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

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 $\hat{I}{¸}_{\mathrm{w}}=30^{\circ }$ 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 (${\hat{I}}^3\le 1.15$). The limits of Mach stem bifurcation (triple Mach-White reflection) in inviscid simulations are plotted in the phase space of $M$- $\hat{I}{¸}_{\mathrm{w}}$-${\hat{I}}^3$. A maximum isentropic exponent of ${\hat{I}}^3\approx 1.3$ is found beyond which bifurcation does not occur (at $\hat{I}{¸}_{\mathrm{w}}=30^{\circ }$). This closely matches the boundary between irregular/regular detonation cellular structures.

29 pages, 22 figures; Submitted to the Journal of Fluid Mechanics