Two equation turbulence models
Two-equation turbulence models are one of the most common type of turbulence models. Models like the k-epsilon model and the k-omega model have become industry standard models and are commonly used for most type of engineering problems. Two-equation turbulence models are also very much still an active area of research and new refined two-equation models are still being developed.
By definition, two-equation models include two extra transport equations to represent the turbulent properties of the flow. Most often one of the transported variables is the turbulent kinetic energy, . The second transported variable varies depending on what type of two-equation model it is. Common choices are the turbulent dissipation, , or the specific dissipation, . The second variable can be thought of as the variable that determines the scale of the turbulence (length-scale or time-scale), whereas the first variable, , determines the energy in the turbulence.
The basis for all two-equation models is the Boussinesq eddy viscosity assumption, which postulates that the Reynolds stress tensor, , is proportional to the mean strain rate tensor, , and can be written in the following way:
Where is a scalar property called the eddy viscosity. The same equation can be written more explicitly as: