An experimental investigation and correlation on buoyant gas

AppliedThermalEngineering51(2013)246e254

ContentslistsavailableatSciVerseScienceDirect

AppliedThermalEngineering

journalhomepage:www.elsevi

http://www.77cn.com.cn/locate/apthermeng

Anexperimentalinvestigationandcorrelationonbuoyantgastemperaturebelowceilinginasloppingtunnel re

L.H.Hua,*,L.F.Chena,L.Wua,Y.F.Lib,J.Y.Zhangc,N.Menga

a

StateKeyLaboratoryofFireScience,UniversityofScienceandTechnologyofChina,Hefei230026,Anhui,ChinaCollegeofArchitectureandCivilEngineering,BeijingUniversityofTechnology,Beijing100124,Chinac

ChinaAcademyofBuildingResearch,Beijing100013,China

b

highlights

<Experimentsarecarriedoutinareducedscalemodeltunnel.

<Gastemperaturedatabeneaththeceilinginasloppingtunnel reisobtained.<Tunnelslopefactorisincludedintothecurrentequations.<Modi edequationsagreewellwiththemeasureddata.

articleinfo

Articlehistory:

Received18January2012Accepted18July2012

Availableonline7September2012Keywords:Tunnel reSlope

MaximumtemperatureTemperaturedecayCeiling

abstract

Theeffectoftunnelslopeonthe reinducedhotgastemperaturepro lebeneaththeceilinghasnotbeenclari ednorincludedinexistingmodels.Thus,inthispaperexperimentsarecarriedoutinareducedscalemodeltunnelwithdimensionsof6m(length)Â1.3m(width)Â0.8m(height),whichispositionedwithina72mlongwindtunnel.Theslopesofthemodeltunnelarevariedatthreetypicaldifferentdegrees,0%,3%and5%.ALPGporousgasburnerisusedas resource.Boththemaximumgastemperatureandthetemperaturedistributionalongthetunnelceilingaremeasuredandcomparedwithpreviousmodels.Resultsshowthatthosemodelsoverestimatesthemaximumtemperaturebeneaththeceilingofasloppingtunnel re.Thegastemperaturedecaysfasteralongtheceilingfortunnelswithhigherslope.Empiricalcorrelationsarethenproposedtomodifythecurrentmodelstoincludethetunnelslopefactor.Thepredictionsbythemodi edequationsofthisworkagreewellwiththemeasureddatainboththemaximumtemperatureandtemperaturedecaybeneaththeceilingofthetunnelwithdifferentslopes.

Ó2012ElsevierLtd.Allrightsreserved.

1.Introduction

Firesintunnelshaveattractedincreasingattentioninrecentyearsduetoitscatastrophicconsequence,suchasthe reofHokurikurailwaytunnelinJapanwith30peoplekilledand715hurt,thatinMont-BlanctunnelAustriain1999andDagueKoreain2003killed41and198peoplerespectively.Thehotgas owspreadsalongthetunnelceilingdrivenbybuoyancyinducedbythe reandatthesametimetransportspoisonouscombustionprod-uctstolongdistanceaway.Studyonbuoyantgas owtemperaturedistributionalongtheceilinginatunnelisfundamentalin rescience,andalsocriticalin resafetyengineeringduetothefollowingfacts[1e17]:

*Correspondingauthor.Tel.:þ(86)5513606446;fax:þ(86)5513601669.E-mailaddress:hlh@http://www.77cn.com.cn(L.H.

Hu).1359-4311/$eseefrontmatterÓ2012ElsevierLtd.Allrightsreserved.http://www.77cn.com.cn/10.1016/j.applthermaleng.2012.07.043

1.Thetunnelhasmuchlargerlength-to-heightaspectratiothantheordinarycompartment.Thismakescommonzonetypemodels,whichassumesthegastemperaturespatiallyuniformbeneaththeceiling,isnotapplicableinsuchastructure[1e12].TheaccuracyoftheCFDsimulationdependsontheaccuracyofthephysicalmodelsemployedintheCFDcodes.CFDsimulationoftunnel res,wherecomplexinteractionbetweenlongitudinalventilationair owandcombustionoccurs,isstillatthedevel-opmentstageandphysicsinsideisnotyetgoodenoughsolved.Weneedequationmodelstopredictthegastemperatureatanydistanceawayfromthe reinengineeringapplications.

