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Initialsetup–Ireferredtutorial1givenbyProf.Huangforinitialsetupexceptfollowingchanges–
1. Iturnedgravity“on”andput-9.81inYaxis(alongheight1mofcylindricaltank)2. Icreatednewmaterialforwaterandgavefollowingvalues
a. Density-"Boussinesq"toallowbuoyancy-driventhermalconvectionb. Operatingdensity=986kg/m^3c. Thermalexpansioncoefficient=4*10^-41/Kd. Operatingtemperature=45C
3. Settheboundaryconditionfortheoutletto"outflow",insteadof"pressureoutlet".4. Chosesecondorderdiscretization5. Useddoubledprecisionformoreaccurateresults6. Refinedmeshto9*10^-3mwithnumberofnodesalmostequalto48,0007. Usedk-epsilonmodelwith“realization”modeon.8. Used“AdaptiveGradient”foraccurateresults.
Task1
Tout = ∫ ∫ vnTdA∫ ∫ vndA
StepstocalculateTemperature1. Createtwodifferentcustomdefinedfunctionfornumeratoranddenominator2. Use “integral” in “user defined” functions in “Results” to calculate the value of user
definedfunction.3. After getting the values, divide numerator by denominator and that is the value for
Temperature.
Fortask1∫ ∫ vnTdA=0.00874708∫ ∫ vndA=2.7965489*10^-5Tout=312.7812145K
Contourplotoftemperatureontheplaneofsymmetry(isometricview)
Contourplotofvelocitymagnitudeontheplaneofsymmetry(isometricview)
Task2IchangeddirectionofgravityformYaxistoXaxiswiththesamevalueof9.81m/s^2.Allothersettingsaresame.
Fortask2,usingsamestepsasTask1tocalculatetemperature,weget-∫ ∫ vnTdA=0.0095174448∫ ∫ vndA=3.0713205*10^-5Tout=309.881199K
Contourplotoftemperatureontheplaneofsymmetry(isometricview)
Plotofstreamlines(rearview)
Task3Iturnedgravity“off”forthistaskanddensityconstant.Allothersettingsaresame.
Fortask3,usingsamestepsasTask1tocalculatetemperature,weget-∫ ∫ vnTdA=0.0085905139∫ ∫ vndA=2.8151461*10^-5Tout=305.15339K
Contourplotoftemperatureontheplaneofsymmetry(isometricview)
Contourplotofvelocitymagnitudeontheplaneofsymmetry(frontview)
ComparisonofTask1,2and3–Intask1,thegravitationalforceisalongtheheightofcylinder,i.e.normaltoplate,hencethefluidistouchingthesurface,fillingtankforsomeheight,gainingheatandthenleavingthetank,hencetheoutlettemperatureismaximumfortask1ascomparedtoothertwo.In task2, thegravitational force isalongXaxis,hence, the fluid ismovingtowardstheXaxis(alongthelengthofinlet/outletpipe).Duetothegravitationalforcedirection,notbeingnormaltobaseplate,theamountoffluidtakingheatfromtheplatewillbe lesscomparedtotask1,hence,theoutlettemperatureislessthantask1.Intask3,theonlyforceisliquid’skineticenergy,duetowhich,theliquidwillfollowdirectionofvelocity,collidefromoppositewall,andduetocollision,itwilldisperseandreachoutlet.Asthereisnoexternalforcepresent,theamountoffluidreachingbottomwillbevery less,hencetheoutlettemperatureisleastinTask3.Task4Fortask4,wehadparta)initialization–30degCb)initialization–40degC.
1. Changedsettingto“transient“.2. Initializetemperatureto“303K”and“313K”forparta)andb)respectively.3. DefinecustomizedfunctionfornumeratoranddenominatorasdiscussedinTask14. Timestepusedforthistaskwas1sec5. Meshsettingsused–finemesh6. Totaltimestepsforwhichsolutionsran–66047. Theplotswerethenplottedusingexcelfromthegeneratedoutputfiles8. Allothersettingsremainedsame.
Steadystatetemperature=312.78KForparta)Toutatlasttimestep=312.53K Temperaturedifferenceforparta)=0.15K<0.3KForpartb)Toutatlasttimestep=313.05K Temperaturedifferenceforpartb)=0.27K<0.3K
Task5For task 5, I used the "FluxReport" function inAnsys-Fluent to obtain the total rate of heattransferoverthebottomplate,andthendividedthetotalrateofheattransferbytheareaofthebottomplatetoobtaintheaverageheatflux(inJs-1m-2)atthebottomplate.AverageHeatFlux=1157.381/(3.14 ∗ 0.254 ∗ 0.5)=11794.96Js-1m-2
Usingthisvalueofheatfluxinsteadofconstanttemperature,Iransimulationagain(adaptivemesh),andthenusingsamestepsasTask1tocalculatetemperature,weget-
∫ ∫ vnTdA=0.0087582831∫ ∫ vndA=2.7996258*10^-5Tout=312.83K»312.78K
Outlet temperature for both cases are almost same. There is a slight difference because ofconductionduetotemperaturedifference.
3.02E+02
3.04E+02
3.06E+02
3.08E+02
3.10E+02
3.12E+02
3.14E+02
3.16E+02
0 1000 2000 3000 4000 5000 6000 7000
Tempe
rature(K)
timestep
Task4:comparisionofToutletfortransientandsteadystate
30degC SteadyState 40degC
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