
;
_
"
)
t
t
!
'
" °'"" QRH -.........
(OMG) I_CY,-_'(_--
+
""'
(C20)(YL).:_..+" (C2L)(YL,) NX _).,-(_,_-A_I
.......
((YLI '_ ,:os (T"T)
(T,T) ......... (AI)(TA,L))I
where: MDA = amplitude of the sinusoidalmass velocity (X _ O) of
[email protected], g/sec cm:' TI- = gas temperature at inlet, hot, end-, K T2 = gas temperature at outlet, cold, end, K OMG = frequency of operation,radians/sec = 2It(NU) B(M",
_rf2- n2M,, . 1 _" N") = 2 .,oSi _" cos""
- 1
at inlet,
e"
o" d
M"= (3 - NX)I2 i • ! i , ' _, _ •"";" I ; :' I _:_"_:_i i "% i '_,
I I
........ .
-
in form H = XK(W)NX W =. mass flow r, ate, glse_ _ \ C2 (XK)(AHT)I((CP)(_IDA)'-"(AF))_ C20 C2 with XK,_ MDA and N evaldated at inlet, hot, conditions C2L = C2 with XK, MDA and N evaluated at outlet, cold, conditions YL = ratio between the maximum mass flow rate at the end of the
,'
._
regenerator to that at the beginning of the regenerator = ,"i' L'2(A'I _(TAUL')_T-fi-T]--_-Au-_
i '_""I
N" = L, (Note Qva'le'sthesis, 67 n, gives a value of NX = 0.59 and B(M", N") = 1.79.) NX = exponent in correlation for tileheat transfer coefficient
'
TAUL 2/((T2/T1) + 1_ \ AI (OMG)(L)(PA)/(/(MDA)(R)(TI)) L : length of regenerator,cm PA = amplitude of sinusoidal pressure swing, MPa THT = phase angle between pressure and mas.s flow at hot end of regenerator, degrees Cl = AI (CV)I(CP)
'
.,
There is some doubt that Equation 4-i05 is interpreted correctly..At a number of places quantities were undefined and guesses had to be made. Also Qvale's tliesis(67 n) gives almost the same formula but would predict QRH one half
._
that in Equation 4-105.
i
A-Tetter from Qvale says Equation 4-105 is correct,
'
cal nlethodwhich also gives the pressure, and the mass flow at tilehot and cold If the.power output for a particular Stirling engine-were evaluated by a numeriends of the regenerator, then one would have tlieinformation necessary to substitute into Equation 4-I05 and obtain an _nswer.
:_
I
Qvale con]paredhis theory with the experimental result_ on a cooling engine
', i
1
i
[
t
,
,
I i
',:.
1 : "
"% i
," i
".
done by Rea.(66• h) and predicts wi thin + 20%.
! .! 7._ .i , i
Rios (69 ar), as was mentionedpreviously,calculatesa work-diagramassuming adiabatic hot and cold spaces and any form of volume change with time that can be specified. His reheat loss uses 4 quantitiesthat are calculatedwhen the work diagramis calculatedby the computerprogram.
i<'i b h
4.3,7
_! _! '_.,'_ }_ ,,. • ...... _i
,
and therefore
the QRH
Shuttle Conduct.ion
.....
L:
--
Figure 4,22 shows how shuttleconductionworks. Shuttleconductionhappens anytimea displacer, or a.hot cap osci.llates across a temperaturegradient, It is usuallynot frequencydependentfo.rthe.speedsand materialsused in Stirling engines. The displacerabsorbsheat during the hotend of it_ stroke and gives
_
the cylinderwall change temperaturesappreciablyduring the process. Shuttle conductiondependsupon involved,the thicknessof the filled gap, off heat during the_old the endarea of its stroke. Usuallyneither thegas displacernor GR, the temperature-gradient (TH-TC)/L,the gas .thermalconductivity,KG, and the displacerstroke, SD. It is also dependenton the wave form of the motion and in some cases, upon the .thermalpropertiesof the displacerand of the cylinderwall. All.formulasin the literatureare of the form:
" ::"_ ,, ..i
(YK)(ZK)(SD)2(KG)(THM- TCM)(DCY) (4-106 QSH = (GR)(LD) The quantityZK dependsupon the type of displacer-orhot cap motion, andYK dependsupon the thermal.properties of the walls and the frequency.ofopera-
:, -, "_I :_ i.
tion. there is Table a substantialdisagreement 4-10 shows the resultsof aboutwhat a literaturesurvey ZK should be.for for ZK. the sinus.oidal Note that case. The author has derived the lower-valueand he would recommendit. This value, _/8, agrees with Rios but does not agree with Zimmerman. However,. there are.no data that would lay thematter to rest.
q_
,_
the ineffectiveness
_'!
Rios has publishedvalues for YK to take into accountthe effect of frequency or wail thermalproperties, which are sometimesimportant. In Rios.LPh.D. thesi_ (69 arl he gives: 2(L.I.). z - LI YK = 2(Ll)Z . I where
_
_! ,!L, .v_
i _,
i r i
i_ , ' _ i li i /_i! ;
!I"
1
(4-107
'I ii-. i, ! I _i i
_ K1, _-OMG) (GR)_ L1 : K'G'V 2(TDI) KI-: thermalconductivityof piston or displacer,w/cm.K TDI : thermaldiffusivityof pistonor displacer,cm2/sec
i _I
(K1) I
j i_/ _: i_
i I
i-
............................ 1! R01 : = (RO1)(CPI) densityof piston or displacer,g/cms CP1 : heat capacityof piston or disp_l_acer_,..Jl_g-.I_ ........................... ,,_iI 129
I *'
I
!!
II
130
!
_
.
I
Table 4-10 Coefficientfor Shuttle lleatConductionEquation (Ignoring
Effect
of Walls)
i
"
I
..
Motion-
Investigator
Ref..
ZK
Square wave _
Zimmern_an
71 be
_ = 0.785
time at one end,
Crouthamel&
75 ac
2F= 0.785
It
_:time at other
Shelpuk
i 11'
Slnusoidal
Martini .......
(I)
_-= 0.393 IT
(effect _/
i....
of walls
ignored)
Zimmerman_
71 be'
Rio_s White .....
,
_-_-4 -= 0.582
71 an.. 71 .1
_- : 0.393 .1867_ = 0.584
69 aa
.186" : 0.584
_
'I
,_
;J
_"
..1
(I) McDonnelI DouglasReports,never published
,i ' i'
I I
q
"'
i
!
_i_: :
' ....
i LTI = Temperature wave length
i
in displacer
i
: 21
i
LT2 = Temperature wave length
:
in cylinder
waql
TD2 = thermaldiffusivityof the cylinder, wall, cma/sec (defined same as TD1)
i,'_:
The above factor appliesfor simple harmonicmotion and for enginesin which LTI is smallerthan the thicknessof the displacerwall and LT2 is smaller then the thicknessof the cylinder, wall. Rios gives equationsfor solvingthe problem for any periodicmotion by using of Fourierseries expansion. To help determine whether the above factor applies, Rios gives some typicalvalues of LT at room temperature(see Table 4-11).
_
•
LT21 K-"_]
Where:
I
j/j_
I KG /LTI
LB =.I
• 1
Tabl e 4-I 1
",
,!I i
Typical Temperature Wave_Lengths, LT, at Room TemperatureConditions
•i: I i
Reference: Rios, 71 an Centimeters
:
! i It i:
....
i
' <, ,
Fre_Z_
i ,I
.....
Materi al
,.!,,.
, ....
1
I
i
1
5
10 .
20
50
Mild Steel StainlessSteel
1.21 0.74
0.86 . 0.53
0.54 0.33
0.38 0.24
0.27 0.17
0.17 _ O.ll
Phenolic
0..85
0.60
0,38 •
0.27
0.19
0.12
.
0.26 "
0.18
0.11
0.08
0..06
0.04
.-
_
Pyrex Glass._
! _ i i
2
then it may be assumed that radial " temperature.distribution in the walls is uniform. Rios (71 an) proposesthe followingdefinitionof YK for this-case: If the wall thicknessis considerablysmallerthanthe temperaturewave length, 1 YK i + (SGM)2 (4-109
._
1
'i
iil I, ili
where:
_I ! i i, _
and:
I
I Icsol(
)
SGM : C_GR)-(OMG.) (RoI)(CPI)(WTI)+"TR'o_-_CP2)(wT2} ................................
'I
WTI = wall WT2= wall ,
_ ,-
thickness thickness
of displacer, cm of cylinder wall, cm
Note that when the thermal properties of the wall do not matter, YK whether evaluatedby Equation4-107, 4-i08 or 4-109 would all evaluate to nearly i. There is not any publishedformulathat treats the case of cylinder and displacerwall thicknessof the order of the temperaturewave length. There are also no publishedformulasfor the case of a thick cylinderwall and a thin displacer or visa-versa, For horsepowersize enginesEquation4-108will apply. For modelengines or artificial heartengines Equation4-109will apply. •Therefore,for horsepowersize, high pressureenginesthe recommendedequation for shuttle heat conductionis: QSH : G!++( '_)'z)#
(SD)Z(KGt(THM ... .... GR)(LD) " T'CM)(DCY)'
(4--110
For model size enginesusing low_gas: pressureand very th:inwalls: QSH =
(4-111
It also should be emphasizedthat Equation4-110 and 4-111 are for nearl-y sinusoidalmotion of the displaceror hot cap. Square wave motion would double this result. Ramp motion should reduce this result some.
tl
!
!'
_
!_
4.3.8 Gas and Solid Conduction This heat loss continueswhile the engine is hot, independentof engine speed. It is simply the heattransferredthroughthe differentgas and solid members betweenthe hot portionand the cold portionof the engine. Heat=canbe transferred by conductionor radiation. In the regeneratorthe gas moves, but under this headingthe heat loss is computedas if the gas were stagnant. In Section 4.3.6, the reheat loss is computed assuming there is no l ongitudi_nal conduction. The uncertaintyabout what thermalconductivitiesand what emissivitiesto.use to evaluatethis loss makes its measurementwith the engine desirable.•In some enginesthe hot and cold spaces are heated and-cooleddirectly. In this case measuringthe heat absorbedby the coolingwater with the engine heated to temperaturebut stoppedwill give this heat loss directly. However,all. the horsepower-sizeengines describedin S_'tion3 have indirectlyheated and.... cooled hot and cold gas spaces, For this _ase the sum of the gas and solid conductionand.the shuttleconductioncan be determinedby measuring the heat absorbedby the coolingwater 'Fora number of slow engine speedswith theengine heater at temper_ature and then extrapolatingto zero engine speed.
133
!
_; /. ; /, I ',
Solutions I i
4.3.8.]
to each one of these
problems
4. Radiation along Constant Area Conduction
will
now be given.
a cylinder
with
_adiation
shields.
,i
Heat loss by conduct.ionof this type is computed by the formula: QC = KG(AHT)(THMLD
TCM)
(4-112
where the thermal conductivities areas and lengths are germain to Path.3 and 4a above, KG is evaluated at mid-point temperature. (See---Table 4-9.)....... 4.3.8.2
Variable Area, Variable ThernialConductivitx
For one dimensional heat conduction where the heat transfer area varies continually and the thermal conductivity changes importantly, the heat conduction path is divided into a number of zones. The average heat conduction area for each zone is calculated. The temperature in each zone is estimated and from this estimate a thermal conductivity is assigned. Figure 4-23 gives the thermal conductivi.ties.for some. probable construction materials in the units used in this manual. It should be noted that there is quite a variability in some common materials like low carbon steel.... Measured thermal c_nductivity different by a factor of 3 is shown. Differences are due.to heat treatment and the exact composition. With conlnercialmaterials having considerable variability, it is strongly recommended that the static heat loss be checked by extrapolating the heat requirementfor the engine to zero speed. This number would then need to be analyzed to determine how much shuttle heat loss is also being measured and how much i:s static heat loss.
, q
i
For purposes of illustration, assume 3 zones are chosen along a tapered cylinder wall'. (See Figure 4-24.) Temperatures TA and TB must be estimated between TH and TC to start. The heat • transfer areas AHTH, AHTB AHTA and AHTC are computed based upon engine dimensions. The heat through each segment is the same. Thus: 2
2
!, ', _ ,_ ;: !'
iI ii _' _ I
J ......
Let:
i
RI = LHB/((KMH ; K,MB) (AHT_H_ +2 AHTB) KMB+ KMA 2
(4-.I14
R3 = LAC/
(4-116
)).
'L._4
'
'AHTA -AHT_.CC
i •
I
i.... , *
,
,
!
,
....... .....
I
i
!
T i
Usually the following
; ,';
Path No. for each engine: I. 2. 3. 4.
,'._
,_ _ '
i • ....i
!
5. 6.
conduction
paths are identified
and should be evaluated
Description Engine cylinder wall. Displaceror hot cap wall. Gas annulusbetweencylinderand hotcap. Gas space inside displaceror hot cap, a. gas conduction b. radiation Regeneratorcylinders. Regenerator packing.
,'i_
The engine cylinder,the displacerand regeneratorcylindersmust be designed
iI IF " _i
strong enough to.withstand.thegas pressurefor wall the life of the enginewithout changingdimensionappreciably. However,extra thicknesscontributes unnecessarily to the heat loss. For this reason the cylinder walls of most high poweredenginesare much thinnerat.the cold end where the creep strengthis high than they are at the hot end. This,__ef course,complicatesevaluationof___ this type of heat loss.
'li
The followingtypes of heat transfer.problems need to be solved to evaluate I. 2. • 3. these heat losses:
Steady,one dimensionalconduction,constantarea, variablethermalconduction. Steady,one diraensional conduction,variablearea, var_iable thermal conductivity. Steady, one dimensional conduction through a composite material (wire screens).
i ! ' _ I i
I
I
' _
i _
,
'
'
I
+ ,
J
t
i
i
;
+
Then: THM - TCM QC = RI +-R2 + R3
............
(4-I17
Once QC 'Iscomputed _then: TB = THM - TI(QC) TA = TB -R2(QC)
and so on
(4-II9
TB and TA are compared with the original guesses. If they are appreciably different so.that the thermal conductivities would be different, then new thermal conductivities based upon these computed values of TB and TA would be . determined and .theprocess repeated, Once more is usual.ly.sufficient.
, - ! '
(4-118
i,I
,.I
This same procedure is used for the engine cylinder and the displacer if the walls are tapered.
ii !i
I, 1 i I
i + ,
L
1 .i !
,
_i
• i
Figure 4-24.
'
--LEVEL B
Computation of Tapered Cylinder Wall Conduction.
1
'
,1.,_.,".._
Usually the re_.lt,llel'_lt,(,l' of a 5tirl inu .,',n_line is illado ll'Olli 111411,7 layers oF finn ,_creell tl_at is l igiYtly sintered together. Tt_e d_._gree oF Silltering would have al_itI [;_artng oil the thel'l]la] conductivity of the screen stack since tile colltl'olling resistance is i:l}e contact between adjacent wires. Some L't'yo_]t_lli(: regentwatof's
' %
1
Cond,pct ion ]'l!.rO,u_h° .ReEen.eratoll _l_a t r:i>:e_
t ..
use a bed of lead spheres. In tile absence of oata, Gorring (61 n) gives the following duc_ion through, a square array of unifor,lly sized cylinders.
formula
fur
con-
KMX = i
I
-:
. i .
(4-120.\! [t--':_ (KM/KG)-] +
Tile heat 4-112.
i I
1
loss
tilrough
i
:
screens
is
then determined
using
an equation
Sometimes the regenerator...is made.from slots in which metal foils tinuously from hot to cold ends. The conductivity of the matri× KMX = _+
'
tile
Tl_en tl_e heat like 4-112. 4.3.8.4
loss
like
run conin ti_is case is:
KM-C-TH F) GR %--T-HF
tl_rough
thematrix
(4-120a is
ti_en determined
Radiati___oiTAlon____q a C__vli_der _ji__tl__ Radiation
using
an equation
Si_ields
Ti_e engine displacers or tile--hot cap for a dual piston machine is usually hollow. Heat transport across this gas space is by gas conduction and by radiation. Radiation heat transport follows tile standard for,lula:
,
i ., _.i 'i
QR = (EA)(FE)(FN)(,,/4)(DID):'(SIG)(iTHM)" - (TCM)') The area factor,. FA, is usually determined by.a graph computed by Hottel (McAdams, Heat lransmission, 3rd Ed., p. 69). For tl_e case of two discs separated by non-conducting but reradiating walls his curve is correlated by tilesimple furmula:
,(
i i
t
FA = 0.50....+ 0.20 Equation
is good for
values
(4-122
of DID/LD fYoill 0 2 to 7.-
For (DID/LD)
0 _
rise :
:i,!
FA _ DID LD
,:
!i _.
,I-122
(oio)
In i"0-
(4-121
I<missivlty factor,-FE, the cold end. Thus:
(4-123 is the product
of tile
emissivity
at. the hot
end and at:
!
(4- 24
(EH)(EC) }
Tl_e i_ot and cold
I ,q4
emissivities
can be obta+ned
from any standard
text
on heat
:1.
--=
r
i: _-
:
I
'
L
:l
transfer. Ibis elnissiva-ly depends upon t.h¢_._urface. finish, tim lt,mperatute __arid the: material. It is not easy to know what. the emissivity in ,_ part.ivular vase i S,
•
,.
I f tlle sivity
end ssi vi t.y of the radi a t.i on slli el ds i s i n_::wmedi at.e between of the hot and cold surfaces, then..from the number of radial
FN _ 1/(1
.7
4.3.9 i,
tlle emi s-. ion shield_,
+ NRS)
(4-]25
eu!! j j_n_LLos _
NRS, the radiationsl_ield factor, FN,. is calculated approximately. A displacer or a hot cap has a radial gap between the [D of the engine
'
cylinder
is pressuri--,'ed and-depressurized, gas flows into and out of this gap. Since the closed end of-the qap is col_i ....extra heat must be added to the qas as it comes back from this gap, Leo (70 ac)gives the formula:
!
"!
I I -___J
I_ f_i _,
,
QPU = 2_-_CY and the OD of ....
In computing
i z,. "I :i!_:; !... _...,,"., ?.. is,: _:.'_
the
reheat
loss
(see Section
4.3.6)
it. was _ssumed that
the
regenerator matrix temperature oscillates during the cycle a negligible alnount. In some cases the temperature oscillation of the matrix will not be negligible. The temperature swing loss is this additional heat tha-t nlust be added by the drop in flow.o.f
ii
)__PIqAX- PMIN) __Hbl - TCM)IGR)<.6 tl_e displacer, l'his gap is sealed at. the cold end. As the engine 1:5(Z_i'R_7< I. . ............. '6(KG)O'6(ITHN + TCM./'2 _ _ 1.6---(4-126
the regenerator matrix temperature g,_s into the hot. space is:
gas heater
all
WH S( CV) heat FCI( THM - TCM)of dueDE to the finite capacity LTM× ......... ........
Thus temperature since the DELTMX starts
'_s: start atswing zero loss at the
along
the line
the regenerator.
of the--flow
due to a single ( 4-I L_ 7 The temperature
aild grows to [IELlblk.
QTS = (FCT)(WHS)(CV)(I_ELTRMX)I2 (,l-l?.,q Creuthanleland SI1elpuk(75 ac) point out this loss but their equation is: t!TS_:(FCT)(NHS)tCP)(IIELIMX )
(,i-],'9
Their equation substitutes CP for CV as was done also in Section 4,3,6, ll]ereason for division by 2 seems to be recoqnized in their-.textbut is nol refleeced in their forinula. Equation ,I-12_was used in Section 7. ll,tsed tlpOll tile discussion 111Section ,1.3.1_, it is IlOWrecc)mnlended tl_at an effec'tive gas heat c,tpaci ty bas_,d tlpOll Lquatioll ,I-97,1 be used in F.quatiol_s ,1-1'J7 and ,1-J.L,S.
i,! , '4
i
'
I
i
' _
, _
_ _
..... ,Il •_
i
,,
,i. _.4 ._
,....
4.3.11 InternalTemperature Swing Loss _- _
_
', I iI
Some types of regeneratormatrices could have such low thermalconductivity (for example,glass.rods)that all the mass of the matrix,would not undergo the same temperatureswing. The interiorwould undergoless swing and the outside would undergomore swing than would be.calculatedby Equation4-127. This additionalswing would result in an additionalheat l.os_, Crouthameland Shelpuk (75 ac)qive this loss as: QITS.: QTS { C3 \ KM-FCI'__J _ (.(_ROM) (CPM_.',)(LMX)2NU I (4-130 The geometryconstantC3 is given as 0.32 by Crouthameland Shelpuk (75 ac) who refer to page 112 of Carslawand Jaeger (59 o) Thisconstant is for a
i
slab. The cons_tant for-a cylinderor a wire is 0.25 (59 o, p..203). 4.3,12 .FirstRound Engine PerformanceSummary
At this point it is necessaryto take stock of the first estimateof the net ..... _........... i power out and the total heat-inbased upon the first estimate of the effective .... : hot and cold gas temperature. The to:talheat requirementwill be used along.... _ . _ith the characteristicsof the heat exchangers, to computethe effectivehot and cold gasbetter temperatures• computedtemperatures willheat be used to determinea estimate These of thenew basic output power and basic input• Heat lossesand power losseswill remain the same. The net power output is-
. i
NP : BP - WP - MFL , w
(4-131
The net heat input is: WPR QN ._=_,..BHI + QRH + QSH + QS + QPU + QTS + QITS - WPH - T
(4-132
4.3.13 Heat ExchangerEvaluation _ :,
_
Once the first estimateof.the net heat input, QN,.is computed,the duty of the gas heaterand gas cooler are determined:
!
_'_ I: I __
QGH : QN QGC = QN - NP
(4-133 (4-134.
Next, the heat transfercoefficientfor the gas heater and gas cooler is computed. The most common type is the tubularheat exchanger. Small machines can use an annulargap heat exchanger,-Isothermalizer heat exchangersare possible• How .tocomputethe heat transfercoefficientfor each one of these types of heat exchangerswill be presented. Then the way of estimatingthe temperatureoffset will be shown. 4.3.13.1 TubularHeat.ExchanBers The Reynoldsnumber for the gas heater is: RE : i 1
._ ,L
:i
140
WHS _DI.H) (NTH)(MU)
(4-135
,
,
A similar
! i
equation
would be used for
the cool_,r,
lhe heal
transfpr
cortficic.nt
}."o
is the correlation on l.i_.lureNote 4-1:1. lines bocausr the derived surface fronl teml._erature is controlled. t,hat tlso therethe issolid an iillpoi'tailt effet'tof length to dia.mot,er, t.ll/lllll, for the heater. The ortrinant o-f interest in l-iqure • 4-19-is-(H/(CP(G)))(PR).' / -_. lhe last: factor shown on l.iL, ll, ll'e 4,19 is
i,
i!lnored
=, i;!_:., _
bacau:_e the heat
ent, ferences. let i
G =In WHS/.(_DItt) evaluatinq
tile coo]el'. 4.3,13 '" Annular
c,..xchanger wi-ll
operate,
with
small
the above (NTH)) for ordinate the hea-ter.and for II, athe.heat similar
hap tleater
temperature
dif-
1
transler relationship-for coefi'icl-
_";;'_ ' ....
Exchm_ers
_.,
:',',i ,_ _,
Small Stirling engines can use annular, gap heat exchangers effectivel:,,. The heat is applied from one. side and the surface temperature is assumed censtant ..... From reference 64 I., page 103:
+,
H___
: 4.s_
Isothermalizer
(4-._3_-
5:
4.3.13.3
; a,_ .,_ "
The gas in the isothermalizer is chiefly heated or cooled by conlpressio;; or expansion. Under these conditions the._as inthe hot space is uniformly cooled by expansion and atthe same-time heated from both surfaces oF t.he qa_, layer.. In the cold space an analogous process-goes, on. llnder +_-,,_ "_,,.._. ,conditions the gas layers are. effectively in. the form of a slab. Ap_:e.ndi:; A shows that:
, ;
Heat E=xcll_j_.rs
QGH(GTA_} TH = THM - _-AH=F-) _ •
., (4-I,, 7
TC : TCM +
(4_i_8,_
i
:": _"
4.3,14
_:
,1.3. I+4.1
,_,
In tubular
i _.i
To Find Effective
Gas Temperature
Flow Hc_t Exchanq,!eze_s or annulai'
gap I_eat exchangers
tl_st, of the heat
during ofgas flow. tl_irdsof the time,2(FCT), to flow times one way or the otherTwothrough the heat excliangers,
+__
QGH = "(FCT)(WHS)(CV)(TH - THO)
:' } +_,£..+
LTH - THO] = II(AHT)L,)TH_f---tH_
( :. + _
Iteration
QGC(GT,A)
_nI,Ti+I--v-,I,i.F-+;
is. transferred gas can be assumed Thus: (4 _38.1 (4-138,2
0t':
:. _+',., '-, _',:
TU .....THM - _Tri"r3_l_+iS)1 _:v) --ii QGH(i-,.-xii(Nl"0"HT
(4-_39......
where : NTUH
H(AHI+ )+{-Fi,-T-) -_.W}(S-_-(+C_[)
'g7
I.I/
:; ;'
' '
.,Q
'_
i
t
t
t
,'
1
,!
| " " I
!_ ' ',;_ :i
i
TC = TCM + _TFTTT_,_I G__NTUC--T-7-_,
I-')--
(4-140
i',i :.:
Crouthamel and Shelpuk (75 ac) present most. of the heat transfer in the heater
,_,_ ,_ -.! i_i " ._I ,; _! .<: '-'_
space and that most of the heat transfer in the gas cooler happens during out flow from the cold space. If this reasoning proves true the 2 in Equation 4-139 and 4-140 and in the definition of NTUH and NTUC would be changed to I. More exact third order calculations might be used to showwhat factor should be used in Equations 4-139 and 4-140. Possibly 1.5 would be a good choice. Also, the question of whether to use CP or CV in the above two equations can be settled by more exact third order calculations. Equations 4-139 and 4-140 were used in Section 7, .As discussed in Section 4.3.6 it is now recommended that CP be used .instead of:.CVin the above equation because the pressure change term in Equation _-97,1 would cancel out when one full cycle-is considered
:,.:_ •..... !.' < _i : _i _,: -' ..... i
Equation 4-139 and 4-140 give a much better estimate of TH and TC than was used the first time the.basic power, BP, and.the basic heat input, BHI, were calculated If there is a significant change .in TH and TC the calculation for.BP and BHI are repeated, All other heat loss equations do not use TH and TC and therefore would not change. A new QGH and QGC would be computed, Again by Equations 4-!39 and 4-140 a new estimate of TH and TC would be calculated• These temperatures will probably,be.essentially the same as the previous estimate, and the computation wili be finished.
'_I
' 'i
_ i_ '
s i:,fi I :_rly',
i
i_i " , ..'_ i i_ii -i _j
a similar_calculation but reason that happens during out flow from the hot
•
In the case of the
GPU-3 engine
the cooler
is water
cooled,
Since
the heat
transfer coefficient for the water is much greater than for the gas, the cold metal temperature is very close to the cooling water temperature and ft can be assumed to be the same. On the other hand, the thermocouple measuring the heater temperature is in the gas stream half way through the gas heater• During the time gas is flowing into the hot space the heater must heat the gas to make up forregenerator reheat loss. In addition, during the first half of the inflow, the heater must coo-!the gas due to some compression heating. During the last.... half of tbe inflow-the heater must heat the gas due to some expansion cooling. When the inflow is complete the gas in the hot space is cooled by expansion. The main heat load-for the heater comes during outflow from the hot space, when the expanded gas is heated. During the-first half ofthe outflow some additional expansion cooling occurs as the gas traverses the heater. During the second half of the outflow some compression heating occurs as the gas traverses the heater. If the thermocouple is small enough..tofollow the change in gas temperature, it should c_ange considerably each cycle• Since the change reportedly does not occur, the thermocouple is .large and registers the, average gas temperature at the mid-point of the heat exchanger, Assume, therefore, for the case of the GPU-3-hea.ter..that the effective hot space temperature, TH, is ti_atmeasured by the thermocouple and that for the purpose of computing shuttle heat conduction, static condution and reheat loss, _THM= TH, Nevertheless, the temperature of the flame heated metal tubes will be hotter than the measured temperature. Equation 4-139 can be used to estimate this temperature.
142
_
.....
F
...... '.... r F
4.3.14.2 IsothermalizerHeat Exchange_rs ' ,_I
I
The same kind of iterativeprocessis used as above except Equations4-137 and 4-138 are usedins.teedof 4-139 and 4-140
'Ll_l
4.3.15
Conclusions
anSecond
Order Design Methods
il
'
, _
i, Second order is good for practicalengine design and engine optimization.
iiii I ' |
2. Second order methods identifyand losses. it easier to design determine what must be done quantifythe to minimi_ze the sum of This all makes the losses. 3, Much basic work needs to be done to extend the theoryand experimentally validate the equationsused for second order analysis. 4, The requireddegree of complicationin the analysis-ofa Stirlingengine design to adequately predict performance has not been determined at this stage of. nublic knowledge
" li _ "'.i _, "
I
i_, ; i
_ ! _£
i
4..4 Third Order Design Methods Third order design methods start with the premise that the many different processes assumed to be going on simultaneously and independently i:; the second order design method (see Section 4.3) do in reality importantly interact. Whether this premise is true or not is not known and no papers have been pub_ lished in the open literature which will definitively answer the question. Qvale (68 m, 69 n) and Rios (70 z) have both published papers claiming good agreement between their advanced second order design procedures and experimental measurements.(see Sections 5.1 and 5.2). Thi.rdorder design methods are an attempt to compute the complexprocessgoing on in a Stirling engine all of a piece. Finkelsteinpioneeredthis development(62 a, 64 b, 67 d, 75 el) and in the last year or so a numberof other people have taken up the work. If the third order method is experimentallyvalidated_hen much can be learnedabout the workings of the machine from the computationthat can not be measured reliably. Third order designmethods start by writingdown the differe_:tial equations which expressthe ideas of conservationof energy,mass and momentum. These equationsare too complexfor a generalanalyticalsolutionso they are solvednumerically. The differentialequationsare reducedto their one dimensional
'
additionalsimplifications__eemployed. form. Then dependingon just what author'sformulationis being used
I
In this design manual the non-proprietarythird order design methodswill be discussed. It will not be-possibleto describethese methods in detail. However,the basic assumptionsthat go into each calculationprocedurewill be given.
i
4.4_:I I_.asj c.DesiUn Mf,..iiJlod In hroad outline tho hasit de._i_.ln method 'is.as l"o'llows (s_,eFi_)ure4-',!5): I. Specil"y dimonsions ,indopuratinH conditions, i.e., l;emperatur(_s, char!l(: pressure, motion o1 I)arl:,s, etc, Divide onuiil(:-inl;o control volumes. <.. Convt_.rt tile (liffi_.rL, ntial eqtlatiollS expres._in{l tile ¢oiist_i,.vatioii of iliaSs, illOlilOIlttilll, alld l)iit_.l'tl.7.into dit:feri-;iice. Oqtiatiolls. IiIclude l:lie kini)ti{: ellergy of tile {tas, InclLitie t'nlpirioal l<'oYnltllas-'_' t.tlt_ i'rit:tiOll factor arldthe heal trailsfer coefl'icient. 3. Find a illathemati.cally stable nlethod of solution of the en.Gine parameters after 011(2 tilile step cliven Lhe conditions at the.beginnillUof that tilne. stop. 4. Start at an arbitrary initial condition and proceed throu.qhseveral erlcline cycles until steady state is reached by noting that the work output per cycle does not chan.ge. 5. Calculate heat input. 'l
i ..! i
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4.4.2 '
;
,,t
1 '_"
iI will
be given.in
words and .then in the
symbols
used by
Urieli. _.
f
4.4.2.1
.
Continuit.yEquation
Tile continuity equation created nor destroyed,
merely lI)us:
expresses,
l
the fact
that
nlatter
can--neither
be
net ,lassflux conw_cted- I
!
rate of decrease of '
l
Equation of state Enm.'gy.
These relationships
_'
EcLua..t_jgn__s
.... Following.tileexplanatien of Uriel,i.(77d).,there are 4 equations that must be satisfied for eacll elelnent, They are: i, Continuity 2. MOilientulii 4, 3.
'
Futldai_.lental.. Differential
1
=
outwards through
Urieli (77 d) expr'e_s this relationsliip, as;. IIIlasS ill control _v_oltlllle Oi" control '<m/ 'Jt + V _X_9_ i_ X ,.. 0
.-
surface,i
' (4-141
": ; il
vOltlnle (4-14 2.
1
,
I
'
,
:
'_.............
,
l
1 I.!
1 i
•i
_
_;".',::::.:f..:':',.,".. '_",:_,",'.•.v.':._fi
:'.'.'..:2",,,b::/.',".:,v','C,'_"..:_,"_,,':,';',, :,'.i,_
!.-":.:.:::_?.:") ===================== _C.?,:: : I
I
I
I
I
I
1
i
it;', ?::.t,:::;.::.f;i:;.!!_.;.; ?l _ t I
1:.:_.:_ ..:.x:4:,l'jl':;:l_ I
I
,2,L,
,
'
I
,
,
I i
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Figure 4-25.
Sample
Divisiofl of Engine Working
Gas Space
into_.Control..........................
Volumesfor a ThirdOrderDesignMethod.
_;
,i I
i< ;, y I
2;
!
L
_45
_
t
,_
J
1
I,
L----
'
wher_ : , i i :
m III M t V 9 Vs
:_mlM _ mass of qas in control volume, Kg = mass oF gas in engine, Kq _ time, seconds _ v/vs = volume of control volume-,, m-_ : tot_l power stroke volume of machine,
m-_
= O/(M,RTTkIVs)
g : mass flux density, kg/m>sec R : gas constant forworkinL.1 gas, Tk = cold sink absolute temperature, '}
"
, •_
......
x.= k,l(Vs) _I'_ _ =. distance,....metei_s
-'
.
4.4,2.2
" Momentum Ec_ation
'; ' '
••
.....
IRate of changes of I momentum within tIle_ Icontrol volume V I
, ! _ '.
t
J/Kg, K K
--
I Net momentum flUx convected outwards tllroughcontrol I surface A
+
(4-143
Net surface force acting, l on the fluid in tllecont_ol vo.l unle ..-V .
Urieli (77 d.)-..expresses this relationship as:
i
i
'_
, '
iK
_
+ VT. < (g:'v) + V
_
= 0
(4-144
where in addition:
v -- vl(Vsl l) p = pressure, <_!
N/nf.'
'I
F = F-/ M(R)TK/(Vs) I/'_ E) = I_/(M(R)Tk/Vs). _ : frictional drawl force,
_
to the workinq
N
i
gas
=
_ccumulat.i
011....
1
!
"! ._ _: .
Ifrom environiilent throughthecontrol surface A
;"
INetenerqy flux convectedI loutwards"by the working
,','.i. •;_i
+
%'
I
__Ii-
I ,h,
! "
" ....
"
_+
crossirlqtilecontrol IIgas surface A-II
lwithin the controlI volume V Net rate _t:flow work in pushin_ithe im_ss of| working gas surface thI"Ou_lh the control A I
(4-145
-7
T- -l-7
i
•.... " +q "
' ....
"
;
,..+.......
_
, .... ii4
_itll_ll_ii
i
7 "-':'.i
'
Net r,lte of: illechanical
;'"' ._.. i
.t
i
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Urieli
nleilttheby workint! by virtue, ell" _.la.S t:tl_ Oil l',i{t) the ellvil'OllL.f cllall_]O of tile Illaqllittldt. _ Of the coilti_l voltlllle
(77 d) expresses tills
,
work done
relationship
.,<.,<
+
finally,
as:
I - <,iv', ),
where in addition: .......
i ...It
V
' { ",_xt F
at
i :: f .'...:>.1
q, : Q/(MR(Tk)) q -' ileat t:i.'ansferred,
d
_< Wil:
: .-.,".:
_ _ ratio of specific
heat capacity of workintl gas = CPICV
j.
'
..-_:
T = workinq
' .,"
4.4.2.4
i.,
Due to tlle normalizino
7 i
gas
tenllJerature
in
control
volulne
K
i-
W = f_!(M(R)Tk) . _].--nlechanici:xl work done,.J
! _..I ' : i ,_
" i
E_uation of State
_i .!
parameters Urieli
uses the equation of state
ilmrelv is:
_",
i
;J _°
i ",
.....
p(V) = hi(T)
(4-147
!_I i i
i
4;.1.3 .......
'L
:.
'7_
Conlparison
of--lLtltt'd
Order
Desiqn
pl.e.t_t!.ods.
ll_.thods. A iltllllber o1 them areor soon will nlethods wilI now be describedbriefly.
.",.
4.4.3.1
_.>, .I ._. i _;
I _,
be in the literatul'e.
to
"....
Uriel i
engine was chosen because and fluid flow correlation,.; is built aild Souttl Africa.
is
design illethod,
of
operatitl_l at Tile intention
lh'teli
ease in for tubes
progranlnling, and because heat t.ransfer are well knowll. Also an engine like this
the I,illiversity is to obtain
of Wit.watersral_dill Jotl,lllnesbtir{!, experilllt, ntal confirination of this
t'OllVel'ts ttle above parti,ll
equatitms
to a
.equations by converting all the tiiiw-2-variable, lllen lie
differe
to ordin-
systenl of ditfer_nce
f. ,_,L _; "_'
ary dil:fei'elltial t_qLlatit)llS ll5tll.q tile 4th ol'del' Rllllqe-Klltta illetilod stal'tillq l'l'Olll a stationary initial condition, Tile thesis, contains the FORIRAN pt'otll'alll, rile first copies of tills tilesis has thl'ee el'l'ors ill tile illaiil pl'o{li'alll, Later copies el tile t.llesis-will probably .have these COl'l'ectiOll_.: added, COl'l't'c(.ic!llS
"_,_.
should
,
.
ordinary differential quotit_nts i_..xct,._t _ ",) for
differential
t: _.
)_-
._.. '
These
lhis design method is describedfully in Israel Urieli'sfile.sis (77 at). A _.Iood short e×planationis given in this IECEC paper (77 d). He applies his m,,,_thod to an experimentalStirlingengine of tiletwo piston type.. Tilehot ...... cylinder is connectedto tilecold cylinder by a .lltilllbel, or tubes in parallel.. Sections of each one. of these tubes are heated, cooled or allowed to seektheir own temperature lev_l in the regenerator part (see Figure 4-26). Ibis type of
; [ lf:_ I ._, ..... I m' "¢.i
::,1
It is generally beyond ttle Scope el" this first edition-of the design inanual g.ive tile reader a COlllpleteexplanation of flow to conlpute by third order
•
_,>
"l
be obtained
ii'Olll
I.
tlrielt,
{)t'llklt
lul'billes,
L-L__-JJo\
t4_l,
Yavlle.
israel,
: ': _: ii _.
