Openfoam nut and k_sgs equation

EnigmaFluids · July 10, 2020, 16:11

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

$\nu_t=C_k\Delta\sqrt{k_{sgs}}$

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

$\frac{k_{resolved}}{k_{resolved}+k_{sgs}}$

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

Tibo99 · July 11, 2020, 21:25

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.

superkelle · July 14, 2020, 16:46

Maybe this helps:

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

EnigmaFluids · July 17, 2020, 17:07

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

$\nu_t=c_k\Delta\sqrt{k_{sgs}}$

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.

Tibo99 · July 21, 2020, 18:13

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

July 10, 2020, 16:11	Openfoam nut and k_sgs equation	#1
EnigmaFluids New Member Graham Join Date: Nov 2017 Posts: 5 Rep Power: 9	Greetings, I have noticed while completing LES that openfoam uses the equation $\nu_t=C_k\Delta\sqrt{k_{sgs}}$ 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 $\frac{k_{resolved}}{k_{resolved}+k_{sgs}}$ So once again, where does this equation come from? Thanks!

July 11, 2020, 21:25		#2
Tibo99 Senior Member René Thibault Join Date: Dec 2019 Location: Canada Posts: 114 Rep Power: 6	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.

July 14, 2020, 16:46		#3
superkelle Member alexander thierfelder Join Date: Dec 2019 Posts: 71 Rep Power: 6	Maybe this helps: https://caefn.com/openfoam/wale-sgs-model

July 17, 2020, 17:07		#4
EnigmaFluids New Member Graham Join Date: Nov 2017 Posts: 5 Rep Power: 9	The actual WALE model as originally written does not use a relationship between nut and k. However, I believe that Openfoam uses the equation $\nu_t=c_k\Delta\sqrt{k_{sgs}}$ 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.

July 21, 2020, 18:13		#5
Tibo99 Senior Member René Thibault Join Date: Dec 2019 Location: Canada Posts: 114 Rep Power: 6	That being said, it's a calculation? And not use for resolving the turbulence model?