2.Themaximumgastemperaturebeneaththeceilingabovethe reisacriticalparameterindesigningandevaluationofthe re-proofmaterialperformanceofthetunnelceiling[13e15].Italsodiffersfromthatofthecompartment re,asthelongi-tudinalventilationair owinatunnelde ectsthe ameand

L.H.Huetal./AppliedThermalEngineering51(2013)246e254247

Fig.1.Dimensionsofthemodeltunnel.

plume.Suchinteractionbetweentheinertialforceofthelongitudinalventilationair owandthebuoyancystrengthofthe resourceneedstobequanti edtopredictthemaximumgastemperaturebeneaththeceilinginatunnel.

3.Thebuoyancystrengthofthegas owdecaysduetoitstemperaturedecreasealongthetunnel.Thiswillresultinacriticalsituationthatatadistanceawayfromthe resource,thebuoyancyforceisweakerthantheinertialforceofthelongitudinalventilationair owleadingtothelossofthehot-gas-cool-airstrati cationstructure[16,17].Thisisaverydangeroussituationforthepeopleinevacuationbelowthegas ow.So,knowingthegastemperatureatanydistanceawayfromthe reisveryimportantforthisevaluationofthestabilityofthestrati cation.Thegastemperatureatanydistanceawayfromthe resourcecanbepredictedifweknow:a)themaximumtemperaturebeneaththeceilingrightabovethe resource;andb)howthegastemperaturedecayswithdistancealongthetunnel.

Oka[18,19]conductedexperimentstocharacterizetheeffectsoflongitudinalventilationon amepropertiesincaseoftunnel reanddevelopedempiricalcorrelationmodelsfor ametilt-angle,maximumtemperatureofsmokelayerundertheceilinganditsposition.Forthemaximumgastemperaturebeneaththeceilingabovethe re,Kurioka[13]proposedfollowingempiricalequationbasedonthecorrelationofscalemodelexperimentalresults:

Table1

Experimentalconditions.

Testno.Tunnelslope(%)Ventilationvelocity(m/s)Heatreleaserate(kW)1e50

0204060901206e100.32040609012011e150.62040609012016e200.92040609012021e251.22040609012026e303

02040609012031e350.32040609012036e400.62040609012041e450.92040609012046e501.22040609012051e555

02040609012056e600.32040609012061e650.62040609012065e700.92040609012071e75

1.2

20

40

60

90

120

DT max

*2=3!3

Ta

¼g

Q_Fr(1)

Q

_*2=3=Fr1=3<1:35;g¼1:77;3

¼6=5Q

_*2=3=Fr1=3!1:35;g¼2:54;3

¼0

whereQ_*isthedimensionlessheatreleaserateofthe rede nedas:

Q

_*¼Q

_raCpT5=2

(2)

ag1=2Hd

FristheFroudenumbergivenby:

2Fr¼

u(3)

d

top surface

middle layer

Fig.2.Porousgasburner resource.

248L.H.Huetal./AppliedThermalEngineering51(2013)246e254

Fig.3.Changeoftunnelslopeandpositionsofthe

thermocouples.

whereraistheambientairdensity,Taistheambientairtemper-ature,Hdistheheightfromthe resourcetothetunnelceilinganduisthelongitudinalair owspeedinthetunnel.Li[15]obtainedanotherequationtopredictthemaximumexcessgastemperaturebeneaththeceilingbasedonaxisymmetric replumetheoryandmodel-scaleexperiments:

8>>>>Q_>u>0:19

DT<ur1=3H5=3dmax¼

>>(4)

>>:17:5_2=3>QH5=3u 0:19

d

where

u0¼

uu(5)

Q_!1=3

u*¼

cg(6)

apa

ristheradiusofthe resource,Q_c

istheconvectiveheatreleaserateof resource.

Forthegastemperaturedecayalongthetunnel,ithasbeenbuilt[19e23]thatthedecreaseofthegas owtemperaturealongthetunnel,withneglectofairentrainmentatthehot-gas-airlayerinterface,followsanexponentialdecay

http://www.77cn.com.cnparisonofexperimentaldatawithpredictionsbyKuriokamodel(Eq.(1)

).

