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AppliedThermalEngineering36(2012)227e235
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AppliedThermalEngineering
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cate/apthermeng
Theapplicationofentransydissipationtheoryinoptimizationdesignofheatexchangerq
JiangfengGuoa,MingtianXub,*
ab
InstituteofEngineeringThermophysics,ChineseAcademyofSciences,Beijing100190,PRChinaInstituteofThermalScienceandTechnology,ShandongUniversity,Jinan250061,PRChina
articleinfo
Articlehistory:
Received25January2011Accepted21December2011
Availableonline29December2011Keywords:
Entransydissipation
EntransydissipationnumberGeneticalgorithm(GA)OptimizationdesignHeatexchanger
abstract
Theoptimizationofheatexchangerdesignisinvestigatedbyapplyingtheentransydissipationtheoryandgeneticalgorithm.Itisfoundthattheroleplayedbythe uidfrictionisnotfullytakenintoaccountwhentheworking uidofheatexchangerisliquidinsingle-objectiveoptimizationapproach.Inordertocircumventthisproblem,amulti-objectiveoptimizationapproachtoheatexchangerdesignisestablished.
Ó2011ElsevierLtd.Allrightsreserved.
1.Introduction
Withthesharpdeclineoffossilfuelssuchaspetroleumandcoal,touseenergyef cientlyisoneofeffectivewaystofacetheincreasingenergydemand.Heatexchangerasanimportantdeviceinthermalsystemiswidelyappliedinpowerengineering,petro-leumre neries,chemicalindustries,andsoon.Hence,itisofgreatimportancetodeveloptechnologieswhichenableustoreducetheunnecessaryenergydissipationandimprovetheperformanceofheatexchanger.
Theevaluationcriteriaforheatexchangerperformancearegenerallyclassi edintotwogroups:the rstisbasedonthe rstlawofthermodynamics;thesecondisbasedonthecombinationofthe rstandsecondlawofthermodynamics.Theheattransferinheatexchangersusuallyinvolvestheheatconductionunder nitetemperaturedifference,the uidfrictionunder nitepressuredropand uidmixing.Theseprocessesarecharacterizedasirreversiblenon-equilibriumthermodynamicprocesses.Hence,inrecentdecadesthestudyofthesecondgrouphasattractedalotofattention[1].Inspiredbytheminimumentropyproductionprin-cipleadvancedbyPrigogine[2],Bejan[3,4]developedtheentropy
*Presentedatthe14thInternationalHeatTransferConference,Washington,DC,August8-13,2010.RepublishedwithpermissionfromAmericanSocietyofMechanicalEngineers(ASME).
*Correspondingauthor.Tel.:þ865319930006503;fax:þ8653188399598.E-mailaddress:mingtian@(M.
Xu).
generationminimization(EGM)approachtoheatexchangeropti-mizationdesign.Inthisapproach,Bejan[3]tookintoaccounttwotypesoftheirreversibilitiesinheatexchanger,namely,theheatconductionunderthestream-to-streamtemperaturedifferenceandthefrictionalpressuredropthataccompaniesthecirculationof uidthroughtheapparatus.Therefore,thetotalentropyproduc-_genisthesumofentropyproductionsasso-tionratedenotedbyS
ciatedwithheatconductionand uidfriction.However,amongallthevariationalprinciplesinthermodynamics,Prigogine’sminimumentropygenerationprincipleisstillthemostdebatedone[5].Accordingly,theentropygenerationminimizationapproach,widelyappliedtomodelingandoptimizationofthermalsystemsthatowetheirthermodynamicimperfectiontoheattransfer,masstransfer,and uid owirreversibilities,demonstratessomeinconsistenciesandparadoxesinapplicationsofheatexchangerdesigns[6].Thisisbecausethefocusoftheentropygenerationminimizationapproachisontheheat-workconversionprocesses,whileinheatexchangerdesignstherateandef ciencyofheattransferaremoreconcerned.Byanalogywiththeelectricalconduction,Guoetal.[7,8]de nedanewphysicalconcept,entransy,whichdescribestheheattransferability.Basedontheentransy,theheattransferef ciencycanbede nedandtheopti-mizationdesignofheatexchangercanbediscussed.Itisfoundthatintheirreversibleprocessestheentransyisdissipatedandtheheattransportcapabilityattenuates[9].Themoredissipationoftheentransyimpliesthehigherdegreeofirreversibilityinheattransfer
1359-4311/$eseefrontmatterÓ2011ElsevierLtd.Allrightsreserved.doi:10.1016/j.applthermaleng.2011.12.043
228J.Guo,M.Xu/AppliedThermalEngineering36(2012)227e235
process.Thustheentransydissipationmayserveasa gureof
meritforassessingtheperformanceofheatexchanger.
