Reduced-Order Aerothermoelastic Framework for Hypersonic Vehicle Control Simulation

Abstract

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...

Effect of Control Surface-Fuselage Inertial Coupling on Hypersonic Vehicle Flight Dynamics

“…The other involves the fact that K * uu (T ) and K * ur (T ) on the right-hand sides of Eqs. (5) and (14) are evaluated at the reference thermal state and held constant throughout the simulation. In order to distinguish the errors due to these approximations from the errors due to modal truncation, three different cases are simulated as shown in Table 5.…”

“…Additionally for case E3, K * uu (T ) and K * ur (T ) on the right-hand sides of Eqs. (5) and (14) are evaluated at the reference thermal state and held constant throughout the simulation. Therefore, the difference between cases E1 and E2 will demonstrate the error incurred solely due to the use of the modal subset in the structural ROM.…”

A Quasi-Steady Method for Unsteady Flows over Surfaces with Structural Deformation

“…이 때문에 공 력, 구조 변형에 대한 축약모델(reduced-order model)을 구축하고, 이들을 통합하여 공탄성 혹 은 열공탄성(aerothermoelastics) 해석을 수행하는 방법론을 연구하고 있다 [1][2][3][4][5][6][7][8][9].…”

“…한편, 미국의 McNamara 교수와 Cesnik 교수 연구팀은 Kriging 및 POD 기법을 적용하여 공 력, 구조, 열전달에 대한 축약모델 구축하고 [3][4][5][6][7], 이를 이용해 초음속 플러터해석을 수행한 바 있 다 [7][8][9]. 특히 이들은 초음속 비정상(unsteady) 표 면 압력 분포를 축약 계산하기 위해 피스톤 이론 을 적용하였다.…”

Transient Temperature Effects on the Aerothermoelastic Response of a Simple Wing

“…Whereas the early research was instrumental in providing the basis for the aerothermoelastic design of the X-15 and the space shuttle [3][4][5], the current focus is on the development of hypersonic technologies for next-generation reusable launch vehicles and hypersonic cruise vehicles [6][7][8]. Current research includes: development of reduced order models for aerothermoelastic systems [9,10], structural optimisation [11], uncertainty propagation [12,13], coupling CFD with aerothermoelastic models [14], two-dimensional nonlinear flutter models [15] and three-dimensional flutter models [16]. This work has shown that the dynamic behaviour of the structure under the harsh thermal environment must be investigated for hypersonic aircraft to become a reality.…”