DTx¼TxÀTa

(7)

0T0a

¼eÀKxThisexponentialpro lewasveri edbyHu[21e23]byfullscaleexperiments.

However,inallthoseformerresearches,theslopeoftunnelwasnotconsidered.Infact,itiscommonthattransportationtunnel

has

a

b

http://www.77cn.com.cnparisonofexperimentaldatawithpredictionsbyLimodel(Eq.(4)).

L.H.Huetal./AppliedThermalEngineering51(2013)246e254249

Fig.6.Correlationofcorrectioncoef cientwithtunnelslopeforamendingmaximumgastemperatureriseequationbasedonKurioka

model.

aslope.Inlongmountainoustransportationtunnels,thisslopeisusuallylessthan5%.Suchaslopewillalterboththemaximumgastemperaturebeneaththeceilingbychangingthetiltingangleofthe replumerelativetothetunnel;aswellasthegastemperaturedecayalongthetunnelastheentrainmentintothehotgas owatitsinterfacewiththebelowambientair owchangesduetothechangeoftherelativegravitationalforcedirectiontothegas owfromperpendicularinahorizontalcase.Ko[24]investigatedtheeffectsoftunnelslopeonthecriticalvelocityintunnel resbytheexperimentsandPalazzi[25]developedamathematicalmodeltoobtainthecriticalventilationvelocityinthecaseofaslopedtunnel.Intheformerstudies[e.g.,Ref.[26],]onthecriticallongitudinalventilationvelocity,ithasbeenshownthatsuchcriticalventilationair owvelocity(representingthebalanceoftheinertialforceofthelongitudinalventilationair owandthebuoyancyforceoftheupstreamgas ow)changeswithtunnelslopeandalinearcorrectionmodelhasbeenempiricallyproposedtoaccountforthetunnelslopeeffect,

ucðbÞ¼ucð0Þ½1À0:014b

(8)

whereuc(0)isthecriticallongitudinalventilationair owvelocityforahorizontaltunnel,andbisthetunnelslopeindegrees(%)whichisnegativeforadownhilltunnelandpositivefortheuphillcase.Ithasalsobeenshown[14]thatthemeasuredmaximumgastemperaturesbeneaththeceilingissomelowerinuphillsloppingtunnelsthanthosepredictedbyEq.(1).Thefocusofourworkisonhowtheslopeofthetunnelaffectsboththemaximumgastemperaturebeneaththeceilingandthetemperaturedecaypro leinatunnel re.However,thishasnotbeenclari edinthelitera-ture,ataskundertakeninthispaper.

Aseriesofexperimentswereconductedinalaboratoryscalemodeltunnelinthispaperwithdifferent rebuoyancyreleaserates,longitudinalventilationair owvelocitiesandtunnelslopesasdescribedinSection2.TheexperimentalresultswereanalyzedandcorrelatedtomodifytheaboveequationstoincludethetunnelslopefactorinSection3followedbyasummaryofmajor ndingsofthiswork.2.Experimental

Areduced-scaleexperimentalmodeltunnelisconstructedtostudythegastemperaturebeneaththeceilingasshowninFig.1.

a

b

Fig.7.Correlationofcorrectioncoef cientwithtunnelslopeforamendingmaximumgastemperatureriseequationbasedonLi

model.

Themodeltunnelhasdimensionsof6m(length)Â1.3m(width)Â0.8m(height),withitsceilingand oorcoveredwith re-proofgypsumboard.Itssidewallsaremadeoftoughenedglassresistanttohightemperaturetoallowforvisualobservationof

the

http://www.77cn.com.cnparisonofexperimentaldatawithpredictionsofmodi edmodelsonmaximumgastemperaturebeneathtunnelceiling(Eq.(12)).

250L.H.Huetal./AppliedThermalEngineering51(2013)246e254

combustionandsmokemovementphenomenon.Theslopeofthemodeltunnelcanbechangedbyadjustingtheheightatitsend.Inthisstudy,threetypicalslopesof0%,3%and5%areconsidered.Themodeltunnelispositionedinsideabiggersizewindtunneltoallowforuniformlongitudinalair owvelocitypassingthroughthemodeltunnelcanbemaintainedatdesignedlevels.Thelongitu-dinalventilationair owvelocityismonitoredandmeasuredbyadigitalhot-wireanemometeratthecenterlineofthetunnelentrance.Inthisstudy, vekindsoflongitudinalventilationair owvelocities,0m/s,0.3m/s,0.6m/s,0.9m/sand1.2m/swereconsidered.Total75testswerecarriedoutassummarizedinTable1.

