Investigation of multimodality in aerodynamic shape optimization based on the Reynolds-Averaged Navier-Stokes equations

摘要

This paper presents an improvement to a multi-start method for gradient based exploration of moderately multimodal design spaces in aerodynamic shape optimization problems. Free form deformation geometry control is used in conjunction with a gradient-based multistart algorithm to generalize cascading linear constraints for a sampler algorithm into a geometry-independent form. This permits large, high-quality, feasible samples of the design space to be generated and optimized quickly and efficiently. This algorithm is then used to explore multimodality in viscous aerodynamic shape optimization problems, including wings in transonic and subsonic flow, as well as a transonic blended wing-body design. Both wing cases are found to be multimodal, while the blended wing-body case is believed to be unimodal based on available evidence. A brief investigation of the effect that three degrees of freedom - twist, taper, and sectional control - have on multimodality in the viscous optimization of the common research model wing is undertaken. This investigation finds little evidence of multimodality related to twist and section control, while the addition of taper design variables leads to clear indications of multimodality.