ПАРАМЕТРЫ, ОПРЕДЕЛЯЮЩИЕ ОТСУТСТВИЕ ДИССИПАТИВНЫХ ПОТЕРЬ ВО ВРАЩАЮЩЕМСЯ КОЛЬЦЕ ЖИДКОСТИ

Abstract

The article covers the problem of studying thermal processes in rotating by inertia in the absence of gravity capillary viscous fluid ring with free boundaries that are acted by pressure of gas medium. Thus there is no heat exchange with the environment at the boundaries of the ring. System under consideration depending on the initial angular velocity, initial radial perturbation and geometry is able to be in different move modes such as infinite expansion, collapse, periodic oscillations. In a series of numerical experiments where only one parameter that determine the character of motion changed and the rest remaining unchanged the effect of minimization dissipative losses was detected at certain critical values of the parameters (viscosity, size, pressure in the cavity). That is, a new mode of ring motion was detected; mode in which regardless of the initial radial perturbations it has minimum dissipative losses. That means that the distribution of the tangential component of the velocity vector is close to a linear function of ring radius. Such kind of dependence inherent to a rigid body motion. That distribution causes liquid layers do not move relative to each other and therefore there are no friction effects, no heat losses of the ring and no loses of initial rotational energy. Analysis of the mathematical model of the motion of liquid ring yielded analytical formulas for calculating the critical values of dynamic viscosity, surface tension, the difference of the gas pressures in the cavities of the ring, the ring sizes. Critical parameters, calculated according to the formulas and found in the course of the numerical experiment coincide with good accuracy. Received 11.12.20 16; accepted 0 2.02.20 1 7