Reduced-Order Modeling of Two-Dimensional Supersonic Flows with Applications to Scramjet Inlets

TLDR: In this paper, a reduced-order model is presented, which predicts the solution of a steady 2D supersonic flow through an inlet or around any other two-dimensional geometry.

Abstract: 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 CFD solutions and experimental results. Nomenclature a = local soundspeed [m/s] c = specific heat [J/kg K] h = specific enthalpy [J/kg] H = length normal to flow [m] M = Mach number n = number of a given quantity L = length tangent to flow [m] p = pressure [Pa] Pr = Prandtl number r = radius [m] R = normalized gas constant [J/kg K] R = 8314.47 J/kmol K 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 = flowpath angle = dynamic viscosity [kg/m s] = ln p0=p = += 2