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Aerodynamic Shape Optimization PDF

Th. Lutz
Colloquium on Fluid Dynamics Research - Selected Recent Results, University of Stuttgart, May 7, 2004


Abstract:

For the aerodynamic design of wings or airfoils inverse methods were preferred for a long time. With an inverse design, the user has to prescribe the intended pressure distribution or the development of relevant boundary-layer parameters in order to obtain a shape with specific aerodynamic characteristics. The quality of the result, thereby, mainly depends on the experience of the user.
An alternative to this approach is given by direct numerical optimization (DNO). With DNO an automated, computer-based, search for an optimal solution with respect to a given scalar objective function is performed. The objective function may be the drag at a certain design point or a weighted mean for a complete design range. The optimization is accomplished by means of a more or less systematic variation of the design variables which parameterize the shape to be optimized. A multitude of different optimization algorithms, ranging from gradientbased methods to stochastic approaches with highly sophisticated schemes for the adaptation of the individual mutation step sizes, are available. In general, gradient-based methods converge fast for simple topologies of the objective function but will get trapped in a local optimum if multi-modal objective functions are considered. Evolutionary optimizers offer a greater chance to avoid this problem and can also cope with complex, noisy objective function topologies. As a drawback, they usually require much more iterations to converge, especially if a large number of design variables is considered.