Calculation of High-speed Inlet Flows Using the Navier-Stokes Equations

Abstract

A numerical code has been developed to calculate the flowfield in two-dimensional high-speed inlets using the Navier-Stokes equations. Arbitrary inlet geometries may be treated, with variable bleed on the ramp and cowl surfaces. Turbulence is incorporated through an algebraic turbulent eddy viscosity. The code has been applied to the calculation of the flow in a simulated high-speed inlet operating at a Mach number of 2.5 and Reynolds number of 1.4 xlO 7 based on inlet length. Two different bleed schedules were considered, which differed principally in the extent of bleed in the vicinity of the shock-turbulent boundary interactions on the ramp surface. The computed results are compared with detailed measurements of the ramp and cowl static pressures, and boundary-layer pitot profiles. The agreement with the experimental data is generally good, although the experimental data display evidence of three dimensionality over a portion of the inlet flowfield. Nomenclaturem = bleed mass flux =p w v w (m<0 for bleed) p = static pressure p p = pitot pressure p t -total pressure «. = friction velocity =Vr vv /p vv v w = bleed velocity at wall x,y,z = Cartesian coordinates y' = distance normal to wall y' m -height of computational sublayer Af, Arj = mesh spacing in f and 77 directions 60 = reference boundary-layer thickness for relaxation model 6 = boundary-layer thickness e = turbulent eddy viscosity f, 17 = transformed coordinates X = relaxation length v = kinematic viscosity p = density T = shear stress Subscripts oo = evaluated upstream of body w = evaluated at wall