# About sigma1 and sigma2!

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 May 11, 2006, 05:17 About sigma1 and sigma2! #1 akang Guest   Posts: n/a Hi,everybody. I know that Ce1 and Ce2 are the constants of epsilon-equation and they can be modified under GUI/Advanced Model Control/Epsilon Coefficients, but I wonder where sigma1 and sigma2 of k-equation are. Can someone give any advice? Thanks!

 May 12, 2006, 03:30 Re: About sigma1 and sigma2! #2 akang Guest   Posts: n/a In Fluent, TKE Prandtl Number represents sigma_k, and TDR Prandtl Number represents sigma_e. But in CFX I can not find the same constants. Why?

 May 12, 2006, 11:17 Re: About sigma1 and sigma2! #3 opaque Guest   Posts: n/a Dear akang, I assume you are calling sigma1 and sigma2 the Turbulent Prandtl/Schmidt numbers used to scale the turbulent eddy viscosity in the diffusion term for the k/epsilon equations. If so, look into the Turbulent Flux Closure section for K Coefficients and Epsilon Coefficients.. There you can set the Turbulent Schmidt Number (sigma_???) for each equation.. The name Prandtl number is usually meant for heat transfer (Prandtl = mu * Cp/ k ), while Schmidt is more the generic name for scalars (Schmidt = mu / (rho * diffusivity) ).. Just a matter of style.. The literature uses both naming conventions.. Good luck, Opaque

 May 12, 2006, 21:22 Re: About sigma1 and sigma2! #4 akang Guest   Posts: n/a opaque, thanks for response! In some papers, some model constants were also given below the k-e equations. for example,Ce1=1.44,Ce2=1.92,σk=1.0 and σe=1.3. σk is the TKE(Turbulent Kinetic Energy) Prandtl Number, and σe is the TDR(Turbulent Dissipation Rate) Prandtl Number. Ce1 and Ce2 are obvious under Advanced Model Control in CFX_Pre, but σk and σe are not. I also found that Turbulent Schmidt Number under K coefficients and Epsilon Coefficents both have the value of 0.9. Not the same as I wrote before. So I'm not sure if they are what I want.

 May 14, 2006, 02:18 Re: About sigma1 and sigma2! #5 akang Guest   Posts: n/a I'm not sure whether the Turbulent Schmidt Number below Turbulent Flux Closure of K Coefficients is SIGMA_k(TKE Prandtl Number). So could anybody help me?

 May 14, 2006, 16:26 To: opaque #6 Jianping Guest   Posts: n/a Hi, opaque In CFX help file, it is stated that the default values of SIGMA_kå'SIGMA_e in CFX for standard k-e model are 1 and 1.3 respectively. I can not see ways to change these coefficients through cfx-pre GUI. Regarding the 'turbulent schmidt numbers'(default 0.9) for k and epsilon coefficients in cfx-pre GUI, I understand that they actually are schmidt numbers for buoyancy production term and dissipation term in k and epsilon equations. Thus they may only affect the k and epsilon models when the Buoyancy Turbulence option in CFX-Pre is set to 'Production' or 'Production and Dissipation'. Please correct me if above understandings are incorrect. Also, obviously we can set different 'schmidt numbers' for k or epsilon coefficients in CFX-pre GUI. Do you know which number is same as the Prandtl/Schmidt numbers for heat transfer/scalar transport? Regards! Jianping

 May 15, 2006, 03:01 Re: About sigma1 and sigma2! #7 akang Guest   Posts: n/a Does CFX treat SIGMA_k and SIGMA_e as universal model constants?

