Variable-density oscillatory flow and heat transfer in 2D models of a Stirling microrefrigerator

117 Pages·1996·2.6 MB·English

by  Guo, Guobao

VARIABLE-DENSITYOSCILLATORYFLOWANDHEATTRANSFER
IN2DMODELSOFASTIRLINGMICROREFRIGERATOR
By
GUOBAOGUO
ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL
OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILMENT
OFTHEREQUIREMENTSFORTHEDEGREEOF
DOCTOROFPHILOSOPHY
UNIVERSITYOFFLORIDA
1996
ACKNOWLEDGMENTS
Iwouldliketothankmysupervisor,ProfessorUlrichH.Kurzweg,forhis
guidance,constantencouragementandpatience. 1havegreatlybenefitednotonlyfrom
histeachinginengineeringbutalsofromhisintegrity,whichhashadapositiveinfluence
onmylife. IsincerelythankDr.Chen-ChiHsuforgivingmetheopportunitytojoin
thegraduateprogramhereandforteachingmemanyofthefundamental,yetimportant,
aspectsofCFDduringmyfirstphaseofgraduatecoursework. Likewise,Iamvery
gratefultoDr.WeiShyyforourdiscussionsandhisfruitfulsuggestionsinmywork.
Ialsoexpressmyappreciationtomyothersupervisorycommitteemembers.Dr.David
M.MikolaitisandDr.KermitN.Sigmon,fortheirinterestandsuggestions.
Myspecialthanksgotomyfellowgraduatestudentsofthedepartmentherefor
theirhelpandcompanionship. IespeciallythankDr.Ming-HsiungChenforhiswarm
friendship,helpandencouragementovertheyears.
IamthankfultotheDepartmentofAerospaceEngineering,Mechanicsand
EngineeringScienceforprovidingfinancialassistance.IextendmyspecialthankstoDr.
MichaelA.DeLorenzooftheDairyandPoultryScienceDepartmentandDr.Ranganatha
NarayananoftheChemicalEngineeringDepartmentforofferingmepart-timejobs
during mystudy, whichexposed metosomeotherinterestingengineeringand
managementproblems. Theyhavecertainlyenrichedmyeducation.
IamtrulygratefultomywifeYingforherlove,patienceandencouragement
duringthiswork,whichweremorethanIcouldeverhaverequested.
ThePittsburghSupercomputingCentersupportedthisworkthroughtheallocation
of183ServiceUnitsontheCrayC90supercomputerforthreeandhalfyears,andis
acknowledgedhere.
21
TABLEOFCONTENTS
page
ACKNOWLEDGMENTS ii
LISTOFTABLES vi
LISTOFFIGURES vii
ABSTRACT ix
CHAPTERS
1 INTRODUCTION 1
1.1 BackgroundofStirlingRefrigerators 1
11..3 L2iDterCaotmupruetRaetvioineawlModelsandScopeofthePresentWork 1137
2 GOVERNINGEQUATIONSAND
PRESSURE-SPLITTINGTECHNIQUE 22
2. GoverningEquations 22
2.2 SeparationofHydrodynamicandThermodynamicPressures 25
2.3 BoundaryConditions 28
2.4 NondimensionalizationofGoverningEquationsandBoundary
Conditions 30
2.5 GeneralFormoftheGoverningEquations 34
2.6 DimensionalAnalysis 35
3 NUMERICALTECHNIQUESANDCODEVALIDATION 37
3.1 NumericalGridGeneration 37
3.2 DiscretizationoftheGoverningEquations 40
3.3 SolutionProcedures 49
3.4 InitialandSlow-StartBoundaryCondations 54
3.5 CodeValidation 57
4 RESULTSANDDISCUSSION 65
4.1 VelocityandThermodynamicFieldsforaTypicalCase 68
4.2 ModelComparison 82
4.3 ComparisonofUsingHeliumandAir 85
4.4 PhaseAngleEffect 86
4.5 ImpactofVaryingRefrigerationTemperaturesonPerformances... 87
4.6 ChangingChannelLength 89
4.7 EffectsofChangingtheRatioofChamberWidthtoChannelWidth 90
4.8 DiscussiononRegeneration 91
5 CONCLUDINGREMARKS 95
REFERENCES 98
BIOGRAPHICALSKETCH 104
LISTOFTABLES
Table page
Table2.1 Termsinthegoverningequation(2.34) 35
Table4.1 Listofthecasesinvestigated 66
Table4.2 ComparisonofModelsAlandA2 83
Table4.3 ComparisonofModelsA2andB2 84
Table4.4 Comparisonofheliumandair 85
Table4.5 Comparisonofcaseswithdifferentchannellengths 89
LISTOF FIGURES
Figure page
Fig.1.1 Stirlingcycleandathree-componentStirlingrefrigerator
configuration 2
Fig.1.2 Schematicofafive-componentStirlingrefrigerator 5
Fig.1.3 Single-channelmodels,(a)ModelAl;(b)ModelA2 18
Fig.1.4 Multichannelmodels,(a)ModelBl;(b)ModelB2 19
Fig.2.1 IllustrativeIDdiscretization 26
Fig.3.1 Twotypicalgrids,(a)cot=ir/4;(b)oit=r 39
Fig.3.2 IDgrids 39
Fig.3.3 Controlvolumesforscalarquantities 42
