WIXLIB

Heat convectionClassification Solver Conduction Convection CHT Radiation Including buoyant forcesIRemember, that we have a temperature difference about 100K,Boussinesq approximation is not guilty!max 15K for airII have used upwind to get convergence.The applied interpolation schemes are to diffusive – temperaturedisappears in the solution after a short range better use boundedGauss linearUpwind grad(U)IBetter divergence schemes shows no convergence for this case :-)IUse buoyantBoussinesqPimpleFoam if possible!c Copyright silentdynamics GmbH2018-02-2235/81

Heat convectionClassification Solver Conduction Convection CHT Radiation Including buoyant forcesIIIRun foamJob buoyantBoussinesqPimpleFoamTrying to get convergence for each timestep good for initial heattransfer calculationsgedit logDILUPBiCG: Solving for T, Initial residual 2.04079e-06, Final residual 2.53797e-08, NoIterations 1DICPCG: Solving for p rgh, Initial residual 0.0287143, Final residual 0.000274784, No Iterations33DICPCG: Solving for p rgh, Initial residual 0.00027785, Final residual 2.6717e-06, No Iterations53c Copyright silentdynamics GmbH2018-02-2236/81

Heat convectionClassification Solver Conduction Convection CHT Radiation Including buoyant forcesIHere is the result after 70sec of realtimec Copyright silentdynamics GmbH2018-02-2237/81

Heat convectionClassification Solver Conduction Convection CHT Radiation Compressible buoyant forcesISince our coffee is too hot for the Boussinesq approximation we haveto include the variation of material properties through pressure andtemperature Relevant solvers areIbuoyantSimpleFoam:Steady-state, natural convection, compressible (sub-sonic), includingradiationIbuoyantPimpleFoam:transient, natural convection, compressible(sub-sonic), includingradiationc Copyright silentdynamics GmbH2018-02-2238/81

Heat convectionClassification Solver Conduction Convection CHT Radiation Compressible buoyant forcesIIIIIChanging of material properties requires underlaying thermophysicsof the fluidsGenerally the thermophysics within OpenFOAM are a little bit of amysterium since it is not well documentedLet’s bring light into the darknessThermophysical properties for each case are defined inconstant/thermophysicalPropertiesAll models are located under FOAM SRC/thermophysicalModelsIIFluid and solid properties (water, air)Mixture and pre-definitions for combustion (really complicated .)c Copyright silentdynamics GmbH2018-02-2239/81

Heat convectionClassification Solver Conduction Convection CHT Radiation Thermophysical modelsIThermomodels are the basis for determination of all materialquantitiesIMost of the models are implemented for combustion simulationssince the temperature and pressure variations are enormouslyIModels needed for heavy reactions are based on compressibilityIFor heat transfer analysis density based models are preferableIOtherwise phase changing is present which requires VOF methodsincluding a fast interface capturing (see Level Set methods, big painfor unstructured meshes .)c Copyright silentdynamics GmbH2018-02-2240/81

Heat convectionClassification Solver Conduction Convection CHT Radiation Thermophysical modelsIgedit constant/thermophysicalPropertiesthermoType{type heRhoThermo;mixture pureMixture;transport const;thermo hConst;equationOfState perfectGas;specie specie;energy sensibleEnthalpy;}c Copyright silentdynamics GmbH2018-02-2241/81

Heat convectionClassification Solver Conduction Convection CHT Radiation Thermophysical modelsTypes of thermo classhePsiThermo General thermophysical model calculation basedon compressibility ψ 1/(RT )Only gasIhRhoThermohSolidThermoc Copyright silentdynamics GmbH2018-02-22General thermophysical model calculation basedon density ρGas, liquid, solidsOnly solids42/81

Heat convectionClassification Solver Conduction Convection CHT Radiation Thermophysical modelsIILet’s look for the airgedit constant/thermophysicalPropertiesthermoType{type heRhoThermo;mixture pureMixture;transport polynomial;thermo hPolynomial;equationOfState icoPolynomial;specie specie;energy sensibleEnthalpy;}c Copyright silentdynamics GmbH2018-02-2243/81

Heat convectionClassification Solver Conduction Convection CHT Radiation Thermophysical modelsIILet’s look for the airgedit constant/thermophysicalPropertiesmixture{// coefficients for airspecie{nMoles 1;molWeight 28.85;}equationOfState{rhoCoeffs 8 ( 4.0097 -0.016954 3.3057e-05-3.0042e-08 1.0286e-11 0 0 0 );}c Copyright silentdynamics GmbH2018-02-2244/81

