换热器设计外文翻译原稿(4)

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