[EliotSch]

Hello everybody !

I am having trouble calculating radiation heat transfer with the P1 model, here is my case.

Numerical configuration
I am currently trying to model a problem of conjugate heat transfer between a hot air jet and an opaque solid plate on openFoam-4.1. This problem involves thermal conduction in the solid, convective heat transfer and radiation thus chtMultiRegionFoam seems to be a good choice.

The case is very similar to the following threads:
chtMultiRegionSimpleFoam: Thermal Conduction + Surface-To-Surface Radiation
and
Lack of knowledge simulating radiation in solids
The following threads gives information concerning the calculation of G and Qr: Difference between IDefault and G (radiation)

Fluid/solid thermal coupling
The coupling between the fluid and the solid regions is made using a compressible::turbulentTemperatureRadCoupledMixed boundary condition as follows.

  //location    "0/solid";
  //object      T;
      solid_to_fluid 
      {
          type            compressible::turbulentTemperatureRadCoupledMixed;
          Tnbr            T;
          kappaMethod     fluidThermo; 
          QrNbr           none;
          Qr              Qr;
          value           $internalField;
      }

  //location    "0/fluid";
  //object      T;
      fluid_to_solid 
      {
          type            compressible::turbulentTemperatureRadCoupledMixed;
          Tnbr            T;
          kappaMethod     fluidThermo; 
          QrNbr           Qr; 
          Qr              none;
          value           $internalField;
      }

Radiation model P1
For the radiative heat transfer, the fluid is considered a non-participating media and the solid is an opaque solid with a surface emissivity equal to 1.

  //location    "0/fluid";
  //object      G;
      fluid_to_solid
      {
          type            MarshakRadiation;
          emissivityMode  solidRadiation;
          value           uniform 0;
      }

  //location    "0/fluid";
  //object      Qr;
      fluid_to_solid
      {
          type              MarshakRadiation;
          T                 T;
          value             uniform 0;
      }

  //location    "0/solid";
  //object      G;
      solid_to_fluid
      {
          type            MarshakRadiation;
          emissivityMode  solidRadiation;
          value           uniform 0;
      }

  //location    "0/fluid";
  //object      Qr;
      solid_to_fluid
      {
          type                mappedField;
          sampleRegion    fluid;
          sampleMode      nearestPatchFace;
          samplePatch      solid_to_fluid;
          offset                  (0 0 0);
          field                     Qr;
          setAverage         no;
          average               0;
          value uniform    0;
      }

  //location    "constant/fluid";
  //object      radiationProperties;
  radiation       on;
  radiationModel  P1;
  solverFreq 3;
   
  absorptionEmissionModel constantAbsorptionEmission;
  constantAbsorptionEmissionCoeffs
  {
      absorptivity    absorptivity    [ m^-1 ]       0;
      emissivity      emissivity      [ m^-1 ]       0;
      E               E               [ kg m^-1 s^-3 ]  0;
  }
  scatterModel none;
  sootModel none;

  //location    "constant/solid";
  //object      radiationProperties;;
  Radiation               on;
  radiationModel          opaqueSolid; 
  solverFreq 3;
   
  absorptionEmissionModel constantAbsorptionEmission;
  constantAbsorptionEmissionCoeffs
  {
      absorptivity    absorptivity [ 0 -1 0 0 0 0 0 ] 0; //opaqueSolid
      emissivity      emissivity [ 0 -1 0 0 0 0 0 ] 1;
      E               E [ 1 -1 -3 0 0 0 0 ] 0;
  }
  scatterModel none;
  sootModel none;

Question 1
With this particular setting, I expect the radiative flux Qr at the solid/fluid interface to be
Qr= Qin-Qem where
Qem = emissivity*Sigma*T⁴
Qin=0 as absorptivity=0

However the result is different: for T=850 K --> Qr=58055.75
Qr should be emissivity*Sigma*T⁴= 29600
So there is a factor 2 between the theoretical radiativ heat flux and the Qr field. Is there a problem in the definition of the boundary condition and radiationProperties or have I misunderstood the definition of Qr?

Question 2
As the P1 model seems to be less accurate than fvDOM for exemple, is it possible this large difference between theoretical and numerical radiation flux is due to the model ?

Question 3
I have doubt about the setting of my "0/fluid/Qr" boundary condition with "mappedField". Is it necessary for the calculation of the radiative heat transfer and if yes, is it writen in a proper way ?

I would really appreciate if someone could help me with this problem.
Many thanks in advance.

Regards,

Eliot

[dlahaye]

My humble suggestion would be to check the continuity of the heat flux first.

Cheers, Domenico.

[Daniel Bakonyi]

Hello EliotSch,

I know it has been quite a while, but have you found asolution for your problem? I am currently facing what seems to be the exact same issue.

Regards,
Daniel

Edit:
I am sorry, I accidentally posted to the wrong thread. Please disregard this post.