Response Surface Technique for Static Aeroelastic Optimization on a High-Aspect-Ratio Wing

Abstract

I T IS a key subject in aircraft design to have the maximum lift and the minimum drag. Computational fluid dynamics (CFD)-based optimization design has been widely used to optimize rigid configurations in aircraft engineering [1,2]. As is well known, for a highaspect-ratio wing, structural deformation can reduce its cruise aerodynamic performance. Because the aeroelastic characteristic has not been considered in the original optimum design, the real flight performances will deviate from the rigid-design results. Therefore, an optimum design that contains the aeroelastic effect needs to be developed. However, the static aeroelastic optimization is usually coupled with the aerodynamicmodel, structural model, optimization algorithms, and even such related issues as response surface method (RSM), fluid–structure interface, and moving grid. Therefore, it is muchmore difficult and time-consuming than the CFD aerodynamic optimization. High-fidelity CFD tools are now available to aircraft designers and are commonly used in the design of aerodynamic configuration. CFD codes are capable of accurately predicting flowfields about complex aircraft configurations. Compared with linear aerodynamics, CFD tools are characterized by large computational costs due to complex geometrical modeling and grid generation. They require a higher level of proficiency from the users in defining run parameters and interpreting results. Endeavors to exploit CFD solvers for aeroelastic analyses and aircraft structural design are relatively advanced, due to the main hindrance of large computational cost. They are typically characterized by iterations between CFD and a structure solver, which aggravate the problem of computational cost. Bennett and Edwards [3] reviewed the current state of computational aeroelasticity (CA), where CA is defined as the numerical analyses of coupled CFD and structural dynamics. They listed the main efforts needed in the development of CA: that is, the reduction of elapsed run times, improvement of the credibility of CFD tools, and simplification of methods for further applications. For the interface between fluid and structure, Smith et al. [4] provided a comprehensive review of spline methods, their mathematical formulation, and practical applications, which contain the infinite plate spline (IPS) for plate configuration and the beam spline for fuselage configuration. A large amount of literature exists on the subject of grid deformation, which mainly contains the algebraic transfinite interpolation (TFI) [5], the springnetwork analogy by Batina [6] and Farhat et al. [7], and the boundary element method by Chen and Hill [8]. Even fluid–structuremultidisciplinary optimizationmay cut down the design cycles and reduce the reliance on wind-tunnel and flight tests; the drawbacks are the repeated fluid–structure coupling analyses during the optimization process. At present, there are very few studies that consider the adaptation of CFD-based aeroelastic analyses in structural-design optimization. Applications of CFDbased structural and multidisciplinary design optimization were reviewed by Guruswamy and Obayashi [9]. Martins et al. [10–12] presented a CFD-based methodology for aerodynamic-structural optimization. Cross sensitivity is computed by the adjoint method, which was shown to be vastly more computationally efficient for a supersonic business jet optimization involving a larger number of design variables than ever. Reuther et al. [13] presented a structural optimization in which the aerodynamic and structural analyses were performed separately. CFD analyses were used to generate a response surface, and the response surface was incorporated in the structural optimization to improve the roll maneuverability, in which only the generation of a response surface required an amount of CFD-based analyses. In this Note, a quadratic polynomial response surface model is put forward based on the CFD-based static aeroelastic calculations. The structure is represented by a finite element model and holds fixed in the optimization process. The genetic algorithm (GA) optimization method is used for the improvement of static aeroelastic performance through the optimization of the spanwise sectional airfoil shapes. To reduce the amount of CFD-based static aeroelastic analyses for the generation of RSM, only two sectional airfoils are chosen for the optimizations. Either for singleor multi-objectives optimizations, the study shows that the optimization of aeroelastic performances can be greatly improved compared with the original static aeroelastic results.