_
i
._._ -_. i i L
1 tt
i
;
t I 1
&
I
i
FT
,
F........ F--T I
/i].
.
]
,
,
•
i
!/
......
'
'
q
'
..
i, Urieli is now attemptingto calculatethe data points for the GPU-3 engine C()MPRIISS I{)_] by appropriately program. SPA{I[c modifyinghis HEAT EXCHANGERSECTION
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t
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ii
1
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t
I
--
;.7'! . i-' !
',
--
Ii
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I
i
EXPANSION SPACE e
,
_
......j I
.......... i
I .
.
, I_ZZ_I
i
I HEATER h I REGENERATOR r .......... Figure4-26, Urieli.Engi'ne Model.... 4.4.3.2 Schock
I COOLER k
_
Al Schock, Fairch.i!d Industries,Germantown,Maryland,presentedsome results of calculationsusing his 3rd order design procedureatthe Stirling EngineSeminarat the Joint Center for GraduateStudy in Richland,Washington,August 1977. His calculationstartedwith the same differentialequationsas Urieli but his method of computermodelingwas differentbut undefined. He confirmed what Uriel.ihad said at the same meeting that the time step must be smaller than the time it takes for sound to travel fromone node to the next through the gas. A1 Schock'sassignmentwas to develop an improvedcomputer program for the free displacer,freepiston Stirling engine built by Sunpowerfor DOE. The enginehadavery porous regenerator. Althoughthe pressuresin the expansionand compressionspace of the engine were different,they were not visablydifferentwhen the gas pressurevs,.timewas plotted. This programis as yet not publiclydocumented. Schock is awaitinggood.... experimentaldata with Which to correlatethe model. 4.4.3.3 VanderbruB
I .
In reference77 ae, Finegoldand Vanderbrugpresenta generalpurpose Stirling engine systems and analysisprogram. The programis.explainedand listed in a 42 page appendix. Quotingfrom 77 ae: The technicalapproach used in the StirlingCycle AnalysisModel (SCAM)is based on obtainingsystem transientresponseby lumped parameter,or nodal, numericalintegration. The integrationtechnique assumes that-thethermodynamicprocessesare quasi-static ..... during a small time intervalfor each system node or control volume. The Stirlinganalysis programsdevelopedat LeRC (77 bl), the recent Finkelsteinmodels (67 d), and most thermalanalyzer programsemploy this method to avoid direct integrationof many non-linearuncoupleddifferentialequations.
148
_
_ _'
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_ _. ' i i ,i _" "! • ' i _i I .,_ _' ,. • ._! :_.! ii _'i B 'i :_ ._i 1i i _i -:
I
,i
.
_:" ._!
i
_i
The ,lumpedparametermethod is desirablebecause either empiricalor theoreticaldefinitionof componentperformance characteristicsis easily achievedwithout"use of transform functions. Also, discontinuitiessuch as those producedby flowing from laminar to turbulent,or from subsonicto choked, are readilysimulated. One disadvantageof tllisapproach• is the extremelysmall computing time interval which is required to satisfy the quasistatic assumptionfor pneumaticsystems, The small computing intervaluhavoidablytranslatesinto a high computerdollar charge.
................
The SCAM programwas designed tO provideextremeflexibility due to the modular structureand varietyof use_ input options. The SCAM consistsof a compilation,or li.brary, of individual modeling routines. Each.routinecontainsthe logic and generalized equations,such as chamber,volume,duct, temperaturecontroller, heat exchanger,etc., required, to simulatea pneumaticsystem component, This allows the user to select componentsfrom the library and assemble( ,t,hem.into flow and logic control functionalsegments .egs"or fluid "loops")representative of•the physicalsystem being,modeled. The user specifiesinitial conditions,boundaryconditions,and other key.parameters describingthe performancecharacteristicsof each component. All input parameterscan be either constants,curve,data, or forced to vary as a functionof time, temperature,or some other control-value, such as crank angle.
_, _.
At this . point, there is nothingavailable..-to show how well this computer model works. 4.4.3.4 Finkelstein
:i
j T!.: _ •_ _! _ ....
.
t
!
Ted Finkelsteinhas made his computeranalysis program (75 al) available throughCybernetat about $25 per case. Instructionsand directionsfor use are obtainablefrom TCA,.P.O, Box 643, BeverlyHills, California90213. One must become skilled in the use of this program-sinceas the engine is optimizedit is importantto adjust the temperatureof some of the metal parts so that the temperatureat the end of the cycle Ss nearly the same as at -thebeginning.
Urieli and Finkelsteinuse the same method in handlingthe regeneratornodes in that the flow conductancefrom one node to the next dependsupon the directionof flow. Finkelsteinsolves the same equationsas Urieli presents but he neglects the kineticenergy of the flowinggas. By so doing, he is able to increasehis time step substantially. Neglectingkineticenergy will .......... cause errors in predictingpressuresduring the cycle. However,it is not clearwhat effect this simplifyingassumptionhas upon power output and efficiencycalculations. To make a comparisonone would have to use the same correlationsfor frictionfactor and heat transfercoefficientand be certain that the geometriesare identical. The author has directionsfor using this program. Possiblya comparisonof this programwith the GPU-3 measurements
14q
[
L
'_,
!
and other
calculation
procedures
can be made in the
i:uture,
Finkelstein claims that his program has been validated that the results are proprietary. 4.4.3.5
Lewis Research
Center
experimentally
but
(_LeReR__
The author has attempted to formulate a design procedure based upon some computation concepts originally used by M. Mayer at McDonnell Douglas. A simplified version was presented (75 ag). However, an atteinpt failed to extend the method to include a real regenerator with dead volume and heat transfer as a function of fluid flow. The procedure was computationally stable and approached a limiting value as the time step decreased. But wlienthe heat transfer coefficients were set very high, there should have been no heat loss through the regenerator, but j
I
the computation procedure did not allow this to happen, because gas was always entering the hot space at the temperature of the hottest regenerator element. There was als_ the probleinof finding the proper metal temperature for the regenerator elements,
i i' I
T_
Parallel and independently of the author, Roy Tew, Kent Jefferies and Dave Miao at LeRC have developed a cc, mputer program which is very similar to the author's (77 bl). In addition, they have come.up with.a way of handling the regenerator which gets around the problem the author found.
!i _
'
The LeRC method _'.ssunles that the momentum equation need not be considered along .
!i f
I
with for continuity, energy andengine equation state. that the the equations pressure is uniform throughout the and of varies withThey timeassume during the engine cycle. LeRC combines the continuity, energy equation and equation of state into one equation. dT
: _
hA
(TW
wi T) + _ (T i
Wo _,rV__._ _L T) + _ (T O - T) * _ ,._,_ change
(4-148 .
This equation indicates that the temperature change in a control volume depends ..... upon heat transfer, flow in and out and pressure change. Equation 4-IA8 could besolved by first order numerical integration or by higher order techniques such as 4th order heat Runge-Hutta. LeRC did not use this..approach. transfer flow in flow out . pressure
D
I
LeRC used an approach of separating the three effects and considering them successively instead of simultaneously. From a previous time step they have the masses, temperature and volumes for all 13 gas nodes used, From this they calculate a new con_llon pressure. Using this new pressure and the old pressure and assunling-noheat transfer during this stage, they calculate a new temperature for each gas node using the familiar adiabatic compression fornlula. Next, the volumes of nodes i and 13, the expansion and compression space, are changed to
I
the new value based upon the rhombic drive.
i
New masses are calculated for each
_
I i.
1
a
i i
,
\,I
-_
,i .I : i :
....
..I _'_ .. _'_,,._ ._._ ,., ,,!, i!/ ,_" i:,;l '_" •i:, :._ _,_, i_ -_ _.:i '..... ,../ ,,"::_ " " .... ?.,: , :..! ,,4 _,.._ ' ._'! A'!
ii
' _i , _ _._, _i _I i_
! _;
i
COi1tl;Ol
w11ullle.
OlICe
i,he
new
Mass
distribution
is
kllOWll,
the
flew flow
rates
between nodes are calculated ir_nl tile old and flow mass distributions. The new _,las tempe,raturL: is now nlodified to take into account tile _.las flow into and out of the control volun_s during the time step. [)urin;l this calculation it is assumed that each reqenerator centrx)l volume has a temperature _}radient across it. equal to the parallel metal temperature, gradient and that the temperature of tile fluid that flows across the boundary is equal to the average temperature of the fluid before it crossed the boundary; heater and cooler control volumes are at tile bulk or average temperature throughout. Next,local heat transfer coefficients are calculated based upon the flows. Temperature equ.i!ibration with the nletal walls and nlatrix is,now calculated for the time of one time step and at constant pressure. An exponential equation is used so that no matter flow large the hea_ transfer coefficient, the gas temperature cannot, change more than the _[ between the wall and tlle gas. Heat transfer during this equilibration is .... calculated. In the-regenerator nodes heat transfer is used to change the temperature of the nletal according to its heat capacity. In the. other nodes where the temperature is controlled, the heat transfers are summed to give tile basic heat, input and ileat output, lhis final temperature set after temperature.equilibration along with the new masses and vo.lumes calculated during this time step are now set to be the old ones to start tile process for tlie .. next time st_p. The mode,l is set. up to take into account leakage between the buffer space and the workint,1 gas volunle. LeRE has developed an elaborate method of acceleratl,,g "" convergence of the metal nodes in the regenerator to the steady state temperature. On the-final cycle LeRC co_Isidersthe effect..offlow friction to nlake the pressure in t.hecompression and expansion space different from each other in a way to reduce indicated work per cycle.. .............
To quote Tew (77 bl): Typically.it takes about 10 cycles with regenerator temperature correction Due to the before leakagetlieregenerator-metal between the working and temperatures buffer spaces, steady a number out. of cycles are required for the mass distribution between working and buffer space to settle out. The smaller the leakage rate, tile longer the time required for the mass dis-tribution to reach steady-state. For the range of leakage rates considered thus far it takes longer fo_' -thu. mass distribution • to steady-out than for the regenerator n_tal tenlperatures to sett2e out. Current; procedure and at the metal 15th cycle. The model is then scheme allowed on toat run is tooff turn tenlpe_.'ature convergence the for .5th cycle 15 to 25 n_ore cycles to allow the mass distribution to settle out, When a sufficient number of cycles have been completed for steady Current COlllpUti llg tillle is 5nlninutes 50 cycles on a UNIVAC 1100 or 0.I minute about per cycle. This for is based on 1000 iterations per cycle or-a time increment of 2 x I0''._ seconds when tI_eengine frequency is 50 H;'. lllenumber ef iterations per cycle _and therefore computing time) can be reduced by at operation to be achieved, the run is terminated.
....
i
!
' /,
least a factor of 5 at the expense-of accuracy of solution; on the order of 10% increase in power-and eff.iciency results when iterationsper__cycle are reducedto 200,
.................................
4.4.4 Conclusionson Third Order Design Methods _ i : _ ..... ,
I, A number.ofwell constructed_.third order design methodsare or will soon be available. 2. A choiceis availablebetweenrigorous 3rd order (Urieli,Schock, Vanderbrug),3rd order ignoringfluid inertia(Finkelstein)and3rd order assuminga co_nmonpressure (LeRC). 3. There,isa spectrumof design methods reachingfrom the simplestfirst order throughsimple and .complexsecond order culminatingin rigorous3rd. order analysis. However,all thesemethods depend upon heat transfer and fluid flow correlationsbasedupon steady flow insteadof periodic flow, becausecorrelationsof,periodicflow heat transferand flow..f_iction which should be used have not.beengenerated. 5. Third order analysis can be used to computeflows-andtemperaturesinside
I . i
!
the engine which cannot be measured in practice., i Third order analysis can be used to develop simple equations to be used i : in second order analysis, I 7. Eventuallywhen all calculationproceduresare perfectedto agree as well ........ '. .... as possiblewith valid tests of Stirlingengines, thY'idorder design I methods wi.llbe the most accurateand also the longest..The most rigorous ' formulations o.f third order will be much longer and more accurate than the. i l.east rigorous formulations.
6.
t
I,L :
5
, :,
_
_"
1
_"
1
1
" ., '[,
_L _-i
COMPARISONOF THEORYWITH EXPERIMENT
Among conventional engines with tubular heaters and coolers and porous regenerators, there are only three engines that are well enough known and accurately enough measu_d to be considered: I. The A1lison Stirling engine 2. The MIT cooling engine 3. The GPU-3 engineEach one of thesewill now be described and the comparisons given in the literature will be made. 5.1
:
......
i_'j !!
'l_ l_
'; '
!
_i :'!, _i
•
• J
Qvale (67 n) gives the most complete specification of the Allison Model PD-6/#L engine (62 n). ?hese are: . ................. Phase angle between two volumes --_B= -1180 Engine speed 3000 rpm (50 Hz)
VAC ==amplitude 2.33 in3 :Of_38.18sinusOidalcm 3 volume variation in cold space 1.715vo]ume in3:28.10 cm3heat (ducting and clearance accourts for VC = dead of cold exchanger and.ducting and clearance 1.215 in3 : 19.91 cm3) VR = regenerator dead volume : 4.388 in3 : 71.91 cm3 (this includes 0.488 in3 on one side and 0.55 in3 on the other side of the regenerator) VH : of hot heat exchanger andcm3 clearance : dead 2.59 volume iln 3 : 42.44 cm3 (/includes 1.29and in ducting 3 = 21 14 from the hot volume ' Surface Temperature - Hot = 1680 R = 933.3 K Cold : 628 R : 348.9 K Working gas - Helium Mean pressure = 1544 psia = 10.64 MPa Cold heat.exchangers number(_f tubes : 152 ID of tubes = 0 040 in = 0.102 cm =
length of tubes = 2.6 in Regenerators, matrix: screen stack wire diameter = 0.0016 in 1 i
,,!
Allison Engine
VAH = amplitude of sinusoidal volume variation in hot sp_ce 2.475 in 3 = 40.56 cm3 _
i'
mesh = 250/inch filler factor : length = 0.8 in cross sectional
i:i ;_
_' _i
!i _, ,,] i! i wi; Ii. _ _I' _il l "i ! i _ I
"i 1
6.6 cm = 0.0041
cm
: 98.4/cm 0.31 = 2.0 cm area_of a]l regenerators : 6.24 in_ = 40.26 cm_
number of _egenerators not known
,_ I i ,i
i _ i
I'
, _:
!
_
!
1
i
_
i¸
i '
i
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i
i
_
i
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i _
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'
Hot heat exchanger number of tubes :_ 76 i.nner tube diameter ;: 0.060 in .= 0,152-cm-length = 6.0 in = 15.2 cm i
,, '" _
Allison builttwo engines which differed onlyAn the phase angle between the two volumes. One was 1180, and one was I12 °, Qvale analyzed the engine performance according to his methods (67 n, 68 m,) and showed the agreement given in Figure 5-I and 5-2. Qvale (67 n) also gives a breakdown of tile predic.ted losses and the experimental uncertainties. The_eare. given in Table 5-I. 5.2
MIT Cooling Engine
Rios (69 ar, 69 o) built a-cooling engine and made-performance measurements on it. Since it used tubular heat exchangers andporous solid regenerators, it is of interest to large Stirling engine designers.
:_
,
The dimensions of this engine are as.follows: Warmcylinder diameter: stroke: con. rod length: end clearance: Warmexchanger number of tubes: outside diameter: wall thiGkness: tube material: average length: (bent in quarter circle) Regenerator shell inside diameter: shell wall thickness: shell length: matrix: ave. diam. of powder: porosity: matrix retainers: shell material: Cold exchanger
",I
number of tubes: outside diameter: wall thickness: tube material:
• I 1 j _I 154
c, i
Cold cylinder diameter: lungth: s.troke: con. rod length: cold cap length: cold cap clearance: .... coldcap material: end clearance:
2.0 in 3.0 in 14.4 in 0.010 in
5.08 cm 6.62 cm 36.6 cm 0.025 cm
210 0.047 in 0.008 in 304 stainless 21.5 in 2.065 in 0.030 in 3,4 in
.....
,_
0.119 -cm 0.020 cm _..o cm
..............5.245 cm 0.076 cm 8.6 cm
copper-ni ckel/spheroi daI powder 0.010 in 0,025 cm O.39 I00 mesh screens at each end stainless steel 231 0.047 in 0,008 in 304 stainless
0,119 cm 0,020 cm steel
1.625 4.128 cm 9.4 in in 23.9 cm 2.5 in 6.4 cm 12.0 in 30.5 cm 7.19 in 18.3 cm 0.004 in 0.010 cm linen-filledmicarta 0,010 in 0.025 cm
,, 1 _ C i,_ ,:
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Table 5..1 Breakdown of Losses and Powers for the Allison Model PD-67A Engine with 118° Phase Angle ....
.. '
Operating Conditions Speed Heat source temperature Heat sink temperature Work Mean Outputgas pressure Basic work, hot cylinder corrected for heat exchanger performance Basic work, coldcylinder correctedfor heat exchangerperformance Net basic work Flow losses - cooler 8.8 - regenerator 4.1 - heater 22.6
_ , i
1 ....
1
, i
-,
Predictednet work (neglectingmotoring and leakagelosses) Experimentalnet work Heatinput Basic work at hot cylinder correctedfor heat exchanger Heat conductionof metal parts Regeneratorloss Flow loss in hot controlvolume Predictedheat input Experimentalheat,input
3000 rpm !680 R 628 R
50 Hz 933.3 K 348.9 K
1544 psia 285 ft Ibf/_,
10.64 MPa 386.5 J/_
283.... 122.5
383,7 166.1
125.5 157.5
170.2 213.6
iJ
11,9_, 5.6 30.6 35.5
48.1
122.0 108.5
165.4 147.1
283.0
383.7
, I
..I
12.6 ft Ibf/_ 25.6
PredictedEfficiency
:
-24.7 296.5 287.0 122 _-
ExperimentalEfficiency
=
108.5 _
17.1J/,_ 34.7 -33,5 0;_0-2.1 389.2
:
0.411
=
.0.378
PredictedPressureRatio = 1.80 ExperimentalPressureRatio............. = .................... i;79............. ExperimentalAccuracies Net work + 4% Heat Input ¥4% Efficiency _6%
' i i
e
i
i
T 4 ,
!11
:
...........
1
"
i
I
i
The warm end crank was dr_.ven by an electric motor and .it in turn drove the cold end crank by a timing belt. The warm-heat exchanger was water cooled. Th_ cold heat exchanger was covered by a brass shell. An electric heater was soldered to the cold exchanger shell to adjust the load to the refrigerator. I F 1 ,
.......
Refrigerant boiling out of this space was. measured with a rotameter. Heliumwas used as a working gas. The fillingof the shell of the cold.heat exchanger was either nitrogen, Freon 12 or Freon 13. In steady operation the power to the cold-exchanger-shell heater was adjusted to boil the liquid at the same rate that the vapor was condensed on the exchanger tubes-. A steady pressurein the cold exchangershell indicateda,steadyopera_a_ILt_g, temperature. The basic data taken by Rios were as follows: i. Indicator diagram for the cold and warm end cylinders and indicator diagrams for the pressure drop. These diagrams provided values for comparison against the model with perfect components and pressure drop losses. 2. Cold exchanger and warm exchanger temperatures. The warm-end temperature was the cooling water outlet, while the cold end temperature was that of the condensedfluid, Differencebetweeninlet and outlet coolingwater was negligible, ,_
,,;_ " _=_
! _i .............. i ;
i,!i !_ :i "i
4... 5. 3. 6'
refrigeration. Refrigerator RPM. Volume variationphase angle. Cold-exchanger-heater power. Providesa direct measurementof the net Rate at which gas is vented from cold-exchangershell
_-:I :li_
,_
i ,i
(Pw)maxVAC
__
VAC : cold(VmaxCylinder_ Vmin)/2v°lume amplitude .... ............. PwdVw Ww.: (PwlmaxVA ';,..here in addition: ..
Vw
i
i
Pw instantaneouspressuremeasured in the warm space Vc : instantaneousvolume ofcold space
,_J
,
)
!# pdVc
",' ._!
!-
Windage Power : _ = angularvelocity,radians/sec 6p : pressuredrop throughheater regeneratorand cooler dVc : differentialchange in cold volumes
:
/ _,I 'i! /
Rios publishedthe resultsof 20 data TheseThe arefollowingdefinitions Copied from (69 ar) for the convenience of the reader (seepoints, Table 5.2). are used in Table 5.2.
,
_ ii
instantaneousvolume of warm space, cm_
VAW : warm cylinder volume amplitude_,__c _m___ ,:! 157
Table 5.2 Sumnlary. of Rios' Data (69 ar) Tes t No.,
, i
Tc
TW
F
F
Phase Angle o
Vapor around cold HX
Speed RPM
Refri g. Load Watts
i
- 14,_
42.0
62,0
Freon 12
_326
91.0
2
- 6.0
41.5
89.5
Freon 12
326
111.6
4
- 12..5
41.0
7.6_0
Freon 12
326
..-
,!
___86.0
,i
+
I " _. ". "
i
3 5
11.0 -163.3
42.0 38.5
102_0 7510
Freon12 Freon 13
326 325
98.0 86.6
i
6
-163.3
37.5
88.5
Freon 13
325.
93.0
I
7.......... 167_3
38.5
101.5
Freon 13
325
8 9
38.5_ 38.5
62.0 61.0
Freon 13 Freon 13
325 483
74.0
Freon 13
483
120.0
-162.0 -162.0
i
101.5
.
i
76.0 .93.6
k !_,
I
,I
i
10
-164.7....... 37.5
i
11
-164.0
37.5 .....87.5
Freon 13
483
125.0
_
12
-164.0
37.5
101,0
Freon 13
483
108.0
!{_
13
-317.2
38.3.
87.0
Nitrogen
480.•
48.5
_i
14
-315.4
.38.3
73.5
Nitrogen
480
44.0
_!i
15
-314.2
38.3
...... I01.0
Nitrogen
481
0.0
_+_:i
16
-311.6
36.3
61.5_
Nitrogen
485
_i
17
-313.0
36.0
87.5
Nitrogen
325,
,_i
18
-316.2
37.0
I01.0
Nitrogen_
325
0.0
i _:'
19 20
-316.8 .......... 38.3 -311.2. 38 3
75.0 62.0
.... Nitr-ogen Nitrogen
325 325
O.0 0.0
.i
i
'I
,i :I
.................*
-I
._I
29.5
i,
kL
158
•
--
...........
Ji
*'Z_"
:'_ "_
*
'
"" - ........
.
,= ,
_
i
cl
i !
I
_
ii
' "
! ,,
! "'%
Table 5.2 Continued
i
Test No. ...._ _
(o f '_PdVc 2-_T (watts)
Wc --
-Ww
Pmax psia
Pmin psia
rp
,:.
I
11.1
0.521
0.432
176.4
73.6 ........ 2.41
/
2
20.0
.... 0.601
0.496
177.1
91.8
I 1 ,
'%:_i _ci
3
24.4
0.637
0.525_
160.6
83 7 ........ i q2
4
15.7
0.571
0.486
165.9
75.8
i
;', ,',C
5
17.0
0.441
0.625
289.1
124.1
2.33
6
21.8 o.48o o..6 7
8
22.9
0.388
0.580 ....
279.9
117.2
2.38
9
31.4
0.377
0.589
228.0
87.5
_.61
10
42.0
0.439
0 638
242.7
100.0
2 43
;
11
57.6
0.499
0.681
226.4
103.5
2.18
*_
12....
72.2
0.519
0.619
220.9
108.7
2.04
_!_'_,!
'?'
1.93
....... 2.18
• 1
,_LLI_: !
13
74.6
0.325
0.806
313.0.
131.7
2.38
, !
14
56.4
0.299
0.750
321.7
125.3
2.56
i
15
76.9
0.366
0.827
224.2
96 5
2.33
i
16
26.5
0_279
0.710
169.8
62.0
2,74
_ _
17
23.4
0.320
0.722
301.0
133.3
2.26 --
_
18
29.4
0.336
0.799
269.9
125.8
2.14
19
17.2
0.286
0.760 ......... 298.6
122.0
,_.45
38.6
0._80
0.672
120.5
2.56
.,]
I
20
I
'1
L
-
heal
leek at
i ai;m
39
308.7
,_
Static
,:•
Static heat leak at 2,0 torr -_ 25 watts * venting!nitrogen vapor from cold exchanger sh_l! wiLh ::nI(_ad =
_"
WEi .... S
i
I
) i
and finally:
,"
(pw)
.... i
rp __
max
Explanations of the Rios theory were not given in Section 4, During the current effort the author was not able to completely review and become familiar with. it. However, he-now has the computer program and one might be able to use it without really understanding it. Rios claims very close agreement.between his theory and experiment. In Figures 5-3, 5-4 and 5-5 the points are the experimental points from Table 5-2. The lines are calculated by his computer program. These results show very good agreement at almost every point. The parameters used in the captions in Figures 5-3 to 5-5 are defined as follows:
I !
i ....
rv_[ : displaced-mass
ratio
= VAcTw*/VAwTc*
T = heat _xchange temperature, absolute VD mDRT w /PVAw : reduced dead volume.
i
" •
degrees
mD : mass of gas in dead space, grams R =...gas cons.tant, J/g K p : instantaneouspressure,MPa rcs : ratio of connectingrod length to one-half the stroke
!.
_
/_i
The quantity VD is given as a constantalthough both mn and p vary during the cycle. If the deadvolume gas temperaturesdo not change,mD is proportional to p and Vn would be a constant. This needsto be discussed. The quantityr_ is given aN 4.8. But in appendixG of the Rios thesis (69 ar) the ratio for _ the connectingrod length to the ful_._]_l stroke is 4.8. Rios writes that the la-tteriscorrect,
i i i i /i
Measuredand calculatedpressuredrops are given for Rios' 20 data points (see Table 5.3 and Figure 5.6). Good agreemen.t.is shown althoughthere is increased scatterat the lower values,
_, _
i
C/ I
;Ji /d
' _-_
l
5.3 The GPU-3 En_.ine
!
This engine is describedin detail in Section 3.3. Figures3-24and 3-25 show that the efficiencyand engine power now at NASA-Lewisare about as good as they were when the engine was first tested at Ft. Belvoirby the U.S..Army.... Eight test points are given in Table 3-8. It is plannedthat the variousways of computingStirlingengine performancewill be comparedwith experimental measurementsnow being made withthe engine.
<
Table 5-4 shows the computedresultsusing the NASA-Lewis3rd order calculation procedureexplained_izL_Section 4.4. i i i
Table 5-5 shows the Gomputedresultsusing the 2nd order calculationprocedur_ .... given in Section 7, Both Table 5-4 and Table 5-5 give a detailedbraakdown of the basic powers and heat inputs along with an itemized list of the losses in approximatelythe same format. Table 5-6 compares the indicatedpower output 160
"ii
i i" ..,,Ji
i
and the indicated
effici_.ncay obl;ained from the two methods of-computation., .....
.=......-.-_-_
. " -._-,
-..-i-__.i_ .....
i_ "I
I
No_te__, :I
11 4
i'
.a,
, I
! I
i
i "I
i
.! •
i
!
!
1/_,?
Table 5-4 LeRC Computed Performance for GPU-3 Test Points Heater Average Gas Temperature 978 K (1760 R) Cold Metal Temoerature 295 K-(530 R) Test Point
1
Engine Speed, RPM -. Hz
!
Mean Pressure,.MPa psia
1500 25 .......
2.068 300
2 2000 33.33 2.068 300
5
6
7
8
2500 41.67
3
3000 50
4
3000 50
1500 25
3000 50
1500 25
2.068 300
2.068 300
4.136 600
4.136 600
2.758 400
2.758 400
4347 (5.83)
5824 (7.8i)
2938 (3.94_ -
157
783
119
(.215 4191
(1.05) 5041
(.16) 2819--
- (10.2)(5.62) 1730 872 (2.32) (1.17) 5876 3318 (7.885 (4.45)
(6.76) 1163 (1.565 3878 (5:2)
(3.78) 589 (.79) 2230 (2.99)
i I
11051 (14.82)
5563 (7.46)
_
Power,watts (HP) 2163 2968 • Basic (indicated + windage) ............... (2.90) (3.98)
3758 (5.04)
4541 8650 (6.09) .... (11.6)
Total Flow Friction (heater + regenerator + cooler + end effects)
44.7
96.9
(.06) 2118
(,13) 2871
Indicated Power
(2.84) 432 (.58) 1685 (2.26)
(3.85) 597 (.80) 2274 (3.05)
(4.80) (6.69) 753 910 (1.01) (1.22) 2826 3333 (3.79) (4.475
4004 (5.37)
5391 (7.23)
6786 (9_I05
8158 (10.94)
4!0
410
410
410
336
336
336
336
Static Conduction
(.55) 1044 (1.40)
(.555 1044 (1.40)-
(.55) 1044 (1.40)
(.55) 1044 (1.40)
(.455 1044 (1.40)
(.45) 1044 (1.40)
(.45) 1044 (1.40)
(.45) 1044 (1.40)
Windage Credit (total
-22.4
-44.7
-89.5
-149
-522
-74.6
-388
(-.03) 5436 (7.29)
(-.065 6801 (9.12)
(-.70) 17561 (23.45)
(-.i0) 9702 (12.91)
(-.52) ]2118 (16.15)
(-.08) 6957 (9.23)
Brake Efficiency (%)
31.0
33;4
34.7
35.2
32.2
32.4
i I
i
Indicated Efficiency (_)
39.0
42.2
43.9
44.8
41.9
41.0
;_ i
)
Temperatures, K (R)
Mech. Friction (.2xBasic) Brake Power
179
298
(.24) 3579
(.40) 4253
1044 (1.4) 7606
} i
!
Heat Input, watts (HP) Basic (includes everything except shuttle loss, static conduction and windage credit) Shuttle Loss I
i
16629 (22.30)
8322 (11.16)
i_ I ,
-. _
! I ;
,_
"i
i i
windage loss/2) Net Heat Input, watts (HP)
" r:l •i
Time averaged gas temperature in heater (Point 5, Fig, 3-27)
_t j!
Cold Metal
(-.12) 8151 (10.93)
(-.20) 9463 (12.69)
.......... 33.6 34.5 43.5
43.5
-59.7
,., _ .:T_
!_! • . 979 (1762)
979 (1762)
979 (1762)
979 (1762)
979 (176-2)
978 (1760)
_75 (1755)
978 (1760)
294 (530)
294 (530)
294 (530)
294 (530)
294 (530)
294 (530)
294 (530)
294 (530)
_
i: i k ! i; i .:
i
'
_i
i!
_' ' ;'(
L
REPRODUCI3II,ITYOF THI_ (fftlGINA}, PAGE I8 POOR
I, ( 163
I!
' t
Table 5-5 ..... Computed Performancefor GPU-3 Test Points Hot Gas Temp. 978 K (1300 F) Cooler-Temperature 295 K (70 F) Cooling Water Flow, 6 GPM
. Test Point Working Fluid S/
....
_f_ "
!I
I 1I
H2
H2
He
6
7
He ...... He
8 He --
3000 50
3000 50
1500 25
3000 50
1500 25
Mean Pressure,
2.068 300
2.068 300
2.068 300
2.068 300
4.136 600
4.136 600
2.758 400
2.758 400
2287 3113 12 ....26
3940 49
4742 82
9405 289
4736 41-
6293 209
3067 30
169-
267
389
912
217
880
211
......... 7
MPa psia
93 2
4
11
39
6
28
4
2180
2914
3617
4260
8165
4472
5176
2822
457
623
' 788
949
1882
947
1259
613
Brake Power, NP
1723
2291
2829 .... 3311
6283
3525
3917
2209
Heat Input,.watts Basic, BHI Reheat Loss, QRH
3415 I04
4603
5791 214
6960 277
13860 337
6957 126
9259 191
4566 . 72
449 1118
448 Ill8
447 Ill8
445 Ill8
379 II08
381 ll08
379 ll08
381 ll08
Pumping Loss, QPU
14
22
31
79
26
42
14
Temp. Swi.ng,QTS InternalT.S., QITS
52 0
69 0
87 0
146 1
73 0
65 0
33 0
Mecha,ical Friction,MFL
Shuttle Loss, QSH Stat.icConduction,QS
_l
5
6
41 I04 1
!
Heater FrictionCredit, WPH
-12
-26 ........ 49
-82
-289
i
Half Regen..W.Credit, WPR/2
-47
-85
-134
-195
-456
-109
-440
Net Heat Input, QN, watts
5102
6305
7505
8769
15165
8521
10395
6049
Brake Efficiency-, %
33.8
36.3
37.7
37.8
41.4
41.4
37.7
36.5
IndicatedEfficiency,% Temperatures,K Hot Metal
42_7
46.2
48_2 -. 48.6
53.8
52.5
49.8
46.7
978
978
•
EffectiveHot Space Regenerator EffectiveCold Space Cold Metal
|
H2
5
2500 41.67
IndicatedPower, IP
-
H2
4 -
2000 33.33
Flow FrictionCooler, WPC
i .I I
3
1500 25
Flow FrictionRegen. WPR
I i
2
Enoine Speed, Hz RPM -
Power, watts Basic Power Output, BP Flow FrictionHeater, WPH
I
1
164 ........
n o t 978
978
978
-41-. -209
0
_
i _ i_ !
!
1
-30 -106 ......
c a I c u.l a t e d 978
978 -. 978
570 570 570 570 570 570 570 570 323.33_ 316.55 312,62 311.66 314.30 312.07 313.24 321.25 295.48 295.70 295.93 296.17 297.41 296.02 296.66 295.66
_
!.. i
!
I
I
,
I
, _
Table 5-6
'i
! _
Comparisons of Indicated Power Output and Indicated Efficiency for GPU-3 Test Points
-,3 i i i_L:_
Test Point
i
_i:,, L
Working Fluid
H2
Engine Speed__ RPM Hz
!:! ,i.i if!
Mean Pressure, MPa psia
_; ";_ ,--,
Indicated Power,watts LeRC Sec. 7
,:, i , i_,!
2_
3
4
5
H2
H2
H2
He
1500 25
2000 33.33
2500 41.67
2.068 300
2.068 300
2.068_ 2.068 300 300
.
3000 3000 50 .... 50
J
6.......
7
8
'.'
He
He-
He
1500 .... 25
3000 50
1500 25
2.758 400-
2,758 400
i
i
4.136 600
4.136 600
_; 21.18 2180
2871 2914
3579 3617
4253 4260
7606 " 8165
4191 4472
5041 5176
2819 2822
I I !
, , I
i: :._ ' .i _!
_i
Indicated Efficiency,% LeRC Sec. 7
I 39.0 42.7
42.2 46.2
43.9 48.2
44.8 48.6
43.5 53.8
43.5 52,5
41.9 49.8
41.0 46,7
_i i
thatagreement is usua]_ly good between the two calculation methods for low engine speed-(25 Hz). As speed increases the second order design, method describedin Section 7 predicts a higher rate of increasein power than the third order_calculation procedureformulatedby LeRC and describedin Section4-4.
_, _ i:
I!:! i i! _
_
i' At this point, no experimental measurements have been received. very interesting to see how they compare with these predictions.
It wi.l,l be
i'
,.'_
k!
,i
1 i
"'
1_'"r_'_'"'_l;li("i
''It
I'I"Y
(_t,'
'I'I]IC
,!
!:i
._-:
_
I
165
I 1
1 :
I
r
"
:
!
i
i
,
_
(
i
I*
k
....
I,
i'
6.
AUXILIARY STIRLING ENGINE DESIGN PROBLEMS
.
More than is usually the case for engine design, the design of a proper Stirling engine requires the close and interactive cooperation, among I) the engine thermodynamicists who figure the power output and heat input for a particular engine confiquration, 2) the mechanical designer who works out the seals and the mechanisms that operate the pistons and the displacer, 3) the designers who add required components, such as the burner and air preheater, s.tarting motor, power control system, transmission system, etc., and 4) the manufacturing engineer who determines whether the machine as designed can be built so as to be sold for an attractive price in the market place. Discussion of the various Stirling engine component design problems falls outside the scope of the--present effort. Some of these problems were discussed briefly in Section 2 and Section 3. The subject index to the references (Table 8--5.)
• i
II,
•
--
can give
the
reader
-°_
access to pertinent
literature.
i
i iN
# 1
i
7,
SAMPLEDESIGN PROCEDURE
AS was discussed in Section 4, first order a preliminary indication of how a.._Stirling applied in a new situation.
_., _I 'i
Thi.rd order design procedures are-much more realistic but also much more laborsome. Even the simplest procedure requi.res the use of a large computer. Third order procedures will be useful for studying in detail the performance of a given engine. If proved valid by agreement with experimental measurements it can provide valuable insight to how the engine functions by providing much....... information that cannot be measured reliably. Specifically, third order procedures have the-following uses:
2.
'i
_'_I _!_.ii _"A ,_"
procedures are useful to give designed by experts ca_ be
A good second order design procedure can be used to design a Stirling engine from scratch, The simplifying assumpti_)ns that are made have been found bycomparison with some small engine tests to lead to reasonable accurate predictions over a usable range of engine operating conditions. A second order design procedure is simple enough to be done a few times by hand. The procedure can be incorporated in a computerized search routine to search out the best design out ..... of many thousands of possible designs.
I.
I!
design engine
Third order model predictions of how internal engine variable change over the cycle could help improve simple equations used to calculate losses and powems in second order-procedures. Third order calculations areneeded to assess the limits of the observation that for normal engines, the assumption of isothermal hot and cold spaces gives the same basic power as the assumption of adiabatic hot and cold spaces.
3.
A third order kind of mathemati.cal model would be needed to calculate the effect of engine imperfections such as non-uniform temperature distributions in heater head and flow maldistributions.
4.
The most rigorous third order mode, produced by Urieli (77 af), by Schock, (no reference), and by'Vanderbrug (77 ae) can be used to show how significant the effects of fluid inertia and pressure wave dynamics' are in a par.ticular case. Puzzling performance might be explained only when the most rigorous third order model is employed • Comparison of these rigorous models with simpler third.order models like the LeRC model (7.7 bl) and to second order models could lead to rules to determine the limits for-each method.
