Abstract
A detailed numerical simulation of a shock accelerated heavy gas (SF6) cylinder surrounded by air gas is presented. It is a simplified configuration of the more general shock-accelerated inhomogeneous flows which occur in a wide variety of astrophysical systems. From the snapshots of the time evolution of the gas cylinder, we find that the evolution of the shock accelerated gas cylinder is in some ways similar to the roll-ups of a vortex sheet for both roll up into a spiral and fall into a self-similar behavior. The systemic and meaningful analyses of the negative circulation, the center of vorticity and the vortex spacing are in a good agreement with results obtained from the prediction of vorticity dynamics. Unlike the mixing zone width in single-mode or multi-mode Richtmyer-Meshkov instability which doesn’t exist, a single power law of time owing to the bubble and spike fronts follow a power law of tθ with different power exponents, the normalized length of the shock accelerated gas cylinder follows a single power law with θ = 0.43 in its self-similar regime obtained from the numerical results.
Highlights
When an impulsive acceleration impinges on the corrugated interface between two fluids of different densities, the instability at the interface will arise due to the deposited vorticity induced by the baroclinic torque produc-How to cite this paper: Wang, B., Bai, J.-S. and Wang, T. (2015) Numerical Investigation of a Shock Accelerated Heavy Gas Cylinder in the Self-Similar Regime
When a planar shock wave impacts on a heavy gas (e.g., SF6) cylinder around by an ambient gas, a shock wave is reflected and a refracted shock wave transmits into the heavy gas cylinder
Because the heavy gas acoustic impedance exceeds that of the ambient gas, the refracted shock is slower than the incident shock wave, and a convergent shock refraction pattern occurs
Summary
When an impulsive acceleration impinges on the corrugated interface between two fluids of different densities, the instability at the interface will arise due to the deposited vorticity induced by the baroclinic torque produc-How to cite this paper: Wang, B., Bai, J.-S. and Wang, T. (2015) Numerical Investigation of a Shock Accelerated Heavy Gas Cylinder in the Self-Similar Regime. In the RM instability researches, an interesting configuration is a shock wave interacting with a cylindrical interface (circular interface in two dimensions) between two fluids. Because the heavy gas acoustic impedance exceeds that of the ambient gas, the refracted shock is slower than the incident shock wave, and a convergent shock refraction pattern occurs. Because of this and the curvature of the cylinder, the transmitted shock focuses at the downstream vertex. This focusing will induce a pressure rising that eventually leads to a cusp-like protrusion [6]. The evolution of the interface will be dominated by the vortex pair and falls into a self-similar regime, which is in some ways similar to the roll-ups of a vortex sheet [7]-[9]
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