Flare-Induced Interaction Lengths in Supersonic, Turbulent Boundary Layers

TLDR: In this paper, the effects of Mach number, Reynolds number, and corner angle on flare-induced separation of a supersonic, turbulent boundary layer were investigated, and a simple correlation formula was obtained and used to compare results from other investigations and also to correlate incipient separation data.

Abstract: Experimental results are presented for the effects of Mach number, Reynolds number, and corner angle on flare-induced separation of a supersonic, turbulent boundary layer. In particular, measurements were obtained for the variation with flare angle, α, of the ratio l_0/δ_0 of the upstream interaction length to the boundary-layer thickness at the beginning of the interaction for Mach numbers 2≤M≤4.5, boundary-layer thickness Reynolds numbers 10^5 < R_δ < 10^6, and adiabatic wall conditions. The model consisted of a hollow cylinder of 12-in. diameter and 51-in. length. Flares of angle 9°≤α≤40° were attached to the cylinder model at either of two location, viz., at x_c= 14 or 28 in. downstream from the sharp leading edge. Measurements consisted chiefly of surface-pressure distributions. Profiles for the undisturbed (flare-off) boundary-layer were also obtained. By varying the several parameters upstream interaction lengths as large as l_0/δ_0 = 30 were observed. It was found that l_0/δ_0 decreases with increasing Mach number and Reynolds number and, of course, increases with flare angle. It was also found that, for constant α, when l_0/δ_0 is plotted vs the local skin-friction coefficient, C_(f0), the Mach-number dependence disappears. From this observation, a simple correlation formula was obtained and used to compare results from other investigations, and also to correlate incipient separation data. The present results complement the incipient-separation data obtained previously by us in the next higher decade of Reynolds number and further confirm the trends established there. It was also found that, for large α, the separated region upstream of the flare has free-interaction characteristics similar to those of upstream-facing steps at high Reynolds number.