Heat convectionClassification Solver Conduction Convection CHT Radiation Thermophysical modelsLet’s look for the airgedit constant/thermophysicalPropertiesthermodynamics{Hf 0;Sf 0;CpCoeffs 8 ( 948.76 0.39171 -0.00095999 1.393e-06-6.2029e-10 0 0 0 );}transport{muCoeffs 8 ( 1.5061e-06 6.16e-08 -1.819e-11 0 0 0 00 );kappaCoeffs 8 ( 0.0025219 8.506e-05 -1.312e-08 0 00 0 0 );c Copyright silentdynamics GmbH}2018-02-2245/81II

Heat convectionClassification Solver Conduction Convection CHT Radiation Thermophysical modelsIJust make a small mistake to see which combination is possbile!thermoType{type heRhoThermo;mixture pureMixture;transport polynomial;thermo hPolynomial;equationOfState icoPolynomial;specie bananas;energy sensibleEnthalpy;}c Copyright silentdynamics GmbH2018-02-2246/81

Heat convectionClassification Solver Conduction Convection CHT Radiation Run the compressible caseIINow we are able to run the simulation with changing materialparametersfoamJob -parallel buoyantSimpleFoamc Copyright silentdynamics GmbH2018-02-2247/81

Heat convectionClassification Solver Conduction Convection CHT Radiation Run the compressible caseIINow we are able to run the simulation with changing materialparametersfoamJob -parallel buoyantSimpleFoamc Copyright silentdynamics GmbH2018-02-2248/81

Heat convectionClassification Solver Conduction Convection CHT Radiation Run the compressible caseIKeep care of the residualsILarge residuals hard to get convergence for steady simulations.Better use unsteady solver buoyantPimpleFoamIc Copyright silentdynamics GmbH2018-02-2249/81

Conjugate Heat TransferClassification Solver Conduction Convection CHT Radiation Case SetupILet’s get to interesting stuffIIncluding solids and more fluids in the analysisINames of the regions are defined in the fileconstant/regionPropertiesFor our case:regions(fluid (air coffee)solid (cup));Ic Copyright silentdynamics GmbH2018-02-2250/81

Conjugate Heat TransferClassification Solver Conduction Convection CHT Radiation Case SetupIEeach region properties are defined separately in the folders0,constant,systemIAll other parameters for each region are defined in the region folders(e.g. ls system/air)IA useful tool to setup the simulations: changeDictionaryDictIInitialize the start fields for e.g. the region airchangeDictionary -region airIHowever be careful, empty fields are requiredc Copyright silentdynamics GmbH2018-02-2251/81

Conjugate Heat TransferClassification Solver Conduction Convection CHT Radiation Case setupIIgedit 0/air/Tair affleMixed;Tnbr T;kappa fluidThermo;kappaName none;value uniform 300;}Additional multiple layers with different thermal resistances can bespecified at the interface:thicknessLayers (1e-3);kappaLayers (5e-4);c Copyright silentdynamics GmbH2018-02-2252/81

Conjugate Heat TransferClassification Solver Conduction Convection CHT Radiation Case setupILets’s look at our interfaces:c Copyright silentdynamics GmbH2018-02-2253/81

Conjugate Heat TransferClassification Solver Conduction Convection CHT Radiation Edit mesh setupIEntry in the snappyHexMeshDictIExample: refinementSurfaceszone1{level (0 0);faceZone faceZone1;cellZone cellZone1;cellZoneInside inside;boundary internal;}c Copyright silentdynamics GmbH2018-02-2254/81

Conjugate Heat TransferClassification Solver Conduction Convection CHT Radiation Case setupICoupling is based on nearest neighbor search!ISo please be careful to couple meshes with totally different meshresolutions at the wallIOtherwise the interpolation will give bad resultsIAlso remember, that the heat fluxes are not strictly conservativeIToo strong differences in the mesh resolution will induce heat sinksor heat source at the coupled patchesc Copyright silentdynamics GmbH2018-02-2255/81

Conjugate Heat TransferClassification Solver Conduction Convection CHT Radiation Case setupIgedit constant/air/polyMesh/boundaryair cup{type mappedWall;sampleMode nearestPatchFace;sampleRegion cup;samplePatch cup air;nFaces 3307;startFace 616900;}c Copyright silentdynamics GmbH2018-02-2256/81

