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LES Compressible Smagorinsky Model

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Old   January 29, 2013, 16:40
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Quote:
Originally Posted by gregor View Post
Hi H

take Eq. 5 and divide it by k^(1/2) and you get:

- c_B*rho*k*Delta^(-1) = 2/3 rho*k^(1/2)*trace(D)-2*c_k*Delta*D^2

now substitute k by k=K^2, this yields

- c_B*rho*K^2*Delta^(-1) = 2/3 rho*K*trace(D)-2*c_k*Delta*D^2

solve for K and resubstitute K=sqrt(k). That is at least my opinion of whats happening
Dear Gregor and other openfoam users,

Thank you for your reply. About the Smagorinksy model (for compressible flows) in openfoam, I still have three questions:

1, The compressible form of Smagorinksy model use the equation B.D + epsilon =0, this is discussed in the paper (but the models in this paper are for incompressible models):
http://pof.aip.org/resource/1/phfle6...sAuthorized=no

But they did not the normal form, Eq. (4), and instead they use B.D + epsilon =0, which can be derived from Eq. (5) when the local equilibrium assumption is introduced.

In fact, there is another paper by the same author and this paper discussed the compressible LES models:

http://pof.aip.org/resource/1/phfle6...sAuthorized=no

In compressible Openfoam, they do not use the Smagorinsky model from this paper. Does any one know what is the reason?

2, Return to the first paper, it was mentioned that B.D + epsilon =0 can make model B1 reduce to A1 model. Actually in Openfoam, for TKE k, a algebraic equation is solved. Thus, how B1 can be reduced to A1?

3, I also found that it is difficult to relate these model constants ck and ce in compressible Openfoam to the standard Smagorinky model: nusgs=(Cs*delta)**2*||S||.

Your any comments and suggestions are welcome.
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Old   January 31, 2013, 05:32
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Quote:
Originally Posted by hz283 View Post
2, Return to the first paper, it was mentioned that B.D + epsilon =0 can make model B1 reduce to A1 model. Actually in Openfoam, for TKE k, a algebraic equation is solved. Thus, how B1 can be reduced to A1?
this is thr algebraic equation for TKE k:
- c_B*rho*K^2*Delta^(-1) = 2/3 rho*K*trace(D)-2*c_k*Delta*D^2

in the incompressible case:

2/3 rho*K*trace(D) = 0 (continuity)

thus k=c_B/c_K Delta^(2) D^2

which gives with

nu_t = c_k Delta sqrt(k) = sqrt(c_k^3/c_e)Delta^2 D

Quote:
Originally Posted by hz283 View Post
3, I also found that it is difficult to relate these model constants ck and ce in compressible Openfoam to the standard Smagorinky model: nusgs=(Cs*delta)**2*||S||.
yes excactly, the "compressible" smagorinsky reduces to the standard smagorinsky model in the incompressible case and you can recover the smagorinsky constant. but i am not certain if it makes sense to look for a smagorinsky constant in the compressible case.

I dont know if i am getting Q1 ?!
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Old   June 19, 2013, 14:52
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Hi Mr. Gregor
Please throw some light on why k is defined in two ways in the smagorinsky model.

// Member Functions

//- Return SGS kinetic energy
// calculated from the given velocity gradient
tmp<volScalarField> k(const tmp<volTensorField>& gradU) const
{
volSymmTensorField D(symm(gradU));

volScalarField a(ce_/delta());
volScalarField b((2.0/3.0)*tr(D));
volScalarField c(2*ck_*delta()*(dev(D) && D));

return sqr((-b + sqrt(sqr(b) + 4*a*c))/(2*a));
}

//- Return SGS kinetic energy
virtual tmp<volScalarField> k() const
{
return k(fvc::grad(U()));
}
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Old   June 26, 2013, 05:32
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well if you have a close look you'll see that the second function
Code:
virtual tmp<volScalarField> k() const
only calls the first function
Code:
tmp<volScalarField> k(const tmp<volTensorField>& gradU) const
thus the second function is some kind of an alias which is needed because of inheritance.
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Old   June 28, 2013, 19:21
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Thanx Gregor for the explanation. I observed a peculiar thing in the Smagorinsky Model.

For compressible Smagorinsky Ck = 0.02
For Incompressible Smagorinsky Ck = 0.094

I think this is wrong.
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Old   November 16, 2013, 13:12
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Hi All,

In Openfoam, the model constants for compressible Smagorisnky model are:

Ck=0.01
Ce=1.048

I checked the following paper:

Fureby, C

On subgrid scale modelling in large eddy simulation of compressible fluid flow.
Physics of Fluid, 8(5) 1996.

In this paper, there are four models for the subgrid scale modelling, but I found that no models exactly correspond to the one used in the Openfoam code (compressible).

Actually, in openfoam, the compressible Smagorisnky model is not a standard. I did not found how the two model constant (ck and Ce) come from and if there are validated by the experimental data. Does anybody know how these two constants come from? Thank you.

Quote:
Originally Posted by rajeshkunwar View Post
Thanx Gregor for the explanation. I observed a peculiar thing in the Smagorinsky Model.

For compressible Smagorinsky Ck = 0.02
For Incompressible Smagorinsky Ck = 0.094

I think this is wrong.
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Old   September 9, 2014, 07:22
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Hi openfoammaofnepo,
have you found an answer to your question about the coefficients?

I find it very difficult to resolve the OpenFoam coefficients c_k and c_e from the compressible smagorinsky model, and I wasnt able to do so yet. I would appreciate any help.

From what gregor already posted (I think there is a mistake in it), I was able to derive the quadratic equation for k, which is solved in the model. But I cant figure out the relationship between the OpenFOAM smagorinsky and the one published by Fureby (1996).

Fureby says:
muSgs = rho*c_d*delta^2*D

with the coefficient c_d = 0.038

OpenFoam says:
muSgs = ck*rho*sqrt(k)*delta

with ck = 0,02. There are of course coefficients in sqrt(k), but my main problem is that I cant calculate the resulting coefficient!

In http://croccolab.umd.edu/publication...FD00_vol13.pdf on page 5 it is said that the final coefficient should be the square of the standard smagorinsky coefficient Ck = 0.16.

I am very confused now. Please dont hesitate to give me your hints.
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