,_ i_ _,_
The procedure outlined in this section is second order. A less complete version of this procedure has been used by the author to oalculate artificial heart engines. Equations have been added to quantify loss mechanisms found important in cooling engines. The procedure has been broadened to apply to crank operated machine and machines using many different types of heat exchangers and regenerators. This procedure is not publi-shed elsewhere. At this point it is not known whether this procedure is a "good" procedure because it has not as yet been checked out by comparison with experimental measurements of-Jarge engines. 167
il
i
lhe procedures outlined in this sectio_l will starl: with engil_e dimensions and operating conditions and proceed to calculate the input hoar r(,quireme,_t and the output power. Tile procedure uses the equations described.in Sections 4.? and 4.3. Section 7.1 gives the blank desiqn fornis adapted to a number of dif.ferent kind of engine designs. It is also adapted to the use of helium,. hydrogen or air as the working fluid. Air has not been used recently in large power enqines, however, some designers may want to consider it for simple engines. Section 7.2 uses the design form from Section 7.1 to calculate the performance of ope-rating po-int 1 on Table 3-8. 7.1
Stirlin__ine I..Type I.I
Desi_!! o.f Piston Alpha:
October,
of- expansion, of expansion
hot,
piston
cm.
piston
cm.
DC = diameter of compression.,cold, piston SC = stroke of compr..ession piston
I
1977
Dual Piston
SE = stroke
i
W. R. Martini,
Arrangement
DE = diameter
•
Forni--
I cm.
!
cm.
_,
I
I
_ '
i
1.2
Beta:
Displacer-Piston Overlapping_Strokes
DCY = diameter of engine cylinder i'
SD .-.stroke of displacer
....I
cm. cm-
SP : stroke,of power piston -'_
cm.
DDR : diameter of displacer drive rod 1.3
Gamma: Displacer DD : diameter
,,
and Piston
of displacer
cm 1_
in Separate
Cylinders
cylinder
SD : stroke of displacer
i ,
cm. ' cm.
DP : diameter of power piston cylinder, SP = stroke-of power piston
cm. ,!
cm.
DDR : diameter of displacer driver rod
cm...
I
2.
Dead Volumes_nd 2.1
,.GL
Heat Exchangers and Wall Thicknesses
Volumes and Heat Exchangers at Heat Source Temperature
,
:i
4
_ :! :I
i
i
i_
i
_'_'_
'_'_'_--_,_'__.wK_w
__.,-,_-i._
...... :wj ......
k'_,,._,_
',,_m _,_,_
_W
Z
,
_
VHDR = extra
hot
dead volume besides
:
_"
Tubular
Gas lleater
NTH _- number of heater .tubes
'!'!
per power unit
LH : total length of each heater tube
;!
cm.
LHHT = heated length of each.heater tube
DIH = inside "_.:
diameter-oF
heater
cm.
tubes
cm.
DOH : outside diameter of heater tubes
..... :.... .:
i
in "the gas heater
Cm3 . 2.1.1
2.1.2
_ "
I
that
cm,
single annulus heater gap thickness
kHHT : heated-lengthof heater surface
_'
NC-: p_umber of cones on pis.ton.or 2.1.3...... Nesting Cone Isothermalizer DCl : diameterof cone at. base_
! i
2.2
•
i_
Annular Gap.Gas Heater
GH
'_:;
-_
LCl - length
of cone
SCL : stroke
clearance
cm.
displacer
cm.
.... cm.
cm.
ili:
cm.
Volumes.at Regenerator Temperature
!I
2,2,1 Screen Regenerators
}I 1 !!
LR .- lengthof regenerator
_
NR = number of regenerators/uni,t DR = diameter
of each. regenerator
cm.
_'
, cm.
NS = number of screen layers MSH = mesh size _
,._
wires/cm.
THW = thickness of.. wire in screens
.-
_i
.c_m.
FF = filter factor,fraction, of regeneratorvolume
' r
¸ F-T-T-T r r
......
r
-'--'T'-
T
t
.i
2.2.2
i i _
Slot Regenerators Screen material
..................
LR = length of regenerator
.
cm.
i'
•
i
i .....
GR = free AF regenerator-gap flow area through thicknessregenerator _
THF = thickness
of foil
separating
cm.
cm2.
gaps
:
cm.
2.2.3. Displacer or Hot Cap Gap Volume LD = length of displacer ,:
cm..........
DCY = diameter of cylinder around displacer
cm.
GR = gap between displacer and cylinder wall
cm.
Displacer wall material Cylinder wall material
j.
WTI : wall _VT2= wall ......
::,_ i .
thi.ckr]ess thickness
' .
of displacer, of cylinder
EH : emissivity
of hot
EC = emissivity
of cold
surface
surface
cm. cm.
wall inside
inside
of displacer
il _' ! or hot
of displacer
or hot
cap , NRS = number of_radiation shields inside the displacer or hot cap
_
2.3
.i "
cap
',I
_:_
I
I
,i
.
Volumes and Heat Exchanqers
at Heat Sink
Temperature
.i 'i
_.._
VCDX = extra cold dead volume besides that in the gas cooler 3
":
2.3.1
,._
Tubular
N_
'_
number of cooler
LC = total
I Ill
Gas Cooler
length
tubes.per_j_ower
of each cooler
tube
unit
. cm.
! i
li
t
i_
'_
, I
i
i_
LCELT___cooledlength DIC = ifiside _s_ ,:
_
of each cooler _tube__
diameter
of cooler
2.3.2
_,
GC : single 2.3.3
tubes
of cooler
annulus
cooler
_,_
cm.
gap thickness
cm.
Nesting Cone Isothermalizer_ or displacer
DCI = diameter of cone at-base
2.4
',i
cm.
surface
NC....-number of cones on piston
i
cm.
Annular Gap Gas Cooler
LCHT = cooled length
;":
cm.
tubes
DOC= outside diameter of cooler 1
i
LC1 : length
of cone
SCL = stroke
clearance
Regenerator
.. cm.
cm. cm.
Wall Dimensions
(see.-l_gure
4-24)
AHTH= heat conduction
area at hot end
cm2.
AHTB-- heat conduction
area at level
B
cm2.
AHTA: heat conduction
area
A
cm2.
AHTC= heat conduction
area at cold end
LHB = hot length LBA : middle
at level
regenerator
length
regenerator
wall
cm2. cm,
wall
cm.
-Jl Regenerator wall material LAC = cold_l_ength regenerator
i _i
Temp K
. wall
cm. Thermal Conductivity
THM:
KMH:
w/cm°K-
.!
i
TB :
(est.)
KMB:
TA =
(est.)
KMA=
TCM:
KMC: 171
,/
L i
,
2.5
'
Cylinder
Wall Dimensions (see Figure 4-23)
AHTH = heat conductionareaat hot end
.
'
cm2.
AHTB = heat conductionarea at level B.
cm2.
AHTA = hearconduction area at l_:.vel A
cm2.
AHTC = heat conductionarea at cold end....... LHB : hot length regeneratorwall
cm2.
cm........
LBA = middle lengthregeneratorwall
cm.
LAC = cold length regeneratorwall
cm.
Cylinderwall materiM
I
i
Level Temp_ K
ThermalConductivity
THM =
KMH =
..
TB =
(est)
KMB :
TA =
(est)
KMA =
TCM = 3_
'_
'
w/cm.K _
!'
KMC :
Drives
i
N = Number of power units/engine 3.1 Alpha ..Swashplate(Fo_rd-Philips) ALPH --phase angle (usually90°)
o.
3.2 Alpha - Crank (UnitedStirling)
,
{
LCR = connectingrod length RC = crank radibs
cm
cm.
ALPH : phase an_,:.(usually90o )
o, I p
3.3 Beta-RhombicDrive
i
LCR = connectingrod length
cm,
i RC = crank radius
172
cm.
£ , .2
ECC : crank eccentricity(s___e__Figure 4-15) .
.. cm,
3.4 Beta or Gamma - Crank LCRP = lengthof power piston connecting_rod ,_ '* _,,_
,,
!,,,,:, i i;I ' {
"! '! _;i :'i
:*,
RCP = crank_radius for power piston
cm.
LCRD = length of displacerconnectingrod RCD = crank radius for,,displacep
ALPH = crankangle-
cm.
cm. cm.
o , usuallyabout 90° .
3,5 Beta or Gamma ,-Scotch Yoke or other.-SHM Linkage ALPH _=crank angle 4. Given OperatingConditions
o..
TC = effectivetemperaturein co_d, compressionspace
,_,_
K = C + 273 l
!_'
K : ( F +,460)/I 8
K.
M_,_einitial
i
estimate
i
]_"
i_'E
I
TH = effectivetemperaturein hot, expansionspace,
!
_':
_*_ I'_i *'!
_i "i
_,i
i
i
initial
estimate
or measurement
FCW : coolingwater flow
--
K.
gisec,
TCWI= Temperatureof coolingwater into engine NU = engine frequency•
K..
I
I
HZ.
(HZ = RPM/60) _!,i ,,:,_
PMAX = maximumengine pressure.
]_i
MP_..
I
MPa = 0.006894 (psia),..........
#/ = O.lOl3 (atm)
:i • _,i J*i ":
PAVG = time.averagedmean pres.'ure THM =.heat sourcemetal temperature
! MPa. K.
,i
.-....,
TCM : heat sink metal temperature
_,
WorkingGas
V i
.
K.
5. Computationof Engine Volumes 5.1 1ire Volumes VHL = hot live.volume,
cm3 for alpha
dual
pistoni
SHM,
(simpleharmonicmotion) ! ! ,
_I I
_-(DE (SE) 71 )2
I
I
_-( 71
)=
for beta, SHM = _- (DCY (SD) : _ ( for
cm3
)2(
]
)
)
:
I i_
cm3.
gamma,_SHM_
"'_
2 ) (
II
7r (DD)2 (SD) = _-(
.
3 cm
) =
: ,,_
)
1
Note:: Live volumesfor crank,and rhombicdrives will need not be calculated..
•i ( _ ) ._ .i
VCL = cold live for alpha,
,
SHM
IT =
volume, .cm3
2
_- (DC)
IT
(SC) : T (
)21
) :
cm3 •
_
,
1 (i i
I ,i" :,
,
for beta or gamnla,Slim = _1_ DD2 DDR2 _ 4 ( " )SD : T(
2
2
-
)x (
:;'
.-_ ,..i
,#, )i
i i'
T
i i :
):
._
cnl 3 '
VPL : power piston for
live
volume, cm3
gamma,SHM 11
71
: T_-(DR)2(SP) : _-(
)2(
) =
cm3.
5.2 Dead Volumes
,
VHD=.hot dead volume, cm3
'
,
for-.tubular gas heater
+
" (OiH)2(LH)(NTH) = VHDX + _-
i.
,
li, .I
:
I, i
•
!
i
i
:
I
....
2.
+T(
)(
)(
_o ____
3
cm.
for : VHDX annular + _(DCY gap gas or DD) heater (LHHT)(GH) .......
: for
+ _( nesting
)(
)(
):
cm 3.
cone isothermalizer II
: VHDX + _(DE orOCYorDD)_.(SCL) , !
:
2 ).(
+T(
cm3"
) :
,,
....
VRD = regenerator,dead volume, cm3 "
'
for screen.regenerators, short ca_r_!lation /_ 2 VRD-NR_-_(DR)(LR)(1 - F_) \_,/: ...
(
)2 (
) _-(
)-(I
,-
) :
cm3"
i_
for screen regeneratcrs, long calculation VRD = NR
_
: (
DR)2
LR) -
) T(
)
_;_
NS)(MSH)(THW)2
"T (
)
(
) (
)2 3
=
!
:
cm
.
for slot regenerators VRD : AF(LR) =
:
(
) =
cm3.
for alpha or-gamma type VCD = cold.dead volume . for tubular gas coolers 2 VCD = VCDX + _(DI(;)(LC)(NTC)
.
:
__
)_(
) (
) =
cm3.
):
cm_.
for annular gap gas cooler
,
VCD = VCDX + _(DCY or DD)(LCHT)(GC)
: ............
,
+ _-(
+_(
)(
)(
for nesting cone isothermalizer
I,'_
i
_
'iT
II
i
_! I
=
i.
-3
+ T-(
(
)= _
._
For beta type,+ _-(0E ALPHo = r-Dc¥)I_ 90o - vcD× DD)2(SCL) VCDHX=.VCD, calculated above
'!
!i
VCD.- VCDHX- VCL 1 -
,,
i
_
6.
:
General Intermediate TAU.: TC/TH = (
cm
Parameters )/(
) :
TR = (THM - TCM)/In(THM/TCM).: : (
-
)lln(
KAP : VCL/VHL :
I'
I
,
:
t
/
:
I
(.
) :
+_
K
,
+ _.)
!
!
_,
DEL-
/'V/TAU)2 + 2(.TAU)(KAP)cos(ALPH) + .(KAP)_ '_ (TAU_+ KAP-+ 2S) ..... -
_ v'_
//:
"
:
4(I =
, :( IP
PMIN =
1
:
7.
,
_
I
PAVG : -,DEL)/(1 + OEL)
)cos,(
+2 4(I
PMAX(I - DEE) - : (I + DEL)
-
_(I (l +
)/(1
MPa
Alpha Engine - Schmidt Equation
) )
) +(
)2
)
MPa
Basic Power Outputs
7.1 176
),(.
{
PMAX=
., _-1
)2 + (.
+
)
BP = NU(_r)(l__ T.AU)_PMAX)(VHL)(K)sin(ALPH)_I Y/:T . X Y +_X2 _Y +X
: (
r)_(l "
:
watts
_*
)I
)(
)(
_'
)sin(
.12 "C. __12
)_/
.
+
:i ......
i i J
i j
7.3 Gamma Engine --SchmidtEquation
'!
i
EvaluateK, D, VD and X in 7.2 _
1
' ; . -: l
!
Z= 4
,:
VD (TAU) _+ IHL(I + TAU}7 1 + TAU + K
= 4
( .(I+
!
+l+
+ ...........
i'
't
I i
i
z:
t
Then:
BP= (NU)_(1- TAU)(PMAX)(VHt.I(K)sin(At.PH)/Z _X .j
i
{ ,I ',l
BP -.(
)_(l -
':i
)(
)(
)sin(
+ 'V'1--------)2- (______)2
q
i
_ ! ........
)(
:
7.4
)_.. I/
-
+
watts.
Rhombic Drive Philips
,t
Engine
(See Figure 4-15 and 4-16)
A = V(LCR) z - (ECC - RC)2
:V( B =V(LCR) 2
)2" .(
-
)z
:
cm
(ECC + RC)2
178
L_
rL
__
i
I!
_-.:
1. I
, 't
-_(
,
)P"- (
-_
_'m
For a Check:
J
I
I
,.
_(
'd.
-
)g
) ,
(
m
)
cm3
--_
t
L,
_..,.
-
_,._. -'
-
..................
'"
-
cos PHI
ii_ i"
.........
!._:
VC : VCD + VCLX :
; ',_
VC =
t<,
_
+
-
-
-
VC is calculated for.PHI : O, 30, 60, ......
,?,
!$:
_,,_;[
cos{
, 3600 and
_"_
entered on the next page.
i!_
•
I
L"
Dl = _(LCR + RC)2 " (ECC)2
i i
_'_.
i
:':_ _,:,
-V(
_t:
:
C =
,
=
_./, +_'! "_
_'
i
-
: (
_
:
cm.
_ i,
cm
::
RC}2(ECC)2
LCR -
_
)2 (
)2 _
-
_ )-_- (
"
VH = VHLX + VHD : _(DCT)2
2 )
(LCR)2
+ RC sin (PHI) - C}
+ ,
)2
VHL : (DI - C) _-(DCY)
i:-
-_,
)2 - C
+
i
sin(PHI) -
:
cm3.
CC - (RC)cos(PHI) 2 + VHD
}+ ] 7q
I
" i
I+
VH is.calculatedfor PHI : 0 -_360 and enteredon previousI_age. VT : VH + VC + VRD: VH + VC +
b
VT is calculatedfor PHI = O
VH
and entered on previouspage.
;i
P = VH + VRD +'VC -
+
+
"VC
'
'
P is calculatedfor PHI : 0 to 360 and enteredon previouspage.
'
....
i
PM :
PHIl= 360 P / PHI = 30
_,,
Note:
'_ li'
PAVG : M(R)= -FR-
_;
t,, i
!:,i l_
12.
PM :
l
i!I _ (see previous
page)
Do Not Add in P at PHI : 0
PC =,P
:
P (
J/K-
)
,.i
PC is calculatedfor PHI,= O, 30, ...., 360 and enteredon previouspg.
,_._
PC is integratedverses VT using the trapezoidalrule,ie.
::I _._ ._,i ;'
DELW -
_"
PC1 +-PC2 (VT2 - VTI),.................. 2
For-thefirst in_nt
'
the s,hscript1 stands for PHI = 0°
:,i
:I ,:}
i
and the subscript2 stands for PHI : 300` For_the__second incrementthe subscript1 stands for PHI : 300 and the
f'l
"i
12 increments. (See previouspaeg_)____..
;_ £'_
subscript2 stands for PHI = 600
:
DELW is sumed for all
• I 181
,F_
",
f
_
i
I
f
,i
J
#
!
!
<
!
d
1
•
]
"
i
;L
...............................................
12 BP :,NU(I.045)
:
_.=_ 1
DELW
.(.I.045)
:
watts.
The mass flow rates are now.computed........................... P(VH) ._ FH : M(R)(TH):
I
P(VH)
)(
M(R) :
' ')
J/K
M= M__M_(_RL _ 8,314 8,314 M= i:_ _
g mol
FH is calculatedfor PHI : 30 to 360 and entered2 pages back.
i! _:
FHMAX:
FHMIN:
F_His graphed and effective _,
FCTI...................
times for stead)' fl.ov_ in and out are determined (See Figure 7-I) FCT2 :
FCTH-- -FCTI + FCT2 _ 2
+ 2
:
-
!
WHS-(FHMA_cT_HMIN)M(MW)NU
'I,
=
(vclP(vcl )(-_
FC : M_R)(TC) : ( .... FC is calculated
and effective
FCT3 = FCTC=
i:i
i!
FCMIN:
FC is.graphed
;_
)
for PHI = 30 to 360° and entered 2 pages back,
FCMAX-
,]
/, i; ii
)
times for
steady flow in and out are determined
FCT4 : FCT3 + FCT4 _ 2
+ _"
-
WCS- (FCMAX- FCMIN)M.(_IW)_..
_._
7cTClNu....
_,,
- ( 1P,2
(
I
)/( )(
) ).(- - ):
,g/sec
I
-
] t I i
! I
:
:
, _ !
,
i
For tilere!_rator
-
i}._
FCT :_..(FCTH+ FCTC)/2 = (
! : i
'
il
_
,I! 1
+
WRS = (WHS + WCS)/2 = ( :
)/2
+
)/2
.g/sec
7.5 Crank Drive - Alpha Engine
I
: _ (D"-V) 2
' _i , '!
_ = T
-
i,
}
i
VH
- (RC sin (
+ RC cos (PHI)+ LCR i+ VHD (RC) -V(LCR)2 PHI))2 ) -_J( sin (PHI
(
'
+
cos (PHI)+
2
+
I
1 "
VH :
-
..... ;:":
' _
+
VC
_-
",-
cos (PHI)
- (DDR)
'""'
: T
(
.._5
(LCR)2
- (
RC sin (PHI + ALPH 2
)
(
(PHI + _. .
VC =
I
, >_i" iT,
-
+ VCD
(
-cos
+
.
+
- RC cos (PHI + ALPH) - LCR+ RC
_.
i;
sin (PHI))2
- _
"'
) sin
:_i
(PHI + _.)
:"_.
+
-
."'".z.
_,,,,_
sin (PH,I+ _)
cos (PHI +
) -
2 }
_:_
+
VT : VH + VC + VRD : VH + VC +
'_ L;_ ,,_ ii,
t
p : _
1
VH " VRD . _/C = T"H T.. _.___
1 VH
+
+
i
VC
q 183
-i
,
qql T T_ITI ;
,
o
,.,
.
,
.q
,.
--._+,
• ill
1)#-iI
_ ........
i VH, VC, VT and.P are calculated
for PHI = O, 30, 60, .
. . 360o
and entered on the next page.
,
PM:
P
,
12
PM =
PHI : 30 Note: Do Not Add in P at PHI = 0
. k
,
M(R) :
PAV____GG : ( PM -(
PC : P p Calculate :
G = p
I: ;
J/K
( )
J
PC and enter on next page,
PC is integrated
,_
,_
vs VT using the trapezoidal
rule
as explained
!
i
in previous
section. 12
i
Lm
BP : NU (I 045)
)
i
.:.,i
>__ DELW I
= (1.045)
:
watts
Effective flow rates and effective fractions of the cycle tinles these flows are assumedto occur in are computedusin,qthe method qiven in 7,4.
7.6
Rhombic Oroi.ve.Beta with adiabatic
hot ana cold
i
1
spaces. i
:
CalculateVCLX and VHLX-asin 7.4.
I i
VT = VCLX+ VCD+ VRD+ VHD+ VHLX : VCLX +
I + VHLX I
: VCLX +
1H,1
+ VHLX
i
F _
.... i ,_(,
i
I
l.nlerVCLX,
VHLX and VF I'oi" PIll
= II, i_0, ......
3600 on
m'xl l_aqe.
'
'
iI
:
VHD
VRD
VCD _
+ ......
K1 = '-Tii + -i%- _ TC
_.
[
-
cm31K
.............. _.,q_a}_.. h_xdrog_qeT! _L helium E
For X = 1 first '4
calculate
IH (check
O. 286
air
.0.400
O. 286
I) .......
it" VHL.I > VHLI2 [_]
if
VHLS < VHLI2
[__
i
<' j
IH =
:
IH _
VHLI2
VHLI - VHLI2
VHLI
+
IH :
,_",
For the first
-_ L
I
_
i
time
around,
THSI2 = TH and PI2 = PI,
THSI2 and PI2 will so no..matter
which
not be known. inequality
is
Assume true:
.....
TH ',;
D1ter
"
Next, calculate IC (check I) IH - VHLI _ :
i
at top of XH column on next
if VCLI , VCLI2 IC = •
paqe cm3/ K
_ ........
VCLI2
if.VCLl _ VCLI2
VCLI = VCLI2
TCSI2 P(p-CT:[) E _
TC (P12)
[_
VCLI
E
IC = TCS12 ( p_l _:[)P1 E
'I.: i
1C =
_}i
/'L 1
+ .....
_i_
1C ...........
_
1
.l_
I
__J,,
........... :rr :
q-l-T ' '
I
;
'
I
'
'
i
i i
!
r
i
;
I
!
L
i
•
t '_
" =
I
i
!
T:
t
. "
ol !
_J
i
For the= firs.____tt TCSI2 and PI2 will inequality not be known, Assume TCSI2 TC and time PI2 =around, PI. So no matter which is true! IC - VCLI TC ..
=
Enter at top of XC column on Drevious page•
i
Now P1 is-determined _:
by:
1 P1 : IH + KI +-ic In general,
I i
cm3/ K
....
solve for
P1 by a successive approximation
method.
Enter Pi on previous page at top of column PX. Then. knowin_ P1 calculate IC and IH-and enter top of colunlns XC and. XH on previous page.
For the first
time around P1 can be •solved directly.
. '
i
•
::_ i
_
P1 :
-
1 +
-
_
MPa
_
+
Then:
I _ VHLI THSI- T :
!
TCSl-
VCL1 TC :
Enter these .at the top of their
=
K
-
K
columns on previous
! i page.
For X =-2 VHL2 > VHLI ,/1
2H :
F"]
VHLI THSI (__) E
OR + VHL2 - VHLI
"r,-,
E
VHL2.< VHLI 2H =
VHL2
F"]
_F I"I_-T----F-. _,, J i
'_
!
I
_o,
',
VCL2 > VCLI 2C =
?
_
OR
VCL1
VCL2 < VCLI
+ VCL2 - VCL1
2C =
F'-I
VCL2
, ..
,! J
2C :
+
P2 -
l 2H + K1 + 2C =
2C =
..,i
: _'!
,,
,!
•2H =
2C =
i
1
,I
d ,,i
I
:: !
THS2-
VHL2 .: _
-
K
i
: T,
VCL2 _ TCS2 = --_
-
K
k
! i
P2, 2H, 2C, THS2 and TCS2 are now entered on the second line of
i "i
_ ._
the table
2 paqe back.
The process
continues
as is outlined
for
the
1
j
rest ol_ the cycle back to PHI = 360o
X = 11_ The pressure at 360o
?I,
!, d
,
will be different than_the pressure at 0°, PI.
The calculation
I,_
procedure.must continue until the-hot space and cold space temperature and the cycle pressure repeat with adequate accuracy.
.,
This-procedure
must
be programmed
on a-hand-held
computer,
at
least_to be practical.
I i
8.1 Regenerator Windage 8.- Fluid Friction loss 8.1.1 Screens-- VHL :
cin 3 (from 5.1 or •7.4)
"i
i :'i .! '!I o!
TR : PAVG =
OK
(from 6)
MPa (from 4) 18q t
for hy_drogen : MU = 88.73 x I0"6 + 0.2 x 10-6 (TR - 293) + 0.I18 x 10-6 (PAVG)
_ .....
: .
.,
.g./cm sec
"c_
for helium: MU= 196.14 x lO'6 + 0.464
x IO'6(TR - 29.3) - 0.093 x IO'6(PAVG)
,
glcm sec
,]
for air:
_
i
J{
MU= 181.94 x 10"6+
',
0.536 x 10"6(TR
- 293) +. 1.22 x 10 -6 (PAVG)
J:
i.
!;
--
Iil +,
--
=
"' iI
i'
glcmsec
I.; ., .
.
RHOM - mean gas de.nsity
MW =
H2
He
_ir
2.02
4.00
29
.,.
,_., i_i,i
MW = _
PAVG 273 _ MW(PAVG) x _ x _0.1202 - TR .......
7!
"_i , _i"i
",_"i
:--_: i
_ 0.1202( (
)( )
) .=
g/cm3
For analy__ical SchmidtAnalysis WRS = (VHL)(NU)(3)(RHOM):3( :
)(
WRS=
I
VRD AC = LR -
i
G : W_F =
I
tgo..............
"I, L
,,'.t
)
i
g/sec
For numericalSchmidtanalysis (from7.4) :.
)(
i i
'
glsec _
2 cm
-
g/sac cm2
'.
•,
'L
' '{i oi
AHT =
(MSH)(THW)(DR)2(NR) (NS)
q,
L'.
I"
,_,-i :" i
= _2
(
)(
)(
)2(
)(
)
"' ,.iI:•
cnl2
.
.c'
._
RH = AC(LR)/(AHT) = C
: .-,
)(
), =
RE = 4(RH)G = 4( )( MU ....................... ( )
_
---
cm
) =
If RE < 60:
L{;
(_,
log F = 1.73 - 0.93 log (RE)
I!L
ii
If 60 < RE < lO00"
"t
_"
t
log F = 0.714
_
0.365 log (RE)
!,
If RE > I000:
'_
log F = 0.015 - 0.125 log (RE)
DELP =
F(G)2LR 2(I07)(RH)(RHOM)
DELP= ( )( (2 x I07)(
,i
I
For analytical j
)2( )(
) )
MPa
=
!
Schmidt Analysis
WPR :.(DELP)(VHL)(2)(NU) : 2(
_i
!i
.
=
)(
)(
)
i
watts
ii
,
i,
,!
!
"
I
! _
_
,..,
.......
31 I _
L
i
'i
For numerical
Schmidt analysis
WPR-- (DELP)(WRS)(2)(FCT) ....... _I.-TOM-) _ ( 8.1.2
)(
Slot
or Annulii
)2(
) =
Regener.ator
RH = GR/2 = I
). : 2 MU, RHOM,and.WRScalculate._in
_ "
watts
G = A]_SF :
.
.=
cm 8,1,l. ....
g/sec cm2
I
I
_
RE
"
4( -- 4(RH)G MU ............ : ...... (
)(
) =
)
,
!: if
RE < 2000
24 F--.- RE - (
If RE • 2000
24
log F = -1.34 - 0.20-.. log(RE)
)'.:
:_ i
_ z
WPR : F(G12L(VHL)(NU): 10"(RH) (RHOM)
lO7(.
)(
)
i
i
WPR:
watts
i
liI i
8.2 ,;
Gas Heater-.Windage "i
8.2.1 TubularHeater fo_ Hydrogen:
.....
,
MU = lO-6188.73 +.• O.2(THM - 293)+ O.ll8 (PAVG)1 i
=
i
i
192
g/cm.-sec
i ! ' r.... [ t .... T-l-r-T-, i
i!
t
,
I
i
for Ilelium: .i
•
"
I
Mll,-I0"{i_196.1.1+ 0,464(IIIM- ?,_,13) - 0.09,,'(PAVG)
: .!
_
'i:,w
!
9/t'111-SPq .......................
.I
t
,{
,
for
i_
MU _ lO'b{
i
MLI_:
'i
Air:
,. NW = .
I 181.94
tt,,
He
2.0',:
4.00-
4. 0.536(TIIM
- 2q.l) + 1 ..... _"_ (PAVGli'.I
_,
9/cm" sec air 29
RHOM = O.1202.bIW(PAVG)/(THM)
o.l,.c._( I'or analylical
Schmidi
)(
)/ (
)
................
9! cm"
analysis
!
WHS:, (VIIL)(NLI)(3)(RHOM)_:_
3(
)(
)(
)
,, '
_ l
:i
I
_ For numevica!
5chmidt
_-lsec
analysis
]
I
i
(.from. 7.4)
WItS -
tl/SoC
,. ,%
AC_= (NTtt)(DIH)2rnI4 ......
:_
=
(
)(
)-'" ,_!4 =
.___cm'
{
! ',
G .=-WHSIAC= C (
t:
=
.............. qlcilfsec - "
L
._?I_t)_ L tt
.
i
If
r'm
i
RE =
_
blti
=
RE _ 2000,
_)_L
---(""
.)
"-) .....
F _ 16/RF. = 16!(
) _
l f RF " 2000, 1o{1 F :_ .1.3.4.-...O..i.'O 109 (Rt /
¢
"
il 5
i
,,_
j
I,l._
.
i Ill !
1
F I _' __
i' I
I •
_
WPH::
'
_ i¸
watts
l-_r1_ume_.ic,_1-Schlui dt al}alys is
-:i
_Ez._, :_-:-U-I)-LG-L_(-L-H-).-I-OZ-{_D.LL_ _HOM) ',' ............. )__ _-.:,,( .............. )I.........___)_!_L_ 107( ;: i
)(
'
Mr_
)
,
DELP(WHS)2( FCIH) WPII....... _A_Tr, f..........
t 4
....
_
,
':'- ............
p
war ts ,_
,_._._ AnnularGap Heater
i Find MU,.RHOM and WHS in 8,2 1........... AC : _(DCY)(GH) = _(
G_ - WHS -A_-. RE = LL_.__ NU
)(
)=
cm"
_q/see cm" -
-
.--_T. ,-.._ :
•
•i!
,i
:_
If RE < 2000, F _ 241RE = 24/(
)=
I
i'i
•_
If RE.,
2000,
log F = -1.34
- 0.20 lo9 (RE)
•',i ,,
2F.(,G_L_T___ !NU_]_ WPH...... ] _-(GH) (RHOM)"
:
'i
,_
WPH= ;l_..]_L_
.)._L[........ __]1
]_L.___,
=
watts
i
1
1
_i2./-- ! .... I I--i "i--___ :_--_.... ___,_.._x___'--_
,
....... iL
,......... .--
I(_5
I
,'_.3 Gas Cooler Windage 'J,3.1 TubularCooler for Hydrogen:
t
MU ;_10-6 18tI,73+ O,2(TCN-.293)+ O,II_(PAVG)}
: i ,
glct_sec
for Heliurn:
.............
........
MU = lO"6 1196.14 + O,464(TCN- 293) - O.093(PAVG)_
++
<'
NU =
g/cm sec
i
for Air:• NU = lO"6 , _181,94+ O,536(TCM- 293) + l,22(PAVG)_ + I
MU :
g/cm sec.+ H2
i _:_' "
He
air '
Mw= 2,02, 4,00, 29 RHOM: O,1202(MW)(PAVG)/TCM
t'' .:
: 0,1202(
)(
For analyticalSchmidtanalysis
-
)/(
):
g/cm3
_
.
WCS : VCI.(NU)(3)(RHOH) = 3(
)(.
)(
)
For mmlericalSchmidtanalysis (from 7.4) = g/sec WCS : 9/sec
"_"i ":!
__.J__.
I i i .... t
I i ] I, ! 1 t --_t---L--L--_-_-'----'.+_-"
i
_"
......._].... '- J............... "
AC _ (NTC)(DIC) '!_i_ ( a =''J
)(
............
q/see cm_
11 RE < 2000,F ,.=.16/RE : 16/( If RE - 2000, log F=
)' 4.... ........... cm'-
)=
-1.3,1- 0.20 log(RE)
'
_i .¸ _II-i'll !
'
_
!
i
I __ i
'
L i _
'
_
, ....
,.
' ,
' ,
i i
If RE-< 2000, F.= 24/RE = 24/(
):
If RE > 2000, log F = -I.34 - 0,20 log(RE) u,,
c! '! _i
_! '!i'. _ -<_. ;',_
WPC : 2F(G) --_ 2(LCHT)(VCL) (NU) 107(GC)(RHOM)
=2(
)
watts
8.3.3 Nested.ConeIsothermalizer Find MU, RHOM, andWCS in 8.3.1
GTA=
_
. )( _)(
)( _
WPC =
.... _"i
:
CL + _SC
(
,_
sin (BET]
+----_Isin.(-
) :
cm
DCI !_
AC = _-:
(_)(GTA)(NC) = _-_ ( cm2
)(
....... )(
)
ri,' ' r l........... ! i
i-Tr , t_
'
,
i
:
L :. ( I)'- , L.,i m
_ : 7.7!.
.t......
.....
L,
"[!'- " '
O, 7]{1',;_.. q
:
..........
CII1.
:!I.(G)"(1:7(VOL)(Nti]
":""<"""
w"<:_'..... 17-(]{<-)(1i7m-_7)-
_,
.L(_.....]......... 1(.......... 1(........ _2.
_7c !c
$
'7
i J:.
WPC=
..
8,4
Fluid
watts
Frictton
Gas H_ater, Regenerator " " Cooler, Ga_
" "',,
Loss
_{i
,+.._
watts
WPR...=
i
_.
watts
WPC._=
' :
watts
_
.................... watts WP":::"..................................
])
Mt, chanical Friction Loss blFL =. .....................
It+
i_ _
Sl,lllllll_li'y
WPII _,
l'otal, 9,-
i!_
,;
based upon expei"iiilental
illt_aStli'_lilO, llt
,,_
o1' MFL ,, 0.",_ BI_. = lO,
Basic
float
0.2 (
)
,:
watts
Inl.)ut
liP.
V
It')lti .i,,.1 '
II.
/
Reheat.LOsS.... 11.I Const_lnt. VOlulne Asstililpt:ttm I:CT :
....
(I-qu,ltitln,
4-?7)-
(usually 113) (fi'oill 7.'1)
WR._:. :....,.._._.;._._...... -_i/s_,t" ( i'i'c_lli t!. I)
.'. ?_
'II
CV :_
"
CP =
TR =
K (see .Table 4-[_)
for
TR :
K (see Table 4--8)..
AHT--=.....
cm2 (f_'om 8.1 )
G =
g/cm 2 sec (from
II
log
PR :
for
RE -
__(from
(PR)
log (
_ -0.13
):
H(ANT) NTUV : iTVRS)(CV) :
-_i.
8.1)
- 0._12
log
)
(RE)
':
-o.13 -o.412 _og(
)
(_
)(
(
)(.
I
) = .
)
QRH : (FCTI(WRS)(CV)(THM ......TCM)
: (
1(
!
_
.-
)(........................ 1.( .
:
11.2
OK (see Table 4-9)
wlcm 2 OK.
i
,
8.1)
TR =_
1- (.
H =
I
for
)
(
2 +2/
/
_! i,
watts
Constant
Pressure
Assumption
(Equation
4..-..98) .......
Find WRS, CP, AHT, G, PR, RE and H in-11.1 H(AHT) ( NTUP = CTTR-_,T(-_-= (
_
QRH = ._,(WRS)(CP)(THM-
:
)_( )( ....
) ) =
)
TOM)(NTU 2 + 2"
watts
,
' i
:
i
i
v,
_'.
'L
II,3 L
....
DO not have the information
12.. ',,hi
Shuttle
Conduct'otazk__
to calculate
this.
.... _.....
_
12• 1 High Pressure Engine (Equation 4-110)
_i I
Qvale Equation (Equation 4-I05)
KG :
wlcm, K at TR =
K (FromTable 4-9)
i i
I ._ ..
_
@ NU : cm cmi
LT2 LTI : :
(LT _
..... . From,Eigure wlcm w/cm,• K. K 1
K1 = K2 :
HZ (FromTable 4_II) 4_N'O) 4-22
KG (-zTLT!' LT2 K21
LB = 1 + 2 g....GR LB =.1 + _
(
_
;
'
1
) _+ i
LB =
[, i
+ (
)
g
(GR)(LD}
!I ,il
i
1 +( 1 I
"
i :i! L i
• _,,,
=
)z g " Waits
(' '
1.(
)
;::
I _" I
-
12.2 Low Pressure,Thin WalledEngine (Equation4-11.1)
i
ROI =
g/cm3 displacerwall density
.!
CP-I= R02 = CP2 =
Handbook ........ Jig , K displacerwali heat capacity g/cm3 cylinderwall density } From J/g, K cylinderwall.heat capacity
_: "_ , ! .
,!
_:
'
201
!
'i
_ I
i
d
,
_
:
!
1
I
;
!
L
J
1 ' r ,,
_:
tad
,..,
OMG= 2n(NU) := 2_(
!
KG =
) =
sec
w/cm, K at TR =
K (Table 4-9)
-
,
SGM= (GR)(OMG) ROI)(C-PI)-(WT-TT)+ (RO2-)(-C-PZ)(WT2)
1
: (_:-
!,
....
QSH
_
.(1
"
)
+ (SGM)2 1 /
8., '_
)i
'
)'(
) +C
"'1(
)=('
) .....
(GR)(LD) TCM)(DCY)
(SD)2(KG)(THM, _
t
I
--
+(_
)
Q.$_: 13.
Static
g
=
C .... )(
._
watts
Heat Conduction
13.1 Gas.ConductionInside DisplacerorHotCap i !:} i
DID = DCY - 2(GR) - 2(WTI) = (
) - 2(
) - 2(
,.1
_',
=
i_', _'i "i
_ 2 _ ANT : _ (DID) -, _ (
'_i_.,
KG =
,.
qC :
13.2
Rad._ation DID LD
2
cm2
:
wlcm, C from 12
......
:
q
)
C111
(... watts.
Inside
Displacer
or Hot Cap
)
)
r !
