Wing aerodynamic optimization using efficient mathematically-extracted modal design variables

Abstract

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. 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.

Efficient Modal Design Variables for Optimization of Aero-Elastic Wing

“…However, the sectional deformations can also be applied in a global nature, and while this is not as flexible as local deformation, the authors have shown global deformations to provide reasonable optimization results but at a fraction of the cost. 23 The sectional deformations are applied using the RBF control point approach, where a set of control points are defined in the fluid domain and global volume interpolation translates deformation of the control points to deformation of the aerodynamic mesh. Hence, the modal deformations are used to drive deformation of the control points that subsequently deform the wing surface and mesh.…”

“…These are applicable to aerodynamic optimization of aerofoils 5 and wings. 23 Furthermore, comprehensive experiments 24 have shown singular value decomposition (SVD) modes to be the most efficient approach at representing a generic aerofoil compared to most other commonly used parameterization methods.…”

Objectives and Constraints for Transonic Wing Optimization

“…Modal deformations are applied sectionally at ten spanwise station (on the red main control points), while intermediate control points (shown in blue) are used to permit smooth spanwise deformations between the deformation slices. 35 The deformation of intermediate points uses a partition of unity-blend of the deformation slices at either side. A global twist deformation is also introduced.…”

Efficient Aero-Structural Wing Optimization Using Compact Aerofoil Decomposition

“…Of these, singular value decompositionbased approaches take a training matrix of data (for example a number of aerofoil shapes [24,25]), and project a reduced-order basis approximation of the original data. Work by the authors has shown that this is a very efficient approach for producing a reduced set of aerofoil deformation modes [26] that are suitable for aerodynamic optimization of aerofoils [6] and wings [27]. The reduced set of modes has been used for high-fidelity global optimization of aerofoils [6].…”