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-   -   LES Compressible Smagorinsky Model (http://www.cfd-online.com/Forums/openfoam-solving/58781-les-compressible-smagorinsky-model.html)

iyer_arvind September 26, 2006 06:30

The les Smagorinsky Model inco
 
The les Smagorinsky Model incorporated in OpenFOAM, for compressible flows, add some more terms, which i have not been able to understand, can anyone give me a link to what method has been followed for compressible LES Smagorinsky Model?

iyer_arvind October 9, 2006 00:43

The Smagorinsky model coded is
 
The Smagorinsky model coded is as follows

volTensorField D = symm(gradU);
volScalarField a = ce_/delta();
volScalarField b = (2.0/3.0)*tr(D);
volScalarField c = 2*ck_*delta()*(dev(D) && D);
k_ = sqr((2*b + sqrt(sqr(b) +4*a*c))/(2*a));
muSgs_ = ck_*rho()*delta()*sqrt(k_);

while the model commonly documented is much simpler. This looks like a solution of a quadratic equation, but i am still in search of a link for interpreting the above model.

the incompressible Smagorinsly model is simply

nuSgs_ = ck_*delta()*sqrt(k(gradU));
nuSgs_.correctBoundaryConditions();

i would be very thankful if someone could point out a link to the compressible model.

nishant_hull June 24, 2008 10:13

Is there any reference paper f
 
Is there any reference paper for the implementation of compressible smagorinsky model???
if there is any link either in the forum please provide it to me.

cheers!

Nishant

ngj June 24, 2008 12:02

Hi The following title sug
 
Hi

The following title suggest that it might be interesting. Haven't read it myself:

C. Fureby
On Sub-Grid Scale Modeling in Large Eddy Simulations of Compressible Fluid Flow
Phys. Fluids, 8, 1301, 1996.

Best regards,

Niels

jiejie July 21, 2010 02:51

Quote:

Originally Posted by iyer_arvind (Post 183935)
The Smagorinsky model coded is as follows

volTensorField D = symm(gradU);
volScalarField a = ce_/delta();
volScalarField b = (2.0/3.0)*tr(D);
volScalarField c = 2*ck_*delta()*(dev(D) && D);
k_ = sqr((2*b + sqrt(sqr(b) +4*a*c))/(2*a));
muSgs_ = ck_*rho()*delta()*sqrt(k_);

while the model commonly documented is much simpler. This looks like a solution of a quadratic equation, but i am still in search of a link for interpreting the above model.

the incompressible Smagorinsly model is simply

nuSgs_ = ck_*delta()*sqrt(k(gradU));
nuSgs_.correctBoundaryConditions();

i would be very thankful if someone could point out a link to the compressible model.

Hi iyer_arvind

Have you got the reference for the dynSmagorinsky model used in OpenFOAM by any chance? I am stuck at the same place trying to understand it as it is different from the original dynamic Smagoribsky from Lilly 1992.

Thanks

georg December 1, 2010 12:42

Hello everybody,

I have another question regarding the compressible Smagorinsky model. Why does the model ask for the file k within start directory? I use OpenFOAM-1.6 with rhoPisoFoam. I thought, Smagorinsky works without it. The incompressible model does not ask.

Best regards,
Georg

Fransje December 3, 2010 15:05

Hello Georg,

Looking at the code, I guess that the compressible version of the Smagorinsky model requests the "k" file through inheritance..

The Smagorinsky LES model is a child of the general base class GenEddyVisc. In the GenEddyVisc.C file you can see:
Code:

00073    k_
00074    (
00075        IOobject
00076        (
00077            "k",
00078            runTime_.timeName(),
00079            mesh_,
00080            IOobject::MUST_READ,
00081            IOobject::AUTO_WRITE
00082        ),
00083        mesh_
00084    ),

Which means that the implementation of the compressible Smagorinsky model (and as a matter of fact, all the models having GenEddyEq as a base class) will require k to be in your start directory, and that whether the turbulence model uses it, or not..

I guess this is inconsistent with the incompressible implementation of the turbulent models, where the request for "k" is programmed in the turbulence model itself, meaning that it will not be used/asked for if not needed by the model. Consequently, the incompressible Smagorinsky model does not complaining about "k" not being present in the start directory..

