Title Study on Heat Transfer and Fluid Flow Characteristics ofRectangular Finned Surface in Duct( Abstract, Chapter 1-4 )

Author(s) Didarul, Islam Md.

Citation : 1-100

Issue Date 2007-09

URL http://hdl.handle.net/20.500.12000/5748

Rights

ＰｈＤ・Dissertation

onHeatTransfcrandFluidFlowCharacteristicsStudy

ofRectangularFinnedSurfnceinＤｕｃｔ

September２００７

UniversityoftheRyukyus

GraduateSchoolofEngmeermgandScience

Material,StrucmralandEnergyEngmeermg

IslaｍＭｄＤＩＤＡＲＵＬ

Contents

Abstract

Nomenclature

l・Introduction

L1Whyheattransferaugmentationisimportant？

L2Differentmethodsofenhancingheattransfbr

1.2.1Vortexgenerator-anemergingtechnology

L2・ZExtendedsurftlces

l30bjectiveofthisresearch．

Pageｎｏ．

１

１１１３６

ZExperimentalApparamsandProcedure

2､１Intmduction

2､ZFinpattemsandalTangemems

23Expelimemalsetupfbrheattransfermeasuremem

23・lFinsinsidetheduct

2､3.2Heatingsurfhcewithfins

23.31nffaredimagetechniqUe

2､3.41nsulationtechnique

８

００１２３４５５６７

８８１１１１１１１１１１

2.4Expelimentalapparamsfbrpressuredropmeasuremem

2.5F1owvisualizationapparams

2､5.1Experimentalsetupfbrdienowinwaterchannel

25・zEXperimentalsetupfbrsmokeflowvisualization

2.5.3Expenmentalsetupfbroiltitamumoxidefilmflowvisualization，Ｃ

3.DataReductionandUncertaintyAnalysis

3」Intmduction

32Datareductio、

3.3Uncertaimyanalysis

1８

１８

２０

４HeatTransfbrCharacteristicsandFlowAnalysisofFinnedSurfacesinＣａｓｅｏｆ

TallDuctandNarTowDuct、

4.1Introduction

4.2.Localheattransfbrcoefficiellts

4.2.1Smoothductresults

4ユZEffectofinclinationanglesonheattransfer

4.2.3Heattransfbrthrougdlfinofresinmaterial

4.2.4Effectoffinheightonheattransfercharacteristics

42.sEffectofvelocityonheattransfbrcharacteristics

43Detailedheattransfbranalysis

４４.Area-averagedheattransfer

4・SFlowvisualizationbydyefIowinwaterchanne1

4.6.Frictionfactor

2１

１１１３６７

２２２２２２

2８

０６９

３３３

４１

4２４７Sunmary

SF1uidFlowandHeatTransferAnalysisofDifferentFinPatternsand

ArrangementataNarrowDuct，

5.1Introduction

３３３

４４４

5.2F1owvisualization

5.2.1SurfaceoilfilmHowpattemsaroundfinsattheendwall

5.2.2Smokeflowvisualbration

4３

4６

４８５３Frictionfactor

5.4Detailedheattransferanalysis

5､５Ａ1℃a-averagedheattransfbrCoefficient

5.6Thermalperfbnnancerati０

５．７Sunmary

5０

８３５

５６６

6.TheEffectsofDuctHeightonHeatTransferE血ancementandFlow

CharacteristicsofFinnedSurface．

７７７

６６６

6.1.Introduction

6.2.Detailedheattransfer

6.3AreaaveragedheattransferandNusseltnumbels

64Frictionfactor

6,sVortexstructureanalysis

d6Thermalperfbnnanceratio

6,７Ｓｕｍｍａｒｙ

７・Conclusions

8１

8５

8７

9０

9３

9４

Refbrences 9７

Acknowledgements 100

Abstract

StudyonHeatTransfbrandFluidFIowCharacteristicsofRectangular

FinnedSurfiuceinDuct

AdetailedexperimentalinvestigationoftheheattransfbrandnuidHowcharacteristicsof

rectangLllarfhmedsurfacesoffburdiffbremfinpatterns,co-angular,zigzag,co-rotatmgandco-

counterrotatingwasconductedfbranairflow(Re＝15700-104500)inaductShortrectangular

finsofeitheraluminumorresinmaterialwereattachedin7x7arraystoaheatmgsurface(base

plate)ofconstantheatnuxbydoublesidedthintapaT-typethennocouplesandanin丘ared

camera(TVS8000)withal60x120pointln-SbsensorwereusedtocapturetheinhPared

imagesaswellastomeasurethetemperatureandthedetailedheattransferattheendwallalong

withfinbase.ＤiffbremnowvisualizationtechniqUe,fluorescencedyeflowmwaterchannel，

smokeflowvisualizationandoiltitamumoxidefilmflowvisualizationwereusedtoanalysisthe

Howbehavioranditseffectonheattransfer､Ｉｎｔｈｉｓｓｔｕｄｙｗｅｈａｖefirstinvestigatedtheheat

transferandfluidflowcharacteristicsofco-angularandzigzagfinpatternataflatplate(200mm

ductheight)boundarylayerandnarrowductof20mmheight・Zigzagpattemwerefbundtobe

moreeffbctivemheattransfbratbothflatplateandnaxTowductcase・Ｉｎｃａｓｅｏｆｃｏ－angUlar

pattemdyeflowstagnatedmfiPontofthefinandfbnnedastronghorseshoevortexaroundthefin

whilethelongitudinalvortexesgeneratedbythesidetopedgestouchedthefinsurfaceandthe

endwalLOntheotherhandmcaseofzigzagpattemaweakhorseshoevortexappearedand

longimdinalvortexstrucktheendwallmainlyandasinusoidalwavyflowbehaviorwasobserved

WehavethenfhrtherinvestigatedheattransfbrandUowcharactelisticsofco-rotatingpatternand

co-counterrotatingpatternalｏｎｇｗｉｔｈｏｔｈｅｒｔｗｏｐａｔｔｅｒｎａｔａｄｕｃｔｏｆ５０ｍｍｈｅｉｇｈｔ・Theheat

transferresultshowsthattheco-rotatillgpattemhasthehighestNusseltnumberandtheco‐

angularpatternhastheleastNusseltnumber､ConsideringthethermalperfbnnanＣｅ,co-rotating

patternwithsmallｅｒｐｉｔｃｈｒａｔｉｏｗａｓｆｂｕｎｄｔｏｂｅｔｈｅｍｏｓtrecommendedpattemastheheat

transferaugmemationwithco-rotatｍｇｐａｔｔｅｒｎｉｓｍｏｒｅｔｈａｎｔｈｒｅｅｔｉｍｅｓｔhefin-lessduct・

Horseshoevortex,mainlongitudinalvortexandrolledUpvortexwereagainconfinnedbysmoke

flowandoiltitamumnowvisualization・AmongthefburpatternslargestfiPictionfactorocculTed

fbrtheco-rotatingpatternatsmallerpitchratioowingtothestrongUowinteractionsand

combmedvortexattackontheendwallandfhlsurfacewhereastheleastfiPictiondevelopedfbr

co-angularpattenLFinallytheeffectsofducthei8lltonheattransferandflowcharacteristics

wereinvestigatedandthemostimportantinfbnnationaboutvortexstrucmresatseveral

streamwisepositionswasobtainedwhichshowsthereasonsofheattransfbrenhancement、

Vortexstructuresfbrco-angularandco-rotatingpatternwerefbunddifferemandthe

reattachmentpositionswereobtame｡､Comparativelylargescalevortexrotationwasobservedin

co-rotatingcasewhichisobviouslyresponsiblefbrheattransferenhancemem．

K臼ywo伽JConvectiveheattransfer;HeattransferenhancememRectangularfin;Longimdinal

voltex;Horseshoevortex;Inffaredlmage

Nomenclature

ＤＨ：Hydraulicdiameteroftlleduct,ｍ

ＤＥ：EqUivalentdiameteroftheduct,ｍ

／：Frictionfactor

L：Finlength＝Ｚ０ｍｎ

Ｈａ：Heightofduct20～Ｚ００ｍｍ

Ｈｉ：Heigiltoffin＝５～１５，ｍ

Ａ：Averageheattransfbrcoefficient,Ｗ/m2.Ｋ

A：HeattransfercoefficiemW/ｍ2.Ｋ

ハｘ：Streamwiselocalheattransfbrcoefficient,Ｗ７ｍ２,Ｋ

ｈｚ：Spanwiselocalheattransfercoefficient,Ｗ/m2.Ｋ

jVil：Area-averagedNUsseltnumber(/i､,,/几）

ＭＪＥ：Area-averagedNUsseltnumber(/JDB/几）

IVjJL：Area-averagedNusseltnumber(んL/几）

lViJ｡…,ﾉ：Area-avemgedNusseltnumberonoverall surfacea１℃a(A…"、H/几）

Ｍｲﾉi､:Area-averagedNusseltnumberonfi､base(/i/１，iDH//L）

ＲＰｂｏ：Streamwiseandatmosphericpressurerespectively,Ｎ/ｍ２

jＷ：Walltemperamre,ｏＣ

１６。：Mainstreamtemperature,。Ｃ

Rｅ：Reynoldsnumber[UDH/v］

ReE：Reynoldsnumber[UDE/v］

ReL：Reynoldsnumber[UZ/v］

Ｕ：Meanairvelocity，ｍ/Ｓ

ＰＲ：Ptchratio

Sx：Finspacingmsn℃amwisedirection(showninFig､2.1）

Sｚ：Fmspacinginspanwisedirection(showninFig､2.1）

Ｚ：Streamwisecoordinate(Ｘ＝OatthecemerofrectangularfinoffirstrDw）

Ｚ：Spanwisecoordinate(Ｚ＝Oatthecenterofrectangularfinoffirstrow)．

ｒ：Streamwisecoordinateぽ=OatthecenterofrectangularfInofthirdrow）

Z．：Spanwisecoordinate(Z*＝Oatthecenterofrectangularfinofthirdrow）

Ｇ”ekqy腕ｂｏＫＦ

ａ：Inclinationangle

v：Kinematicviscosityofair,ｍ２/ｓ

/I：Themlalconductivity,Ｗ/(、.K）

Subsripts

s：Smoothsurface

訓Introduction

1.1Whyheattransferissoimportant？

HeattransferorThermalmanagememisanimportantfhctorinengineenngwhichhave

greatcomlibutiontothetechnologicaladvancementofthemodemcivilization・Thermal

managementortemperaturecontrolisagreatconcerntoheatgeneratingbodies,asfbrexample，