:
[
t
;
I
;
I
,\
_]
• ,::q! :5.,,,
If:
'r'! ,"it*t
^ DID U-,-_.....E,_ LU < 0.2
then
DID LD
FA -
If:
.
,"" 2
0.2
_,I
If:
DID , < --__- 7 then FA = 0.50.
In
DID > 7 then FA =--l-, LD
,.;
FE = _EHI(EC) = ( :":'_
1 1 +NRS
FN-
1(
I I +
) : _
AHT =
cm2 (from
QR : (FA){FE)(FN)(AHT)(5.67 :
(
)(
x 10"121 ({THM) 4 - (TCM)4)
1( ((
13.1,)
1(
15.67 x 10 "12
)4.( watts
=
"
)4).
i ..............
;
tH
,:
13.3
Displacer
Cylinder
KM =
Wallw/cm
K at TR =
K (Figure
4-22) 2
;
AHT = T
"!
DCY - 2GR,2
(DID)
,,,,q
= T
- 2(
- {
;
)
"3
:
)
9
Clll _
:]
i QC_= KM{AHT)(THM - TCM)= LD ._ :
: 13.4
Displacer KG =
"
_......
r_a
-7
-
)-
watts Gap w/cm. C from 13.1 /'{1_l
;.i
I
ANT_.."(m:Y)CGR) --,(
)_
)(
,.:m _
', ....
,'
Qc:_.KG A_(A!L!J_T_HMLD " TCMI_ _.... )I____I ...... -
L
j
...........
I
= ,
watts
i"_ ,.
13 .-5__Cyi i nder Wal 1 Using the
numbers in 2.5,
.......
Let: [_ (LHB).4, )1 (_) :
4(
...)
"(
\AHTH + AFITB-):
)
)
:
Then : I
R1
KMH + KMB : (.... )+( --
) =
K/watt
L,
Let: I
Q :
4(LBA)
AHTB +_AHTA =T
4(
)
-):.-,(
)-=
Then :
R2 - KMB-+-R_I_" =
)"
j I
Let :
i
I Then:
i
R3 RlqA_
QC =
= {
_--_-_R_ THM- TCM = _....
:
K/watt
( ) -+() -_----_-
()..+i
(._.T_
watts
,.
I I}
j
TB = I'HM - RI(QC) = (
i
:
) - ( K ....
Original
)(
)
TB estimate
was
K I
I
i
! I
°_t_4
...........
-............
i
TA--TB- R2(QC) =(
)-(
=
K ....
)(
Original
)
TA estimate
was
K
Now:
,
K_ = KMB=
w/cm. w/cm. K at TA TB 1
. Figure 4-22
I
NoW-goaround again.
....
"
R1 : KMH(_)+ KMB = (
) "-()--+-(f
_-R2 = KMB_+ KMA= (
(
+ KMC:.( t
I
') '+'"(
)
)-
K/watt
K/watt
_.]f._)=
). +"(... ............. ) :
R3 = KMAC_) THM- TCM
(
) (
K/watt )_- (
-
)
watts•
;I
'"
TB = THM - RI(QC) = (
,4 '_
:
1.(
)
K .... Previousestimatewas
TA : TB - R2(QC)-: (.-
'."_ ,i
) - (
:
) -(
){
K
)L
K ""-- OriginalTA estimatewas
K
Now
4
T} .; "_
Figure 4-22 KMB = KMA
w/cm. K at a'tTB TA 1
VL' I !'i
Nowgo aroundagain. R/ =_B___X 1
,,( )-+ {.) ' ")=
K/watt
e.
• i
{_i
"}
;'05
F ' I
I i
i
l
F
I
I
I !
4
k
_
:
' , '
•
i
I
TB--THM-R1(Q).--(
)-(
1(
)
t
1
iL
=
K.....
Original
esti,late
was
K
! ._. _
TA =
K ....
Original
estimate
was
K
4 /' ': t
Now:
:;" ,
_):...
KMB: KMA=.
!
wlcm. K at TB [ wlcm • Kat TA
I
, ",g:
"
"
'_ ._
./i
..;
Now go around again-: @ L ) RI,: KMH +,.-KMB = (.:T. ) +-( ....) =
K/watt
R2= KMB_+ 'MA-: (- - (
K/watt
R3 =-KMA(_) + KMC: (.:-
q -_ THM - TCM
,-.
Figure 4-22
)
=
( )-:+-( )
: ("
K/watt
1'=
..( ) +( )-_( ) + .()
TB = THM- RI(Q) : (
) - ( ....
)(
T :
watts
.)_.-
:
K .....
Previous estimate
was
K ..
=
K ....
Previous
was
K
TA = TB -R2(Q).:
(
estimate
. ) - (
)(
)
Does tile difference significantly change the thermal conductlvities? Yes __] then go around again No L_
t I
'
then go on
QC = Q(NR) = (
,{ [_
)(
) =:
.._ watts............
!
• •
._
- A,
=
'_:
Llt:
• . . .............
W, C111°
tNi_,)_,r,l\t:!\_trl)trH)l-T!'_r,1) LR t
_ . )t
(,
)t..
_. )t
.
-
waI_s 13, ,'.Z
Slots, KM,
i%lt.iple
t_t_ ,'DL_O ,1,,.'..
Alliltllii 1
ill,lib,it i<m .1.-l:'Oa_
{tllllllt_t_l'S
l'l'Oltl
.' ..).;')
till ,_ ]ttt;':" :_
aHi
t W ,' cril
:-_-, .,tr (tilt <,i, ,.ltti_
Qt:
-
t
• lk
t Cltl
]-t
' {
/
.!
I_1_I\ t ;\it.'l__1!t,_I: _-,1t't't)
t
)t(
)1,_
°
.)
!I
W,It I S
1 i !
"t%ll
t .....
i
....
-
.
....... :-_-:---_ .......
i
i , ,, , ill
13._
Summary of Static Heat Conduction .................................... Section
"
..................
13 l
Gas Cond
Inside
Displ.
QC =
13.2
Radiation.
Inside
Displ,
QR =
13.3
Displ,
Wall
QC =
,
'
13.4.... Displacer Gap
QC =
'
_' _L
13,5
Cylinder Wall
QC :
i!i
13.6
Regenerator Wall ,.
QC =
13.7
Regenerator Matrix
QC =
i
watts
Total
QS:
14.-..... Pumping Loss (Equation 4-126)
_
, 0
I -
PMAX _
MPa from 6
PMIN =
MPa from 6
i"!
_'. • i'_! [_,
RM =
,:
Z1 :
_'i ,,
QPU"
i_.; _
QPU =
= 8.314
_
j/g,
K
(normally 1 except when gas temp. < 70
(_)0.6..
l.'5('Zli ............... \ (THMTCM)RM" *2(LD){THM TCM) /CP_iAX .- PMiN__
"l .5(
,,,:
•
,,. U_ for I_ _ H2 MW= O0-for He for air
watts
i
K)
i ,i
} 1'6
GR2"6
_ _
-)
)( ),
-
(
)'
L
_.!
DELTHX = ---NU(N,_IX WHS(CV)(FCT)(THM-)(C.-'PM-_F TCbl)_ = _
(........ )()(
K
I
QTS --(FCT)(t_HS)( CV)(DELTNX)/2
_..
: (
)(
)(
_ ":.,
16,
)lZ
watts..
=
l,
)(
Internal Temperature KW= w/cnl SwiiigLoss • K from Figur'¢_4-22 For Screens:
i ,
LHX"= THW/2 ; (
! ..... '1'
)i2 =
cm
)/2
CIll
L.,,:-'0 ""
L
i,
_'i
t
':_"
to,,sl,.,ts :
LHX = THF,'2:
c, =o,,_.'
(
....
=
)()
-
)
4 I I ,
--!
i, h'
L,
:,
QITS : QTS(C31(R-OM)(CPM)(LMX)2(NU](KM)(FCT) = (
I
)=
)(
=
)(
)(
,:" ,,,_ )2(
'
)
:,
watts
.: "d , ,
17. PerformanceSummary
>._:
Net Power.,watts BP = basic
Ist Iteration
friction loss NFL : mechanical (from g) NP :
3rd
_:;,
power=
_
(from 7) (from8.4) WP = windage, power = ,> ..... .,:, '
2nd
_
/
" I .!, 4 i:, I " . :_ "_' "'
1
.... _;_
=
BP - WP - MFL ;
_ 'j
•
'_' ' i
= net power
#
:
Net Heat Input (watts)
Ist It.
3rd
,:.,
,_
!:_!_ !
(Equation 4-132) BHI : basic heat input (see I0)
2nd
:
1
I
1
T'
"
i
"
I
i
'•Z
,. i
' :
Net llet--Input
(watts)
Ist
It..
2nd
3rd
(see ll) _ +QRH = reheat loss : +QSH = shuttleheat cond. = (see 12)
_ ! I
,,
+ QS = static heat cond. = (see 13.8) (see 14) +QPU : pumpingloss +QTS : temp. swing loss (see 15)
i i
:"
: :
I
"! i"
_
+QiTS = internaltemp.• •
...... !
(see 16) swing loss
. ,
-WPH = heaterwindage_ po;:'or (see 8.4) W_=PR_ = half of regenerator Z windage power (see 8.4) ........... ,, .
-
QN
net heat input
; , =
"
I
,
i
k' I' i
=
-
i
=-
i"!
]
18.
I
Heat ExchangerDuty
i!_
Gas..Heater
__IstIt.
QGH = QN = _
2nd
3rd
....
.i '
Gas Cooler QGC = QN - NP =
-(
).(
-',
,
J
) .,
212
_ _=._
t
t.c_,;)'_'L
.,.
i':
! ., i
_
19.
Gas Heater
19,1 TubularType RE =
from 8,2,1
i
i
'_ I
i
LH
_
"
From Figure4-19:
I
.............
,
CP =
j/g.
_i •i
PR : CV :
from Table 4-9 Jig- K.-- from Table. 4..--8}
H : -_CP)IG)
ii
',, "
i',. I
",'_
,i
i
d
>
: ( ,
"
K
from Table 4-8
)(
_ )-(
(
)
for THM=
?
AHT = (NTH)(_)(DIH)(LHHT) : (
)_(
=
_ i'_:i
)(
)
,I
,:i
,! _!.
, K
i
cm2 . It(ANT) ......
NTUH = 2(FCT).(WHS)(CV) = 2(
._ (
)( )(
) )(
K
w/cm2. K
=
,I
_:,i •1
G : ................ glcm2 sec -- from 8.2.1
. )
1st
e._
I tel'ation
Ttt - ltiM
.' 1 ,I
1 I
I
.
QGII _.'(_7'.l")(l_itS.T(O_/)(e;_i,(Nltl_t) .... 1)
!1
I IlL
+
i
J
"'
=(
'i
=
i "i"I
i
) -
= (
"
) -
=
:
,
K
19,.3 Isothermalizer Cone Type Heater (Equation 4-137) KG =--,
w/cm, K -- from Table 4-9 at THM =_
GTA = ,
.
) - _F
3rd.Iteration
;/
i
)(ekp(
K
TH = THM-
,
('
K
=
_,
_'
)(
TH.= THM - (_) = (
'i!il _ ,,./
I " TC '
2nd Iteration
i _i'_"
:,
"_
K
cm -- from 8,2.3
)
_r,! '_ : _;: i _" " I
-_(
)(
= _
)_-T---) +-( cm2
-
Ist iteration 2
.4 ,
,_
i"
._qGH __
((
GTA.........1
TH = THI4- /6{KG)CAHT)_- ( TH,=--------
I
)2
)C6(= K
)1 }(
})
2nd ...Itera ti on TH _: THM-_=
(
)-
$-............_-
3rd Iteration TH = THM- QGH= (.
) - {_t
0-
20.
-_
K
Gas Cooler
°
20.I
Correction of effective rise in cooling water.
QGC
cold metal, temperature due to temperature
L
)
.\T =-F-Ci_(__.II,_i_\,_) ._: _(........ = <._
-)-4-D_-_8
K
TCbl= TCWI + ,.\TI2
I
C
.i
'
.......................
20,? "
=
_(
_.
)- -
K
TubularType RE =
from 8.3.1
I
i
F,.ronlFigure 4-19 : 2
G = WCS --
.....
g/sec cm2 -- from 8.3.1 g/sec -- from 8.3_I From Table 4-8
._
CP=--_--PR =
I'
i
.....
t mL,Ir"
_"......
ii1'_-_1
I
2--
---:
.
j/g,K fronlTable 4-9
I I
for TCM =
K
H : I(CP)(G) " 2
=
(
)(
(PR)]
-2-
(
)(
NTUC
) =
w/cm2, K
)]
AHT = (NTC)(x)(DIC)(LCHT) : ( =
_
).._(
)(
)
cm2 H(AHT) . _ 2(FCT)(WCS)(CV)-2(
)(
)(
)
-//
I
First Iteration qGC., TC = TCM + 2(FCT)(WCS)(.CV)'(exp(NTUC) - I)
TC _ (
) + 2"(
)(
( )(
)
)(exp(
J.... i...
) - I)
2nd Iterat_n
(i)
i
= 3rd Iteration
K
(i)
TC = TCM+ QGC= ( 20.3
i
) + I
I
Annular Gap Type Cooler (Equation 4-i36) KG =
H : _:I'22KG
w/cm, K from Table 4-9 at TCM=
1.22((
ANT : (DCY)_(LCHT) = _(
) ) : .--L)(
K
w/cm2, K ) =
cm2
217 i
!
If! '". r'" :'_ •
1
i
i
i,
' i
20.4 CalculateNTUC I.so".:,ermalizer and Cone TCType in 20.1 Cooler (Equation4-138) KG =
W/Cm ''K"" from Table 4-9 at TCM =
GTA....
K
cm from 8.3.3
From 2.3.3:
....
2+
AH'F.-_(NC)(DCI)
(LCI)2
.I
i!
cm2 Ist Iteration
"_
TC : TCM +(_)QGC TC =
:
(--
)_6(
(( .._)( ))
)
.......
K
2nd Iteration.-
_
( TC : TCM+ QGC= ( i .i
,_i C
=
i!
) )
I
K
3rd Iteration
,_i k._
.....) + (
(1) =
K
21
21, Conclusion Final Net Power :
watts I
•
LI
_mm
!
,4,
! "
Final Indicated Power .--
watts
r
i
'
........
_
Final
Net float
Inp_t- =-------
Brake Efficiency _:I
watts
=
%
I ndi cated .Effi ci ency =,
%
_,J,.
i ., ' '
,
:.
7,2
.•_, ,_"' _,_ __,
In Section 7.1 a design form was presented which would_llow the designer to start with a set of dimensions ,and operating conditions for his machine and then calculate through a series of equations, all conveniently,specified,,to determine the basic power output and heat input as well as the power losses
._,_ . ,.' i , ' '! i
and heat losses, The end result, is a computed net heat input and power output and a net efficiency. Ill this section this form is excerpted to:show only, those parts that need to be filled out to calculate the expected performance of the-GPU-3 engine described-in Section 3,3. In particular, ,Test Point 1 on ,Table 3-8 is calculated as a sample. The GPU-3-engine is classified as a Beta type • engine w.ith a single displacer and,power pisten pair and a rhombic drive.
__
1
S_an!p.le Design Calculation
I.
,
Type of
Piston
Arrangement
l.-2..Beta:
Displacer.-PistonOverlapping ,Strokes 7,010 DC¥,,,..= diameter of,engine cylinder co.
_I 1
SD = stroke of displacer '"
.3.068 __cm
SP : stroke of power piston
3,068
.....
DDR = diameter of displacer drive rod
cm.
2, _'!
,,,
0,953
cm
Dead Volumes and Heat Exchangers and-Wall Thicknesses 2,1
Volumes and Heat Exchangers at Heat Source Temperature VHDX = extra hot dead volume bes.idesthat,in the gas.heater 12,389
2.1.1 "
cn_3
Tubular Gas Heater
---
NTH-= number of,..heater_ tubes per power unit LH : total length of-each heater tube LHHT =,.,heated length of each heater tube
! .
40
24,229
, cm,
15.545... cm.
_719
,; , .........II fI •
;.................. _....... i....... i
i
"_"
I
_
:
!
'
Dill= inside diameter of heater tubes
0.302
DOH = outside diameter of heater tubes
2.2
cm.
0.4}{3
cm.
Volumes at Regenerator Temperatu,'e 2.2.1
1
Screen Regenerators LR = length of regenerator
2.261
NR = number of regenerators/unit
cnl. 8
DR.= diameter of,each regenerator ....
NS=
nuinberof screen layers
MSH = mesh siZe
83.9
.
2.261
cnl,
308
wires/cm.
THW : thickness of wir,ein screens
0.0041
cm.
FF = filler factor, fraction of regenerator volume filled with wires
0.286
.....
!
Screen materia]__ Stainless.Steel
.
!,
,
i
2.2.3 ' "
i . i I
Displacer or Hot Cap Gap Volume LD = length of displacer 4.359
cm.
DCY = diameter of cylinder around displacer
.....
7,010
,
GR = gap between displacer and cylinder wall
i
Displacer wall material-
Stainless Steel
.
_' i
Cylinder wall material ..
Stainless Steel
,
#, i
WTI = wail
thickness
of displacer,
WT2 = wall.
thickness
of cylinder
0. I.78
0,025
cm.
"
cm.
cm.
i
EH = emissivity
of hot
inside
wall. of
0.406
displacer
cm. or
cylinder
wall
0.6
,.2,)
EC : emissivityof
cold
wall
,
O. 5
inside
of displacer
or cylinder
-I
r
_..!
i_
'
t
i
NRS= number of radiation or hot cap 2.3
1
shields
2
inside
'
ttie displacer
.
Volumes alld Ill,at I-xcllall{it_r._ at Ileal. Sink Teint)erat;ure
c
VCDX= ex:r.a cold dead volume besides that
'_
ill the gas cooler
s.732c,,3., [_ (0.2as)2(o.G2s) +0.017] 8(2.s4)3
_"'
2.3.1 Tubular Gas Cooler NTC.= number oZ cooler LC = total
tubes
per power unit
length of each cooler
tube
4.470
........................ LCHT : cooled l,_!gthof each cooler tube DIC = inside
2.4
diameter
of cooler
. cir.
b
3.Xi_O__cm.
diameter, of coolertubes.
DOC: outside
3'!2
0.102
tubes.
!
cm.
0.152
,
cm.
Regenerator Wall Dimensions (see Figure. 4-23)
AHTH - he!t conduct.ion area at hot end ,..1.425
cm2.
AHTB - F_:atconductionarea at level B
1.425
cm2,, •
AHTA = heat conductionarea at level A
0.853
cm2.
AHTC= heat
1.425
conduction
area
at_Lcold end
_ ;;. ._
_
i
li
i
cm2.
o,
/
LHB : hot length regeneratorwall
1.016
_i k_
LBA = middle length regeneratorwall
_i
LAC : cold length
I.! i"
Regenerator
regenerator
wall material
cm.
1,194
wall
0.051
Stainless
Steel
!
_cm............. cm. .
t
t! i'.}, ._i ;} ,p/
Temp K THM= 978
Thermal Conductivity KMH= 0.25 w/cni.K._
I_B: _00
(est.)
KMB =
CI.225
TA : 350
(est.)
KNA =
0.16
KMC:
0.15
I'CM :
;;94
I
i', , _
_
I
_i_"
'
i
!
'
1 -;_i
2.5 CylinderWall-Dimensions(see Figure 4-24)
,'_ _"
1
AHTH : heat conduction, area at hot end
15.915
_
AHTB = heat conductionarea at level B
10.726
cm2
!
AHTA = heat conductionarea at,levelA
9.469
cm2 e
_
;"
cm2.
AHTC = heat conductionarea at cold end 15.915.
_i
LHB = hot length.regeneratorwall 2.858
_:_ ,,_ I,i
LBA = middle length regeneratorwail
1 016 '
LAC = Cold,length regenerator wall,
1,245
1
cm2.
cm cm. cm.
Cylinderwall material, StainlessSteel : ,
,
_
Level Temp K
Thermal Conductivity
THM =
KMH = 0,25 w/cm,K
_ 'i
TB =
,_il
TA = TCM =
:
978
.... 800 350
(est)
KMB = 0,225
(est)
KMA = -0.16
294.
i
KMC = 0.15
3. Drives.
Ls,
i i ,i
N =-Number of power units/engine
i"k,_,"
l
b
3,3
l
_.
Beta-RhombicDr_ive LCR = connectingrod length 4.602 cm,
,
RC = crank radiuS.,1.397 cm,
'
ECC =.crankeccentricity(see Figure3-30) 2..065 cm. 4. Given OperatingConditions.
".......
TC = effectivetemperaturein cold, compressionspace 300 ' 1
K = -C + 273.1
t
K = (. E+ 460)11.8
Make initial estimate
TH = effectivetemperaturein hot, expansionspace, 222
K.,,
978
K,
..... _ i_ _ I
I
111 1
1 I k
'i ¸
i i
'
FCW= cooling
water flow
,17g
! :
g/sec.
TCWI ;:Temperatureof cooling water into engine 2!14.,I K. NU : engine frequency
o
'25
II_
(Hz = RPM/60) PMAX = maximum engine
pressure
i. _ Not Spec.
MPa.
# i, r
'
= 0.1013 (atm) MPa = 0.006894 (psia) PAVG: time averaged mean pressure
'
THhl : heat
source
metal
TCM = heat sinkmetal
Working Gas
i 2.068.
temperature
978
temperature
295
hIPa. K.
!_
K.
i,'_
Hvdroqen
:', :,:_
5. Computatiunof Engine Volumes
',
5.1
L_ve Volumes Note:
_' ,i
Live volumes for cl'allk and rhomhic drives need not be defined ....
:;. . if"
I
5.2 Dead Volumes........... VHD
hot dead volume , cm3
:
'_" '_y,
for tubular gas heater
_
_
2
-VHOX+_-(OIH) (LH)(NTH) 12.389.+_-(0.302) 2 (24.229),.( 40
: :
a' ) :
81,811 c,._3 .
_. ,,
VRD = regenerator dead volume, cm 3 __
for
scr_n
regenerators,
VRD : NR
calculation
DR) (LR)(I - FF) g
= (
short
,R
) _.(
"'
o
2._61)_"
(2.261)
(1 -
.286t
_- 51._154
cm3.
.
II
_,._ .... _
__4
,__
° _
,Q
i
i
'
i
VCD = cold dead volume for tubulargas coolers II.
,
VCD= VCDX+ 4-(DI_,)2(LC).(NTC) 71
= 6.
General
5.782+ ;_(0.102)2(4.470) ( 312 ) : 17.178 cm3.
Intermedia.te
Parameters
TR-- (THM- TCM)/ln(THM/TCM) = (978
'
-
295 )lln(
978 / 295
7.4 Rhombic Drive PhilipsEngine
) :
570
K
(See Figure 4-15 and 4-16)
A = _(LCR) ? - (ECC - RC)2--
:_(4.602)_- (2.005- 1.397) z : B :_(LCR) 2 :V(4,602
4.553cm
,,
(ECC + RC)2 )2-
( 2,065 + 1.397 )2
:
3.034
cm
']
For a Check:
VCL= (a- B)g DCY) - (DDR)
--(_._ - _.o_)_-I 7.olo 12 Io._ 12)--l_.°°_m 3. VCLX = _{DCY) 2 - (DDR) -
= --
4.553
-
A-V(LCR) 2 -
21.178 -
C- RC cos
PHI) 2
2.065 - 1.395 cos(
)
VC.=.VCD + VCI.X=
VC-= 17.178+ 224
J
VCLX+ 17. 178
75.762
4.553
-
1.178
.
2.065
.
1.395
cos(PHI)
I
:, I_, I
i> • ;
,i _, ....,_i
:
! i
!
i ,
i
I
_
!
'I
i '
,, •
_ •i
,,
_.•
.,
_
, , ,>':/ ,
i t
,
7"
ii '_
..... !
:li
PHI --.360
'
!r
i
PM =
I,,____:c
_
I_'
_ PHI-
30
12
PM = 2.436 (see previous
page)_
PAVG 2,068 M(R) :. = 0.8490 JIK PM 2,436
L_, !
G__
i_',"! i,, 4 ,_!
i....
l
P
Note: Do Not Add in P-at PHI = 0
i_, i 'ii,,_ - .,!,;._.,
......'_i
#
PC- PPA\V]=p_(0.849(:I PC is _alculated For.PHI.: O, 30,,
_.rj_ _ic-,: I
'
..... , 360 on previouspage,
PC is integratedverses VT using the trapezoidalrule,ie. _"
DELW = PC1 + PC2 (VT2
VTI)
2 "
For the first.incrementthe subscript1 stands for PHI.-=0° and the subscript-2stands for PHI.= 300.
For the second
increment,thesubscrip:l..standsfor PHI - 30° and the ,
.
subscript2 stands for PHI = 60°. DELW is sumed for all 12 increments, 12 BP : NU(l.045)
I! ;
I )
2 '
DELW
= .___,5(1.045) 94.218 : -.2461- watts.
}
I
,; .i
I
i__
t
'
.
'_
i --I
.
@
I t
The mass flow rates are now computed
P(VH) FH = M-CR_
P(VH)_).iI...9"78---_ _ M(R) : 0.8490 JIK = (_0..8z190 M(R) 0.8490
'
M : 8.---_I--4-= 8_ M = O.1021-.
g.mol
FH is calculatedfor PHI = 30 to 360 (resultson previous page) and is........... graphedon Figure 7-I. FHMAX = 0.560 FHMIN -- 0.155
" 2,77
4
I p
i
8.
Fluid
i -
Friction
'
'
i
i
_
:
, "
loss
122.784
I
8.1.1 Screens -- VHL = Regenerator Windage TR =
,
PAVG=
2.068
8.1
/
(from 5.1 or 7.4) cm3 OK (from 6) o.... , ......o.
570
.....'
.MP_._ (ft_om4)'"
_
t
for hydrogen:
! "
MU : 88.73 x 10-6 + 0.2 x 10-6 (TR - 293) + 0.118 x lO"6-(PAVG)
I
570
!
=
RHOM:
144.4 x I0"6 g/cm
,
MW :
PAVG _x
= _x
_ 0.1202(2.02
2 068
sec
mean gas density MW
;
.... i
273 _
zLO0
0.1202
)( 2.068]_ :
29
i
MW{PAVG) TR '
i
8.81 x lO"4
_L:S _
g/cm3
( $7o )
•
_ i_
i!
For numerical Schmidt analysis (from_7,.4) WRS =
AC :
7.482 VRD _ LR
g/sec 51.854 2-.261
_ WRS _ G - _=22.93
AHT: _
:_ :
= :
22.93
0.3262
cm2 g/sec cm2
L
._
(MSH)(THW)(DR)2(NR)(NS)
(83._)( .004!!! 2.261)2( 8 )(a08)............... 21382
cm2
!i
23O
....
l
(
I
-
i
I I
I
II .........
_
:Ul
,, _1
.
.
.(.22.93)(2.261 ) - -"2T3',_ '=
RH = AC(LR)/(Alrr)=
2.425 x 10-3
cm
1 (l?Ii _s::I
RE = 4_RH_ = 4__2.425Z x I0_ 0(3_.3262_)_ = 21.97 MU_ (I • 44 x 10-4 ) .................
4,
_ If RE < 60:
/
log I e : 1.73 - 0.93 log (RE) 3.035
21.97
If 60 < RE < I000:
,!,
.
F : 0:714 -0.365 1..o_g (RE) if RE---------I°g > I000:
_
!i i t
log F
0.015
: DELP
0.125 lo9 (RE)
(LR)
: :i
'"_
i
2(10')(RH)iRHOM)
DELP : 3.._3..__3.5 )={"_}262 )2(2,261)_
-_;
-_
= 0.0172
MPa
For numepical Schnlidt analysis (2xlOT)(2"42xlO-3) _81xlO "4) (p.EI.P!(WRS)_L2) II_C!Zr]_ .. WPR ....
]
(RH-O-bI-) --
= (0.0!72_.)(
7.482
)__2_0.320
(a.,,u x Io- "1
1=
93
watts
8.2
Gas Heater Windage 8.2.1
Tubular Heater
1
for Hydrogen:
Mu: I0"6{ 88.73 + 0.2(THM - 293)_ ,mIIS"(PAVG)} : i
:
978
2. O68
.
2, 26 x 10-4 " g/cm.sec
! J
il 1
_
i_::
He
MW: 4.00 29 RHOM: 0.1202 MW(PAVG)/(THM) : 0.1202(
' _ i
r
air-
Eor numerical
WHS= Schmidt.analysis
2.02 )( 2.068)/(
978._): :
5.13 x 10-4
g/cm3
6.425 g/sec -(from 7.4)
i' !,
AC : (NTH)(DIH.)2 _/4 : ( 40
2,87
:
RE - (DIH)G : (.302..)(.2,239)
MU
)(
.302 )2 _/4 :
2. 239 =
2,.87' cm2
g/cm2, sec
2991
(2.26 x 10-4)
If RE< 2000. F : 16/RE : 16/(
) =
_/ If RE > 2000, IO£LF = -1.34 - 0.20 log (RE) 9.22 x lO"3
:
2991
For numericalSchm_dt analysis )(_).. DELP-= ..2.(F _ 2 (LH) I_(DIH) (RHOM)
!I
., P ,i
2.239 )212423 )
= 2(9.22xi0" ,. " : 0,00145 MPa 107(0..302 X5.13xlO"4) ..........................................
i
'4 232 -
I
F-
I
i
' l
'
'
h
• " i
:
8.3
!
DELP(WHS)2 (FCTH) -..... RHOM
WPH
I
:
(0..00145)(6.425 (5.13
Gas Cooler
I
'
_,
)2._( 0.325 x 10-4 )
_ =
11.77
watts
Windage
.!
.i
8,3.1
Tubular
Cooler
1
_:
MU = I0 -6
88.73
+ 0,2(TCM - 293) + O,II8(P_AVG)
;
295 =
8.94
x lO'5g/cm
MW
2. 068
sec
4,00, 29 He a_r
!,
_
RHOM = O.1202(MW)(PAVG)/TCM = 0.1202( 2.02
',I(2.068)/( 295
) : 1.70xlO"3.g/cm3
_
ii For numerical Schmidt analysis (from 7.4) ,--
_
WCS :
i
8. 538
h
g/sec
i
I'
:
AC : (NTC)(DIC)2 T:
,I
Ii....
G..-= .WCS ._ - 8.538 2.5---T -T =
IQ
RE =-(DiC)G
'_!
" MU
#
:!
=
(
312 )(0 •102 .... )2 _- =
3.348
(0.102 )( 3,348 ) (8,94xi0.5) :
li_ RE < 2000, F.. = 16/RE°.=16/(
g/sec cm2
3820
2.55
cm2 _
.-,
.........
J =
L_
_ T_
_::(
:
..
If RE > 2000, log F.: -1.34 - 0.20-1og(RE) 8.78xi0=3
3820
233
_,
J
,
1
i
____LLL " i
: I
! . i
'__'T
L_:I
For numerical
Schmidt analysis ....
;_;', i!
DELP.= 2(.F)(G) ) : 2_7___88xI0-3)( 3.348 )2( 4.4-7 ) I07(DIC)(RHOM) _OT( 0.102 )(l,70xlO-_ .
b
i _'
= 5.075xi0 -4
'l{{
MPa
WPC-- DELP(WcS)2!FcTC)
' '._ :,,:l !q
RHOM
'_i
:_!
= (5.075xi0"4)(_
ii
8.538)2(. . . 0_..3]_4_.. ) =
1.60
watts
(1._7o × io-3>
.... :_i
8.4
Fluid FrictionLoss Summary
!i
J
.,
Gas Heater,
I_H
WPH-=
12....
watts
Regenerator,WPR : ..... 93 Gas Cooler,WPC =
watts
2
watts.....
!
L
'
Total..,
WP =
I07 ......
wa-tts
::
_
)
9 i
Mechanical
Friction
Loss
MFL :
" based upon experimental
measurement
or 0.2 (2461.)
:
492
watts
I0. Basic Heat Input BHI -
BP 1
=
tC
i 2461
=
3550
watts
300 78...-
_, ,
II. Reheat Loss l l.1 ....
J
!
MFL : 0,2 BP : i
!.i
Constafit
Volume Assumption
(Equation
4-97)
FCT =-
0.32
(usuallyI/3) (from 7.4)
WRS =
7.482
g/sec (from 8.1)
I
[
[
!
'_
|
"
' I'
I :
,
"
['
._
W
'
7'"
CV =
10.4,2....
for
TR =
570
K (.see Table 4-8)
CP =
14.55
for
TR =
570
K (see
AHT =
21382
cm2 (.from 8.1)
'_
G=
0.3262
g/cm2 sec
PR =
0.753
for TR =
RE =
21.97
Table 4-8)
(from 8.1) 570
°K(see Table 4-9)
(ffrom8.I)
;_._
;:'-i
2
_.!
lOg!Gt _H
(PR
: -0.13 - 0.412 log (RE)
7' i
t,
•._ :;_i
H ) 14.55)"
log (_.3262)(
(0.753)
w/cm2
= -0.13
-0.412
_ ! .........
H = .. 1.190
,_
NTUV: __ = (7. 482 )(10.42).. H_(_AHT) _ 1.190)( 21.382 ) :
I'--" i
QRH : (FC.,T) (WRS)(CV)(THM . TCM) NTU + 2
K
: ( 0.32 )(7 482 )( 10.42)( '
,_ .... 12.
= ....
Shuttle
log (21.97)
103.76
978
326.4
-
295
)
2 326.4 + 2
w-_ tts-
Conduction .....
12.1 HighPressure Engine (EquAtion4-110) KG =
,
28.06 x lO"4
w/cm K at TR =
570
K (From Table 4-9)
LTI =
0.152
cmI @ NU = ,. 25
_. HZ (From Table 4-11)
LT2 :
0.152
cml
_-NO)
0.19 0.19
w/cm K I From Figure 4-23 w/cm K I
Kl = K2 =
(LT _
235
LB-='I
+2
KG [LTI LT_T2 _ 11GR._-'KT + K2/
LB.-=..... 0.!.29 !
= / 1 + LB \
_
ISD)2(KG)(THM _.TCM)(DCY)
I
) (-__ _ _3.06s _ (28.06xlo'4)(07s 29s)_7.010 \l + ( 1.029)2] (0.'C)25-)(4.359 )
i I
:
449
watts
---
13. Static Heat Conduction. 13,1 Gas ConductionInside Displaceror Hot Cap DID = DCY - 2(GR) - 2(WTI) =
6.604
cm
(Directfrom engine dimensions) ,
AHT :4
!
_ (6.604 )2 : (DID)2 : T
................
34.25
cm2
..-
I I
"
KG : 28.06xi0 "4
w/cm. C from 12
QC - KG (AHT)(THM- TCM)_ (28.06xi0"4),(34.25)( 978- 295 (LD] '_ (-4.359) =
15
watts.
13.2 RadiationInside Displaceror Hot Cap DiD : 6.604 : LD "z[T3Tg-
1.515
If: DID DID 0 < _ < 0.2 then FA - LD
I
23G
)
-------
I
'
!
!
I
I
_
d
_
o
!
"
i,',
' _;:' _,
i
DID 0.2 < -_-_ < 7 then
FA - 0,50 + 0.20 In
FA ,, 0.583
"
If:
t
i !
DID L---D > 7 then FA = l
i i ' _
FE = (EH)(EC):.( 0.6 )-(0.5 ): 1 FN :T-T,_-:
i
AHT =
1 1+ 2
34.25
.. j0.3___
_ I/3 cm 2 (from 13.1)
l
, ,.,
QR = (FA)(FE)(FN)(AHT)(5,67
_
: (0.583)( 0.3 )( I13 )(34.25 )5.67 x 10-12
(( 978 )4-
i :. i :, 13.3 _!:
i .,i .i
'
!_ I!
x 10"12 ) ((THM) 4 _'- (TCM)4)
=
10
Displacer
Cylinder
( 295
<_
)4)
i!
watts Wal.l
...
i_
KM : ...... AHT :
0.19
w/cm K at_TIL:
DCY - 2GR)2 - (DID)2
570
K (Figure4-22) 6.96
i.
- 2
= - (6.604))
=
3.788
--
cm2
QC : KM(AHT)(.THM " TCM) CO.19 )(3.788)(978 LD : ' (4.359 ) =
113
- 295 _ )
watts
i
13.4 DisplacerGap KG=
28.0E. x lO"4
w/cm, C from 13.1
AHT : _(DCY)(GR) : _(7.01
)(
0.025) =
..........
0.551
cm2
i!
• , _
r
- ,
TA :- lfi - R2(QC) -: ( 678 ) - ( _),573)( 332
_I
_.
:_I
504
,
)
K .... Original TA estim,_te was
350
I,
Now:
";..,
Kblg= K_ =
: ""i_
0.21 (I, 18
w/cm K at TB 1 wAcm K at TA I
Figure 4-23
_"
I
i '
]
Now go around again.
i
. .....
'.}
_
i
/C
R1 :
_)
( 0.429 )
-
0.933
K/watt
0.515
K/watt
0.594
K,/watt
K IH + R IB-(0.25)+i 0.21)"
,
',_ _
_ (D'20!) R2 : KMB-+k_ -= (_0.21) +( 0.18 )"-
® R3 : K_tA-+ K_C
( 0.18 )
,+ _ 0.15 )"
i 9.
THM_ _ _978 ) ,- (795 ;_ QC = R-I + R2TCM + R3 = (0.933) _ (0.515) ¥ (_.5.64) _'
334 ',_:atts
=
TB = THM - RI(QC) = ( 978 ) - (0.933)( 334 ) =
:
_
=
666
K .... Previous estimatewas
678
= TB - R2(QC) = ( 666' )
(0.515)( 334 )
=
Previousestimatewas
494
K ....
K
504
k
,.
Doe; the differenceslqnificantlychanqe the tl_erm.al conductivi_is: [_
Yes ...... Then go around again
[_
NO ...... Accept last QC as accurate
_C
:_,
L}C 334
13.6 RegeneratorWalls _
"
One regeneratorwall will be calculatedand thei_multiplied NR..Using the numbers from 2.,I
....
i
L
Let 0 = __!(_L!!_B_)__ 4(I,0_LL.._L AHTH+ AHTB = "('i] }I75") +--_ I. 4?5 ) -
].426
Tllen R1 = KMH+-Kh-B = "( t 25..........
•
4(LBA) 4(1.194) : Let (_)- ;EH-T-13 ¥ TA-H-I-_ = ( 1 425) '+:"(0.853 ) ""
i
( 2.097 .16 ) Then R2 - KMB+_KM]A_- _-_-,_25_),+-(
:
) :
2 097 "
r
5.446
K/watt
i i
4(LAC). _ 4(0.051 Let (_)= AHTA+ AHTC: (0.853) + (I.
