3.2.8. Inlet Conditions for Turbulence Quantities

3.2.8.1. Turbulent Kinetic Energy

The inlet turbulent kinetic energy must be specified for any simulation that involves a velocity-specified inlet. If actual values of the inlet turbulent kinetic energy are not available, then a suitable value based on basic definitions is used. In general, the kinetic energy associated with the turbulent flow is defined by,

(3.232) $k = {1 \over 2} \left(\overline{ u'^2} + \overline{v'^2} + \overline{w'^2} \right) .$

The turbulence intensity $T_i$ , is related to the kinetic energy by,

(3.233) $T_i = { { \left({2 \over 3} k\right)^{1/2} } \over {U_{ref}} } .$

Rearranging (3.233) for the turbulent kinetic energy yields a working form for the specification of inlet turbulent kinetic energy based on a reference velocity, $U_{ref}$ ,

(3.234) $k = {{3} \over {2}}\left(U_{ref} T_{in} \right)^2 .$

The value of $U_{ref}$ can typically be taken to be the magnitude of the velocity.

3.2.8.2. Turbulence Dissipation Rate

As with the turbulent kinetic energy inlet condition for specified velocity, the inlet value of the turbulence dissipation rate must also be specified. If values are known, for instance based on experimental data, then the available data should be used. Otherwise, the following assumed form of the turbulence dissipation rate is used,

(3.235) $\epsilon = C_{\mu}^{3/4} {{k^{3/2}} \over {l}} ,$

where $l = 0.07L$ ; $L$ represents a characteristic length scale of an inlet eddy and $k$ represents the inlet turbulent kinetic energy as determined above.