Abstract
Under consideration is some dynamical mixed problem concerning some separated impact and subsequent motion with constant velocity of a rectangular cylinder in an ideal incompressible heavy liquid. The specificity of this problem is that an attached cavity forms after impact and a new internal free boundary of the liquid appears. The shape of the cavity and the configuration of the outer free surface are unknown in advance and are to be determined during solution of the problem. Studying the problem is carried out at short times with consideration of the dynamics of the points of separation of the internal free boundary of the liquid. Location of the separation points at every time is defined from the Kutta–Zhukovsky condition. The influence is studied of the physical and geometric parameters of the problem on the shape of free boundaries of the liquid at short times. The asymptotic analysis is carried out of the internal free boundary of liquid near the separation points.
Similar content being viewed by others
REFERENCES
L. I. Sedov, Two-Dimensional Problems of Hydrodynamics and Aerodynamics (Nauka, Moscow, 1966) [in Russian].
M. Norkin and A. Korobkin, “The Motion of the Free-Surface Separation Point During the Initial Stage of Horizontal Impulsive Displacement of a Floating Circular Cylinder,” J. Eng. Math. 70, 239–254 (2011).
M. V. Norkin, “The Motion of a Circular Cylinder in a Liquid after Impact at Short Times with Formation of a Cavity,” Izv. Ross. Akad. Nauk. Mekh. Zhidk. i Gaza No. 3, 101–112 (2012).
M. V. Norkin, “A Cavity Formation at the Inclined Separated Impact on a Circular Cylinder under Free Surface of a Heavy Liquid,” Sibir. Zh. Industr. Mat. 19 (4), 81–92 (2016) [J. Appl. Indust. Math. 10 (4), 538–548 (2016)].
B. I. Smetanin and K. E. Fedyaeva, “Cavitation Separation with the Impact of a Plate Located in a Layer of a Fluid Parallel to Its Free Boundary,” Ekolog. Vestnik Nauchnykh Tsentrov ChES No. 2, 51–57 (2014).
A. I. Korotkin, Associated Masses of a Ship: Handbook (Sudostroenie, Leningrad, 1986) [in Russian].
I. K. Ten, “Nonstationary Motion of a Floating Body of Squared Shape,” Prikl. Mekh. Tekhn. Fiz. 42 (5), 84–92 (2001).
N. E. Kochin, I. A. Kibel’, and N. V. Roze, Theoretical Hydromechanics, Vol. 1 (Fizmatgiz, Moscow, 1963) [in Russian].
V. I. Yudovich, “One-Valued Solvability of a Problem of a Solid Body Impact on a Inhomogeneous Liquid,” Vladikavkaz. Mat. Zh. 7 (3), 79–91 (2005).
M. Yu. Zhukov and E. V. Shiryaeva, Application of Software Package of Finite Elements FreeFem++ for Problems of Hydrodynamics, Electrophoresis, and Biology (Izd. Yuzhn. Federal. Univ., Rostov-on-Don, 2008) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by L.B. Vertgeim
Rights and permissions
About this article
Cite this article
Norkin, M.V. The Movement of a Rectangular Cylinder in a Liquid at Short Times after Impact with Formation of a Cavity. J. Appl. Ind. Math. 14, 385–395 (2020). https://doi.org/10.1134/S1990478920020155
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1990478920020155