A new engine model has been developed for applications requiring run times shorter than a few seconds, such as design optimization or control evaluation. A reduced-order model for mixing and combustion has been developed that is based on nondimensional scaling of turbulent jets in crossflow and tabulated presumed probability distribution function flamelet chemistry. The three-dimensional information from these models is then integrated across cross-sectional planes so that a one-dimensional profile of the reaction rate of each species can be established. Finally, the one-dimensional conservation equations are integrated along the downstream axial direction and the longitudinal evolution of the flow can be computed. The reduced-order model accurately simulates real-gas effects such as dissociation, recombination, and finite rate chemistry for geometries for which the main flow is nearly onedimensional. Thus, this approach may be applied to any flowpath in which this is the case; ramjets, scramjets, and rockets are good candidates. Comparisons to computational fluid dynamics solutions and experimental data were conducted to determine the validity of this approach.

Control-oriented models of hypersonic vehicle propulsion systems require a reduced-order model of the scramjet inlet that is accurate to within 10% but requires less than a few seconds of computational time. To achieve this goal, a reduced-order model is presented, which predicts the solution of a steady two-dimensional supersonic flow through an inlet or around any other two-dimensional geometry. The model assumes that the flow is supersonic everywhere except in boundary layers and the regions near blunted leading edges. Expansion fans are modeled as a sequence of discrete waves instead of a continuous pressure change. Of critical importance to the model is the ability to predict the results of multiple wave interactions rapidly. The rounded detached shock near a blunt leading edge is discretized and replaced with three linear shocks. Boundary layers are approximated by displacing the flow by an empirical estimate of the displacement thickness. A scramjet inlet is considered as an example application. The predicted results are compared to two-dimensional computational fluid dynamics solutions and experimental results. Nomenclature a = local sound speed, m=s c = specific heat, J=kg K H = length normal to flow, m h = specific enthalpy, J=kg L = length tangent to flow, m M = Mach number n = number of a given quantity Pr = Prandtl number p = pressure, Pa R = normalized gas constant, J=kg K R = 8314:47 J=kmol K r = radius, m T = temperature, K u = velocity magnitude, m=s W = molecular weight, kg=kmol x = forward body-frame coordinate, m Y = mass fraction z = vertical body-frame coordinate, m = shock angle = ratio of specific heats = thickness of layer, m " = ratio = ln p 0 =p = dynamic viscosity, kg=m s = flowpath angle = =2 = M 2 1 p = sin 1 1=M, Mach angle = Prandtl-Meyer function = density, kg=m 3 = wave angle = flux of subscripted quantity = reference angle Subscripts A, B, . . . = region label a, b, . . . = point label bs = curved portion of bow shock cl = property of inlet cowl e = value at edge of boundary layer ex = expansion i = species index j = index of expansion discretization k = region index le = leading edge p = constant pressure s = constant entropy sp = pertaining to species w = wall value 0 = stagnation value 1 = index for inlet portion of flow 2 = index for inlet outflow 1 = freestream Superscripts = value at Mach number of 1 = reference value for boundary layer

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