- Runs have been performed with two turbulence models (k-w and Spalart-Almaras), two flux-limiters (Min-mod and Van Albada), and four grids (coarse, fine, superfine, and megafine) at Pe/P0i=0.72. Combination of these parameters gave 16 cases.
- In addition to the nozzle efficiencies (figure 9), for each case, three measures of error were calculated in order to compare the numerical results with the experimental
wall pressure distributions:
1. Integrated Error (E_int):
2. L1 Norm Error (E_L1):
3. L2 Norm Error (E_L2):
- In the above error terms, P_c is the wall pressure obtained from the CFD calculations, P_exp is the experimental wall pressure value, and N_exp is the total number of
- In figures 4 and 8, minimum pressure locations at the top and the bottom walls are compared with the experimental data.
experimental data points (N_exp=36). In order to obtain the CFD results at the experimental data locations, cubic-splines were fit to the numerical pressure values.
Pressure values were scaled with the inlet-total pressure (P0i) and the x locations are scaled by the throat height (ht). Figures 1, 2, and 3 give the errors for the top wall
pressure and the figures 5, 6, and 7 show the errors for the bottom wall pressure.
- In figure 10, the nozzle efficiencies are plotted against h, a measure of grid spacing. If h is scaled with the finest grid level value, it can be defined as:
where N is the number of mesh cells and k is the grid level (k=1,2,3,4, from megafine to coarse). Figures 11 and 12 show the E_int vs h for the top and bottom walls.
- For the Spalart-Almaras cases, we see a converging trend in nozzle efficiency and errors, regardless of the limiters used, as we refine the grid size.
- For each turbulence model, the results obtained with two different limiters get closer as the grid size is refined.
- Compared with the experimental data, Spalart-Almaras turbulence model give better results than the k-w model.
Figure 1. Integrated error for the top wall pressure at Pe/P0i=0.72.
Figure 2. L1 norm error for the top wall pressure at Pe/P0i=0.72.
Figure 3. L2 norm error for the top wall pressure at Pe/P0i=0.72.
Figure 4. Minimum pressure location on the top wall at Pe/P0i=0.72.
Figure 5. Integrated error for the bottom wall pressure at Pe/P0i=0.72.
Figure 6. L1 norm error for the bottom wall pressure at Pe/P0i=0.72.
Figure 7. L2 norm error for the bottom wall pressure at Pe/P0i=0.72.
Figure 8. Minimum pressure location on the bottom wall at Pe/P0i=0.72.
Figure 9. Nozzle efficiencies at Pe/P0i=0.72.
Figure 10. Nozzle efficiency vs. h (scaled with the h of the
finest grid level) at Pe/P0i=0.72.
Figure 11. Integrated error of the top wall vs. h (scaled with
the h of the finest grid level) at Pe/P0i=0.72.
Figure 12. Integrated error of the bottom wall vs. h (scaled
with the h of the finest grid level) at Pe/P0i=0.72.
Figure 13. Pressure distribution at the top wall for Pe/P0i=0.72.
Figure 14. Pressure distribution at the bottom wall for Pe/P0i=0.72.