[modest_may]

In Ansys CFX, the eddy (turbulence) viscosity can be specified in the Turbulence option (Domain->Fluid Models->Turbulence->Advanced Turbulence Control->Eddy Viscosity). The Ansys Help documentation denotes that the defined eddy viscosity will be picked up by the specified turbulence model and the internal algorithm will not be used. Does anyone know that what's the internal algorithm for the CFX solver?

In fact, i am encountering a problem that a flow field needs to be calculated by solving the NS governing equations, while the eddy viscosity at each grid node of the domain is known in advance (this can be specified using the initialize profile function). In this case, I wonder that whether the turbulence model still needs to be solved? If the eddy viscosity is known, what's the function of the turbulence model?

Hope to receive any kind reply.

Sincerely,
Min

[ghorrocks]

If the eddy viscosity is known then there is no need for a turbulence model. But an easier way of fixing the turbulence model and running the mass and momentum equations is to do a normal restart from the initial run, but to turn the turbulence equation solvers off with expert parameters. This will be easier to implement than overwriting the eddy viscosity.

But I am puzzled why you would want to do this. The turbulence field is coupled to the flow field, so changing one will change the other. Why would you want to run just the flow equations but keep the turbulence fixed? When the flow variables change then so will the turbulence variables.

[modest_may]

Thank you, sir, for your kind advice.

In fact, this problem is simulated for modeling an adjoint system in the adjoint optimization. This adjoint equation is similar to the primary governing equation, and the eddy viscosity should be the same in both two equations when using a "frozen turbulence" assumption. Details can be referred to Zymaris et al. [1]. I reckon that there may be no physical meaning but just have mathematical foundation for the adjoint problem.

According to your reply, i have an another question: if we use k-omega (ω) turbulence mode and do not turn the turbulence modeling off with the expert parameters, can the k and ω be solved under the known eddy viscosity?


[1]A.S. Zymaris, D.I. Papadimitriou, K.C. Giannakoglou, C. Othmer, Continuous adjoint approach to the Spalart-Allmaras turbulence model for incompressible flows, Comput. & Fluids 38 (8) (2009) 1528–1538.[/SIZE][/SIZE]

[ghorrocks]

I do not understand your k-w question.

Are you asking whether you can run the k-w turbulence model but overwrite the eddy viscosity and just use a pre-determined eddy viscosity? (Answer: Then why run the k-w turbulence model?)

Or are you asking whether we can determine the k and omega field values are for a specified eddy viscosity field? (Answer: no, this is an inverse question and they are complex to solve. There is no simple way of doing this.).

[modest_may]

Originally Posted by ghorrocks

I do not understand your k-w question.

Are you asking whether you can run the k-w turbulence model but overwrite the eddy viscosity and just use a pre-determined eddy viscosity? (Answer: Then why run the k-w turbulence model?)

Or are you asking whether we can determine the k and omega field values are for a specified eddy viscosity field? (Answer: no, this is an inverse question and they are complex to solve. There is no simple way of doing this.).

What I want to know is whether we can get the k and omega field under a specified eddy viscosity field, and this is the reason why run the k-ω turbulence model, even if this running may have no physical meaning.

In fact, the reason for getting k and omega field values is also attributed to the adjoint method. Zymaris et al. (above Ref.[1]) derived the adjoint SA turbulence model and I am trying to deduce the adjoint k-ω turbulence model. Meanwhile, Papoutsis-Kiachagias and Giannakoglou [2] derived the adjoint k-ε turbulence model. I use their results here to explain. The primary and adjoint governing and k-ε turbulence model equations is shown in Figures 1-2.

First, the primary equations are sloved and the eddy viscosity (v_t) is obtained. Then, in the adjoint system, with the known eddy viscosity (v_t), k and ε values should be calculated by solving the adjoint k-ε turbulence model, see Eq.s (58b)-(58c) in Fig.2. Solved k and ε are used to add source terms to adjoint momentum equations, i.e. AMSi in Eq.(56) in Fig.1. Those source terms are functions of adjoint k and ε as implied by Eq.(57b).

So similar procedure will be conducted to the adjoint system with k-omega model.

I am sorry if it sounds a little complicated. Nevertheless, i will try to solve this problem. Thank you, sir. I really appreciate your reply.

It is too late now and i am so sorry to bother you. Thank you and have a good rest.

[modest_may]

PS:
Ref.[2] E.M. Papoutsis-Kiachagias and K. C. Giannakoglou.Continuous Adjoint Methods for Turbulent Flows, Applied to Shape and Topology Optimization: Industrial Applications.Arch Computat Methods Eng (2016) 23:255–299.

[ghorrocks]

This is a research question, so I will leave it up to you to solve it and publish the paper on it

Some comments from me:
* Basic mathematics says you can't get k and omega/epsilon from an eddy viscosity field. In short, you only have one input variable and are looking for two output variables. You need more information. The additional information could come from many places (boundary conditions, momentum or mass equation coupling etc)
* Getting the k and omega/epsilon from an eddy viscosity field is an inverse problem (https://en.wikipedia.org/wiki/Inverse_problem). I already said this - they are a particularly difficult area of mathematics so do not expect any easy answers here.
* The SA turbulence model is far simpler than the two equation k-omega or k-epsilon equations. Deriving the adjoint equations for these two equation models will be significantly more complex than SA. But I suspect you already knew this

[modest_may]

Originally Posted by ghorrocks

This is a research question, so I will leave it up to you to solve it and publish the paper on it

Some comments from me:
* Basic mathematics says you can't get k and omega/epsilon from an eddy viscosity field. In short, you only have one input variable and are looking for two output variables. You need more information. The additional information could come from many places (boundary conditions, momentum or mass equation coupling etc)
* Getting the k and omega/epsilon from an eddy viscosity field is an inverse problem (https://en.wikipedia.org/wiki/Inverse_problem). I already said this - they are a particularly difficult area of mathematics so do not expect any easy answers here.
* The SA turbulence model is far simpler than the two equation k-omega or k-epsilon equations. Deriving the adjoint equations for these two equation models will be significantly more complex than SA. But I suspect you already knew this

OK, sir, I will keep on going to solve this problem. Again, thank you very much for your suggestions.