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 $M_\infty=5$ 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 $0\leq ζ\leq 0.7$ in steps of 0.1 are considered. No unsteadiness is observed for $ζ\leq 0.2$ and severe unsteadiness is found for $0.3 \leq ζ\leq 0.7$. The frequency of unsteadiness ($f$) increases rapidly with $ζ$. As $ζ$ 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 like the freestream Mach number ($M_\infty$) and the isolator inlet Mach number ($M_i$). Factors like the mass occupied by the duct volume, the characteristic unsteady frequency, throttling ratio, and the exit mass flow rate through the duct are used to form a non-dimensional parameter $β$, which scales with the upstream design parameter $ξ=M_i/M_\infty$. 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.