191KKU Res. J. 2013; 18(2)

Combined Convective and Radiative Heat Transfer on Transpiration Cooling System in Al-Co Open-celled Foam having PPI of 20

Pipatana Amatachaya,1 Bundit Krittacom1,* and Rapeepong Peamsuwan2

1 Development In Technology Of Porous Materials Research Laboratory (DITO-Lab), Department of Mechanical Engineering, Faculty of Engineering and Architecture,2 Department of Applied Physics, Faculty of Sciences and Liberal Arts, Rajamangala University of Technology Isan (RMUTI), 744 Suranarai Road, Maung, Nakhonratchasima, 30000, THAILAND, Tel: +664-423-3073, Fax: +664-423-3074* Correspondent author: bundit.kr@rmuti.ac.th and bundit_krittacom@hotmail.com

Abstract

One-dimensionaltranspirationcoolingsysteminopen-celledfoamhasbeenconductedexperimentally

and numerically to investigate the heat transfer characteristics of combined convection and radiation.The

Alumina–Cordierite (Al-Co) open-cell foamhaving porosity of 0.875 and pores per inch (PPI) of 20was

employed.Theuppersurfaceofporousplatewasheatedbytheheatfluxofincomingradiation(qRx,f)varyingfrom

0.97-16.59kW/m2whereasairinjectionvelocity(uf)fedintothelowersurfacewasvariedfrom0.364-1.274

m/s,andwasthenrearrangedasReynoldsnumber(Re).Forthereportoftheresultsinthepresentstudy,two

efficienciesincludingoftemperature(hT)andconversionefficiency(h

C)werepresented.Theh

Tincreasedrapidly

withtheairinjectionvelocity(Re).ItwasthensaturatedandhadaconstantvalueatRehigherthan15.Forthe

resultofhC,itwasdecreasedslightlywithincreasingofq

Rx,fandu

f(Re).Thenumericalpredictionsalsoagreed

withexperimentaldataverywell.

Keywords: Open-cellfoam,Radiation,Transpirationcooling,Reynoldsnumber

KKU Res. J. 2013; 18(2): 191-199http : //resjournal.kku.ac.th

192 KKU Res. J. 2013; 18(2)

1. Introduction

Transpirationcoolingoreffusioncooling(1)

is theprocessof injectingafluid (Air) intoaporous

materialwhichcanbeservedasaveryefficientcooling

methodforprotectingsolidsurfaces thatareexposed

tohigh-heat-flux,high-temperaturefromenvironments

suchasinhypersonicvehiclecombustors,rocketnozzle,

gasturbineblades,andthestructureofre-entryaerospace

vehicles(1–5).Theperformanceofthiscoolingsystem

is governed by several parameters such as radiative

propertiesofporousmedia,thevolumetricheattransfer

coefficientbetweenthesolidphaseandfluid,fluidvelocity

andirradiation.Thus,theknowledgeofparametersfor

thedesignoftranspiration-cooleddevicesisclassified

intotwomaingroupsincludingthephenomenaoffluid

flowandheattransferprocesswithintheporousplate.

Sofaranumberofexperimentalworks(6–8)

andnumericalstudies(9–12)havebeenconductedon

transpirationcoolingsystem.However,mostofprevious

studiesweremainlyintendedtodeterminetheeffects

of convectionmode.Therewere only a few studies

have taken into account the radiativeheat transfer in

thetranspirationcoolingsystem.Recently,Jiangetal.

(13)andKamiutoetal.(14)investigatedexperimentally

andanalyticallytoextendthevalidationofnumerical

model.Jiangetal.(13)foundthatthenumericalresults

correspondedwellwiththeexperimentaldataincluding

thesurfacetemperatureandheattransfercoefficients.

