What's the source term in this turbulent momentum equation?
 

Hello

Could anyone correct me the source term in the momentum equation of a turbulent flow (the turbulence model used is K epsilon ).
You can see the equation in the attached file (doc) .

Regards

Hi,

The First Equation seems to be close to a form that I have encountered in the past - The Cartesian Tensor form. Basically this is the time-averaged momentum equation and the first term on the left, may be written as d/dx_j(u_i u_j)\bar. The pressure gradient is driving the flow (RHS 1st term) and the 2nd RHS term is diffusion term, since it is the 2nd Order Laplacian with the kinematic viscosity. This is also grouped with the Reynolds Stress terms u_i\bar u_j\bar. Hence, the source term is the last group of variables g_i \beta (T\bar - T_0), which appears to be driven by the temperature gradient relative to the mean?...

Please confirm whether you are clear and satisfied with the response.

Crank-Shaft

These are RANS equations, for which you solve a statistically steady equation. Any term to be modelled comes from the convective flux. In general for a convective flux (V Phi) you write:

<(V Phi)> = <(<V> + V') (<Phi> + Phi')> = <V><Phi> + <V'Phi'>

This decomposition is valid for any transport equation, hence you can easy check that you model the term <V'Phi'>. Note that is not exact that you have a source term, it is an additional flux acted by the diverge operator