This will be followed by force and moment results obtained using both turbulence models on the Workshop supplied grid.
Next a solution reconstruction analysis procedure will be described that pinpoints regions of the grid that could benefit from grid refinement.
The supplied grid is refined in accordance with the results of the solution reconstruction procedure, and force and moment results of the refined grid are compared to the supplied grid results.
Only results for the Workshop Case 2 (Drag Polar at M=0.75 and Re =
3 million) will be discussed.
The CL-alpha curves for both turb. models are nearly identical, over predicting lift. This trend was consistent with many of the results of the workshop participants.
The drag polar is plotted using the idealized profile drag (drag - idealized induced drag) in order to expand the drag scale. Spalart-Almaras results are about 14 drag counts above the mean of the experimental data (at CL = 0.5). Menter's SST model is about 4 drag counts below the mean and skirts the lower edge of the scatter in the experimental data.
Both CL squared vs CD slopes of the computed data are high w.r.t. the experimental data.
Both turbulence models predict similar pitching moment variations with CL. The over prediction of the pitch-down moment is consistent with many of the results of the workshop participants.
To assess the solution-dependent grid resolution associated with a cell i, compare the computed cell-averaged value of cell i to the reconstructed cell-averaged value of cell i, and call this sigma. The computed cell-averaged value is known. The reconstructed cell-averaged value must be approximated from known information; namely, from the computed cell-averaged values of the cells surrounding cell i. The approximation of sigma works out to be no more than a discrete Laplacian of the solution for cell i. Actually, sigma is a vector norm of the discrete Laplacians of each of the primitive flow variables.
Sigma is not an estimate of solution error. It is an indicator of how well the grid is locally refining the solution. Higher values of sigma indicate lower solution-dependent grid resolution. Lower values of sigma indicate higher solution-dependent grid resolution.
This analysis can be easily applied as a post-processing step to any solution obtained on any grid type using any solver.
Compared to the supplied grid analysis (slide 7), the refined grid solution is better resolved. However, it appears that the solution could further benefit from additional grid refinement in the chordwise direction in the region over the upper surface of the wing, and possibly from better refinement of the wing tip vortex.
Grid refinement had little effect on the Spalart-Almaras predicted lift. However, the grid refinement caused Menter's SST predicted lift to decrease towards the experimental data.
Grid refinement had a significant impact on the Spalart-Almaras predicted drag, producing about a 14 drag count reduction (at CL=0.5) towards the mean of the experimental data. Grid refinement had a lesser impact on Menter's predicted drag, increasing drag by about 1.5 counts at CL=0.5.
The effect of the refined grid was to reduce the scatter between the drag predicted by the two turbulence models from about 18 to 3 counts.
Both turbulence model's refined grid CL2 vs CD curves are in better agreement with experimental data.
Menter's refined grid solution shows a marked improvement in predicted pitching moment. The Spalart-Almaras predicted pitching moment changed very little using the refined grid.
Changes in the Spalart-Almaras drag are largely due to changes in the skin-friction drag.
Feedback on
Langley Products and Services
Accessibility