On the unsteady throttling dynamics and scaling analysis in a typical hypersonic inlet-isolator flow

The flow field in a two-dimensional three-ramp hypersonic mixed-compression inlet in a freestream Mach number of M-infinity = 5 is numerically solved to understand the unsteady throttling dynamics. Throttling conditions are simulated by varying the exit area of the isolator in the form of plug insets. Different throttling ratios between 0 <= zeta <= 0.7 in steps of 0.1 are considered. No unsteadiness is observed for zeta <= 0.2, and severe unsteadiness is found for 0.3 <= zeta <= 0.7. The frequency of unsteadiness (f) increases rapidly with zeta. As zeta increases, the amount of reversed mass inside the isolator scales with the frequency and the exit mass flow rate. A general framework is attempted to scale the unsteady events based on the gathered knowledge from the numerical study. The inlet-isolator flow is modeled as an oscillating flow through a duct with known upstream design conditions such as the freestream Mach number (M-infinity) and the isolator inlet Mach number (M-i). Factors such as the mass occupied by the duct volume, the characteristic unsteady frequency, the throttling ratio, and the exit mass flow rate through the duct are used to form a non-dimensional parameter beta, which scales with the upstream design parameter xi = M-i/M-infinity. The scaling parameters are further exploited to formulate a semi-empirical relation using the existing experimental results at different throttling ratios from the open literature. The unsteady frequencies from the present two-dimensional numerical exercise are also shown to agree with the proposed scaling and the resulting semi-empirical relation.