Oblique Impact of an Elongated Three-Dimensional Body on a Thin Liquid Layer
E. A. Batyaev1,2, T. I. Khabakhpasheva1,2
1Lavrent'ev Institute of Hydrodynamics, Siberian Branch Russian Academy of Sciences, Novosibirsk 630090, Russia
2Novosibirsk State University, Novosibirsk 630090, Russia
Keywords: взаимодействие тела и жидкости, удар по тонкому слою жидкости, метод сращиваемых асимптотических разложений, метод плоских сечений, удлиненный эллипсоид, body and liquid interaction, impact on a thin liquid layer, matched asymptotic expansions, plane section method, elongated ellipsoid
Abstract
The problem of the impact of an elongated solid body with a flat bottom on a thin layer of an ideal incompressible liquid is considered in the case where the horizontal component of the body velocity is substantially greater than its vertical component. The initial stage of the impact is studied in which the a priori unknown contact area between the body and the liquid is rapidly expanding. The loads on the body are determined by the plane section method. The method of matched asymptotic expansions is used to determine the position and size of the contact spot in each section. The coupled problem is solved: the liquid flow due to the motion of the body and the body motion itself are determined simultaneously. A system of integrodifferential equations was obtained and used for numerical investigation of the body motion under the action of hydrodynamic loads, and the hydrodynamic pressure distribution over the contact spot was determined.
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