However, theirwork still focused on the effects of

convectiveheattransfer.Radiationmodewasconcerned

intheinvestigationofKamiutoetal.(14).Theyreported

thattheagreementbetweentheoreticalpredictionand

experimentalresultswasacceptable.AlthoughKamiuto

andco-worker(14)regardedtheradiationmodeinthe

transpirationcoolingsystem,thetheoreticalresultwas

moreemphasizedandthereexistthedifferencebetween

theoryandexperiment.

BasedontheworkofKamiutoetal.(14),the

presentresearchaimstofurtherexperimentandanalyze

theheat transferphenomenaas combinedconvection

and radiation in the transpiration cooling system

usingopen-cellularporousmaterial.Alumina-Cordierite

(Al-Co)havingPPIof20isadoptedowingtothisAl-Co

hasahigherporosityresultingtoahigherefficientof

heattransferandiswidelyusedasthermalinsulationof

industry(15).Obtainablequantitiessuchastemperature

atthesurfacesandwithintheporousplate,fortheoretical

results,arepresentedandcomparisonwithexperimental

dataisalsoreported.Atipfordesignisrecommended.

2. Nomenclature

Cf, isobaricspecificheatcapacity(J•kg-1•K-1)

DC anormalcelldiameter(m)

DP equivalentstrutdiameter(m)

asymmetricfactorofscatteringphasefunction

G incidentradiation(W/m2)

hv volumetric heat transfer coefficient betweengas

andsolidphases(W•m-3•K-1)

kf thermalconductivityofagasphase(W•m-2•K-1)

ks thermalconductivityofasolidphase(W•m-2•K-1)

qRx netradiativeheatfluxinxdirection(W/m2)

Tf temperatureofagasphase(oC)

TR radiationblackbodytemperature(K)

Ts temperatureofasolidphase(oC)

T∞ ambienttemperature(K)

uf airflowvelocity(m/s)

w dimensionlesswidthofastrutwithasquarecross

section(m)

x coordinateintheflowdirection(m)

193KKU Res. J. 2013; 18(2)

Greek Symbols

β scaledextinctioncoefficient(m-1)

f porosity

hT temperatureefficiency

hC conversionefficiency

rf densityofagasphaseorair(kg/m3)

s Stefan–Boltzmann constant (=5.67×10-8

W•m-2•K-4)

t opticalthickness

w scaledalbedo

3. Theoretical Analysis

3.1 Mathematical Model

Thepresentmodelofatranspirationcooling

system is shown in Fig. 1. The assumptions of the

numericalmodelaresimilartothoseofKamiutoetal.

(14).However,somemodificationwasmadetoimprove

the accurate prediction. The following assumptions

were introduced for this analysis as follows: 1)An

open-cellular porous plate of thickness x0 is placed

horizontally; 2)The front surface of porous plate is

uniformly irradiated by blackbody radiation at an

equivalenttemperatureTR(K),whilethebacksurface

is subject to uniformblackbody radiation at an inlet

air temperature; 3)A low-temperature air is injected

throughthebacksurfaceofporousplateandisassumed

tobenon-radiating;4)Theporousmediumisgrayand

is capable of emitting, absorbing and anisotropically

scattering thermal radiation; 5)The porousmedium

isnon-catalytic;6)Thephysicalpropertiesdependon

temperaturedifferedfromKamiuto’swork(14)thatthe

physicalpropertiesofhiswork(14)didnotdependon

temperature;7)Theheattransferwithintheporousplate

isinanone-dimensionalsteady-state;8)Thebehavior

of air flowwithin porous plate is under local and

non-thermalequilibriumcondition.

Figure 1. The theoreticalmodel and coordinate of a

transpirationcoolingsystem.

Under these assumptions, the continuity

equationisgivenby:

(1)

Thegoverningenergyequations for thegas

andthesolidphases(porousplate)maybewrittenas

follows:

(2)

(3)

(4)

Fourphysicalproperties,i.e.,f,β,hvandw

fromEq.(2)to(4)weresummarizedbyKrittacom(16)

andwerebrieflyrecalledasfollowing:

(5)

(6)

194 KKU Res. J. 2013; 18(2)

(7)

(8)

(9)

(10)

TheGrepresentstheincidentradiationandqRx

denotesasthenetradiativeheatfluxintheflowdirection.

