Spherical piston problem in water

Bhatnagar, P. L. ; Sachdev, P. L. ; Prasad, Phoolan (1969) Spherical piston problem in water Journal of Fluid Mechanics, 39 . pp. 587-600. ISSN 0022-1120

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Related URL: http://dx.doi.org/10.1017/S0022112069002345


In this paper, we study the propagation of a shock wave in water, produced by the expansion of a spherical piston with a finite initial radius. The piston path in the x, t plane is a hyperbola. We have considered the following two cases: (i) the piston accelerates from a zero initial velocity and attains a finite velocity asymptotically as t tends to infinity, and (ii) the piston decelerates, starting from a finite initial velocity. Since an analytic approach to this problem is extremely difficult, we have employed the artificial viscosity method of von Neumann & Richtmyer after examining its applicability in water. For the accelerating piston case, we have studied the effect of different initial radii of the piston, different initial curvatures of the piston path in the x, t plane and the different asymptotic speeds of the piston. The decelerating case exhibits the interesting phenomenon of the formation of a cavity in water when the deceleration of the piston is sufficiently high. We have also studied the motion of the cavity boundary up to 550 cycles.

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ID Code:4940
Deposited On:18 Oct 2010 08:33
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