Über die optimale Gestaltung von widerstandsmindernden Zusatzelementen eines Tragflügels

Finding the drag minimizing wing shape and in particular wing tip shape is one of the important unsolved problems in aerodynamics. Of all the designs proposed so far, the vortex diffuser is particularly well suited for optimization due to the separation of lifting surfaces and drag reducing devices. In this context the thrust of a vortex diffuser was formulated within the framework of lifting line theory and an analytical solution obtained by applying the variational principle. If experimental data regarding the profile characteristics are available, viscous forces can also be accounted for. Alternatively the drag minimizing shape may be found by numerical optimization. To this end Multhopp's method was extended to (radial) periodic assemblies with the results being in excellent accordance with the analytical solution. By varying the parameters such as the number of winglets or their radial extension the best diffuser setting may be found. The crucial unknown for the analysis is the velocity distribution of the incoming trailing vortex which may either be determined empirically or calculated by three-dimensional aerodynamic codes. By comparison with a small-scale experiment, calculations of a low-order panel code were found to give reliable and accurate results and were therefore the method of choice for further investigations. Finally, the developed methods were applied to a small-scale and a full size configuration. Although drag reduction is sensitive to minute geometric details of the vortex diffuser, the obatined thrust does not depend on the used profile given a correct adjustment. The only restriction is that the vortex diffuser winglets work at reasonably large Reynolds numbers. For the rectangular wing at very high angles of attack about 30$% of the induced drag could be recovered.