Zero-Equation Eddy Viscosity Models

Mixing-Length Model

The Prandtl mixing-length model for Reynolds-averaged Navier-Stokes (RANS) is based on the assumption that turbulent eddies can be expressed in terms of a product of a velocity scale and a length scale. It has the advantages of fast computation and relatively accurate prediction for simple two-dimensional flows.

However, there exists a limitation in predicting turbulent flows where the turbulent length scale varies (for example, separation or circulation). Currently, the applications of mixing-length models are hardly adopted in commercial CFD codes, but are usually employed to describe near wall behaviors such as wall boundary treatments for more complex turbulence models.

Kinematic Eddy Viscosity

The kinematic eddy viscosity for the mixing-length model is computed using the following relationship (1)

ν_{t} = l_{m}^{2} | \frac{\partial \bar{u}}{\partial y} |

where $l_{m}$ is the mixing-length and $\frac{\partial \bar{u}}{\partial y}$ is the mean velocity gradient.