Proper Orthogonal Decomposition for Reduced-Order Thermal Solution in Hypersonic Aerothermoelastic Simulations

Abstract

The ability to perform full-order aerothermoelastic simulations of hypersonic vehicles is hindered by the strong coupling exhibited between the aerodynamics, heat transfer, and structural dynamic response in the hypersonic ight regime. As a result of these interactions, alternative techniques are necessary to obtain computationally tractable systems of governing equations and their solutions. This work addresses the use of proper orthogonal decomposition for reduced-order solution of the heat transfer problem within a hypersonic modeling framework. The specic challenge of handling time-dependent boundary conditions due to transient aerodynamic heating is discussed. An overview of the proper orthogonal decomposition is given and two methods for solution of the reduced system of ordinary dierential equations are outlined. The methodology is applied to a representative hypersonic vehicle control surface model for two cases in which the time-history of the thermal load vector is known a priori: one in which the boundary conditions are time-independent and another in which they are time-varying. Results demonstrate the ability of the reduced-order solution to approximate the full-order solution with reasonable accuracy. Finally, a time-marching hypersonic aerothermoelastic framework is described in which proper orthogonal decomposition is used for the transient thermal solution.