Air-breathing hypersonic vehicles are based on an airframe-integrated scramjet engine. The elongated forebody that serves as the inlet of the engine is subject to harsh aerothermodynamic loading, which causes it to deform. Unpredicted deformations may produce unstart, combustor chocking, or structural failure due to increased loads. An uncertainty quantification framework is used to propagate the effects of aerothermoelastic deformations on the performance of the scramjet engine. A loosely coupled airframe-integrated scramjet engine is considered. The aerothermoelastic deformations calculated for an assumed trajectory and angle of attack are transferred to a scramjet engine analysis. Uncertainty associated with deformation prediction is propagated through the engine performance analysis. The effects of aerodynamic heating and aerothermoelastic deformations at the cowl of the inlet are the most significant. The cowl deformation is the main contributor to the sensitivity of the propulsion system performance to aerothermoelastic effects.across thickness of skin h 1 , h 2 = thickness of thermal protection system layers h 3 = thickness of structural layer k = thermal conductivity M = Mach number m f = expected value of f _ m air = air mass flow rate _ m f = fuel mass flow rate P = pressure q aero = aerodynamic heat flux q ∞ = dynamic pressure Re = Reynolds number based on length of 1 m T = temperature T r = recovery temperature t = flight time u = axial displacement v = lateral displacement w = transverse displacement w j = weight in numerical integration x 0 ; y 0 ; z 0 = coordinate system for corrugated panel x = coordinate along vehicle, from leading edge, positive aft y = coordinate in spanwise direction, from centerline of vehicle z = coordinate normal to vehicle, from leading edge point, positive up α = angle of attack α T = thermal expansion coefficient α f = angle of attack of trajectory γ = specific heat ratio, c p ∕c v ξ 1 , ξ 2 = uncertain variables ν = Poisson ratio ϵ = emissivity ρ = density of air ρ M = density of material σ f = standard deviation of f ϕ j = interpolation function Subscripts i = initial value st = stoichiometric condition wall = at wall 0 = total condition 4 = condition at exit of combustor ∞ = freestream condition

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A framework for aerothermoelastic-stability-boundary calculation for hypersonic configurations using computational fluid dynamics combined with radial basis functions for mesh deformation is developed. Application of computational fluid dynamics enables one to consider different turbulence conditions, laminar or turbulent, and different models of the air mixture, in particular real-gas model, which accounts for dissociation of molecules at high temperature. The effect of transition on the flutter margin of the heated structure is also considered using an uncertainty-propagation framework. The aerothermoelastic-stability margin of a three-dimensional low-aspect-ratio wing, representative of a control surface of a hypersonic vehicle, is investigated for various flight conditions. The system is found to be sensitive to turbulence modeling, as well as the location of the transition from laminar to turbulent flow. Real-gas effects play a minor role for the flight conditions considered. This study demonstrates the advantages of accounting for uncertainty at an early stage of the analysis, and emphasizes the important relation between transition from laminar to turbulent, thermal stresses, and stability margins of hypersonic vehicles.

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This study presents a framework for aeroelastic stability boundary for hypersonic vehicles using CFD and radial basis functions for mesh deformation. The results are presented for two cases: the aeroelastic stability of a two-dimensional typical cross section and a three-dimensional low aspect ratio wing, representative of a control surface of a hypersonic vehicle. Different models of the air mixture are considered: calorifically perfect gas, and imperfect gas models. Chemistry is also considered to account for dissociation of molecules at high temperature. The effect of turbulence and gas modeling on the flutter boundary are investigated. Turbulence can affect the stability boundary by up to 7%. For the flight conditions considered, real gas effects do not modify significantly the flutter Mach number of both systems considered.