Wing-shape optimization

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.

Abstract: Equivalent plate structural modeling and doublet point lifting surface unsteady aerodynamics are used to obtain analytic sensitivities of aeroelastic and aeroservoelastic response with respect to wing and control surface planform shape parameters. Rational function approximations for unsteady aerodynamic forces, their shape sensitivities, and the resulting linear time invariant state space models of aeroservoelastic systems and their shape sensitivities are examined. The goal is to develop effective and numerically efficient approximation techniques for wing shape optimization for use with nonlinear programming and approximation concepts as a multidisciplinary optimization strategy. Effects of structural and unsteady aerodynamic modeling errors are studied. Examination of approximation accuracy using alternative approximation techniques (and the resulting move limits) provide insight and experience on the way to realistic wing/control surface shape optimization with active controls and aeroservoelastic constraints.

Abstract: Ultra-High Bypass (UHB) fanjet engines offer substantial improvements in fuel burn and take-off noise, and are an important part of efforts to reduce the environmental impacts of commercial air travel. To fully achieve the performance gains offered by UHB engines, an integrated design approach is necessary where the wing and nacelle shapes are optimized simultaneously. The new Cart3D-Adjoint Optimization Framework was used to design a representative single-aisle transport configuration with a UHB nacelle. The optimization process produced an integrated wing–nacelle design with a number of interesting features, including an unusual spanwise lift distribution and local tailoring of the supercritical wing shape in the viscinity of the nacelle. Viscous effects were accounted for by using an inverse design method coupled with a viscous flow solver to adjust the shape of the wing to maintain the desired span loading and section pressure distributions of the inviscid optimized design. Selected computational and experimental results are presented which highlight interesting characteristics of the integrated nacelle-wing design and its performance.

Abstract: This article aims to contribute to numerical strategies for PDE-constrained multiobjective optimization, with a particular emphasis on CPU-demanding computational applications in which the different criteria to be minimized (or reduced) originate from different physical disciplines that share the same set of design variables. Merits and shortcuts of the most-commonly used algorithms to identify, or approximate, the Pareto set are reviewed, prior to focusing on the approach by Nash games. A strategy is proposed for the treatment of two-discipline optimization problems in which one discipline, the primary discipline, is preponderant, or fragile. Then, it is recommended to identify, in a first step, the optimum of this discipline alone using the whole set of design variables. Then, an orthogonal basis is constructed based on the evaluation at convergence of the Hessian matrix of the primary criterion and constraint gradients. This basis is used to split the working design space into two supplementary subspaces to be assigned, in a second step, to two virtual players in competition in an adapted Nash game, devised to reduce a secondary criterion while causing the least degradation to the first. The formulation is proved to potentially provide a set of Nash equilibrium solutions originating from the original single-discipline optimum point by smooth continuation, thus introducing competition gradually. This approach is demonstrated over a testcase of aero-structural aircraft wing shape optimization, in which the eigen-split-based optimization reveals clearly superior. Thereafter, a result of convex analysis is established for a general unconstrained multiobjective problem in which all the gradients are assumed to be known. This results provides a descent direction common to all criteria, and adapting the classical steepest-descent algorithm by using this direction, a new algorithm is defined referred to as the multiple-gradient descent algorithm (MGDA). The MGDA realizes a phase of cooperative optimization yielding to a point on the Pareto set, at which a competitive optimization phase can possibly be launched on the basis of the local eigenstructure of the different Hessian matrices.