Thesequantitiescanbedeterminedfromtheequationof

radiativetransfer.Oncetheradiationfieldisspecified,

thequantitiesGandqRxcanbereadilyevaluated.The

radiativeheatequationofthepresentresearchissolved

bytheP1approximation(17)andiswrittenas:

(11)

(12)

Theboundaryconditionsfor(2),(3),(4),(11)

and(12)aregivenasfollows:

(13)

(14)

3.2 Numerical Method

Forconvenienceofcalculations,thegoverning

equations and associated boundary equations are

transformed into dimensionless forms, and then the

dimensionlessequationsaresolvednumericallyusing

animplicitdifferencemethod.Forsolvingtheequation

oftransferwiththeP1equations,andcalculationsofthe

TfandT

s,theporousplateisdividedinto300equally

spaced increments,whereas the optical thickness is

dividedinto600equallyspacedincrements.Toobtain

thesolutionsofTfandT

s,Gorq

Rxarefirstdetermined

basedonantheassumptionoftemperatureprofile,and

thenthequantitiesofGandqRxaregainedbysolving

equation of transfer or theP1 equations at staggered

latticepoints(17).OnceGisobtained,thefinitedifference

equationsforTfandT

scanbesolvedreadilybyGaussian

elimination.Thereafter,thederivedsolutionsofTfand

TsaresubstitutedintotheequationoftransferortheP

1

equationsandtheenergyequationstogetnewsolutions

of these quantities; similar calculations are repeated

until the following convergence criterion is satisfied:

Here,Q representsTf, T

s,

Gor qRx, and n is time interval of calculation.After

obtainingtheTf,T

sandG,twoefficiencies,temperature

efficiency (hT) and conversion efficiency (h

C) are

evaluatedasfollows:

(15)

(16)

ThephysicalmeaningofhTistheindicating

howclosethemeantemperatureofaporousheatplate

tothatofinletairandhCisregardedastheabilityof

porousmaterial in transferring energyby convection

afterabsorbedfromheatradiation,

4. Experimental Apparatus and

Procedure

4.1 Experimental Apparatus

Figure 2 shows a schematic diagramof the

presentexperimentalapparatus.Theexperimentalset-up

wasconstructedsimilartothatofKamiutoetal.(14),

195KKU Res. J. 2013; 18(2)

butthedouble-tubeheatexchangerwasinstalledatthe

airinlettokeepairtemperatureat25–30oCwhenit

reachedthebacksurfaceoftheporousplate.Therefore,

the present transpiration cooling systemconsisted of

4 sections includingheat exchanger, inlet air, porous

medium,andradiationsection.Airfromablowerthat

wasusedas the transpirationgaswasblown through

theheat-exchangerandmeasuredtheflowrateusinga

rotameter.Theairwasthenflowedupwardthrougha

stainlesspipe(0.01minnerdiameterand0.6mhigh)

insteadofacrylicpipeasinKamiutoetal.(14).Aporous

platemadeofAlumina-Cordierite(Al-Co)wasplacedon

thetopofthestainlesspipe.Thephysicalcharacteristics

oftheexaminedporousplateweresummarizedintable

1.Four250-Winfraredlampswerealignedabovethe

porousplatetoirradiatetheheatintotheuppersurface

oftheplate.Theamountofradiantenergywasmeasured

using heat flux sensormanufactured byHukesflux

Thermal Sensor,modelHFP01-05.The intensity of

theinfraredlampswasregulatedmanuallyfrom50V

to250V;thustheradiativeheatfluxwasvariedfrom

0.97to16.59kW/m2.

Figure 2.Schematicdiagramoftheexperimentalapparatus.

