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Impulsive Motion Inside a Cylindrical Cavity

1
Institute of Hydromechanics of the National Academy of Sciences of Ukraine, 8/4 Zhelybova Street, 03680 Kiev, Ukraine
2
Department of Mechanical Engineering, University College London, Gower Street, London WC1E 6BT, UK
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 192; https://doi.org/10.3390/math8020192
Received: 17 December 2019 / Revised: 22 January 2020 / Accepted: 31 January 2020 / Published: 5 February 2020
Experimental studies of supercavitating models moving at speeds in the range from 400 m/s to 1000 m/s revealed a regime of bouncing motion, in which the rear part of an axisymmetric body periodically bounces against the free boundaries of the supercavity. The impulsive force generated by the impacts is the main concern in this paper. The analysis is performed in the approximation of two-dimensional potential flow of an ideal and incompressible liquid with negligible surface tension effects. The primary interest of the study is to determine the added mass taking into account the shape of the cavity. The theoretical study is based on the integral hodograph method, which makes it possible to obtain analytic expressions for the flow potential and for the complex velocity in an auxiliary parameter plane and obtain a parametric solution to the problem. The problem is reduced to a system of two integro-differential equations in two unknowns: the velocity magnitude on the cavity boundary and the slope of the velocity angle to the body. The equations are solved numerically using the method of successive approximations. The obtained results show that the added mass of an arc impacting a cylindrical cavity depends heavily on the arc angle. As the angle tends to zero or the radius of the cavity tends to infinity, the obtained solution predicts the added mass corresponding to a plate impacting a flat free surface.
Keywords: supercavitation; fluid/structure interaction; impulsive impact supercavitation; fluid/structure interaction; impulsive impact
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MDPI and ACS Style

Savchenko, Y.; Savchenko, G.; Semenov, Y.A. Impulsive Motion Inside a Cylindrical Cavity. Mathematics 2020, 8, 192.

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