Conjugate Heat TransferClassification Solver Conduction Convection CHT Radiation Run the CHT CaseIAfter the long road of setting up the caseIdecomposePar -allRegionsfoamJob -parallel chtMultiRegionFoamIAfter finish the simulationIparaFoam -touchAllIparaviewc Copyright silentdynamics GmbH2018-02-2257/81

Conjugate Heat TransferClassification Solver Conduction Convection CHT Radiation Analyze the resultsILet’s have look what our alu cup saysIYour hand will be quite hot after 1 sec :-)c Copyright silentdynamics GmbH2018-02-2258/81

Conjugate Heat TransferClassification Solver Conduction Convection CHT Radiation Analyze the resultsICheck the residuals!INot good for the coffee fluid.c Copyright silentdynamics GmbH2018-02-2259/81

Conjugate Heat TransferClassification Solver Conduction Convection CHT Radiation Analyze the resultsIUse potentialFoam to get initial flow fieldsIUse strong under relaxation for p rgh and hIEspecially for heat transfer the temperature range is enlarged for inareas of bad cells or high velocity gradientsIEasy way to limit the temperature range is to use the verycomfortable fvOptions methodIfvOptions can be added individually to the solver (e.g. porosity, .)INo need to recompile and adopt solver propertiesILocated FOAM SRC/fvOptionsc Copyright silentdynamics GmbH2018-02-2260/81

Conjugate Heat TransferClassification Solver Conduction Convection CHT Radiation Stabilize the resultsIgedit system/air/fvOptionstemperature corrections{type limitTemperature;active yes;selectionMode all;Tmin 300;Tmax 373;}c Copyright silentdynamics GmbH2018-02-2261/81

Conjugate Heat TransferClassification Solver Conduction Convection CHT Radiation Using fvOptionsIOpenFOAM gives us the following possibilitiesIIIIconstantHeatTransferConstant heat transfer coefficient, need Area to Volume ratio (AoV)variableHeatTransferCalculates heat transfer coefficient using Nusselt number correlationNu a pow (Re, b) pow (Pr , c)tabulatedHeatTransferCalculates heat transfer coefficient using a predefined 2D table forheat transfer coefficient and velocityInterpolation of enthalpy h between each fluid regionc Copyright silentdynamics GmbH2018-02-2262/81

Conjugate Heat TransferClassification Solver Conduction Convection CHT Radiation Using fvOptionsILet’s solve the heat exchange between to cross streams of water andairc Copyright silentdynamics GmbH2018-02-2263/81

Conjugate Heat TransferClassification Solver Conduction Convection CHT Radiation Using fvOptionsIIThe coupling is defined in system/air/fvOptionsgedit system/air/fvOptionsair water{type constantHeatTransfer;active on;selectionMode mapRegion;interpolationMethod cellVolumeWeight;nbrRegionName water;master true···c Copyright silentdynamics GmbH2018-02-2264/81

Conjugate Heat TransferClassification Solver Conduction Convection CHT Radiation Using fvOptionsIWe have to provide the Area of Volume ratio (AoV)Igedit 0/air/AoVIAnd the constant heat transfer coefficientIgedit 0/air/htcConstIfoamJob chtMultiRegionSimpleFoamc Copyright silentdynamics GmbH2018-02-2265/81

Conjugate Heat TransferClassification Solver Conduction Convection CHT Radiation Using fvOptionsILook at the resultsc Copyright silentdynamics GmbH2018-02-2266/81

Conjugate Heat TransferClassification Solver Conduction Convection CHT Radiation Using fvOptionsIIIIHowever, the regions do not only interact through heat transferFlow resistance due to e.g. heat exchanger pipes is present inducinga pressure dropWithout modeling each pipe the flow resistance is included usingporosity modelsOpenFOAM uses Darcy-Forchheimer law to calculate pressure dropSi [µdi 0.5ρ ui fi ]uiI(9)Please note, that the porosity can be defined for a cellZone(explicitPorositySource) or a region(interRegionExplicitPorositySource)c Copyright silentdynamics GmbH2018-02-2267/81

Conjugate Heat TransferClassification Solver Conduction Convection CHT Radiation Using fvOptionsIIf we add the porosity we get pretty physical results inside complexheat exchangersc Copyright silentdynamics GmbH2018-02-2268/81

