УДАРНОЕ ВЗАИМОДЕЙСТВИЕ ТЕЛА В ВИДЕ КРУГОВОГО СЕГМЕНТА С ЖИДКОСТЬЮ С ОБРАЗОВАНИЕМ ЗОНЫ ОТРЫВА

Abstract

The problem of impact of a smooth curvilinear body previously immersed in a fluid occupying an unlimited half-space in a flat formulation is considered. The fluid is considered incompressible, and the body part immersed in the fluid has the shape of a circular segment. It is assumed that at some point in time, an off-center impact occurs, as a result of which the body instantly receives the horizontal U and vertical V velocity of motion, as well as the angular velocity of rotation ω around the axis perpendicular to the plane in which the flow is considered. It is also assumed that with a certain combination of kinematic and geometric parameters of the immersed body part in the form of a segment, the liquid can instantly tear itself away from the body surface and form an additional area of the free surface. The complexity of the problem lies in the fact that the position of the separation zone (the coordinate of its extreme point) is not known in advance; it depends on a combination of kinematic and geometric parameters. The appearance of the separation zone significantly complicates the initial hydrodynamic problem, since the fluid velocity field depends on the position of the separation zone, and the geometric parameters of this zone, in turn, on a combination of kinematic parameters. In the work, to determine the position of the separation zone (its extreme point), the so-called Ogaso principle was used, which expresses the variational principle, which consists in the fact that the separated flow of liquid realized in reality provides an extreme value of the potential among other possible solutions to the mixed shock hydromechanics problem. This principle allows you to filter out all those possible mathematical solutions that allow the presence of negative impulses on the surface of the contact of the body with the liquid, which contradicts the physical nature of the hydrodynamic phenomena. The general solution to the problem of determining the field of velocities and momenta in a fluid at the instant immediately following the impact, with a pre-arbitrary parameter characterizing the separation, was obtained by conformally mapping the region occupied by the fluid (half-plane with a cut segment) onto the auxiliary half-plane, and also by reducing the original problem to the Keldysh-Sedov problem for this half-plane. It is very significant that the application of the Ogaso principle leads to a transcendental equation for determining the parameter q, which determines the position of the extreme point of the separation zone, containing singular integrals, which should be understood in the sense of the Adamard finite part. A numerical procedure based on the Adamard-Mangler method made it possible to determine the value of the parameter q as a function of kinematic parameters and the geometric parameter α characterizing the indicated segment. After the parameter q is determined, which determines the position of the separation zone, the determination of the potential is reduced to calculating some integral understood in the sense of Cauchy. The paper presents the results of calculating the impulsive pressure over the segment surface, taking into account the existence of a flow separation section.