Muchefforthasalreadydevotedtothestudyofentransydissipationtheory.Wangetal.[10]derivedanentransytransferequationdescribingtheentransytransferprocessesofamulti-componentviscous uidsubjectedtoheattransferbyconductionandconvection,massdiffusionandchemicalreactions.ChenandRen[11]de nedaratiooftemperaturedifferencetoheat uxasthegeneralizedthermalresistanceofconvectiveheattransferprocesses,anddevelopedtheminimumthermalresistancetheoryforconvectiveheattransferoptimization,itwasfoundthattheminimumthermalresistanceprincipleisequivalenttotheentransydissipationextremumprinciple.Chenetal.[12]optimizedtheconvectiveheattransferprocessinatwo-dimensionalfoursquarecavitywiththeentropygenerationminimizationprincipleandentransydissipationextremumprinciple,andtheresultsindicatesthattheformeryieldedthehighestheat-workconversionwhilethelattermadetheconvectiveheattransferef ciencymaximum.Xiaetal.[13]studiedtheoptimumparameterdistributionsintwo- uidheatexchangerbyusingoptimalcontroltheoryunderthe xedheatloadconditionandtakingtheentransydissipationminimi-zationastheoptimizationobjective.Guoetal.[14]foundthatthetotalentransydissipationratereachestheminimumwhenthelocalentransydissipationrateisuniformlydistributedalongtheheatexchanger,whichiscalledtheprincipleofequipartitionofentransydissipation.Liuetal.[15]investigatedtheapplicabilityoftheextremumprinciplesofentropygenerationandentransydissipa-tionforheatexchangeroptimization,andfoundthattheformerisbetterfortheheatexchangeroptimizationwhenitworksintheBraytoncycle,whilethelattergivesbetterresultswhenheat
exchangerisonlyforthepurposeofheatingandcooling.Recently,thein uenceofviscousdissipationheatingontheentransyintwo- uidheatexchangerswasinvestigatedin[16],andtheentransydissipationextremumprinciplewasextendedtotheradiativeheattransferin[17]andtheoptimizationoftransportnetworksin[18].Xuetal.[19,20]derivedtheexpressionsofentransydissipationduetoheatconductionand uidfrictioninheatexchanger.Whentheentransydissipationisappliedtotheperformanceevaluationandoptimizationdesignoftheheatexchanger,itisnecessarytobenon-dimensionalised.In[21],anon-dimensionalisationmethodfortheentransydissipationinheatexchangerwasintroducedandanentransydissipationnumberwhichcanbeusedtoevaluatetheheatexchangerperfor-mancewasde ned.
Inthepresentwork,thenon-dimensionalisationofthetotalentransydissipationincludingentransydissipationcausedbyheatconductionandentransydissipationdueto uidfrictionwillbeenemployedastheobjectivefunctiontooptimizetheshell-and-tubeheatexchanger.Inaddition,themulti-objectiveoptimizationdesignofshell-and-tubeheatexchangerwhichtakestheentransydissipationnumberduetoheatconductionandthenon-dimensionalisationoftheentransydissipationcausedby uidfric-tionastwoobjectivefunctionswillbedemonstrated,andthetwooptimizationdesignapproacheswillbecomparedwitheachother.2.Thermalcalculationofshell-and-tubeheatexchangerInthepresentsection,thebasiccalculationsofheattransferandpressuredropintheshell-and-tubeheatexchangerarepresented.Inthefollowingdiscussiontheoptimizationdesignof
the
J.Guo,M.Xu/AppliedThermalEngineering36(2012)227e235229
Fig.1.Diagramofatypicalshell-and-tubeheat
exchanger.
shell-and-tube3
heatexchangerasshowninFig.1istakenasanexampletodemonstratetheapplicationoftheentransydissipationtheoryinheatexchangerdesign,sinceitisthemostcommontypeofheatexchangerappliedinthermalengineering.IntheheatexchangerillustratedinFig.1,thehot uidisinthetube-sidewhilecold uidintheshell-side.2.1.Heattransfercalculation
Undertheusualassumptionssuchasnolongitudinalheatconduction,negligiblepotentialandkineticenergychanges,negligibleheattransferbetweentheexchangeranditssurround-ingsandsoon[22],theenergybalanceequationforheatexchangeriswrittenas
Q¼Àmc
_ÁÀÁÀÁÀÁphTh;iÀTh;o¼mc_pcTc;oÀTc;i(1)
whereQistheheattransferrate,m
_isthemass owrate,cpisthespeci cheatof uidatconstantpressureandassumedtobeaconstant,Trepresentsthetemperature,thesubscriptshandcrefertothehotandcold uid,respectively,thesubscriptsiandorefertotheinletandoutletofheatexchanger,respectively.Theheatexchangereffectivenessisde nedastheratiooftheactualheattransferratetothepossiblemaximumheattransferrate(Qmax)asfollows[23]
¼
QQ(2)
max
Theshellinnerdiameterisexpressedas[24]
DÀ:1p nÀ1Á
s¼1piþ3do
(3)
whereDsistheshellinnerdiameter,nisthenumberofheatexchangetubes,piisthetubepitchfortheequilateraltriangulararrangementoftubes,doistheouterdiameterofheatexchangetube.AschematicdiagramoftubelayoutisdemonstratedinFig.2toexplainEq.(3).The rstterminEq.(3)estimatesthedistancebetweenthecenteroftubebundleandthecirclecenterfortheoutmostheatexchangetubeinthetubebundle,andthesecondtermaccountsforthedistancebetweenthecirclecenterfortheoutmostheatexchangetubeinthetubebundleandtheshellinnerwallasshowninFig.2.AccordingtotheBell-Delawaremethodtheshell-sideheattransfercoef cientcanbeexpressedasfollows[23]
am
0:14
s¼jocp;s
_smAPrs
ss;w
s
À2=3
(4)
wherem
_sistheshell-sidemass owrate,Asisthecross owareaatthecenterlineofshellforonecross owbetweentwobaf es,cp,sisthespeci cheatoftheshell-side uid,msistheshell-side uiddynamicviscosityatbulktemperature,ms,wisthe uiddynamicviscosityatwalltemperature,Prsistheshell-sidePrandtlnumber,joisheattransferfactor.Theheattransferfactorjoisgivenby[23]:
Fig.2.Theschematicdiagramoftubelayout.
