Number of equation by using eddy viscosity turbulence models

LuckyTran · August 3, 2019, 04:15

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.

bumper · August 3, 2019, 05:04

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 ?

FMDenaro · August 3, 2019, 05:38

Quote:

Originally Posted by bumper

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 ?

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

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August 3, 2019, 04:15		#21
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,675 Rep Power: 66	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.

August 3, 2019, 05:04		#22
bumper New Member Join Date: May 2019 Posts: 18 Rep Power: 6	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 ?