Effects of Mach and Atwood numbers on the shock-induced evolution of a double-layer gas cylinder

Abstract

The evolution of a double-layer gas cylinder under various Mach numbers (M = 1.27, 1.5, 1.7, and 2.1) and Atwood numbers (A = 0.504, 0.392, 0.194, and −0.202 for the first layer) are studied numerically. At M ≥ 1.5 and A = 0.504, a bulge is generated near the upstream pole of the outer cylinder due to the impingement of a reflected shock wave, which promotes the formation of an upstream jet. At a higher Mach number, the evolution of the jet is suppressed under the influence of a higher pressure upstream of the jet head. The compressibility effects are quantified by the widths and heights of the gas cylinders. The Atwood number is associated with nonlinear acoustic effects, and the sign of A results in a significant variation in the wave patterns. The development of vortex pairs slows down with the decreasing Atwood numbers in the scenario of A > 0 for the first layer gas cylinder, while vortex pairs emerge and propagate in both upstream and downstream directions from the outer interface in the scenario of A < 0 for the first layer. As the Mach numbers and the magnitude of the Atwood numbers are increased, the mixing of various gases is promoted by detecting the circulation and mixed mass. The net circulation can be predicted by the linear summation of the Picone and Boris model and the Samtaney and Zabusky model under various Mach and Atwood numbers.