powerplants,nuclearreactors,engines,motors,heatexchangers,processindustries,generators，

electronicequipment,digitalcomputerseventhoughinspacecraft・Iftheheatgeneratedina

machineisnotremovedatasufficientrate,ｓｏｍｅproblems,ｅｖｅｎthebreakdowncantakeplace

mthemachineduetooverheatmg・Ｔｈｉｓｓｏｒｔｏｆｐｒｏｂｌｅｍｃａｎｏｎｌｙｂｅｏｖｅｒcomebyamore

effectiveheattransfbnSoagreatdealofresearchworkisgoingonmthisfieldtodevelopa

moreeffbctivetechnology．

1.2.Differentmethodsofenhancingheattransfer

Therearemanywaysofenhancingheattransfbr､Coolingbyjetspray,especiallyathigh

temperatures,vortexgeneratorsandfinsorextendedsurfacesareveryimportanttechnologyand

commonlyencounteredinheattransfbraugmentation・Iwouldliketolimitmyliteraturereview

onvortexgeneratorsandextendedsurfaces．

1.2.1.Vortexgenerators-anemergingtechnology

Avortexgeneratorisanemergingtechnologytoenhanceheattransfbr・Smdies

concemingtheinfluenceoflongimdinalvorticesonheattransferareagreattopictothepresem

１

daydevelopmentofhighperfbrmancethennalsystems・Theuseoflongimdinalvortices

generatedbydifferentkindofvortexgeneratorstoenhancetheheattransferintheairsideof

heatexchangershasbeenconsideredpmmising・Umillastdecade，fewresearchworkshave

shownthepotentialuseofvortexgeneratorsinenhancingheattransferincompactheat

exchangers・Mostlyearlierworksdealtwitlllongimdinalvorticesandheattransferrelatedto

mrbinebladecooling,OneoftheearliestisreportedbyEdwardsandA1ker［19741who

investigatedtheeffectofbothcounterrotatmgandco-rotatingvorticesonheattransferof

boundarylayers、Spatiallyresolvedheattransiierratesweredeterminedbypassingflｏｗｏｖｅｒａ

ｗａｌｌｏｆｕｎｉｆｂｍｌｈｅａｔｆｌｕｘ・Cubesandvortexgeneratorsbladesｗｅｒｅusedtocreatethe

longimdinalvorticesandfbundtllatthecUbespmducedthehighestlocalheattransfer

improvememofupto160％whilethegeneratorseffbctwasextendedatfartherdownstream・The

counterrotatingvortexpairsshowedmoreeffbctivenessthantheco-rotatmgpairswithan

increasemheattransferofmaximum６５％thannatplatevaluesfbrthecounterrotatmgvortex

generatorswithl5oattackanglaTurkandJunkhan[1986]measuredthespanwiseheattransfer

downstreamofarectangularbladetypevortexgeneratorsmountedonaflatplateandthe

spanwiselocalheattransfercoefficientswerefbundvarymgwiththespanwisebladespacing

Fiebigandcoworkers（1986,1991）haveconductedaseriesofexperimemalandnumerical

simulationabouttheinfluenceofwmgtypevortexgeneratorsonheattransfbrandpressureloss

inductHows､Theytriedtoimprovetheperfbnnanceofplate-finheatexchangers､Heattransfer

infm-tubeconfigurationwasfirstsmdiedbyRusseletal[1982]andfbcusedontheuseofvortex

generatorstoenhanceheattransferinfintubeconfigurations・Theirexperimemalworkwasvery

promisingbecausetheyshowedthatthevortexgeneratorscouldenhanceheattransfbr・Inamore

applicationbasedeXperiment,FiebigetaL[1993,1994］studiedtheinfluenceofwinglettype

vortexgeneratorsinfinmbeconfigurationswiththreetuberowsandmeasuretheheattransfer

andpress､巴lossfbrdifferemfinSpacmg,tubearrangement(inlineorstaggered)andmbefbnn、

２

TheyfbundthattheheattransfercoefYicientwasenhancedby５５％－６５％fbrcirculartubewith

aninlinearrangementwhereasstaggeredarrangementcaused9％．

1.2.2.Extendedsurfnces

Ｆｉｎｓａｒｅｗｉｄｅｌｙｕｓｅｄａｓｔｈｅｐｒｉｍａｒｙｍeansofheatexchangingdevices・Theneedfbr

moreefficientcoolingtechniquesofdeviceshasrecemlypromptedsmdyintoheattransfbrand

nowcharacteristicsofvariousconfigurationsoffinnedsurftlces・Thepinfinisatypical

configurationthatisoftenusedtocoolthetrailingedgeregionofmrbineblades；theintemal

passageofturbinebladｅｓｃａｎｂｅｖｅｒｙｎａｎＰｏｗ,sothatthechoiceofcoolmgsCllemeislimited、

TheeffectiveheattransfbrofstaggeredalTaysofshortpinfinswasstudiedbyVanfbssen[1982］

ａｎｄｆｂｕｎｄｔｏｂｅｈａｌｆｔｈａｔｆｂｒｌｏｎｇｅｒｐinfins、However，thisstudydidnotdetailthelocal

characteristicsofpinfinarrays・SpalTowetal．［1976］investigatedthelocalheattransfer

coefficientoveraplatesurfacebythenaphthalenesublimationteclmiqUefbratwo-rowplatefin

andmbeheatexchangerlfindingthatthecoefficientwaslowestbehindthepin･Theeffectofpin

finarrangementonheattransferoveranendwall,theheatingsurfacewherethefinsareattached，

wasexaminedusingathennosensitiveliquidcrystalfilmbyMatsumotoｅｔａＬ［1997],Who

concludedthattheheattransfbrfiomtheendwallwasenhancedbyflowaccelerationbetweenthe

pinfinsratherthanthehorseshoevortexaroundthepinRectangularfinisfbundtohavean

extensiveuseinheatexchangersurfacesandinmanyapplications,Geometncparameters,such

asaspectratio,finheighttoductblockageratio,finmclinationangle,orientationoffini.e・fin

pattern,finpitchratioinstreamwiseandspanwisedirectionandfInshapeshavepronounced

effectsonthelocalandoverallheattransfbrcoefIiciemsaswellasonthethennalperfbrmanceof

theheatexchangingdevices、Withtheincreasingdemandofcompact，lightweighthigh

perfbnnanceheatexchangingdevicesresearchersaretryinghardtoservethefinsasextended

３

surfaceaswellasvortexgeneratortoobtainthecombinedeffbctofextendedsurfaceandvortex

generatorwhichisanemergingtechnologyinthefieldofheattransfbr，

Recently,inclinedrectangularfinembeddedｔｏｔｈｅｅｎｄｗａｌｌｉｓｆｂｕｎｄｔｏｂｅａｎｅｆｆｅｃtive

confIgurationfbrheattransfbrenhancemem，becausetheinclmedfinproducethelongitudmal

vortexofwhichintensityexistatfardownstream､Itisexpectedthattheheattransfbrffomthe

endwallandthefInsurfacecanbeimprovedbythismclinedfinsandhencethisconfigurationis

identifiedasbeingverypromising・ToriiandYanagihara[1997]hasreviewedonheattransfbr

enhancementbylongimdinalvorticesanddiscussedhowlongitudmalvorticesareproducedby

diffe泥ntkindofvortexgeneratorsandenhancesheattransfbr・Thatreviewfbcusedontheeffect

oflongimdinalvorticesgeneratedbywingsontheheattransferenllancementinboundarylayers，

ductsandplatefintUbegeometlies・HeattransferenhancementinalTaysofrectangularblocks

hasbeeninvestigatedbymanyresearchers､SpalTowetaL［1982,1983]studiedtheheattransfer

andpressuredropcharacteristicsofarraysofrectangularmodulesconⅡnonlyencoumeredin

electronicequipmentlntheirexperiment,heattransferenhancementsexceedingafactoroftwo

wereachievedbytheuseofmultiplefbnceslikebalTiers,withtheimerbarrierspacingandthe

balTierheightbeingvariedparalnetricallyalongwiththeReynoldsnumber・Igarashi［1983］

studiedheattransfbrfromasqUarepnsmwithdiffbrentinclinationanglesandobserved

reattachmentflowfbrinclinationanglesofl4o-35o、HeattransfbrfiomananFayofparallel

longimdinalfinstoamrbulemairstreampassmgthroughthemterfinspaceshasbeen

mvestigatedbothnumericallyandexperimemallybyKadleandSparrow[1986]・Theyfbundthat

thelocalheattransfercoefIicientsvariedbothalongthefinsandthesurfaceofthebaseplate・

OyakawaetaL［1993]smdiedtheheattransferofplatesettingrectangularfinswithincUnation

angleof20oandshowedtllatthisconfigurationcanenhanceheattransfbr幹MolkietaL［1995］

experimemallysmdiedtheheattransferattheentranceregionofanarrayofrectangularheated

blocksandpresemedempiricalcolTelationsoftheheattransfbrfbrthealTay・Ｅｌ－ＳａｅｄｅｔａＬ

４

[2002]investigatedheattransferandfluidUowinrectangularfinarraysandfbundthatthemean

