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Home » Issues » Archive of Issues » 2019 - 2 issue » pp. 261-274

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Russia Rostov-on-Don
Year
2019
Volume
29
Issue
2
Pages
261-274
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Section Mechanics
Title Cavitational braking of a cylinder with a variable radius in a fluid after impact
Author(-s) Norkin M.V.a
Affiliations Southern Federal Universitya
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
UDC 532.5.031
MSC 76B07, 76B10, 76B20
DOI 10.20537/vm190209
Received 14 January 2019
Language Russian
Citation Norkin M.V. Cavitational braking of a cylinder with a variable radius in a fluid after impact, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2019, vol. 29, issue 2, pp. 261-274.
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