Optimization of a wheel fairing airfoil

Recently, we have applied the SUMO toolbox on an application from the aerospace industry. It is based on ``Airfoil Geometry Design for Minimum Drag'' by Z. Wang [#!WangZheng2005!#] and is a nice example of airfoil design. Whang is concerned with finding an optimal design of a wheel fairing (or wheel pant) on a solar powered vehicle. When designing airfoils, the typical goal is to optimize the lift-to-drag ratio, i.e., design an airfoil that has a high lift while having not a too high drag coefficient. However for a wheel fairing for a vehicle or airplane the main aim is to have a low drag coefficient. There are several published standard airfoils, for example the NACA series of the, now dissolved, National Advisory Committee for Aeronautics [#!uiic2008!#] who created series of airfoils for different purposes using analytical equations (see figure below for an example NACA profile). Nonetheless, in many cases it is useful and more efficient to create a custom-made design. See wikipedia for more information about wheel fairings.



Additionally it is always interesting to have a complete idea of the behaviour of the different parameters. As such we tried to model the objective function (for optimizing wheel fairing airfoils) using the SUMO toolbox. We utilized the open source xfoil program for simulation with the following objective:



The resulting surrogate model (a 4-14-2-1 neural network) had an accuracy of 1% (RRSE) on a validation set.



Due to the ANN model being cheap to evaluate we can now apply as many optimization algorithms as we want on this surrogate model. In this case we just applied the DIviding RECTangles (DIRECT) algorithm, resulting in the following wheel fairing airfoil:



Ivo--