CFD Online Discussion Forums - Number of equation by using eddy viscosity turbulence models

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The first is the definition of the turbulent kinetic energy k.
$k = \frac{1}{2} \overline{u_i' u_i'} = \frac{1}{2} \left(\overline{u_x'^{2}} + \overline{u_y'^{2}} + \overline{u_z'^{2}} \right) = \frac{3}{2} \overline{u'^{2}}$

The second is a relation between k, epsilon, and the turbulent length scale (a pseudo definition).
$\varepsilon=\frac{k^{3/2}}{l}$

Note that a new unknown (the turbulent length scale) is introduced.

Neither will directly help you determine k or epsilon nor the turbulent viscosity. You still solve transport equations for k and epsilon. Keep in mind the purpose of the turbulence model is not really about k or epsilon (or any fancy variables you can think of), but to get you the turbulent viscosity.

The main aim is the tubulent viscosity, that's clear.

But for what do i need the equations above? You don't do any definitions or equations just for fun. Are they for the calculation of initial values ?

Quote:

Originally Posted by bumper (Post 740951)

The hystorical turbulence model starts with a single relation without adding further PDE. Then, people tried to add more equations to the original model with the goal to obtain a more physical representation of the model.
I remember some RANS formulation with dozens of supplied equations.....
Have a reading to the Wilcox's textbook