Modeling supersonic inlet boundary-layer bleed roughness

Abstract

Boundary-layer mass removal (bleed) through spanwise bands of holes on a surface is used to prevent or control separation in supersonic inlets. The rough wall algebraic turbulence model of Cebeci and Chang was added to both boundary-layer and Navier-Stokes analyses to simulate the overall effect of bleed on the growth of a boundary layer. Roughness values were determined for seven bleed configurations, a range of Mach numbers between 1.3-4, and bleed rates between zero and choked values. For the bleed experiments considered, the roughness was found to be a function of the fraction of the upstream boundary-layer mass flux removed. Choked bleed flow through holes at a low angle, with respect to the surface, minimized the roughness effect and gave the best improvement in the boundary-layer velocity distribution for separation control. Nomenclature A+ = Van Driest parameter, 26 d ~ bleed hole diameter k = von Karman constant, 0.4 ks = equivalent sand grain roughness Lid — hole aspect ratio / = local turbulent length scale M = Mach number N = number of rows of bleed holes in bleed band P/POO = local static pressure/freestream static pressure R = roughness parameter, in. ulue — ratio of local to freestream velocity within the boundary layer «r = (TJPJ1 u' = local turbulent velocity scale