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Old   November 24, 2005, 10:04
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  #1
beginner
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hi all, this may be a really simple question but if i favre average the navier stokes equations, i get favre-averaged 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?

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Old   November 24, 2005, 16:30
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Jonas Larsson
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I wrote a fairly comprehensive article on favre averaging for the CFD-Wiki recently. You can find it here:

http://www.cfd-online.com/Wiki/Favre...okes_equations

I think that the article quite clealy illustrates why the pressure becomes time-averaged whereas other variables are Favre averaged (or density weighted averaged).
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Old   November 26, 2005, 14:34
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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 time-averaged. 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?
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Old   November 26, 2005, 17:31
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Jonas Larsson
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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 density-weighted average of properties like velocity, total energy, heat-flux etc. and a normal average of the pressure. It all follows from the way the original non-averaged 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.
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Old   November 27, 2005, 07:36
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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?
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Old   November 28, 2005, 04:38
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Jonas Larsson
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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.
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Old   November 28, 2005, 17:48
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Thanks!
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