Energy equation - where is the turbulent kinetic energy?

usv001 · June 24, 2016, 13:04

Greetings everyone,

In the derivation of the Favre-averaged energy equation, the total energy comprises of the internal energy, mean kinetic energy and turbulent kinetic energy:

$\overline{\rho} \widetilde{e_{tot}} = \bar{\rho}\tilde{e} + \frac{1}{2}\bar{\rho}\tilde{u_i}\tilde{u_i} + \overline{\frac{1}{2}\rho u_i^{''}u_i^{''}}$ (See Chapter 5.3 of Turbulence Modelling for CFD by Wilcox for derivation)

But the compressible flow solvers do not include the turbulent kinetic energy term (k) in the energy equation. Similarly, a few terms on the RHS of the energy equation are also missing.

Does any know why this is the case?

Thanks for all the help!

C. Okubo · January 25, 2022, 16:04

Hi!

Old topic, but maybe this still helps somebody.

With respect to the doubt, the link below comments a little about the terms being neglected.

https://openfoamwiki.net/index.php/RhoSimpleFoam

If I understood correctly, the reason "is to have the same equation whether one solves for e or h".

I don't know about when this simplifications are OK and when they can cause problems, but I would guess that they may be acceptable for the flow regimes rhoSimpleFoam is intended to solve.

Also, it is not hard to modify the code and test it.

Hope this helps.

June 24, 2016, 13:04	Energy equation - where is the turbulent kinetic energy?	#1
usv001 Senior Member Join Date: Sep 2015 Location: Singapore Posts: 102 Rep Power: 11	Greetings everyone, In the derivation of the Favre-averaged energy equation, the total energy comprises of the internal energy, mean kinetic energy and turbulent kinetic energy: $\overline{\rho} \widetilde{e_{tot}} = \bar{\rho}\tilde{e} + \frac{1}{2}\bar{\rho}\tilde{u_i}\tilde{u_i} + \overline{\frac{1}{2}\rho u_i^{''}u_i^{''}}$ (See Chapter 5.3 of Turbulence Modelling for CFD by Wilcox for derivation) But the compressible flow solvers do not include the turbulent kinetic energy term (k) in the energy equation. Similarly, a few terms on the RHS of the energy equation are also missing. Does any know why this is the case? Thanks for all the help! C. Okubo likes this.

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January 25, 2022, 16:04		#2
C. Okubo New Member Join Date: Jan 2017 Posts: 22 Rep Power: 9	Hi! Old topic, but maybe this still helps somebody. With respect to the doubt, the link below comments a little about the terms being neglected. https://openfoamwiki.net/index.php/RhoSimpleFoam If I understood correctly, the reason "is to have the same equation whether one solves for e or h". I don't know about when this simplifications are OK and when they can cause problems, but I would guess that they may be acceptable for the flow regimes rhoSimpleFoam is intended to solve. Also, it is not hard to modify the code and test it. Hope this helps.