Philipp Gittler, Andreas Mehrle,
"Comparison of Analytical and Numerical Solution for Optimal Vortex Diffuser Design"
: Proceedings in Applied Mathematics and Mechanics (PAMM), 2005
Comparison of Analytical and Numerical Solution for Optimal Vortex Diffuser Design
Sprache des Titels:
Proceedings in Applied Mathematics and Mechanics (PAMM)
The contribution deals with optimization of wing tip devices, so called vortex diffusers. A comparison is given between an analytical approach for obtaining the optimal circulation loading and the results of a numerical investigation using a lifting line method.
The purpose of most wing tip devices is to reduce the induced drag of the main wing by converting vortex energy into thrust. In order to achieve an optimal design, a variational formulation originally proposed by Betz and Prandtl for air screws is applied to the circulation distribution of the diffuser blades. In extension to the inviscid formulation, a viscous correction is applied in order to account for frictional forces.
In an effort to validate the analytical results, a comparison is given with numerical solutions from a lifting line method. The loading of the diffuser blades is parametrized and optimized with respect to resulting thrust by use of a quasi-Newton gradient method.
The results show that, knowing the velocity distribution in the near wake of the wing, considerable decrease of induced drag may be achieved making use of vortex diffusers. Although actual circulation loading may differ between the analytical and numerical estimation, resulting thrust agrees within a few percent.