 May 15, 2006, 09:08 Re: To: opaque #8 opaque Guest   Posts: n/a Dear Jianping, In turbulent flow, every equation requires a Turbulent [name you like] Number to reconcile the analogy with the momemtum equation turbulent model assumption (Eddy Viscosity assumption).. For the Turbulent Kinetic Energy (TKE), this parameter can be changed within the TURBULENCE MODEL/Advanced Control/K Coefficients/TURBULENT FLUX CLOSURE section. For the Turbulent Eddy Dissipation (TED), the location isTURBULENCE MODEL/Advanced Control/EPSILON Coefficients/TURBULENT FLUX CLOSURE section. For Buoyancy contribution to TKE, TURBULENCE MODEL/Advanced Control/Buoyancy Turbulence section. For energy, it is not in the GUI.. Add the CCL below to the HEAT TRANSFER MODEL section (for each fluid domain) HEAT TRANSFER MODEL: Option = Thermal Energy TURBULENT FLUX CLOSURE: Option = Eddy Diffusivity Turbulent Prandtl Number = 0.9 END END Similar for Total Energy.. Except for the Energy equation, everything else is on the GUI... The default value shown is not the internal value for some of them... I hope this helps, Opaque

 May 15, 2006, 09:48 Re: To: opaque #9 Jianping Guest   Posts: n/a Dear opaque: Could you confirm the following are correct? The reason I doubt these is that all the default values shown in CFX GUI are 0.9, but the document says that the defaults are 1 and 1.3. Regards! Jianping "For the Turbulent Kinetic Energy (TKE), this parameter can be changed within the TURBULENCE MODEL/Advanced Control/K Coefficients/TURBULENT FLUX CLOSURE section. For the Turbulent Eddy Dissipation (TED), the location isTURBULENCE MODEL/Advanced Control/EPSILON Coefficients/TURBULENT FLUX CLOSURE section."

 May 15, 2006, 10:17 Re: To: opaque #10 opaque Guest   Posts: n/a Dear Jianping, yes.. The value for k Turbulent Schmidt Number is 1.0, and for epsilon is 1.3 For energy is 0.9 For turbulence buoyancy is 1.0 (non-Boussinesq buoyancy), or Turbulent Prandtl Number (energy) otherwise.. Good luck, Opaque

 May 15, 2006, 10:18 Re: About sigma1 and sigma2! #11 opaque Guest   Posts: n/a Dear Akang, What do you mean by universal model constants? Regards, Opaque

 May 15, 2006, 10:26 Re: To: opaque #12 Jianping Guest   Posts: n/a Thanks, Opaque Then, could you please explain why the defalt values for k and epsilon Turbulent Schmidt Numbers are all shown as 0.9 (instead of 1 and 1.3) in CFX-pre GUI? Please check these defalts under TURBULENCE MODEL/Advanced Control/K Coefficients/TURBULENT FLUX CLOSURE section. Regards! Jianping

 May 15, 2006, 11:23 Re: To: opaque #13 opaque Guest   Posts: n/a Dear Jianping, I do not know that.. Sorry.. Opaque..

 May 15, 2006, 21:09 Re: About sigma1 and sigma2! #14 akang Guest   Posts: n/a SIGMA_k ,SIGMA_e and other model constants were concluded from certain experiments. They may be applicable to some flows, but not to all the flows. So is it possible to improve the results by optimizing these empirical constants when they fail to work?

 May 15, 2006, 23:04 Re: About sigma1 and sigma2! #15 opaque Guest   Posts: n/a Dear akang, Though ANSYS CFX allows users to modify the turbulence model constants, I rather stay away from changing them unless there is overwhelming experimental data and clear theoretical explanation of why the current coefficients are flawed. These coefficients are not independent of each other, and there are subtle physical balances that they satisfy. These coefficients have been tested for quite a few years (30+) and only very specific flows (like round jets if I am not mistaken) have a different set of values. I rather research the literature to see which turbulence model is best for your particular application, and the why. You may also try contacting the CFX help desk for additional information. That is all I can say about it.. Opaque.

 May 17, 2006, 13:06 Re: To: opaque #16 HekLer Guest   Posts: n/a It's probably just a bug. Don't worry about it. The solver will use the right values (1 and 1.3) if you don't activate these options.

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