jo¼jHjcjljbjsjr
(5)
wherejHistheheattransferfactorforpurecross owofanidealtubebank,jcthecorrectionfactorforbaf ecutandspacing,jlthecorrectionfactorforbaf eleakageeffect,jbthecorrectionfactorforthebundlebypass ow,jsthecorrectionfactorforvariablebaf espacingintheinletandoutletsections,jrthecorrectionfactorforadversetemperaturegradientbuildupinlaminar ow.Thesecorrectionfactorsareverycomplicatedtodetermine,thedetailscanbefoundin[23,24]andarenotlistedhereintosavespace.Forthecasethatthehot uidisinthetube-side,theDittuseBoelterequationgivesrisetothefollowingexpressionofthetube-sideheattransfercoef cient [23]:
0:8
at¼0:023
lrtvtdi
Pr0t
:3
d(6)
i
twherethepartinbracketsindicatesthetube-sideReynoldsnumberdenotedasRet,diistheinnerdiameteroftheheatexchangetube,rtthetube-side uiddensity,vtthetube-side owvelocity,mtthetube-side uiddynamicviscosityatbulktempera-ture,Prtthetube-sidePrandtlnumber.FromEqs.(4)and(5)thetotalheattransfercoef cientbasedontheexternalsurfaceareaoftheheat"
exchangetubeiswrittenas
K1
dd
o¼
o
t
þri
t
odwdoþ
þr1
#À1
i
wi
sþ
(7)
s
wheredwisthewallthicknessoftheheatexchangetube,lwisthewallthermalconductivity,rtandrsstandforthetube-sideandshell-sidefoulingresistances,respectively.2.2.Pressuredropcalculation
Thetotaltube-sidepressuredropincludesthreeparts:pressurelossalongtube,pressurelossinbendaswellasinletandoutletpressurelosses.Ignoringthesecondpartforthesingletubepass,thetotal
tube-sideL pressurem drop
iswrittenas[23,24].
DPt¼
tÀ0:144ftrtv2t
þ1:5
(8)
it;w
whereftisthetube-sidefrictionfactor,Listhetotallengthoftube
passes.Fortheheatexchangerwithmultiplepasses,pressurelossinelbowsshouldalsobetakeninto
account.
230J.Guo,M.Xu/AppliedThermalEngineering36(2012)227e235
AccordingtotheBell-DelawareMethod,thepressuredropforanidealsubscriptssectioncanbewrittenas[24,25]:
DPm
_bk¼2fsÀmÁs
s=ms;wÀ0:14A(9)
chereAcisshell-sidecross owarea,thesubscriptsrepresentsshell-side.Thepressuredropfortheidealwindowsectioncanbewritten
as[23,24]:
DPm
_wk¼s2AAcð2þ0:6NcwÞ;Re!100
b(10)
DPwk
¼26msm_s
Ncwls rAþm_2s
Re3100
bAcpiÀdoþDw
AbAc;hereAbisthecross owareathroughonebaf ewindow,Ncwthe
effectivenumberoftuberowscrossedinthebaf ewindow,lsthecentralbaf espacing,Dwtheequivalenthydraulicdiameterofasegmentalbaf ewindow.Finally,thetotalshell-sidepressuredropisexpressedasfollows[23e25]:
D
Ps¼½ðNbÀ1ÞDPbkRbþNbDpwk R1þ2DPbkRb1þ
Ncw
NRs(11)
c
whereNbisthenumberofbaf es,Rbthecorrectionfactorforbypass ow,R1thecorrectionfactorforbaf eleakage,Ncthenumberoftuberowsinonecross owsection,Rsthecorrectionfactorforunequalbaf espacingatinletand/oroutlet.Thecorrectionfactorsforshell-sidepressuredropinBell-Delawaremethodaregivenintheformofcharts,theyarenotlistedhereinduetolengthlimitation,thedetailedinformationcanbefoundin[23e25].FromEqs.(8)and(11)thetotalpumpingpowercanbewrittenas[26]
1
W¼
m
_tm
s
t
DPtþ
_s
Ps
(12)
wherehistheoverallpumpingef ciency.
3.Optimizationdesignofshell-and-tubeheatexchanger3.1.Objectivefunction
Entransyisaphysicalquantitydescribingheattransferability.
Thermalenergyisconservedinheattransferprocess,whileentransyisdissipatedduetotheirreversibilitiesofheattransferprocess[7,8].Thelesstheentransydissipationis,thehigherthedegreeofreversibilityisinheattransferprocesses.Therefore,itisveryimportanttominimizetheentransydissipationinheatexchangerinordertoobtaintheoptimalthermodynamicperfor-manceofheatexchanger.Inheatexchangertheheatconductionunder nitetemperaturedifferenceand uidfrictionaretwomainirreversibilitiestoinducetheentransydissipation.Inthefollowing,we rstcalculatetheentransydissipationrelatedtotheseirre-versiblelosses,andthentheoptimizationdesignofheatexchangerbyminimizingtheentransydissipationnumberispresented.
