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Tutorial:PremixedCombustioninaConicalChamberusingtheZimont(meanprogressvariablebased)Model

Purpose

Thepurposeofthistutorialistoprovideguidelinesandrecommendationsforsettingupandsolvingapremixedgaseousmixtureusingthepremixedcombustion(Zimont)model.Both,adiabaticandnon-adiabaticpremixedcombustionmodelswillbeused.

Prerequisites

ThistutorialassumesthatyouarefamiliarwiththeFLUENTinterfaceandthatyouhaveagoodunderstandingofthebasicsetupandsolutionprocedures.Somestepswillnotbeshownexplicitly.

Inthistutorial,youwillusethepremixedcombustionmodel.Thistutorialdoesnotcoverthemechanicsofusingthismodel.Instead,itfocusesontheapplicationofthismodeltosolvetheproblem.Ifyouhavenotusedthismodelbefore,refertoSection16:ModelingPremixedCombustionintheFLUENT6.2User’sGuide.

ProblemDescription

TheconicalcombustorconsideredisshowninFigure1.Asmallnozzleatthecenterofthecombustorintroducestheleanmethane/airmixture(equivalenceratio=0.6)at60m/sand650K.Thehighspeedflowreversesdirectioninthecombustorandexitsthroughtheco-axialoutlet.

Chemicalreactionforequivalenceratioof0.6is:

CH4+3.33(O2+3.76N2)=CO2+2H2O+1.33O2+12.53N2

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PremixedCombustioninaConicalChamberusingtheZimontModel

Somerelatedparametersareasfollows:

Table1:PremixedMixtureProperties

ParameterMassofair(forequivalenceratio0.6)Massoffuel

Massfractionoffuel

Heatofcombustion(j/kg)AdiabaticTemperature(K)CriticalStrainRate(1/s)LaminarFlameSpeed(m/s)Value2×(32+3.76×28)/0.6=457.616

0.03383.84e+07195050000.35Figure1:ProblemSchematic

Preparation

1.Copythefile,conreac.mshtoyourworkingdirectory.2.Startthe2DversionofFLUENT.

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PremixedCombustioninaConicalChamberusingtheZimontModel

SetupandSolution

Step1:Grid

1.Readthemeshfile(conreac.msh).2.Checkanddisplaythegrid.

GridFLUENT 6.2 (2d, segregated, lam)Figure2:GridDisplay

Step2:Models

1.Definethesolversettings.

(a)UnderSpace,selectAxisymmetric.

(b)Retainthedefaultsettingsforotherparameters.2.Enablethestandardk-epsilon(2eqn)turbulencemodel.3.DefinetheSpeciesmodel.

(a)UnderModel,selectPremixedCombustion.

(b)UnderPremixedCombustionModel,retaintheselectionoftheAdiabaticmodel.(c)SettheTurbulentFlameSpeedConstantto0.637.

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PremixedCombustioninaConicalChamberusingtheZimontModel

Step3:Materials

1.Createanewfluidmaterialcalledpremixed-mixturewiththephysicalpropertiesshowninTable2.

Table2:PremixedMixtureMaterial

ParameterDensity(kg/m3)

DensityofUnburntReactants(kg/m3)TemperatureofUnburntReactants(k)

AdiabaticTemperatureofBurntProducts(k)LaminarFlameSpeed(m/s)CriticalRateofStrain(1/s)Value

premixed-combustion1.265019500.355000Fortheadiabaticmodel,thetemperatureiscalculatedfromthetemperatureoftheunburntmixtureandtheadiabatictemperatureoftheburntproducts.Formorein-formation,refertoSection16.2.4:CalculationofTemperatureintheFLUENT6.2User’sGuide.

Step4:OperatingConditions

1.Retainthedefaultoperatingconditions.Step5:BoundaryConditions

1.Settheboundaryconditionsforfluid-6.

(a)Selectpremixed-mixtureintheMaterialNamedrop-downlist.2.Settheboundaryconditionsforvelocity-inlet-5.

(a)SettheVelocityMagnitudeto60m/s.

