# RANS equations for compressible flows

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 November 25, 2010, 17:53 RANS equations for compressible flows #1 Senior Member   Stuart Join Date: Jul 2009 Location: Portsmouth, England Posts: 488 Rep Power: 15 Hi, The CFX User Guide gives details on how the RANS equations are obtained using time-averaged reynolds decomposition. But I've read that for compressible flows mass-weighted (aka Favre) averaging is used as a step after the reynolds decomposition (http://www.cfd-online.com/Wiki/Favre...okes_equations). Does CFX use the Favre averged Navier-Stokes equations instead of the RANS or perhaps they are used depending upon the Mach number? I cannot find any information about if they are used in the User Guide and I need to put a explanation and derivation of which ever CFX (and by extension me) is using for my transonic external aerodynamics simulations. Thanks.

 November 27, 2010, 05:32 #2 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 12,832 Rep Power: 100 Yes, CFX uses the Fauve averaged equations for compressible flows. I am pretty sure that is in the documentation somewhere.

 December 9, 2010, 10:38 #3 Senior Member   Stuart Join Date: Jul 2009 Location: Portsmouth, England Posts: 488 Rep Power: 15 Thanks Glenn. Now found that it says on page 54 of the CFX-Solver Theory Guide: "For compressible flows, the averaging is actually weighted by density (Favre-averaged), but for simplicity, the following presentation assumes that density fluctuations are negligible." So I guess that be selecting a compressible fluid (Air Ideal Gas and Total Energy) CFX uses the Favre-averaging formulations. The CFX Theory Guide also shows that the RANS energy equation has 2 extra terms: reynolds stress tensor and a turbulence flux term on the right hand side and a turbulent kinetic energy term on the left hand side. Since we can switch ON/OFF the viscous work term which contains the reynolds stresses which terms (if any) does CFX omit from the Favre-averaged energy equation? The Favre-averaged energy equation has extra terms in it due to the avergaing process: molecular diffusion, turbulent transport of heat and turbulent transport of turbulent kinetc energy (see Wilcox's book on Turbulence Modeling in CFD for the full equation). So what I'd really like to know is: when using a compressible flow what actual terms in the equation is CFX solving and what is it omitting? Thanks.

 December 9, 2010, 17:53 #4 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 12,832 Rep Power: 100 I suspect the extra terms from Fauve averaging are ignored in CFX but I am not sure. You would have to ask CFX support for further details.

 December 18, 2010, 13:21 #5 Senior Member   Stuart Join Date: Jul 2009 Location: Portsmouth, England Posts: 488 Rep Power: 15 Hi, I need some more help with the Favre averaged equations. I've put a post on the main board as they are not CFX specific, see the link: Favre averaged Navier-Stokes equations help but I've also posted here as it's linked to this request and some people might not see it otherwise. Thanks

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