Accordingtothede nitionofentransy,theentransydissipationcausedbyheatconductioninheatexchangercanbeexpressedasfollows[21]:
Zo
GDÀ
T¼À
mc
_dTÁpTh;ci
¼
1À2mc_Á pTh2;iÀTh2 ;oþ1À2
mc_Á pc2 cT;iÀTc2h;o(13)
Theentransydissipationnumberduetoheatconductioncanbe
obtainedbydividingEq.(13)byQ(Th,iÀTc,i)asfollows[21]:
G*DT¼
GQT(14)
h;ic;iTheheatconductionentransydissipationnumbercanberegardedastheratiooftheactualentransydissipationtothemaximumentransydissipationinheatexchanger.
Theentransydissipationrelatedto uidfrictionfortheincom-pressible uidinheatexchangerisexpressedasfollows[19,20]
Zo
GDmT
_
P¼À
dPm
_DPToÀTi
¼
i
oih;c
¼m
_tDPtTh;oÀTh;iDPTc;Tþm_ssoÀTc;i
tln(15)
h;o=Th;islnTc;o=Tc;i
Thus,applyingthesamenon-dimensionalisingmethodasdone
totheentransydissipationrelatedtoheatconduction,theentransydissipationnumberdueto uidfrictioncanbeexpressedas
G*DP¼
G
QTh;iÀTc;i
(16)
Thetotalentropygenerationrateinliquideliquidheatexchangercanbewrittenas[27]
_¼À
mc_Á
TÁgenph;oÀTc;om
_lnÀTÁ
S
tDPth;o=Th;ihlnTþmc_hpclnþ
tTh;oh;iþ
m_À;iÁ
Tc;i
sDPslnTc;o=Tc;i(17)
sTc;oc;iTheentropygenerationnumbercanbewrittenas[3]:
NS
_s¼genmc
(18)
pmax3.2.Single-objectiveoptimization
3.2.1.Optimizationdesignforgivenheatload
Thetotalentransydissipationnumbercanbeobtainedbysummingtheentransydissipationnumberduetoheatconductionandtheentansydissipationnumbercausedby uidfrictionasfollows:
G*¼GDTþGDP
(19)
NowwetakeG*astheobjectivefunctioninthesingle-objectiveoptimizationdesignofshell-and-tubeheatexchanger.TheknowndatafortheheatexchangerdesignaredocumentedinTable1.Theworking uidsonthetubeandshell-sidesarewaterinourconsideration.Thedesignvariablesandtheirrangesareselectedasfollows:
(1)Thetubeouterdiameter,do,itsdiscretevaluesandthecorre-spondingtubepitchesarelistedinTable2.
Table1
Knowndataforheatexchangerdesignwiththe xedheatload.Parameters
Tube-sideShell-sideInlettemperatureTi(K)368.15283.15OutlettemperatureT343.15eMass owratem_o(K)
(kg/s)50e
Densityr(kg/m3
)
970991.15Constantpressurespeci c42004174heatcp(J/kgK)
Kinematicviscosityn(m2/s)3.36Â10À76.96Â10À7EntrancepressurePi(MPa)6.5
5
Foulingresistancer(m2K/W)0.0000860.00017PrandtlnumberPr
2.015
4.5878
J.Guo,M.Xu/AppliedThermalEngineering36(2012)227e235
Table2
Tubeouterdiametersandthecorrespondingtubepitch.do(mm)pt(mm)
1013.4
1216
1419
1622
1925
2026
2228
2532
3038
3240
3544
3848
4557
5064
5570
231
5772
(2)Thewholenumberofheatexchangetubes,n,rangingfrom50
to550;
(3)Theratioofthebaf espacingtotheshellinnerdiameter,Bs,
variesbetween0.2and1.0;
(4)Thecentralangleofbaf ecutq,rangingfrom1.8546to2.9413
inradian.
(5)Theoutlettemperatureofcold uid,rangingfrom313.15Kto
343.15K.Theconstraintconditionsfortheheatexchangerdesignare:(1)Length-diameterratioisbetween6and10;(2)Thebaf espacingisgreaterthan50mm;
(3)Thetube-sidepressuredropislessthan5Â104Pa;
(4)
Theshell-sidepressuredropislessthan5Â104Pa[27,28].
Thisoptimizationproblemformulatedabovewillbesolvedbythegeneticalgorithm.Thereasonforustoutilizethegeneticalgorithmisexplainedinthefollowing.
Thetraditionalapproachestosolvingtheoptimizationproblemsrequiretheinformationofthegradientsofobjectivefunctionsandsufferfromgettingtrappedatthelocaloptimum.Thus,theycan’tensurethattheglobaloptimalsolutionisachievable[29].Althoughdirectsearchmethoddoesnotrequireanyinformationaboutthegradientoftheobjectivefunction,itdependsheavilyontheinitialpoint,andfrequentlypointstolocaloptimumunlesstheobjectivefunctionisunimodal[30,31].Thegeneticalgorithmstartsthesearchfromapopulationofpoints;thedependenceofthismethodontheinitialpointisnotasstrongasdirectsearchmethod.Furthermore,itprovidesahighlevelofrobustnessbysimulatingnature’sadaptationintheevolutionprocess[30].More
Fig.3.Flowchartofgenetic
algorithm.
importantly,thegeneticalgorithmhasverystrongcapabilityto ndtheglobaloptimum[32].Therefore,thegeneticalgorithm[33]isemployedtosearchthesolutionoftheoptimizationproblemoftheheatexchangerdesign.Theinitialgenerationwhichsatis estheconstraintconditionsisrandomlygenerated.
