Integrated Aerodynamic Thermal Structure Design Optimization Method of Lifting Surfaces

Abstract

A ERODYNAMIC heating of lifting surfaces of high-speed flight vehicles should be seriously considered. A high-temperature field may cause the characteristics of materials to change, and an inhomogeneous temperature with inhomogeneous temperature gradients may induce thermal stress. As a result, resultant structural stiffness and stiffness distribution probably change, which will lead to the changes of structural normalmodes and unsteady aerodynamic loads. Furthermore, these changes will influence performances of aeroelasticity for lifting surfaces, such as the critical flutter velocity, a crucial parameter for high-speed flight vehicles. The structural design of lifting surfaces in high-speed flow is highly complicated, which involves serious coupling among aerodynamic, thermal, and structural disciplines. Aeroelasticity and aerothermoelasticity in hypersonic conditions were first researched in the late 1950s and during the 1960s [1–3]. Because of the development of computational technologies and relevant modeling methods, since about 2000, studies of aeroelasticity and aerothermoelasticity in hypersonic flow have drawn more and more attention [4–6]. Bisplinghoff [7] summarized the important aspects of aerothermoelasticity and pointed out that aerothermoelasticity can be considered as the expansion of Collar’s aeroelastic triangle including the coupling of aerodynamic heating. Ericsson et al. [8] studied the aerothermoelastic features of an aluminum finned missile. Spain et al. [9] presented an overview of selected National Aero-Space Plane (NASP) aeroelastic studies at the NASA Langley Research Center. Rodgers [10] performed the aerothermoelastic analysis of a NASP vertical fin. Thornton and Dechaumphai [11] investigated an integrated code using the finite element method (FEM) including flow and thermal and structural coupling. Recently, Friedmann [12] pointed out that modern aeroelasticity encompasses a much broader set of problems by the aeroservothermoelastic hexahedron. Tran and Farhat [13] accomplished the aerothermoelastic analysis of a flat panel using an integrated fluid-structural-thermal solver. McNamara et al. [14] studied the aeroelastic and aerothermoelastic behaviors in hypersonic flow using NASA Langley Research Center code CFL3D. All the works above only considered one-way thermal coupling. In addition, McNamara and Friedmann [15] conducted a comprehensive survey of the past, the state of art, and the future on aeroelasticity and aerothermoelasticity in hypersonic flow. With the existing level of knowledge and the computational capability of the current computers, to solve this fully coupled aerodynamic-thermal-structural problem is rather difficult in engineering design. A hierarchical solution approach from [14] is feasible in engineering design,which decomposes the original highly coupled problem into a series of separated simple problems. In this solution, the aerodynamic heating and the internal transient heat transfer analysis of structures are not calculated simultaneously, that is, the transient heat transfer analysis follows the computation of the aerodynamic heating. Afterwards all the temperature fields resulting from the transient heat transfer analysis are considered as the thermal boundaries for the thermal structure analysis and the thermal mode analysis, respectively. The first six orders of thermal modes of each temperature field are chosen as the input data of flutter analysis. This solution is also a one-way coupled process. Because of the high performance requirement of high-speed flight vehicles, structural design only considering strength criterion is not sufficient in applications. Aeroelastic characteristics should be used as constraints in structural design optimization, especially for aerothermoelastic design problems. Therefore, in this paper, an integrated aerodynamic-thermal-structural analysis and design optimization method is presented, and the entire integrated analysis will be computationally expensive. For the purpose of decreasing computational cost and reducing optimization time, a novel global optimization strategy using adaptive radial basis functions based on fuzzy clustering developed by the authors [16] is used to optimize the lifting surfaces consideringmultidisciplinary coupling. Based on this integrated analysis and design optimization method, a design optimization of lifting surfaces in high-speed flow is carried out. Under the constraints of the displacement and the flutter velocity, the structural mass of the lifting surface is minimized through adjusting the distributions of the structural stiffness and the mass, simultaneously.