Difficulty reproducing the near-stagnation heat flux in the SU2-NEMO HEG cylinder case

[caicaifen]

Hello everyone,

I am trying to reproduce the HEG cylinder validation case in Section 5.2 of:

Maier et al., "SU2-NEMO: An Open-Source Framework for High-Mach Nonequilibrium Multi-Species Flows", Aerospace, 2021.

I am using SU2 Release 8.3.0 "Harrier".

The wall pressure distribution agrees reasonably well with the published result. However, the wall heat-flux distribution near the stagnation region is difficult to reproduce correctly.

The main issue is not only lack of smoothness. In some runs the heat-flux curve is smooth, especially with first-order spatial accuracy, but the maximum heat flux does not occur at the stagnation point. In other runs, I observe an apparent artificial dip or bump near the stagnation point.

For a zero-angle 2D cylinder case, I expected the maximum wall heat flux to occur at the stagnation point, followed by a physically reasonable decrease along the cylinder surface. This is also the behavior shown by the published SU2-NEMO result in Fig. 7(b).

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SU2 version and build information

• SU2 version: Release 8.3.0 "Harrier"

• Source code: downloaded as a GitHub code zip archive for SU2 8.3.0

• Git commit hash: not available because the source was not cloned as a git repository

• Mutation++ version: unknown; Mutation++ was built/linked through the SU2 8.3.0 source tree

• Compiler: GCC 14.3.0

• MPI: Intel oneAPI MPI 2021.16

• CMake: 3.31.9

• Platform: Linux HPC cluster

• Number of MPI ranks: 192

• Command:

  mpirun -n 192 SU2_CFD HEG_M8.cfg > log_m8_static.out 2>&1

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Case description

I am reproducing the HEG cylinder case from Section 5.2 of the SU2-NEMO paper.

U_inf = 5956 m/s
p_inf = 476 Pa
rho_inf = 1.547e-3 kg/m^3
T_inf = 901 K
M_inf = 8.98
Y_N2 = 0.7543
Y_O2 = 0.00713
Y_NO = 0.01026
Y_N = 6.5e-7
Y_O = 0.2283
T_wall = 300 K

Geometry:

• 2D cylinder
• Radius: 45 mm

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Observed behavior

The wall pressure result is much easier to reproduce than the wall heat flux.

For the wall heat flux, I observe the following behavior:

1. With first-order spatial accuracy, the heat-flux curve can be relatively smooth, but the maximum heat flux is shifted away from the stagnation point.
2. With second-order spatial accuracy, the heat-flux curve often shows an apparent artificial dip or bump near the stagnation point.

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Expected behavior

Based on Fig. 7(b) of the paper, I expected a smooth wall heat-flux distribution near the stagnation region, comparable to the published SU2-NEMO result.

I understand that the non-catalytic simulation may underpredict the experimental heat flux, especially near the stagnation region. My concern is not only the absolute value, but the non-smooth local shape of the computed heat-flux curve.

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What I have tried

I have tried:

• Shock-aligned quadrilateral grids.
• Different first-cell heights near the wall, including values around (10^{-7}\ \mathrm{m}).
• Different CFL numbers.
• Different limiter coefficients.
• First-order and second-order spatial accuracy.
• Restarting second-order calculations from first-order solutions.

The near-stagnation heat-flux distribution remains difficult to reproduce robustly.

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Questions

1. Which SU2 version or commit was used to generate the HEG cylinder result in Maier et al. 2021?
2. Is the original HEG cylinder mesh and configuration file used for Fig. 7 available?
3. If the original mesh is not available, are there key mesh requirements for this case, such as first-cell height, wall-normal stretching, and number of cells between the wall and the bow shock near the stagnation line?
4. Was the published heat-flux result obtained by running one fixed configuration file from the beginning, or did it require a continuation procedure, such as first-order initialization, CFL/limiter adjustment, and then restarting with second-order accuracy?
5. If a continuation procedure was used, could you share the main steps?

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Attached files and figures

The attached files are:

• [HEG_M8.txt](https://github.com/user-attachments/files/28665543/HEG_M8.txt): SU2 configuration file.
• [HEG_Qtr_Sho_425x1500_1.su2.zip](https://github.com/user-attachments/files/28665545/HEG_Qtr_Sho_425x1500_1.su2.zip): compressed SU2 mesh file.
• [log_m8_static_head_tail.txt](https://github.com/user-attachments/files/28665544/log_m8_static_head_tail.txt): shortened SU2 runtime log, including the beginning of the run, selected warning/error messages, and the final residual history.

The attached figures are shown below. Surface-78.csv corresponds to the second-order run, and surface-119.csv corresponds to the first-order run using the same mesh and otherwise similar settings.

Wall heat-flux comparison:

Wall pressure comparison:

Mesh overview:

Please let me know if there is any obvious issue in my setup, or if a smaller minimal test case would be more useful.

Thank you very much for your time and help.