Multipoint Wing Planform Optimization via Control Theory

Abstract

This paper focuses on wing optimization via control theory using a multi-point design method. Based on the design methodology previously developed for wing section and planform optimization at a specific flight condition, it searches for a single wing shape that performs well over a range of flight conditions. A new cost function is defined as the weighted sum of cost functions from a range of important flight conditions. Results of multi-point optimization of a long range transport aircraft show that improvement at each flight condition is not as large as the result from single-point optimization at one of the design points. However improvement in performance measures such as drag divergence Mach number and the lift-to-drag ratio over a range of Mach numbers is significantly greater.

Multipoint High-Fidelity Aerostructural Optimization of a Transport Aircraft Configuration

“…The fidelity of the models used for aerodynamic shape optimization has also been increasing, and it is now possible to use computational fluid dynamics (CFD) to optimize a design with respect to hundreds of design variables using both Euler [15,16,17,18] and NavierStokes models [19,20,21]. In the design of transonic wings it is particularly important to use high-fidelity models to correctly predict the drag due to viscous and compressibility effects.…”

Unsteady Adjoint Approach for Design Optimization of Flapping Airfoils

“…Most previous design works were conducted focusing on uniform sinusoidal plunging and pitching motions, where the number of design parameters is small (limited to two or three), because of a prohibitive computational cost in unsteady optimization problems-even with an efficient gradient-based method. In a realistic aerodynamic shape optimization, the number of design D parameters needed to adequately describe an airfoil shape in transonic flow can vary from O (10) to O(100), even for a two-dimensional airfoil application [8][9][10]. As a result, the design cost of optimization based on CFD is expensive, even with today's computation power; hence a judicious choice of optimization approach for the current problem is warranted.…”

“…The adjoint approach has been regarded as a very efficient sensitivity analysis method for aerodynamic shape optimization because the computational time cost is almost independent of the number of design variables [8][9][10]. To apply this method to an unsteady aerodynamic application, two different ways of accounting for physical time can be taken.…”

“…As a result, the design cost of optimization based on CFD is expensive, even with today's computation power; hence a judicious choice of optimization approach for the current problem is warranted. In our study, we adopt the approach of using adjoint sensitivity analyses [8][9][10] in our aerodynamic shape and trajectory optimizations for flapping airfoils.…”

Single- and Multi-Point Aerodynamic Shape Optimization Using a Parallel Newton-Krylov Approach

“…3,4 The main advantage of the adjoint method is that the time required for each gradient computation is nearly independent of the number of design variables. Adjoint methods are further divided into continuous [5][6][7][8][9][10] and discrete [11][12][13][14][15][16][17][18][19] approaches. Both have been implemented successfully in aerodynamic design optimization.…”