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Rotational stabilisation of the Rayleigh–Taylor instability at the inner surface of an imploding liquid shell

Published online by Cambridge University Press:  25 June 2019

Justin Huneault Open the ORCID record for Justin Huneault [Opens in a new window] ,
David Plant  and
Andrew J. Higgins
Justin Huneault
Affiliation:
Department of Mechanical Engineering, McGill University, 817 Sherbrooke St. West, Montreal, QC H3A 0C3, Canada
David Plant
Affiliation:
General Fusion Inc., 108-3680 Bonneville Place, Burnaby, BC V3N 4T5, Canada
Andrew J. Higgins*
Affiliation:
Department of Mechanical Engineering, McGill University, 817 Sherbrooke St. West, Montreal, QC H3A 0C3, Canada
*
†Email address for correspondence: [email protected]
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Abstract

A number of applications utilise the energy focussing potential of imploding shells to dynamically compress matter or magnetic fields, including magnetised target fusion schemes in which a plasma is compressed by the collapse of a liquid metal surface. This paper examines the effect of fluid rotation on the Rayleigh–Taylor (RT) driven growth of perturbations at the inner surface of an imploding cylindrical liquid shell which compresses a gas-filled cavity. The shell was formed by rotating water such that it was in solid body rotation prior to the piston-driven implosion, which was propelled by a modest external gas pressure. The fast rise in pressure in the gas-filled cavity at the point of maximum convergence results in an RT unstable configuration where the cavity surface accelerates in the direction of the density gradient at the gas–liquid interface. The experimental arrangement allowed for visualisation of the cavity surface during the implosion using high-speed videography, while offering the possibility to provide geometrically similar implosions over a wide range of initial angular velocities such that the effect of rotation on the interface stability could be quantified. A model developed for the growth of perturbations on the inner surface of a rotating shell indicated that the RT instability may be suppressed by rotating the liquid shell at a sufficient angular velocity so that the net surface acceleration remains opposite to the interface density gradient throughout the implosion. Rotational stabilisation of high-mode-number perturbation growth was examined by collapsing nominally smooth cavities and demonstrating the suppression of small spray-like perturbations that otherwise appear on RT unstable cavity surfaces. Experiments observing the evolution of low-mode-number perturbations, prescribed using a mode-6 obstacle plate, showed that the RT-driven growth was suppressed by rotation, while geometric growth remained present along with significant nonlinear distortion of the perturbations near final convergence.

JFM classification

Drops and Bubbles: Bubble dynamics Instability: Nonlinear instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 873 , 25 August 2019 , pp. 531 - 567
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Copyright
© 2019 Cambridge University Press 

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Huneault et al. supplementary movie 1

Off-axis view of the shell inner surface for unperturbed cavity experiments at initial angular velocities of 79, 105, and 131 rad/s. The shell inner surface only comes into view at a radius of approximately 40 mm to focus on the final stages of collapse near turnaround.

Download Huneault et al. supplementary movie 1(Video)
Video 7.8 MB

Huneault et al. supplementary movie 2

Normal view of the unperturbed cavity experiments at initial angular velocities of 79, 105, and 131 rad/s. The dark edge which delineates the cavity surface is notably broadened in the 79 and 105 rad/s experiments due to perturbation growth.

Download Huneault et al. supplementary movie 2(Video)
Video 4 MB

Huneault et al. supplementary movie 3

Normal view of mode-6 perturbed implosion experiments showing the entire implosion at initial angular velocities of 79, 105, and 131 rad/s. The obstruction plate fins can be seen on the periphery.

Download Huneault et al. supplementary movie 3(Video)
Video 6.8 MB

Huneault et al. supplementary movie 4

Normal view of mode-6 perturbed implosion experiments at initial angular velocities of 79, 105, and 131 rad/s, zoomed-in to focus on perturbation growth near turnaround.

Download Huneault et al. supplementary movie 4(Video)
Video 7 MB

Huneault et al. supplementary movie 5

Off-axis view of the shell inner surface for mode-6 perturbed implosion experiments at initial angular velocities of 79, 105, and 131 rad/s. The shell inner surface only comes into view at a radius of approximately 40 mm to focus on the final stages of collapse near turnaround.

Download Huneault et al. supplementary movie 5(Video)
Video 6.8 MB

Huneault et al. supplementary movie 6

Normal view of a mode-24 perturbed implosion experiment at an initial angular velocity of 131 rad/s.

Download Huneault et al. supplementary movie 6(Video)
Video 4.5 MB