Table 1. PhysicalcharacteristicsofaAlumina-Cordierite(Al-Co)open-cellularporousmaterial

Coefficients Quantities

Porosity f 0.875

Poresperinches PPI 20

Thickness x 0.0103m

Extinctioncoefficient β 365.89m-1

Opticalthickness t 3.77

196 KKU Res. J. 2013; 18(2)

4.2 Experimental Procedure

Theprocedureoftheexperimentaloperation

of thepresentcooling system isalso similar to those

ofKamiuto et al. (14).After the infrared lamps are

switchedon,ittakesabout40-60minutestoattaina

steady-stateofthetemperaturesoftheporousplate.Six

type-Kthermocoupleelementsof0.0003mindiameter

are adhered on the upper and lower surfaces of the

porousplatebydividingasthreeforeachsurface.Inlet

andoutletair temperaturearemeasuredusingtype-K

sheathedthermocouple.Theairvelocityisvariedfrom

0.364-1.274m/s.

5. Results and Discussion

5.1 Effects of Air Flow Velocity (uf) on

Temperature Profile

Figure3presentedthetheoreticalresultsofthe

temperatureprofilesofthesolid(Ts)andthegasphases

(Tf)insidetheAl-Coporousplate,underthecondition

ofirradiatedheatfluxqRx,f=12.48kW/m2.Asseenfirst

inFig.3(a),themeasuredmeansurfacetemperaturesof

thefrontandbackporousplateareindicatedbysymbols,

whilethecalculatedresultsforthesolidphase(Ts) is

presented using the lines.The trend ofTs increased

alongtheporouslengthbecausetheincidentradiation

fromtheinfraredlampswasemitteddowntothefront

surface.For afixedpositionof the thickness (x), the

temperatureprofilesofTfdeceasedastheairvelocity

(uf)increasedowingtotheeffectsofahigherconvective

heat transfer (10).Agreementbetween theprediction

calculatedbybasingontheP1equationintheradiative

transferequation(RTE)andtheexperimentalresultsat

theback(x=0mm)andthefrontsurface(x=10mm)

weresatisfactory.InFig.3(b),thetemperatureprofiles

ofTfshowedthetrendsimilartoT

scase;itincreased

alongtheporouslengthanddeceasedwithufincreasing.

ForcomparisonofTsandT

f,itwasobviouslyfoundthat

Tswashigher thanT

fbecause thesolidporousphase

receivedtheradiationheatfluxdirectlyandthen,next

step, the energy absorbed by porousmaterial was

transferredtotheairsuppliedintosystem(18).

Figure 3. Profiles of Ts and T

f within the Al-Co

open-cellularplatefortheeffectofuf

5.2 Effects of Heat Flux on Temperature

Profile

Figure4showedthetheoreticalresultsofthe

temperatureprofileofthesolid(Ts)andthegasphases

(Tf)insidetheAl-Coporousplate,underthecondition

ofairflowvelocity(uf)of0.848m/s.AsseenfirstinFig.

4(a),thetrendofTsincreasedalongtheporouslength

duetoincidentradiationfromtheinfraredlamps.For

afixedpositionofthicknessx,thetemperatureprofiles

197KKU Res. J. 2013; 18(2)

ofTsincreasedwithradiativeheatflux(q

Rx,f)owingto

porousmediumabsorbedahigherradiantenergyfrom

theinfraredlamps.Agreementbetweentheprediction

basedon theP1model ofRTEand the experimental

resultsattheback(x=0mm)andthefrontsurface(x=

10mm)weresatisfactory.InFig.4(b),thetemperature

profilesofTfexpressedthetrendsimilartoT

scase;it

increased along the porous length gradually and

increasedwithqRx,f.ForcomparisonofT

sandT

f,itwas

obviouslyfoundthatTswashigherthanT

fwhichwas

describedbythesamereasonofFig.3(b).