Conjugate Heat TransferClassification Solver Conduction ConvectionIThere are more fvOptions availableIsee FOAM SRC/fvOptionsc Copyright silentdynamics GmbH2018-02-22 CHT Radiation 69/81

Heat RadiationClassification Solver Conduction Convection CHT Radiation Basic backgroundIRadiation is very important and is often not consideredIInteraction of different devices in respect of thermal radiation isbasis of thermal problemsIThrow radiation heat transfer beside will often lead to wrongphysical results aIRadiation heat transfer takes place in form of electromagnetic wavesIWave length for heat transfer: 0.8 – 400µm (ultrared)IAt higher temperatures, the amount of visible radiation is larger andcan be seen e.g. lightning bulbc Copyright silentdynamics GmbH2018-02-2270/81

Heat RadiationClassification Solver Conduction Convection CHT Radiation Basic backgroundIIIIIWith increasing temperatures the intensity of heat radiationincreases e.g. the human body radiates continuously about 1000Win a vacuum(note: no media is required for thermal radiation)From surrounding walls the human adsorbs thermal energy of about900WSo the typical loss of a non-working human is about 100WElectromagnetic waves can be adsorbed, reflected or transmittedaccording to the surface properties τ ρ 1I(10)Coefficients depend also on wave lengthc Copyright silentdynamics GmbH2018-02-2271/81

Heat RadiationClassification Solver Conduction Convection CHT Radiation Basic backgroundIFor simplification a black body is introducedIIAll waves are adsorbedWaves are emitted with maximum of intensityIEmission coefficient for a black body is 1ILaw of Kirchhoff αc Copyright silentdynamics GmbH2018-02-2272/81

Heat RadiationClassification Solver Conduction Convection CHT Radiation Basic backgroundIIThe emission for a black body is independent of the wave length andsolid angleStephan-Boltzmann-law for hemispheric thermal radiationQ/A σT 4Iσ 5.6696 · 10 8 W /m2 K 4(11)Remember: include radiative heat transfer when the radiant heatflux, is large compared to the heat transfer rate due to convection orconduction44qrad σ(Tmax Tmin)c Copyright silentdynamics GmbH2018-02-22(12)73/81

Heat RadiationClassification Solver Conduction Convection CHT Radiation Basic backgroundIOpenFOAM gives us three radiation models to calculate the heatfluxesIIIP1 modelfvDOM (finite volume discrete ordinates model)viewFactor modelIWe don’t have time to review the models!IBut let us take a closer lookc Copyright silentdynamics GmbH2018-02-2274/81

Heat RadiationClassification Solver Conduction Convection CHT Radiation Decision of radiation modelIIIIIIIIIndicator is the optical length a L where L is typical length scaleand a absorption coefficientIf a L 1 then use P1 modelOtherwise if a L 1 use fvDOMSince fvDOM also captures the large optical length scales it is themost accurate modelP1 model tends to overpredict the heat fluxfvDOM consumes a lot of CPU power since it solves the transportequation for each directionfvDOM can handle non gray surfaces (dependence of the solid angleis included)viewFactor is used if non participating mediums are present (spacecraft, solar radiation)c Copyright silentdynamics GmbH2018-02-2275/81

Heat RadiationClassification Solver Conduction Convection CHT Radiation Get the case startedI gedit constant/radiationPropertiesradiation on;radiationModel P1;// Number of flow iterations per radiation iterationsolverFreq 1;absorptionEmissionModel ionCoeffs{absorptivity absorptivity [ m 1 ] 0.5;emissivity emissivity [ m 1 ] 0.5;E E [ kgm 1s 3 ] 0;}scatterModel none;sootModel none;c Copyright silentdynamics GmbH2018-02-2276/81

Heat RadiationClassification Solver Conduction Convection CHT Radiation Get the case startedIIIWe have to define the incident radiation field G for the P1 modelAnd the field for radiation intensity I in case of the fvDOM modelLet’s look at the radiative heat flux Qr for the P1 modelc Copyright silentdynamics GmbH2018-02-2277/81

Heat RadiationClassification Solver Conduction Convection CHT Radiation Get the case startedI Properties for the fvDOMnPhi 3; // azimuthal angles in PI/2 on X-Y.(from Y to X)nTheta 4; // polar angles in PI (from Z to X-Y plane)convergence 1e-3; // convergence criteria for radiationiterationmaxIter 10; // maximum number of iterationscacheDiv false; /

Title: Heat transfer in OpenFOAM Author: Dr. Johann Turno