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COMPUTER HYDROMECHANICS, 2024
IX International Scientific & Practical Conference "Computer Hydromechanics"
HYDRODYNAMICS AND ACOUSTICS
2024 ◊ Volume 3 (93) ◊ Issue 1 ◊ p. 95-110
Yu. A. Semenov*, Yu. M. Savchenko*, G. Yu. Savchenko*, O. I. Naumova*
* Institute of Hydromechanics of NAS of Ukraine, Kyiv, Ukraine
Impulsive impact of a submerged body
Gidrodin. akust. 2024, 3(1):095-110
TEXT LANGUAGE: Ukrainian
ABSTRACT
An analytical solution of the impulsive impact of a cylindrical body with an arbitrary cross-section submerged in an undisturbed water surface is obtained by solving a free boundary problem. The studied case of a rigid body moving in a fluid is kinematically equivalent to the case of a fluid moving around a fixed rigid body with acceleration. The problem is formulated in a non-inertial coordinate system attached to the body. After solving the problem, one can find all the flow characteristics in the coordinate system attached to the undisturbed fluid before the impact. The integral hodograph method is applied to derive the complex potential and the complex velocity, both defined in a parameter plane. The boundary-value problem is reduced to a system of the Fredholm integral equations of the first kind. One of them is in the velocity magnitude at the free surface, and the other is in the velocity direction at the bottom surface. The velocity field, the impulsive pressure on the body surface, and the added mass are computed in a wide range of submergence depths for various cross-sectional shapes of the body, such as a flat plate, a circular cylinder, and a rectangle. The associated added masses are found depending on the submergence depth. As the submergence depth tends to infinity, the added mass tends to the value corresponding to that in an unbounded fluid domain. The upward and downward impacts are shown to generate similar magnitudes of the velocity on the free surface and added mass coefficients but with the opposite velocity directions. The obtained solution may be considered as the first-order approximation when solving the problem by the method of small-time series. The presence of the free surface does not change the structure of the flow near the body, determining the added mass. Therefore, the obtained results are expected to reflect practical situations similar to those occurring in the case of the unbounded fluid domain.
KEY WORDS
pressure impulse, added mass, complex potential, the integral hodograph method