4.9.6 Modeling the Turbulence Kinetic Energy

In general, when the turbulence kinetic energy is needed for modeling a specific term, it is obtained by taking the trace of the Reynolds stress tensor:

As described in Section  4.9.9, an option is available in ANSYS FLUENT to solve a transport equation for the turbulence kinetic energy in order to obtain boundary conditions for the Reynolds stresses. In this case, the following model equation is used:

where $\sigma_k = 0.82$ and $S_k$ is a user-defined source term. Equation  4.9-28 is obtainable by contracting the modeled equation for the Reynolds stresses (Equation  4.9-1). As one might expect, it is essentially identical to Equation  4.4-1 used in the standard $k$- $\epsilon$ model.

Although Equation  4.9-28 is solved globally throughout the flow domain, the values of $k$ obtained are used only for boundary conditions. In every other case, $k$ is obtained from Equation  4.9-27. This is a minor point, however, since the values of $k$ obtained with either method should be very similar.