Inthegeneticalgorithmmethodametriccalled tnessfunctionis rstde nedthatallowseachpotentialsolution(individual)tobequantitativelyevaluated.Theparametersarestructuredintheformof oatpoint.Afterarandominitialpopulationintherangesofdesignvariablesisgenerated,thealgorithmcreatesasequenceofnewgenerationsiterativelyuntilthestoppingcriterionismet.Inthisprocess,offspringaregeneratedbymergingtwoindividualsincurrentgenerationwithacrossoveroperator,orbymodifyingachromosomewithamutationoperator.Anewgenerationisformedbysomeparentsandoffspringbasedon tnessvalues,thepopulationsizeiskeptinvariantbyeliminatingtheinferiorones.Thechromosomeswithhigher tnessvalueshavehigherproba-bilitiestosurvive;thisensurestheconvergencetoabestindividualaftercertainnumberofgenerations,whichprobablyrepresentstheoptimalsolutionofthegivenproblem[34].The owchartofthegeneticalgorithmisshowninFig.3.Thesizeofinitialpopulationandthemaximumgenerationaresetto40and500,respectively.
Thevariationofthebestindividuals’ tnessvalueforsomegenerationvs.thenumberofgenerationsisdepictedinFig.4.Itisclearthattheentransydissipationnumbersduetoheatconductionand uidfrictionsharplydecline rstly,andthenalmostkeepconstantbeyondthe50thgeneration.FromFig.4onecanseethatthegeneticalgorithmhasveryhighef ciencyatsearchingtheglobaloptimalsolution.Therefore,themaximumgenerationnumberwhichissetto500inthepresentworkisenoughtogettheglobaloptimalsolution.Fig.5illustratesthevariationsoftheexchangereffectivenessandpumpingpowerwiththetotalentransydissipationnumber.Obviously,withdecreasingthetotalentransydissipationnumber,theexchangereffectivenessapprox-imatelyincreaseslinearly,whilethepumpingpowerdeclinessharply.Therefore,throughtheoptimizationprocess,theperfor-manceofheatexchangerhasbeenimprovedsubstantially.Inordertofurtherdemonstratetheadvantagesofthesingle-objectiveoptimizationdesignunder xedheatloadcondition,thecompar-isonbetweenarandomlygeneratedinitialdesignandtheoptimal
Fig.4.ThevariationsofG*DTandG*DPversusgenerations.
232J.Guo,M.Xu/AppliedThermalEngineering36(2012)227e235
3
Table4
Theknowndataforheatexchangerdesignwiththe xedheattransferarea.
Tube-side
InlettemperatureTi(K)
_(kg/s)Mass owratem3
Densityr(kg/m)
Speci cheatatconstantpressurecp(J/(kgK))
Dynamicviscositym(kg/ms)EntrancepressurePi(MPa)
Foulingresistancer((m2K)/W)PrandtlnumberPr
368.15509704200326Â10À66.5
0.0000862.015
Shell-side283.1520
991.154174690Â10À65
0.000174.5878
Fig.5.Thevariationsoftheeffectivenessandpumpingpowerwithtotalentransydissipationnumber.
oneisshowninTable3.Fromthistable,itisevidentthattheexchangereffectivenessincreasesfrom0.448to0.706,whilethepumpingpowerisreducedby75.2%andheatcapacityrateratiodecreasesfrom0.656to0.417.Unfortunately,thenumberoftransferunitincreasesbyabouttwotimes.Sotheperformanceofheatexchangerisimprovedattheexpenseofenlargingtheheattransferarea.Howeverfromtheviewpointofeconomics,itcanbefoundthatthegrosspro tisfarmorethantheincreaseoftheinvestmentcost,andthedetailedanalysisispresentedin[28].WhenmoreattentionispaidtoTable3,itcanbefoundthattheentransydissipationnumberdueto uidfrictionisaroundthreeordersofmagnitudelessthanthatcausedbyheatconduction.Infact,theirreversibilitydueto uidfrictionisfarlessthantheirreversibilityassociatedwithheatconductionforliquidsinmostsituations[35].Hence,thesingle-objectiveoptimizationdesignofheatexchangerwhichtakesthetotalentransydissipationnumberastheobjectivefunctionmayleadtosomeunwantedconse-quences.Thiscanbedemonstratedbytheheatexchangerdesignwiththe xedheattransferarea.
3.2.2.Optimizationdesignforgivenheattransferarea
TheknowndatafortheheatexchangerdesignisshowninTable4,thetotalentransydissipationnumberandentropygener-ationnumberaretakenastheobjectivefunctions,thedesignparametersandtheirrangesarethesameasthatpresentedinthelastexample,excepttheoutlettemperatureofthecold uid.Theheattransferareais xedat60m2,thesizesofinitialpopulationandthemaximumnumberofgenerationsaresetto40and500,respectively.Thesamegeneticalgorithmisemployedtosolvethisoptimizationproblem.
ThevariationoftheheatexchangereffectivenesswiththedecreaseofentropygenerationnumberisshowninFig.6.Fig.6showsthatthedecreasesofentropygenerationnumberresultsinthedecreaseoftheeffectiveness,whichiscalled“entropygenera-tionparadox”[36].TherelationbetweentheeffectivenessandthetotalentransydissipationnumberisdemonstratedinFig.7.FromFig.7,onecanseethattheeffectivenessincreasesasthetotal
entransydissipationnumberdecreases,andthe“entropygenera-tionparadox”doesnotappear.Therefore,theentransydissipationnumberdemonstratesanobviousadvantageovertheentropygenerationnumberinheatexchangerdesign.
