# LES modelling of non-Newtonian fluid flow

AA09
Member
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**1**Hello,

I have a question about large eddy simulation (LES) when using one of the available models in Fluent for shear-dependent viscosity, μ_a. Is the software solving the following grid-filtered (~) momentum equation?

or is it solving this other form?

Thank you in advance.

Best regards,

Arturo.

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## Answers

327Forum CoordinatorHello,

It uses somethin similar to the second form. Please check this link for additional details [https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/corp/v212/en/flu_th/flu_th_sec_turb_les_filt_ns_eq.html?q=LES%20equations]

Regards,

SD

5MemberDear SD,

Thank you for the reply. I saw the documentation but the given equation seems to correspond to constant viscosity (Newtonian fluid) since only the strain-rate tensor is being filtered.

Do you know which grid-filtered momentum equation is solved for a fluid with shear-dependent viscosity?

Best regards,

Arturo.

327Forum CoordinatorHello,

Shear Dependent non-Newtonian viscosity model is compatible with Laminar viscous model only.

You will see that the Power law, Herschel-bulkley, etc. models under viscosity are turned on only for Laminar Viscous model.

Regards,

SD

5MemberHello SD,

Once again thank you for replying to my post.

I checked the Fluent User's Guide and it does seem possible to do turbulence modeling for shear-dependent viscosity (https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/corp/v212/en/flu_ug/x1-106100013.14.19.html) although the guide also remarks what you mentioned in the section for temperature dependent viscosity (https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/corp/v212/en/flu_ug/flu_ug_sec_viscosity_non_newtonian.html).

Nonetheless, let's say that instead of using the in-built models, we incorporate the shear-dependent viscosity with a user-defined function (https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/corp/v212/en/flu_udf/flu_udf_ChapIntroduction.html). In that case, which grid-filtered momentum equation would be solved for the fluid with shear-dependent viscosity?

Best regards,

Arturo.

11,770Forum CoordinatorThe value you add into Fluent's material property for viscosity is the laminar viscosity. The turbulence models then do "stuff" to that to give the turbulent viscosity. I suspect that whatever the UDF puts into the cell (laminar viscosity) is then acted on by the turbulence model. Hence why we allow you to switch nonNewtonian and turbulence on with a low Re correction via the TUI. The two models were made mutually exclusive in v6.0 after we tested some combinations that didn't make (physical) sense: yes, I was learning then too.

5MemberDear Rob,

Thank you for the reply. If I understood correctly, in your opinion, the filtering operation (probably) takes place once a model for the dynamic viscosity has been introduced. Does that mean the following form is been solved?

Thank you in advance for the follow-up to my original question.

Best regards,

Arturo.

11,770Forum CoordinatorPass - @DrAmine is much better with the squiggles than me!

7,893Forum CoordinatorLet me look and read the whole thread.

7,893Forum CoordinatorFluent does not take any additional precautions when dealing with shear dependence of molecular viscosity. It uses the same formulation as for constant molecular viscosity. Mathematically might be wrong but sincerely the molecular viscosity is small and it would not really matter for typical applications. For cases with very high molecular viscosity things are different and it requires some precautions.

Additional comment: Do not use low-Re terms in k-omega: omega based models do already operate well for Low-Re regimes ( viscous sublayer) and they do not require any extra treatment!

5MemberHello DrAmine,

Thank you for the reply. Just a final clarification; simply put, when considering LES of a fluid with shear-dependent viscosity, is Fluent solving the following?

where μ_a is not being filtered and ρ is a constant (incompressible flow).

Regards,

Arturo.

7,893Forum CoordinatorYes