NusseltnumberincreaseswithincreasingReynoldsnumber,inter-finspaceandfinthicknessbut

didnotexamineendwallheattransfbr､BilenandYapici［2002］investigatedheattransfer

enhanceｍｅｍｆｒomasurfacefittedwithrectangularblocksatdiffbrentinclinationangleand

fbundthatthemaximumheattransferwasobtainedatanangleof４５．whiletheeffectof

inclinationangleislittlefbrlargerthan225｡,thoughthelocalheattransfercharacteristicswere

notreported・

IncontrasttorectangUlarfins，cylinder-likepinfinshavebeenfbundtoexhibitalarge

pressu頬dropduetothedragfbrceandflowaccelerationordecelerationthroughthefins､This

difIbrenceisduetothefactthatrectangulararraysdonotfbnnextremelynarrowpassages，

whichalsocausestheheattransferfbrrectangularfinstoberelativelylower・However,thepoor

heattransferregionbehindthepmmaybeimprovedbylongimdinalvortexesgeneratedbythe

fmFurthermore,WhenthefInarrayissetsuchthattheinclinationangleofeveryrowischanged

altemately>thelongimdinalvortexproducedbythetopedgeofthefinreattachestothatofthe

fbllowmgfinincreasingtheheattransferffomthefinsurhlce・Astheaboveliteraturereview

shows,previousstudieshaveinvestigatedheattransferenhancememfromsurfnceswitharraysof

shortrectangularfinsandafewsmdieshaveconcentratedonheattransferffomendwallfbrshort

rectangularfinswithdiffbrentinclinationangles､However,adetailedheattransferanalysisfrom

anendwallwitharraysofshortrectangularfInsofdiffbrentpattems(co-angular,zigzag,co-

rotatmgandco-counterrotatmg)intheductflowhasnotyetbeencompletedBilenandYapici

[2002]haveconductedasmdyfbrtheco-angularcaseonly,butdidnotclarifythelocalheat

transfercharactelistics・Inco-angularpattern,finsarrangedatsameangletothesamedirectionat

eachandeveryrow・Thisinclinationangleofthefinswillfbrmlongitudinalvortexwhichwill

stlikethenextfinsurfhceandendwalLF1owwilltouchbothsidesofthefinsurfaceandsoitis

expectedtheextendedsurfhceeffbctwillbehigherthanvortexeffectontheendwalLWhenthe

５

ｆｉｎｓａｒｅｓｅｔａｔｓａｍｅａｎｇｌｅａｔｅａｃｈｒｏｗbutthedirectionsarealtematelychangedthenwedefine

thatpattemaszigzagpattern,Duetothealtematedirectionsofthefins,aslnusoidalwavyUow

behaviorisexpectedtoobservewhichwillincreasethevortexeffbctontheendwaUmorethan

theextendedsurfaceeffect､Inco-rotatmgandco-counterrotatingpattern,ｆｉｎｓａｒｅｓｅｔｉｎｓｕｃｈａ

ｗａｙｔｈａｔｉｔｆｂｎｎsconverginganddivergmgfinpairsｉｎａｒｏｗ・Inco-rotatingpatternthe

convergmganddivergingfinpairsremainsameatcoITespondingfinrows・Inco-counterrotating

pattemtheconvergmganddivergingfinpairsarealternatelychanged､Thisdivergmgfinpairs

willfbnnacoupleoflongimdillalvortexwhichmightstrikestheendwallstronglyandthis

combineddownwashisexpectedtoenhanceheattransferhPomtheendwallsignificantly．

L30bjectiveofthisresearch・

Therefbre，wehaveinvestigatedtheheattransferenhancementfbrfinarraysoffbur

diffbrentpattemsatnalTowandtallductbysettingshortrectangularfinsonaductwalLWehave

chosenthefburfInpatterns,becausetheorientationsofthefinpattemgreatlyaffbcttheflow

fleldandasaresultheattransferisaugmented､Ｉｎｔｈｉｓｓｍｄｙ,shortrectangularfinswithfbur

differempatterns,areinvestigatedbecauseofitssignificantheattransfbrenhancementcausedby

thelargescalevoltexeffbctandextendedsurfaceeffect・Inadditionto,determiningtheoverall

heattransfbroftherectangularfInarray,therelativemagnitudesofheattransferbetweenthefins

andendwallcanbedetemlinedinthisstudy､Thissmdyattemptstoanalyzethedetailedheat

transfercharacteristicsoffinbaseandendwallsurfhcefbrdiffbrentfinpatternsandexaminethe

extendedsurfaceeffectfiPomthefinsurfacesandthevortexeffbctontheendwallfbrvarylng

pitchratioinstreamwisedirection、Detailedheattransfbrs，aswellasaverageheattransfer

coefficientsareestimatedffomtheinffaredimagesoftherepresentativefinregion・Theflow

behavioramundthefinsisfUrtheranalyzedtodetermmethelclationbetweentheheattransfer

andfluidflowcharacteristics，Furthelmorewediscussedthethermalperfbrmanceofthefbur

６

differentfInpattemsundertheconstantpumpingpowercondition，becausetheheattransfer

enhancementalwaysaccompaniesthedragfbrceandpressuredropsimultaneously・Ｓｏｗｅｍｉｇｈｔ

comparetheheattransfbrenhancementrateofthissystemwithtjhatofsmoothduct．

７

Z’ExperimentalApparamsandProcedurｅ

2.1Introduction

Inthissectionwehavemainlydiscussedthediffbrentfinpatternsandtheexpenmental

setUpfbrtheheattransfermeasurements，pressuredropmeasurememsandflowvisualization

technique・Heattransfercoefficientsweremeasuredbytwotypesofapparams；heattransfbr

measurementbyTtypesthermocouplessolderedonthebacksideoftheheatmgsurfaceandthe

othertypeisheattransfermeasurementbymfiaredcamera．

2.2Finpatternsandarrangements

FourtypesoffinpattemsaresmdiedmthisresearchworkasshowninFi9.2.1

Thefinsweremadeofeitheraluminumorresinmaterialsandwererectangularwithdimensions

20mmlong,Smmthickandthreeheights,５，１０ａｎｄｌ５ｍｍ・Thefinsweresetinlinesandrows

ofseveneacｈＦｉｎｓｐａｃｍｇ，fincentertocenterdistanceSx，mstreamwisedirectionwere

maintaｉｎｅｄ４０ｍｍ,６０ｍｍａｎｄ７０ｎⅡnwhereasqinspanwisedirectionwａｓ４０ｍｍ､Theratios

SyLandS/Laredefinedaspitchratio,ＰＲhereafter・Theanglesofthefinstotheflowdirection

weremaintainedatcL＝0.,20．ａｎｄ25..Intheco-angularpattemthefinswerｅｓｅｔａｔｔｈｅｓａｍｅ

angleandinthesamedirection・Inthezigzagpattemthefinshavethesameanglebutaresetin

alternatedirectionsaftereachrow､Incaseofco-rotatingpatternfinpairsarerotatedinsame

directionandfbnnconvergentanditbecomessameateveryfinrows・Contrarily,ｉｎｃａｓｅｏｆｃｏ‐

counterrotatingpatternfinpalrsaresetasconvergentanddivergentaltematelyatroｗ－ｗｉｓｅ

direction．

８

Aとらら鼻うらみＢつつつつヴグＰ

Ｃ色-Vぞa且２－色_色_PamidlineDグーヅー少･ヴー･グーダーゲｃｅｎｔｅｒｌｉｎｅ

ＥＰＰＰＰＰＰＰ－

ＦつＰＰＰＰＰＰ－Ｑａ

ｎＰ－Ｐ尊Ｐ（a)Co-angularpattem

７Ｐづづ多づづＰ

】・

６，勺、一、、、、

一一

５つＰつ一錫つググ趣ａ

４勺。、一も、。、秤Ｚ

３グググー惨ＰＰＰ醜

２，，，－、、、、⑥

』’

１グジグーづつＰＰ

ＡＢＣＤＥＦＧ

７ｐｐｑ夢ｐｐｑ

６勺Ｐ負やＱＰＱｍ

５勺ロロラロリ、脚

４勺つ勺稜ｑＰＱ煙ａ

３勺ヴローサロつＱｍｏ

２勺つＱ－ＰＱつ勺加

ｌロヮロラロつＱ

ＡＢＣｌＤＥＦＧ

７勺つ９づＱＰＱｍｅ

６つ。つ一句つ。つ剛

』』

５勺つローヴＱＰＱ・唾ａ

４。Ｑつ一句ＰＱＰｍｅ

３勺。。－ザＱＰＱｍＯ

２つ。Ｐ一句つＱＰＫ

－－

Ｃ

ｌＱつＱ－ＰＱｐＱ⑥

ＡＢＣｌＤＥＦＧ

Fig.２．１Diffbrenttypesoffinpattems

９

2.3ExperimentalsetupfDrheattransfermeasurement

2.3.1Finsinsidetheduct

Expelimemswereconductedinlongrectangularducｔｓｂｏｔｈｏｆ２０ａｎｄ２００ｍｍｈｅｉｇｈｔ，

230mmspanwidthand784mmlengthThefirstrowoffinswaslocated200mmawayfromthe

ductentrance､TheeXperimentalapparamsandfinsettingsareshowninFig､2.1.ＡｓｓｈｏｗｎｍＦｉｇ

２・ZfbraductheightofHa＝２００，Ⅱn,thevelocityfielddoesnotdevelopoverthetestsection，

butratheritassumesfinsaremflatplateboundarylayerOntheotherha､｡,ａｔＨａ＝２０mmthe

flowisfUllydevelOped・ThefinswereattachedtothelowerwalloftlleductbymeaｎｓｏｆａｌＯＯ

似mdoUblesidedthintape・Theupperplateofductwasmadeofatransparemacrylicresinplate

fbrobservationoftheimenoroftheduct．◆

目L１ｒｌｌｃ

~＞'二

Fig.2.2Finsinsidetheduct(alldimensionsareinmm）

1０

2.3.2Heatingsurfacewithfnns

Tomeasurethelocalheattransfbrcoefficients,ｔｈｅlowerwallwasfblmedofaBakelite

plateofthicknesslOmmanda30umthickstainlesssteelfbil(200ｍｍ×７８４ｍｍ)asaheating

Surface・Aconstantheatflux9wasfbnnedattheheatingsurfaceusingadircctcurrentsource．■

Topreventheatlossfiomtheheatingsurfacethroughthelowerwall,alayerofglasswoolwas

placedundertheBakeliteplate,Thewalltemperamre恥wasmeasuredusing70ⅡmdiameterT-

typethennocouples,solderedonthebacksideofthelowerwallat58discretelocationsalongthe

centerlineoftheheatingsurfaceandthemidlinebetweenthefinsinthespanwisedirection,ａｓ

shownｉｎFig.2.3.

