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

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 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

Reduced-Order Modeling of Turbulent Reacting Flows with Application to Ramjets and Scramjets

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“…(3)(4)(5)(6)(7)(8)(9)], solving them in the following manner. We avoid formulating the problem in terms of c p and directly use the enthalpy curve fits, which are available from NASA CEA [32,33].…”

“…MASIV consists of several reduced-order models (ROMs). One is an inlet ROM that computes losses due to multiple shock/ expansion wave interactions; this ROM is described elsewhere [5]. The other is a fuel/air mixing/combustion ROM that is the focus of the present paper.…”

Switching control of thrust regulation and inlet unstart protection for scramjet engine based on strategy of integral initial values resetting

“…Several control methods have been proposed in the control problem of scramjet engine [3,[8][9][10][11][12][13][14][15][16]. Most of these studies focused on the inlet control or the combustion control separately.…”

A non-intrusive reduced-order model for compressible fluid and fractured solid coupling and its application to blasting

“…Recently there have been a number of papers on reduced order modelling of compressible fluids, e.g. with shock waves [2,53,54,55,56,57,58,59]. Most of existing ROMs for shock waves use the Galerkin (or Petrov-Galerkin) projection and POD approaches to generate the reduced order models.…”