ThevariationsofGDTandGDPwiththenumberofgenerationsareshowninFig.8.Fromthis gure,itisevidentthatwithincreasingthenumberofgenerations,theentransydissipationnumberduetoheatconductiondecreasesremarkably,whiletheentransydissipationnumbercausedby uidfrictionrisessigni -cantly,whichisundesirable.Fig.9showstherelationbetweenthetotalpumpingpowerandthetotalentransydissipationnumber.Withdecreasingthetotalentransydissipationnumber,theexchangereffectivenessisimprovedsigni cantlyasshowninFig.7,whilethepumpingpowerincreasesdramaticallyasdemonstratedinFig.9.Recallthattheheattransferareais xedinthisexample,thustheimprovementoftheexchangereffectivenessisattheexpenseofthelargerpumpingpowerconsumption.FromFigs.7e9,onecanseethattakingthetotalentransydissipationnumberastheobjectivefunctionisalmostequivalenttominimizingtheentransydissipationnumberduetoheatconduction,andtheentransydissipationcausedby uidfrictionisalmostneglectedsinceitisfarsmallerthanthatcausedbyheatconduction.Inanattempttosolvethisproblem,themulti-objectiveoptimizationdesignofheatexchangerisestablishedinthefollowingsubsection.
3.3.Multi-objectiveoptimization
Mathematically,themulti-objectiveoptimizationminimizesseveralobjectivessimultaneously,withanumberofinequalityorequalityconstraints.Itcanbemathematicallyformulatedasfollows:
minfðxÞ¼½f1ðxÞ;f2ðxÞ;/;fkðxÞ
x X
(20)
Subjectto:
gjðxÞ¼0;j¼1;2;/;MhkðxÞ 0;k¼1;2;/;K
wherexisavectorandcalledthedecisionvector,Xistheparameterspace.Ifandonlyif,fi(x) fi(y)fori¼1,2,/kandfj(x)<fj(y)foratleastoneobjectivefunctionj,afeasiblesolutionxissaidtodomi-nateanotherfeasiblesolutiony.AsolutionwhichisnotdominatedbyanyothersolutioninthefeasibleregioniscalledParetooptimalsolution.Thesetofallnon-dominatedsolutionsinXiscalledas
the
Table3
Thecomparisonbetweenaninitialandtheoptimaldesign.
do(m)
InitialFinal
0.0190.020
n243322
Bs0.9770.858
q(rad)
2.0382.557
Tc,o(K)321.26343.15
NTU0.7171.501
C*0.6560.417
W(W)1403348
0.4480.706
G*DT0.630.50
G*DP
8.14Â102.13Â10À4
G*0.62960.5002
J.Guo,M.Xu/AppliedThermalEngineering36(2012)227e235233
Fig.6.Thevariationoftheheatexchangereffectivenesswithentropygeneration
number.
Paretooptimalset(P*),thevaluesofobjectivefunctionscorre-spondingtotheParetooptimalsetarecalledParetofront(PF*)[35,37,38],
PF*:¼ffðxÞjx P*g(21)
Speci cally,inthefollowingtheentransydissipationnumberscausedbyheatconductionand uidfriction,respectively,aretakenastwoseparateobjectivefunctions.Thedesignparameters,theirboundsandtheconstraintsremainthesameasthatspeci edinthesingle-objectiveoptimizationdesigncaseunderthegivenheatloadcondition.TheknowndataoftheheatexchangerisshowninTable1.
Acontrolledelitistgeneticalgorithm(avariantofNSGA-II[38])isadoptedforsearchingtheoptimalsolutions,whichcanhelpincreasethediversityofthepopulationeveniftheyhavelower tnessvalues.Thediversityofpopulationiscontrolledbytheelitemembersofthepopulationintheprocess;thedistancecrowdingfunctionhelpstomaintaindiversitybyfavoringindividualsthatarerelativelyfarawayonthefront.TheParetofractionissetto0.35soastolimitthenumberofindividualsinthecurrentpopulationthatareontheParetofrontto35percentofthepopulationsize[35,39].Thetotalnumberofgenerationsissetto500,whichservesasthestoppingcriteriatoterminatetheiterativeprocess.
Fig.7.Thevariationoftheheatexchangereffectivenesswithtotalentransydissipation
number.Fig.8.ThevariationsofG*DTandG*DPwiththenumberof
generations.
Somerepresentativeoptimalsolutionsobtainedbymulti-objectiveoptimizationareshowninTable5.Fromthistable,onecanseethatthelargereffectivenesscorrespondstothesmallerpumpingpower.ThecomparisonbetweenTables3and5showsthattheoptimalsolutioninTable5whichhasthesameexchangereffectivenessasthatinTable3requireslowerpumpingpowerconsumption,therequiredpumpingpowerisreducedby22.4%throughthemulti-objectiveoptimizationprocess.Therefore,themulti-objectiveoptimizationdemonstratesobviousadvantagesoverthesingle-objectiveoptimization.
