Current Research 4.12.2006
As discussed before (Previous Update), I have decided to group the wing control points into four groups for ease of computation. Our main goal with this particular part of research is to verify that changing the spacing on the surface of the wing has a positive effect on the accuracy of the downstream wingtip vortex produced. This refinement is done in a way in which the wing is only refine in places where it is deemed "needed". The figure 1 below depicts the control point groupings:
Figure 1: Control Point Groups
Through many trials, we have decided that in order to see this positive effect produced by the refinment of the wing's surface, the area downstream, particularly the region containing the wingtip vortex, needs to be finely resolved. This fine resolution downstream is achieved by placing a transparent, finely spaceed cylinder in the flow where the vortex is. This embedded cylinder can be seen below in figure 2:
Figure 2: NACA 0012 wing with embedded cylinder
This cylinder size, its placement, and shape were determined by trying a very large cylinder and running and computing the solution and changing the cylinder to fit the vortex. This process was done repetitively in order to get the shape as small as possible and still be the correct shape and size in order to accurately capture the vortex. After this was done, the spacing optimization using steepest descent could be performed. I initially thought this was going to be a smooth process but I ended up running into numerous problems including solution divergence and problems with the vortex analysis program VTAG. I am now back on track and am performing the iterations of the optimization. The results of the first two iterations can be seen below in figure 3. The inital control group spacing was 0.02 (2% of the chord). As shown, the first iteration went in the opposite direction of refinement, which scared me, but the second iteration turned around in the right direction. In the following weeks I will continue to perform the iterations until convergence.
| Design Vars |
Iteration 1 |
Iteration 2 |
| β1(Ctrl Grp 1) |
0.0200470863319801 |
0.0229996298271857 |
| β2(Ctrl Grp 2) |
0.0200497222080706 |
0.0186627684704360 |
| β3(Ctrl Grp 3) |
0.0206629752547489 |
0.0181310795413818 |
| β4(Ctrl Grp 4) |
0.0200104386683811 |
0.0180618087121162 |
| Initial Spacing = 0.02 |
Figure 3: Iteration table
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Last modified: Wed Mar 1 13:55:29 CST 2006