Boundary-Layer Transition on Supersonic Cones in an Aeroballistic Range

Abstract

Research was undertaken with the purpose of determining the effect of the unit Reynolds number on boundary-layer transition under conditions where disturbances associated with wind tunnel flows would not be present. The location of boundary-layer transition was determined from shadowgrams of nominally sharp, 4° and 10°s emi-angle cones in an aeroballistic range at freestream Mach numbers of 23 and 5.0 and unit Reynolds numbers of 0.3 x 10 6 to 8 x 10 6 per in. Owing to constant and equal freestream and cone skirt temperatures, the average ratio of cone wall-to-adiabatic recovery temperature was 0.52 at Mach 2.3 and 0.19 at Mach 5.0. Features of free-flight experimentation that may be suspected of influencing boundary-layer transition were investigated. These included 1) oscillatory motion and finite angles of attack, 2) surface roughness, 3) vibration of the model, and 4) non-uniform (hot-tip) surface temperature. There was no evidence that any of these conditions influenced the major results. The data show local Reynolds number of transition increasing with unit Reynolds number for both Mach numbers. A siren was used to elevate the fluctuating sound pressure ratio by a factor of 200, but that produced no measurable effect on transition locations. Nomenclature c r = phase velocity of disturbance = velocity of wave propagation in freestream direction / = frequency of vibration of cone; also "function of" k = roughness depth profilometer reading M = Mach number N = number of cycles of vibration p --pressure p -fluctuating sound pressure amplitude Re = Reynolds number s = distance measured along surface from stagnation point T = temperature U = velocity a = total angle of attack a p = angle of attack in plane of photograph /? = characteristic angular frequency of disturbance spectrum y = ratio of specific heats 5 = boundary-layer thickness 6 = characteristic orientation of disturbance spectrum 9 C = cone semi-apex angle / = characteristic wavelength of disturbance spectrum fj, = absolute viscosity v = kinematic viscosity -n/p p = mass density (f > = orientation of a cone meridian relative to the windward stagnation line where 1fa= 0 a) = exponent in the approximation \i oc T C) Subscripts aw = adiabatic wall j = at station of temperature discontinuity o = total, e.g., total temperature; also designates a = 0 t = transition w = cone wall 6 = local flow parameter at outer edge of boundary layer oo = freestream a = denotes a ^ 0

Effects of Nose Bluntness on Hypersonic Boundary-Layer Receptivity and Stability over Cones

“…The present predictions also fall in the same range as in the experiments and computations. Potter [1] found that, from a series of aeroballistics range experiments on nominally sharp cones, the . These frequencies correspond to 312, 292, 468, and 234 kHz, respectively, and streamwise wavelengths for slow mode correspond to 0.1007, 0.1074, 0.0671, and 0.1343 in., respectively, for these Reynolds numbers.…”

“…These frequencies correspond to 312, 292, 468, and 234 kHz, respectively, and streamwise wavelengths for slow mode correspond to 0.1007, 0.1074, 0.0671, and 0.1343 in., respectively, for these Reynolds numbers. To remain in the linear regime, the amplitude of the forcing freestream acoustic waves was given a small value of p ac =p 1 …”

“…The growth rate of the most-amplified disturbances was overpredicted by about 60% compared to the experiment. It was also established by the computations that the effect of unit Reynolds number observed in the aeroballistics range data of Potter [1] was in fact a nose bluntness effect. Esfahanian [9] and Rosenboom et al [10] also performed linear stability analysis for Stetson's experiment.…”

“…In supersonic and hypersonic boundary layers, one important geometrical parameter is nose bluntness. The effects of bluntness on transition in supersonic and hypersonic boundary layers have been studied experimentally [1][2][3][4][5][6] and numerically [7][8][9][10][11][12][13] by many researchers. It was identified that the entropy layer that is formed near the bow shock region persists for a long distance downstream and makes the boundary layer more stable when compared to the sharpcone case.…”