Forthesecondexamplewith xedheattransferarea,theknowndataforheatexchangerdesignisshowninTable3,thedesignvariablesandtheirrangesremainthesameasspeci edinthelastsubsection,whiletheentransydissipationnumberscausedbyheatconductionand uidfrictionaretakenastwoseparateobjectivesintheoptimizationdesignproblemunderconsideration.TheParetofrontobtainedbythemulti-objectiveoptimizationisshowninFig.10.Fig.10(a)illustratesthevariationsoftheheatconductionand uidfrictionentransydissipationnumbersfordifferentoptimalsolutionsintheParetooptimalset.ThepumpingpowerandtheexchangereffectivenesscorrespondingtotheoptimalsolutionsareshowninFig.10(b).Inthis gure,therearetworegionswhichareformedbytheParetofront.ThesolutionsinregionIarefeasiblebutnon-optimalsolutions,whileonesinregionIIrepresenttheinfeasiblesolutions.Notethatasetof
optimal
Fig.9.Thevariationofthepumpingpowerwiththetotalentransydissipationnumber.
234J.Guo,M.Xu/AppliedThermalEngineering36(2012)227e235
Table5
TheParetofrontobtainedbymulti-objectiveoptimizationdesignwith xedheatload.
do(m)
Multi-objective
0.0220.0220.0220.0220.0220.022
n283283283283283283
Bs1.001.001.001.000.950.91
q(rad)
2.3622.3492.3202.2992.2952.294
Tc,o(K)69.1469.2669.5369.7169.8670.00
Ko(W/m2K)1260.51263.11268.61272.51276.61280.2
C*0.4230.4220.4200.4190.4180.417
W(W)260.2260.2260.2260.3265.0270.2
0.6960.6970.7000.7030.7040.706
G*DT0.5050.5040.5030.5020.5010.500
G*DP1.581.581.581.581.611.64
ÂÂÂÂÂÂ1010À410À410À410À410À4
G*0.50520.50450.50290.50190.50100.5002
*Fig.10.TheParetofrontforheatexchangerwith xedheattransferarea:(a)G*DTversusGDP;(b)thepumpingpowerversustheexchangereffectiveness.
solutionsareavailableforthemulti-objectiveoptimization
approach,therefore,itprovidesmorealternativesforheatexchangerdesignthanthesingle-objectiveoptimizationapproach.4.Concludingremarks
Accordingtotheentransydissipationtheory,theentransydissipationcanbeusedtodescribetheirreversibilitiesinducedbyheatconductionand uidfriction,whilesuchirreversibilitiesarethemainfactorstodeterioratetheperformanceofheatexchanger.Therefore,inthepresentwork,basedontheentransydissipationtheoryandgeneticalgorithm,twooptimizationapproachesforheatexchangerdesignareproposed.Firstly,asingle-objectiveoptimizationapproachisformulated,wherethetotalentransydissipationnumberistakenastheobjectivefunction.Whentheheatloadis xed,thesingle-objectiveoptimizationdesigncansigni cantlyimprovetheperformanceofheatexchanger.However,forthe xedheattransferareacase,theimprovementofexchangereffectivenessthroughtheoptimizationprocessisattheexpenseoftheincreaseofthepumpingpower.Inordertoaddressthisproblem,themulti-objectiveoptimizationdesignofheatexchangerisestablished,wheretheentransydissipationnumbersrelatedtoheatconductionand uidfriction,respectively,aretakenastwoseparateobjectives.Incomparisonwiththesingle-objectiveoptimizationapproach,themulti-objectiveoptimiza-tiondesignofheatexchangercanachievethesameexchangereffectivenesswithlessconsumptionofpumpingpower.Further-more,themulti-objectiveoptimizationleadstothenon-uniqueoptimalsolutionswhichprovidemore exibilityfortheheatexchangerdesign.Acknowledgements
TheSupportofourresearchprogrambyNationalBasicResearchProgramofChina(ProjectNo.2007CB206900)isgreatlyappreciated.
References
[1]M.Yilmaz,O.N.Sara,S.Karsli,Performanceevaluationcriteriaforheat
exchangersbasedonsecondlawanalysis,exergy,AnInternationalJournal1(2001)278e294.
[2]I.Prigogine,IntroductiontoThermodynamicsofIrreversibleProcesses,Wiley,
NewYork,1967.
[3]A.Bejan,EntropyGenerationThroughHeatandFluidFlow,Wiley,NewYork,
1982.
[4]A.Bejan,EntropyGenerationMinimization,CRCPress,Florida,1996.
[5]V.Bertola,E.Cafaro,Acriticalanalysisoftheminimumentropyproduction
theoremanditsapplicationtoheatand uid ow,InternationalJournalof
3
HeatandMassTransfer51(2008)1907e1912.
[6]J.E.Hesselgreaves,Rationalisationofsecondlawanalysisofheatexchangers,
InternationalJournalofHeatandMassTransfer43(2000)4159e4204.
[7]Z.Y.Guo,X.G.Cheng,Z.Z.Xia,Leastdissipationinprincipleofheattransport
potentialcapacityanditsapplicationinheatconductionoptimization,ChineseScienceBulletin48(2003)406e410.
[8]Z.Y.Guo,H.Y.Zhu,X.G.Liang,EntransyeAphysicalquantitydescribingheat
transferability,InternationalJournalofHeatandMassTransfer50(2007)2545e2556.
[9]G.Z.Han,Z.Y.Guo,Physicalmechanismofheatconductionabilitydissipation
anditsanalyticalexpression,ProceedingoftheCSEE27(2007)98e102(inChinese).
[10]S.P.Wang,Q.L.Chen,B.J.Zhang,Anequationofentransytransferandits
application,ChineseScienceBulletin54(2009)3572e3578.
[11]Q.Chen,J.X.Ren,Generalizedthermalresistanceforconvectiveheattransfer
anditsrelationtoentransydissipation,ChineseScienceBulletin53(2008)3753e3761.
