Compressibility correction for SST model

[sun5k]

Proposed Changes

Compressibility Correction(CC) for the k-w SST model.

Two kind of CC is implemented. Both CC were based on Wilcox's book(Turbulence Modeling for CFD 3rd) and the paper of Rumsey

The k-w SST model transport equation :

*The production term is according to version or options for SST model(SU2 ver 8.0.1 has 1994m or 2003m).

1. Wilcox
   
   
   
   The H is the Heaviside function.
   

2. Sarkar
   In the Sarkar's CC, the pressure dilatation() is considered. The k transport equation is :
   
   
   
   

Validation Case

Validation analysis is conducted for the hypersonic flat plate. Two different wall temperature(T_w/T_free = 1.090 and T_w/T_free = 2.725) results are presented and compared with simulation results of ANSYS Fluent.

The CC of Fluent and Wilcox is almost same, but they have different coefficients(Wilcox : / Fluent : ). So, The results show a similar behavior to the Fluent results.

PR Checklist

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• I am submitting my contribution to the develop branch.
• My contribution generates no new compiler warnings (try with --warnlevel=3 when using meson).
• My contribution is commented and consistent with SU2 style (https://su2code.github.io/docs_v7/Style-Guide/).
• I used the pre-commit hook to prevent dirty commits and used pre-commit run --all to format old commits.
• I have added a test case that demonstrates my contribution, if necessary.
• I have updated appropriate documentation (Tutorials, Docs Page, config_template.cpp), if necessary.

[bigfooted]

That would be a nice addition! Can you also add a testcase (this flat plate testcase) for each of the cases, and add the cfg + regression tests to this repository? Maybe do the regression test on one of the coarsest meshes. Best would be to have set it up with a restart file that is completely converged.

[bigfooted]

Regrading the results: Why do we not see the dip in skin friction coefficient for low Reynolds like we see in the paper of Rumsey? The paper shows that predicting this dip is a feature of the model, and it makes it different from the van Driest theory.

[sun5k]

That would be a nice addition! Can you also add a testcase (this flat plate testcase) for each of the cases, and add the cfg + regression tests to this repository? Maybe do the regression test on one of the coarsest meshes. Best would be to have set it up with a restart file that is completely converged.

Hi @bigfooted.

I made regression test on "parallel_regression.py". Should I make extra regression test on "hybrid_regression.py" and "serial_regression.py"?

[sun5k]

Regrading the results: Why do we not see the dip in skin friction coefficient for low Reynolds like we see in the paper of Rumsey? The paper shows that predicting this dip is a feature of the model, and it makes it different from the van Driest theory.

I thought it depended on the grid resolution. The case of fine resolution grid(545 x 385), we can see "dip" in SU2 result(but relatively small).

From the "Coarse-Zoom" plot, The "dip" in coarse mesh(138 x 97) also appears in SU2, but it is really weak.

[bigfooted]

I copy the comment in the review here as well:
Can you check the equation for the pressure dilatation that you give above? Should I compare it to eq (39) of the paper? The equation (39) in the paper is $(-a_2 P M_t^2) +(a_3 \rho \epsilon M_t^2)$ which is different from what you write above and what is in the code. I guess you use the relationship $\epsilon=\beta^{\star} \omega k$, so the above becomes:
$(-a_2 P M_t^2) +(a_3 \beta^{\star} \rho \omega k M_t^2)$

You have in the code $(-a_2 P M_t) + (a_3 \beta^{\star} \rho \omega) + k M_t^2$

[bigfooted]

Can you add the updated results here? Did the results improve?

[sun5k]

Can you add the updated results here? Did the results improve?

Hi @bigfooted , I'm sorry to forgot shearing the updated result.

Here is the result fixed for the correct source term. The Cf is slightly shifted up.

This is a comparison of the previous and the fixed result.

[bigfooted]

@pcarruscag @sun5k Anything else necessary for this PR?