# Smagorinsky model details

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 July 12, 2011, 11:31 How about dynamic Smagorinsky? #21 Senior Member   Bernhard Join Date: Sep 2009 Location: Delft Posts: 790 Rep Power: 13 Hi all, I have some questions about this same issue with respect to the dynamic Smagorinsky model. I think I am making a mistake somewhere, but please correct me if I am wrong. I've tried to look at other locations for the same issue, but couldn't find it. I compare the dynamic model in OpenFOAM (not caring about the domain averages coefficient) with the dynamic model (described in Lilly and Pope). I think we agree on the following (D defined in OpenFOAM, S common definition) Now, looking at the code (dynSmagorinsky 1.7, homogeneousDynSmagorinsky 2.0), in the .C file at line 57, 62 respectively: as compared to the original of Lilly (in Pope this expression If D_ij=S_ij, but |S|=sqrt(2) |D|, then the second term in the OF implementation is off by a factor sqrt(2). (Where the factor 4 is from the double width of the test filter, and the minus sine is also present in L) Somewhere I must have skipped a step, I hope one of you can point it out for me. Thanks in advance! bmikuz likes this.

 July 15, 2011, 02:35 #22 Senior Member   Bernhard Join Date: Sep 2009 Location: Delft Posts: 790 Rep Power: 13 Anybody that can give a comment on this?

July 18, 2011, 03:47
#23
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Bernhard
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Mistake is this:
Quote:
 Originally Posted by Bernhard

August 26, 2011, 06:39
#24
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Gregor Olenik
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Quote:
I think the reason is to have a consistent formulation for incompressible an compressible LES models :

let symm(gradU) be S, then dev(S) = S - 1/3 trace(S)I

however in a incompressible case
1/3 trace(S)I = 0, since trace(S) is the continuity eq. . Therefore in an incrompessible case it doesnt matter whether you take dev(S) or not , but consider a compressible case then 1/3 trace(S) doesn't vanish.

In a compressible or variable density case the solver calls divDevRhoBeff to compute the source term due to SGS stress B = 2/3k I - 2 nu_t S_D. (See Fureby http://pof.aip.org/resource/1/phfle6/v9/i5/p1416_s1 Eq. 3) There you have the deviatoric part of D. But i guess openFoam uses nu_t = c Delta^2 ||S_D|| and B = 2/3k I - 2 nu_t S. So it takes S_D for the turbulent viscosity and S for the SGS stress tensor B.

January 24, 2013, 11:40
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Quote:
 Originally Posted by MaximeIST Hello I may keep on confusing people, but the way it is coded, if I am not doing mistake is Cs=sqrt(ck*sqrt(2*ck/ce)) in the incompressible Smagorinsky.H line 114. There is a factor 2 added in the root-mean squared. And in the case where Ce=1.048 and Ck=0.094, and with this factor 2, we obtain Cs=0.1995. May be I miss something? Maxime
Hi All,

For the compressible Smagorinsky model, the parameters for ck=0.02, ce=1.048

Following the following line:
Cs=sqrt(ck*sqrt(ck/ce))
=> Cs=0.0525...

Does anybody know the references for these specification of the ck and ce for compressible Smagorinsky model?

 March 11, 2013, 22:25 #26 Member   sqing Join Date: Sep 2012 Location: Dalian Posts: 77 Rep Power: 5 Hi Yingkun, As you mentioned, in the incompressible solvers Cs=sqrt(Ck*sqrt(Ck/Ce)). So if I want to set Cs=1, Do I just need to modify Ck and Ce in the LESProperties？Or are there other rules I must obey? Code: SmagorinskyCoeffs { ce 1.05; ck 0.0472; } regards