[12]Q.Chen,M.Wang,N.Pan,Z.Y.Guo,Optimizationprinciplesforconvective
heattransfer,Energy34(9)(2009)1199e1206.
[13]S.J.Xia,L.G.Chen,F.R.Sun,Optimizationforentransydissipationminimization
inheatexchanger,ChineseScienceBulletin54(2009)3587e3595.
[14]J.F.Guo,M.T.Xu,L.Cheng,Principleofequipartitionofentransydissipationforheat
exchangerdesign,ScienceChinaTechnologicalSciences53(2010)1309e1314.[15]X.B.Liu,J.A.Meng,Z.Y.Guo,Entropygenerationextremumandentransy
dissipationextremumforheatexchangeroptimization,ChineseScienceBulletin54(2009)943e947.
[16]J.F.Guo,M.T.Xu,L.Cheng,Thein uenceofviscousheatingontheentransyin
two- uidheatexchangers,ScienceChinaTechnologicalSciences54(5)(2011)1267e1274.
[17]J.Wu,X.G.Liang,Applicationofentransydissipationextremumprinciplein
radiativeheattransferoptimization,ScienceChinaTechnologicalSciences51(2008)1306e1314.
[18]X.B.Liu,M.Wang,J.Meng,E.Ben-Naim,Z.Y.Guo,Minimumentransydissi-pationprincipleforoptimizationoftransportnetworks,InternationalJournalofNonlinearSciencesandNumericalSimulation11(2)(2010)113e120.
J.Guo,M.Xu/AppliedThermalEngineering36(2012)227e235
235
[19]M.T.Xu,L.Cheng,J.F.Guo,Anapplicationofentransydissipationtheoryto
heatexchangerdesign,JournalofEngineeringThermophysics30(2009)2090e2092(inChinese).
[20]M.T.Xu,J.F.Guo,L.Cheng,Applicationofentransydissipationtheoryinheat
convection,FrontiersofEnergyandPowerEngineeringinChina3(2009)402e405.
[21]J.F.Guo,L.Cheng,M.T.Xu,Entransydissipationnumberanditsapplicationto
heatexchangerperformanceevaluation,ChineseScienceBulletin54(2009)2708e2713.
[22]R.K.Shah,D.P.Sekuli c,FundamentalsofHeatExchangerDesign,JohnWiley,
Hoboken,2003.
[23]T.Kuppan,HeatExchangerDesignHandbook,MarcelDekkerInc.,NewYork,
2000.
[24]M.Z.Shi,Z.Z.Wang,PrincipiaandDesignofHeatTransferDevice,Southeast
UniversityPress,Nanjing,1996,(inChinese).
[25]J.W.Palen,HeatExchangerSourcebook,HemispherePublishingCor.,New
York,1986.
[26]A.C.Caputo,P.M.Pelagagge,P.Salini,Heatexchangerdesignbasedon
economicoptimization,AppliedThermalEngineering28(2008)1151e1159.
[27]J.F.Guo,L.Cheng,M.T.Xu,Optimizationdesignofshell-and-tubeheat
exchangerbyentropygenerationminizationandgeneticalgorithm,AppliedThermalEngineering29(2009)2954e2960.
[28]J.F.Guo,M.T.Xu,L.Cheng,Theapplicationof eldsynergynumberinshell-and-tubeheatexchangeroptimizationdesign,AppliedEnergy86(2009)2079e2087.
[29]B.V.Babu,S.A.Munawar,Differentialevolutionstrategiesforoptimaldesignof
shell-and-tubeheatexchangers,ChemicalEngineerScience62(2007)3720e3739.[30]Y.H.OH,T.Kim,H.K.Jung,Optimaldesignofelectricmachineusinggenetic
algorithmscoupledwithdirectmethod,IEEETransactiononMagnetics35(1999)1742e1744.
[31]O.A.Mohammed,G.F.Uler,Ahybridtechniquefortheoptimaldesignof
electromagneticdevicesusingdirectsearchandgeneticalgorithms,IEEETransactiononMagnetics33(1997)1931e1934.
[32]A.Fanni,M.Marchesi,A.Serri,ai,Agreedygeneticalgorithmfor
continuousvariableselectromagneticoptimizationproblems,IEEETrans-actiononMagnetics33(1997)1900e1903.
[33]C.R.Houck,J.A.Joines,M.G.Kay,AGeneticAlgorithmforFunctionOptimi-zation:AMatLabImplementation.TechnicalReportNCSU-IE-TR-95-09,NorthCarolinaStateUniversity,Raleigh,NC,1995.
[34]G.Cammarata,A.Fichera,D.Guglielmino,Optimizationofaliquefactionplant
usinggeneticalgorithms,AppliedEnergy68(2001)19e29.
[35]J.F.Guo,M.T.Xu,L.Cheng,Multi-objectiveoptimizationofheatexchanger
designbyentropygenerationminimization,ASMEJournalofHeatTransfer132(2001)081801.
[36]A.Bejan,Secondlawanalysisinheattransfer,Energy5(1980)720e732.[37]D.Copiello,G.Fabbri,Multi-objectivegeneticoptimizationoftheheattransfer
fromlongitudinalwavy ns,InternationalJournalofHeatandMassTransfer52(2009)1167e1176.
[38]K.Deb,Multi-ObjectiveOptimizationUsingEvolutionaryAlgorithms,John
Wiley&Sons,Chichester,England,2001.
[39]MatlabCompany,MatlabUserGuide:Version7.9.0(2009).
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