2
25 )
:
0.090
!
:
h I
(0.090.) Then R3 = .. Q) KMA+ KMC ( .16 ) + ( .15
'!
)
=
0,289
K/watt
78 800
watts,
i, _
, "
Q = RI + R2 + R3 = -(3.002 + ( ; 6
TB = THM- RI(Q) : ( _978 ) - (3.002).( 78 ) THM- TCM 978 () " 289) = 743 K .... Original estimate was
_
TA : TB - R2(Q) = ( 743 TA :
317
) - ( 5.446)(
K ....
Original
K:
'
L, iv
78 )
estimate
was
350
K
Now:
_! Figure 4-22.
KMB= K_ =
0.21 0.155
w/cmlK K at TA TB 1 w/cm
Now go around again: R1 : _+(_ KMH ..KMB: (' R2
_ = = KMB..._-KMA.-_
R3-
,2 _ 1.426) ") + ( .21 ') = ( 2.097 ) )-¥( .]55'j':
_ : ( ".15_ _,09Q) KMA-_+ 'KMC + ( ,150 )- :
THM- (295 Q : R1 + R2TCM' + R3 = (3.10 _ 978 -) + ( ) 5.744)-+
240
3.100
K/watt ......
5.744
K/watt
0.294 ) (0.294-)
K/watt :
74.75
watts
t
k
13,_ Summary of Static Heat Conduction Section ,_........
13.1
Gas Cond. Inside
Displ.
QC --
15
13.2 RadiationInside Displ.
QR=
I0
13.3 Displ, Wall
QC,_
113
13.4 DisplacerGap ........
QC =
0
13,5-Cylinder Wall
QC :
334
13.6 RegeneratorWall
QC =
598
13.7
QC =
48
watts
..........
i
' ! i
i !7
=.
' ;_ ,_ ,i
(
.4
Regenerator
biatrix
i
t
_
Total QS =
i
14.
<
_
.) i i!i 'i
.....
I ,', I:'! 4 1 ii i
Pumping Loss (Equation
4-126)
P_t_X--.
2_880
MPa from 6
PMIN =
1.337
MPa from 6
R 8.314 RM = _ : L_ :
i
II18
2.0 'for H2
4,116 j/g. K
MW =
,.
for He for air
'"
Zl :
1
(normally
1 except when gas temp. < 70 K)
----li.5-T_T_.H_ Ii
QPU =
[i
QPU =
-
(_i_
:
13.6
6 GR2"
°'_2(4.3_>( 97_. __gs_ L
\(28xi0-4)/
-1.5( 1
978 )
12 •
-
)
295 ){_l-(4_-------y ((1.025)2.6
watts !
24 ;:'
I
• -_
-%
i
I
,i_'
FCT =
i
i
0.32
'_!'
_i
_
,
_
_'_ "_' •
i_
, I
"
see II
ROM =
_
,
from Standard References g/cm3 /
7.5
CPM 1.05 j/g. K For : Screen Regenerators: If
!_
MMX: NR_- (DR)2(LR)(FF)(ROM)
) T( 2.261''J22.261)(0.286)( ,7.5 )
= (. 8 = _
155.78
g
DELITMX WRS(CV)(FCT)(THM- TCM) NU(MI,IX) (CP'Ii')M =
4.167
_? _2"
(I0. )( 0.,32 )( 978 5) )(155.78)(1.05 42 )
-
295
K
QTS = (FCT)_VRS)(CV)(DELTMX)/2 ,!
= (0.32)(7.482 )( I0.42)(4.]67)/2 =
51.98
...wa..tt s
.i
'i
........ !..6... Internal KM =
Temperature Swing Loss 0.19
For Screens: '!
w/cm, K from.Eigure
4-22
............
LMX = ?HW/2 = (0.0041)/2=
0.00205
cm
C3 = 0,25
: -
QITS : QTS( • 'C3I! KM)TFc--O 'ROM)_P___ ..... (LMX)_(NU) , ....
.!<
: (51.98)(0.25)( =
,
O. 177
7.5 )( 1.05 )(0.00205)2( 25 ) (0.19)( 0.32 ) --watts
24 J
)_
17, PerformanceSummary I
Net Power, watts
'
!
j
'
..... -__
Ist Iteratior_
BP = basic power.= (from7) .
2461
2287
WP = windage power= (from 8.4)
I07
107
MFL = mechanical friction loss = (from 9)
492
NP = BP - WP - MFL :
,1862
= net power
457 1723
r
Ist It.
2nd
:
3550
3415
=
I04
244
_ ]
449............ llI8 14
=
52
:
0
(see 16) swing loss -WPH = heaterwindage_ : power (see 8,4) WPK "T = half of regenerator = windage power (see 8.4) QN : net heat input.
3rd
:,I
+ QS = staticheat cond, = (see 13..8) +QPU = pumping loss : '(see 14) +QTS = temp, swing loss (see 15), +QITS : internaltemp,
I '/ i f
_' ............. ii _
+QSH = shuttle-heatcond..= (,see12).
.
.
.
BHI = basic heat input (Equation4-132) "-"(seeI0) +QRH = reheat loss (see II)
,
3rd
,
Net Heat Input (.watts)
i__ _
2nd
=
.
.i 1687
12
i, I_ _
47 -
5237 _
5102
i,
'
18. Heat ExchangerDuty Gas Heater
i
it.
2rid
3rd
'_ _!.i
QGH= 8as CoolQN er =
5237
5102
,
'" ,,,
QGC = QN
3375
3379
_'
,!
',_i
NP =
: (5237) - (1862)
:;E,,, _ii
1st
ii'i ",'I
,
19. Gas Heater
_,
Not needed because in GPU-3 the effective gas temperature assumed to_be measured with a thermocouple. TH = 978 K.
-,
,_
is
1 !i
'
i
_,,_•
20. Gas Cooler ---
i.
20.1 Correctionof effectivecold metal temperaturedue to temperature rise in cooling water,
• , ":, :i_
AT =
'-I
:
_{i.
QGC _ ( 3375 ) FCW(4,1868): ( 379 )4.186"8 2.13
i' i
............
K
TCM: TCWI + AT/2
'I ':I
:
294.4
+ ( 2.13 ) 2
:
295.5 ......
K
,_ "1
C_
_i _,i !'
20.2 "ubular•Type RE =
}i
3820
From. Figure 4-19:
!'.] _' _, c.
from 8.3 1
,
...............................
"(!)"o.oo31 G =
..........
LCHT 3.48 DI_ = ().I0_: 34.1
WCS=
3 .348
g/sec cm2 -- from 8.3,1
8.538
g/sec
..............
"
-- from 8,3.1
'i
!i •'
! 245
,__..
<
I
/!'i
•
CV :
10.18
j/g-K
CP :
14.31
j/g,K
PR =
0.72
2
( O.72
--
TCM=
295
0.1848
w/cm2, K
)T
I
347.92
First
!
_ cm2
H(AH_T): .. _: NTUC=2(¢CTC)-{WCS)(CV) =
,
C
AHT = (NT.C)(:_)(DIC)(LCHT) : ( 312 )_(C}.I02)( 3.48 ) =
K
......
( 0.0Q31)I:14_ _ i)(3.348..)=
(PR)_-
H-
for
from Table 4-9
_L_CP)(G)
_I!
From Table 4-8
L, (0.1848)(347.92) 2(0'.314)(8.538 )_ I0.18)
1.178
Iteration
.....
QGC TC : TCM+ 2_(FCT)(WC_S-)-(CV)(exP-(NTUC) - I) t
, TC:
( 3375) (295.5) +)(0L314)(8.5381(lOilS)('exp'(l]i78) - I) (_=
i ] 'I
=
323.00
K
....
122.73
:
' !
I '
i._
1
I
..... I
_
' •
: _
x
L _ ,
,I
ii
i
/,
i
I
1 :I
An additional
iteration
was now made by programmable calculator.
I
TH.- 978.00
I ,I
PHI
PC
FH
FC
•I ...
0 30
2.653 2.394.
.... 0.561
0.175
ill
601 90 120
2.118 1.827 1.562
0.585 0.453 0.341
O.231_ 0.345 0.486
150
l 388.
0.239
0.607 ....
180
1.361 0.176 0.673
240
1.908
0.195
0.594
270
2.418
O.276
0.457
300
2.807
O.384
O.3C5
330
2.85i
O.477
O.208 ....
360
2.653
0,537
0.170
3I ',
':;_: _i
_!
•! :
TC = 323.00
M(R) : 0.8258 12 DELW : 8.7,538 1 BP = 2287 BHI = 3415
L'
_.':_,, __ _
FH and FC are plottedin Figure 7-I. The second iterationis seen to offset the resultsand does not change the flow rates or times. BP and BHI are then used in 17 to calculateNP and QN as the second iteration. Then these are used to calculateQGH and QGC in 18. Finally, in 20 a new TC is calculated: 2nd Iteration
:"
TC = TCM +.QGC(_ = (295...5) + (122 3379 .73(1
:
= 21.
323.03
K
Third iterationnot necessary.
Conclusion Final N_t Power = 1723 Final In_ "atedPower = 2180 Final Net Heat Input = Brake Efficiency
=
IndicatedEfficiency=
L_
watts watts
5102 33.8
watts %
42.7
%
247
:,
t
I
_
_
_'
!
"
"
'
r
'I I
o'
I
8.
REFERENCES
The references given in this section (See Table 8-I) have been accumulated from previous bibliographies particularly Walker (Ref. 73 j) and United Stirling of Sweden, compiled by Karin Adler. They also have been obtained from the authors own files and publications and from the references listed in these papers and reports that relate directly to Stirling engines. Fur the recent material..the following computer based literature files have been_searched:
:
Compendex1970 -- (Engineering I
ISMEC1973 -- Information (INSPEC)
1
NTIS 1964-NASALiterature
1
i i !
1
I ! _ !
i ! 1
t
,, ! i !i ! !_ ! I_
Index)
service
in Mechanical Engineering
Search No. 35884
The references have been organized by year of publication. Within each year each reference has been given a letter designation. The reference list has been indexed by personal, author (See Table 8-2) and by corporate author if applicable(See TableS-3). Not every publication listed in the reference list has been obtained by the author_. In most cases theseswere not sought because the main results are given in subsequentjournalarticles. Patents are includedif they were referencedin publicationsor were in the authors file. The author is indeptedto Ted Finkelsteinwho graciously allowed his file of Stirling engine patents to be copied. No independent searchwas made of the patent literaturesince this search would need to be done-byspecialistsat the patent office. The author intendsto maintainthis.file of Stirlingengine references. He would appreciatereceivingcopies of publicationsthat are not now included. The author has a copy of the paper on file if anasterisk (*) appearsat the endlof the reference. Besides indexingthis referencelist by author and corporateauthor this publicationdiscussesthe different _aspectsof Stirlingengines and refers to this referencelist by number and sometimesby chief author name. In the 1900'S the 19 is omitted for brevity. Also each article has been classified by subject using the classification scheme given in Table 8-4. The kind of Stir-ling engine is classified by type of heat input, arrangement of parts and intended use. Design considerations and experimental results is also divided into a number of categories. Table 8-5 gives the paper numbers that relate to each classification from Table 8-4. These classifications have been determined by a perusal of the publication if it were available, otherwise the classification was determined from the title or possibly the abstract. This classification index has been founduseful in preparing this publication. It is hoped that the readerswill find it useful.
248
r, _
t
I
I I
•
Table 8-I Stirling Organized.
*
_'_
1807 a
Cayley, G,, (letter).
Engine References by Year of Publication
Nichplson's
Journal,
November 1807_ pg.
206
1816 a
Stifling, R., "Improvements for Diminishing the Consumption of Fuel and in Particular, an Engine Capable of Being Applied to the Moving of Machinery on a Principle Entirely New," British Patent No. 4081, 1816. A5, B3, 86, 88.
1826 a
Ericsson, J., British Patent No. 5398_ 1826.
• "
1827 a
Stirling, R., and Stirling, No. 5456, 1827. B3. *
• :
1833
-_ i
a
Ericsson, J,, B5. *
d.,
"Air
Engines,"
i
British
Patent
_!
"Ai r Engines,
i'
" British
Patent
No. 6409,
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1968 z
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1970 o
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Tr-_nsactionsASME, Jnl. Eng. pg. 182-188, April, T_70• :(Same as -1969o) DI5 ,._for E7 .power,
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1970 aa
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1971 i:
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Riggle, P., Noble, J., Emigh, S. G.., Martini, W.. R.,-and Han_Hson, L, T,, "Development of a Stirling Engine Power Source. for-..Artificial Heart Application," MDACPaper No. WD 1610, Sept ....1971. A3, A6, B2, B7, -. C4, E4, E5, E9. *
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Walker, G., and Vasishta, V., "Heat-Transferand Friction Characteristics of Dense-Mesh Wire-Screen Stirling-Cycle Regenerators," Advances in .Cryogenic .Engng., Vol. 16, pp. 324-332, 1971. E9, El3. *
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1971.aftvan Witteveen,R. A. J, 0., "The StirlinH Cycle En_line," [ethnicalRe}_ort: of the Conf. on Low PollutionPower _ystemsDe.velop., l!i_ii_lho_ei{, ...... NtQii_i,3.71G_ilS,-i__l_'ri_-},13iT"l,-'(_,iiT£&r " V,TT'AT,-B._,_ B(i ,.-B_), Cl. * 1971 ah Orteklren, L. G., "StirlinqEngine Activi.ties at Llnite.d Stirling (Sweden),"TechnicalRe_ort'ofthe Conf. on Low PollutionPower Sxstems Dev_op-"p'_'-E', Ei1-1-c_i()v_Ce'n_., [Nethe-Tie-r_-'an'd_-, ]_ebr-ua'rT_ 1-97-i_ Chapter vi-I___I-_'-'B.%C{_, B_, Cl, El. * 1971 ai "Developingthe StirlingEngine,"AutomotiveDesjg!lEn!gn]_g., (British), pp. 57-58, October, 1971. AO. - " 1971 aj
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' 3 _" " Kim, J. C. , and qvale _ E. B., "Analytical anti,Experimental Studies o.f Compact Wire-Screen Heat Exchanger," Advances in Crvoqenic Enqn_q., Vol. 16, pp. 302-311, 193_I. DI5, E6. -_ ...................
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Kim, J. C., Qvale, E. B., and Helmer, W, A., "Apparatus for Studies of Reqenerators and Heat Exchangers for Pulse Tube, Vuillemier, and. Stifling-Type Refrigerators, 8th International Congress of Refrigeration, Paper No. 1:46, August,-_-_.9711. C3,. DI5. _ "Low Pollution
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1971 am Sherman, A. "Mathematical Analysis of a Vuilleumier Refrigerator," ASMEPape_ No. 71-WA/HT-33, Nov. 28-Dec. 2, 1971. Bl, D3.. * 1971 an , ., i ,
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Rios, P, A., "An .Approximate Solution to the Shuttle Heat-Transfer Losses in a Reciprocatinq Machine," Jou)_!_al of Eng.ineerinq fo_ Power, pp_. 177-182, April, 1971. DI5. *---
1971 ao Johnston,R. P. and White, M A '!Simulation of An Artificial Heart Systen," MDACPape_tNo. WD1589, April, 1971. 83, 87, _ 89, C4, D2. * 1971 ap West, C., "The Fluidyne Heat. Engine,'" AERERe__.9.rtNo. AFRE- R 6775, 1971 C4, D2, DlO, E3. * 1971 aq
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1971 at- Wilkins G., "Hot Air E,._qine Runs Quietly and Cleanly Illustrated, pp. 68-71, October, Ig71. AO. *
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1971 as
.,,
" Mechanix
Hinton, M. G., Jr., i.ura, T., Roessler, W. LI., and Sampson, H. T., "Exhaust Emission Characteristics of Hybrid Heat Engine/Electric Vei_icles," SAE.P;_!_e]L 710825, October _,,-_. -_ _}, 1971. C1.
i971 at Neelen, G. T. M,, "PrecisionCasting.is Advance the Develop,lent of the Stirlin!l Engine,"Giesserei,Vol. 5_I,No. 7, pp. 166-170, April 8, 1971. Dl_'.
i i i
.i..
_I_ |: ",1_
i
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_
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L
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"
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1971 au Za_larias,D, F., "Der Stirlingmotorfdr Aufgabender MeerestecIlnik," Sonderdruckaus der Zeitschrif.t Schiffestechnikheft '.1?,.May, 197.1, Pp. 39-45,.Cl.*
'i "
1971 av Organ,A. J., "TileStirlingCycle Regenera.tive Thermal Machineas a Low--Pollution Prime Mover,.!' InstitutoTecnolo_co de Aeronautica, Sao Jose dos Campos,Sao PauoI-6_'-, B_'_il_'l-971-T AO." 1971 aw Vacant
i
_ 1
';
-
"
1971 ax
Vacant ......
.--
1971 ay
Buck, K. E., "Artficial Heart Pumping System Powered by a Modified StirlingCycle Engine-Compressor Having a Freely Reciprocable Displacer Piston," United-States Patent 3,597,766,...August, 1971.. .... C4, B7, Bg. *
197-Iaz Bazinet,G. D., Faeser,-R.. J., Hoffman,L. C., Mercer, S. D., and Rudnicki,M. I., "Developmentand Evaluationof a Modified.StirlingCycle Engine,"AerojetLiQuid Rocket CO..,Semi-AnnualRept_, No. PHS-71-2488,Jmle-November,1971. A3, B2,-B7, C4.
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1971 ba Martini,W. R., "ImplantedEnergyConversionSystem,.'.' MDAC Annual Report,No. PH43-67-1408-4,July 8, 197D-July7, 1971. A3, C3, D8,...E3.. * 1971 bb Meltzer,J., and.Lapedes,D., "HybridHeat Engine/ElectricSystems Study," AerospaceCorp. , Final.Rept., Volume l: Sections.ltilrough
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13, No. TOR-OOSg-(6769-Ol).-2-Vol.-l, June 1970-June1971. Dl-
k_
_;_i !,_'i _!
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1971 bc "Developingthe Stir.ling Engine,,' AutomotiveDesignE_gi.ngering, pp. 57-58.,October.1971. Cl, * _97.1bd "ExternalCombustionEnginesCut Noise and Air Pollution,"DesignEnn_na_, (London),pp..66-68,April 1971. Cl. * 1971.be Zimmerm._n., F..j., and Longsworth,R. C-.,"ShuttleHeat Transfer," Advancesin CryogenicEngineer.ing, Vol. 16, pp. 342-351, Plenum Press, 1971. D3, * 1971 bf Leo, B., "Vuill_umierCycle-CryogenicRefrigerationSystem TechnologyReport,"_F..F.I_L-TR-T1-85, DDC NumberAD888992L, Sept., 1971.. Bl-,C3.
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1972 a
Michels, A. P. J., "C.V.S. Test Simulation of a 12_ kw Stirlinfl Passenger Car Engine," IECEC Record No. 729133, pp. ,'_7-5-,°,F_6, 1972. AI, Cl, El, E2, E6. *
1972 b
White, M. A., Martini, W. R., and Gasper, K. A., "A Stirling Engine Piezoelectric (STEPZ) Power Source," 25th Power Sources S_)1]zosium, May, 1972, or MDACPaper WD 1897. B2,"B7, E3, E5, _3-/-_--
1972 c
Hermans, M. L., Uhlemann, H., and Spigt, C. L., "The Combination of a Radioisotopic Heat Source and a Stirling Cycle Conversion System," Power from Radioisotopes Proc., pp. 445-466, 1972. A3._B5, B8, DI.
1972 d
Harmison, L. T., Martini, W. R., Rudnicki, M. I., "Experience with Implanted Radioisotope-Fueled
. I
and Huffman, F. N., ArtiffLial Hearts.,"
'EN_IB/IO, May 29-June Symposium Ii,i_1972. on A3,Power C3, "E3. Second International for Ra,dioisotopes, I_972 e
1972 f
Mott,
Paper
W. E., "The U. S. Atomic.Energy Commission Nuclear-Powered Artificial Heart Programme," Second International Symposium on Power from RadioisotoPe s , Paper En/IB/57, May 2G-June I, 1972. A'3, C3, DI. *
"Isotopes Development Programs Pesearch and Development - 1971," Division of Applied Technology, USAEC, Progress Reports and gp-on-s_red Wo-rk, NO.T-TID-4067, _ Feb-F_-y, 1972. A3, B3, B6, B8, C4.
1972 g
Knoos, S., "Method and Device for Hot Gas Engine or Gas Refrigeration Machine," Uni ted States Patent 3, 698,182, Oct. 17, 1972. B3, B6, B8, C3. *
1972 h
Harmison, L. T., "Totally Implantable Nuclear Heart," Nati ona_l_____d_l_l]_S_i2i_t,££_;:,
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.H_alth,
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1972.
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Heart Assist and Artificial N a_tio_na.lL_l_n_s titute of
C4.
1972 i
Walker, G., and Wan, W. K.•, "Heat,.Transfer and Fluid-Friction Characteristics of Dense-Mesh Wire Screen at Cryogenic Temperatures,."Proc. 4th Int. Cryogenic Engng.. Conf., Eindhoven,.Netherlands, 1972.
1972 j
Walker, G., "Stirling Engines for Isotope Int. Conf. on Power from Radioisotopes, A3, B6, BT, BS, Bg, D2. *
1972 k
Andrus, S. R., Bazinet, G. D., Faeser, R. J_, Hoffman, L. C., and Rudnicki, M. I., "Development and Evaluation of a Modified StirlingCycle Heart Engine," Ae.rg_,i_etl__iqu]_cL_E_o_ckP._t._Co., Semi-Annual Rept.. No. PHS-71-2488, December 1971-May 1972. A3, B2, B7, C4.
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1972 1
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Norman, J. C., Circulatory E3, *
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L. T., and Huffnlan, F. N., "Nuclear-Fueled '_ Systems, II _rch. Surg., Vol. I05. Oct. 19/" .... A3,
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i!
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1972 t
BDrgan, N. I-., Liqueflels,
"Ana.lysis Air
and lh'elimillary
ForCe l:li_ht
AFFDL-II_-71-171_:I_']3_S'_.
Desi.qn of All'borne Air
Dvnamics
Laboratory,
T'.£f2,- i_l-.-iLT,-C_,-lil.
Repo_'t No.
*
i
'
1972 u
1
1972 v
Finkelstein,
I.,
"Computer
Analysis
of Stifling
[n.qines.,"
G,,2, pp, '269-
Bjerklie, ,I. W., "Comparison of Co._ Cycles for Automotive Power Plants," IIzI;LC Record, Paper No. 729135_ pp. ,_]96-904, 197'2. i".l, DI.._. * . ................
!
1972. w
., _
I'}.7_" x
W,n'd, E. J., Sprig_js, ,I. 0., and Varney, F. hi., "New Prime Movers for Gl'ound Trallspo|'tatioll - I..OWl'ollution, Low Fuel l'onsni_Iption," IECEC-Recm'd, Paper No, 7791,l_, pp. 1013--1021, I,'7_',,.. C1 , I-2, [6.
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Beale, W. T. , "St.irliml . Cvcle_Tvpe Thermal [li-wIce Si_.l'vo I'II1111_," tlni_.ed . , States Patonl....,l,645,649, l.eb. ;"_,. ,,_.._,,e-,._ I,,_," B<,".Bg, t'4, * ]
1972 y ! I i
1972 ;"
197;!, --",L._ BT, lh_. * ."Free Piston l;ngine lh'iven Gas Fired Air Conditioner,"
!l_ILi_o!Iniypj'sity,
Riha, F. J.. "llevelolmlent oi: l.om.l-l.ife, lligh-Capacity Vuilleumier Refrigeration System for Space. Application._," "Part I11 - Refrigeralor Pesign and lhenl_al Analysos,!' A.I-_I-IIL_ !!LtjV'.i]IL !__ej, t.,, August lqTI-March
1'_7'
B1 t,,"
i
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i
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1
1972 aa _:_.
,,
,
L
"Ford l_uys License for Old Stirlinq Enpine, Eventual t.oFight Pollution," _all Stj'_eet_]ou_"n_a _, 1972.
Use Is Possible CI. *
1972 ab. "Ford Siqns Licensin!lPact to D_welop Stirlinq En_]ine,"AMM/M_N, Atlgust14, .1972. Cl, * 1972 ac
i_i ,,;-!
1972 ad In?2 ae
....
1972 af
: ._ •. ._ ,
"Ford Will August
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Dutch Partner,"
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Engine Driven Inertia Compressor for Gas Fired Air Conditioninq Conf. on Nat. Gas Res. 2nd Prec., SessionStifling III, Beale, W. T.,.Rauch, J. S., and and Technol., Lewis, R.S., "Free-Piston Paper 5, Jun_ 5-?,- 1-972. B9. K_euer,.. R., Persen, K., Stephan, A., Gass, J., Villard, J. C., Marinet, D., Solente, P., Wul.ff, H. W. L., Claudet G;, Verdier, J., Mihnheer, A., Danilov, I. B., Kovatchev, V. T., Parulekar, B.B., and Narayankhedkar, K. G., "_nter_ Cryq.g.eni_c__EE_1_in_g Conference, 'l 4th Proc.,.May 24-26,..1972. C3.
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Crouthamel, M. S., and Slielpuk, B., "A Combustion-Heated, Thermally Actuated Vuilleumier Refrigerator," Gryogenic Engoq, Conf.,.
pp,
1922 ag........ Schirmer, R. M., LaPointe, C. W., Schultz, W. L., Sawyer, R. F., Norster, E R., Lefebw'e, A. H., Grobman, J.. S , Breen, B.P., Bahr., D..W., Wad_, W. R., and Cornelius, W., "Emissions f_om Continuous Combustion Systems," Prec., svm.p.,Plen_ Press, 1972. E7 _ °
_
1972 ah
Asselman, G. A. A., Mulder, J.., and Meijer, R. J., "A High Performance Radiator," IECEC Recot'd729132, p. 865-874, 1.972. Dl7, Ell. *
1972 ai
Gipps, G. de V., between.page
"Mac!_ine for Many Purposes," 8 and 13, March, 1972. AO.
Austrailias
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!i
i "
EncI.. 5 pages
Inst. Mech. Engng., (Londo_), Prec. Vol. 186, Pap. II/72 for meeting March 13, 1972. AO, CI. .......................... I
1972 ak aj 1972
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I
Estes, E. W. M.,R.,"Alternative Plants Purposes," Martini, Riggle, P., Power Harmison, L. for T., Automotive "Radioisotope-Fueled
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StirlingEngine Artificial Heart-System," Nucl. Technol., Vol. 13, No. 2, pp. 194-208, Feb., 1972. A3, A6, B,_-_"_4. * _i
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1972 al
Buck, K. E., "Modified Stirling Cycle Engine-Compressor Having a Freely Reciprocable Displacer Piston," UnitecLStates Patent 3,678,686, July 25,39]2. B2. * -
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1972 am
"Final Engineeri_g Report on the Design and Development "ofTwo Miniature. Cryogenic Refrigerators," .T2_,_a__s___l__Ls_t_r_u_9_L_L____!1_., Rept. No. DAAK02-73-C-0495, June 1972. C3.
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1972 ar
Fryer,• B. C., "Desim_, . Lonstluctlon:,and " ' ' Testin.qof , a New Valved, Hot-Gas Engine-," D.Sc, Thesis, N,I,T,, October, 1972, B5, B$, E3... *
19Z3 a
Alto, C. t_.. S., Carlqvist, S. G., Kuhlmann, P. F., Silverqvist, k. H., and ,.acha_las, F. A., "Environmental Characterist.ics of Stifling Engines and their Present State of Development in Germm\v and. Sweden,'*lOth Inter. Co_)q.q_.on Combust.ion..En>_.lines, Paper No. 28,
1973 b
Bealo, W., Holmes, W.-,Lewis, S., and Cheng, r "Free-Piston St.irling Engines -- A lh'oslress Report," Soc. of Auto. E_ys., Paper No, 730647,
_
.
•
.: , _"' _:
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,
_.
_
June,l.,.,.-IL_,'I_7, Bg,c4,C71-_)-G-T_-g71,_l_,-1%i,_-o, El2 E3. *
_.I_ ._ --
1973 c ..win I!eukeringH. C. J., and Fokker, H., "WherePhilips Stands on.the Stirlin_lEngine - I," Automot..i.y_,.[n_n_l. Vol, 81, No. 7, pp. 37-43,. July. IbT_ AI AS, A6\-_._TB3, B6,-I_ C1 [4, E6, E5, E3 Ell F.12, * 1973 d
van..,l_eukering, Ii.II.J., and I'okker,H., "PresentState-ef-the-A_'t of the Philips Sti_ilimlEngine," Soc. of Auto. En_rs., Paper No. 730646
1973 e
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"
[:n_ine," "
' (.ombustion Engine " .......................
Prom'_,_, .pp _= .....
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44-47
;
1973 f- l.udvi_.isen, k.. "Sti_'lin,_ En_line,"Road and lrack, Vol. 24
No. 7
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1973 g
Norby_., J. B., and Dumle, J., "Ford's Gamnle -- Stirlin(l-Cycle Fnqine Promises Low Einission._ Without Add-Ons," .Pp__ul_ai_S_:.ig!Lc_., PP. 77-75, & 154, Feb.-1973. C1 *
1973 h
Postma, N. P., van Gie._sel, R., and Reinink, F., "The Stifling Engine for Passenger Car Application," Soc. of Auto. Engr_s., Paper No. 730648, June, 1973. AI,.B3, B6, B8, CI, E3, E6. *-
1973 i
Walker, G.,."Stirling Engines," yon Karmen Institute for Fluid Dynam.i.cs, Lecture Series 53, Brussels,-1973,_'-_sind-lar to igT-3=j-)
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_"" i_F _:"
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i
1973 1
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Kim, J. C., "An Analytical and Experimental Study of Flow Friction Characteristics for Periodically Reversing Flow," ASMEPaep_ez_, No,. 73-WA/FE-13, pp. I-8, 1973. D4,.DI5, E9.... * for Stirling Engines with Walker, G., "Optimum Design Configuration Two-Phase Two-ComponentWorking Fluids," ASMEPaper No. 7-WA/DGP-I, 1973. D2, DI8 *
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1973 in
"
1973 n
Walker,_ G., "The Stirling Engine," Scientific No. 2, .pp. 80-87, August, 1973. 'Cl • *
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1973 o
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1973 p
Benson,G. M., "ThermalOscillators,"IECEC Record No. 739076,pp. 182189, 1973. B3, B7, Bg,.C3, C7, D2",D9. *
:_
1973 q
White, M. A., "Proof-Of-Pri.nciple Investigate, on of 300.W(E)Stirling.......... Engine Piezoelectric(Stepz)Genera.tor," MDAC Final Report, No. MDC G4420, September,1973. C7, D3, D7, DS, Dg, E5, E3. *
1973 r
Moise, J. C., Rudnicki,M. I ., and Faeser, R.J., "Developmentof a The_ocompressorPower System for ImplantableArtificialHeart Application,"IECEC RecordNo. 739152,pp. 51'I-535, 1973. B2, C4, E3. *
',_ ' i
_1973
i'_ "! .,!_ :,
s---Lia,T. A., and Lagerqvi.st, R. S. G., "StirlingEngine with UnconventionalHeating System,"IECEC Record No. 739073,pp. 165......... 173, 1.973. Dl4, Dl6. *
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American, Vol. 229,
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1973.u
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I]., "Theoretical and Experimental Pe_-'fo_ll_ance hi the I_,al_, -Free Piston Stirlin!l End.line," IECI'C Record No. 739[1._'1.4. ,. pp. 5_3-587, 1_73. 1_7, Bq, D2. *
1973 v
Walker, G., "Stirlin.q_Engine _!_E_CEC t3ecord No. 739037,
1973 w
Fei_lenbutz, I.. V., Griffith, W. R., llinderman, J. D., Mart-ini, W. R., and Perrone, R. E., "A Stirliml Engine Approach to an Implantable Nuclear Heart-Assist. System," IECEC Record No. 739137, Ill) . 441-448,
Power Sul_plies for Remote Llnattended pp. 594-600, 1973. C7, [)1. *
Sito._,"
1973. c.4, E3.*
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1973 x .....Jaspers, H. A•, and Du Pre, F. K., "Stirlinq Engine Design Studies of an Llnderwater Power System and a-Total Enerqy System," IECEC Record No. 739035, pp. 588-593, ].__.73.: A7, C6. * 1973 y
Zacharias, .F.A.., "Unique Requirements for the Cooperation of Computation and Design in the Development of Stirling Engines," yon Karman Inst. for Fluid_ Dy]!am_i_c_s_, Lecture Series 53, Feb. 12-16, 19T. --A=l_, B5, Cl ,. Ug, L)I4• *"
1973 z
Umarov, G. Ya., Tursunbaev, I. A., Lashkareva, T. P., and Trukhov, "Influence of Regenerator Efficiency on the The_nal Efficiency Stlrling Engine Qynamic Energy Converter," Gel.ictekhnika, Vol. No. 3, pp....58-61,. 1973. D3. *
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1973 ab
I 1973 ac
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V..S•, o£. a 9,
I
Medvedev, E. M., Murinets-Markevich, B. N., and Nosov, M.E., "Microrefrigerator w_th Opposed Compressor and Expander," Khim. and Neft. Mashinostr.,(USSR), Vol..q,.No. 7, July, 1973• C3.. Hapke,..H.,"The Influence of Flow Pattern and Heat-Transfer in the Heat-Exchanger Unit of Stirling Machines on the Thermodynamic Cycle;" Brennst.-Waen_e-Kraft, (Genl}any), Vol. 25, No. I0, pp. 389 .... 392, 393-& 394, Oc_,ob-e-g,T9-'/-3-. DI4, DI6. _
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Organ, A. J., "Stirling Engine Beats Pollution's Threat:,'l..._ .E__!_ineer, Vol 43 No 6_ May, Iq73 C1 *
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,
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1973 ad, Kuhlmann, P., "Das Kennfeld Des Stirlin_ Motors," Motortech Z__,Vol. 34, No. 6, pp. 135-139, May, 1973. 1973 ae
1973 af
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th_it_,d .';t,1_os
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1,_73
Pd_,_iSOther _.
_. K., "Miniature \"ol 13, No. 3
ql
S>s_,c:,l, '' MDACAnnual
b_Hssions wi4h X,,, 4, pp..,.-.,.,,
Refl'i,lm'ators t,p 13.1-1.10
t.he
for Flectro!l_c M,_rch ia",'
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I_);', _ ,IS • .II01"11,
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R. F.,
J,'.,
"Rot'ri,let'at.
R. _tlld Ht'llt_ill N, "1 Combustion LIh_ines,"
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"Pllt'U,lati_"
k'O,Ipr_'s'_or," B3 '
UNited '
St il'I
_tates
illq
ion Svstou,_... for
lr,msport
S,\t"C_x%,,_rati_c Spot. Publ. _ual>si'_ SP-3"O,
k'>Cl_'
l"atent
L'OOl_q'
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NOll-L'Olltdlllil1,1t
October,
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I,_73 ,It
A,,Irus, _., Faeser, R. J., Moise, J., Hoffman, L. 0., and Rudnicki, M.I., "llevelopillent and Ev,._lu;_tion of a Stirling Cycle Ener_ly tonversion System," Ae_ojet L.iquid Rocket Co., Rept. PHS-73-2930, July, !973. A3, B2, B7, C3.
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Arkharov, A. M., Bondarenko, L. b., and kuznetson, B. G., "The Calculacion of (Piston) Gas Ret'rigeratingMachines and Heat _,_Qi,1_s " Fore.iqn Tech. Div Wri_.lht-Patterson AFB, No FTD-HT_.-O._bO-,., June 5, 1973. C3 D2.
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1973, av ,
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"
Sergeev, P. V., and Sllmerelzon, Ya. F., "Synthesis of Mechanisms of Rllombic Drives for Machines Operating on the Stirling Cycle," Foreign Tech. Div., Wright-Patterson AFB, No. FTD-HT-23-533-73, D2. May 24, 1 q.7_, " Feurer, B., Dmqree. of Freedom in the Layout of Stifling __Lg.LLK__rnlan Inst. for Fluid Dynamics, Lecture Series 1973. D3. * "Evaluation
of Practicability
of a Radioisotope
Engines 53, Feb. 12-16,
Thel_l_al Converter
t
for
b
!. .
a_', and Artificial I! Final 1973 ay
....
Westinqhouse Electric Corp., _3-'_'-_3, C2___-_'-E_3.-_E-4.
Fryer, B. C., and Smith, J. L., Jr., "Design, Construction, of a New Valved, Hot-Gas Engine," IECEC Record 739074, I_.,._. BS, B,<, Pll, E3. *
| i
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Daniels, A., "The Stifling Engine as a Total Energy Mover," Phili]_s Laboratories, 1974. E3. *
'i
1974 c
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*
Syste_l_ Prime
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_;
I
Sept.
Nov. ,_-,q.-Y_7:4-.-i_.i,"_).i_-3/-_--
I _
I •,:
_Time, p. 61,
,
and Testing pp. 174-181,
"A Stifling
'_
Perfonl}ance,"
Phase I *
1974 a
.,
D.
"New Stirlinq-L:ycle
llt, at " I__oJ)ul>___:..Syi>,)_y_, pp. 1974 F
Zero-Pollut-ion "
"
Car Runs o, Stoi'ed
148, June,
1974
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Cooke-Yarborou!lh, E. H., "A New The_o-Mechanical Generator frem , I ," S.cifn_tl f-ic _an>i_Tecl_lilic_l__ (_L_b,',Ne)vs .....Sg]:v !'._c_e Harwel ., Pect_llber, 1974.
c;,I 7,
I
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Heart Device, Reports, 1973.
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1974 _I
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Cooke-Yarborouqh, E. H., "Thermo-Merhanical .Cenerator: An Efficient Means of Converting Heat to Electricity at Low+Power Levels," Pruc. IEE, Vol. 121, No. 7, pp. 749-751, July, Ig74. C7, B7, +,--,
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Cooke-Yarborough, E. H., "Fatigue Characteristics oi: the Flexing Members of the Harwe11+Thermo-Mechanica_l Generator," Harwell, AERE-R7693, March, 1974. DII. * "
1974 i
C_oke-Yarborough, E• H., "Simplified Expressions_for the Power Output of a Loss_ess Stirling Engine," Harwell AERE-M2437,March,__lg/_4__ D2. * " '
l
:'I2,._I +_:: ' %
I._7.+`h
+'
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Cooke-Yarborough, E. H., Franklin, E., Geisow, J., Howlett, R., and West, C. D. "The HarWell Thermo-Mechanical Generator," Harwell AERE-R7714,March 1974. B7, B9 C7
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Harkless,L. B., "Demonstrationof AdvancedCryogenicCoolerInfraredDetectorAssembly,"Air Force Flight DynamicsLab., AFFDL-TR-74-15, March, 1974• Bi, C3, "DI, E4, E8, Eg-,+Ei.O. *
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1974 In _ Raetz, K•, "Development and Application
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West, C. D., "AE.+H., New Electrical Power-Source for Howlett,R., Long-Term and Cooke-Yarborough, Franklin,E., Geisow,J., Unattended Operation," Harwell, AERE-R7753, May, 1974. C7. *
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Heating," PTB-FMRB-57, Sep_tember, 1974. D5, DI5. Braunschweig, *
B2, B6 ' B8'+-
!