Figure 4. Profiles of Ts and T

f within the Al-Co

open-cellularplatefortheeffectofqRx,f

5.3 The Temperature Efficiency (hT)

Figure5showsvariationsinthetemperature

efficiencyhTagainstReynolsnumber(Re).Inthisstudy,

Rerepresentstheairflowvelocitywhichisdefinedby

usingrfu

fD

s/m

f,wherem

fisviscosityofagasphase

(Pa•s), andDs is theequivalent strutdiameter (m)as

describedinKrittacom(15).Theexperimentalresults

areshownusingsymbols,whilethenumericalresults

areindicatedbyusingthelines.Thefiguredepictedthat

thehTincreasedrapidlywithReandthenasymptotic

toaconstantvaluefortheRehigherthan15.However,

atafixedRe,thehTdecreasedwiththeincreaseofthe

incidentradiationduetoahigherdifferenceofanaverage

temperatureofporousplateandairtemperaturefedto

systemwasobtained.For theRehigher than15, the

values ofhTwere greater than 95 percentage. This

indicatedthattheaveragetemperatureoftheporousplate

wasveryclosetotheaverageheatshieldtemperature

andinletairtemperature.Agreementbetweentheoryand

experimentwasacceptablewhichindicatedthevalidity

ofthepresentnumericalmodel.

Figure 5. Temperature efficiency (hT) of theAl-Co

open-cellularporousplate

5.4 The Conversion Efficiency (hC)

Figure6showsvariations in theconversion

efficiencyhC againstRe. The results demonstrated

that thehC increased slightlywithRe inwhich the

hCvalueswerevariedintherangeof40%to60%.But

the value ofhCwas asymptotic to a constant value

fortheRehigherthan15.ForafixedvalueofRe,hC

198 KKU Res. J. 2013; 18(2)

increasedwithincidentradiation(qRx,f)becausetheporous

mediaabsorbedenergyfromahigherheatfluxandthen

transferred via convection through the cooled-air

flow.Thus,theabilityoftransferringenergyofAl-Co

open-cellularporousplatebyconvectionafterabsorbing

heat radiation decreasedwith the increasing of heat

flux.Agreementbetween theory and experimentwas

acceptable.

Figure 6.Conversion efficiency (hC) of theAl-Co

open-cellularporousplate

6. Conclusion

Themajorconclusionsthatcanbedrawnfrom

thepresentstudyaresummarizedasfollows:

1) The temperatureprofilesofgas (Tf)and

solid(Ts)phasedeceasedasairinjectionvelocity(u

f)

increasedbecauseoftheeffectsofahigherconvective

heattransfer,whereastheprofilesofbothtemperature

increasedwith incident radiation (qRx,f) owing to the

effectsofhigherradiantenergy.

2) Thetemperatureefficiency(hT)increased

rapidlywithReandthenasymptotictoaconstantvalue

fortheRehigherthan15butthehTdecreasedwiththe

increaseoftheqRx,f.

3) Theconversionefficiency(hC)ofaAl-Co

open-celledfoamincreasedslightlywithReandandthen

asymptotictoaconstantvaluefortheRehigherthan15

aswellasthevalueofhCwasgovernedbyheatflux

(qRx,f).

4) Agreementbetweenthepredictedresults

based on P1 equations and experimental data was

acceptable, thereby the validity of theoreticalmodel

wasconfirmed.

Suggestions and a Designed Tip

Incoming radiation from a radiative

environment can be almost completely protected as

longastheReoftheopen-cellularplatewasabout15

orhigher.Asaresult,thetranspirationcoolingsystem

asusedinthepresentopen-cellularporousplateshould

bedesignedfortheRe=15.

7. Acknowledgement

WearegratefultotheRajamangalaUniversity

ofTechnology Isan (RMUTI) for the research fund.

WealsoexpressourthankstoMr.JeerasakKamluang,

Miss Pensiri Thikumrum,Mr.KriengkaiDastaisong,

Mr.KritsadaPoohbunyaandMr.ChutchaiKrongpeug,

studentswho is themembers of theDevelopment in

TechnologyofPorousMaterialsResearchLaboratory

(DITO-Lab), for their assistance in performing some

partoftheexperiments.

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