Airfoil Optimization Using Practical Aerodynamic Design Requirements

Practical aerodynamic design problems must balance the goal of performance optimization over a range of on-design operating conditions with the need to meet design constraints at various off-design operating conditions. Such design problems can be cast as multipoint optimization problems where the on-design and off-design operating conditions are represented as design points with corresponding objective/constraint functions. Two methods are presented for obtaining optimal airfoil designs that satisfy all design objectives and constraints. The first method uses an unconstrained optimization algorithm where the optimal design is achieved by minimizing a weighted sum of the objective functions at each of the operating conditions. To address the competing design objectives between on-design and off-design operating conditions, an automated procedure is used to efficiently weight the off-design objective functions so as to limit their influence on the overall optimization while satisfying the design constraints. The second method uses the constrained optimization algorithm SNOPT, which allows the aerodynamic constraints imposed at the off-design operating conditions to be treated explicitly. Both methods are applied to the design of an airfoil for a hypothetical aircraft where the problem is formulated as an 18-point multipoint optimization.The funding of the first and second authors by the Natural Sciences and Engineering Research Council of Canada and the third author by the Natural Sciences and Engineering Research Council of Canada and the Canada Research Chairs program is gratefully acknowledged