换热器设计外文翻译原稿(6)

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