[fvi]

Hi everybody,

I have read that a cubic formulation of the k-w SST model exists in Star CCM+. However, I couldn't find any reference to a specific paper reporting the details of such a model in the document I was reading.
Is there anyone who could post the reference of a published paper giving such details (i.e. the paper referenced in the code Theory Guide) ?

Thanks in advance.

fvi

[fluid23]

Where did you read that?

Is it possible you are confusing the low-Re k-epsilon model, sometimes called the Lien cubic low Re model?

Lien, F.S., Chen, W.L., and Leschziner, M.A. 1996. “Low-Reynolds number eddy-viscosity modelling based on non-linear stress-strain/vorticity relations”, Proc. 3rd Symp. on Engineering Turbulence Modelling and Measurements, 27-29 May, Crete, Greece.

[fvi]

Thank you for your reply.

In the following paper (and it's not the only one from the same authors), a cubic SST k-w model is mentioned :

https://doi.org/10.1016/j.nucengdes.2019.110376

Indeed, Lien et al.'s paper is referenced when talking about this cubic model. This is unclear for me, since the model described in Lien's paper is an epsilon-based model. Therefore, I wonder why Lien's model should be named cubic k-w SST.

Menter et al. proposed a cubic model (see Menter et al., "Explicit Algebraic Reynolds Stress Models for Anisotropic Wall-Bounded Flows", 3rd European Conference for Aero-Space Sciences, July 6-9th 2009 Versailles), but I have no idea whether this model is available in STAR CCM+.

I hope somebody can help me in clarifying this topic.

[fluid23]

Based on the context of how it appears in this paper, I believe they are referring to the curvature correction option for k-w SST.

The flow field is analysed in terms of mean axial velocity component, turbulent kinetic energy and uv Reynolds stress for four different turbulence models, namely realizable k-ε, k-ω SST, RSM-EB and k- ω SST cubic. It is worth noting that the first two approaches are linear, while the last two include non-linear functions of the strain and rotation tensors, which are expected to capture the effects of secondary flows, streamline curvature and rotation Lien et al. (1996). Non-dimensional fields are used, consistent with the DNS reference data of Shams et al. (2018).

You should be able to activate this option under the model settings. I do not believe that it is default to the k-w SST model.

[fluid23]

I found this discussion that you might find useful.

SST K-Omega Cubic constitutional relation

And then, this in the help files.

Simulating Physics > Turbulence > Reynolds-Averaged Navier-Stokes (RANS) Turbulence Models > K-Omega Turbulence > K-Omega Models Reference

Constitutive Option
Controls the type of constitutive relation used. Consider applying a non-linear relation in the presence of anistropic turbulence. See Accounting for Anisotropy of Turbulence.
•Linear: Selects the linear constitutive relation as implied by the Boussinesq approximation (see Eqn. (1030).
•QCR: Selects the quadratic constitutive relation (Eqn. (1121)).
•Cubic: Selects the cubic constitutive relation (see Eqn. (1122)).

There is a cubic constitutive relationship option that may be what is meant.

[fvi]

Originally Posted by fluid23

I found this discussion that you might find useful.

SST K-Omega Cubic constitutional relation

And then, this in the help files.

Simulating Physics > Turbulence > Reynolds-Averaged Navier-Stokes (RANS) Turbulence Models > K-Omega Turbulence > K-Omega Models Reference


There is a cubic constitutive relationship option that may be what is meant.

Exactly, I do think that "cubic" is related to the constitutive relation of Reynolds stresses rather than to curvature correction.

Thank a lot for posting the code's help: however it is astonishing that no reference to a scientific paper is given. As far as I understand, it is only said that a cubic formulation exists and that it is applicable to SST model. How seems to be a mystery

[fluid23]

Go to the Steve Portal and submit a help ticket (assuming you have access). Explain this to them and they should eventually get you in touch with someone who can answer your question.

I have done this before regarding a similar gap in information in the help material and they came back with a white paper. They were very helpful. I am not saying that you'll get the same result... but you might.

I would be interested to see result if you ever figure this out. You made me curious.

[fvi]

Unfortunately I have no access to Steve Portal. I tried to contact some Customer Service guy on LinkedIn, let's see if it works. If I have news, I'll let you know.

Thanks for your answers!

[fluid23]

I can see about submitting a ticket on this for you. I likely won’t have an answer until mid next week.

[fluid23]

I found the formulation for cubic k-w in the help material.

See Theory > Turbulence > Reynolds-Averaged Naiver-Stokes (RANS) Turbulence Models > Eddy Viscosity MOdels > K-Omega Model > Constitutive Relations

The cubic model references the following papers:

Spalart, P.R. and Rumsey, C.L. 2007. “Effective Inflow Conditions for Turbulence Models in Aerodynamic Calculations”, AIAA Journal, 45(10), pp. 2544-2553.

Durbin, P.A. 1996. “On the k-e stagnation point anomaly”, Int. J. Heat and Fluid Flow 17, pp. 89-90.

[fvi]

Dear Matt,

I want to thank you once more because you are really trying to help me.

Concerning the two references you cited, I don't think they're what we are looking for. Indeed, Spalart's paper deals with boundary conditions used in CFD, whereas Durbin's paper proposes a limiter in the turbulent time scale which is partially taken into account in the SST model formulation. No mention to the cubic formulation of the SST model in both of them.

To me, we should be able to find something like the following paper:
Vitillo et al., "An anisotropic shear stress transport (ASST) model formulation", Computers & Mathematics with Applications, Volume 70, Issue 9, November 2015, Pages 2238-2251

As I told you, I could get in touch with a customer service guy I used to work with. I am waiting for an answer from him.

[fluid23]

Originally Posted by fvi

Dear Matt,

I want to thank you once more because you are really trying to help me.

Concerning the two references you cited, I don't think they're what we are looking for. Indeed, Spalart's paper deals with boundary conditions used in CFD, whereas Durbin's paper proposes a limiter in the turbulent time scale which is partially taken into account in the SST model formulation. No mention to the cubic formulation of the SST model in both of them.

To me, we should be able to find something like the following paper:
Vitillo et al., "An anisotropic shear stress transport (ASST) model formulation", Computers & Mathematics with Applications, Volume 70, Issue 9, November 2015, Pages 2238-2251

As I told you, I could get in touch with a customer service guy I used to work with. I am waiting for an answer from him.

Regardless of whether the papers appear applicable, they are specifically referenced in the cubic k-w model. They are likely to point you to the same location and references. All of the equations are documented in the help section I quoted. You should be able to connect the dots from there.

Good luck.

[fvi]

Dear Matt,

Finally I could have a (partially) satisfying answer from the Support Center.

The references we were looking for are:

- Hellsten, A. 2005. "New Advanced k-omega Turbulence Model for High-Lift Aerodynamics", AIAA Journal, Vol.43, No. 9, pp. 1857-1869.

- Wallin, S. and Johansson, A. V. 2000. "An Explicit Algebraic Reynolds Stress Model for Incompressible and Compressible Turbulent Flows," J. Fluid Mechanics, Vol. 403, pp. 89-132.

Here is the path from the user guide:

Theory > Turbulence > Reynolds-Averaged Navier-Stokes (RANS) Turbulence Models > Eddy Viscosity Models > K-Omega Model > Constitutive Relations

I personally think the talking about a cubic SST model is somehow misleading, since the two papers never talk about a baseline SST model for their cubic formulation. However, some features of these two models can partially explain the reason why STAR CCM+ guys wanted to link these models to the more famous SST model.

Thanks again for your help.

fvi