Openfoam nut and k_sgs equation
 

Greetings, I have noticed while completing LES that openfoam uses the equation



or if you check WALE.C

this->nut_ = Ck_*this->delta()*sqrt(this->k(fvc::grad(this->U_)));

but where does this equation come from? I have been reading the original smagorinsky model and also WALE model papers, but I don't see it contained there. I am looking for a literature source because I want to know if this k_sgs is actually a physical quantity or just an intermediate calculation on the way to get nut.

For example, in the original WALE paper by Nicoud and Ducros (1999), we notice that the model gives nut alone and not k_sgs. However, I assume that openfoam calculates k_sgs first and then nut after, for coding convenience. I would like to know whether the openfoam k_sgs is a real quantity so I can estimate whether 80% of the turbulence kinetic energy is being resolved in my field via



So once again, where does this equation come from? Thanks!

That is a good question.

As I expect to use the WALE model in the near future, I would be interested to know the answer also.

Maybe this helps:

https://caefn.com/openfoam/wale-sgs-model

The actual WALE model as originally written does not use a relationship between nut and k. However, I believe that Openfoam uses the equation



for coding convenience.

I believe that this is from the so-called One-equation TKE model. Specifically read section 3.4 of https://link.springer.com/content/pd...016-9751-4.pdf

This paper references Bardina et. al. (1980) where a similar equation is found in Table 3 and Equation 15

This is all to say that once again, the WALE model does not use said equation, but rather I believe Openfoam has implemented it as a convenient way to get both k_sgs and nut during runtime. From this conclusion, I assume then that we inherit all the assumptions of the one-equation turbulence model if we are using the openfoam nut field to recover k_sgs. This is important since I am comparing k_sgs with a calculated k_resolved from the instantaneous fluctuations to determine how if 80% of the TKE is being resolved.

That being said, it's a calculation? And not use for resolving the turbulence model?