How do I select an appropriate turbulence model?

Question

Turbulent flow involves extremely small scale fluctuations which are usually too small to resolve by using the Navier-Stokes equations directly. To overcome this, we model each transient variable $\Phi$ (e.g. velocity, pressure, etc...) as the sum of a time average quantity $\bar{\Phi}$ and some small fluctuation. By introducing both of these new variables into the navier stokes equations, we obtain more unknowns than equations. In order to obtain a unique solution, we need to introduce a turbulence model which consists of at least one additional equation.

There are a number of different turbulence models developed from the Boussinesq Hypothesis, which roughly says that the Reynolds stresses are proportional to the mean rate of deformation by way of the so-called "turbulent viscosity". The different turbulence models vary by how they estimate the turbulent viscosity. Models of this type include, but are not limited to:

1. $k-\epsilon$ models
2. $k-\omega$ models
3. Mixing Length models
4. Spalart-Allmaras models
5. Reynolds Stress models

With such a wide selection of turbulence models, it can be difficult to assess which model is appropriate for each modeling situation. I understand that with infinitely many potential simulation needs, there is no one-size-fits-all answer. But, are there any general guidelines on how to select an appropriate turbulence model? What factors should I consider when selecting a model? What kinds of problems are known to be effective for the models listed above?

While I'm mostly interested in the time-averaged turbulence models, I also welcome responses for spatially-averaged models (e.g. Large Eddy Simulation models).

Answer 1

Disclaimer: As you requested general guidelines here they are. After having a converged solution, you need to investigate it thoroughly and look for clues that the choice of the turbulence model altered the flow in an un-physical way.

My Rules of Thumb for Turbulence Models

1. The more additional transport equations you solve:

   • the more possibilities exists to make errors (e.g. wrong assumptions)
   • the better the capabilities of the simulation are to capture the physics involved

Usually mixing length models have ONE additional transport equation, k−ϵ and k−ω have TWO and Reynolds Stress models have SEVEN.
The Spalart-Allmaras model is a highly tuned model and has only one additional transport equation. It was tuned for flight regimens (Reynolds and Mach number) of airplanes. The application in other fields might result in bigger errors.

2. k−ϵ models
   

The k-ϵ-Model is commonly optimised for external flow (around bodies)

3. k−ω models
   

The k−ω-Model is commonly optimised for internal flows (inside pipes, close to walls)

4. Mixing Length models
   

Are very very basic and will only produce meaningful results when the turbulence modelling was not necessary in the first place.

5. Spalart-Allmaras models
   

Are very robust, fast and widely tested. Additional testing is required when not applied in their actual scope (flow around airplanes)

6. Reynolds Stress models
   

Cutting Edge Models need a lot of computational power and are not as robust.