Viscous jetting and Mach stem bifurcation in shock reflections: experiments and simulations

TL;DR

This study combines experiments and simulations to investigate shock reflection phenomena, revealing how variations in Mach number, Reynolds number, and isentropic exponent influence Mach stem bifurcation and vortex formation, with implications for detonation structures.

Contribution

It provides new experimental and simulation data on shock reflection, identifying the conditions under which Mach stem bifurcation occurs and its relation to flow parameters and detonation patterns.

Findings

Bifurcation occurs at low isentropic exponents and high Mach/Reynolds numbers.

Kelvin-Helmholtz instabilities cause large-scale mixing behind the Mach stem.

Maximum isentropic exponent for bifurcation is approximately 1.3.

Abstract

Shock reflection experiments are performed to study the large-scale convective mixing created by the forward jetting phenomenon. Experiments are performed at a wedge angle of $\theta_{\mathrm{w}} = 30^{\circ}$ in nitrogen, propane-oxygen, and hexane with incident shock Mach numbers up to $M = 4$. Experiments are complimented by shock-resolved viscous simulations of triple point reflection in hexane for $M = 2.5$ to $6$. Inviscid simulations are performed over a wider range of parameters. Reynolds numbers up to $Re \lesssim 10^3$ are covered by simulations and Reynolds numbers of $Re \sim 10^5$ are covered by experiments. The study shows that as the isentropic exponent is lowered, and as the Mach number and Reynolds number are increased, the forward jet approaches the Mach stem, forms a vortex, deforms the shock front and in some cases bifurcates the Mach stem. Experiments show Kelvin-Helmholtz instabilities in the vortex cause large-scale convective mixing behind the Mach stem at low isentropic exponents ($\gamma \le 1.15$). The limits of Mach stem bifurcation (triple Mach-White reflection) in inviscid simulations are plotted in the phase space of $M$- $\theta_{\mathrm{w}}$-$\gamma$. A maximum isentropic exponent of $\gamma \approx 1.3$ is found beyond which bifurcation does not occur (at $\theta_{\mathrm{w}} = 30^{\circ}$). This closely matches the boundary between irregular/regular detonation cellular structures.