 February 28, 2014, 04:03 #27 Member   Florian Ries Join Date: Feb 2014 Location: Darmstadt, Germany Posts: 88 Rep Power: 4 Hi Bernhard and everybody, I compare the dynamic model in OpenFOAM (homoDynSmag OF 2.2.2) with the dynamic model (described in Lilly and Pope) and I have the same Problem. To reanimate the discussion: In Pope (F(.) means filtered): [1] nu_SGS = cS * delta^2 * sqrt(2 * S_ij S_ij) [2] cs = (M_ij L_ij)/(M_kl M_kl) where [3] S_ij = 0.5 (ui,j + uj,i) [4] M_ij = 2 * delta^2 * (F(sqrt(2 * S_ij S_ij) S_ij) - F(sqrt(2 * S_ij S_ij)) F(S_ij)) [5] L_ij = F(ui uj) - F(ui) F(uj) In OF 2.2.2 (homogeneousDySmagorinsky, <.> means averaged): [6] nu_SGS = cD * delta^2 * sqrt(S_ij S_ij) [7] cD = 0.5 ()/() [8] S_ij = D_ij = S_ij Pope [9] M_ij = delta^2 * (F(sqrt(S_kl S_kl) Sij) - 4 * sqrt( ) ) [10] L_ij = F(ui uj) - F(ui) F(uj) I marked the differences of these models. - First difference is the factor 0.5 in Eq[7] in comparison to Eq[2]. This comes from the factor 2 in Eq[4]. If we put this in Eq[2] we get 0.5 (ok) - Second difference is the different filtering in M_ij. What effect does this have???? (x) - Third difference is the factor 4 in Eq[9] in comparison to Eq[4]. Bernhard: here the factor 4 is from the double width of the test filter can you please explain that?? Why we dont get a fector in the other filtered terms??? (x) - Fourth difference is the factor 2 in mag(S_ij). (x) In my opinion these models are different or Im not able to bring the OF-model in the form of pope-model. If it is possible, anyone can please give some advice? kind regards Florian bmikuz likes this.

October 28, 2014, 02:39
#28
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Wen Xu
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Quote:
 Originally Posted by lakeat Sorry, I do not understand, I saw in "Smagorinsky.H", Code: tmp k(const tmp& gradU) const { return (2.0*ck_/ce_)*sqr(delta())*magSqr(dev(symm(gradU))); } As I remember: Question 1: Why using magSqr(dev(symm(gradU))) instead of symm(gradU) && symm(gradU) to get ???? Question 2: If magSqr(dev(symm(gradU))) = symm(gradU) && symm(gradU) = , then But I saw in "Smagorinsky.C" Code: nuSgs_ = ck_*delta()*sqrt(k(gradU)); Which means Then, replace K with Compare with We'll get But I heard somone said So, I'm puzzled, I wonder if it was a mistake, that k should be written as Code: tmp k(const tmp& gradU) const { return (ck_/ce_)*sqr(delta())*magSqr(dev(symm(gradU))); } Thank you

the third one shoub be sqrt(2*Sij*Sij)

 December 11, 2014, 06:40 How to change ck and ce in Smagorinsky approach #29 Senior Member   Bobi Join Date: Oct 2012 Location: Chicago, Illinois Posts: 312 Rep Power: 6 Greetings All I have performed a Smagorinsky-based compressible LES simulation with the Coefficients as follows: HTML Code: { ce = 1.048; ck= 0.02; } According to the relation: I will get . My case is a reacting non-premixed combustion with a bluff-body separating fuel and oxidizer streams. I want to change the value into 0.13. which value between and should be modified to retain the nature of the problem? Best, Bobi Last edited by babakflame; December 11, 2014 at 07:45.

March 21, 2015, 19:27
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Actually in this paper, we cannot find the information about how the model constants c_k=0.094 and c_{\epsilon}=1.048 come out. So which one is correct reference when I use these two constants? Thanks.

Quote:
 Originally Posted by alberto

 September 21, 2015, 10:11 Openfoam #31 New Member   Liuyue Join Date: Sep 2015 Posts: 1 Rep Power: 0 Hi Lakeat,now I want to write the Scalar SikSkj,but how to write that in openFoam, Thanks.

 January 15, 2016, 13:56 Change the smagorinsky coeff #32 New Member   Elyas Join Date: Dec 2015 Location: Iran Posts: 1 Rep Power: 0 hi friends How can I change the smagorinsky Coeff (Cs) in OF?I want to use Cs=0.1... Regard

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