Aerodynamic Shape Optimization Investigations of the Common Research Model Wing Benchmark

Abstract

Despite considerable research on aerodynamic shape optimization, there is no standard benchmark problem allowing researchers to compare results. This work addresses this issue by solving a series of aerodynamic shape optimization problems based on the Common Research Model wing benchmark case defined by the Aerodynamic Design Optimization Discussion Group. The aerodynamic model solves the Reynolds-averaged Navier-Stokes equations with a Spalart-Allmaras turbulence model. A gradient-based optimization algorithm is used in conjunction with an adjoint method that computes the required derivatives. The drag coefficient is minimized subject to lift, pitching moment, and geometric constraints. A multilevel technique is used to reduce the computational cost of the optimization. A single-point optimization is solved with 720 shape variables using a 28.8-million-cell mesh, reducing the drag by 8.5%. A more realistic design is achieved through a multipoint optimization. Multiple local minima are found when starting from multiple randomly generated geometries, but the minimum drag values are within 0.1 drag counts of each other, and the geometries differ by only 0.4% of the mean aerodynamic chord. The effect of varying the number of shape design variables is examined. The Common Research Model wing benchmark problem proved to be useful for evaluating our design optimization framework, and the geometries and meshes for both the baseline and optimized wings are available as supplemental materials in this paper.

Aerostructural optimization of the Common Research Model configuration

“…Optimality refers to how closely the current point satisfies the first-order Karush-Kuhn-Tucker (KKT) conditions [29]. Approximately 2 orders of magnitude reduction in the optimality are achieved, which is similar to previous aerostructural [1] and aerodynamic optimizations [28]. A complete overview of optimized configuration with the initial design is shown in Figure 10.…”

“…The leading edge radius constraint ensure no reduction in leading edge radius, potentially causing reduction in the low-speed C Lmax performance. Previous aerodynamic optimizations have shown that single point optimized designs without this constraint produce very sharp leading edges in transonic flow [28]. The trailing edge constraints are used to ensure a manufacturable trailing edge that is not too thin.…”

Weighted Gradient-Enhanced Kriging for High-Dimensional Surrogate Modeling and Design Optimization

“…The computational cost of evaluating the partial derivatives of an objective or constraint function is insensitive to the number of design variables, requiring only one flow solution and one adjoint solution. This method becomes the most practical one for the design of complex aerodynamic configurations [56,57] because it can deal with the optimization problems with 100-1000 design variables [58,59] or even more. The drawback of a gradient-based method is that the solution optimality can be sensitive to the initial guesses, and it can become trapped into a local minimum [60].…”

Global Optimization of Wing Aerodynamic Optimization Case Exhibiting Multimodality

“…Along with the fluid flow model, the ASO framework requires a surface parameterization scheme which mathematically describes the aerodynamic shape being optimized by a series of design variables; changes in the design variables, which are made by a numerical optimization algorithm, result in changes in the aerodynamic surface. Numerous advanced optimizations using compressible computational fluid dynamics (CFD) as the aerodynamic model have previously been performed [3][4][5][6][7]. The authors have also presented work in this area, having developed a modularised, generic optimization tool, that is flow solver and mesh type independent, and applicable to any aerodynamic problem [8,9].…”

“…For aerofoil optimization, it has been suggested that ASO problems exist that are unimodal [11] and multimodal [30,31], while the same is true of wings exhibiting unimodality [6] and multimodality [11]. Furthermore, recently, aerodynamic topology optimization results have suggested multimodality for a number of supersonic flow problems [32].…”