:++
_,.+'_
.._
_i
1974 n+ Martini' W.R. ' Emigh, S. G • ' White, M• A•, Griffith,W. R.' Hinderman+, J. D., Johnston,R. P., and Perrone,R. E., "Unconventional StirlingEngines+forthe Artificial. Heart Application,"M_D.AC. paper No. WD-2337,August, 1974.or+.+IECEC Record 74911.7, pp. 791-798.C4, E3. *
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1974 o .. i
""
Martini,W. R., De Steese,J._G..,and White, M. A., "How Unconventional Stirling EnginesCan Help ConserveEnergy,"_ No. WD 2336, August,.1974 ,orIECEC Record 749151,pp. 1092-1099,1974. B7, B9, C3,-.C4. *
1974 p .... Martini, W, R., "Development and- Evaluazion o,f a Modified StirlingCycle Engine,"MDA.C. quarterlyReport.,No MDC G4438,April, 1974. +. -B7, B9, C4, [{.3. * 1974 q+_ .... E+L_od,H. G., "The FluidyneHeat-Engine:How +o Build One -- How it Works,'! NationalTech. Info. Serv., No. AD/A-O06 367, December, 1974. BT, B9, -C-4, Di+.i* 1974 r
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i
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i i
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IL)'/4 ._.---Mor,l:_h, R. I'.,,rodM,Ir_h,ill. O. W., "Tht,R,t,:_.l ('.l(_ed C,ycl,lh,al; In!llno,"IIit'It', Record,Nn.-14_Ib.i, Pl).II17_11'J4, 'ILW4.I_14,DIG. * ' i
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. :, '
:'
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Slirllml
InLim,
I",lvl_l"ed,'l I.A...lime-,•
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llhlelll,lnll, I1., ,_pi_r(.-,C. I.., and Ilori,ans., M. I..., "The Collll_inal ion oI" a S-I:i rlin, In_lil!e wiIh Retool e!"yPlacod Ileat' Sourco," T[(GI!_. Record• No, 7,19tl!d q ppL._ l;:'ll'-_i;_/• 1974• A4 • tit.I)14 e "_ _
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1974 v
I_rank, G.,. Keller, t1., PIiI;,, W., I_ichter, C., Schnrid, I'., and v. Relh,. R. I1., "An Imt_lantable lhermal Converl:ei_ as Power Soul:ce For an Art.:ificial Ileart,!' II'ClC Record• No. 74911.5, Pp. 775-7_1, lq74. C4, Ira. '_ ..........
I,<174 w
Pouchot,W. D, and l_aniels, A., "NuclearArl:ific'..ial llearl. Bench " . '.-7. t, I_17.4. C4, E3.. * Model-, _!;_C!_C_!_,o_'Oy.d, No 749116.pp. 7,g _ ql
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I_174,x Moise, J. C.,.F;_eser, R. J., and Rudnicki,M. I., "Sl;aI:us oF a lhermocompressor-Powered h,planlableArtificialIlearlSvstenl," II!Cl_C.Rgc.o.i'd ....No. 7491I,'_, IM. 7mi-,g(14, 1074. B2., (,4. *
i
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Shel puk, 11., "A So'lar Vui I I eumier System," Wor..ksh_)p.]")'_c. SQl_i!'.Cn_oli.!i_j. for zl_uildin_Js ..... • NSF-RA-N-74..063, Feb. I_174_ I_'l t'3. *-
1974 .'
llakansson, S. A, S., "lleat 17xchan_lersFor. Sfirliml Cw'le Enflines," Unil:ed SLates Palent 3,,'_34,4!,5,..SepI:', lO, 1974. M.I. *
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Andersen, N. I!., and Qw_le, I_., "Model For Tnst:al'lonar Stro,lning .T W_rnlevekslel' for Stirl i m.lmotor," .L.aboratoriet for Ener_i_.knik, _lune 1974. I14. *
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"New l'hel_llo-Mechantc,_l Gonerator from ilarwell," )leat and Air Cond. ,.lo_lr., Vol 43, No !,15 October, 1!17,I B3 BT, Bg, C7
.._
a .
.. ,
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s' . .es ".,..., :
E., Franklin,
._"
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"'_',; .. :"
E., i_:isow, O., lloi_lett,
Compact
R., ,rod West• C.,
S,Vmposiun,/triqhton, Sus,.;c_x,t:[n_ll,uid, Rese,lrch alld Dew,lop. in NonMet:h
') i
i
1._1'/ilae
II,Irtlev, 0., "Stlrlln_l Set tor l{IBtl," Aul.onlolive llesi_n.l-ngng., t'P. ;'.7 & ;.'>D_Sept:. 191,1. A1, I_!,, Bi_,"i:3..7.;;..._" .......
l'll4.al
"lhelllill-l_let'hJntc,ll
AI, CI.
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Vol.
13,
No. n, Sepl. lnt4.
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1974 ag-Hartley, J., Engine,"
:
I L/1-_'; _ _ _
19/4 all
Amann, C. A., "Why the Piston Engine No. 5, Feb. 21, 1974. Cl. *
1974 ai
Boltz, C. L., "New Research Work Regarding an Old Machine," Antriebstechnik, Germany, Vol. 13, No. 3,4, March-April, .
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AO. Lefebvre, A. H. "Pollution Control in Continuous Combustion Engines, Symp. on Combust. - 15th Int. Prec., pp. 1169-1180, Aug. 25'31, 1974. FI. II
.....
i
1974 al
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Rochelle, P., and Andrejewski, J., "Optimizing Maximum Efficiency CYcles," Rev. Inst. Fr. Pet. Ann. Combust. Li.cL., Vol. 29, No. 5,.pp. 731-749, Sept.-Oct 1974. D2
In_trum. Exp. Tech., Vol. 17, No. 3, Part 2, pp. 795-798, June, 1974. C3, 1974 am Minaichev, V. E., and Zykov, V. M. "Cryocondensation Booster
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1974 an ......
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1974 ak -Blinov, I. G., and Minaichev, V. E., "Condensation, Cryopump with Independent Cryogenerator," 6th Prec. Int. Vac_,_Congr.,pp. I01-I04, March 25-29, 1974. C3.
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i
E !
i_
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Brogan, J., "Developments in Power for Transportation," ASMEJ-. Annual Symp., 14th Prec.: pp. Systems 45-57, Feb_ 28-Mar. I, 1974.
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1974 ao
Walker, G., "Stirling Cycle Cooling Engine with Two-Phase, Two-Component Work-ingFluid," Cryogenics, Vol. 14, No. 8, pp. 459-462, August, 1974..C3, D2, Dl8. *
,
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' _:! 'I_
1974 ap. Penn, A. W., "Small Electrical Power Sources,!'Phys. Technol., Vol. 5, No. 2, pp. 115-140, 1974. DI.
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_,i
1974.aq
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Longsworth, B. C., "Split Stirling Cycle Cryogenic Refr.igerator,"Air Products and Chemicals Inc., Final Tech. Rept., No. DAAK02-72-C-0316, 1-973--I Richardson, 9-74=.c3" R. W., "Automotive --Engines for the 1980's,
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1975 a
Doody, R. D., "Long Life: liigh Capacity Vuilleumier Refrigerator for Space Applications," Air ForceFl_t D_n_s Laboratoq__y_, No. AFFDL-.TR-75-108, Smpt_lT-)erT 1975. BI-,-.DI, E_, E-_. k'-
1975 b
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1975 c
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1975.£
Biermann, U. K. P., "The Lithium/Sulphurhexafluoride Heat Source _. in Combination with a. Stirling Engine as an Environmental Independent Underwater Propulsion System," iECEC Record, No. 759153 pp. 1023-1030, 1975. A7 DI4, D_. "*
1975 g
von Reth., R. D., Haerten, R.,_Nemsmann, U., Henning, E., and Bucherl, E. S., "Development of Power Sources for Blood Pump Applications," IECEC Record, No. 759180, pp. 1214.-1222, 1975. C4. *
1975 h
van der Sluys, W. L. N., "A Lithium/Sodium/Sulphurhexafluoride Heat Source in Combination with a Stirling Engine as a Propulsion System
_
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w_ 2,
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for 1975.Small A7. Submersibles,"
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1975 i..
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_'._
1975 j
Gabrielsson, R. G., and Lia, T. A_, "New Emission Combustors for Stirling Engines," IECEC Record, No. 759139, pp. 927-932, 1975. AI, DI4. *
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1975 k
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1975 l
Cooke-Yarborough, E. H., and Yeats, F. W., "Efficient The;_o-Mechanical Generation of Electricity from the Heat of Radioisotopes," IECEC Record, No. 759150,..pp. 1003-1011, 1975. A3, C7. *
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1975 In
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Spigt, C.. L., and Daniels, A., "The Phillips Stirling Engine: Progress Report," IECEC Record, No. 759138, pp. 919-926,_ CI. *
A
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2_9
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rlli 1975 n
,, 1975 o
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B_ale, W. T., and Rankin, C. F., "A I00 Watt Stirling Electric Generator for Solar or Solid Fuel Heat Sources," IECEC Record, No. 759152, pp. I020-I022, 1975. .A4, A5, B3, B7,-B-9-,--C_.----*-- . Rauch, J. S., "Steady State Analysis of Free-Piston Stirlin.q Dynamics," IECECRecord, No. 759144, pp. 961-965, 1975. D2. *
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7;
1975 p
IYloise, J. C., Rudnicki, M. I., and Faeser, R. J., "Thermocompressor Powered Artificial Heart Assist System, " IECEC Record, No. 759183, pp. 1242-1245, 1975, B2, A3, E3_ *
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1975 q
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W. R., "An Efficient
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1975 r
Johnston, R. P., Noble, J..E., Emigh, S. G., White, M. A., Griffith, W.R,, and Perrone, R, E. , "A Stirling Engine with Hydraulic Power Output for Powering Artificial blear.ts, " IECEC Record, No. 759212 pp. 1448-1455, 1975, A3, 04, B7,.B9, *._
1975 s
Beale, W. T., "A Stirling-Hydrostatic Drive for Small Vehicles," Record, No. 759143, pp. 958-960, 1975. B7, B9, CI. *
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Stephenson, R. R., "Should We Have A NewEnqine?" Jet Propulsion Lab., An Automobile Power Systems Evaluation, Volume_I: :_Te_ch.Rpts., October, 1975 or SAESpec. Publ. SP399, SP4OO,.Vol. I & II, Aug. 1975. B3, B8, CI_ DI, DII; *
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IECEC
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/
1975 u
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1975 v
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a Modif-ied Stirling
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Scott, D., "Flame-PoweredPush-PullGeneratorRuns a Year Without Maintenance,.Refueling," Popular...Science, Feb.1975. Al, B7, B9, C7. *
1975 aa "BritishDevice Runs TV on .PropaneGas," New YorkTime_, June 12, 1975..... C/: * _1
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30O
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1975 x
, ;_ ;;;>
I.,
Engines," Los Angeles Times, Sept. 4, 197-5. CI.
.,.
.L_.
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1975ab
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'
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Pouchot,W. D., Bifano,N. J., and H_nson,J. P., "ArtificialHeart System ThermalConverterand Blood Pump ComponentResearchand Development,,IECEC Record,No. 759181,pp. 1223-1231,1975. A3, B6, B8, C4. *
1975 ac Creuthamel,M. S., and Shelpuk,B., "RegenerativeGas CycleAir ConditioningUsing Solar Energy,"AdvancedTechnology• Laboratories, No..ATL-CR-Z5.-.IO, August, 1975. A4, BI, C3,..D3,Dl4, DIS, DI6. * 1975ad •
Scott, D., "Stir.ling-Cycle Liquid-PistonEnginewith no Moving Parts," Popular. Science,January,.197.5-. B7,.B9, C4. *
1975 ae Kettler,J. R., "The Thermal Vehicle-.A PollutionFree Concept," IECECRecord__ No, 759084,pp. 548-553,.1975,.A6,Cl. *
,
;]
1975 af Summers,J. L,, "Hot Gas Machine,,' United State_ Patent 3,879,945 April 29, 1975. B3, BS, B6, B8','C3.''* ' " '
._ ,
1975 ag Martini,W. R., "The Free-Displacer, Free-PistonStirlingEngine -PotentialEnergy Conserver,!' IECEC Record, No. 759149,pp._9951002,=.1975.D3. *,
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1975 ah Higa_W. H., ."StirlingCycle Engineand RefrigerationSy.s.tems," Patent App.l.ication., May, 1975. C3. *
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1975 ai Hagen•,K. G., Ruggles,A.-E., Fam,.S.S., and Torti,V. A., "Annulari, Tidal RegeneratorEngine for NuclearCirculatorySupportSystems, IECEC Record,No. 759182,pp. 1232-1241,1975. A3, B4,,.B6,B9, C4,'D2,'E3. *
"i +_, ,!
1975aj ;
Grigorenko,N. M., Savchenko,V. I..,and Prusman,Yu, 0., "Resul-ts. of Test of a.Heat,-Using CryogenicMachine,"Khim. and Neft. Mashinostr,
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U.S.S.R.,Vol. II, No, 9,.September,197E. C3, E3. 1975-ak Lyapin,V. I;, Prusman,Yu. 0., and Bakhnev,V. G., "Effectof Efficiency of the End Heat Exchangeron the Start-Up Period.ofa Helium Cooler," Khim. and Neft. Mashinostr,U.S.S,R.,Vol. ii, No. 9, September, 1975.. C3, ET.
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1975 al Finkelstein,T., "computer. Analysis_ofStirling Engines,"Advances in CryggenicEngineering,Vol. 20, pp. 269-282,1975 or._.IECEC Record
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1975 am Bjerklie_J.W., Cairns,E. J , Tobias,C. W., and Wilson, D. G.,. "AlternativePower Sourcesfor Low EmissionAutomobiles," Automotive-.Eng., Vol. 83, No. lO,_Oct.,1975, or SAE Paper 750929,
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1975 an Bougard,J., "Importanceof DrivingM_chanismin Stifling Engines," Rev. "M., Belgium,Vol. 21, No. 2, June, 1975. B6, B8.
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1975 ap Mortinler, J., "Low Cost, Long Life (Stirling)Sngine May be Ideal for the Third World," Enginee.r, Vol. 240, No. 6208, March, 1975. B2, B5, B6, B8. * 1975--aqWilson, S. S., "PossibleDevelopmentsin Transportation," Aspectsof Energy Convers.,Proc. of a.Summer School,LincolnColl.,?bx-ford _, E-_i., JT_TyTT.4T25, _1975,.c1.
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1975 au Andrus, S., Faeser,R. J., Moise, J., Hoffman, L. C., and Rudnicki,M.E., "Development and Evaluation of a Stirling Powered Cardiac Assist System," Aeroj_et Liquid Rocket Co., Annual Rept. No. NOI-HV-3-2930, May, 1974-June,1975. A3, B2, B7, C4. ".: 1975 av Biryukov,V. I.,.and Sergeev,P. V., "Synthesisof.Three-Parameter ,,. ...... Mechanismsof the RhombicDrive of a Stirling Engine,"Izv Vyssh _-i Uchevn Zaved Mashinost% No. II, pp. 70-76, 1975.. B6, B_
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1975 aw Shah, R. K ° ' "A Correlationfor LongitudinalHeat ConductionEffects in Periodic-FlowHeatExchangers,"Journalof Engineeringfor _Power,pp. 453-454,July, 1975. OlS. _ 1975 ax Mott, W. E., "NuclearPower for the ArtificialHeart," Biomater. Med Dev Artif, Organs,Vol 3, No. 2, pp. 181-191,197_. A3, C4._-1975 ay .
Balas, C., Jr., "Desiqn. and Fabricationof a RhombicDr.iveStirling Cycle CryogenicRefrigerator,"Phil_i__s__Labs Final Rept. No, DAAK0272-C-0224,April, 1975. B3, B_ .
1975 az Carlqvist,S. G., Lia, T., and Lundholm,G, S. K., "Stirl_ing Engines: Their PotentialUse in CommercialVehiclesand Their Impact on Fuel Utilization,"Inst....Mech. En_., Paper C4/75, pp. 35-46, 1975. Dl. * 1975-ha Smith, L., Sandquist,G., O.Isen,D. B., Arnett, G., Gentry,S., and Kolff,W. J., "Power Requirementsfor the-A.E.C.., ArtificialHeart," Trans. Amer. Soc. Artif. Int. O.r_ans, Vol. XXl,.pp.540-544, 1975,_A3, B2, C4. *
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,I
.!: _! .r/,. ! i,._! L
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1976 ap Garbuny, M., and Pechersky, M. J., "Optimization of Engines Operated Remotely by Laser Power," Conf. on Laser Energy Conversion, NASA SP--,395,pp. 173-180, 1976. A7, D2, DI8.. * ..................
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1.9.76aq Andrus, 5., Carriker, W., Faeser, R. J., Helwig,. J. W,,. and Hoffman, L.C., "Development and Evaluation of a Pneumatic Left Ventricle Assist System_" Aerojet Liquid Rocket Co._ Rept. No. 9280-430-76, May,. 1976. A3, B2_ B7, C4. 1976 ar
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Johnston, R. P., Bakker,.L.P., Bennett, A., Blair, C. R., and Emigh, S. G., "Implanted .Energy Conversion System," McDonnell Douglas Astronautics Co., Annual Rept. No. MDC-G4448,May i, 1975-JUne-30,-l_976. C3,. DI, E3, El3. *
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Umarov, G. IA., Trukhov, V. S,,.Tursenbaev, I. A., and Orunov, B, B.,."Methodof OptimizingHeat Exchangersfor a Stifling Engine,"Geliotekhnika,No. 6, pp. 18-23.,_i.nRussian),1976. DI4, Dl6.
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A., Emigh, S. G., Griffith, W. R., Noble, White, M-. A., Martini, W. R., and Niccoli,
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1976 ba
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_'i" ..... _:_
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1977 d
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Llrieli,I., F_allis,C. J., and Berchowitz, P. M., "Computer Simulation of Stifling Cycle Machines," IECEC Record 77_)252,pp. 1512:1521, 1977. D4, DIC'..*
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Rallis, C. ,I.,Urieli, I., and I_erchowitz,D. M., "A New I'ortedCon_tani Volume IJxternalIleatSupplivRe!leileratiw, Cvclo," IIC[C Record ' It.1, I,._. If?. * 71o;'.56, pp, 15./.l-l!Lt, ' , 1
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Lehrfeld, [1;, "Pra_'tic,lbilit.v Study of Stirlinq IIt'l-t" 17,1'.,I, pp,'l,,O,i-l"_,ll, l_t';t A.} To,till + , R,,,ort [ ........ i,
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1971 _.1 Ilerchowit.', I1. M., lallis, C. J., and tlrieli, I., "A New l_lathenlatical blodl,1 For Stifling t'yclo Machinl,," IFt't.t" ......... I_l_t'Ill'd.. "'}_'l'_i'14. ... , pp. l"_,.-.... 1527, 1'!77. 11;7,BS, * 1977 h
Martini, W. R., Hauser,.S.G., and Martini, M. W., "t[xperimeltal and Colnpu.tatiolia} [v,tluations of [Sot!lernlali;'ed Stirliuq {llqin_s .... I_l__t'.FJ_rj 779;]50, pp. 1496-150., , 1977. b.. Ba,. B6, B,,, t.,, C5, Ea.* _.i
1977 i
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1
Rosenq¢ist, N, K. G., (itllllilleSSOil, .¢. G,., alld Ltiildhollll, 7, G, K,, "The Development of a 150 kw (200 llp) Stirlin9 Encline for bledium [l'uty Automotive Application --- A Status Report," SAE Paper No. 770081, February ,,o-March .,o 4, 1977, Al, Ba, ., BS, BT, CI, El, _F3. *
1977 ,i
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koininanditbolaQot, United B.T_'B-.'-C, -_`'--'l,,,tl,..... t.,.'" *
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Fo ,M., "$olar Dome House and Automobile witt_ Self-Colltained [norg.y Sf..stem," January, 1977. A1, C1, C3. t',l, t'5, C7o *
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l_lankenship, C. P., and SchuIz, R. B., "Opportunities in H_e ERDA/NASA t'Olltintious t'olllbination Proptllsion Pl'ogi'aill,'] N.A!SA,IM X-7"3t_9'?. J,lil. 1977. PI3. PlS. tl. t_., ,tlld lltli'kt _, a. A., "D-Cycle Ab,_tracl Potlrtf_ |liter. SVlilp. on At to. 1<177 II,,, P!:,, I_7, P,g, Ill;l, * '
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for Ceramics S),stenls *
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t-tlqino,"
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4pi'il
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1977 t
Cooke-Yarborough, E. 11., "A Data Buoy Powered By A Thermo-Mechanical Generator_: Results of a Year's Operation at Sea," IECEC Record 779230, pp • 1370-1377, 1977• A1 , B7, B9, 83_ E2. *
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....
1977 x
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Johnston,R.P.-,Bennett, A., Emigh,S. G., Griffith,W, R,, Noble-, J,..sE., Perrone,R. E., White, M. A., Martini., W ....R., and Alexander, J_ E., "Stirling/Hydraulic Artificial Heart Power Source," IECEC Record 779016,pp. 104-111,1977• C4. *
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1977..y Boser,,0., "SafetyConsiderationsfor High.Temperature.-Thermal. Energy. Storage in FluorideSal-ts,"IECEC Reco_ 779092,pp. 575-582,1977. A6, DII.
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1977 ac Selcuk,M. K., Wu, Y. C., Moynihan,P I., and Day, F. D., "Solar. Stirling Power Generation; Systems Analysis and Preliminary Tests," Jet Propulsion Laboratory, International Solar Energy SgcietySolar World Conference,Orlan--n'6r6_F'Ci'orida,: June--6-9, 1977. . 1977 ad
Diction, D., B9, Maxwell, B., *and Ward, D, , "A Laboratory Investigation of A4, BT, C7, DI. Seminar a StirlingEngine Driven Heat Pump," 1977 International. 9nH_ eat Transfer in Building_, Dubrovnik, Yugoslavia. AI, C3, E3 * "
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a{_ Ftneq{}ld, (I. G., and Vandm'brufl, 1. G.,."Stirling Enqines for Ilndersea V_qli{:l|,s, Flllal Roport No. 5030-63, Joi: ProL)ul'.,ion I:ahoralsory,
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1977 bm "DOE, Ford Sign. Cost-Sharing Pact For Development of Stirling Engine," Energy Users Report, Bureau of National Affair, No, 218, Pgi.26, bct'o'ber i3:,1977. Cl.. *
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'
.("| _! ..
"Will the stirlingEngine FiaallyGet.Out of the Garage?" ChemicalEngineering,page 57, April 25, 1977. C7.... *....
1977 bp Valentine,.._.., PersonalCommunication,November 23, 1977. E3. *
I i
' 0000 a
Vonk, G., "A New Type of CompactHeat Exchangerwith a High Thermal Efficiency,".Advances in CryogenicEngng.,K-3, pp, 582-589. DIS. *
O000_b_"Applications of CryogenicEquipmentin HydrocarbonProcessingand Transport,"..Pb_ilips Corp__C3. * 0000 c
Zacharias,F. A.,."Advanc_dDevelopmenton Stirling Enginesat MWM." ..... 2nd NATO-CCMSSymposium,Dusseldorf,West Germany,Nov. 4, 1974.
0000 d
"CryogenicEquipment,"Phili_p_s c_CgJLpC3, C4. *
.
_.
I )
-
'
> i
I
i, 7"
i¸
TABLE8,2 P'I
-t
PERSONALAUTHORINDEXTO REFERENCES
'L i
) .
i
Abell, T. W. D., 69 ai
Baumgardner,A. R., 73 al
.._
Agarwal, P. D., 69 j..
Bayley,F. J., 61 a, 61 g, 65 s
;
.,;: .i
, i
Agbi,
iii! _._
Babtunde,
71 k, 73 u, 73 ag
Bazinet,
G. D., 71 az,
72 k.
'
Alexander,J, E., a 77 x Alm, C..B.S._73 Amann, C. A., 74 ah
Beale, William 71 aq, 72.x,T., 72 69 ad,h, 7369 b,ac,.71 73t, g, 75 n, 75 s ,. .......
_._ .i
Ambrosio, A., 66. b
Bell,
),i ._
Ammamchyan, R. G,, 76 ab Andersen,N. E., 74 ab, 76.w
Bender, R. J., 70 n Bennett,.A.,76 as, 76 ay, 77 x
:
Anderson,G. A., 1897a
Benson_ G. M,, 73 p,.77 a, 77 u
),
!! '_.
Anderson, Lars, 13 a Andrejewski, d., 74 al
Ber_chowitz, 77 bq
: _ !,
tF,i
Andrus, "
S.,
72 k, 73 at,
74 au, 75 au,
76 aq
Andrew J.,
Biermann, Bifano,
_ il,
77 c
DavidM.,
77 d, 77 e, 77 g,
U. K. P.,.75_f____ N. J.
,
75.ab
1 !
Anzelius,A., 26 a.
Biryukov,-VnI., 75 av
1
•i_
Arend, P. C., 64 k
Bjerklie,
,
!._
Arkharov,A. M., 73 au
Bla._r,.C.R.,76 as
_ "i
Arnett, G., 75 ba Artiles,A. A., 77 ar
Blankenship,CharlesP., 77 p Bledsoe, J. A., 77 aj
.... _:i
Asselman,G...,A. A ,.72ah, 73 aj, 76 f, Blinov, I G , 74 ak 77 bb Bloem, A. T., 57 h
,'i :,i
Auxer, W. L., 77 w.. Ayres, Robert V., 73 af
Bloemer, J...W.,65u Boelter, L. M. K., 43 a
."
Baas, H. B., 63...r
Boestad,._G., 38 a
Babcock,
Bohr,
E., 48 g J
J.. W., 72_v, 75 am
!
:i
G. H.,
1.885 a
._ ._ I,
i,
Bahnke, G. D , 64 a
Bolt
A., 68 b
''
Bahr, D. W., 72 ag
Boltz,
_-i! _; ._, _i
Bakhnev,V. G., 75 ak Bakker.,L P , 76.as
Bondarenko,L. S..,73 au Bornhorst,W. J., 71 b
:!._ '_
_ _,'.
Balas,Charles, Jr.,_Z5ay, 77 ax
Boser, 0., 77y
, .: |
_
Barker;J. J., 65 r
Bougard,J..,75.an, 75 bc
i i._
C. L., 74 ai
L
t
I
r t..... 7"
: r 1:i I ._iI ,,' ;
t
{
,
I r
,:_r
_
l
I,
l
[ r
}
i j
1
!
'
t
'-_"-
I
' 'r ......
F
,
'"
:-'I
,
•
i
:
'\
_;_
Bourne,
}, i
I
O.,
1878 b
Breazeale,
W. I.,
Coppage, J. E.,
74 k,
74 f,
74 ad,
52 a, 53 a, 56 a
Crandall,
S.'H.,
56 c
Creswick,
F. A.,
57 a, 62 m, 65 a, 68 o
E. S.,. 75 g E.,
68 e, 68 h, 68 j,
69 ak, 70 r-, 71 ay,
J. A.,
69 i, 72 al
Crouthamel,
M..S.,
Damsz, G..., 67 e Daniels, A., 65 v,
77 q
Burn,
K. S.,
76 ax
71 I,
Bush,
J..F..,
74 aa
74 w, 75 m
Bush, Vannevar, 69 aq, Byer,
R. L.,
Cairelli,
70 s 76 ak
El.ton J.,
..
Carlqvist,
:
Carney,
i
Carriker,
I,
Cayley, Cella,
38 b, 38 c, 39 a, 49.a,
James E,,
Cairns,
77 ab,
75 am
S. G., 75 az H. C.,
69 ak
W., 76 aq G., AI,
Chaddock,
1807 m.._ 77 b
D. H.,
77av
I.
B.,
Darling,
G. B.,
Datring,
R.,
...
72 af,
75 ac ,y:
66 I,
71 p, 73 ae,
Danilov,
67 e,
73 ap,
'
69 1
Davis,
Stephen
R.,
51 a, 71 q, 72 r,
77 q
Day, .Frederick
D.,
H., a
Delabar,
77 ac
47b,.48
O.
a, 52 i
G.., 1869 a
de Lange,
Challis,
F. F.,
61 h
den Haan, Jose J. W., 58 i
Chelton,
D. G.,
64 k
Denham, F. R.,
53 b
Denton,
51 d
Leendert,
W. H.,
56 f,
Clapham, , 77 Churchill-, E S. W.,aw61_n
de Steese, J. 67 G., a 74 o Socio, L.,
Codegone-, C., 55 f Claudet, G., 72 ae Colem.]n,_S. J., 71 b
Didion, Davi.d,..77 ad de Wilde de Ligny, J. H., Dineen,, John J., 65 m
Combes, Par M.,
1853 a
.q4 Collins,
77 bh
F. M.,
"
71 t
68 o
68 a
:
.
E. S.,
N, P.,
_--
73 ar
Davoud, J. G.,
de Brey,
74 b,
59 a
John G., 63 h, 63 p
73 ao,
71 h,
72 ae
Daunt,
n^h_,., 77ag
.i
Cheaney,
Chironis,
if-"
....................
74-j,
70 e,
Bucherl,
\
'
74 g, 74 h, 74 i, 75 I, 75 y, 77 t
67 i,
Cornelius, W., 72 ag Cowans, K. W., 68 w
Burke,
_!
65 y
E. H.,
Breen, B. P., 72 ag _.. Brogan, John J., 73 ak, 74 an
69 af,
i "
Cooke-Yarbo_ough,
Bourne, R. J., 77 bg Brainard, D. S., 60 s
Buck, Keith
........
..............
Doering,-R ......D...,.._68x
57 i
.I i
:_
71 e ................
I
,: :
l"lonkin,
'_'_::I ',_
DoOd.V, R. [I., 75 a Dresser, 11. [ 60 b
_]i
Dros,.A.A.,
,,
:
_...,I
" i i '
_)iLi: _<,# _i'::]
i
Brian,
11 /,
•
Iine_told, Finkelstein, 60 j
_
51 f,
65 b, 66--k
5;> I:, 56 b, 57 k,
Frits
66 I,
Fisher,
71 I,
Eckerth, Edwards
1869 b P A 61 a
Eibling,
J. A.,
[fan, 6,_lo,
Flenlinfl,
71 p, 73 y,
Flint,
Jerry,
Plynn,
G.,
73 ap
R. B.,
Fokker, Folsom,
6] e, 65-u,
66 c,
67 b
Ford,
76 d
60 a
_., 73 c, 73 d L. R. 77 ar
H.,._._40a
Porrest, D. L., t_o "" e
Elukhin, N. K., 64 h,.69 ah
Fosdick, R..J....,.76 ae
Emerson,
Frai;:e,
;_ +"_.-_ ....
G., 74 q
D. C.,
Endgh, S. G., 75 t,
5<.l..b
71 i,
75 be,
74 n, 74 av, 76 as,
75 r,
76 _,y, 77 x
DT_
Frank,
"
iV.. E.., 70 b G.,
Fra,lklin,
74 v
Fritz,
E., B.,
74 j,
74 k,
74 ad
1875 a
__ -_'
Engel, Edwin F., 13 a Ericksson, E. A., 1897 a
Fryer, B. C., 68 y, 73 ar-, 73 ay ...... Pumas, C. C., 30 a, 3:_ a
,_.
Ericsson,
Gabrielsson,
_.
John,
1826 a, I
]B,qO b Essex, H.,
:"!i_.]_'_t
Estes, E. M., 72 aj Fabbri, S., 57 b
03 a
R. J.,
13 ,It,, Falil, S. S.,
Garay,
70 r,
71 az,
7b ai
t:arber, [.. A., Farrillgttlll, ll
t
l',lx, I_. tt., toJgenbut,',
Ft)llV't'l', I1,., 7.4 aw
60 ill
72 k,
73 r,
76 aq
Garrett,-K., Gasbai'ovic,
75 ao N
72 q
(,a._s Gasper, J., K. 7;'. A.,ae 72. b
65 o, t_l s h
!,,1 I. cV.,
P_N.,
Garbully, H. ,.7{ _,
74 ,lu, 75 p, 75 all,
t '
}1
75 j
Gamson, B. W., 51 e, 63 b.
_']
Paeser,
R. G.,
i,I tv
Geisow, Gt,iltry,
J., S.,
Gibson, Gifft;rd,
B.W.bl., j ,i, 11., 71 {_._1
65 d
74 ,i, _'4 k, 75 ba
/,lad
60 d, (,.I q, (_,1d, ........
i
d,
62 b
_".,_
t
67 c,.67
74 t
Ell"od,H.
i
t75 c,
I
70 g, 72 u, 75 al
"="i-<;,
_:_.
i
I
46 a, 52 c. 65 v
;7;'". i),_; _. _:_
lheodor, ._,._"' b,.53 c, !,9 c, 61 b, 61 d, (41 e 6;_ a (_.] l
70f,
Karel
70 h,
I
77 ae
_:4 a, 6,1 b, 64 c,
,
Durin, P.J., D. 73 Dtlmle, ,_..75-!, g Du Pre,
,]oSu'l,dl G.,
•
i
'
I
L
i
:
Gipp_,
G.
72 ai
G.lassferd,A.
i
i
Harris,.W.S.,
P. M.., 62 c
Hartley,
70 y,
J.,
74 ae,
"
Hauser, S. G., 11 c, 31 b, 42 a Hausen, H., 29 77 a, 29 Havemann, H. A., 54 a, 55 a, 59 k
Goldwater,
Heffner,
Bruce,
77.b,
77 s
F, E.,
60 a, 63 i,
Goranson, R..B., Gorring, R, L., 6168n c, 68 s, 70 v
Hellingman, Evert, 56 b.. Helmer, W. A., 71 ak
Grashof, F.,.1890 a.
Helwig, J. W., 76 aq Henderson, R E 60 b " "' Henning, E
75 r, 75 be, 76 ay,.77 x Grif_fith,W. R., 73 Green, D. B.,.73 aj w, 74 n, 74-av, Grigorenko, N. M., 75 aj, 75 as Grobman, J. S,,
72 ag
Grossman, D. G., 77 o F.,
Guilman,
I ....I.,
76 ab
Hinderman,
G.,
Hinton,
R.,
73 aq
77 i
75.g ....
i i ! i i ,,
Hagen, K. G., 71 a, 74 ba, 75 ai Hahnemann,.H., 48 b
i i .: , i
Hallare, B,, 77 bj Halley, J. A.,.58 a Hamerak, K., 71 r
Higa,
Hoess,
W. H.,
Hanold, R. J., 62 g Hanson, J. P., 75 ab Hanson, K, L., 65 k Hapke, H., 73 ab
"..... i!
751bb.
65 n, 75 ah, 76 ar J.
M. G., J. A.,
D.,
73 w, 74 n
71.as,
74 at
68 o, 69 d
Hoffman, L. C...,. 71 az,.72k, 75 au, 76 aq,.77 be Hogan, Walter
Hakansson, Sven Ande.rsSamuel, 74 z
69 f
75 g
Heywood, John B.,
Robert
Haerten,
Jr.,
65 t,
!
.
i, 1
Henriksson, L., 71 z.. Hemans Naeim M."'L., c 7472u r, 73 ao, "" 73 ar Henein, A.,7271-q, ' ' Herschel, J., 1850 a
Guilfoy,
Gummesson, Stig
I
74 ag
Goldberg, Louis F,, 77c Godoy, Juan Vilchez, 14 a Goldowsky, M.., 77 v
Gratch, Serge, 76.ah
.
71 s
H.,
61 h, 63c,
Holmgren,
J. S.,
70 x
Honrbeck,
C. J.,
71 j
73 at, 74 au, 63 s,
64 f
Horn, Stuart B., 73 as Hornton, J-.H., 66e Hougen, J. 0., 51.b Hougen, O. A., 63 b Howard, C. P., 63 d, 64 a, 64.e Howle-tt,R., 70 aa, 70 ab, 74 j, 74 k,
........
Harkless, Lloyd B., 74 I ,
74 ad Harmison, L. T., 71 b, 71 i, 71.j, 72 d, Hubbard, F. B.,.06 b 72 h, 72 l, 72 ak Huffman, F. N., 71 a, 71 b, 72 d, 72 l, Harp, J. L., 72 ap
,lib
} i
,-
'
v
I
•
_'ii , I '
.i:._
lli£./e,
!'L,
Jacoby, H. D., 75 bb
,..!
Jake,lan, R. W., 60 u
55 g, 56 d, 56 e, 57 h,..57 j,
Jakob, M., 57 c
60 ¢,. 60 t, 65 f, 6Bac
_ _.! _ '_
C• E,, 48 c
Koenig, K. , 66 p Kohler,
J. W. L., 54 b, 54 e, 55 c., 55 e,
Jakobsson, E. G., 63 p
Kohlmayer, G. F.,
Janicki,
Koi.zumi., I.,
E., 76 aa
59 h,
67 m
76 ac
Jaspers, H. A., 73 x
Kolff,
Jack, 75 ba, 76 au
Jayachandra, P., 59 k
Kolin,
I.,
Johnson, Owen,.46 b
Koopmans, 52 d, 52 f,.57
68 k. i-
Johnston., .J.R., 77 at Kovatchev, V. T., 72 ae Johnston, R. D., 62 g Kovton, I. M., 67 h Johnsto._, R. P., 68 a, 68 c, 69 a, 69 x, Kuhllnann, Peter, 70 i, 70-_, 71 m, 73 ad 70 v, 71 ao, .72an, 73 al, 73 an, .____Kunii, D..,61 m 73 aw.,74n, 74-av, 75 r, 75 be,..... Kuznetso,,B. G., 73 au ....
'
"
i ....
L ! " i
76 as,_76..ay, 77 x
Lagerqvist,R. S. G., 73 s
Jones, L. L.,.54 c
Lambeck,A. J, J., 55 d ........ -
Jonkers,CorneliusOtto, 54 b, 54 e,
Lambertson,T. J., 58 d
55 b, 55 c, 58 c, 60 t Joschi, J., 70 g
Lanni.ng,J. G., 77 0 Lapedes,D..E., 71 bb_ 74 at .....