Asthelongitudinalair owwillposecomplexeffectonthecombustionbehaviorandsoasheat/buoyancyreleaserateofsolidandliquidfuels[1,3],gaseousfuelisburnedas resource.Aporousgasburnerisdesignedas resourceasshowninFig.2.Thegasburner,whichisweldedbysteelplateswiththicknessof2mm,hasasquaretopsurfacewithadimensionof0.3mÂ0.3mÂ0.03m.Total361smallholesaredrilledwithinasquareregionof0.27mÂ0.27monthetopsurfaceofthegasburner.Theintervalbetweentheholesis1.5cm.Thegasburnerissetatthecentralaxisofthetunnelentrance.Lique edPetroleumGas(LPG)isusedasfuel.Gas owratemeter,withaccuracyof0.1m3/h,isinstalledtomonitorandcontrolsthegasfuel owrate.Theheatreleaserateiscalculatedbyfuelsupply owratemulti-pliedbytheheatofcombustionofthefuel.Fivebuoyant/heatreleaseratesof20kW,40kW,60kW,90kW,and120kWwereconsidered.

K-typesheathedthermocoupleswithdiameterof1.0mmareinstalledtomeasurethegastemperaturebeneaththeceiling,upto1200 C.Twosetsofthermocouplesaremounted0.03mbelowthecentralaxisoftheceilinglongitudinallyalongthemodeltunnel.The rstsethas8K-thermocoupleswiththe rstandthelastthermocoupleat0mand1.4mfromthe resource,eachat0.2mintervals.Thesecondsetconsistsof14K-thermocoupleswiththe rstandthelastoneat1.7mand5.6mdownstreamawayfromthe resource,eachat0.3mintervals.Thetotalnumberofthether-mocouplesis22,asshowninFig.3

.

a

b

Fig.9.Exponential ttingofthenormalizedgastemperaturerisedistributionalongtunnelceiling.

L.H.Huetal./AppliedThermalEngineering51(2013)246e254251

3.Resultsanddiscussion

3.1.Maximumgastemperaturebeneaththeceiling

ThemaximumexcessgastemperaturesmeasuredbeneaththeceilingarecomparedwithKurioka’sequation(Eq.(1))inFig.4andcomparedwithLi’sequation(Eq.(4))inFig.5,respectively.Itcanbeobservedthat:a)thepredictionsbythesetwoequationsagreewellwiththemeasureddataforslopeof0%,butareobviouslyhigherforslopesof3%and5%;b)themaximumgastemperaturedecreasesasthetunnelslopeincreases.Afactoroftunnelslopeisthenincludedtomodifythecurrentequationsasdescribedbelow.

Proposingacoef cientfactorKctoaccountforthetunnelslopeeffect,themaximumexcessgastemperaturebeneaththeceilingcanbeexpressedas:

0DTmax

DTmax¼

8_KcQ>>>>5=3><ur1=3Hd>_2=3>KcQ>>>:17:55=3;

Hd

u>0:19

(9b)

u 0:19

basedonKurioka’sequationandLi’sequation,respectively.Thecoef cientKcisthendeducedempiricallyfromtheexperimentalresultsforeachtestcase:

Kc¼

0DTmaxmax

(10)

Ta

or

*2=3!3

_Q

¼Kcg

Fr(9a)

0whereDTmaxisthemeasuredvalueandDTmaxisthatcalculatedby

Eq.(1)or(4).

Thededucedvaluesofcoef cientKcarethencorrelatedlinearlywiththetunnelslopeforageneralengineeringapplication,asthesamewaywetreatthecriticallongitudinalventilationvelocityforsloppingtunnels(Eq.(8)),asshowninFigs.6and7.The

correlation

cd

Fig.9.(continued).

