The testing of aeroelastically and aerothermoelastically scaled wind-tunnel models in hypersonic flow is not feasible; thus, computational aeroelasticity and aerothermoelasticity are essential to the development of hypersonic vehicles. Several fundamental issues in this area are examined by performing a systematic computational study of the hypersonic aeroelastic and aerothermoelastic behavior of a three-dimensional configuration. Specifically, the flutter boundary of a low-aspect-ratio wing, representative of a fin or control surface on a hypersonic vehicle, is studied over a range of altitudes using third-order piston theory and Euler and Navier-Stokes aerodynamics. The sensitivity of the computational-fluid-dynamics-based aeroelastic analysis to grid resolution and parameters governing temporal accuracy are considered. In general, good agreement at moderate-to-high altitudes was observed for the three aerodynamic models. However, the wing flutters at unrealistic Mach numbers in the absence of aerodynamic heating. Therefore, because aerodynamic heating is an inherent feature of hypersonic flight and the aeroelastic behavior of a vehicle is sensitive to structural variations caused by heating, an aerothermoelastic methodology is developed that incorporates the heat transfer between the fluid and structure based on computational-fluid-dynamics-generated aerodynamic heating. The aerothermoelastic solution procedure is then applied to the low-aspect-ratio wing operating on a representative hypersonic trajectory. In the latter study, the sensitivity of the flutter margin to perturbations in trajectory angle of attack and Mach number is considered. Significant reductions in the flutter boundary of the heated wing are observed. The wing is also found to be susceptible to thermal buckling. Nomenclature a 1 = speed of sound C L , C M , C D = coefficients of lift and moment about the elastic axis and drag C p = coefficient of pressure CFL = Courant-Friedrichs-Lewy three-dimensional input parameter regulating pseudo-time-step size C w = Chapman-Rubesin coefficient c = reference chord length of the double-wedge airfoil c pw = specific heat of the wall h ht = heat-transfer coefficient k ! = reduced frequency M = freestream Mach number M, K = generalized mass and stiffness matrices of the structure M f = flutter Mach number n = normal vector n m= number of modes p = pressure p 1 = freestream pressure Q = generalized force vector for the structure= heat-transfer rate due to aerodynamic heating, radiation, conduction, and stored energy q i = modal amplitude of mode i q vf = virtual-flutter dynamic pressure q 1 = dynamic pressure Re = Reynolds number S = surface area of the structure T = temperature T AW = adiabatic-wall temperature T E = kinetic energy of the structure T R = radiation equilibrium wall temperature= potential energy of the structure V = freestream velocity v n = normal velocity of airfoil surfaces w = displacement of the surface of the structure x, y, z = spatial coordinates y = law-of-the-wall coordinate Zx; y;...

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An aeroelastic and aerothermoelastic analysis of a three-dimensional low aspect ratio wing, representative of a fin on hypersonic vehicles, is carried out using piston theory, and Euler aerodynamics. Studies on grid convergence are used to determine the appropriate computational domain and resolution for this wing in hypersonic flow, using both Euler and Navier-Stokes aerodynamics. Hypersonic computational aeroelastic responses are then generated, using Euler aerodynamics in order to obtain frequency and damping characteristics for comparison with those from first and third order piston theory solutions. Results indicate that the aeroelastic behavior is comparable when using Euler and third order piston theory aerodynamics. The transonic aeroelastic behavior of the wing is also analyzed using Euler aerodynamics. The aerothermoelastic behavior of the wing, using piston theory aerodynamics, is studied by incorporating material property degradation and thermal stresses due to non-uniform temperature distributions. Results indicate that aerodynamic heating can substantially reduce aeroelastic stability. Finally, hypersonic aeroelastic behavior of a generic vehicle resembling a reusable launch vehicle is performed using piston theory. The results presented serve as a partial validation of the CFL3D code for the hypersonic flight regime.

The aeroelastic and aerothermoelastic behavior of three-dimensional configurations in hypersonic flow regime are studied. The aeroelastic behavior of a low aspect ratio wing, representative of a fin or control surface on a generic hypersonic vehicle, is examined using third order piston theory, Euler and Navier-Stokes aerodynamics. The sensitivity of the aeroelastic behavior generated using Euler and Navier-Stokes aerodynamics to parameters governing temporal accuracy is also examined. Also, a refined aerothermoelastic model, which incorporates the heat transfer between the fluid and structure using CFD generated aerodynamic heating, is used to examine the aerothermoelastic behavior of the low aspect ratio wing in the hypersonic regime. Finally, the hypersonic aeroelastic behavior of a generic hypersonic vehicle with a lifting-body type fuselage and canted fins is studied using piston theory and Euler aerodynamics for the range of 2.5 ≤ M ≤ 28, at altitudes ranging from 10,000 feet to 80,000 feet. This analysis includes a study on optimal mesh selection for use with Euler aerodynamics. In addition to the aeroelastic and aerothermoelastic results presented, three time domain flutter identification techniques are compared, namely the moving block approach, the least squares curve fitting method, and a system identification technique using an Auto-Regressive model of the aeroelastic system. In general, the three methods agree well. The system identification technique, however, provided quick damping and frequency estimations with minimal response record length, and therefore offers significant reductions in computational cost. In the present case, the computational cost was reduced by 75%. The aeroelastic and aerothermoelastic results presented illustrate the applicability of the CFL3D code for the hypersonic flight regime.

This paper presents a treatment of the hypersonic aeroelastic problem, using both Euler and Navier-Stokes aerodynamics. The approach is based on the use of computational uid dynamics coupled with structural nite element analysis. The structural motion is represented by a nite series of normal modes. Studies were carried out in the Mach number range of 2 to 15, and for di erent altitudes between 5000 and 100,000 feet. The validation of the approach is carried out by considering the aeroelastic response analysis of a double wedge airfoil, using Euler, Navier-Stokes, and piston theory aerodynamics. Good comparison between piston theory and Euler aerodynamics is observed at all the operating points, and at higher Mach n umbers, signi cant difference is observed between the viscous and inviscid aeroelastic response. This technique is then applied to the generic hypersonic vehicle, and the results presented. NOMENCLATURE a Parameter denoting the o set between the elastic axis and the origin a 1 Speed of sound b Semi-chord c Reference length, chord length of double wedge airfoil f(x) Function describing airfoil surface Ph.D. Candidate y Fran cois-Xavier Bagnoud Professor of Aerospace Engineering z Arthur F.