Joule, J., 1852 a
LaPoint,C. W.,72.ag .
Joyce, J. P., 77 ar Kar-avansky, I. I., 58 b
Lashkare.va, T. P.,.73 z Lavigne,Pierre, 73 am......
Kays,W., 64 I. Keller,H., 74.v
Lay.,R. K., 70 b Leach, Charles F., 68 y
Kern_ J., 76 x ......
Lee, Royal, 37 a
Kettler,Jack R., 75 ae
Leeth, G. G., 69 c
Khah, M., 62 h, 65 i
Lefebvre,A. H., 72 ag, 74 aj.
Kim, J. C., 70 m, 71 aj, 71 ak, 73 l Kirk,
A., 1874 a.
Kirkley,
D.. W., 59 e, 62 d, 62 e, 65 e
.......
..Leffel, C. S., 77 ax Lehrfeld,
D., 75 ab, 76 aj,
76 am, 77 f,
77 v
_._
Kitzner, E. W., 77 k Kliuchevskii, IU. E., 76aw .....
Leo, B., 70aG, 71 bf Lewis, R. S., 71 g, 72 ad
_
Kneuer,R., 72 ae Knoke, J. 0,, 1899 b
Lewis, Stephen, 73 t Lia, TorbjornA., 71.z, 71 af, 73 e,
_..
Knoos, Stellan,72 g
};
,4;
73 s, 75 j, 75 az
"
F! '
'
L.ie.nesch, .J.ll.,6,q_ 69 k
McP.lahon, H. D., 59 j,.60 d
..
Linden,LawrenceH., 75 bb
Medvedev,E. M., 73 aa
I
Locke, G. L., 50 a Linds.ley,. E. F., London,A. L., 5375 a,x56 a, 58 a, 64 l
Meijer., R. J.,.57 c, 57 g, 59 f,..._59 l, Meek,59 R.m, M.60 G., e,6t 60fo, 6(_p, 60 q, 60 r,
,.
Longsworth,Ralph C., 63..q,64 d, 65 d,
I
66 i, 71 j, 71 be, 74 as
II
Lowe, J, .F.,76 q
_i " I
65 g.,65 h, 66 g,.68 q, 69 e, 69 m,
.
69 t, 69 u, 69 z, 70 d, 70 j, 72 n, 72ah, .74c, 77 bb, 77 bc 58 h.
Ludvigsen,Karl, 72 s, 73 f,.73 k
Meltzer, Joseph,58 b, 7i bb, 74 at
Lucek, R., 67K. e S., 75 az, 77 i Lundholm,G. Lundstrom,R. R., 71 q
Meijer,Hugo H.M., Menzer_, M. S.-, 77 r Mercer, S..D., 71 az
Lura, T., 71 as
Meulcnberg,R. E., 6:_ai
,.,
Lyapin,V " I"' 75 ak_ Magee, F. N., 68 x, 69 1
Michels,A. P. J., 71 f, 72 a,.76e
!" El
Magladry,
Mihnheer, A., 72 ae
, !i !
'
R., 69 aj
ii
Maikov, V..P., 69.ah
Miklos,A. A., 69 f
Maki, E
Mitchel, R..K. 62 m
R., 71 t-
Malaker,Stephen F., 63 h, 63-p Malik, M. J., 68 i
/ I
_'
I
_,_
Moise, J. C., 73 r, 73.at, 74 x,.]4 au, 75 p, 75 au, 76 al
Malone,J. F. J., 31 a
Mondt, J. R,, 64 g
...;
Mann, D. 13.,64..k MargoliS, Howard, 75 bb
Monson, D. S., 62 i Moon, J_ F., 72 o
I
Marinet, D., 72 ae
Mooney, R-,J., 69 j
..
Marshal, Otis W., 74 s
Morash,RichardT., 74 s
Martin, B. W., 61 g
Morgan,N. E., 72 t
k
Martinelli,R. C.,_43 a
Morgenroth,Henri, 66 o
,
Martini,
M. W., 77. h
Morrow, R. B., 77 s
'
Martini,
W. R., 68 c, 68 I, 68 u, 69. a,
Morse, F. W., 06 b
"
69 x, 69 al, 70 v, 71 i, 71 ba, 72 b, Mortimer,J.,.75 ap, 76 ad
I
Moynillan, PI_ilipI ,.77 ac 74 o, 74 p, 74 av, 75 q.,75 ag, 76 c, . 72 d, 72 73 aa w, 73 al, 74_n, Mott, WilliamE., 76ay, 77 m, h, 72 77 ak, x, 77 Mulder, G. A. A., 72 e, ah 75 ax i
•
_
Ma×well,Barry, 77 ad
Mullins,Peter J., 75...bd ............................. I
qH
Mattavi,J. N., 69 f
_L
Mulej, P., 71.g
................. __
i
' I
]
i
,
Murinets-Markevich,
.,_Z
r
Pechersky, M. J,, b, 1854 b
Narayankhedkar, K. G., 72 ae Naumov, A. M,, 67_h i
Neelen, G. T..M., 71 at
I i'
,.. i,_i ..,_.,.l _, : ,
__Pedroso,
_'"." i '_/. •'. .<,,
R. I.,
76 ao, 76 ap
•
76 ba
........... Penn, A.. W., 74 ap Percival, I C., 6a.a-,...68 ae, 74 bc,
67 J, 70 u, 71 m
Nemsmann,.U,, 75 g Nesterenko, V. B. 67 h '
i ..
"
L................................................ |
Paul, B., 70 s
Murray_ J. A., 61 g...
.... .,i.I:' .;,
,,}
°
B. N,, 73 aa
Napier., James Robert,.1853 _I
J
76 bb Perlmuter,
'." {.i
M., 61 i .
Perrone, R. E.., 73 w, 74 n, 74 av, 75 r, 75 be, 76 ay, 77.x
., ..
_
Newhall, Henry K., 74 aq Persen, K., 72 ae Newton,Alwin B., 57 f, 59....i, 59 n, 61 c Piller,Steven,77 b
i'.! ..q
Niccoli,L. G., 76 ay Nicholls, J. A., 77....r
Piret, E. L.,.51 b Pitcher, Gerald K., 70 h, 75 b
i _
Noble, Jack E..,69 a, 69 x, 71 i, 74 r,
Plitz, W., 74 v
74 aw, 75 r, 75 be, 76 t, 76 u, ....... 76 ay,..77x
Poingdestre,W. W., I]345a
"'- .
Polster,Norman E., 76 c, 76 p
.,
..
Nobrega,. A. C., .65 w
Postma, N P
,.,..i ;_.i
Norbye, J. B., 73..g Norman,John C., 72 1
Pouchot, W. D., 74 w, 75 ab,. 76 aj,
_.}:.. "" ;_.,;,
Norster,E. R,, 72ag Nosov, M. E., 73 aa
Prast, G., 63.e, 63 o, 64 i, 65 x, 70 p
_.,:. _:' ,'_;i_. ....
Nusselt,W,, 27 a, 28 a Oatway, T. D., 72 ap
Pronko,V, G., 76 ab
_:_>
Olsen, Don B., 75 ba, 76 au.......
'_
Organ A. J., 70 k, 71.u, 71.av, 73 ac, 75 i, 76 h, 77 z, 77 an, 77 ba
Z.,':''
....
O'Keefe; R, J.,
73 h
_; 76 am
!i ';
Prescott,F. L., 650
, i
Prosses, 17. d Prusman, Yu 0.,
69 ak
Ortegren,Lars G. H., 71 m, 71 y_, .... _
"_
71 z, 71 ah
75 aj,
75 ak, 75..as
.....
Qvale, Einer Bjorn, 67 n, 68 m, 68 r,
i
..
69 n, 69 an, 71 aj,.71-ak,74 ab Raeser,R. J., 74 x, 76..•ai Raetz,..K., 74 m
_ ', •
...... -"
Orunov,B..-.B., 76 av, 76 aw Pakula,A., 50 e
Ragsdale,R. G., 77 as Rahnke,C. J., 77 1
_]_
Pallabazzer,R., 67 a
Rallis,Costa J.,.75 w, 76.i, 76 y, 77 c,
I
Parker,M. D., 60..f
77 d, 77...e, 77 g, 77 ay, 77 az,
1
Parulekar,B. 72 ae Patterson,D. B., J.,_68 b
77 bq
.....
_-_i
-
il
_ I 3 }q
'
I
....
ii
i ,
'
/ :
:
!
Ranch, J.,--71g
Ruggles,A. E., 74.-ba.75 di, 76 bc
Rankin,C. F., 75 n
Russo, V..E,, 76 al
Rankine,M..,1853 b, 1854 a,...1.854 b
Sadviskii,M. R., 69 ah
Rao, N. N, Narayan,54 a, 55 a, 59 k
Sampson,. H. T., 71 as
Rapley C. W., 60 g, 61.g, 65 s
Sandquist,Gary, 74 az, 75 ba, 76 au
Rauch, Jeff S., 72.ad, 73 t, 75 o, 77 b
Sarkes, L. A., 77 r
._
Saunders,O. A., 40 a, 48 d, 51q Raygorodsky,A. E., 76 ab
Savchenko,. V. I.,_..15. a.j,75 as
'.
Rea, S, N,, 66 h, 67 l Reed, B., 68 f
Sawyer_R. F., 72 ag Schalkwijk,W. F., 56 e, 57 i,..-59 g
_
Rees, T. A., 20 a
Schin_er,R. M.,.72 ag
._
Reinink,F., 73 h
Schmid,.P.,74 v
Ricardo,Sir H., 66 m
Schmidt,Gustav.,1861 a, 1871 a
Rice, G..,75 k
Schock,Alfred, 76 ag
ii
_,
Rechardson,Robert-W.,74 ar
Schottler,R,, 1881 a
_
_
Richter,C., 74.v
Schultz,B. H., 51 c, 53 e
!.
Rider, A. K., 1871 b.. Rider, T. J., 1888 b, 1888 c
Schultz,.RobertB., 77 p Schultz,W. L., 7?__ag
'L
Rietdijk,..J.A.,70 p, 65 h
Schuman, Mark, 75 v
Riggle,Peter, 71 i, 72 ak
Schumann,T. E. W., 29 b, 34 a
Riha, Frank J., 72 z
Scott, David, 71 d, 71 ac, 71 ad, 74 e,
_I_ _-_ii i
..
....
Riley, C, T_, 72 ap...........
.............
75 z, 75 ad
Rinia, H,, 46 a, 46 d, 47 b
Selcuk,M. Kudret, 77 ac.
Rios, PedroAgustin, 68 g, 68 r, 69 o,
Senft, James R., 74 bd, 75 bg,_.-76 n,
69 am, 69 an, 70 z, 71 s, 71 an Rochelle,P.,.74_al Roessler,W. U., 71 as I;
'_
77 ak, 77 bf Sergreev,P....V., 73 av, 75 av
.............. Serruys,Max, 73 ah
Romie, F. E., 66 b
Shah, R. K., 75--aw
Rontgen, R., 1888 a Roozendaal,K., 61.n
Shelpuk., Benjamin, 72 af, 74 y, 75 ac Shen1_an, Allan, 71 am
Rosenqvist,_N.Kaj. G., 77 i, 77 al, 77 bj Rossi, R. A., 63 p Ross, M. Andrew, 73 ai, 76._, 76 b i
Shuttleworti_, P., 58 e Shmerelzon,Ya. F., 73 av
73 r, 73 at, P., Rudnicki,M. I.,74 70x, r,74 71au,. az,75 72p, d,75 72au k, Singh, Siegel,P. R,, 6161 ia
! ,.
t
. ,
*i
r i.... i
'
I
;
I
TTT-T-T-T, i
;
'.
I
,
i
i
,D,_
l I
";:::i
Singh, T., 72 r
Thorson,d. R., 65 u
Singham, J. R,, 51 a
Thring,
R. H., 75 k
Slaby, A., 1878 a., 1879 a, I_180 a,
Tipler,
W., 47 a, 48 e
18,89 a , i
Smal, Pieri_e, 05 a
"
i:_
Smith, C. I..,60 f SmitIl,Harry F., 32 b, 42 b
"
_
i
]
,i
.;.i ...._i
'
:_
Tobias, Charles W., 75 ain
i"
Toepel, R. P., 69 j
i.
_
Tomazic,WilliamA., 76 ai, 77ab Torti, V A. 75 ai, 76 bc . , L. Jr , 67 I, 68 g, 68 m,.68 r.,
Smith, J
69 n, 69 o,.69 an, 70.z, 71 s, 73 ay, 75 bf Smith, Lee-M.., 74 az,75 ba, 76 au
Trayser,D. A.i 65 u, {$6c, 67 b, b8 o
v. ,.
av,
Solente,.P., 72 ae
._
Spigt, C. L., 72 c, 74 c, 74 u, 75 m,
Tsou, M. T., 63 k
77 bb.... Spriggs,James.O.,72 w. Stahman,R. C., 69 d
Tursenbaev,I. A., 73 z,.74 bb, 76 av, 76 aw Uhlemann,H., 72._c,74 u
Stang, J. H., 74 aa.
Umarov, G. Ia., 73 z, 74 bb, 76 av, 76 aw
I
/'
i,,
!7 1"
:I i
_.i I "iI
i
.
,..
Stephan,A., 72 ae /
*_
Stephans,.J.R., 77 at
Underwood,A. E., 63 k, 70 a
Stirling,James, 1827 a,_1840a
Urieli, Israel,75 w, 76 i, 76 y, 77 c,.
Stirling,Robert,1816 a, 1827 a, 1840 a, 1845 b
•.'
7.7d, 77 e, 77 g, 77 af....
Urwick,W. D..,77 bi
Stoddard,D., 60 l Stoddard,& S., 60.k
Valentine,H.,.77 bd, 77 bp Vallance,J. K., 77 1
Storace;A., 71 v Strarosvitskill, S. I., 64 h
van Beukering,. H. C. J., 65 h, 67 g, 73 c, 73 d.......
Stuart,
van der Aa, H. H. M., 65 h, 67 g
R. W., 63 c
Sun,hers, J. L., 75 af Tabor, H. Z., 67 k
.....
i
Vanderbruq,Tom G., 77 ae... van der Laan,.G.M.J., 61 n
i. i'
Tamai, H. W., 68 e, 69 ak, 70 r Taylor,&. T., 52 d
van der Sluys, WillenlL. N., 75 h ..
vailder.Ster-,.J., 55 g,.60 h.
, I
Tew, R., 77 bl Thieme, L. G., 77 av
van Giessel,R., 73 h van Heeckeren_ W. J.., 49 c, 52 h, 59 d
i
Thodo_,G., 63 b_
van Nederveen,H. B., 66 d .Ip 1
i i i '
I
i van Weenen, F, L,,
47 b, 42 e, 48 a,
Welsh, H, W,, 62 i,
5! k
West, C,_),,
van Witteveen,
R. A. J. 0.,
62 k, 66 f,
71 .ag .... Vasishta,
Vedin,..B.A.,.68
Verdier,
E. J, J.,
J.,
Vi.llard,
J. C., 72 ae
•
63 r
1
Wiedenhof, N., 7_4d VLilding, Tony, 71 aa Wile,
D. D., 60 s
Wil.kins,
Gordon, 71 ar
Wilson, David Gordon, 75 am Wilson, S. S., 75 aq
von.Retb, R. D., 74 v, 75 g Vonk, G., OOa, 62 j
Winberge, E. B., 43 a Wingate, C. A., 77 ax
',
Voss, V.., 34 a
Wintringham,
i ,
_.. #:
Vuilleumier, Waalwijk, J
Witzke, W. R., 77 at Wolgemuth, C .H , 58 m, 63 n, 69 b,
#
Wade, W. R., 68 p, 69 k, 72 ag
i:i" ._ii _"
',,i
t
White, Ronald,.76
72 ae
G. D., .72 p
74 n, 74 o, 75 r, 76 ay,
68 d
,,: ,i
'i
73 q,.73 al, 77 x
69 r
Vicklund,
Volge_.,. J., I
M,, 72 w, 77 n t
ver Beek, H. J., '
74 k, 74 ad,
76 k
V., 69 p, 71 n
Veldhuijzen,
71 ap,_Z.4 j,
White, M. A., 68 c, 70 v,. 71 ao, 72 b,
Varney,-Frederick '
72 ap
_.I _ _i _, _.i _i I'_! .._ ... :: i."_ • ! _'_ ,;i '
R., 1918 a M., 74 d
_., ;_!
69 ag
Wadsworth,....J., Wakao, N., 61 m61 j Walker, G., 61 k, 61 I, 62 f,
J. S., 60 n
Wu,.Yi-Chien, 77 ac Wulff, H. W. L., 72 ae 63 f,
63 g,
z:
65 i, 65 j, 65 z, 67 f, 68 n., 68 ad, 7Og, 71 n,.71 ae, 72 i, 72 j, 73 i, 73 j, 73 m, 73 n, 73 v, 73 ag, 74 ao, 76 ax Wuolijoki,J, R., 48f
;_ ,_
_'
Walters,S., 7(_t Wan, W. K..., 71 o, 72 iWard, David, 77.ad
WuYTn,Jaroslav., 75 e Yagi,S,, 61 m '"
i : '
Ward, Edward J.,.72w
Yano, R. A,, 72 ap
i
Watelet,.R.P., 76 bc
Yeats, F. W., 75 l, 75 y
Watson,G. K., 77 at
Yendall, E. F., 52 e, 58 f Yzer,.Jacobus,A L , 52 b, 56 g ' '
Weimer, George A., 76 o..... Weinhold,J., 63 1
,!
_._
Weissler,P., 65 p
k
:
"'_ ' i
,
._
•....
i¸
I
"_
'
i i
i_
Zacharias,F. A., O0 c, 71 m, 71 w, 71 au,
i
73 y Zanzig, J.,
_
. _
i
I i
71 be
Zimmerman,.M. D., 71 c, 71x
Zapf, Horst,_70
i,
Zarinchan_,
7.5 d
J.,
1
Zeuner,G., 1887 a Zimmerman, F. J.,
65 q
J
70 1
Zindler,
G. F.,
69 aj
Zykov, V. M., 74 am
.
Tabl e 8-3 Corporate Author
Advanced Technology Lab 69 aa
............. Boeing 77-au
AERE-HarwelI
Brigham Young.University
67 i, 70 z, 70.aa, 71 ap, 74 f, 74 g, 74 h, 74 i, 714,i, 74 k, 75 I,._75.y, 77 t
ii]
AerojetLiquid..Rocket Co. .......
Index
68e, 68 j, 69 i, 72 d, 73 r, 74 x,..75, p.,76 al, 76 aq
77 h BucknellUniversity 77 ad ControlData Corporation 71.n
AFFDL
CorningGlassWorks
72 t, 74I, 75_a, 75 b Air Product & Chemicals,Inc. .::.I -"_
77 o D,CyclePower.Systems, Inc.
71 j, 7.1be
77 q
American..Gas Association
Departmentof Energy
77 r },! ,_:i
,_*.! _:_ '_ ,-i
Arthur....D. Little_,Inc. 5q j,._.6.O.d, 61 h
Departmentof Transportation 72w, 75 bf
Atomic Energy commission
ERDA
72-e, 73 ax
_
Battelle 61 e, 62 m, 65 a, 65 u, 66 c, 67 b, 69 d, 73 ay
74 bc, 76 j, 77 b, 77 s, 77 ab, 77 aj, 77 ao, 77 aq, 77 as, 77 at, 77 av
..,
!
!
-f
i
I
_, i ,
,
LI
ERG, Inc. 73 p, 77 a, 77 u Fairchi.ld
Space & Electronics
Kaiser Engi_n_ers 60 m Co.
76ag •
I
:
_I
73 h, 76 ah, 77 k, 77 I, .i
London. --
61-a, 61 k, 62 e, 62 f, 63 f, 63 g, 76 h, 77 z,.77 ba
Ford Motor Co.
"_ _
Kings College,
'
Laboratorietfor Energiteknik
77 aq, 77 bk
,.
74 ab, 76 w
GeneralElectric
:
LafayetteCollege
76.j, 77 w, 77 aj,.77bn
71 be
General• Motors Corporation
M.A.N,-MWN
.' !
•
..
42 b, 60 a, 64 g, 65 t, 68 p, 68 v, 69 f, 69 k, 69 v, 69 ao, 69 ap
;! •
HEW 69 d I,
:.
i
McDonnellDouglasAstronautics 68 c, 68 I, 68 u, 69 a, 69 x, 69 al,_70 v, 70 x, 71.i, 71 ao,. 71 ba, 72 b, 72 d., 72 m, 72 ak, 72 an, 73 q, 73 w, 74 o-, 74 n, 74 av, 75 r, 75 be, 76 r, 76 v, 76as, 76ay, 77 x
GoddardSpace Flight Center 69 aa
1 ! I
71 m, 71 w_ 71 au, 72 aq, 74 u
_ _ L _-_ . ! .!_ ._ ! ! ' ] i
Hughes Aircraft.
i,
$
68 x, 72 t, 75 a
Mechanical.Technology Inc.
,,
lIT Research Institute ........ 65 i,
72 v, 76 az, 77b, 77 m, 77 s
I i
65j ]
i
Instituteof Gas Technology 67 f, 75 e._
73 w Medtronic,Inc. M.I.T.
Jet PropulsionLaboratory 75 t, 77 ac, 77.ae
68 r, 69 n, 69 o, 71 an, 73 ay
Johns Hopkins University_... 77 ax _
NASA-Lewis -.
Joint Center for GraduateStudy 75 ag, 76 c, 76 ay, 77 h, 77 x, 77 aa, 77 ao
61 i, 71 am, 77 p, 77 ab, 77 ao,.77 as, 77 at, 77 au, 77 av _. NationalBureau of.Standards 77..ad
Josam ManufacturingCo. 76 p
324
i
t
:,_.;.i ._ i i , ,: •_
NationalHeart and Lung Insti.tute 69 al, 70 x, 71 b, 71 i, 71 j, 71 ba,_72 d, 72 ak, ' 72. an, 73 an, 74 av, 75 be,
!,.!
76 as
Rocketdyne 64 c, 65.c, 67 c, 67 d Roesel.Lab
•
74 s
w'(i
_
NationalResearchCouncil
iii _:;_i 'i;J
61j Ohio University
'' I
_i
i
!I
i
,", _! ,:! ..; !:! i_ -i_ I! j.! ,_ " i_'. i.il :.. i .I i_i
° .....
50 a, 76 ak .......
Stone and WebsterEngineeringCorp.
69 h,-71 g, 73 .t Penn State College
71 ak .
58 g, 69 b
75 n, 75 s
Philips_Eindhoven .43b, 46 c, 48 j, 48 49 e, 49 f, 49 g, 49 49 j, 50 b, 50 c, 50 51 h, 51 i, 51 j, 51 51 m, 51.n 51 o, 51 - 52 I,' 52 m, 52 52 k, 52 p, 52.q, .52r; 52 ' 53 f, 53 g, 53 h.,53 54 d, 60 c, 60 e.,.63 65 b,.65 g, 65 h, 65 68 d, 69.e, 69 r, 70 71 e, 71 f, 71 m; 72
__.
SyracuseUniversity.. k, 49 d, h, 49 i, d, 51 g,. k, 51 I, .. p, 52 j, n,.52 o, s,_53 d, i, 53 j, e, 64 i, x, 66 k, d, 70 u, a,.._72 ah,
73.d, 73 h, 74 c, 74 d, 74 u, 75 a f, 75..h,75 m, 76f, 77*bb, O0
i "_I:i I
Philips,North American 57 g, 57 k, 58 c, 58 h, 58 i, 59 d, 59 h, 59 I, 59 m, 65 v, 71 v, 73 x, 74 b, 74 w, 75 b, 66 I, 67 e,._70 h, 71 75 m, 76 e, 76 am_ 77I, f,71 77p, v, 77 y, 77 ax Purdue University
i I, I _.I
.
Sunpower
I:! ji i,!
._I
Stanford. University
68 r, 71 aJ, 71 ak
64 d,,65 d TCA StirlingEngine Research and Development Company ..... 70 g, 72 u Thermo ElectronCorporation ........ 71 b, 72 d,_24 ba, 76bc United Stirling 70 o.,...71 m, 71 ah, 73 s, 74 z, 75 j, 77 i, 77 j, 77 al, 77am, , 77 bj
Universityof 68 n, 69 Calgary q, 70 g, 71 n, 72 j, 73 j, 73 m, 73 u,
.....
73 v, 76 Un.iversity of ax Florida 65 o Universityof London 67f
RCA '
72 af _.
Universi.ty of Michigan 68 b
ReactorCentrum Nederland 66 d
I
J
I
1
._
Univers4ty_ of T_kyo 61 m University
I ....
Washington Stat_ University,. Medical Colle_je
of Wisconsin x Wayne77State University
60 j_ 61 b ................
!
72 r
. !
75 w, 76 i, 76 x, 76 y, 77 c, 77 d, 77e, 77 g.
i I
Universityof Witwatersrand
i:i
•
Westinghouse 73 ax, 76 am, 76 ao,.7.6T..ap
-"
,.
i
Table 8-4 Classificationof StirlingEngi_neReferences
!! i:, 1
AO Code.
GeneralStirling Engine News Mean_i ng Intended
_, I_.
.
i 1
or Actual. Heat Source
A1
Liquid or GaseousFuel.
A2
Nucl ear Reactor..
A3
Radi oi so tope
A4
Solar Heat
A5
Solid
A6
Stored ..Thermal Energy
A7
None of Above
_._
f
-_
Fuel
i
J
_
Type of Engine
i
Displacersonly engines
"i
B1
VM cycle
-i q
B2
Thermocompressor
,. ....
B3
Displacerinline piston,engines
I t-
3,_(_
i
_.i !
, ,,i
D6
Sealing
D7
Engine Starting
D8
......
D9 • _
Engine Control Power Takeoff
D10
Gas .Transport
Dll
Materialsof Construction
_i
'_ I,I
Dl2
Other Heat Transfer and Fluid Flow
.....
I '
Dl3
_.
Air Preheater
Dl4
Working Gas Heater
Dl5
Regenerator
DI6
Working Gas Cooler,
Dl7
Heat Rejection
Dl8
Working Fluid Selection
'"
ExperimentalResults Full Systems
C
El
Vehicles
E2
Other
E3
Engines.... Components
E4
Seals t
, ....
328
E5
MechanicalPower Train
E6
ControlMechanism
E7
Air Preheater
E8
Working Gas Heater
,_ I.I Ic
i
E9
Regenerators
i
ElO
Working Gas_Cooler
"
Ell
'I'
i 'i
•
"
Heat Rejection
'r!
I
._i I
El2-
Working Fluid Tests
El3
MaterialTests
_'_
•l
•;_,,! ,i,
;_,
Table 8-5
_.i
Paper NumbersRelatedto Each
,
'I
_
Stirling Engine SubjectClassification
j
'r 'L
:i !
AO
GeneralStirling_EngineNews
'i i I -i "I
1875 b 1885 a 1888• a 1899 a, b
t,_ ,, i__ i i*i ' !
1911 a 1917 a, c 1947 d, e 1948 a, f, g, h, i 1950 e 1955 .a
i!, • i ' '-i
1957 b1959 k 1962 i 1963 k, I, m 1965 p, q 1967 j 1968.q,t 1969.ao 1970 i, n 1971 af, r,y, ai, z, ar, aa, av 1972 p, s, i_l,. aj.1973 e, f 1974 ai 1976 ac 1977 aa, ai, ar .....
Intendedor Actual Heat Source A1
'_
Liquid or GaseousFuel 1903 a 1906 b 1946 d 1961 m 1963, i 1966 e, g .. 1967 f 1968 p, z 1969 f, v, z, ab 1970 c, d,.j.,k,.l, o 1971 c, d, e, f, w, x, ab, ag 1972 a, r, af 1.973c, d-,h, j, o, y,.. aj, ao 1974 ae, bc, bd 1975 j, z, ao, bd, bg 1976 d, g, o, ae 1977 i, j, n, t, w, ab, ad, bj, bk
329
i
t 4
_.!
'
A2
i '
,NuolearReactor
A5
1975 ao-1977a f
1816 a 1853 a
• • '_ I ......... _......... r i ., I
A3
1875 1889 1-871 1973 1975 1976 1977
' Radioisotope 1964 1965 1966 1967 1968
j y d, f, n i h j, k, I, s,.._x, y, ab 1969.i, aa, aj, ak 1970 r, t, v 1971 a, b, i, j, az, ab 1972...c, d, e, f, h, j,
i _ i :_ . , I_ i i :
A6
:} :i i _i::_ ---] ......'..i
"
]_i _)) .j
A4
A7
1960 b 1961 e 1962 n 1965 o, u 1966 c 1.967b 1968 x 1970 q 1971 g, h 1973 j
aw
'Li,
it,' j,..
1977 u, ac
o
Thermal
Energy
g h, I, v f, t, z, ap o, t,_x
None of Above 1961 1968 1969 1970 1973 1974 1975 1976 1977
So.larHeat
1974.u, bb 1975 n,. q, ac 1976 e-,k, m, o, af,
a ab j n f, u
,971 i, ac 1972_ak, an 197.3c, d, j. 1974 e, av 1975 ae, ao, be 1976 c, o, p, ae, am, ay .......
i '
Stored
1962 1968 1969 1970
k, I.,m,.ak, an 1973 c, d, j, am, at, ax 1974 au, av, ax, _,y, az, ba 1975 l, p, r-,y, ab, ai, au, ax, ba, be 1976 j, r, s, v, ag, aj, am, aq, au, ay
.
Sol.idFuel
-
d, h e, l_ f, .g d c, d, x u, af f, h ak, ao, ap f, ae .........
", i
,
J
!
I
,' .,, , .
I
I, 1 I
iii
Type of Engine
_ontinued
f
._
Displacers
,I I
B_]_I VM Cycl e 1918 a 1952 c 1961 h
7 I , I
1 ,
-
., _.
OnlX Engines
1.947 1951 cf, 1 1952 d, f, g 1953 f 1954 f
1969 1968 aa x 1970. g, h, ac
1956 cd, e 1955 1957 i
1971 1972 I= t, 1974 I, 1975 a, 19761
1958 1959 ic,_d, 1960 e, j, 1961_c, e 1962 e, f, 1963 e, f, 1965 f, .1,
am, z., afbf y b, ac._
l :i
-.
I
: _,', If! \_ "_
1932 b 1937 a
B__22Thermocompressor a f c e, h, I, u, ak a, i, r,..x f, r, v a, i, j,_ az b, k., ak, al r, at m, x, au, aw, bb p, v,.ap, au, ba t, u, aj, al, aq, ay, bc 1977 c, h
_ : .,! _._ "
_"
Displacer
Piston. Engines
B__3 Inline 1816 1827 1840 1853 1880 1888 1897 1903 1906 1913 1914
a a a a b b, c a a a a a ........................
i, n i, r u, v
_
1966 1967 g c, f 1968 a, i, k, I, y, z, ad 1969 a, e, f, h, v, ab 1970 a, d, .g, j, o,. v 1971 c, d, e, f, g, l,.p, v, .x, .ab, ac, ag., ao, aq.. 1972 f, m, t, x 1973 b, c, d, h, j,. p, al, as 1974 r, ac, ad, ax, ay., az, bc 1975 n, t, x, af, ao,. ay - -1976 a, b, e, j, n, z, ae, am, ax, az, ba 1977 e, i, j, m, ab, at, ax, bg
1949 1957 1962 1968 1969 1970 1971 1972 1973 1974 1975 1976
_
f, h t
B4
Offset 1879 1880 1889 1906 1947 1951
a a a a c f
_31
;
i
. .
J
,
•
L
, i Continued
B_66 Crank O_peratedDisplacer
1959 c 1960 J 1961 e 1966 c, o 1968 k 1970 p 1973 j 1974 bd. 1975 ai, bg 1976 c, n, p,.r, v, ax. 1977 e,.k • Piston Engines -
1948 1949 1952 1954
1816 a 1853a 1880 b 1888 b, c 1897 a 1903 a 1906 a1913 a 1932 b 1946 a ........ 1947 c 1949 b, c 1951 f-
.......................................... _. _,
1952 b, f,.9 1954 f 1955 c 1956-d, e 1957 i 1958 i
1833 a 1853 b 1854 1871 b b 1881 a 1905 a 1938 b 1919 a 1946 a 1947 b
i
, _
'
,_,.,
1959 c, d, f,.h, n 1960 e, j, t
'
1962 i, 1961 c, d, I, 1963 f, i, 1964 f 1965 f, I, 1966 g, m, 1967 f 1968 a ' f,
c
k c. se
1957 k 1958 a
_
1959c 1961 d, 1962 l .. 1963 e, h 1965 b f, l ' 1966 k,.m i.967c 1968 g, r, w 1969 f 1970 1971 d c, d, w, x, ag.... 1972 c, ar 1973 j, y, ay_ _ 1974 ae. 1975 af, ap, bd, bf 1976 1977 d, c, g, e, k, g, m, h, o, i, q j, ae, aq, bb, bj
'
i,
n e r
.... !. _!_ i i ' I
m, u o
k,..ad ' 1969 a,.e, f, r, v, ab 1970.a, d, h,..j,o, p, v 1971 cj d, e, f, I, v, w., X, ab, ac, ag 1972 f, j, m,.q, an 1973 c: d, h, j 1974 m, ax, ay, az, bc, bd 1975 ab, af, ai, an' .ao, ap, av, ay,.bd,ag 1976 a, b, c, e, j, n, p, ae, am, ax, az 1977 c, h, ab, aj, at, ax
_ " '. : I
. ,
0000 c B_Z Free Displacer
(not crank,)
1968h, i, z
_i
1969 a, h, ak 1970 p, r
_i
i
117 Continued
1'i "-I _. , _-: _ .'.: I ... ' i,_ ",i_ '
. ....
:., ._
_
B8
,;: , _ _ .. i ....
,,. .
,,, _. i i!i , ._ '_ ', .W , , ., -. ""
B8 .__ Conti nued
1971 g, i, ao, aq,_ay,az
1968 a, f, k, I, w, y,
as, at 1974 b, f, g, 1973 j, j, p, o, t, p, u, q, al, r, ac, ad, au 1975 n, o, q, r, s, . v, x,.z, ad, au, be 1976 k, r, v, z, ak,
1970 a, d, h, j, o, p, v f, v, ab 1969 s, a, e, 1971 c, d, e, f, l, t, v, w, x, ab, ac 1972 c, f, j, m, q, af, ar
1977 a, aq b, i, j, m_ r, s, t, u, ac
1973 ay c, d,.h, j, ai, 1974.m,r, ae, ax, ay, az, bc,.bd 1975 t,.ab, af, an, ao, ap, av, ay, bd, bf, bg 1976 a, b,.c, d, e, g, j,.n, p, q, r,.v, z, ae, am, ax, az, ba .]977c, h, k, q, ab, aj, aq, ar,-ax, bb, bg 0000 c
Crank OperatedPower Piston 1816 a 1853 a 1871 b 1880 b 1881 a 1888 b, c 1889 a 1897 a 1903 a 1906 b 1913 a 1932 b 1946 a ..... 1947 c 1949 b, c 1951 f 1952 c, d, f, g. 1954 e, f 1955 c 1956 d, e 1957 i 1958 a, h, i 1959 c, d, f, h, i, j, n 1960 e, j, t'-.*, 1961c, d,_e 1963 f, h, i, r, s 1962 i, f, I, n 1965 b, I, u 1966 c, g, j, k, m, o
!._. _.. _ i ! ! . _.i _
,, B9
Free Power Piston
(not crank)
1968 i.,.. z 1969 a, f,.h, ac 1970 d. 1971 c, d, g, k, ag, ao, aq, ay 1972 j,.m,.x,y, ad 1973 b, j, p, t, u 1974 f, g, j, o, p, q, ac, ad. 1975 n, o, q, r, s, x, z, ad, ai 1976.k,m, ak,.bb1977 a, b, m, r,.s, t, u, ac
', i_
_
i¸ ' I"I
'
'
1
1 I
=, ..
_ ,, !
, " i
' ,m:
!
,,.... ,, '; ,,h
._. "." i , ...... ._ •
1906 a 1962 c 1967 f
1960 i 1962 i, 1963 i
1968 c, e, h, j, I, u 1969 i, af, ak 1970 k, r, t 1971 a, g, i, j, ao, ap, ay, az 1972 f, h, k, m, x, .... ak 1973 b, r, w, al, am, ax 1974 n, o, p, q, r, v,. w-,x, au, aw, ax, ay-,az, ba 1975 c, g,.r, ab, ad, ai, au, ax, ba 1976 k, m, q,.r, s, v, aj, al, am, aq, au, ay 1977 c, n, v, x -. 0000 d
1964 j 1965 k, u,1966 c, f, n 1967 b, f, i 1968 f, v 1969 aj 1970 e, v 1971 t_ 1972 m 1973 b, j, p, q, v 1974-._f, g, j, k, ac, ad, af, bb 1975 l,.n,y, z, aa 1976 j, aw 1977 a, b, f; m, n, s, u, ac, aj, bj, bo
n--
Desi 9n Cons_,der,at i _ns :,
D1 C5 _
_"_
Gas _
• • 1939a 1962 m 1974.bd 1975 bg 1977 h, n
C6 ...Other 1973-x
i
I
.......
System Studies 1.963j 1967 b, k 1968 b, o, r 1969 d, x, aa 1970 b, o, w 1971 bb 1972 c, e, iI,t,.ao, ap 1973 j, v,.ak, ar 1974 l, q, ap,.at 1975 a, e, t, _z, bb 1976 c, d, j, o, ah, as, aw 1977 r, s, ac, aj, al, as, bb, bc
._ _. _., '_ . '
l
I i
'
D3 r!!mdyg_a{j.!i.'_L Order 1871 a . 1890 a. 1946-d 1952 b 1953 b 1954 e 1°,56 c 1958 b, g !960 c, e, j, k, 1 196.1 e, h, 1 1962 e 1963 n 1965 i, j, u, w,_x 1967 a, h 1968 c, k, u 1969.b, e, Lh,a9 1970 v.. 1971 ao, ap _972 j, af 1973 d, j, m, p, u, 1974 1975 1976 1977
ad, ah, au,.av i, al,.ao, bb o, w, ai y, ao, ap, aw, ax e, g, ae, ak, an, ao, ay, az
"
i
Continued 196_ 1969 1970 1971 1973 1975 1976 1977
m, x a, aa g, aa, ab, ac am, be q, z, aw. d, ac, ag l b, ao, be................................