Fig.3.4 Staggereduandvcontrolvolumes 42
Pig-3.5 Schematicofageneralcellfor<t>atpointP 43
Fig.3.6 AsouthboundarycellwithDirichletboundarycondition 48
Fig.3.7 AsouthboundarycellwithNeumannboundarycondition 48
Fig.3.8 Solutionproceduresforvariable-densitytime-periodicflowand
heattransferproblems 55
Fig.3.9 Apiston-cylinderset-up 58
Fig.3.10 Computedhydrodynamicpressuredistributionsalongthexaxis
forthepiston-cylinderset-up 58
Fig.3.11 Thermodynamicpressureinthethirdcycleforthepiston-
vii
cylinderset-up 61
Fig.3.12 Temperaturedistributionsalongthexaxisforthepiston-
cylinderset-up 61
Fig.3.13 P-Vdiagramofthesecondtestcase 63
Fig.4.1 Transientprocessesofpressures.
(a)Thermodynamicpressure;(b)Pressuredropbetweenpistons. 69
Fig.4.2 Convergencehistorytotime-periodicstate 71
Fig.4.3 VelocityfieldsofCase1
(a)wt«0;(b)ut=ir/2; 72
(c)out=7r;(d)ut=3ir/2 73
Fig.4.4 HydrodynamicpressurecontoursofCase1
(a)cjt=0;(b)ut=x/2; 74
(c)ut=7r;(d)tot=3?r/2 75
Fig.4.5 TemperaturecontoursofCase1
(a)ut=0;(b)o)t=Tr/2; 77
(c)ut=x;(d)wt=3x/2 78
Fig.4.6 DensitycontoursofCase1
(a)cot=0;(b)wt=ir/2; 79
(c)ut=x;(d)cot=3x/2 80
Fig.4.7 P-VdiagramofCase1 81
Fig.4.8 Phaseangleeffects 87
Fig.4.9 Refrigerationtemperatureeffects 88
Fig.4.10 Effectsofchangingtheratioofchamberwidthtochannelwidth 91
Fig.4.11 T(ae)mjp8er=at0u.r0e29d8i;str(ibb)utio=ns0a.l2o9n8gxaxisfortwodifferent/3's 94
AbstractofDissertationPresentedtotheGraduateSchool
oftheUniversityofFloridainPartialFulfilmentofthe
RequirementsoftheDegreeofDoctorofPhilosophy
VARIABLE-DENSITYOSCILLATORYFLOWANDHEATTRANSFER
IN2DMODELSOFASTIRLINGMICROREFRIGERATOR
By
GuobaoGuo
May1996
Chairperson: Dr.UlrichH.Kurzweg
MajorDepartment:AerospaceEngineering,MechanicsandEngineeringScience
Two-dimensionalmodelsofthree-componentStirlingmicrorefrigeratorsare
examined.Themodelsconsistofheaterandcoolerendedwithpistonsoscillatingoutof
phaseandconnectedbynarrowchannelswithalinearwall-temperaturedistribution,
simulatingtheregenerator. Navier-Stokesequationsgoverningthevariable-density,
oscillatory flowand heattransfer withintwo-dimensional domains with moving
boundariesarenumericallysolvedbyusingtheSIMPLEalgorithmincorporatedintoa
movinggridtechniqueandapressure-splittingtechniquethatisnewlydevelopedinthis
study. Suchasolutionmethodologyisaccurateandefficientforthecomplexflowand
heattransferproblemsinStirling-typedevices.Thepressure-splittingtechniqueseparates
thehydrodynamicandthermodynamicpressures,whicharedifferentbyordersof
magnitudeforgaseousflowswithheattransferlikethoseinreciprocatingmachines.
Separationofthepressuresincreasesthecomputingaccuracyandefficiencysubstantially
(withsavingonmemoryby50%andonCPUtimeby30%),andthetechniquecanbe
easilyincorporatedtoanypressure-basednumericalalgorithms. Themodel'scooling
performanceissensitivetoadimensionlessparameterthatistheproductofPrandtl
number,Womersleynumbersquared,andtwodimensionlessgeometricparameters.This
parametershouldbekeptsmallenoughfortheregeneratortofunctionwell. Asthe
refrigerationtemperaturedecreases,thecoolingcapacitydecreaseslinearly,butthe
powerinputincreaseslinearly,andconsequentlytheperformancedegrades. Itisfound
thatforasetofgivenoperationconditions,thereexistsalowesttemperaturebelow
whichnocoolingbecomespossible. Thisiscausedbytheincreasingcoolingloss
throughthechannelastherefrigerationtemperaturedecreases.Lengtheningthechannels
decreasessuchloss,butmeanwhileincreasesthedeadspace,whichinturnreducesthe
coolingmadebytheexpansion. Theneteffectdependsonthesetwocompetingfactors
underspecificconditions. Thephaseangleaffectsthecoolingcapacityandefficiency,
andtheoptimumphaseangleforeithercoolingcapacityorefficiencyisnear90°. For
themultichannelmodel,theratioofthechamberwidthtothechannelwidthalsoaffects
thecoolingperformance,andtheoptimumratiodependsonspecificoperationconditions.