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Spherical piston problem in water

Published online by Cambridge University Press:  29 March 2006

P. L. Bhatnagar ,
P. L. Sachdev  and
Phoolan Prasad
P. L. Bhatnagar
Affiliation:
Department of Applied Mathematics, Indian Institute of Science, Bangalore 12, India Present address: University of Rajasthan, Jaipur, India.
P. L. Sachdev
Affiliation:
Department of Applied Mathematics, Indian Institute of Science, Bangalore 12, India
Phoolan Prasad
Affiliation:
Department of Applied Mathematics, Indian Institute of Science, Bangalore 12, India
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Abstract

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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 39 , Issue 3 , 27 November 1969 , pp. 587 - 600
Copyright
© 1969 Cambridge University Press

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References

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