Analysis of Highly Unsteady and Quasi-steady Shocks in Hypersonic Inlets Based on the Principle of Minimum Entropy Production

Abstract

The stability of shocks in hypersonic inlets to flow perturbations can be determined analytically from the principle of minimum entropy. Experimental data from a Mach 9.55 test run at AEDC's Hypervelocity Tunnel 9 showed a bow shock transitioning from steady to unsteady during an angle-of-attack sweep at a normal Mach number between 1.59 and 1.74. This is in close agreement with derived analytic results, which suggest shocks become unstable to perturbations at normal Mach numbers of 1.58 for Mach number perturbations and 1.74 for a Mach 10 angle perturbation. Shocks are likely unstable to all highly unsteady oscillatory downstream perturbations in thermodynamic variables. The principle of minimum entropy suggests that shocks are stable to highly unsteady perturbations in upstream thermodynamic variables at lower normal Mach numbers. The range of normal Mach numbers where this occurs increases with frequency. This range decreases as the perturbaton size increases but the effect is several orders of magnitude smaller compared to increasing frequency.