A model for pulsation in high-speed double cone flow

Abstract: Periodic large-scale shock-wave unsteadiness over a canonical double cone, termed in literature as "pulsation," is experimentally studied at Mach 6. The general double cone geometry is defined by three non-dimensional geometric parameters: fore- and aft-cone angles ($θ_1$ and $θ_2$), and ratio of the conical slant lengths ($\mathitΛ$). While existing literature on pulsation offers detailed qualitative and phenomenological discussions, it is seen that analytical approaches to obtain insight into the unsteady flow phenomena are missing. The present effort is aimed at addressing this gap. Self-sustained flow pulsations for a particular double cone configuration with $θ_1 = 0<sup>\circ$ and $θ_2 = 90<sup>\circ$, commonly referred to as the spike-cylinder, is investigated in the $\mathitΛ$ parameter space. High-speed schlieren imaging and time-resolved pressure measurements are performed in the unsteady flow. The non-dimensional pulsation frequency (Strouhal number) is observed to increase monotonically with $\mathitΛ$. Schlieren and pressure data suggest that the unsteadiness is driven by a cyclic process involving the formation of high-pressure gas near the aft-cone and its subsequent expansion through the separation region formed over the fore-cone. Building on this understanding, a detailed analytical model for the flow is developed with no empirical parameters. The model successfully predicts the experimentally-measured Strouhal number, and provides an in-depth understanding of the mechanisms that drive flow pulsations.