D Models of Simple Wings
For low-speed, low-drag wing design, the NACA experimental report by Sivells and Spooner  is a useful source of results. This gives the lift, drag, and moment values for two slender, tapered, unswept wings of aspect ratio 9 at moderately high speeds (Re = 4.4 x 106 and Mach= 0.17) with a range of trailing-edge high-lift devices, with and without leading-edge roughness. If one is able to recover some of the details of this study with CFD approaches, then confidence can be had that results for less slippery wings with thicker boundary layers will be sensible.
This NACA study is based on the NACA 64-210 and 65-210 sections. Results for two-dimensional tests of the NACA 64-210 section can be found in Abbott and von Doenhoff  and also, both dry and in heavy rain, on the NASA server (Bezos et al. ). Interestingly, even for the dry cases, these two sources of experimental data differ, particularly with regard to the section drag coefficients. We show both these sets of data in Figure 13.17 together
Figure 13.17 Experimental [20, 22] and computationallift and drag data for the NACA 64-210 section. Source: Adapted from Abbott 1959.
with those calculated using meshes from the octree-based tool Harpoon, again with both lower resolution Spalart-Allmaras and higher resolution к - m SST turbulence models and appropriate meshes. Also shown are results from XFoil, which predict the Abbott and von Doenhoff data quite well but are some way from the later Bezos et al. data. The Harpoon meshes have 460 000 and 4.97 million cells, respectively, using 3D models, again with spans of 0.05 chord length between symmetry planes.
The XFoil and к - m SST results predict the low AoA lift and drag behavior well but, again, neither gives the ultimate stall angle that accurately, although the errors are less than the differences between the two sets of experimental data! Figure 13.18 shows a RANS solution when the airfoil has begun to stall; in fact, wind tunnel data suggest that the onset of such stalls may well be delayed at this angle for very smooth airfoils in low-turbulence wind tunnels.
Turning next to the complete Sivells and Spooner wing, Figure 13.19 includes two sets of experimental results and shows data calculated using XFLR5 and Fluent with Spalart-Allmaras and к - m SST turbulence models with Harpoon meshes. Figure 13.20 shows the XFLR5 model. First, the NACA 64-210 airfoil is loaded and analyzed from Reynold’s numbers from 105 to 6 X 106 and at angles of attack from -4° to 16°. This builds a database of results that can then be used for the wing analysis. At the Reynold’s number used in the reported work, XFLR5 gives lift and drag results from -3° to 13.5°; outside of this range, some of the sections stall and the results cannot be computed for the whole wing. For the Fluent models, just the octree-based Harpoon meshing tool has been used. The Spalart-Allmaras Harpoon mesh has 1.225 million cells, giving y+ values between 30 and 100. The к - m SST Harpoon mesh has 13.6 million cells including a trailing-edge wake mesh, giving mean y+ values 1.3, that is, not quite as fine as before.
Figure 13.18 Pathlines from a RANS k — m solution for the NACA 64-210 airfoil at 12° angle of attack. Note the reversed flow and large separation bubble on the upper surface.
Here there is little to choose between the RANS-based solutions: both give good estimates of lift at low AoA but overpredict the drag compared to the experiments with the smooth wing, while the XFLR5 results underpredict the drag. In addition, the behavior at maximum lift still cannot be accurately resolved using octree-based meshes. Even the XFLR5 model fails to solve some 2° before the smooth wind tunnel model stalls. If the degree of mesh resolution is increased for the k - m SST Harpoon mesh, using 76 million cells so that y+ can be brought mainly below 1, better results can be obtained for the drag, see Figure 13.21. Figure 13.22 illustrates the computed flow around the wing for this refined mesh at 11° AOA, the point of maximum lift predicted in this case. Note that some of the pathlines show the onset of stall. Sivells and Spooner  give a sketch for this wing at 11.5°, albeit with a roughened leading edge, that shows separation to begin at just this location in the span-wise direction (the pathlines oscillate and the static pressure suction at the front of the wing collapses). In summary, with a very refined boundary layer, the Fluent model behaves at separation rather like the experimental wing with roughened (and thus more realistic) leading edge. Such results need to be treated with caution but clearly are of use in understanding the behavior of the wing over a range of operational conditions.