## The Turbulence Model Can Make a Big Difference in Your Results

Turbulence models are necessary because we cannot afford big enough computers to directly capture every scale of motion. Also, users of CFD typically want a steady-state solution (with all the unsteady fluctuations averaged out) rather than a detailed time-accurate one that captures every little vortex. As a result, there are unsteady (turbulent) motions affecting the flow that cannot be resolved directly; they must therefore be modeled.

In some cases, the turbulence model you use can have a huge effect on the results you obtain from CFD.

This kind of disparity is largely due to the fact that no model is right all the time; they all have their limitations. Because of this, there are dozens (if not hundreds) of variations available, and more are being developed all the time.

If all these choices have you confused, then read on. This page will provide a brief overview of the major classes of steady-state turbulence models. Related pages provide further comparisons of how different models affect a solution, and a few guidelines to help you choose from among them.

## Families of Turbulence Models

Turbulence models are generally classified according to which governing equations they apply to (e.g. Reynolds-averaged Navier-Stokes or Large Eddy Simulation equations). Within these broader categories, they are further broken down by the number of additional transport equations which one must solve in order to compute the model contributions.

I will focus on models for the Reynolds-averaged Navier-Stokes (RANS) equations here, because these are the models that will be used for most production applications. I will also limit the discussion to steady-state situations. Unsteady modeling is a topic for another page.

Algebraic (Zero-Equation) Models

The simplest (and least computationally expensive) models are the algebraic models. These are also called “zero-equation” models, because they do not solve an additional transport equation in order to predict the contributions of the turbulence. These models are not very general, so they are not used much anymore, but when they can be applied, they often give very good results.

One-Equation Models

One level up in the turbulence modeling hierarchy are the one-equation models. These solve a single transport equation for a quantity which is used to obtain the turbulent viscosity.

Currently, the most popular one-equation model is the Spalart-Allmaras model. This model has been shown to give acceptable results for a wide variety of situations and is known for its stability. Other one-equation models that are available in production codes include the Baldwin-Barth model and the Goldberg pointwise model.

An advantage of the Goldberg model is that is does not require the calculation of the distance from each field point to the nearest wall. This makes it easier to implement than many other models. On the other hand, its results are often not as good as from the Spalart model (which does require a wall distance calculation).

Two-Equation Models

As their name implies, these models require the solution of two additional governing equations in order to compute the contributions of turbulence to the mean flow. Along with the Spalart-Allmaras model, two-equation models make up the bulk of the turbulence models used for production CFD. Two of the most common models are the Menter SST model and the k-epsilon model, but there are many others (too numerous to mention).

The SST model is a blend of a k-omega model, which is used near walls, and a k-epsilon model, which is used in regions far from walls. This model is fairly robust and generally does a good job near solid boundaries. It also is often found to do a better job at capturing recirculation regions than other models.

The k-epsilon model would more properly be called a family of models. Specialized version have been developed for so many specific flow configurations that there are now almost as many different k-epsilon models as there are CFD practitioners trying to use them. Some of the more common variants include the Jones-Launder, Chien, and RNG k-epsilon models.

A side note: You may have been confused, like I was, to read about "low Reynolds number" models applied to obviously high Reynolds number situations. The "low Reynolds number" designation means that the model can be used throughout boundary layers and beyond. A model that is not "low Reynolds number" requires additional wall functions in order to correctly handle the effect of viscous walls.

More Exotic RANS Models

More recently, as greater computer resources have become available, there has been a renewed effort to look at modeling the Reynolds stresses directly instead of reducing the all effects of turbulent eddies to a turbulent viscosity term. As a result, there are now several variations of Reynolds stress models and algebraic stress models available in major CFD codes.

These models are often quite computationally expensive, compared to a conventional one- or two-equation model, but under the right flow conditions, they have been shown to provide improved results.