Reduced-Order Aerothermoelastic Framework for Hypersonic Vehicle Control Simulation Nathan J. Falkiewicz * and Carlos E. S. Cesnik † University of Michigan, Ann Arbor, Michigan 48109-2140 and Andrew R. Crowell ‡ and Jack J. McNamara § Ohio State University, Columbus, Ohio 43210-1226 DOI: 10.2514/1.J050802 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 reduced- order 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%. Nomenclature A = snapshot matrix a i = ith snapshot corresponding to ith column of A C = correlation matrix c = modal coordinate of thermal proper orthogonal decomposition basis vector Cx = 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 in reduced-order aerothermodynamic model _ q = heat flow rate vector R = residue r = number of degrees of freedom of reduced system in modal space after modal truncation Rx = regression model for kriging s = number of degrees of freedom of full-order thermal system St = Stanton number T = vector of discrete nodal temperatures t = time U = matrix containing left singular vectors of A u i = ith left singular vector of A V = matrix containing right singular vectors of A, velocity v i = ith right singular vector of A w = structural displacement in z direction Presented as Paper 2010-7928 at the 2010 AIAA Atmospheric Flight Mechanics Conference, Toronto, Ontario, Canada, 2–5 August 2010; received 27 July 2010; revision received 20 January 2011; accepted for publication 2 February 2011. Copyright © 2011 by N. J. Falkiewicz, C. E. S. Cesnik, A. R. Crowell, and J. J. McNamara. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0001-1452/11 and $10.00 in correspondence with the CCC. * Ph.D. Candidate, Department of Aerospace Engineering, 1320 Beal Avenue. Student Member AIAA. † Professor of Aerospace Engineering, Department of Aerospace Engineering, 1320 Beal Avenue. Associate Fellow AIAA. ‡ Ph.D. Candidate, Department of Mechanical and Aerospace Engineering, 2036 Neil Avenue. Student Member AIAA. § Assistant Professor of Aerospace Engineering, Department of Mechanical and Aerospace Engineering, 201 W. 19th Avenue. Senior Member AIAA. AIAA JOURNAL Vol. 49, No. 8, August 2011 1625