252L.H.Huetal./AppliedThermalEngineering51(2013)246e254

resultssuggestthefollowinglinearequationforthemodi cationofthecurrentmodels:

FortheKuriokamodel,

Kc¼1À0:077b Kc

FortheLimodel,

(11a)

However,itshouldbenotedthatthevalueofbshouldbenegativewhenthetunnelslopeisdownhill.Fig.8showsacomparisonofexperimentalresultsofmaximumexcessgastemperaturebeneaththetunnelceilingwiththosepredictedbyaboveequations.Itisshownthatpredictionsbythemodi edequationsagreewelltheexperimentalvalues.

1À0:067b;u0>0:191À0:061b;u0 0:19

(11b)

3.2.Gastemperaturedecayalongthetunnelceiling

whichgivethemodi edequationsbasedonKurioka’sandLi’sequation,respectively.

DT max

*2Ta

¼ð1À0:077bÞÂg

Q

_=3!3

Fr1=3

8>>>>>ð1À0:067bÞQ_u>0:19DTmax

¼<ur1=3Hd>>>>>:ð1À0:061bÞ17:5Q_2=3H;u 0:19d

Fig.9.(continued).

Fig.9presentsthevariationofnormalizedtemperaturerisebythemaximumtemperaturerisewithdistancedownstreamfrom(12a)

the resourceandthecollapsebyanexponentialfunctionbasedonEq.(7).Itcanbeobservedthat:

1.Overall,thetemperaturepro lealongthetunnelceilingcanbewellcollapsedbytheexponentialfunction,asinconsistent(12b)

withthetheoreticalequationsintheliterature.

2.Thegastemperaturedecaysabitfasterwithdistancecorre-spondingtoahigherabsolutevalueoftheexponentialpowerindexcoef cientwhenthelongitudinalventilationair owvelocityislower,butalmostindependentofthebuoyancy/heatreleaserateofthe resource.

3.Thegastemperaturedecaysmuchfasterwithdistancewhenthetunnelslopeishigher.Thisisduetothehigherentrainmentatthegaslayerinterface.Whenthetunnelishorizontalandthegravitationalforceisperpendiculartothegas owdirection,theentrainmentofcoolairintotheupperhotgas owisonlycausedbythesheeringeffectanddispassionattheirinterface.However,whenthetunnelhasaslope,thebuoyancyinducedentrainmentduetogravitationalforcewillmakeconsiderablecontribution.Asthecoolairentrainmentintothegas owisenhanced,thedecayofgastemperaturewithdistanceisfaster.So,thefunctionongastemperaturedecayalongtunnelceilingreportedintheliteratureonhorizontaltunnelsneedstobemodi edtoincludethetunnelslopefactor.Alinearcorrelationisproposedtoincludethetunnelslopeeffectintothecoef cientofxintheexponentialfunctionpowerindex:

DTxTxÀT0¼a

¼eÀKcKx(13)

0T0a

ThevaluesofK0c

arecorrelatedwithtunnelslopesinFig.10showingagoodlinearrelationship,suggestingthefollowingfunctiontoaccountforthetunnelslopeeffectonthegastemper-aturedecayalongthetunnelceiling,

K0c¼1þ0:09b

(14)

or

DTxTxÀTmax¼a

Tmax¼eÀð1þ0:09bÞKx

(15)

a

So,thegastemperaturebeneaththeceilingatanydistanceawayfromthe resourcecanbepredictedbycombiningEq.(12)andEq.(15).Itshouldbenotedthatthevalueofbshouldbepositivewhenthetunnelslopeisuphill,butnegativewhendownhill.Fig.11comparesthepredictionsbythemodi edequa-tionswithallthemeasuredvalues.Itcanbeseenthattheyareingoodagreement.

