# Turbulence modelling

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 November 28, 2009, 19:02 Turbulence modelling #1 New Member   Kluni Join Date: Nov 2009 Posts: 4 Rep Power: 10 Hello everyone, I am a German student and have to make a simulation in turbulent flow. So far no problem. But I am asking me, how CFX is modelling this turbulent flow. I just don't want to use CFX without knowing what I am doing. We use the SST model and I am trying to understand the standard k-epsilon model. I understood the derivation of the k-turbulence energy in the transport equation. However the second equation, of the dissipation, where does it come from? I know Jones und Launder made this equation, but how? Is there a good book, where these things are written down? I also tried to search for the paper of Jones und Launder, but couldn't find it. I just want a better understanding in the SST modelling. Thanks in advance for eny help. Lot of greetings, Kluni

 November 28, 2009, 21:45 #2 Senior Member   N/A Join Date: Mar 2009 Posts: 189 Rep Power: 10 The epsilon equation is one of the biggest concern when using the RANS models. The dissipation equations are mostly empirical in nature. For further details refer to the book of Wilcox on turbulence modeling.

 December 1, 2009, 04:51 #3 Senior Member   karine Join Date: Nov 2009 Posts: 158 Rep Power: 10 The equation of epsilon is just derived to have the same form than the k equation...the destruction term is modeled in a manner to handdle big k variations...... It is a bit wierd to invent an equation like that....but it gives good results anyway

December 1, 2009, 11:05
#4
Senior Member

andy
Join Date: May 2009
Posts: 130
Rep Power: 10
Quote:
 Originally Posted by kluni I understood the derivation of the k-turbulence energy in the transport equation. However the second equation, of the dissipation, where does it come from?
It is derived in exactly the same way as the k equation:
- write down the exact transport equation for epsilon
- provide models for the terms involving unknown quantities in terms of known quantities and empirical coefficients
- determine the empirical coefficients from measurements

Quote:
 Originally Posted by kluni Is there a good book, where these things are written down?
Pretty much any course or book involving turbulence modelling for engineering CFD will discuss it because it is the simplest most commonly used general turbulence model.

 December 1, 2009, 14:29 #5 Senior Member   karine Join Date: Nov 2009 Posts: 158 Rep Power: 10 hi how can u derive the epsilon equation from NS? Regards

 December 1, 2009, 14:54 #6 Senior Member   N/A Join Date: Mar 2009 Posts: 189 Rep Power: 10 The book of Wilcox provides detailed information on deriving the epsilon equation from the Navier-Stokes equations. The general idea is to multiply the Navier-Stokes equation with gradients of uprime and perform a considerable amount of algebra to obtain the equation for dissipation.

 December 1, 2009, 17:46 #7 Senior Member   karine Join Date: Nov 2009 Posts: 158 Rep Power: 10 ah ok thank you

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