Heating CenterlineMidline

thcrmocouplethermPcouplcsｕｒｌａｃｅ

露》雫一

ニニニエニジニー

ニジニニニー

蟇霄二一

窕露》画一

ＬＸ

Ｚ

Ａ

784

Sidetopontside、

Fig.2.3Heatmgsurfacewiththennocouplelocations(Dimensionsinmm）

1１

2.3.31nfraredimagetechnique

lnordertoobservethedisnibutionsofthetemperatureandtheheattransfbrcoefficients

aroundthefinsattheendwall，infraredimagesweretakenusinganinffaredcamerawitha

indium-antiｍｏｎｙ(In-Sb)sensor,whichcanmeasurcthetemperatureatl60x120pointswitha

resolutlonofOO25oCfbrablackbody､Hereitshouldbementionedthatanotherheatingsurftlce

similartothepreviousoneismadeexceptthethemlocouplesattachments・Inthiscase，the

temperaturewasmeasuredatthebackoftheheatingsurfacethroughawindowcovercdby

polyvinyledenefilmwithatransmissivityfbrinfraredenergyofnearlyunity､Thebackofthe

heatingsurfacewaspaintedblackandthewholeexperime､talapparatuswascoveredbyblack

clothtoensurethatthesurroundingｓｗｅｒｅｃｏｍｐｌｅｔｅｌｙｄａｒｋａｓｓｈｏｗｎｉｎＦｉ9２４．

囮］E窪匡團巨塞曇ＱＬＤ

Blackoutcurtain

、Ａ ｡,LLocalheattmnsfe

coefficients

繍糟w…T>|＜耐多し

Ｆｏａｍ

ＭＷ,｡.､。NozzleIA

Bakeliteplate

÷f1ii箒篶予

ＣつＮ１つＮⅡ百田

〆

Fig.2.41nfraredimagetechnique

1２

First,wemeasurcdtheheattransferusingthethennocouplesinthelargerregiontodeterminethe

effectofthefinsetting・WethenestimatedthedetailedheattransferandaveragedNusselt

numbersintherepresentativeregionbythemfraredimagetechnique、

2.3.41nsulationTechnique

Figure25（a）ａｎｄ（b）showsthethelmalinsulationoftheheatingsurfacewith

thermocouplesandwithoutthermocouplesrespectively・Thestainlesssteelfbil,attachedtothe

bakeliteplatewasusedastheheatmgsurftlceandthatbakeliteplatewascoveredwith60mm

thickmsulator,fbamtopreventheatlosshomthebackoftheheatingsurface,Therefbreheat

losseshPombackoftheheatmgsurfaceexceptwindowmayassumetobeverylittleThe

measurementwindowwascoveredwithtwolayersofpolyvinyledenefnmwithlmmspace

clearance・Heatlosseswere1.3％oftheheatfluxsuppliedtothesurfhcebymeasurementof

temperature difference betweensurfaceheatingandbacksurface．

Ｓ

0.1

plate

〃'''BakcliteF

fbil

ape

(b)Thennalinsulationoftheheatingsurfaceexceptwmdow(a)Thennalmsulationoftheheatmgsurftlce

attachedwiththennocouples．

Fig25Thennalinsulationtechnique(dimensionsareinmm）

1３

２．４ExperimentalapparatusfOrpressuredropmeasurement

TomeasurethepressuredlDpresultingfromthepresenceofthefins，0.5mmdiameterstatic

pressuretapswereplacedatl3vanouslocationsofupstreamanddownstreamofthefinsonthe

pressureplatewith60-l20mmspaceintervaLExperimentalapparatusfbrpressuredrop

measurememisshowninFig2.6.Herethepressureplateisapolishedaluminumplateandthe

finsweresetontheplatebydoublesidedthintape・Pressurewasmeasuredbyadigitalmicro

manometerwithanaccuracyof±Ｏ１ｍｍＨ２０．

に一一一一

Ｏ～２００

Fig.２．６Experimentalsetupfbrpressuredropmeasurement(dimensioninmm）

1４

2.5Flowvisualizationapparatus

InordertoObservethebasicUowpatternandtheflowbehavioraroundthefin,Ｈｏｗ

visualizationisveryimportant・Therehavebeenuseddiffbrentmethodstovisualizetheflow

behavior・Ｉｎｏｕｒｅｘｐｅｎｍｅｎｔ,thef1uidnowwasvisualizedasfbllows:Dyeflowmwaterchanne１，

Titaniumoxideoilfilmflowvisualizationandsmokeflowvisualiｽﾞation．

2.5.1Experimentalsetupfbrdieflowinwaterchannel

Dyeflowmwaterchanneliso､eofthegoodvisualizationtechniquestogetaclearview

oftheflowpattelnFigure27showstheexperimentalsempfbrdyeflowinwaterchannel・Flow

wasvisualizedbyinducingfluorescentdyeinthewaterchannelatlowerReynoldsnumberto

observetheflowpatternclearly・Thewaterchannelwasmadeofatransparentacrylicplateof

Overflowtank

Hallidelight

Nozzle

ﾄｰﾗz５－ｌ

Ｔ＜一面一＞

|’雲霧富

Testsection

era

Fig.2.7Experimentalapparatusfbrdyeflowinwaterchannel

1５

ｄｉｍｅｎｓｉｏｎ５０ｍｍｈｅｉｇｈｔａｎｄＺＯＯｍｍｗｉｄthFinswereattachedtｏｔｈｅｓｉｄｅｗａｌｌａｓｓｈｏｗｎｉｎ

Ｆｉ92.7.FluorescentdyewasinducedjustattheffontofthefinsbyanalTowtube・Ametalhalide

lightsetatthetopofthechannelandadigitalcamera(NikonD70)setpelpendiculartochannel

sidewallwereusedtoobserveandshotthephotographsatpropertime．

2.5.2Experimentalsetupfbrsmokef1owVisualization

lnordertodetelminethenowbehaviorindetailsaroundtherectangularfInofdiffbrentpattern，

thenuidflowwasvisualizedbyflashlightsheetmethodusingsmokeasatracersuppliedat

upstreamsideatlowerReynoldsnumber・SmokeUowvisualizationapparatusisshownin

Fi9.2.8.ItconsistsofarectangularductmadeoftranSparentacrylicsheet,greenNd:YAGlaser

light,digitalcamera(NikonD70)andasmokegeneratorthatproducesmokeoffinedropletof

diameter0.3～１Ｕｍ・ForsmokefIowvisualizationfinsweremadeoftransparentacrylicsheet・

TheNd:ＹＡＧｌａｓｅｒｓｈｅｅｔｗｈｉｃｈｗａｓｕｓｅｄｈａｓａｎemittedradiationofwavelengthof５３２ｍn．

Camerawaspositionedattopoftheductandthelaserlightwassetatthesideoftheductparallel

tothelowerwalloftheductwherethefinset､Oncethecameraandlasersheetwerepositioned，

thesmokegeneratorsuppliedthesmokeattheentranceoftheduct,thenimagesofflowpattem

wererecorded．

〃Air

F1ow ａｓｅｒ

へ

SmokeGenerator Imageprocessor

Fig.2.8EXperimentalapparamsfbrsmokeflowvisualization

1６

2.5.3ExperimentalsetupfUroiltitaniumoxidefilmfIowvisualization

ExpenmentalsetupfbrtheoiltitaniuｍｏｘｉｄｅｆｉｌｍｆｌｏｗｉｓｓｈｏｗｎｉｎＦｉｇ2.9．Titanium

oxideoilfI1mflowpattemsatthelowerwallaroundthefinswereobservedatthesameReynolds

numberofthatofthcmainexperlmentｎｏｗ・Ｉｎｔｈｉｓｅｘpenment,athinblackfIlmwasattachedto

thelowerwallandblackpaintedfinsweｒｅａｔｔａｃｈｅｄｔｏｔｈｅｆｉｌｍＴｈｅｌｏｗｅｒｗａｌｌａｎｄｔｈｅｆｉｎ

ｓｕｒｆａｃｅｗｅｒｅｐａｉｍｅｄｂｙａmixmreoftitaniumoxide,lmseedoilandoleicacidofsuitabledensity

andwereeXposedtoairflowtoobservetheoiltitaniumoxidefilmflow・Aftercompletionofthe

run,photogPaphsweretakenbyadigitalcamera(NikonD70)．

Ｃａｍｅｍ

ＮｉｋｏｎＤ７０:蝋、／

’一

４円ＦＩＩ ｅ

Fig.2.9Expenmentalapparatusfbroiltitaniumoxidefilmflowvisualization●

1７

３DataReductionandUncertaintyAnalysis

３．１１ntroduction

Inthischapterdatareduction,heatbalanceanduncertaintyanalysisaredescribed,because

theheatbalanceanduncertamtyanalysisareveryimportantfbrthereliabilityofthe

experimemalsmdy．

3.2.Ｄａｔａreduction

InthissmdywehaveinvestigatedthefluidUowandheattransfer・Theessentialquamities

determinedwerethefiictionfactorandtheheattransfercoefficientsfbrthedifferentfinpattems．

ＴI1etotalheatgeneratedfiomtheheatingsurfaceisdistributedintotheheattransfelTedby

convectiontｏｔｈｅｆｌｏｗｉｎｇａｉｒ,heatlossesfbroughtheinsulationandthewindow､Heatlosses

hombackoftheheatmgsurfaceexceptwindowmayassumetobeverylittleasthebakeliteplate

wasinsulatedby60mnthickinsulator,fbamtoprevemheatloss・Itwasfbundthattheheatloss

ffomwindowwas1.3％oftheheatUuxsuppliedtotheheatingsurface・Soitsvalueissosmall

comparedtotheheatinputvalueanditcanbeneglectedConseqUentlythetotalheattransfbrred

byconvectiontotheUowingairequalstheheatfluxsuppliedtotheheatingsurface，

Thehictionfactor／wasevaluatedfromthepressuredifferencebetweenpointsjust

upstreamanddownstreamofthefinsattachedtotheheatingsurfaceusmgtheEq.(3.1）

／＝Ploss(DH/O/(paU2/2)，（3.1）

whereノisthedistancetotherefbrenceregion,i､e・thedistancebetweenjustupstreamofＤ１ｆｉｎ

