Abstract
Aerodynamic shape optimization of a transonic wing using mathematically-extracted modal design variables is presented. A novel approach is used for deriving design variables using a singular value decomposition of a set of training aerofoils to obtain an efficient, reduced set of orthogonal ‘modes’ that represent typical aerodynamic design parameters. These design parameters have previously been tested on geometric shape recovery problems and aerodynamic shape optimization in two dimensions, and shown to be efficient at covering a large portion of the design space; the work is extended here to consider their use in three dimensions. Wing shape optimization in transonic flow is performed using an upwind flow-solver and parallel gradient-based optimizer, and a small number of global deformation modes are compared to a section-based local application of these modes and to a previously-used section-based domain element approach to deformations. An effective geometric deformation localization method is also presented, to ensure global modes can be reconstructed exactly by superposition of local modes. The modal approach is shown to be particularly efficient, with improved convergence over the domain element method, and only 10 modal design variables result in a 28% drag reduction.
Highlights
Numerical simulation methods to model fluid flows are used routinely in industrial design, and increasing computer power has resulted in their integration into the optimization process to produce the aerodynamic shape optimization (ASO) framework
These design parameters have previously been tested on geometric shape recovery problems and aerodynamic shape optimization in two dimensions, and shown to be efficient at covering a large portion of the design space; the work is extended here to consider their use in three dimensions
Along with the fluid flow model, the ASO framework requires a surface parameterization scheme, which describes mathematically 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
Summary
Numerical simulation methods to model fluid flows are used routinely in industrial design, and increasing computer power has resulted in their integration into the optimization process to produce the aerodynamic shape optimization (ASO) framework. Along with the fluid flow model, the ASO framework requires a surface parameterization scheme, which describes mathematically 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. The optimization algorithm traces a movement path through the design space until the gradient values become very small where the result has converged These approaches are the most common methods used in the ASO framework (e.g., Imiela 2012; Hicken and Zingg 2010; Lyu et al 2015), driven primarily by the low cost associated with them compared to global methods (Chernukhin and Zingg 2013), and an efficient gradient-based optimizer is used here. The method itself has been presented recently by the authors (Poole et al 2015), and has been shown to outperform other commonly-used parameterization schemes (Masters et al 2017b) when considering geometric inverse design in two dimensions, often requiring fewer than a dozen variables to represent a large design space (Poole et al 2017)
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