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

TL;DR

This study numerically investigates unsteady throttling dynamics in a hypersonic inlet-isolator flow at Mach 5, revealing how throttling ratios influence flow unsteadiness and proposing a scaling framework validated by numerical and experimental data.

Contribution

It introduces a novel scaling framework for unsteady throttling dynamics in hypersonic inlets based on numerical simulations and existing experimental results.

Findings

Unsteadiness occurs for throttling ratios above 0.2.

Unsteady frequency increases rapidly with throttling ratio.

The proposed scaling relation agrees with numerical and experimental data.

Abstract

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 $0\leq \zeta \leq 0.7$ in steps of 0.1 are considered. No unsteadiness is observed for $\zeta\leq 0.2$ and severe unsteadiness is found for $0.3 \leq \zeta \leq 0.7$. 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 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 $\beta$, which scales with the upstream design parameter $\xi=M_i/M_\infty$. 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.