ａｎｄｄｏｗｎｓｔｒｅａｍｏｆＤ７ｆｍａｎｄＤＨｉsthehydraulicdiameteroftheduct．

1８

Theheattransfercoefficiems，

ノz＝９/('鵬一t｡｡)，（32）

ｗｅｒｅobtainedatrepresentativeregion，whereｔｗｉｓｔｈｅｗａｌｌｔｅｍｐｅｒａｔｕｒｅａｎｄｔｌｌｅｔ,cisthe

mainstreamtemperature・

WeconsideredthreekindsofReynoldsnumbersandexaminedtheireffbctsontheheat

transfercharacteristicsattheflatplateboundarylayerandthenalTowductwithfinarrays．

Reynoldsnumberbasedonthemainstreamvelocityandfinlengthcanbeexpressedas

(3.3）ＲｅＬ＝ＵＺ〃

Reynoldsnumberbasedonthemainstreamvelocityandtheducthydraulicdiameterandcanbe

expressedas

Ｒｅ＝ＤＤＨ〃 (3.4）

Reynoldsnumbersisbasedonthemeanvelocityandtheductequivalentdiameterandcanbe

expressedas

ReE＝ＵＤＥ" （3.5）

Thearea-averagedNusseltnumberbasedontheducthydraulicdiametercanbeexPressedas

(3.6）Ｍ＝ハＤＨ／几

Thearea-averagedNusseltnumberbasedontheductequivalentdiametercanbeexpressedas

(3.7）/VjlE＝ADE／几

Thearea-averagedNusseltnumberbasedonthefInlengthcanbeexpressedas

jVZZL＝AL/ス （3.8）

1９

３．３Uncertaintyanalysis

Thepressurewasmeasuredbyadigitalmicromanometerofaccuracy土０．１ｍｍｏｆＨ２０・

Theheatingsurfaccwascoveredwith60mmthickinsulator,fbamtopreventheatlossffomthe

heatingsurface・Therefbreheatlossesfrombackoftｈｅｈｅａｔｉｎｇｓｕｒｆａｃｅｍａｙａｓｓｕｍｅｔｏｂｅｖery

little・Ｗindowwascoveredwithtwolayersofpolyvinyledenefilmwithlmmspaceclearance

andheatlosseswere1.3％oftheheatfluxsuppliedtothesurface､Asaresult,heattransfer

coefficientcontainedlessthan３％uncertamty、Thetemperaturewasmeasuredbyboththe

themlocouplesusingadataloggerandtheinfiParedcamera・Thepercemagerelativeuncertainty

mthemeasuredtemperaturefbrthethermocouplesandtheinfiaredcamerawere±0.25％ａｎｄ±

1.3％respectively､Ｔｈｅｐｅ1℃entagerelativeuncertamtymthemeasuredelectricpowerinputwas

±1.4％、Thepercemagerelativeunceltaintｙｉｎｔｈｅｃｏｍｐｏｕndvariableswerefbundtobeless

thａｎ±５％bothfbrthevelocityandtheReynolｄｓｎｕｍｂｅｒａｎｄ±３％bothfbrtheheattransfer

coefficientandNusseltnumber．

2０

(1１伽司『HeatTransferCharacteristicsandFlowAnalysisofFinnedSurfacesinCaseof

TallDuctandNarrowDuct．

4.1Introduction

Inthischapterwewouldliketodiscusstheheattransfercharacteristicsandfluidflow

analysisoffinnedsurfacesofco-angularandzigzagpatternExperimemswereconductedfbr

finssettingataHatplateboundarylayeri.e・intallductandnarrowductcolTespondingto200

mmand20mmductheight．

4.ZLocalheattransfercoefficients

4.2.1Smoothductresults

ThedistributionsofthelocalheattransfbrcoefficientsArattheendwallwithout

rectangularfinsareshowninFi9.4.1.Tochecktheaccuracyoftheheattransfermeasurements

andtodetenninethecharacteristicsofbothductswithoutfins，wemeasuredthelocalheat

transfercoefficientonthesmoothductsurface・Fig.4.1(a)presemsthestreamwisedistributions

ofthelocalheattransfercoefficiemalongtheendwallfromtheductentranceintheductofHd＝

20ＯｍｍｆｂｒＵ＝５，１０ａｎｄ２０ｍ/s・Thedistributionsgraduallydecreaseinthestreamwise

direction・Sincetlleductheightwassolarge,ｂｏｔｈthehydmdynamicandthennalboundary

layerswerestilldeveloPmg,evenatthetestsection・Duetotheroughsurfaceattheducti､let，

actlngasatriPPingsurface,theflowwasmrbulent,ThelocalNusseltnumber,basedoMrand

thedistance,Xfmmentranceagreeswiththeequatｉｏｎ

Ｍ↓漣＝0.0296Rejro8Pﾉ"０６ （4.1）

2１

fbramrbulentboundarylayeronanatplate,asshownbythesolidlinesinFig4l（a).Inthe

figure,theopenandsolidsymbolsdesignatethecenterlineandthemidlme,respectivelyBoth

setsofdataareequalregaldlessofspanwisepositionindicatingthetwodimensionalityofthe

1５０

国100ｍ

ｇ彦一

二i<５０

０

-10－５０５１０１５２０

ＸＬ

(a)Ｈｂ＝200ｍｍ

1５０

口１００ＧＪ

日～

芦一

旦<5０

0

-10５０５１０１５２０

Ｘ/Ｌ

(b)Ｈｕ＝20ｍｍ

Fig41Localheattransferdistlibutionswithoutfinonsmoothsurfhce

heatingsu1face､ThedatashowsgoodagreementwithEq.(4.1)．

TheresultsfbrthenarrowductareshowninFig4.1(b).Thedistributions獣adually

decreasetowardthedownstreamdirectionatlowerReynoldsnumbers,ＡｔＲｅ＝Ｚ３４ｘ１０４ａｎｄ

２２

３５ｌｘ104,thedistributionslowlyincreasesandcoillcideswiththefbllowingequationfbrafUlly

developedhydrodynamicboundarylayerfbrairflowatthedownstreamregionasshownbythe

solidlines：

ｊＶｊｌ＝0.Ｏ１９Ｒｅｑ８ （4.2）

HencetheductheightsofHa＝Ｚ００ｍｍａｎｄＨｔｉ＝２０mmrepresentsaflatplateturbulem

boundarylayerandaMlydevelopedductHowintestsection,respectively．

4.2.2EffCctofinclinationanglesonheattranSfer

Theeffectoftheinclinationangleoftherectangularfinonthelocalheattransfer

coefficientispresentedinFigs､４２.(a),(b),ａｎｄ(c)fbru＝０．，２０.ａｎｄ２５゜,respectivelyEach

graphrepresemsthestreamwiselocalheattransferCoefficientatthecemerlmeandatthemidline・

Cemerlmeandmidlinedataarecalculatedalongthecenterofthefinrowsandmiddlebetween

finlinsrespectivelyasshowninFi9.2.LTY1edatafbrthecemerlinedecreasesgraduallyuptothe

firstrowoffIns,whereitexhibitsarapidincreaseandattainsamaxⅡnumvaluebefbrerapidly

decreasinｇｔｏａｍｉｎｉｍｕｍｖａｌｕｅ，withthepatternrCpeatedperiodically,Maximumvaluesare

obtamedatfinpositionsandtheminimaareobtamedbetweenthefinsalongthestreamwise

direction・Ｔｈｅｍａｘ１ｍｕｍｖａｌｕｅａｔｔｈｅｆｉｎｃｅｎｔｅｒｍａｙbethecombinedeffectoftheextended

surfaceandlongimdinalvortex・Eventheminimumvaluesarehigherthanthosewithoutfinsand

henceitmaybeconsideredthatheattransfbrisenhancedbyturbulenceorlargescalevortexes

generatedbythefins・Thesolidsymbolsinthefiguredescribetheheattransfbrenhancementsat

theendwallcausedbythelongimdinalandothervortexes・Asthelongitudinalvortexfbmledby

thetopsurfaceofthefinstrikestheendwallbetweenfinssotheheattransferisaugmentedof

thatにgion、Ａｔｔｈｅｓａｍｅｔｉｍｅｔｕlbulencecausedbythecorneredgealsoincreasestheflow

mixing;asaresultheattransferisincreasedbehindthefins､Fig.４２(a)showsthepeliodical

2３

distributionfbroL＝0．whiletheheattransfbrincreasesbetweenthefinsinthespanwisedirection

anddecreasesatotherplaces・Thoughtheheattransfercoefficientsalongthecenterlineposition

ofthefinfbru＝２０｡(Fig.4.2(b))and２５｡(Fig.４２(c))mcreasesinthesamemannerasibru＝

0.,theheattransfbrcoeffIcientsalongthemidlinearesomewhatdifferent・Alongthemidlme,the

localheattransfercoefficientsareaffectedbythelongimdinalvortex,maimaminglargevalues

fbru＝２０．ａｎｄ２５゜comparedtoOo・TheheattransfbrcoefIicientfbru＝Z0oiscomparatively

higheramongthethreeinclinationangles,whichagPeeswiththedataobtainedｂｙＢｉｌｅｎｅｔａＬ

[2002]whofbundthattheeffectofinclinationangleonheattransferenhancementissmallfbr

inclinationanglesfbrlargerthan22.5.．Aninclinationangleof20ocausedconsiderable

enhancementinheattransfer,Thisisbecauseoftheedgeeffectoftherectangularfin,which

increasestheHowmixmg・Ｗｈｅｎｔｈｅｆｉｎｓａｒｅｍｍｅｄａｒｏｕｎｄｔｈｅｍｉｄpoint,thesideedgescan

producemoreturbulence・Becauseofmrningaroundmidpoint，thefinwillactasvortex

generatorandproducethelongimdinalvortexconstructingtrailingvortex，ｃｏｍervortexand

inducedvortex・Thelongitudinalvortexisalsocalledthestreamwiseonewhichaxisisinsame

directionasthestreamwise,andpersistsoveralongstreamwisedistance,distulbingtheentire

velocityfieldandtemperaturefIeld・Asaresultheattransfbrratemcrcases・Alsothecomeredges

increasesthemrbulenceleveLThissituationhasbeendiscussedbyHennan[1994]andHelman

andKang[2001］Therefbre,aninclinationangleof20oispreferredfbrfUrtheranalysis．

2４

150

ＯＣＣｓ

［】對三］然函

０

-５ ０ ５１０

Ｘ/Ｌ

(a)CFO。

1５

－０－centerline

＋ｍｉｄｌｍｅ

００００

ｓ０５

１［】判：β］詫二Ｐ￣Ｆ’■■ＦロＰ￣Ｆ￣

-５ ０ Ｓ１０

Ｘ/Ｌ

○

(b)ＧＩ＝2０

1５

-O-centerline

-十midline

1５０

０００５

画週」宴］耳

戸一■■￣￣￣■■￣Ｐ￣■■￣￣￣

０

-５ ０ ５１０

Ｘ/ＬＯ

(c)ｕ＝2５

1５

Fig.４．２EffectofinclinationangleonlocalheattransfercoefficientsfbrHf＝１０ｍｍ，Ｈｂ＝Ｚ００ｍｎａｎｄＵ＝１０ｍ/ｓ

