A study of unstable axisymmetric separation in high speed flows

Abstract

A study of unstable axisymmetric separation was conducted using spiked cones in flows with free stream Mach numbers, M, of 6.0 and 2.21. Reynolds numbers based on the model diameter, Re_D, were 0.13x10⁶ and 0.9x10⁶ at M = 6.0 and 0.05x10⁶ and 0.12x10⁶ at M = 2.21. The body cone half angle, Φ_D, for the range 30° ≤ Φ_D ≤ 90°, and non-dimensional spike length, l/D, up to l/D = 3 were varied in small increments. Pressure measurements made on the model face using fast response instrumentation showed the pressure to exhibit a regular or periodic wave form. These wave forms were analyzed in terms of the time averaged frequency, f, and amplitude, Δp.

Based on these pressure measurements synchronized with spark photographs of the flow, two distinct modes of unstable axisymmetric flow were observed namely, oscillation and pulsation. Both modes showed the non-dimensional frequency to decrease as t/D was i~creased independent of Φ_D, Re_D, and M. The amplitude, Δp was found to be a strong function of l/D, Φ_D , Re_D and M. However, the maximum Δp of the oscillation mode was one tenth that of the pulsation mode which was of the order of magnitude of the pitot pressure.

To provide further information on which a theoretical analysis could be based specialized experiments were carried out on specific models. These techniques included thin film gauges and a high speed cine in the streak mode.

These data were then examined with the purpose of establishing the mechanisms of the modes of unstable flow. An original hypothesis was developed for the oscillation mode based on a viscous mechanism. Comparison with experiment was made which showed this hypothesis to be a sound physical model. The pulsation mode was similarly treated revealing this mechanism to be of an inviscid nature.

Finally, the results of this study were used to predict the unstable flow parameters of an idealized ablation model of current practical interest. A comparison of this with experiment shows the results of the present study to provide a useful engineering guideline.