Hi,

Could someone please explain to me Favre filtering as applied to LES. In the Navier-Stokes equations, the Favre filtered quanties are used as well as standard filtered quantities. How is the "average density" as used in compressible Favre-filtered problems found? It seems to be used as part of the calculation rather than an instantaneous value of density. Can someone explain this to me, or else give me a reference.

Thanking you all most kindly.

In LES, the most used filter are tophat filter, Gaussian filter.

I also wish someone can explain what is Favre filtering

If I remember correctly, the Favre averaged density is used in RANS (Reynolds averaged N-S), again it is not LES at all.

Hi,

We have BOTH "Favre filtering" for LES and "Favre averaging" for RANS, although "Favre averaging" is more known. For compressible flows, use of the conventional Reynolds- or time- averaging (that are widely used for incompressible flows) is cumbersome. Alternatively, a density-weighted (or mass-wighted) average (or filter for LES) may be used. For a dependent variable "f", the Favre average is defined as (We denote the RANS Reynolds average of any variable or its LES filtered value with _BAR symbol and Favre average with _HAT):

f_HAT = (rho*f)_BAR / rho_BAR

where the "overbar" will represent either a FILTERING PROCESS used in "LES" or an AVERAGING PROCESS used in "RANS" approach.

Unlike "hall"'s opinion, I believe that it can be used in both RANS and LES.

More refernces on this subject:

1) Wilcox, D.C., Turbulence modeling for CFD, DCW Ind., 1993.

2) Chen, C.J., and Jaw, S.Y., Fundamentals of Turbulence Modeling, Taylor & francis, 1998.

3) Metais, O. and Ferziger, J., (eds.) "New Tools in Turbulence Modeling", les editions de physique, Springer, 1997.

Hi,

Similar to Favre average that is a convenient way to reduce the complexity level of the RANS compressible equations, density-weighted (Favre) filtering allows to simplify the filtered compressible NS equations used in LES : the number of unknown terms to model in the momentum and energy equations is then greatly reduced.

By the way, have a look at the original O. Reynolds (1894) article : the ensemble average he defined is already a density-weighted one.

Best regards.

Hi there,

Thanks guys. Is the Original paper available online?

Also, in LES, if using Favre-filter, how do I take this into account in the discretised equations? I know what the Favre-filtered N-S equations look like, but when I discretize them, how do I use the Favre filtered values? What is different in the discretized equation apart from a reduction in complexity?

Hi

Unfortunately, I haven't find copy of Reynold's paper online.

Concerning the way to treat the Favre filtered equations, you have first to choose the form for the fifth equation (total energy, enthalpy, computable energy, ..., see for instance Vreman et al. 1995, J. Engineering Math, 29, pp.299-327"), because it affects the form of the subgrid terms that have to be modeled. The discretization of the selected set of equations is standard.

Then, there are two possibilities:

1- you assume implicit filtering (i.e. grid filtering). If you choose a SGS model that doesn't require a second level filter with a higher filter-width (for instance Smagorinsky), there is nothing to do. Otherwise (dynamic models, scale-similarity models), you have to select direct filtering or density-weighted filtering for the test filter. According to my knowledge, almost everybody use direct filtering.

2- you use explicit filtering, i.e. you filter the results from the numerical scheme for each timestep. In my opinion, you can be hold as a ``purist'', so I think you have to choose density-weighted filtering for consistency. If a test filter is required for the SGS model, again use density-weighted filtering.

You may also consider Approximate Deconvolution Models for compressible flows : see for instance N. Adams and S. Stolz papers (Ph .Fluids 13(10), pp 2895-3001,2001, among others)

Hope this help a little bit.

Best regard