However,duetotheheightlimitationofthewindtunnelwherethemodeltunnelispositioned,themodeltunnellengthisonly

7.5

L.H.Huetal./AppliedThermalEngineering51(2013)246e254253

Fig.10.Correlationofexponentialgastemperaturedecaypowerindexcorrectioncoef cientwithtunnelslope.

times(6/0.8)ofitswidth.Foralongsloppingtunnel,thebuoyancyinduced“stackeffect”cannotbeignored.Thiseffectismoreconsiderablewhenthetunnelslopeislarge.Itwillacceleratethesmokeandlongitudinalair owinsidethetunnelsomehow.Itseffectontheabovetwopointsinvestigatedinthisstudyarefurtherdiscussedbelow:

(1)Forthemaximumtemperature,itisonlyaffectedbytheheat

releaserateofthe re,tunnelheightandthelongitudinalair owspeed.Andthisparameterisonlydeterminedbythenear re eldcondition.So,itcannotbeaffectedbythelimitationofthemodeltunnellength;

(2)Forthetemperaturedecay,itismainlydominatedbytheheat

lossthroughtheboundary.Theentrainmentoffreshairintothesmoke owattheirinterfacewillalsomakesomeweakercontributiontothetemperaturedecay.The“stackeffect”accelerationwillenhancetheentrainmentatthesmoke-air owinterfacetosomeextentandthusthetemperaturedecay.Thiscannotbeansweredduetothelengthlimitationofthemodeltunnelofthecurrentstudyandwillbeinvestigatedinthefuture.

http://www.77cn.com.cnparisonofexperimentaldatawithpredictionsbymodi edmodelongastemperaturedownstreambeneathtunnelceiling(Eq.(15)

).

4.Conclusions

Aseriesofexperimentsarecarriedoutinthispapertoinves-tigatetheeffectoftunnelslopeonthegastemperaturebeneaththeceilingundervariousbuoyant/heatreleaserateofthe reanddifferentlongitudinalventilationair owspeeds.Themajor nd-ingsare:

1.TheKurioka’sandLi’sequationhavegoodpredictiononthemaximumsmoketemperaturebeneaththeceilingforahori-zontaltunnelwithslopeof0%,butbothoverestimatesthetemperatureinanuphilltunnel.

2.Themaximumgastemperaturebeneaththeceilingdecreaseswiththeincreaseinslopeofanuphilltunnel.TheequationsproposedbyKuriokaandLiaremodi edtoincludethefactoras

DT slope

max_*2=3!3

Ta¼ð1À0:077bÞÂgQ

Fr1=3

andDTmax¼8>>>>><ð1À0:067bÞQ_ur1=3H5=3u>0:19d

>>>>>:ð1À0:061bÞ17:5Q_2=3whosepredictionsare

H5=3u 0:19;d

ingoodagreementwiththemeasuredvalues(Fig.8).

3.Thegastemperaturebeneaththeceilingdecaysalongthetunnelceilingexponentiallymuchfasterwithdistanceawayfromthe resourceinanuphilltunnelthanthatinahorizontalone.TheeffectofthetunnelslopeonthegastemperaturedecaycanbeincludedintothecurrentmodelbyalinearfunctionexpressedasDTx=DTmax¼TxÀTa=TmaxÀTa¼eÀð1þ0:09bÞKx,asalsoingoodagreementwiththeexperimentalresults(Fig.10).Acknowledgements

ThisworkwasjointlysupportedbytheNationalNaturalScienceFoundationofChinaunderGrantNo.51176180,NationalKeyTechnologyR&DProgramofChina2011BAK03B02,ProgramforNewCenturyExcellentTalentsinUniversityunderGrantNo.NCET-09-0914andShenzhenMunicipalScienceandTechnologyIndustryandInformationTechnologyCommissionResearchGrantsforFundamentalResearchunderGrantNo.JC201005260236A.References

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335e341.

Nomenclature

Cp:speci cheatofairatconstantpressure(kJ/kgK)Fr:dimensionlessFroudenumberg:gravitationalacceleration(m/s2)

HQ:

_d:heightfrom resourcetotunnelceiling(m)heatreleaserateofQ_ resource(kW)Dc

:convectiveheatreleaserate(kW)Tmax:maximumexcessgastemperature(K)Ta:ambientairtemperature(K)

u:longitudinalventilationair owvelocity(m/s)u*:characteristicKc;K0velocity(m/s)

c

:modi edcoef cientfortunnelslopeeffectTx:temperatureatxmetersfromthereferenceposition(m)To:temperatureatreferenceposition(K)r:radiusof resource(m)Greekrsymbols

ga:ambientairdensity(kg/m3):coef cientinEq.(1)

3b:

coef cientinEq.(1)

:percentageofthetunnelslope

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