Thermoelastic Formulation of a Hypersonic Vehicle Control Surface for Control-Oriented Simulation

Abstract

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,

Reduced-Order Aerothermoelastic Framework for Hypersonic Vehicle Control Simulation

“…The thermoelastic portion of this study is a continuation of previous studies on reduced-order modeling of the heat transfer and structural dynamics problems [20][21][22]. The earliest of these [22] introduced the reduced-order thermoelastic modeling framework, which used proper orthogonal decomposition (POD) for reduction of the thermal problem and a modified modal method for reduction of the structural dynamics problem.…”

“…The framework was applied to a representative HSV structure and results demonstrated the accuracy of the POD formulation as well as the coupling of the equations of motion that results due to heating. A subsequent work [21] employed a quasi-steady aerothermoelastic time-marching procedure to assess the effect of thermal loads on the aerodynamic forces over a control surface. A more recent work [20] described an extension of the previous papers to unsteady form and specifically addressed the use of POD with time-dependent boundary conditions.…”

“…For this simulation, t AE and t HT are each 1 s and t AT is 4 s. To calculate the aerodynamic heating in this simulation, the Eckert reference temperature method [71,72] is used. The details of the implementation of the Eckert reference temperature method are given in a previous work [21]. Using the 5001 snapshots, the snapshot matrix is assembled, its SVD is taken, and the POD modes are extracted.…”

“…The pressures consist of a component in the direction of the local normal to the deformed configuration due to aerodynamic pressures and a component in the direction of the local tangent to the deformed configuration due to viscous stress. The viscous stress is computed using local skin friction coefficients for each finite element using an Eckert reference temperature formulation [21]. Note that local normal and tangent vectors for each finite element are updated at each aeroelastic time step based on the deformed configuration at the end of the time step.…”

Enhanced Modal Solutions for Structural Dynamics in Aerothermoelastic Analysis

“…[11][12][13][14] The earliest of these 11 introduced the reduced-order thermoelastic modeling framework which utilized Proper Orthogonal Decomposition (POD) for reduction of the thermal problem and a modified modal method for reduction of the structural dynamics problem. A subsequent work 12 employed a quasi-steady aerothermoelastic time-marching procedure to assess the effect of thermal loads on the aerodynamic forces over a control surface.…”