# Example Three-dimensional Airfoil Analysis

Next we consider a three-dimensional slice of the NACA0012 airfoil that is 0.05 chord lengths wide and sandwiched between a pair of symmetry boundary conditions. In this case, Harpoon meshes are used and again compared to the 2D data available on the NASA Web site. Results are calculated using both simple meshes (30 < *y+ <* 150 and the Spalart-Allmaras turbulence

Figure 13.14 Computed two-dimensional flow past the NACA0012 foil when almost fully stalled.

model) and fine boundary layer models (y+ < 1 and the *k -* ® SST turbulence model). The meshes used are those already shown in Figure 13.6 and Figure 13.15. The Harpoon meshes have 548 000 and 5 344 000 cells, respectively. The *y+* plots for these meshes are those already given in Figures 13.7 and 13.8.

The resulting lift and drag data are plotted in Figure 13.16. Note that at low AoAs, both the meshes again correctly predict the lift, while the finer *k -* ® SST turbulence model mesh is better at predicting the drag, as would be expected. Once separation begins, the approach to stall the quality of the mesh critically impacts on the ability to predict the angle of maximum lift and the drag. Here the lower resolution Spalart-Allmaras mesh gives drag values that are more than 100% in error and stall much too early. Neither of the three-dimensional meshes is as good at predicting high AoA behavior as the two-dimensional meshes considered in the previous subsection. In summary, neither of these models is completely accurate, again making clear the limitations of RANS-based analysis. Of course, the mesh quality is as much related

Figure 13.15 Section through a fine-grained Harpoon 3D mesh around the NACA0012 foil suitable for the *k — m* SST turbulence model. Note the wake mesh extending from the trailing edge.

Figure 13.16 Experimental and 3D computational lift and drag data for the NACA0012 airfoil (using the Spalart-Allmaras and *k — a* SST turbulence models). NASA.

to the effort and experience of the user as the underlying tool, but these results indicate that octree-based meshing tools are not as well suited to this analysis as the block-structured ICEM mesh or the very high quality NASA test meshes, though they are much easier and faster to use when meshing complicated three-dimensional airframes.