Turbulence Models

Turbulence:
Due to the high degree of mixing, turbulent flow exists. The heat and mass transfer rates are high and can not be explained by molecular transport only. It was seen as a random process in attempt to be specified in statistical parameters. Yet, it is not completely random.

Turbulence is normally expressed in terms of velocity. So there are extras terms in N-S equations, called Reynolds stress, described in terms of turbulence viscosity. This eddy viscosity is a strong function of the distance from the wall, where the eddy diminishes.

In turbulent flow, the kinetic energy imparted to the flow is dissipated into smaller eddies, and finally all the energy dissipated as thermal energy. Two sets of equations in CFD simulation are added to address the conservation of turbulence kinetic energy, $k$, and the turbulent energy dissipation rate, $\varepsilon$.

Prandtl Mixing Length:
When two eddies come closer, they are mixed. The mean distance between eddies is called the "mixing length", which analogous to the mean-free path in gases. The mixing length is a function of distance to the wall.