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 flight 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 specific 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 differential 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.

Hypersonic vehicle control system design and simulation requires models that contain a low number of states. Modeling of hypersonic vehicles is complicated due to complex interactions between aerodynamic heating, heat transfer, structural dynamics, and aerodynamics in the hypersonic regime. Though there exist techniques for analyzing the effects of each of the various disciplines, these methods often require solution of large systems of equations which is infeasible within a control design and evaluation environment. This work therefore presents an aerothermoelastic framework with reduced-order aerothermal, heat transfer, and structural dynamic models for time-domain simulation of hypersonic vehicles. The problem is outlined and aerothermoelastic coupling mechanisms are described. Details of the reduced-order models are given and a representative hypersonic vehicle control surface to be used for the study is described. The error between the reduced-order models is characterized by comparison with high-fidelity models. The effect of aerothermoelasticity on total lift and drag is studied and is found to result in up to 8% change in lift and 21% change in drag with respect to a rigid control surface for the four trajectories considered. An iterative routine is used to determine the necessary angle of attack needed to match the lift of the deformed control surface to that of a rigid one at successive time instants. Application of the routine to different cruise trajectories shows a maximum departure from the initial angle of attack of 7%.

Hypersonic vehicle control system design and simulation require models that contain a low number of states. Modeling of hypersonic vehicles is complicated due to complex interactions between aerodynamic heating, heat transfer, structural dynamics, and aerodynamics. Although there exist techniques for analyzing the effects of each of the various disciplines, these methods often require solution of large systems of equations, which is infeasible within a control design and evaluation environment. This work presents an aerothermoelastic framework with reducedorder aerothermal, heat transfer, and structural dynamic models for time-domain simulation of hypersonic vehicles. Details of the reduced-order models are given, and a representative hypersonic vehicle control surface used for the study is described. The methodology is applied to a representative structure to provide insight into the importance of aerothermoelastic effects on vehicle performance. The effect of aerothermoelasticity on total lift and drag is found to result in up to an 8% change in lift and a 21% change in drag with respect to a rigid control surface for the four trajectories considered. An iterative routine is used to determine the angle of attack needed to match the lift of the deformed control surface to that of a rigid one at successive time instants. Application of the routine to different cruise trajectories shows a maximum departure from the initial angle of attack of 8%.corresponding to ith column of A C = correlation matrix c = modal coordinate of thermal proper orthogonal decomposition basis vector Cx = correlation model for kriging c p = specific heat at constant pressure d = structural modal coordinates, kriging sample point E = modulus of elasticity F = thermal load vector of full system in physical space f = generalized thermal load vector of reduced system in modal space F s = structural load vector of full system in physical space f s = generalized structural load vector of reduced system in modal space H i = coefficient matrices for integration of equations of motion h i = thickness of ith layer of thermal protection system K = thermal conductivity matrix of full system in physical space k = generalized thermal conductivity matrix of reduced system in modal space K G = geometric stiffness matrix K s = structural stiffness matrix k s = generalized stiffness matrix of reduced system in modal space k T = thermal conductivity of material K s = modified structural stiffness matrix L = aerodynamic lift, length M = thermal capacitance matrix of full system in physical space, Mach number m = generalized thermal capacitance matrix of reduced system in modal space M s = structural mass matrix of full system in physical space m s = generalized mass matrix of reduced system in modal space n = number of proper orthogonal decomposition snapshots n e = number of snapshots for kriging evaluation cases n k = number of kriging snapshots n s = number of structural parameters in reduced-order aerothermodynamic model n t = number of thermal parameters...

Hypersonic vehicle simulation is complicated due to coupling between aerodynamics, the propulsion system, heat transfer due to aerodynamic heating, and structural deformations. The high speed involved in hypersonic flight results in the existence of a large heat flux at the vehicle surface. Heat transfer through the internal structure leads to temperature gradients that load the structure due to differential thermal expansion. Additionally, the structure is loaded by aerodynamic pressure. Of particular interest in this study is the extent to which structural deformation alters aerodynamic performance as it relates to vehicle control. As the control surfaces are expected to produce a significant portion of the aerodynamic forces and moments on the vehicle, this paper will focus on the integrated aerothermoelastic modeling of such a structure with the goal of evaluating the effect of structural elasticity on flight dynamics and control system performance. The Eckert reference temperature method is used to calculate the aerodynamic heat flux boundary condition at the surface and finite element representations are used to calculate the temperature distribution and structural displacements. The aerodynamic pressures over the deformed configuration are found using the analytical oblique shock/expansion fan relations. The resulting pressures are integrated over the surfaces to calculate the total lift and drag. For the trajectory points considered, the maximum relative change in lift and drag were found to be 2% and 6%, respectively. A lift-based trim routine is outlined for use in assessing the control surface deflections required to account for the change in aerodynamic lift and drag. Recent research into air-breathing hypersonic vehicles (HSVs) has been aimed at efficiently modeling the the aerodynamics, propulsion system, structural dynamics, and heat transfer and integrating these models into a comprehensive simulation that can be used for stability and controllability analysis and control law design. There are two approaches to developing these models. The first is the development of first-principles models that are low-order, but lack the fidelity found in more complex representations. The second approach is the development of reduced-order models derived from state-of-the-art, high fidelity computational tools. These tools are not utilized for design due to their complexity and long run-times. However, they are useful for generating reduced-order models that capture the essential physics with a relatively low number of states and therefore they can be used for design. The primary difficulty associated with design of HSVs stems from the high degree of coupling they exhibit between the aerodynamics, heat transfer, elastic airframe, propulsion system, flight dynamics, and controls. Due to the strongly coupled nature of hypersonic vehicle design,

Hypersonic vehicle design and simulation require models that are of low order. Modeling of hypersonic vehicles is complicated due to complex interactions between aerodynamic heating, heat transfer, structural dynamics, and aerodynamics in the hypersonic regime. This work focuses on the development of efficient modal solutions for structural dynamics of hypersonic vehicle structures under transient thermal loads. The problem is outlined, and aerothermoelastic coupling mechanisms are described. A previously developed reduced-order time-domain aerothermoelastic simulation framework is used as the starting point for this study. This paper focuses on two main modeling areas: 1) a surrogate modeling technique is employed for directly updating the generalized stiffness matrix and thermal loads based on the transient temperature distribution, and 2) basis augmentation techniques are employed in order to obtain more accurate solutions for the structural dynamic response. The techniques to be studied are described and applied to a representative hypersonic vehicle all-movable lifting surface.