# Smagorinsky model details

 Register Blogs Members List Search Today's Posts Mark Forums Read

 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
Senior Member

Bernhard
Join Date: Sep 2009
Location: Delft
Posts: 790
Rep Power: 13
Mistake is this:
Quote:
 Originally Posted by Bernhard

August 26, 2011, 06:39
#24
Member

Gregor Olenik
Join Date: Jun 2009
Location: http://greole.github.io/
Posts: 80
Rep Power: 8
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
#25
Senior Member

Join Date: Nov 2012
Posts: 168
Rep Power: 5
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: 3 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
Senior Member

Wen Xu
Join Date: May 2014
Posts: 174
Rep Power: 3
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: 286 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
#30
Senior Member

Join Date: Jan 2013
Posts: 252
Rep Power: 6
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

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are On Pingbacks are On Refbacks are On Forum Rules

 Similar Threads Thread Thread Starter Forum Replies Last Post Luis CFX 8 May 29, 2007 18:13 sam Main CFD Forum 13 September 21, 2006 10:15 Chris Bailey FLUENT 1 March 7, 2006 11:38 Ajay S. Parihar Main CFD Forum 9 June 2, 2002 16:24 Wen Long Main CFD Forum 4 May 15, 2002 05:54

All times are GMT -4. The time now is 19:53.