- With the original experimental geometry data, between x/ht=0.0 (the sonic throat) and the shock wave position, the wavy character of the pressure was observed (Figures 2 and 3). A sudden expansion and compression can be seen around x/ht=0.5. This was due to the geometric irregularity between the throat and x/ht=0.9 (Figure 1). Two experimental data points (3rd and 5th point from the throat) seemed to cause the local expansion and compression by creating local bumps. The locations of these two points were modified by moving them in the negative y direction halfway between their original value and the analytic equation value obtained at the corresponding x/ht locations. These modified locations are shown with black circles in Figure 1. Before fitting cubic splines to the modified data, the convexity of the modified locations were checked.
- New grids were generated for the modified experimental geometry. These grids have the same dimensions as the previous grids g1, g2, g3, and g4. The same cases with the Sp-Al and k-w turbulence models, Van Albada and Min-mod limiters at Pe/P0i=0.72 and 0.82 were run with the grids g1, g2, and g3.
- With the modified geometry, local expansion and compression region seems to be smoothed (Figures 2 and 3), although there is still difference between the experimental pressure distributions and the numerical results.
- The results may indicate that the difference between the experiment and the CFD upstream of the shock is more likely due to the geometric uncertainty.
Figure 1. The geometry of the nozzle in the vicinity of the throat for different cases.
Figure 2. The top wall pressure distributions obtained with
different geometries (equation, experimental geometry, and the modified-experimental
geometry), Sp-Al model, and the Min-Mod limiter at Pe/P0i=0.72)
.
Figure 3. The top wall pressure distributions obtained with different geometries (equation, experimental geometry, and the modified-experimental geometry), Sp-Al model, and the Min-Mod limiter at Pe/P0i=0.82)
Figure 4. Nozzle efficiencies with different geometries at Pe/P0i=0.72.
Figure 5. Nozzle efficiencies with different geometries at Pe/P0i=0.82.