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November 24, 2005, 10:04 
Favre Average

#1 
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hi all, this may be a really simple question but if i favre average the navier stokes equations, i get favreaveraged terms for momentum etc, but why does the pressure remain just normal averged.
sorry if this is simple but think it is to do with my lack of understanding of what a favre average actually is. any comments? 

November 24, 2005, 16:30 
Re: Favre Average

#2 
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I wrote a fairly comprehensive article on favre averaging for the CFDWiki recently. You can find it here:
http://www.cfdonline.com/Wiki/Favre...okes_equations I think that the article quite clealy illustrates why the pressure becomes timeaveraged whereas other variables are Favre averaged (or density weighted averaged). 

November 26, 2005, 14:34 
Re: Favre Average

#3 
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"In order to obtain an averaged form of the governing equations, the instantaneous continuity equation (1), momentum equation (2) and energy equation (3) are timeaveraged. Introducing a density weighted time average decomposition (11) of ui and e0, and a standard time average decomposition (10) of ρ and p gives the following exact open equations."
So does that mean the Favre averaged equations have p as a standard time avaeraged quantity? I am slightly confused. Is the reason for this that the pressure and density are so closely coupled, that the standard average of thed ensity applies to the pressure? 

November 26, 2005, 17:31 
Re: Favre Average

#4 
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The Favre averaged equations are derived using a normal averaging of the governing equations. As the Wiki page explains this naturally produces a densityweighted average of properties like velocity, total energy, heatflux etc. and a normal average of the pressure. It all follows from the way the original nonaveraged equations look. Try to write it down yourself starting from the governing instantaneous equations as shown in the Wiki and you'll see how it works out.


November 27, 2005, 07:36 
Re: Favre Average

#5 
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"Introducing a density weighted time average decomposition (11) of ui and e0, and a standard time average decomposition (10) of ρ and p gives the following exact open equations."
If you have 'introduced' Favre averaging for the ui field, and normal averaging for the p and rho field, I don't see how this 'naturally' shows anything??? Surely it all just depends on your original choice? 

November 28, 2005, 04:38 
Re: Favre Average

#6 
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The choice of averaging follow naturally from the governing equations. The pressure term in the governing equations is not multiplied by density and hence will only produce a normal average, whereas for example the momentum/velocity term is multuplied by density and wil produce a density weighted average.


November 28, 2005, 17:48 
Re: Favre Average

#7 
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Thanks!


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