[me45]

Hi
I am interested in obtaining wall heat flux of a rocket engine (so 2D axisymetric).

• I am using k omega SST turbulence model
• solver is rhoPimpleFoam (modified to account for viscous heating).
• My divergence schemes are :

       default         none;
      div(phi,U)      Gauss upwind;
      div(phid,p)     Gauss limitedLinear 1;
      div(phi,K)      Gauss limitedLinear 1;
      div(phiv,p)     Gauss limitedLinear 1;
      div(((rho*nuEff)*dev2(T(grad(U))))) Gauss linear;
      div(phi,h)      Gauss limitedLinear 1;
      div(phi,k)      bounded Gauss upwind;
      div(phi,omega)  bounded Gauss upwind;                                                                                   div((nuEff*dev2(T(grad(U))))) Gauss linear;
  // For viscosity heating
      div(U)          Gauss linear;
      div(((((rho*nut)+thermo:mu)*(grad(U)+grad(U).T()))&U)) Gauss linear;
      div((((0.666667*((rho*nut)+thermo:mu))*div(U))*U))  Gauss linear;

• I have seen on several post that for heat transfer problems, a low Re formulation is better, so I initiallly used that.

• My mesh is ok except for high aspect ratio (but this is inevitable when resolving the whole boundary layer and should not be a problem according to many CFD users). My cells gets a growth factor around 1.15 in the BL and have a constant size far from it.
• Wall conditions are:
  

  k:  kLowReWallFunction;
  
  omega: omegaWallFunction;
  nut:    nutLowReWallFunction;
          Cmu             0.09;
          kappa           0.41;
          E               9.8;
          value           uniform 0;
  
  alphat: compressible::alphatWallFunction;
             Prt             0.85;
             value           uniform 0;

I have run a first simulation, the maximum y+ value is 7 (the first 2 pictures represents y+ and wall heat flux qw). Results does not seem bad: same shape of qw but overestimated by 15% of results obatin with an over software.
Then I refined the mesh to get my maximum y+ closer to 1. Now trouble starts: the time step loss 3 order of magnitude (to respect the maximum Co=0.5) so computational time becomes really high. Besides my residuals falls to 1e-7 (instead of 1e-5) and results get mad: y+ and qw distribution becomes really bad. I have upload the residuals, y+ and qw for this case.
There is clearly something going wrong as I get a courant Number of 0.5 in a small part of the nozzle close to the wall whereas my mean Co is two order of magnitude lower (the part where Co=0.5 change when I change refine more or less the mesh).
My mesh is ok except for high aspect ratio (but this isinevitable when resolving the whole boundary layer and should not be a problem according to many CFD users). My cells gets a growth factor around 1.15 in the BL and have a constant size far from it.



I also have run a High Re simulation (changing the wall boundary condition),

k:  kqRWallFunction;

omega: omegaWallFunction;
nut:    nutUSpaldingWallFunction;
    
alphat:  compressible::alphatJayatillekeWallFunction;

the first simulation is done with y+ totally in buffer region but gives almost same results than the Low Re simulation (the one that gives acceptable results). As y+ was in buffer region region I increased it to be >30 as CFD guys recommend to avoid buffer layer because results would be bad, but then my results are bad, esoecially in the high velocity region of my mesh.
I have done many simulation to investigate that but can't answer these question:

1. Why when refining to get a lower y+ values my simulation show this bad behaviour? What can I investigate?
2. CFD guys recommend to avoid buffer layer because results gets bad, but this was not the case for my example. Does k omega SST enables to get good results even if we are in buffer region as it use blended function? Can I trust these results ?
3. I get bad results when y+>30, is it because of that that usually people advise not to use High Re (wall function) for heat transfer study or can it comes from something else ?
4. I also have in some simuation a high frequency variation of omega residuals (between 1e-5 and 1e-6), I can't find what cause that. Can it have an impact on results?
5. about the alphat wall condition, we have the choice between compressible::alphatJayatillekeWallFunction; and compressible::alphatWallFunction. According to alphatWallFunction vs alphatJayatillekeWallFunction , the Jayatilleke is better for high and low Re so what is the alphatWallFunction good for ?

Ask me If you need more information.
I would really appreciate if someone can respond to at least one of my question.