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On the interaction of a planar shock with a three-dimensional light gas cylinder

Published online by Cambridge University Press:  04 September 2017

Juchun Ding
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Ting Si*
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Mojun Chen
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Zhigang Zhai
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Xiyun Lu
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Xisheng Luo
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Email address for correspondence:


Experimental and numerical investigations on the interaction of a planar shock wave with two-dimensional (2-D) and three-dimensional (3-D) light gas cylinders are performed. The effects of initial interface curvature on flow morphology, wave pattern, vorticity distribution and interface movement are emphasized. In experiments, a wire-restriction method based on the soap film technique is employed to generate N$_{2}$ cylinders surrounded by SF$_{6}$ with well-characterized shapes, including a convex cylinder, a concave cylinder with a minimum-surface feature and a 2-D cylinder. The high-speed schlieren pictures demonstrate that fewer disturbance waves exist in the flow field and the evolving interfaces develop in a more symmetrical way relative to previous studies. By combining the high-order weighted essentially non-oscillatory construction with the double-flux scheme, numerical simulation is conducted to explore the detailed 3-D flow structures. It is indicated that the shape and the size of 3-D gas cylinders in different planes along the vertical direction change gradually due to the existence of both horizontal and vertical velocities of the flow. At very early stages, pressure oscillations in the vicinity of evolving interfaces induced by complex waves contribute much to the deformation of the 3-D gas cylinders. As time proceeds, the development of the shocked volume would be dominated by the baroclinic vorticity deposited on the interface. In comparison with the 2-D case, the oppositely (or identically) signed principal curvatures of the concave (or convex) SF$_{6}$/N$_{2}$ boundary cause complex high pressure zones and additional vorticity deposition, and the upstream interface from the symmetric slice of the concave (or convex) N$_{2}$ cylinder moves with an inhibition (or a promotion). Finally, a generalized 3-D theoretical model is proposed for predicting the upstream interface movements of different gas cylinders and the present experimental and numerical findings are well predicted.

© 2017 Cambridge University Press 

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Ding et al. supplementary movie 1

High-speed schlieren imaging of a shocked 2D N2 cylinder surrounded by SF6 in experiments (top) and numerical simulations (bottom).

Download Ding et al. supplementary movie 1(Video)
Video 4 MB

Ding et al. supplementary movie 2

High-speed schlieren imaging of a shocked concave N2cylinder surrounded by SF6 in experiments (top) and numerical simulations (bottom).

Download Ding et al. supplementary movie 2(Video)
Video 6 MB

Ding et al. supplementary movie 3

High-speed schlieren imaging of a shocked convex N2cylinder surrounded by SF6 in experiments (top) and numerical simulations (bottom).

Download Ding et al. supplementary movie 3(Video)
Video 6 MB