(b)SelectIntensityandLengthScaleastheTurbulenceSpecificationMethodandspec-ifytheTurbulenceLengthScaleas0.003m.(c)Retainthedefaultvaluesfortheotherparameters.3.Settheboundaryconditionsforpressure-outlet-4.

(a)SelectIntensityandLengthScaleastheTurbulenceSpecificationMethod.

(b)SettheBackflowTurbulenceLengthScaleandBackflowProgressVariableto0.003m

and1respectively.(c)Retainthedefaultvaluesfortheotherparameters.4.Retainthedefaultadiabaticboundaryconditionsforwall-1.

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PremixedCombustioninaConicalChamberusingtheZimontModel

Step6:Solution

1.Solveforflowandturbulenceequations.

(a)IntheSolutionControlspanel,selecttheFlowandTurbulenceequations.(b)Enabletheplottingofresidualsduringcalculation.(c)Initializetheflowfieldandcomputefromall-zones.(d)Savetheinitialcaseanddatafiles.

(e)Startthecalculationbyrequesting250iterations.2.Solveusingalltheequations.

(a)IntheSolutionControlspanel,selectthePremixedCombustionequation.(b)Requestanadditional200iterationsorperformiterationsuntilthesolutioncon-verges(Figure3).

Residualscontinuityx-velocityy-velocitypremixckepsilon1e+011e+001e-011e-021e-031e-041e-05050100150200250300IterationsScaled ResidualsFLUENT 6.2 (axi, segregated, ske)Figure3:ScaledResiduals

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Step7:Postprocessing

1.Displaythevelocityvectorsinthedomain(Figure4).

Display−→Vectors...

(a)SetScaleto10andclickDisplay.

6.49e+016.16e+015.84e+015.52e+015.19e+014.87e+014.54e+014.22e+013.90e+013.57e+013.25e+012.93e+012.60e+012.28e+011.96e+011.63e+011.31e+019.86e+006.62e+003.39e+001.54e-01Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.2 (axi, segregated, ske)Figure4:VelocityVectors

2.Displaycontoursofstreamfunction(Figure5).

Display−→Contours...

(a)SelectVelocity...andStreamFunctionintheContoursofdrop-downlists.3.Displayfilledcontoursofmeanprogressvariable(Figure6).

(a)UnderOptions,selectFilled.

(b)SelectPremixedCombustion...andProgressVariableintheContoursofdrop-down

lists.4.Displayfilledcontoursofstatictemperature(Figure7).

(a)SelectPremixedCombustion...andStaticTemperatureintheContoursofdrop-downlists.

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1.26e-031.20e-031.14e-031.07e-031.01e-039.48e-048.85e-048.22e-047.58e-046.95e-046.32e-045.69e-045.06e-044.42e-043.79e-043.16e-042.53e-041.90e-041.26e-046.32e-050.00e+00Contours of Stream Function (kg/s)FLUENT 6.2 (axi, segregated, ske)Figure5:ContoursofStreamFunction

1.00e-009.50e-019.00e-018.50e-018.00e-017.50e-017.00e-016.50e-016.00e-015.50e-015.00e-014.50e-014.00e-013.50e-013.00e-012.50e-012.00e-011.50e-011.00e-015.00e-020.00e+00Contours of Progress VariableFLUENT 6.2 (axi, segregated, ske)Figure6:ContoursofMeanProgressVariable

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1.95e+031.88e+031.82e+031.75e+031.69e+031.62e+031.56e+031.49e+031.43e+031.36e+031.30e+031.23e+031.17e+031.10e+031.04e+039.75e+029.10e+028.45e+027.80e+027.15e+026.50e+02Contours of Static Temperature (k)FLUENT 6.2 (axi, segregated, ske)Figure7:ContoursofStaticTemperature

Step8:SetupforNon-AdiabaticPremixedCombustion

1.Changethespeciesmodel(PremixedCombustionModel)fromAdiabatictoNon-Adiabatic.2.IntheMaterialspanel,modifythefollowingpropertiesofthepremixed-mixturemate-rial:

Parameter

HeatofCombustionUnburntFuelMassFractionValue3.85e+070.0338Forthenon-adiabaticmodel,FLUENTsolvesanenergytransportequationtoaccountforheatlossesorgainswithinthesystem.Thetemperatureiscalculatedfromtheheatofcombustionandthefuelmassfraction.Formoreinformation,refertoSection16.2.4:CalculationofTemperatureintheFLUENT6.2User’sGuide.3.SettheTemperatureforvelocity-inlet-5to650k.

