Research Summary for
- The final version of the AIAA MAO Conference paper (including the changes for the references) is here.
- The RAE 2822 cases (Mach=0.750, Re=6.2 x 10 6 , and alpha=3.19 deg.) with the k-w turbulence model and the Min-Mod limiter exhibits oscillatory behavior at grid levels 2, 3, and 4 (Figure 1). The amplitude and the period of the oscillations get larger as the mesh is refined. The oscillations were not observed for the cases with Sp-Al model, and the Min-Mod limiter. When k-w, grid 2 runs were repeated with Van Albada limiter, the oscillations were much smaller.
- To see the difference in pressure distributions between the results obtained at iteration numbers that correspond to the peak values of the sinusoidal oscillations, grid level 4 results are used (Figures 2 and 3). The difference in the shock location and the Cp distribution at the separated flow region between the solutions at different iteration cycles can be seen. The maximum difference in CL is approximately 5% (The experimental CL value is used as the comparator).
- To analyze the grid and the iterative convergence in the absence of shock waves and flow separation, a generic case with Mach=0.30, Re=6.2 x 10 6 , and alpha=0.0 deg. is being run for the RAE 2822 airfoil. Sp-Al turbulence model and the Min-Mod limiter is used (there should be no effect of the limiter on the solution in the absence of shock waves). Note that there is no experimental data for this case. The results obtained with the grid levels 1, 2, and 3 are presented in the last three figures and Table 1.
Figure 1. CL vs. cycle number with different grid levels and turbulence models for the RAE 2822 airfoil case with Mach=0.750, Re=6.2 x 10 6 , and alpha=3.19 deg.
Figure 2. The close-up view of CL vs. iteration number for grid level 4 (k-w, model and the Min-Mod limiter).
Figure 3. Pressure distributions obtained at iteration numbers 7100 (black), 10000 (blue), and 12700 (red) with grid level 4, k-w model, and the Min-Mod limiter.
Figure 4. Pressure distributions obtained with the Sp-Al model and the Min-Mod limiter for the RAE 2822 airfoil case with Mach=0.30, Re=6.2 x 10 6 , and alpha=0.0 deg.
Figure 5. CL vs. cycle number with different grid levels and turbulence models for the RAE 2822 airfoil case with Mach=0.30, Re=6.2 x 10 6 , and alpha=0.0 deg.
Table 1. The
CL and CD values for the case with Mach=0.30, Re=6.2 x 10 6 , and
alpha=0.0 deg.
|
CL |
CD (in terms of drag counts) |
|
Grid 1 |
0.0567 |
-18 |
|
Grid 2 |
0.1595 |
27 |
|
Grid 3 |
0.1893 |
52 |
Figure 6. L2 Norm Residual history obtained with different grid levels, Sp-Al model, and the Min-Mod limiter for the RAE 2822 airfoil case with Mach=0.30, Re=6.2 x 10 6 , and alpha=0.0 deg..
