Multidisciplinary Aerodynamic- Structural Design Optimization of Supersonic Fighter Wing Using Response Surface Methodology

In this study, the multidisciplinary aerodynamicstructural optimal design is carried out for the supersonic fighter wing. Through the aeroelastic analyses of the various candidate wings, the aerodynamic and structural performances are calculated such as the lift coefficient, the drag coefficient and the deformation of the wing. Based on the calculated performances, the supersonic fighter wing is designed by using response surface methodology to have better aerodynamic performances and less weight than the baseline wing. In general, the supersonic fighter is maneuvered at various flight conditions. The optimal design, therefore, should be carried out on the multi flight conditions. In this study, three representative design points for the supersonic fighter wing are determined such as supersonic dash, long cruise range and high AOA maneuver. At each design point, single-point design is performed to obtain better performance only at that point. Finally, a multi-point design is performed to increase aerodynamic and structural performances at all the three design points. The optimization results of multi-point design are compared with those of the single-point design and analyzed in detail. INTRODUCTION Since the early 1990's, with the rapid advances in computational fluids dynamics(CFD) and computational structural mechanics(CSM), extensive studies have been carried out on the computational design methods for the aircraft. The development of computational design methods reduces the overall design costs and turn around time for the development of aircraft. The use of high fidelity tools, moreover, brings more confidence to the design. * Graduate Student * Professor, Senior Member AIAA, * Professor, Member AIAA Copyright © 2001 by the American Institute of Aeronautics and Astronautics Inc. All rights reserved The design of modern aircraft needs for the integration of multiple disciplines, such as aerodynamics, structures, propulsion and aeroacoustics. These disciplines are mutually interacting, not independent of each other and multidisciplinary design optimization(MDO) is a formal methodology for the integration of these disciplines. Generally, MDO should exploit the synergism of mutually interacting disciplines in order to improve the performance of a given design, while increasing the level of confidence that the designer places on the outcome of the design itself.' The accurate and adequate modeling of interactions among various disciplines is, therefore, the most important part which characterizes MDO. Especially in case of aircraft, the aerodynamic performance and the structural deformation of the wing are tightly coupled. The structural deformation of the wing changes the distribution of aerodynamic forces on the wing surface and this change of aerodynamic force distribution has a reverse influence on the structural deformation. The mutual interaction between aerodynamics and structures, therefore, should be well analyzed and considered during design process. hi general, the supersonic fighter, which carries out various missions, is maneuvered at various flight conditions. Accordingly the single-point design of wing, which considers only one flight condition, has no significant meaning and the multi-point design should be carried out by taking the various flight conditions into account. Over the past several decades, single discipline shape optimization has been successfully applied to two-dimensional airfoil and simple three-dimensional wing." In recent years, interest has grown in the application of multidisciplinary analysis and design optimization to complex three-dimensional wing and aircraft configuration." To give an example, MDO paradigm is successfully implemented for the aerodynamic-structural design optimization of HSCT (High Speed Civil Transport) utilizing variablecomplexity modeling and response surface methodo1 American Institute of Aeronautics and Astronautics (c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. logy(RSM)." But performing MDO for a complete airplane configuration is still a challenging task with high-fidelity analysis tools. In this study the multidisciplinary multi-point design of supersonic fighter wing is carried out in order to show the feasibility of MDO with highfidelity analysis tools. The MDO paradigm introduced here uses RSM, high-fidelity aeroelastic analysis tool combining CFD and CFM and a multiobjective approach. The objectives of the present research are summarized as follows; (1) to investigate the multidisciplineary multi-point design optimization of the supersonic fighter wing based on high-fidelity aeroelastic analysis; (2) to demonstrate the advantages of multi-point design as well as the limitations of the single-point design; (3) to develop a new design procedure for the multiobjective design problem which improves the performances evenly and moderately. To achieve these goals, the three-dimensional Euler code has been coupled with a nine-node shell mixed FEM(Finite Element Method) code for the accurate analysis of aeroelastic phenomena. For the development of MDO framework, RSM is employed to select candidate design points and to construct numerical approximation models for objectives and constraints. Because the design problem here is essentially a multidisciplinary and multi-point, there exists multiple objectives. In order to deal with the multiple objectives, the weighting method is introduced and the weighting factors are designed to improve the performances evenly by using genetic algorithm. RSM is a kind of approximation method based on design of experiment theory (DOE). In this method, a designer performs a limited number of computational analyses using experimental design theory to prescribe values for independent variables. With the resulting data, the designer creates mathematical approximation models using some type of function. The designer then uses the response surface model in subsequent calculations during optimization process.2' 4,17,20,21 Figure 1. Three-Dimensional Wing Mesh for CFD Calculation (O-Htype) with Van Albada limiter. AF-ADI time marching scheme is used for the time integration. The convergence of numerical analysis is accelerated through the use of the multigrid scheme and the implicit residual smoothing. A wing mesh for CFD calculation is shown in figure 1. It is generated by the transfinite Interpolation technique and has the O-H type grid topology. The number of mesh size is 121 along the airfoil surface, 33 along the spanwise direction and 33 normal to the wing surface. STRUCTURAL ANALYSIS Nine-node shell mixed finite element Nine-node shell mixed finite element has three translational degrees of freedom(DOF) and two rotational DOF per node as shown in figure 2, and each element has nine-node and 45 DOF per element. The element is constructed on the basis of the Hellinger-Reissner principle with the assumed displacement field as well as the independently assumed strain field, which lead to the equilibrium equation (1) and the compatibility equation (2).