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.