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 Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2019, Volume 29, Issue 2, Pages 261–274 (Mi vuu680)

MECHANICS

Cavitational braking of a cylinder with a variable radius in a fluid after impact

M. V. Norkin

Institute of Mathematics, Mechanics and Computer Sciences, Southern Federal University, ul. Mil’chakova, 8a, Rostov-on-Don, 344090, Russia

Abstract: The 2D problem of the movement of a circular cylinder with a variable radius in an ideal, incompressible, heavy fluid is considered. It is assumed that the initial perturbation of the fluid is caused by a vertical and continuous impact of the cylinder semi-submerged in the fluid. The feature of this problem is that under certain conditions (for example, at fast braking of the cylinder or at fast reduction of its radius), there is a separation of the fluid from the body, resulting in the formation of attached cavities near its surface. The forms of the inner free boundaries and the configuration of the external free border are in advance unknown and are subject to definition when the problem is solved. A nonlinear problem with one-sided constraints is formulated, on the basis of which the connectivity of the separation zone and the shape of the free boundaries of the fluid at small times are determined. In the case where the pressure on the external free surface coincides with the pressure in the cavity, an analytical solution of the problem is constructed. To define one of two symmetric points of separation, a transcendental equation containing a full elliptic integral of the first kind and elementary functions is obtained. For the case of cavitational braking of a nondeformable cylinder, an explicit formula for the inner free boundary of the fluid on small times is found. Good agreement of analytical results with direct numerical calculations is shown.

Keywords: ideal incompressible fluid, cylinder with a variable radius, impact, cavitation braking, free boundary, separation point, small times, Froude number, cavitation number.

DOI: https://doi.org/10.20537/vm190209

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Bibliographic databases:

UDC: 532.5.031
MSC: 76B07, 76B10, 76B20

Citation: M. V. Norkin, “Cavitational braking of a cylinder with a variable radius in a fluid after impact”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:2 (2019), 261–274

Citation in format AMSBIB
\Bibitem{Nor19} \by M.~V.~Norkin \paper Cavitational braking of a cylinder with a variable radius in a fluid after impact \jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki \yr 2019 \vol 29 \issue 2 \pages 261--274 \mathnet{http://mi.mathnet.ru/vuu680} \crossref{https://doi.org/10.20537/vm190209} \elib{https://elibrary.ru/item.asp?id=39136251}