Unique solution for optimal airfoil design
P. Venkataraman, P. Venkataraman · 15th Applied Aerodynamics Conference · 1997
Optimization of airfoil shapes has attracted considerable interest in recent years. These investigations reveal the presence of innumerable local optimum solutions, which are obtained when the iterations are begun from different starting airfoil shapes. Some researchers using the genetic algorithm, with reduced scope of the aerodynamic model and a redefined search strategy have obtained global optimal solutions. In this paper an engineering alternative of finding a unique optimal solution is investigated. This solution is optimal in a significantly larger neighborhood and is formulated as an inverse airfoil design problem with constraints. A general piecewise linear pressure distribution is chosen to drive the optimization of the shape. Five existing airfoils representing a range of camber and thickness were chosen to start the iterative search. The optimization problem was formulated to minimize the error in the pressure distribution while satisfying constraints on C L, C0, and area. The flow was incompressible at a moderate Reynolds number. The XFOIL program provided the aerodynamic analysis. The study illustrates it is possible to identify a unique solution to the airfoil optimization problem as three of the five shapes moved close to a common solution without compromising their aerodynamic performance.