2５

4.2.3Heattrans化rthroughfinofresinmaterial

Wenowwanttodiscussthefinmaterialwithregardsestimatingtheeffectofavortex

generatorontheendwall,butnotfbrtheextendedsurfaceThelocalheattransfercoefficientwas

measuredfbraresinmaterialfin，ratherthananaluminumfin・Ｔｈｅｒｅｓultsareprcsentedin

Fig､4.3．Inthisfigur巳cemedmedistributionshowsthattheheattransfercoefficientatthefin

positionfbrtheresinmaterialincontrasttothealuminumfinasshowninFig42(b)issmaller，

becauseofnoextendedsurfaceeffect・Thecoefficientatthemidlinealsoappearstobeequalto

thatofthecenterline・Sotheoverallheattransfermaybeenhancedbyafactorofabouttwotimes

thanthatofwithoutfins､ThisresultsintheeffectofvortexgeneratorwithnoeffecthPom

1５０Ｕ(m/S）

一○－－●－５

－匹－■－１０

一○一一ローcenterline

一一midline０００５

［】Ｍ…Ｆ］ゴ

-４ ２０２４６ ８１０１２１４Ｘ/Ｌ

◎

Fig.４３Variationoflocalheattrallsfercoefficientsfbrresinmaterialｗｉｔｈα＝２０，ＨＩＰ＝１０ｍｍ,Ｂａ＝２００ｍｍ．

extendedsurface・BecausetheBiotnumberfbrtheresinmaterialwasestimatedlOandthe

conductionresistanceofresinmaterialwasnearlyequaltothethermalresistanceTherefbre,the

heattransfere血ancementbyanaluminumfinonlywillbediscussedinthepresentexpenment

asthealuminumfinswillhavetheeffectofextendedsurfaceandthevortexgeneratoratthe

sametime・Asmentione｡,thindouble-sidedtapeofthicknesslOO1unwasusedtoattachthefin

totheheatingsurface・Forthealunnnumfin,theconductionresistanceofthetapewas５％ｏｆthe

２６

totalresistance(fbranaverageheattransfercoefficienthassumedtobe200W7m2K).Therefbre，

thetapedidnothavemuchafTbctontheestimationoftheheattransfbrCoefficient､Also,theBiot

number,Ｂｊｏｆｔｈｅａｌｕｍｉｎｕｍｆｉｎｗａｓａｂｏｕｔ0.009,whichissmallenough､Therefbre,theheat

transferenhancementbyaluminulnfinonlywillbediscussedhereafter．

4.2.4EffectoffinheightonheattransfbrcharacterMics

Theeffectoftheheightofthefinonthelocalheattransfercoefficientisnowdiscussed・

Fig.４．４ｓｈｏｗsthestreamwiselocalheattransfercoefficientdistributionfbrvaryingfinheightin

caseofco-angularpatternataUatplateboundarylayerasatypicalexample､Itwasfbundthatas

thefinheightmcreases,theextendedsurfaceareaalsoincreasesandasaconsequencetheheat

transferratelncreases・Thelocalheattransfbrcoefficientshowsaperiodicdistributionregardless

offinhei甑t・ThediffbrenceintheheattransferenhancementbetweenfinheightsoflOmmanｄ

ｌ５ｍｍｗａｓｖｅｒｙｓｍａｌｌ,whilethediffbrencebetweenfinsof5mmheightandotherfinswas

larger，Consideringthelargerpressurepenaltyfbrl5mmheightfin，１０ｍｍheightflnwas

chosenaSatypicalfi､．

200

０００

５０５

引凶同自刮傷］×畠

０

－４－２０２４６８１０１２Ｘ/Ｌ

Fig.4.4EffectoffinheightonlocalheattransfbrcoefficiemalongcenterlineatcopattemfbrHd＝Ｚ００ｍｍａｎｄＵ＝１０ｍ/ｓ

angular

2７

4.2.SEffCctofvelocityonheattransfercharacteristics

Theeffbctofvelocityonthelocalheattransfbrcoefficientinaductof200mlnheightfbr

aco-angUlarpattemisshowninFig.4.5(a）Thelocalheattransfercoefficientslowlydecreases

inboththeupstreamanddownstrcamregion,ｗｈｉｌｅａｔｔｈefinnedregionaperiodicdistribution

appearswhichisindependentofvelocity・Thedistributionfbrthezigzagpatternissimilartothat

oftheco-angularpattem,asshowninFig､４．５(b),thoughwithsomedifferences・Forthezigzag

pattem,theheattransfercoefficientprofilenearthelowerpeaksappearsconcaveandshows

hi8hervaluesthanthatoftheco-angularpattem・Thepeakvaluesmtheupstreamreglonare

higherfbrtheco-angularpattemthanfbrthezigzagpatternThisisbecauseinthecaseoftheco‐

angularpattemtheflowtouchesbothsidesofthefinsstronglyandthencontinuessmoothly

whereasfbrthezigzagpattemtheUowstmnglytouchestheendwallandthefPontsideofthefin

whiletheothersideremainsuntouchedThus,theextendedsurfaceismoreeffectiveinthecase

oftheco-angularpatternfbraflatplateboundarylayer・Fig.４．５(c)showsthedistributionofthe

heattransfbrcoefficientfbrthezigzagpatteminanalTowduct・Inthisfiguretheupperpeak

valuesarefbundtobethehighestbecausetheupperwallofthenalmwductcausestheflowto

strikctheendwallandthefinmorestlDnglyDatafbrtheco-angularpatternfbrthenalrowduct

isnotshownbutthedistlibutionwasalmostthesameasthatfbrtallduct・I、Fig.４．５(a)－(c)，

themaximumheattransfercoefYicientshowssomediscrepancyatsomestreamwisevelocities

duetosmalldeflectionsofthethermocouplesfromthecenterline．

2８

１３０５０

伽Ｓｌｌ２

ｕＯ８士桿

００００００

５０５０５

２２［昏一副］潔昌

－４‐２０２４６８１０１２１４１６

Ｘ/Ｌ

（a)Co-angularpattemHd＝200ｍｍ

Ｏｏ００００

５ｏ５０５

２２［乢訊目一図］×二

－４－２０２４６８１０１２１４１６

Ｘ/Ｌ

(b)Zigzagpatiem,Ｈｄ＝200ｍｍ

００００００

５０５０５

２２［乢引日へヨ］〆呂

－４‐２０２４６８１０１２１４１６

Ｘ/Ｌ

（c)ZigzagpattemHd＝20ｍｍ

Fig4SVariationoflocalheattransfercoefYicientwithvelocityalongcenteriinefbrHT＝10ｍｍ

２９

4.3Detailedheattransferanalysis

DetailedheattransfercoeffIcientdistributionsattheendwallsurfacesfbrrectangularfinsof

bothco-angularandzigzagpatternsfbraflatplateboundary(tallducOandnaITowductfloware

shownmFigs､4.6-4.9.AsshowninFigs､4.6(a)and４７(a),theheattransfercoefficiemvalueis

higharoundthefinrowsfbrbothpatterns・Thesehigherheattransferregionsarethecombination

ofextendedsulfaceeffbctandvortexeffect,Atflatplateboundarylayer,Leintallductcase，

infraredimageviewoftheco-angularpattemshowsthediffbrenceofheattransfervaluaAt

narrowductcase,co-angularpattemexpenenceshigherheattransfbrthanthatoftallductcase・

Thisdifferenceisapparentlyshownbothatthefinbaseandendwallsurface・Becauseupperwall

ofthenarrowductmfluencestheflowbehaviorandasaresultflowstrikesthefinsurfaceaswell

asdownwashtheendwallmorestronglySoheattransfercoefficiemvalueishi甑eratfinbase

andattheendwalLOntheotherhandupperwallofthetallductcouldnothavemuchinfluence

ontheflowbehavior,ｓｏｔｈｅＨｏｗｄｉｄｎｏｔｃｏｎｔａｃｔｔｈｅｆｉｎｓｕｒfaceandendwallasstronglyas

nalToｗｄｕｃｔＡｓａｒｅｓｕｌtcomparativelylowerheattransfercoeffIciemvaluesareobservedatflat

platewithco-angularpattem、Sametotheco-angularpattemzigzagpattemexpenencesthe

effectofductheiglltonheattransfbrasviewedbytheinhFaredimagewithzigzagpattem、

CompanngvaluesofAJrbetweenthetwopatter､sshowsthatthehigherheattmnsferregions

increasesfbrzigzagpattern・Intheco-angularpattern,thehorseshoevortexisresponsiblefbrthe

enhancementoftheheattransfbraroundthefins・Theheattransferintheregionbetweenfinsin

thespanwisedirectionisalsoenhancedduetolateralmixing､Inthezigzagpattem,thehorseshoe

vortexaswellasthevortexgeneratedbythesidetopandCorneredgesstronglytouchesthe

altematelyangledfinsurfacesandendwaU,whichsignificantlyenhancestheheattransfer・Next

wewilldiscussmoredetailgraphicalpresentationoftheheattransfercoefficientfbrthedifferent

finpattem、

Figs､4.6(b)and４７(b)showtheheattransferdistributionalongthecenterlineandmidlme，

３０

ＡｉｒＨｏｗ

し

3mｒｏｗ ４１１１ 6t11Ｓｔｈ

ｈ

ヴヴゲザググ

霞LＰｇ－

」

Ｆ

〆

-Ｗｈ１２Ｋ1-0Ｉ

１４０曰～

鴨田0.0 －１２０

－１００

－I8IOl-1.0

Eニト６０

ﾛ ２ ４＊６Ｘ／Ｌ

(a〕

０００００

５０５０５

２２１１

厩日彦］ゴ

ｏｃｅｎｔｅ｢ｌｉｎｅ

●ｍＩｄｌｌｎｅ

●

、 ２ ４＊６Ｘ/Ｌ

(b）

Ｘ聯/Ｌ＝００５１１．５２２５３３．５４

1-0

鵜一OCN

-１０

■百■■■ F百■■■ ■苗■■■ |■君■■■ ■■■■■ ■君■■■ l宙■■■■ JBm■■ 蛍■■■■

]MVWinzK］

（c）

1００３００

Fig46Detailedheattransfercoefficientdistributionsaroundtherepresentativeflnsofco-

angularpatternattbeendwallinaflatplateboundarylayerfbrReL＝Ｌ２７ｘｌＯ４,Ｂｒ＝１０ｍｍ．(a)Infiaredimage.(b)Centerlineandmidlinedistributionsand(c)Spanwisedistributions．