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Step9:Solution(Non-AdiabaticPremixedCombustion)1.Solveforflowandturbulenceequations.

(a)IntheSolutionControlspanel,selecttheFlowandTurbulenceequations.(b)SettheUnder-RelaxationFactorsforDensity,Energy,andTurbulentViscosityto

0.8.(c)SetthediscretizationforPressuretoPRESTO!andretainthedefaultsettingsfor

theotherparameters.(d)Initializetheflowfieldandcomputefromall-zones.(e)Startthecalculationbyrequesting250iterations.2.Solveusingalltheequations.

(a)IntheSolutionControlspanel,selectalltheequations.

(b)SettheUnder-RelaxationFactorsforDensity,Momentum,andProgressVariableto

0.5.(c)SettheUnderRelaxationFactorforEnergyto0.9.

(d)Requestfor1500iterationsorperformiterationsuntilthesolutionisconverged

(Figure8).(e)Savethecaseanddatafiles.

Residualscontinuityx-velocityy-velocitypremixcenergykepsilon1e+001e-011e-021e-031e-041e-051e-061e-071e-080100200300400500600700800900IterationsScaled ResidualsFLUENT 6.2 (axi, segregated, ske)Figure8:ScaledResiduals

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Step10:Postprocessing

1.Displaythevelocityvectorsinthedomainwithascalefactorof10(Figure9).

6.49e+016.17e+015.84e+015.52e+015.20e+014.87e+014.55e+014.23e+013.90e+013.58e+013.25e+012.93e+012.61e+012.28e+011.96e+011.63e+011.31e+019.85e+006.61e+003.37e+001.33e-01Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.2 (axi, segregated, ske)Figure9:VelocityVectors

2.Displayfilledcontoursofstreamfunction(Figure10).3.Displayfilledcontoursofmeanprogressvariable(Figure11).4.Displayfilledcontoursofstatictemperature(Figure12).

DisplaycontoursofstatictemperaturebyselectingTemperature...andStaticTemper-atureintheContoursofdrop-downlists.

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1.27e-031.21e-031.14e-031.08e-031.02e-039.53e-048.89e-048.26e-047.62e-046.99e-046.35e-045.72e-045.08e-044.45e-043.81e-043.18e-042.54e-041.91e-041.27e-046.35e-050.00e+00Contours of Stream Function (kg/s)FLUENT 6.2 (axi, segregated, ske)Figure10:ContoursofStreamFunction

1.00e-009.50e-019.00e-018.50e-018.00e-017.50e-017.00e-016.50e-016.00e-015.50e-015.00e-014.50e-014.00e-013.50e-013.00e-012.50e-012.00e-011.50e-011.00e-015.00e-020.00e+00Contours of Progress VariableFLUENT 6.2 (axi, segregated, ske)Figure11:ContoursofMeanProgressVariable

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1.94e+031.88e+031.81e+031.75e+031.68e+031.62e+031.56e+031.49e+031.43e+031.36e+031.30e+031.23e+031.17e+031.10e+031.04e+039.73e+029.09e+028.44e+027.79e+027.15e+026.50e+02Contours of Static Temperature (k)FLUENT 6.2 (axi, segregated, ske)Figure12:ContoursofStaticTemperature

Results

PostprocessingresultscanbeusedtostudytheapplicationofthepremixedcombustionmodelinFLUENT.

Summary

Applicationofpremixedcombustionmodel(Zimontmodel)inapremixedgaseousmixturecasehasbeendemonstrated.

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