I don't know why it was implemented that way, but I guess you could ask the developers themselves via the openfoam/bugs site. I would be curious to know what the reason is.

Kind regards,

Francois.

georg December 8, 2010 06:37

Hi Francois,

thank you for your quick answer. I have reported that issue to OpenCFD. I will keep you informed.

Kind regards,
Georg

georg January 11, 2011 05:20

Hello Francois,

me again. It seems, that there was no reason for the way the compressible model was implemented. The code was reorganized and will be part of the next release.

Regards,
Georg

Fransje January 11, 2011 09:18

Allright!
Good work, and thanks for the update.

Kind regards,
Francois.

morard July 19, 2011 11:50

Hi,
there is no new implementation of compressible Smagorinsky model in OF 2.0! Is there any other reference than Fureby because he doesn't use this kind of modelling? Where I can find more about the version of compressible Smagorinsky, which is implemented in OF? Why a separate calculation of k will be used?
Thx Dejan

gregor January 25, 2012 13:07

Quote:

Originally Posted by morard (Post 316638)
Why a separate calculation of k will be used?

that was a bug see http://www.openfoam.com/mantisbt/view.php?id=389

morard January 25, 2012 13:27

Thanks Gregor!

This question was actually posed by my friend because he didn't have profile at that time. I can't wait to see his face when he find out that this was a bug all the time :)

gregor January 25, 2012 13:35

And furthermore you can actually derive the quadratic k equation from the Fureby1996 paper. I just did't see how in the beginning.

gregor July 11, 2012 07:57

As demanded:

To derive the quadratic k equation you take

-B*D = c_B*rho*k^(3/2)*delta^(-1) (1 equilibrium assumption)

and plug in

B = 2/3 rho*k*I-2*mu_t*D (2 subgrid scale stress tensor )

so you get:

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

with mu_t = c_k*Delta*k^(1/2) (4 Smagorinsky model)

you finally get the quadratic k equation used in OpenFOAM:

- c_B*rho*k^(3/2)*Delta^(-1) = 2/3 rho*k*trace(D)-2*c_k*Delta*k^(1/2)*D^2 (5)

So the basic difference between the Smagorinsky model in the compressible and incompressible case is (at least how it is implemented in OpenFOAM), whether you can neglect the rho*k*trace(D) term or not.

D = Strain rate tensor

deji October 22, 2012 11:53

Gregor,

If I may ask this question: how is D is the strain rate tensor?
volTensorField D = symm(gradU);

Sij = 0.5(dUi/dxj + dUj/dxi) and it is clearly a symmetric tensor
But how is D= symm(fvc::grad(U)) = Sij???

Is the assumption that the cross-stream and span-wise derivatives are minute compared to the wall normal derivates?

Cheers,
Deji

deji October 22, 2012 12:05

D is actually the deformation rate tensor.

deji October 22, 2012 12:10

I think I've figured this out...

hz283 January 23, 2013 19:30

Quote:

Originally Posted by gregor (Post 370796)
As demanded:

To derive the quadratic k equation you take

-B*D = c_B*rho*k^(3/2)*delta^(-1) (1 equilibrium assumption)

and plug in

B = 2/3 rho*k*I-2*mu_t*D (2 subgrid scale stress tensor )

so you get:

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

with mu_t = c_k*Delta*k^(1/2) (4 Smagorinsky model)

you finally get the quadratic k equation used in OpenFOAM:

- c_B*rho*k^(3/2)*Delta^(-1) = 2/3 rho*k*trace(D)-2*c_k*Delta*k^(1/2)*D^2 (5)

So the basic difference between the Smagorinsky model in the compressible and incompressible case is (at least how it is implemented in OpenFOAM), whether you can neglect the rho*k*trace(D) term or not.

D = Strain rate tensor

Hi,

Can I ask you a question about Eq. (5)? Why is Eq. (5) a the quadratic k equation ? I know this is a simple question. I checked the source code and but that OPenfoam did solve it like a quadratic equation. Any suggestions are really appreciated.

best regards,
H

gregor January 24, 2013 08:51

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 ;)


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