Direct method for the design of optimal three-dimensional aerodynamic shapes

A direct optimization method for a broad class of three-dimensional aerodynamic shapes based on the approximation of the desired geometry by Bernstein–Bézier surfaces is developed. The high efficiency of the method is demonstrated by applying it to the design of an optimal supersonic section of an axisymmetric maximum-thrust de Laval nozzle. The method is also tested as applied to the design of a three-dimensional supersonic nozzle section in a dense multi-nozzle setup. In addition to three-dimensional supersonic nozzle sections with a circular throat, nozzles with a varying throat shape are considered. The results suggest that the method can be applied to various problems of 3D shape optimization.