Investigation into Aerodynamic Shape Optimization of Planar and Nonplanar Wings

Abstract

Problems in three-dimensional aerodynamic shape optimization can produce complex design spaces due to the nonlinear physics of the Navier–Stokes equations and the large number of design variables used. In this paper, a Newton–Krylov optimization algorithm is applied to a set of complex aerodynamic optimization problems in order to investigate its behaviour and performance. The methodology solves the Reynolds-averaged Navier–Stokes equations with a parallel Newton–Krylov algorithm. Aerodynamic geometries are meshed using structured multiblock grids, which are then fitted with B-spline control volumes for mesh deformation and geometry control. A gradient-based optimization method is used, with adjoint variables calculated using a Krylov method. The optimization of the Common Research Model (CRM) wing is revisited, with a focus on the effect of varying geometric constraints and on the possibility of multimodality. In addition, several cases are presented that involve a high degree of shape change: two planform optimizations starting from a rectangular wing, and investigation of various wingtip treatments. The results characterize the methodology, demonstrating its robustness and ability to address optimization problems with substantial geometric freedom.