Multimodality in Aerodynamic Wing Design Optimization

Abstract

The application of gradient-based optimization to wing design could potentially reveal revolutionary new wing concepts. Giving the optimizer the freedom to discover novel wing designs may increase the likelihood of multimodality in the design space. To address this issue, we investigate the existence and possible sources of multimodality in the aerodynamic shape optimization of a rectangular wing. Our test case, specified by the ADODG Case 6, has a high dimensionality design space and a large degree of flexibility within that design space. We study several subproblems of this benchmark test case and analyze the multimodality introduced by each set of variables. We find evidence of multimodality with both inviscid and viscous analysis. In the full case we find that optimization with inviscid analysis yields multiple non-intuitive local minima. Adding consideration of viscous effects does not remove the multimodality, but allows the multiple local minima to be explained with physical reasoning. Additionally, we find that the shape of the optimized wing is highly dependent on the interplay between induced and viscous drag, providing more incentive to consider viscous effects in the analysis. The best result found by the optimizer reduces the total drag of the baseline wing by 22%.Many of the applications of MDO to aircraft design have been targeted at optimizing specific configurations or features. In one of the first demonstrations of numerical optimization in wing design, Hicks and Henne [4] modified the design of a swept wing with airfoil shape and twist variables to reduce wave drag and increase L/D. Jameson et al. [5] optimized a wide-body wing and wing-fuselage configuration and recovered a shock-free surface. Several studies have investigated the optimization of winglets [6][7][8]. Martins et al. [9] accomplished a CFD-based aerostructural optimization of a supersonic business jet. More recently, a number of studies have been published on the high-fidelity design optimization of the Common Research Model (CRM) benchmark wing [10][11][12][13]. Application of MDO to future aircraft concepts like the blended wing-body [14] and D8 [15] has also been a fruitful area of research.These results have strengthened the credibility of MDO and its applicability to practical aircraft design problems. However, these studies focused on the refinement of existing technologies, or making good aircraft better. There are sound reasons for starting an optimization problem from a design that already employs state-of-the-art knowledge and techniques. In high-fidelity aerostructural optimizations for example, starting the optimization with a poor initial design can prevent the optimizer from finding a feasible solution. However, in the long term, we want to make MDO robust enough that it can be used to explore the full design space and discover novel designs. Ideally we would be able to start an optimization from a sphere and recover an airplane that would be optimally suited to its mission requirements. Gagnon and Zingg [16] tes...

An adaptive optimization strategy based on mixture of experts for wing aerodynamic design optimization

“…As for the previous use case on CRM wing, the SEGOMOE approach is compared to SNOPT on the same test case. These gradient-based results, as well as other cases related to ADODG Case 6, are presented in more detail by Bons et al 45 Here we just compare the SEGOMOE results for the Euler-based twist and dihedral optimization case, and summarize the corresponding results from Bons et al 45 for completeness. The optimization problem was solved using SNOPT 28 starting from 10 random shapes, as illustrated in Fig.…”

Multipoint Aerodynamic Shape Optimization for Subsonic and Supersonic Regimes

“…Moreover, the relevance of viscous drag and boundary layer-shock interactions increases when subsonic and transonic flight conditions are taken into account. In this sense, the advantages of using a viscid solver for subsonic and transonic ASO problems have been highlighted by previous works [9,10,11].…”

Multi-fidelity efficient global optimization: Methodology and application to airfoil shape design

“…The goal is to find the global optimal geometry of the airfoil as computed by the high-fidelity code ADflow. † ADflow has a Reynolds Averaged Navier-Stokes (RANS) multi-block flow solver developed in the MDO Lab (University of Michigan) that has been successfully applied to a variety of aerodynamic shape optimization problems [21][22][23][24].…”