# LES Compressible Smagorinsky Model

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 September 26, 2006, 06:30 The les Smagorinsky Model inco #1 iyer_arvind Guest   Posts: n/a 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?

 October 9, 2006, 00:43 The Smagorinsky model coded is #2 iyer_arvind Guest   Posts: n/a 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.

 June 24, 2008, 10:13 Is there any reference paper f #3 Senior Member   Nishant Join Date: Mar 2009 Location: Glasgow, UK Posts: 165 Rep Power: 8 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 __________________ Thanks and regards, Nishant

 June 24, 2008, 12:02 Hi The following title sug #4 Senior Member   Niels Gjoel Jacobsen Join Date: Mar 2009 Location: Deltares, Delft, The Netherlands Posts: 1,605 Rep Power: 25 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 __________________ Please note that I do not use the Friend-feature, so do not be offended, if I do not accept a request.

July 21, 2010, 02:51
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Jie
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Quote:
 Originally Posted by iyer_arvind 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

 December 1, 2010, 12:42 #6 New Member     Join Date: Mar 2009 Location: Germany Posts: 17 Rep Power: 8 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

 December 3, 2010, 15:05 #7 Senior Member   Francois Join Date: Jun 2010 Posts: 107 Rep Power: 7 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. skanjosh likes this.

 December 8, 2010, 06:37 #8 New Member     Join Date: Mar 2009 Location: Germany Posts: 17 Rep Power: 8 Hi Francois, thank you for your quick answer. I have reported that issue to OpenCFD. I will keep you informed. Kind regards, Georg

 January 11, 2011, 05:20 #9 New Member     Join Date: Mar 2009 Location: Germany Posts: 17 Rep Power: 8 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

 January 11, 2011, 09:18 #10 Senior Member   Francois Join Date: Jun 2010 Posts: 107 Rep Power: 7 Allright! Good work, and thanks for the update. Kind regards, Francois.

 July 19, 2011, 11:50 #11 Member   Dejan Morar Join Date: Nov 2010 Posts: 78 Rep Power: 7 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

January 25, 2012, 13:07
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Gregor Olenik
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Quote:
 Originally Posted by morard Why a separate calculation of k will be used?
that was a bug see http://www.openfoam.com/mantisbt/view.php?id=389

 January 25, 2012, 13:27 #13 Member   Dejan Morar Join Date: Nov 2010 Posts: 78 Rep Power: 7 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

 January 25, 2012, 13:35 #14 Member   Gregor Olenik Join Date: Jun 2009 Location: http://greole.github.io/ Posts: 78 Rep Power: 8 And furthermore you can actually derive the quadratic k equation from the Fureby1996 paper. I just did't see how in the beginning.

 July 11, 2012, 07:57 #15 Member   Gregor Olenik Join Date: Jun 2009 Location: http://greole.github.io/ Posts: 78 Rep Power: 8 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 chanleonzen likes this. Last edited by gregor; July 11, 2012 at 07:57. Reason: typo

 October 22, 2012, 11:53 #16 Senior Member   n/a Join Date: Sep 2009 Posts: 198 Rep Power: 7 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

 October 22, 2012, 12:05 #17 Senior Member   n/a Join Date: Sep 2009 Posts: 198 Rep Power: 7 D is actually the deformation rate tensor.

 October 22, 2012, 12:10 #18 Senior Member   n/a Join Date: Sep 2009 Posts: 198 Rep Power: 7 I think I've figured this out...

January 23, 2013, 19:30
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Quote:
 Originally Posted by gregor 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

 January 24, 2013, 08:51 #20 Member   Gregor Olenik Join Date: Jun 2009 Location: http://greole.github.io/ Posts: 78 Rep Power: 8 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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