D__4 3rd Order .i 1952 b 1961 b 1962 h 1963 a 1964 b 1965.c "1967C, d, n 1969 am 1970 g 1972 u... 1973 j, 1 _ 1974 1975 1976 1977
ab al h, i, w d, z, af, ba, bl
..... -
I . ,. i
_ I _, " .
.'] _ 4
ao, - , I i
Mechanical. 2nd..Order 1852 1946 1955 1959
a a c e
D_55 Efficiency 1947 b 1954 e 1960 d, j
_
1960 c
1967 h, i
j
1962 1963 1961 1964 1965
1970 1974 1969 1976 1977
c, d, f f k, m c a
v me ao, ay, .ba a, q
, '
i *_I
'
' '
F-"r 1 1] " F-F ......... ',
:
DI2
i ,
q
Other
:'
_
-
DI5 .Regenerator .... 1.917 b, d
I •i l
' 1
I •i :
-i , Heat-Transfer
! i _
Dl3 _
Air
and F_.luid Flow.
Preheater 1947 1951 1968 1971 1974 1976 1977 0000
._ ' "_ i ;" ' _ , .!
1928 a 1929 1927 a, a 1930 a 1931 b-. 1932 a 1934 a 1938.a 1940 a 1942 a 1943 a. 1947 a, 1948 c, 1949 d, 1950 a, 1951 a, 1952 a, 1953 a, 1964 c, 1956 a 1957a, 1958 i 1959 b, 1960 g. 1961 a, n 1962 a, 1963 b, 1964 a, 1965 a, 1966 h, 1967 c, 1968 e,
b j P q bc ae, bb I, o, I_, ab c
"I -
. ,[
y
, , i J i __ /_!s;_. :;';:l_i' / ,. I " -.
Li
DI4
Workin9 Gas Heater 1926 1943 1946 1948 1949 1950 1951 1952
a a c b d, b, g, d, m, 1953 d, 1954d 1957 d. 1959 a
h, c, k, f, o. i,
i, j d o, p h, k, l, j
b, c
" :' "
b d, f, c, b, c, e, f
e g d c, d, e, q m g .......
h, i. g, i f, g, i, b, d, e, j, k 1 r,
j,
k,
c, f, j f, g g, h r ac
1960 p, r
1969,.n, p, aa, ah
1966 a, 1962 1965 c p b, u.. ,_r_,._,m 1969 aa 1971 af !973 s,.y., ab,_aj 1974 s, u, z, aa . 1975 f, i, j,.k, ac 1976 ao, av 1977 b,.l
1971 m, 1970 an I, .u, o, s, y, aj, z ak, .. 1972 i ...... 1973 j, l, ax 1974 Ill, aa, bc 1975 d, i, ac, aw ......... 1976 x, ab 1977 a, p, ab 0000 a .
....
DI6
Working Gas Cooler 1913 a 1948 b 1950-c, d 1952 d, i, k, p ._ 1954 d 1956 f 1957 j 1958 d 1959 a............ 1960 r 1965 a
!
ii
1966 b,.p 1967 m 1969 aa 1970 e 1973 s, ab 1974 s, aa 1975 i, ac 1976 av 1977 z
I
i ._
DI7 Heat Re_ec'tion......... _
DIS Continued 1973 m, ag 1974 ao 1975 ao 1976 ak, ap, ba 1977 a, d, q -E_x.perimental Resul_s Full.Systems E1
Vehic]es:
..i ..
DI__.88 Wor_.._k_n__. FluidSelection ..
1931 a 1957 i 1958 h 1959 n 1960 j 1963 n 1964 f I_65 j 1966 c, e
.....
1967 1969 e, b, h ag 1971 a 1972 v
"
._._.__._
'
1969 z 1970 o ...... 1971 m 1972 a 1976 g, bb 1977 a, f, i,k, .... al, am, aq, bj, bk E2
Other
1948 b 1958 d• 1960 j 1969 aa 1972 ah !974 av
i
,!
t '
_,
IT_I
1962n 1969 k 1971 f 1972 a, w 197-3a 1976 am
_"_._ ,.i:_. :_"_ i:}
1977 m, t
!_
IC_ !',;_.
E._3_3 _
_,_ 1874 a 1889 a 1954 f 1955 c 1958 e1959 e, 1960 a, 1961 rn 1962 c, 1963 g 1964 d,
_ " ,;,
f e, m, u
_ "'_
k, o _' I
i
1965 b, d,.e, I, o, t
g,
_"_'
i
i
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E3. Continued I
_
',966 j= K 1968 e, j, I, m, n, p, u, x, y, ad 1969 e, f, i, o, x, ad, ae, al 1970 a, h, j, v, x 1971 c, e, g, j, m, p, ap, ba 1972 b, d, l, m, af, ar 1973 b, c, d, h_ q, r, w, ao, ax, ay 1974 b, c, g, n, p, w, ae, av, ba, bc 1975 a, b, p, ai, aj, as, ay, be 1976 c, e, r-,v, ae, ak, al, as, ay,
! i _
: ! • J _!i _i ._ il i_, i _
.
i,
i: [ !
£ontrol Mechanism 1967 f 1968 ad 1969 h 1971 e, aj 1972 a, m, w 1973 c, d,-h-_
E7
Air Preheater 1964 I. 1965 s 1970 z 1971 f 1972 r, ag 1973 d. 1974 aj 1975 ak 1977 f
..
bc
1977 b, c, h,.i," j, k, v, ad, ag, av,.. aw, ax, bd, bf, -. bh, bi, bp
I: ii Ii :.I i i ! 1
E6
tl f ! _"_%--i ,_i _ ._ i. li ! i. _'_'L_ _, "
E8
!
i_
i_
'
Working Gas Heate_; 1961 m
Components L4
-.Ii
1964 1 1970 1969kd 1974 l
Seals 1961 m 1962 n 1967 e . 1971 i 1973 c, ax 1974 1 1975 a 1977 au, bj
' E5
MechanicalPower Train 1969 q 1971 i, _ 1972 b, m 1973 c, d, q, t 1976 b 1977 bj
_ E9
Regenerators .... 1874 a 1954 a 1959 g 1961 g, m., n 1964 1 .... 1967 1 1968 u. 1970 y 1971 i, n 1973 l 1974 l, bc 1977 bg
....... i
'
i
'
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,.
9.
"'._ : _i! ,t _:'I .....i_
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::i _,._ ![I "I __ •_ L.I "'
DIRECTORY
A relativelysmall number of individualsand.organizationsare now actively doing anything with Stifling engines. The author hopes that this manual will encourage other individuals and possibly companies to become active in Stirling engine development. To aid in this process, the followingdirectoryis offered• Organizations are listed by their company name and the name of the head is name of..the, head individual, The organizationsand individualswill now.be listed in alphabeticalorder. given. Individuals and groups associated, with. universities are listed by the Aerojet Liquid Rocket Company P.O. Box 13222 Sacramento,California95813
'i" ,'t _!.._
Contacts: John Moise Larry Hoffman
.!
i
Aerojet has been working since 1967 on a small thermocompressor type Stirling engine to power an artificial heart. As the free-displacer oscillates,check-valvespump helium throughthe engine. It produces 5-watts of pneumatic power at 18%overall efficiency.
ii I 'I _
About I0 people are employed on the project.
i •r
•,
AGANavigation Aids Limited 77 High Street Brentford Middlesex TW80AB England ......
'
Contacts:
i
Mr.. K. C. Sutton-Jones Mr. N. Spottiswoode
This Company, a Subsidiary of Swedish AGA, concentrates on marine navigational -aids, and has a large part of the World market.. The Company is sponsoring deve-lopment and application of. the Harwell Thermo.Mechanical Generator, and is contracted to install a 60;,
Coast......... watt version of this
generator
in a major lighthouse
on the Irish
141 California Street Amtech Incorporated Newton, MA02158 Dr. Larr-.y ..... Contact: C. Hoagland, 342
! !
Director
of Research
i
1
.
I
I
_
!
[...... Irl I " F r ..........
r
f
[
-
I
,_",_
Amtech. incorporated
," • '31
i
Continued
i
'_ i :;._._
Current work is under DOE Contract No, EC-77-C-05-5392, "Technology Evaluation of the Stirling Engine for Stationary Power Generation in the-500-2000 Horsepower Range", Energy Research and Generation, Lowell and 57th Streets Oakland, California 94608 Contact:
G.M.
Benson,
inc.
Director
R, D & E
.....
, '
ERG has been developing for over ten years resonant free-piston Stiflingtype machines (Thermoscillators). including hydrostatic drives, linear alternators, heat pumps, cryogenic refrigerators and gas compressors. In addition, development has continued on a cruciform variable displacement crank-type Stirling engine having a Rinia arrangement. ERG is performing R & D on heat exchangers, heat pipes, isothermalizers, regenerators, gas springs, gas bearings, seals materials (including silicon nitride and silicon carbide), and computer model.ing as well as on linear motors and alternators,, hydraulic drive components and external heat exchangers and heat sources (including combustors and solar collectors). ERG has built and tested several test engines and presently has separate electromechanical, hydraulic, engine and heat exchanger test cells. ERG sells heat exchangers, regenerators, linear motor/alternators, linear motor-ing dynamometer test stands, gas springs/bear.ings and dynamic seals, ERG plans to sell soon an oil-free isothermal compressor with linear motor drive and small,lhermoscillators and laboratory,demonstrations. The current status on ERG Stirling engines is given ,in references 77 a and u.
_: i_' _:,
Dr. Benson reports that 5 people funded Stirling engine programs.
_
".-_
Entwicklungsgruppe Stirling M.A.N. Werk, Augsburg,. D8900 Augsburg l Stadtbachstrasse 1 West Germany Contact:
_""
Dr-lng.
are now working
solely
on corporately
Motor M.A.N.-MWM
F. A. Zacharias
M.A.N.-MWM is a licensee of Philips and cooperate with Philips on some few projects. M.A.N.-MWM is following an independent course.drawing on their experience as makers of Diesel engines. The 1973 information from JPL who visited there in 1974 (75 t) indicates that they are using doubleacting, crank-operated pistons in an in-line or in a Vee arrangement. The heater tubes are invest,_nt cast, some with fins. The. tubes are arranged in a line instead of a r,ing as employed by United Stirling. They use a straight accordian folded counter-flow air preheater arranged,in parallel 343
!
i
....... !
Entwichlungsgruppe-
Stifling
to the straight
heater
Motor M,A.N.-MWM Continued tube banks.
Apart
from
the
usual
pressure
level
of power control called intermittent short ci.rcuit control. For part of the time during compression and also expansion a valve is opened control by working gas space.to compressor thethey have space. followed The up fraction a unique ofform connecting the .working buffer the, time •determines the power, "Very quick engine response, moderate efficiency under partical load and moderate construction costs are from this-form of control." expected (00. c) -
i
i '
i !
Together wi.th Battelle Institute, Frankfurt, they have a concept of a hydrostatic drive mechanism with a stroke regulating control. Best partial load efficiencies are expecte_d.
I
Due to another source it. is known that M.A.N. in cooperation with Philips have realized a Stirling engine heating system by Li-SF 6 combustion, via heat pipes. At present
i! I
f
about
40 people
are employed-in
the group.
Fairchild Industries Germantown, Maryland
i:
Contact:
!
A1 Schock
Fairchild has a contract with DOE to perform technical serviGe_. One important thing has been that A1 Schock has. developed a 3rd order computer program to analyze the Beale free-piston engine that Sunpower is furnishing to MTI.
,
Nothing
About 2 people
!
has so far are working
been published. on Stirling
I
engines,
i
FF_ Industrial Products Sweden See:
,t
Stirling_Power Systems
COrp.
FFV is a Swedish government-owned industrial group who is 50% owner of Un.itedStirling, Independent of United Stirling, but using United Stirling technology, they have built a medium performance engine generator set which operates very quietly for commercial and military applications. The first technical paper on this product will be released in late 1978 and the engine-generator will be for sale to the general public in 1979. The product will be sold in the United States by Stirling Power Systems Corp. FFV now employs 50 people on the St-irlingengine project.
id ,t
344
,i
L.- ....
-
m
.
i
i
•
._
il
! .... ii........ I i ....... ! i i _.......... ' I_ l _ "
:
_
_
!
;
.
;:Ii -', i
1
<.
Ford Motor Company Powertrain Research Office.
,I'
Dearborn, Michigan
I
Contact: Norman D. Postma Since 1971, the Ford Motor Company has been working with N.Y. Philips Company.of Holland evaluating Stirling engines for automobile propulsion. The promise,of this development is given in reference 73 h. The present sta, tus is presented in Section 3.1.- Ford is a licensee of Philips. The program at both Dearborn and Eindhoven was designed,to put two Stirling engines into Ford Torino automobiles for evaluation of vehicle p_rformance,
i ".._ . _ i !I I '!_'!_ II
'i_
ecol',on,y, with emissions, Ford1 0ct-1977 i.s now working on a 1985.. $161 mi.llion costof sharing contract DOE to etc go from to 30 Sept The goal this. program is to determine whether or not the-Stirling can be an attractive autoraobi Ie engine.
',i\ I
,!_ _,
Currently Ford has. about 50 employees working directly on the first task of the DOE program which requires a high confidence assessment-, of the Stirl':ng engine fuel economy potential •
_,,'I
: ..
,,_, I
i
'.'_ ".!
Contact:
i i! _
I
General Electri.c,Advanced.. Energy Programs Valley Forge.Space Division Valley Forge, Pennsylvania 19481
i h _
Mr. J. A. Bledsoe
GE is developing a Stirling Radioisotope Power System (SIPS). North American Philips is doing the engine (76 j.), Plutonium-238 oxide is the fue? and lO00 w(e) is the power. Contact:
Mr. L. Dutram ..............
Also on a separate program GE is continuing a developn_n_tprogram started at Sunpower of a gas heated free piston, free-displacer• Stirling engine operating a Freon compressor (77 w). They plan to build and .testa three ton cooling capacity prototype by 1979. The project is sponsored by the American Gas Association, the . Department of Energy and General Electric,
'_I '[ I
Forty people are working on Stirling engines atGeneral I
! i
t 1|
. .
John I. Grifffn Solar Engines_ 2937 West Indian School Phoenix, Arizona 85017
Electric.
Road
Mr. Grif_fin is building and selling model Stirling engines. _e has one . on the market now. and plans to market 6 more models over the next two years. Three thousand 31 Jan 1978•
of the first
model have already
been sold
as of
i I I
1
I I
I
34 b
.
,
Fi
•
I
-
*
i
I I
'
? !
! '.": : ,,._ •i '<_ l ,
I
!
Ilanv(,1 i Laboratory Inst_ru,)c:ntation &,AtoP.lied Physics Division AERE Oxfordshir.e EngI and1 Flar_veI
OXII.ORA
Contact:
I
|
Mr. E. H. Cooke-Yarborough
Work at Harwell is concentrated on Stifling-cycle devices wllich do noL use _otation or sliding surfaces. The primary object of this work has been to generate electricity from heat. The machine which has been evolved has a springmounted displacer oscillating at a frequency in the region of lOOHz in helium, and a metal diaphragm to translate the resultant gas pressure changes into a mechanical movement hav.ing:..an amplitude of the order of Inlm. The oscillating hub of the diaphragm is coupled to a special alternator in which a permanent magnet vibrates between two pole pieces carrying windbags-on which the alternating output voltage is generated.
,,
A number of thermo-n_chanical generators giving alm alternating power output in the region of 30W have.been.built. One of these has been in service since the summer of 1975, to provide the power- for the UK National Data Buoy Seven machines ilavebeen built, one with a heat-to-electricity efficiency
of
,
16.9%.
'i!
i
!
Development sponsoredby-AGA Navigation /_ids Limited has resulted in*the up-rating of this design to 60W. During 1978 AGAwill"install a 60-watt TMG as the main power sour_.e.-_-n a major lighthouse off the Irish Coast.
i T
A further development, which stemmed from the work on the TMG, ,is the Fluidyne,,which uses an oscillating column of-liquid as a displacer, and another liquid column, oscillating underthe influence of the gas pressure changes, to provide the power output. This system is well adapted to the pumping of liquids. Construction and operation, are relatively simple, and this has potentialities for water-pumping in developing countries. An experimentaJ machine-has pumped at a rate in excess of 60 gal,lons perhour.
-
The current program is aimed at improving the power output and efficiency of the TMG to meet specific requirenmnts of users. It is also aimed at adapting the Fluidyne to meet specific user requirements. The equivalent
of two people
Hughes Aircraft Company Centineia & Teale Streets Culver City, California 90230 ConLacts:
Dr. Bruno Leo Mr. Richard Doody
are now working
on Stirling
engines
at Harwell,
i,
_
_,
IIu!lhes Aircraft Colnpany Continued IIuqhesAircrafL Company has been developing Stirling type cryogenic refrigerators since 1960 and a family of these units have been dew,loped for ground, air and space applications. Currently, emphasis is being placed upon Stirlinq and Vuilleumier refrigerators includinq special modified versions ef eacl_-Jco-meet the specific needs of various applications.. About 45-people
are involved
in Stirling
type
cryo
cooler
developrilent.
L
_ 4
.... ::.. ,' I _. ....o _i:"o.. _
Jet Propulsion Laboratory 4800 Oak Grove Drive Pasadena, Cali.fornia 91103 Contact:
Frank W. Hoehn
The Jet Propulsion Laboratory is currently working on a program to develop a St-irliml. Laboratory Research Engine which can eventually be produced commercially and be made available to resea.rchers in academic, industrial, and government laboratories. A first generation lO Kw.engine has been designed, fabricated, and assembled. The preprototype engine is classified as a horizontally-opposed, two-piston, single-acting machine with a dual crankshaft drive mechanism. The-.test engine, which is designed for maxiillum modularity, is coupledto a•universal dynamometer. Individual component and engine performance data will be obtained.in support of a wide range of analytical modeling activities. The laboratory Stirling linear
is also sponsoring work on a. 1 Kw, solar elec,tric generator.
heated
3-6 people
support
the Stirling
engine:related
activities
Laboratoriet {:or .Enerqiteknik Danmarks Tekniske Hojskcle Bygning 403 . DK-2800 Lyngby Denmark Contact: ,,
Professor Professor
Due t:o Professor inLerest in this tory on Stirlinq nOW
!]oing
011 ill
Bjorn Niels
I/,
J:_
free-piston
JPL did the study (75 t) which influenced DOE to concentrate their efforts on the Stirling engine and the-.Gas Turbine for futur-e-automobile e1_gines. Approximately at JPL.
i, _"
Qva.le Ellno Anderson.
Qvale's thespis at MIT on Stir-ling engines and his subsequent Field there have been a number of papers from this-laboraengines. A recent letter states that almost no work is this field.
A4 '
,_._'.,_
if' i ¸.
I
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F..... [Tt I
•
,
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:
,
_
"
"
i
Professor W. R. Martini Joint Center-for Graduate Study lO0 SpPout Road Richland, Washington 99352
i
Professor Martini heads a group varying from 1 to 5 working on various basic aspects of Stirling engines, He is the author of the St-irling engine design manual. He also sends out the Stirling Engine Research Institute Newsletter. He is interested in deternlining the usefulness of isothermalizers in Stirling engine designs and in building a heat operated heat pump using two Stirling cycles. He started the artificial heart power source program at McDonnell Douglas and continues an interest in this..program.
...........
Mechanical :rechnology Inc, 968 Albany-Shaker Road Latham, New York 12]]0
t i ' I
Contact:
Bruce Go.ldwater
In conjunction with Sunpower MTI is developing a Free-Piston Stirling Linear Alternator power" conversion system. They are agressively expanding their own Stifling engine capability. They are working with United Stirling to denlonstrate Stirling engines for automobiles as part of a major DOE funded study. ',
_ i'! ,_
MTI currently
has 20 people working
on Stifling
engines,
ill i i
;! i ,"_
McDonnell Douglas Corp. Richland Energy LaboratoryI00 Sprout Road Richland, Washington 99352 Contact:
R..P,
Johnston
i
.-
Since 1967 this group has been developing-miniature St irling power an artificial heart. The engine produces ahout-Swatts
engines to of hydraulic
power from heat at about 18% efficiency. It employs a free displacer _ngine which applies pulsating gas pressure through a diaphragm to a freely oscillating oil pump. The engine is self starting and is controlled by a single valve adjustment. Fresently
I
348
II
people
are employed on this
project.
"I ,_ i ,.
•
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j
':
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:
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,/ ,, ,_.
NASA-Lewis 21000 BrookparkRoad Cleve.land, Ohio 44135 Contact: R. G. Ragsdale,Manager StirlingEngine ProjectOffice NASA-Lewishas been given the projectmanagementresponsibilities by DOE to produce improved Stirling engine propulsion systems during the next decade. They have obtained two GPU-3 Stirling engines and are testing one to obtain some publicly available information op Stir.ling engine
_
I I i
"
i
They have negotiatBd the $16!.million contract with Ford Motor ,Co./Phi l i ps for development of Stirling and will negotiate a contract with MTl/United Stirling/American Motors for the sa:_ thing. They have sponsored the
i I i
production thisUniversityof Stirling engine design manual. Theyreciprocating have a contractseals, pe_rfo Boeing rmance.ofand with Toledo for evaluationof They are doingwork on materialstechnologyfor both a metal and a ceramic Stirling engine. They have signed a contract with ll]inois Institute of Technology Research Institute to measure hydrogen permeability in metals
Ii I i i
_ ;
and ceramics. Near-term future plans are aimed at establishing advancedsystem a balanced, integratedmix of activitieson improvedengine development,
i1
!4
definition_studies and supporting, researchand technology.
I.-_ ,_ ,
Currently the equivalent NASA-Lewis.
I
l
of 20 people are working on Stirling
enc}ines at
Mechanical Systems Section BuildingEnvironmentDivision Center for BuildingTechnology National Bureau of Standards Washington D.C. 20234 .... Contact: Dr, Davi_L.A.Didion
'
I
1 l,I
j I I
i ' ! ! ! i I
::i ,_ _
The initial work at NBS focused on the laboratory evaluation of a Philips 1-98 engine driving a Rankine cycle heat pumpwhich used recovered engine heat to supplement its own capacity. The system was tested as a function of outdoortemperature,engine speed, and coolanttemperature,and many of the resultsare presentedin reference77 ad. A subsequentanalytical studywas conductedon.the per..formance of a varietyof total energy configurations when powered by Stirling engines. This work will hopefully be presentedat a future IECECmeeting. We are currentlyinvolvedin developinga test and rating,procedurefor engine-drivenheal:pumps which will include Stir ling engines.
_i
One-personis currentlyworking on this project.
1
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349 i
....
Dr. Allan J.. Organ Department of Mechanical En,qi,eering University-of London King's College Strand London, England WC?R?1.._ Dr. Organ is a regular contributor since 1970 to the literature on Stirling engines.. Tile recent ones• have been highly mathematical, Those who have ta_ked with him state that he •i s as filuch concerned with the n_chanical part of the engine as he is with the heat transfer and fluid flow-part. He has a, grant from the United Kingdom Science Research Council for an experin_ntal program. His departnw_nt intends to offer Starting October 1978 a courseunit option (one engineering degree subject credit) in the thenl_odynamics and-computer modeling of.:Stirling.cycle machines. This course wiII be for final year engineering students.
-
i_i _'
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i
' !
N, _. Philips Eindhoven Nethe rl ands
*! !
i
i
•, .i
dr. ir. C. L. Spigt about I00 people.
is in
charge of
'i
Dr. R. J.
Meijer
_
.. _i •', _i_'
Ann Arbor,.. Michigan 48104 439 Huntington Place Dr. A. P, rJ. Michels .......
I |
_'-i,
1828 Mershon Ann Arbor, Michigan
the Eindhoven
Stifling
work --
,!_ Science
I 48104 __
engine
advisors
to Ford
'_ __
Motor Company on Stirling engines "
i 1
J
The Phil.ips Company was the first to recognize that the Stirling engine would be a useful .prime mover if it were modernized. Philips has been publishing on Stirling engines since 1943. Almost all the companies develop.ingStirling engines for sale-are licensees to Philips. These
'
include United Stirling, FFV, M.A.N.-MWM, ar:d. The Ford Motor Company.
._ ,! i I
Philips has developed the rhombic drive Stirl..ing and the 4,cylinder swashplate Stirling. They )lave perfected the oil backed roll sock seal. They have demonstrated very long life and very high efficie,cy in their machines. They have built engines to replace the automobile .........engine in size and power density. Besides developing engines that elf efficiently employ.liquid,fuel they have demonstrated machines that use coal, Li-SF6,.and stored thermal energy. Their Stirling engine cryogenic refriqerators are a com,_.rcial success,
3c_tl
._ ,_
J
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c_
,
4
PhilipsLaboratories , .adivisionof
:
North American PhilipsCorporation Briarcliff
Manor, NewYork 10510
Contact: °
1
Alexander. Daniels
Philips Laboratories have close association, of Holland, and have a number of programs.
with the N.V. Philips
Company 'L
They are working on the SIPS proqramwith the GeneralElectricCompany (76 .i) and they are doinq a study for DOEon-a total energy system using.Stirlingengines (77-f).
i!,_ i i .,, 1
Fourteenpeople are working on Stirling.enqines at North.American Philips.
.:< I
Norman E Polster Argenta, B.C. _
Canada
i
Mr. Polster. has invented a self-starting, intrinsically engine. In a demonstration model made at the..Ontario
' _"i I
s'.: k:,.l _.i _:'_i :,: "<_ _ _, L "I
controlled Stirling Science Centre, a
controllableoperated acceleratinq or decelerating torque,anincluding zero torque manually torque control level provides instantaneous continously for any shaft position,, any shaft speed and directionincludinga stationary condition. Mr. Polster is joined with JOSAMManufacturing Company, Michigan City, Indiana, in further developments. Somework has been done at the Joint Center for Graduate Study, Richland, Washington. (76 c)
L_
'
.... ii_i ..... i
_" .... ,
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Professor C. J. Rallis School of MechanicalEngineering Universityof Witwatersrand 1 Jan Smuts Avenue Johannesburg 2001 South Africa ProfessOr Rallis currently leads a team of 6 graduate and undergraduate and students in developing 2nd and 3rd order computations procedures checking them with experiments. They are-also doing basic-work on pressure drop, time lag effects, and heat transfer in periodic f'iow heat exchangers. They are also experimenting:with fluidyne machines and are consulting with Harwell on the analysis of the thermo mechanical converter ProfessorGraham Rice Dept. of Engineering& Cybernetics .... The Univc.rsity of Reading Whiteknights, Reading RG6ZAY, England Professor
Rice has been involved
,; ' ' .. I
:_ D.: in a number of interesting
Stirling
engine 35i
r
Professor
Grallam Rice
I! ¸ i
FI
_
_
_
"
_
_
"
I
Continued
experiments at the University proposed consortium to-design Kingdom.
of R6ading an.d,.builda
(75 k). Stirling
He is involved engii,e in the
i.n a United ....
;
Ross Enterprises 37 WRst Broad Street Suite #630 Columbus, Ohio 43215 ,
Contact:
_ _ ,
M. Andrew Ross
Mr. Ross is a practicing attorney who is also a model engineer. He designs and builds his ewn machines in his own shop. He is also the author of a number of-popular, articles on Stirling engines (.76 a, 76 b), and has an impressive collection of antique Stirling engines .... Professor J. Senft Division of Science and Mathematics Minot State College Kinot, North DakotaS.8701Professor Senft teaches mathematics, does research on Stirling and other heat engines, builds miniature engines in his own shop, and writes on engineering subjects. He has authored several articles on miniature Stifling engines in model engineering journals, and has also worked as anal_st with the Sunpower group. P.rofessor J. L. Smith Jr. Dept. of Mechanical .Engineering Massachusetts Institute of-.Technology 77 Massachusetts Avenue Cambridge, MassachzLsetts 02139 Professor Smith is developing a valved hot gas engine which may have high _.. torque.at low speed like a Stirling engine but without the severe restrictions on heat exchanger dead volume inherent in the Stirling engine. At this time, one graduate student is working wi.th a test engine, concentrating on the periodic heat transfer between the working gas and the cylinder walls of the compressor and expander.
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Stirling Power SysLems Corp. 7,101 Jackson Road Ann Arbor, Michigan 48103 Contact:
Mr.- Lennart
Johansson.
i _,_
Stirling Power Systems is a marketing organization owned 80.5% by FFV a Swedish go.vernment owned industrial group and. 19.5% by Thetford Company, a recreational vehicle-equipment supply firm of Ann Arbor, Michigan. They will market the FFV engine-generator,
,
....
',+ _I .... '.
Sunpower Inc_ W, T. Beale, President 48 West Union Street
"?i
Athens,
< ......
Ohio 45701
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Sunpower is an out-growth of Professor WilliamT. Beale s work at Ohio University on free-piston. Stirling engines. Sunpower is working with MTI of Latham, New York on a DOE sponsored 2KW(e) space power plant using a free-displacer., free-power piston Stirling engine driving a . linear" alternator, Sunpower has also built a free-piston engine "For NASA-Lewis.
;_! • ,i '_
A new small solar-electric engine designed by Sunpower is being tested. The target for this system is overall conversion efficiency from solar energy to usable electric power approximately twice as high as that of a silicon solar cell using concentrated sunlight,
,._
Sunpower currently employs 12 people working on Stirling engines.
' ' _-._. ,
I
i
.,
!-
Trans Computer Associates Dr. T. Finkelstein, President P.O. Box 643 Beverly Hills, California 90213
,
I ,i
Dr. Finkelstein has worked on Stirling engines for a number of companies. He is now an i.ndependentconsultant and has his 3rd order computer code available for use. He conducts a short course on Stirling engines every _ year at UCLA. He is the authority on the history o.fStirling engines.
_+
"
United Stirling (Sweden) AB &_Co. Fack 201 I0 Malm_ I, Sweden
.]
Contact:
Bengt Hallare, corporate Planning and Marketing
United Stirling's program is well described in Section 3.2 oi_this manual. Brieflyjthey have designed a 40, a 75 and a 150 KW engine to be used in__ :,
3_3
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tJnitedStirling (Sweden)Continued vehicles. Although a licenseeof Philips,tiieyhave deve,loped their own
I
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arrangement. mechanical seal and their
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United Stirling is identifiedalongwith MechanicalTechnologyInc. and
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own engine, designs,
a crank operated Rinia
enginesfor.automobiles. AM General as the "second team" to be funded by DOE.to develop ,Stirling United Stirlingemploysabout I00 people working on Stirlingengines. Dr. IsraelUrieli Ormat Turbines P.O, Box 68 Yavne, Israel Dr. Uriel.i recently received his doctorate from the University of Witwatersrand on the subjectof a third order analysisof a Stirlingengine He is lecturingpart time at the Universityof.Bershevaand is continuinghis researchon Stiflingengines.
j
'!.. :i ! 'i!
'_
Professor G, Wal_er Dept. of Mechanical Engineering Universityof Calgary Alberta, Canada
,. :_
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ProfessorWalker is measuringcharacteristicsof reversingf.lowregenerators. He teachescourseson Stiflingenginesand is,,theauthor of an important book on-Stirling engit_es. (73 j)
;! 'L:! .,
Westinghouse Electric Company Advanced P.O. Box Energy 10864 Systems-Division
'I
Pittsburgh, Pennsylvania 15236 Contact: W..D. Pouchot
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_,_
......................
Westinghousehas been doing the system work and North AmericanPhilips has been doing the.enginework on a DOE sponsoredartificialheart program (76 am). The Stirling engine work was phased out in U.S. GovernmentsFiscal Year 1977.
'
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DERIVATION OF EQUATIONSFOR HEAT FI.OW.
i_
FROMVOLUMES WHICHARE HEATEDUNIFORMLY
j
During entire
!
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f
:
APPENDIXA
"
I
,,'
I
I ...... I .... i..... ' "i -_ i "I_ '
i
Laser
_
expansion
and-compressio_
volume changes uniformly heating
equations
also
.will
gas temperature
before.,.thermal'conductivity
approximates
be derived
of a mas, the
this.
for
heat
For the
flow
the
makes a difference.
purpose_-of
from a slab
of
evaluation
'"
the
and from a cylinder.
From a Slab In Figure
AI the
= I/f_
Qx
,,
where
gas is being
x
flow
x = distance
from
both sides,
The.hearflow
dT : "kGA _
Qw_
Qw = heat
cooled
(AI)
at wall, from
at x_is:
watts
centerline,
m
,J
'
kG : thermal A-:
area for
conductivity
of gas,
w/m °C-
heat.flow,.m
T = gas temperature,
°C
_i
I nteg rat i ng.,
',.;i
s/2 .....'
S
TM
xdx = -
!,_
dT
(A2)
"
iL';
_'
So : Qw -
4kGA s (T__- TM)
if'_ (A3) %:
However,
we need
to
know the
average
gas
temperature,
TA, instead
of
the
center.,
"
line temperature,T_. TA is defined by the equation
I
I
35!,
",!.'i!
::'
i¸
I
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J
I
/I
i
-
i
........
.
.....
L -
_
Figure
AI.
TM
AssumedGas
Conduction
Distance
t
in
'i
a Slab.
I
i; _
t
f,.ct_
I
'
F,,-
Distance
Fiqure
35_
A2.
Assumed
Gas Conduction
in a Cylinder.
1
]
i
1,2.-'_"_
.._L'.
'_il ¸¸ _
r......
_
.
F ,
i
i
,
T
" ':
,X )
I
s/2 (T A - To)g=
(T-
i:
T#..)dx
(A4)
0 Using different
limits
on Eqdation T
x _
2Qw/ s
i
xdx .- -kGA / 0
A2:
dT
(A5)
T¢_
2Qw s x2 2 -
kGA(T.-'_.T_)
(A6)
2 T - T_ : - -ewX SkGa
(a7) r
s/2 So -
I-
Q.__.w_w
TA - T_ = 0
SkGA x2dx s/2
From Equation
Tt
_ Qws 12kGA
-
' i
A3
i
- TM - 4kGA
(Ag)
I [i
(AI0)
ii 1
Therefore, TA - TM : TA - T& + (T& - TH)
Qws
Qws
Qws
- 12kGA + or Also,
standpoint
Qw : -pVCv where
........................................................... i
0-_ - 6kGAs(TA " TM) from the
of heat capacity,
(All}
l
...........................................
dTA do
p : gas density,
i_ _, kg/m 3
3.57
•
IL__
_
(A8)
i
i
,t
' ._
Cv heat volume, capacity m3 at V = -- gas
-i
TA = average
',4!: !!_
from
0 = time, a Czl_inder
constant
volume,
gas temperature,
j/kg
°C
]
°C
|
seconds
i ,
In Figure flow
A2 the. qa,.; is b,eing_-cooled
from the
cylindrical
surface.
The heat
:
at r is:
K', _i'i "";
. 1
_r 2 = -kG(2_r_) 0'r : Qw-_D2 ..
;.i
(__r) _m r
,. i ;]
(A12)
iit
4_,
i':] '
where g = length
,!
1.1 I
Integrating:
i.._
D2(2.,r._kG) -- -
o
,
of cylinder.
n_.kGD2
ra
dT
(A13)
rr l =_IT] TM LYJo .
-T4 -
QwD2
";
.n._kc_-_-_2-_4 : T[ - TM •
I
Qw = 4.,,_kG
_ Ti_ - TM
However, what is needed is
., "
i
the
integrated
average
gas temperature,
TA.
i
_
1
By
_
I
i
.I
-'
4
D/2 (T A
--T¢,_)4"D _- = f 0
(T - Ta)2_rdr
1
(AI 4 )
_efi_itio_, .........
•_
._
(A15)
1
"
j
I,
"
4
or
.,.....
Qw : 8ng'kG(TA " TM)
(A22) 359
I.
Hepo, t N_._
NASA
I
2
(.io¥1'/rll|lt,llt
Acc¢".'.,,..I
N_,
:1. I{,.rlpwnl",
(;at,lh_q
NI)
CR-135382
STIRLING
ENGINE
DESIGN
April 1978 -I_.i'_._f_},:,_],_,j o,g..,,_., ..... (_,,J,.
MANUAL
1 7. A,_thor(s)
!
8.
........ N,I
}: 10
12.
....
'{
,
:
Performing
Organilation
Sponsoring
Agency
•
and
Name
and
15.
Supplementary
Wo_k
Unit N_
?, ,-
A¢ldn_ss
_-.
_. Conu,_c,or Gr_,, No NSG-3152
Study
13.
Type
of
report
Contractor
Address
U.S. Department of Energy Division of Transportation Energy,
Conservation
and
;'_ ,,,_
P;riod
Covered
Report
i)_
9
14.Sponsoring AgencyCode
i_ote:
WFinalshin on report.
_
Name
University of Washington Joint Center for Graduate I00 Sprout Rd. R W 99 5
..
I
I(/,I,o.t
William R. Martii_t 9.
:
Perf()Hurlq Chgdnoziltioll
i'_
D.C. 20545under Prepar.ed
Harold Cleveland_H. Valentine, Ohio 44135.Systems 16 a_$,r_c,
hlteragency Analysis
EC-77-A-31-1011. DOE/NASA/3152-78/I Project Manager,
Agreement and Assessment
Office,
NASA Lewis
Research
Center,
:"" _,, _}
This manual is intended to serve both as an introductionto Stiflingengine analysis methods and
_
i
as a key to the open literatureon Stiflingengines. Over 800 references are listedand these are cross {] •
referenced
by date
of publication,
author
and subject.
Engine
analysis
is treated
starting
from elementary principles and working through cycle analysis. Analysis methodologies are
:.
classifiedas first,second or third order depending upon degree of complexity and probable performance application; first order for prelimhmry engine studies, second order for and engine optimization, and third order for detailed hardware evaluation and engine A fe.w comparisons between theory and experiment are made. A second order design
I ;
is documented high power active
step engines
in Stirling
by step
with calculation.sheets
are .briefly engi,m
described
and a directo_T
development
is included.
very
design
useful
ai_d a worked Much
complicated
and potentially
support will experinmntal
enable a more thorough job of comparing data which should soon be available.
out example
of companies remains
procedures
are
to follow.
and individuals
to be done. now only
all available
Some
referred
design
prediction research. procedure Current who are
procedures
Future ag_.inst
u
17.
Key
Words'(Suggested
Engine
modeling;
Stirllng
cycle
Stirling
engine;
by
Author(all
Advanced
Performance
Unclassified
J 18.
engines;
simulation;
J
O_stl_huhon
Statement
STAR
Category
85
ERDA
Category
UC-96
Unclassified
Unclassified
- unlin_ited
]
370
' F,II ._.d_! bythe N.ih0:_.fl]_'chlu_.dI_h_ll,_Ih _, S,',v, ' Sl_llllchchl V,Iv'lI!u 2216l
i:
of the more
to,
J
A 16
I
:_ '_'
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