３１

ｈ

Ｗ１ｍ２Ｋ－１４０

１－１２ｏ

割－１００－８０

－－６０

、Ｐ！グ

ダダ

Ａｉｒflow

Ｐ

5ｌｈ3rdrow 4111 6t1１

ｈ

[ｗ/m2K］＝し140

一■一旬一■ｊ

ＰｌＰＰ

ｂ－■■ユ

ダーーヂ舌鋲

､1０

、已囚鶉

0.0 1２０

１００

８０

６０

1-0

ﾛ ２ ４＊Ｘ几

目

(a）

０００００

５０５０５

２２１１

口や日雇邑郵

centenine

midline

○⑥

ＩＤ ２ ４ 圖

Ｘ／Ｌ

(b〕

X7L ４0．５１ 1５ ２２５＝０

３’祠

３国旨ご皀冒冒冒ヨョョ剴冒〕皀冒冒冒則

５

1.0

曰一国十斗 ０．０

1０

anﾛ■ ■■■■■ H■■■■F■■■■ ＩＦ、■■ F■■■■

1００３００ＭＷｍ２Ｋ］

（c）

Fig47Detailedheattransfiercoefficientdistributionsaroundtherepresentativefinsofzigzag

patternattheendwallinafIatplateboundarylayerfbrReL＝ＬＺ７ｘＩＯ４,Ｈ｢＝１０ｍｍ.(a）Infiaredimage.(b)Centerlineandmidlinedistributionand(c)Spanwisedistribution

3２

１０００

ｈ肛料烟相即釦

要｜叫一川二

Ｐ

■

鱒＝＝唇

座、輿

、！

Forbothpattems,thecellterlinedistributionisperiodicandthepcakindicatesthehWalueatthe

fincenter､HeattransferdistributionsalongstI℃amwiseandspanwisewithvalyingvclocitywercalso

fbundperiodicalrBgardlessoffinpattemandveIocityintheprwiousexperimentalworｋｏｆｌｓｌａｍet

alPOO61AroundthethirdrowfinsthedistributionsshowhighervaluesofLfbllowedbya

subsequentdeclineinthedownsｎ℃amregion,ThcsIopeofthedeclincisgJ℃aterfbrtheco-anguIar

patternthanfbrthezigzagpattem・Themidlinedistribution,showingtheendwallheattrHnsfbr,is

aImostflatandisnearlyhalfthemaximumvalueltisaIsonotablethatthcslopcofthedeclineis

againhigherfbrtheco-angularpattem・T11clesserslopefbrthczigZagpattemmightbeduetothe

vortexthatstmmgIyattachestothefarthestrowfin

Figs､4.6(c)and4.7(c)showthespanwisedistributionfbrbothpattems・Thet1℃､dsofthe

distributionsaresimilar,butthevaluesofhzaredifYierent・Ａｔｒ/Z＝０，２and4,Le､atthecenterof

eachfinIDw,periodicdistributionsappear・Attheupsb『Bamsidefinsthelowerpeakandhigluerpeak

valuesarChighcrfbrtheco-angularpattem,butatthedownst1℃amsidefinsthezigzagpatbernexhibit

highervalues・Ａｔｒ/Z＝u5and25,thcdistributionstendtowardsbeingflatwhileatr7Z＝land３，

theybecomenearlycompletelyHaLImmediatelybefbrethefins,i,eatｒ/Z＝l5amd3､5,the

distributionsagainbecomeperiodic・Figs､４．８and49showthedistributionsfbrnarｍｗｄｕｃtＨｏｗ,A

comparisonbetweenFigs､4.8(a)and4.9(a)identificsthediffe歴､tshapesofthehcattmnsferproflIe･

Imhecaseofthcco-angularpattern,thelowerheattransferrcgionsa１℃compamtiveIylargeand

hysterisisshaped,whilefbrthezigzagpattern,theIowerheattmnsfbr1℃gionsa1℃compamtively

smaUwithadeltashape・ThehoTseshoevortexesaroundthefinfbrbothpatternsobservedfbrtheoil

HImflowagTcewiththeobservedhigherheattmnsfbrr℃gionaroundthefinintheinfraMimages、

ThelevelofheattlnnsfeTincrcascsinanalTowductcomparedtoafIatplatebecausethcupperwaU

induccsthcflowvortcxtoattachtotheendwalIandfinsurfhcemo”strongly､Largehigherheat

transferregionsaroundeachfinrowareobservedfbrbothpattems・Figs､4.8(b)and4.9(b)showthe

distributionaloH1gthecenterlineandmidline,Thoughthepattcmsofthcdistributionsaresimilarto

thosefbrthefIatplatecase'んrisgrCaterandthercisnosignificantdecIine、

３３

Ａｉｒflow

傍

3rdrow 4０１ Ｓｔｂ 6t]］

ｈヴーグ

ゲ・餌

諄｜｜伊

伊毎 [Ｗ/mzK］1-0

陽1010］『房事|￣曰

篝白００ －１６０●￣牙一

鰹)尾｝－１ZID

-１０

と=←８０

４＊６Ｘ/Ｌ

ロ ２

(a）

Ocenterline

０００００

５０５０５

２２１１

［閏略逗芦］〆昌

４＊６Ｘ几

Ｈ 図

(b）

Ｘ率/Ｌ＝００５１１．５２２．５３３．５４

1.0

鵜已ＣＯ田

-1-0

1００３００

hz｢Ｗｍ２Ｋ］

に）

Fig48DetailedheattransfbrcoefficientdistributionsaroundtherepresentativefInsofco-angularpattemattheendwallinaductflowfiorRc＝２．３４×104,舟＝１０ｍｍ.(a)Inffaredimage.(b)Centerlineandmidlinedistributionand(c)Spanwisedistribution．

3４

Ａｉｒflow

伊

3rdrow 4１１１ 5111 6uｌ

ｈ

,倭財ｐ鷺倭■Ｐ■

ヂロ●弾！

1０[Ｗﾉｍ２Ｉｑ言壽１－２００

旨00 -１６０

－１２０-1-0

皀邑半８０

IＤ ４＊６Ｘ／Ｌ

場

(a）

ocenterline

０００００

５０５０５

２２１１

［図、日一彦］×畠

midline

夢i`是凝汽

ﾛ ２ ４＊６Ｘ/Ｌ

(b）

X7L=00511.522533.54

1.0

驫己ＣＯ■

-1.0

qｎｕ Hｕｕ F酌■■Ⅱ凹凹 ﾛ■■ Hmu ﾛ■■ uZuu ﾛ凹凹

1００３００hz[VWm2K］

（c〕

Fig.４９DetailedheattransfercoefHcientdistrlbutionsaroundtherepresentativennsof

zigzagpatternattheendwallinaductflowfbrRc＝２．３４ｘｌＯ４,Ｂｉ＝１０ｍｍ.(a)InfTaredimage.(b)Centerlineandmidlinedistributionand(c)Spanwisedistribution．

3５

T11elowerpeakpmfilesareconvexfbrtheco-angularpattem,whileincontrasttheprofileisflat

fbrthezigzagpattemandthelowerpeaksarecomparativelyhigher・Themidlinedistributionis

neadystraightfbrbothpatternsbuttheAWaluesaregreaterfbrthezigzagpattern・Figs､４８(c）

and４９(c)ｓhowthespanwisedistributionfbrbothpatternsThcdistributionisalmostperiodic

exceptatr/Z＝land3Boththelowerandhigherpeakprofilesarecomparativelymoreconvex

fbrtheco-angularpattern,whilefbrthezigzagpatterntheprofilesarehigherandsomewhatflat．

4.4.Area-averagedheattransfer

Thearea-averagedheattransfbrcoefficientsattheendwall，finbaseandtheoverall

surfacesoftherepresentativethird,fburth,fifihandsixthrowfinsweremeasuredfiDminffared

lmages・Heattransmissionfiomtheoverallsurfhceisthetotalheattransferf、mthefinsurface

andtheendwallwithoutthefins・Againheattransferratefromthefinsurfaceisequaltotheheat

transfbrfiomfinbase・Sotheareaaveragedheattransfercanbecalculatedusingthefbllowing

equation,Ｅｑ､4.3.

