Uncertainty Propagation in Integrated Airframe–Propulsion System Analysis for Hypersonic Vehicles

Abstract

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

Combustion Efficiencies and Flameout Limits Computed for a Hypersonic Vehicle During Ascent

“…Previously, the advantages of ROMs have been pointed out by U.S. Air Force Research Laboratory (AFRL) researchers Bolender and Doman [26], O'Neill and Lewis [27], O'Brien et al [28], Bowcutt [29] at Boeing, Dalle et al [1][2][3], Torrez et al [4,5], Mbagwu and Driscoll [6], Lamorte et al [7], Mbagwu and Driscoll [8,9], and Chavez and Schmidt [30]. The Bolender-Doman AFRL ROM was developed in 2006 [26] to simulate the flight dynamics, poles, and zeros of a hypersonic vehicle.…”

“…To improve on the Bolender-Doman AFRL analysis, a secondgeneration model, called MASIV (from "Michigan-AFRL scramjet in vehicle") was developed during a joint collaboration between the University of Michigan and AFRL [1][2][3][4][5][6][7][8][9], some details of which are summarized in Sec. III.…”

“…The MASIV combustor submodel was described in detail in [1][2][3][4][5][6][7][8][9], and so only a summary is provided here. The code includes finite rate chemistry, real gas properties, a three-dimensional jet mixing model, a separated boundary-layer model, and gas dissociation.…”

“…T HERE are several interesting tradeoffs that occur when a hypersonic waverider ascends along a trajectory of constant dynamic pressure (q 1∕2ρ ∞ U 2 ∞ ). Figure 1 shows the geometry of the MAX-1 waverider that the authors have analyzed [1][2][3][4][5][6][7][8][9] using their reduced-order model called the University of Michigan-U.S. Air Force Research Laboratory scramjet in vehicle (MASIV). A constant-q trajectory might be selected from one of the three solid curves in Fig.…”

“…A desired trajectory is one that avoids crossing these two limits. Computations of these operability limits have not been reported previously; to do so, our reduced-order model [1][2][3][4][5][6][7][8][9] had to be improved using the approach described in Sec. IV.…”