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:
- $k-\epsilon$ models
- $k-\omega$ models
- Mixing Length models
- Spalart-Allmaras models
- 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).