伽…F-4L恥瑞脇…AOM目,１２〃(43）

where'４.…/listheoverallsurftlceareaincludingthefinbaseand蜘and鋤`wallarethesurface

areasofthefinbaseandendwall，respectively、Ｔｈｅｒｅlationshipbetweenthearea-averaged

NusseltnumberanｄｔｈｅＲｅｙｎｏｌｄｓｎｕｍｂｅｒｉｓｓｈｏｗｎｉｎＦｉｇ4.10．Thearea-averagedNusselt

numberisrepresentedbythecurvefittedlines,A11thedataftl11smoothlyonthecurvefittedlmes

andcanbewellrePresentedbythefbllowingeqUation,Ｅｑ､4.4．

ハノ１Ｍ＝ＣＲＧ0.7． （4.4）

ValuesfbrcfbrdifferentductheightsandfinpattemsarelistedinTableLItisfbundthatthe

zigzagpatternhashighercvalues`Fig.4.10(a)showsthevariationoftheNusseltnumberwith

theReynoldsnumberattheendwallandtheoverallsurfacefbrbothpatternsfbranarrOwduct，

３６

３

２

１

100９８７６５

'二

４

３

２３４５６７８９

1０４ １０５Ｒｅ

(a)Area-averagedNusseltnumberattheoverallsurfaceandtheendwa,,asafimctionoftheductReynoldsnumberfbrHb＝２０ｍｍ．

1００

ざ函

1０４ ＲｅＬ

(b)Area-averagedNusseltnumberattheoverallsurfaceandtheendwallasafimctionoftheReynoldsnumberbasedonfinlengthfbrHa＝200ｍｍ．

Fig.４．１０RelationshipbetweenNusseltnumberandReynoldsnumber

3７

TablelCoefIicientofheattransfercorrelationattallductandnarrowductfbrco-angularandzigzagpattern

ＭノーcReo7FinPatternDuctHeight(nｍ） Ｃ

endwalloverall

Co-angularZigzag

Co-angular

ZigZag

２０

２０

２００

２００

0.151

0.17

0.096

0.100

0169

0.187

0.113

0.108

wheretheNusseltnumberisarrangedbyducthydraulicdiameter・Forallcases，theNusselt

numberincreaseswithReynoldsnumber・ＣＯ､sideringtheoverallheattransfbr，thezigzag

patternshowsahighervaluethantheco-angularpattem・Asnotedpreviously,thisisduetothe

factthatfbrthezigzagsettingthelongitudinalvortexstrikestheendwallandthefinsurfacemore

stronglyuptothefarthestfinrow.Ｃomparingtheendwallheattransfer,thedifferenceintheheat

transfbrbetweentheco-angularandzigzagpattemsismorethanthedifferenceintheoverall

surfacearea,indicatingthattheendwallheattransferismoresigniflcamfbrthezigzagpattern

whiletheextendedsurface(fin)effectissignificantfbrtheco-angularpattern､Theoverallheat

transfbrisfbundtobeenhancedbymorethanfburtimesthesmoothsurfacevalue・

ThevariationintlleNusseltnumberwithReynoldsnumberattheflatplateboundary

layerisshowninFi94.10(b),withtheNusseltnumberalTangedbyfinlength､Theoverallheat

transferenhancemｅｍｆｂｒｂｏｔｈｆｉｎｐａｔｔｅｍｓｉｓｎｅａｒｌｙｔｈｅsamethoughthecoefficientcfbrthe

zigzagpatternissomewhathigher・Theendwallheattransferfbrthetwofinpattemsisfbund

similartoo．

Theheattransferffomasmoothsurfacewasestimatedasfbllows：Theheattransfer

CoefficientswerefirstcalculatedfromtheEq.(4.1)fbrtheHatplateboundarylayerwithinthe

rangeX＝０．２８ｍ-0.36ｍ,correspondingtothelengthbetweenthethirdandfIfihrows．

形｡i`０｡…ﾉｗ過ﾑ“Ｏ２８

Ｘ

(4.5）

3８

TheseheattransfercoefflcientswerethenreplacedbythemeanNusseltnumberbased

onfinlengthandcanberepresemedbythefbllowingequation：

jVjJL＝O0138ReLq8． （46）

Theoverallheattransferwasthencomparedandfbundtobemorethanthreetimesthesmooth

surfacevalue・Hence,itwasfbundthatheattransferisimprovedwiththeuseoffins,Azigzag

PatternfbrHli＝２０mmwasfbundtobemosteffectivefbrheattransferenhancement．

4.5FlowvisualizationbydyeUowinwaterChannel

Inordertodifferentiatetheflowbehavioroftheco-angularandzigzagpattern,dyeflow

inwaterchannelwasobservedatlowerReynoldsnumber・ThedyeHowpattemsfbrtheco-

angularandzigzagpatternsareshowninFig.４．１１.Inthecaseoftheco-angularpattem,thedye

UowstagnatesinffontofthefIrstrowfInandfblmsahorseShoevortexsulToundingthefin,At

therearofthefin,thevortexrollsupandrisestojomtheflowseparatedfmmtheupstream

portionofthefin,whereitthenshowslongitudmalbehavior,Astllefinsaresetatanangle,edge

effbctsareobserved､Thecomeredgescauseturbulenceandenhancenowmixingintheinterfin

regionalongthestreamwisedirectionThemainvortexfloｗｓａｂｏｖｅｔｈｅｆｉｎｓａｓｓｈｏｗｎｉｎＦｉ9.

411(a),touchingthetopofthefinsandthesidewall,Thehorseshoevortexaroundtheco‐

angularpattemissostrongthatthelongitudmalvortexcannotcomacttheinnerportionofthe

horseshoevortexandthevicinityoftheendwallexceptfbrthebothsidewallsofthefins.Ｉt

causesheattransfbrenhancememfromthesurftlce、

InthecaseofthezigzagpattemshowninFi9.4.11(b),alongimdinalvortexgeneratedby

theHrstfInmwtouchestheffontofthesecondrowfinandattachestotheendwallaroundthefin

asthehorseshoevortexthatappearsisnotstrong･Duetothealtematedirectionsofthefins,the

flowdirectionischangedandthelongitudinalvortexstrikestheendwallbetweenthesecondand

3９

thirdrowfIns､Theinterfinregioninthespanwisedirectionatthethirdrowiscontactedbythe

mainvortexBeyondthisｒｏｗ,theHowadvancesandtouchesthefbllowingfinandtheendwall・

Wenotethattheflowattachesstronglytobothsidesofthefinibrtheco-angularpattern,while

化rthezigzagpattｅｒｎｔｈｅｆｆｏｎｔｓｉｄｅｉｓｔｏｕｃｈｅｄｂｙｔｈｅｆlowstronglybutthebacksideissolIly

touchedonly・Therefbre,heattransfiBrfiFomtheHI1shouldbesignificantintheco-angularcase，

whileheattransflerfiDmtheendwallshouldbehigberillthecaseofthezigzagpattern,ａｓｗｉｌｌｂｅ

describedlater

Waterｆｌｏｗ

匡

Rolledupvortex

Horseshoevortex

Ｉ１Ｕ－ＩＩｌＩ１ｌＩＩＩＩＩＵＩＵＩＩ ’１１１１

0.O

Mainvortex(、.v､）

２０ ４０ 6.0

Ｘ几

(a〕

Waterｆｌｏｗ

￣

可も一

鞭ＵＰ■

ylll…剰

戸<夛只 －＝＝

＝髭－１ｐ

鰹露讓愛l學i學邑i雪ごi§霊露Ｉ１ＩＵＩＩＵＩｌｌｌＵＵ１１ １１

００ ２０ ４０ 6.0

Ｘ/Ｌ

(b）

Fig.４.llFlowvisualizationinawaterchannelaroundshortrectangularfmof(a)co-angular，(b)zigzagpatternwithHi-lOmm,ＰＲ＝ZandRe＝1350.

4０

4.6.Frictionfactor

lnordertocalculateftictionfactor,wefirstmeasuredthepressuredropdistribution・

Fig.4.12showsthehictionfMorobtainedffomEq.(3.1）ｉｎａｎａｎＤｗｄｕｃｔ､Inthetallduct,a

hydrodynamicboundarylayerdoesnotfUllydevelop・Thefiictionftuctorfbrlargescale

protrusionpositionedinsurfaceshowsalmostconstantregardlessoftheReynoldsnumberand

thehctionfactorvaluesfbrbothpattemsarelargerduetotllelargescalevortexfbrmedbythe

existingprotrusionsthantheskinfiictionfbrasmoothductwithoutfinsfbrMlydeveloped

mrbulentflow・Ａｓｔｈｅｆｌｏｗｆｂｒｔｈｅｚｉｇｚａｇｐａｔｔｅｍｈａｓmorecontactwiththefinsurfhceand

endwallandconseqUentlyalargerdragfbrceoccursthanfbrtheco-angularpattemAsaresult

thefiictionfhctor,/issomewhathigilerfbrthezigzagpatternthanthatofco-angularpattem．

２

０１Cco-angular

●

恋zlgzag

８６４

､、

一一､一一一２

‐1/４

ｆ=Ｏ３１６４Ｒｅ

０．０１

1０４ ２ ３４５６

Ｒｅ

Fig.４．１２Frictionfactorvs､ReynoldsnumberinananFowductfbrco-angularandzigzag

pattemofHイー１０ｍｍ

４１

４．７Summary

Afterperfbnningthisinvestigationwecanconcludeasfbllows：

LTheinclinationanglehasagreatinfluenceontheheattransferenhancement・Amongthe

inclinationanglesofO･'２０．ａｎｄ２５．，ａｎａｎｇｌｅｏｆ２０･appearsoptimumfbrenhancementin

thisexpenment、

2．Thefifictionfactorsfbrbothpatternswerelargercomparedwiththeskinhdctiononthe

smoothsurfncefbrafUllydevelopedmrbulentｎｏｗ・Thefrictionftlctorvaluewasfbundtobe

almostconstantandlargerfbrazigzagpatternofflnsthanfbraco-angularpattern、

3．Ｉｎｄｙｅｆｌｏｗ,stronglongitudinalvortexesappearedthattouchtheendwallneartheinterfin

space・Inthecaseofthezigzagpattem,onesideofthefinwasalsocontactedbythevortex・

Thoughacornervortexalsotouchesthesidewallofthefin,thehorseshoevortexwasnotas

clearlyobservedIncontrast,alongimdinalvortexisalsoobservedfbrtheco-angularpattern，

whichtouchesthefinsurfnceaswellaslightlycontactingtheendwalLAhorseshoevortexis

alsoclearlyobservedinffontofthefins、

4．Companngarraysofco-angularandzigzagpattems，thelaterismoreeffectivefbrheat

transfbrenhancementinthecaseofnalTowductflow・Theaverageheattransfercoefficient

fbrazigzagpatternismorethanfburtimeshigherthanthatofwithoutfins・TheNusselt

numberincreaseswithReynoldsnumbertothe0.7uIpowerfbrbothpatternsinanaIrowduct

aswellasfbraflatplateboundarylayer．

4２