[Gerrit]

Hi,

I am using the kOmegaSST with simpleFoam and from reading in the forum I know y+ has to be around 1 or smaller. But I would like to understand why this is the way it is.

I know it has to do with the law of the wall in the end, but I don't get the connection. Has someone an explanation (with a source maybe) somewhere, why it is y+ of 1?

For k epsilon as fat as I understood y+ should be bigger than 30, because at 30 the log-law starts. Is that correct?

Sorry for this basic question.

Thanks

Best
Gerrit

[camel]

Hi Gerrit,

first of all - no, the y+ value for kOmega SST does not have to be around 1 or smaller. I'll try to give you a short explanation of my personal research about this particular topic.

When standard kEpsilon model is used, the y+ must be greater than y+=30, which actually means that first cell center node must be in a turbulent region. If y+ < 11.6 (I think OpenFoam uses this yPlus value but please check this), the flow is treated as laminar (u+ = y+), and if y+ > 11.6, the wall function is applied.

Generally, the kOmega turbulence models (including kOmegaSST turbulence model) have one big advantage over kEpsilon model. They permit smooth shift from a viscous sub-layer to a wall function because omega is integrated all way to the wall and due to that there is no necessity for damping functions and high resolution mesh in the near-wall region (which are used in Low-Reynolds models).

You can find in the literature how the all values is calculated in kOmegaSST model:

omega = sqrt(omega_vis^2 + omega_log^2) and uStar = (uStar_vis^4 + uStar_log^4)^(0.25)

OpenFoam uses the same equations for a calculation. Please look the source code:
/src/turbulenceModels/incompressible/RAS/derivedFvPatchFields/wallFunctions/omegaWallFunctions/omegaWallFunction

label faceCellI = patch().faceCells()[faceI];

scalar yPlus = Cmu25*y[faceI]*sqrt(k[faceCellI])/nuw[faceI];

scalar omegaVis = 6.0*nuw[faceI]/(beta1_*sqr(y[faceI]));

scalar omegaLog = sqrt(k[faceCellI])/(Cmu25*kappa_*y[faceI]);

omega[faceCellI] = sqrt(sqr(omegaVis) + sqr(omegaLog));

if (yPlus > yPlusLam)
{
G[faceCellI] =
(nutw[faceI] + nuw[faceI])
*magGradUw[faceI]
*Cmu25*sqrt(k[faceCellI])
/(kappa_*y[faceI]);
}
else
{
G[faceCellI] = 0.0;
}
}

Conclusion would be next. If you use kOmegaSST model, you are able to have even y+ < 1. Basically, if your y+ < 5 or y+ > 20, you are in safe zone and you should not have a problem with your simulation. A region where 5 < y+ < 20 is also safe to run (although some have doubts about that. Find this article if you need more information about this topic -> Ten years of the industrial experience with the SST turbulence model; F.R.Menter, M. Kuntz, R.Langtry).

So my advice to you would be: if your simulation is converged, and results are physical, everything should be fine.

Hope this post helps you. If something is still not clear, feel free to ask and I'll try to answer.

Best regards!

[Gerrit]

Hi thank you very much for your answer! Took me some time to read stuff about the boundary layer and the turbulence models. My models converge and give reasonable results (at least in my opinion). About y+ between 5 and 20: Isn't it not recommended to have these values as the log law not valid there jet and the dimensionless velocity is not equal to y+ any more?


Best and thank you very much again!

Gerrit

[camel]

Hi Gerrit,

I am happy to hear my answer helps you!

Regarding y+ between 5 and 20: It is correct that in this region log law is not valid. But as I already said, some authors say that wall function can be normally applied even in this region (but check your results at the end). If you can avoid this area of y+ values in your simulation, this would be the safest option.

Wish you all best with your research!