Dear all,

I just want to add some information related to the topic. For all who are interested in turbulence modeling in more details should understand what we are doing here and hence it is necessary to understand the general equations first. The main literature that I used in that topic of turbulence modeling are [Ferziger] [Wilcox] and [Bird]. Of course there are plenty of literatures. A summary of the literature that I am using can be found on http://holzmann-cfd.de/index.php/en/literature

In the link you also find the ISBN numbers and titles of the books (maybe you have them already in your library). If you do not want to spend to much time on all the books, you also can use my publication about » Mathematics, Numerics, Derivations and OpenFOAM « that is published on my webspace or on researchgate.

Now I want to give you a brief overview, without going to deep into detail (turbulence modeling is a taff topic)

**LAMINAR**

If we use laminar, the equations are valid for each kind of flow (yes - even turbulent flows). The fact is simple, laminar will solve the general Navier-Stokes equations without any need of modeling. Hence we get natural vortexes and if we make the mesh fine enough, we can resolve the turbulence in all the beauty (DNS). **But** using laminar in turbulent flow fields will lead to extreme fine meshes to resolve the so called Kolmogorov vortexes. The fact that this is never possible for complex geometries, we only use the laminar mode for LAMINAR flow fields. If we have turbulent flow, we need to simplify things.

**RANS Models**

As already mentioned, resolving the turbulence means to resolve the smallest vortexes that lead to extreme fine meshes and therefore the time step will also decrease dramatically. Thus, we introduce the so called Reynolds time-averaging method that will lead to the **R**eynolds-**A**veraged-**N**avier-**S**tokes equations. The complete derivation of these equations can be found in my publications. Deriving the RANS equations lead to unknown terms that have to be expressed with already known quantities. Hence, we introduce some hypothesis to express the unknown with other quantities that finally lead to the already known turbulence models. In the turbulence models we have a lot of approximations and assumptions. If you check out the derivations of the equations you will get a feeling how many terms are approximated and then you get a feeling that turbulence modeling is always a big assumption.

I do not want to go too deep into detail, but there are differences between compressible and incompressible RANS equations.

- For the incompressible equations we always get the mean Reynolds averaged quantities U, p, k, epsilon, T etc. (further more, the pressure p is not the real pressure, here we get an addition kinematic pressure)
- For the compressible equations the derivation is even more complex, hence we introduce the Favre-weighted Reynolds time-averaging method. The results are the mean Favre averaged quantities U, p, k, epsilon, T etc.
**Note** that the Favre-Averaging concept is correct only in a mathematical point of view, but not in the physical point of view.

This models are mostly based on the assumption of isotropic turbulence, that is not always true, especially if we are talking about turbulence near walls or after some rigid body etc. .

**LES Models**

LES models are similar to RANS models but here, instead of averaging the whole flow, we resolve the big vortex scales of the turbulence and model the smallest turbulence scales. This is a much better approach because if we go to smaller and smaller scales, the isotropic assumption is valid in much cases. Hence, we get a better physical approach for the turbulence.

**What happen to the equations if we use turbulence models**

Luckily nothing special due to the fact that we make the Reynolds and Favre averaging in a way that we end up with the (more or less) same equations as we have it for the general flow field. The only important thing is, that we assume a higher viscosity (based on the turbulence), that lead to higher diffusion of momentum, concentration, temperature, enthalpy etc. . The molecular viscosity is increased by this special amount of turbulent viscosity that is also known as eddy viscosity. The turbulence models are simply calculating the eddy viscosity.

**Which model should be used**

That depends on the problem you are focusing on. You will realize that if you use two different turbulence models with the same settings, you will end up with two different solution. As I already mentioned, most models are based on the isotropic turbulence (energy cascade). If you are interested in regions near the surface you should choose a model that has some corrections for the near wall field or even uses an anisotropic hypothesis. If you know that your turbulence is really directed only in two directions (if we assume a 3D flow), you should also use a turbulence model that is not based on the isotropic assumption (there was a nice demonstration video but I could not find it now).

Of course, the more complex the models get, the more effort has to be done to calculate the stuff.

In a very general way we can say for the three simplest models:

- k-epsilon for far fields
- k-omega for near fields
- k-Omega-SST is the combination of both, it switches between them using the dimensionless y+ distance to the wall

I did not check the source code of FOAM for the last arguments but it should be somehow like that. Why is it like that? Its simple, the dissipation of the turbulent kinetic energy field epsilon can be calculated very well in the far field whereas close to the walls it will calculate to high turbulence. Here it is better to use the frequency omega.

Hopefully this can help you to get the first overview of turbulence modeling.