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On the Collapse of a Gas Cavity by an Imploding Molten Lead Shell and Richtmyer-Meshkov Instability

Abstract
The compression of a cylindrical gas bubble by an imploding molten lead (Pb) shell may be accompanied by the development of the Richtmyer–Meshkov (RM) instability at the liquid–gas interface due to the initial imperfection of the interface. A converging pressure wave impinging upon the interface causes a shell of liquid to detach and continue to travel inwards, compressing the gas bubble. The efficiency of compression and collapse evolution can be affected by development of the RM instability.

Investigations have been performed in the regime of extreme Atwood number A ¼ 1 with the additional complexity of modeling liquid cavitation in the working fluid. Simulations have been carried out using the open source CFD software OpenFOAM on a set of parameters relevant to the prototype compression system under development at General Fusion Inc. for use as a Magnetized Target Fusion (MTF) driver. After validating the numerical setup in planar geometry, simulations have been carried out in 2D cylindrical geometry for both initially smooth and perturbed interfaces. Where possible, results have been validated against existing theoretical models and very good agreement has been found.

While our main focus is on the effects of initial perturbation amplitude and azimuthal mode number, we also address differences between this problem and those usually considered, such as RM instability at an interface between two gases with a moderate density ratio. One important difference is the formation of narrow molten lead jets rapidly propagating inwards during the final stages of the collapse. Jet behavior has been observed for a range of azimuthal mode numbers and perturbation amplitudes.

Suponitsky, V., Barsky, S., and Froese, A., 2012. On the Collapse of a Gas Cavity by an Imploding Molten Lead Shell and Richtmyer-Meshkov Instability. Proceedings of the 20th Annual Conference of the CFD Society of Canada. May 9-12, Canmore, Alberta.