Investigation of Multimodality in Aerodynamic Shape Optimization Based on the Reynolds Averaged Navier-Stokes Equations

Abstract

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 e ciently. 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 e↵ect 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.

Approximate Hessian for accelerated convergence of aerodynamic shape optimization problems in an adjoint-based framework

“…Wings in various flow regimes are designed with ease and are now simple enough to be considered as academic base cases [1,6,53,20,26]. Aircraft configurations may be studied through multidisciplinary design optimization that takes into account both the flow and the structure [45,28,24].…”

Identifying Multiple Optima in Aerodynamic Design Spaces

“…For aerofoil optimization, it has been suggested that ASO problems exist that are unimodal [30] and multimodal [31,32], while the same is true of wings exhibiting unimodality [33] and multimodality [30]. Recently, results of the optimization of a rectangular wing in inviscid subcritical flow (this is case 6 of the AIAA ADODG [34]) have been presented investigating the degree of multimodality in that case [35][36][37][38]. However, while some aerodynamic optimization problems are multimodal, there is little effort to attempt to identify and characterise these.…”

“…Similar approaches were performed by Bons at al. [36], and Streuber and Zingg [38]. The current authors performed similar work by running a heuristic global optimizer multiple times on the same problem to analyse whether it converged to different solutions each time [37].…”

Correction: A Parametric Study of Multimodality in Aerodynamic Shape Optimization of Wings

“…9,10 It has been demonstrated that multimodality can exist in aerodynamic shape optimization problems, 11 and the importance of understanding multimodality in this context is underscored by the recent inclusion of a multimodal problem in the Aerodynamic Design and Optimization Discussion Group (ADODG) test suite at the AIAA Aviation 2017 conference. [12][13][14][15] The objective of this paper is to present a detailed study of the relationship between various problem parameters and multimodality in aerodynamic shape optimization of wings. This includes variations in available degrees of freedom, constraints, as well as Mach number, with particular attention paid to di↵erences ⇤ Ph.D.…”

“…On the other end of the spectrum, the existence of multimodality in the aerodynamic shape optimization of a wing in general is demonstrated in several previous works. 11,15,21 Between these extremes must lie a region in which multimodality changes from significant to insignificant and it is a goal of this work to determine the boundaries of these regions within the design space. This is accomplished by utilizing the free-form deformation 22 (FFD) based gradient-based multistart (GBMS) algorithm the authors published previously 15 to thoroughly explore the design space, specifically addressing the causes and extent of multimodality in the optimization of an aircraft wing under varying degrees of freedom, constraints, and operating conditions.…”