MATHEMATICAL DESCRIPTION OF THE DYNAMICS OF CENTRIFUGAL TWO-PHASE FLOW IN THE GRINDING CHAMBER OF A DISINTEGRATOR

Abstract

Rational control of equipment operating modes in the production of building materials is possible only in the case of a mathematical description of various technological processes. The sequence of calculation methods for determining the design and technological parameters of grinding equipment makes it possible to numerically present the results of calculations of rational operating modes of the equipment. The study presents a mathematical description of the dynamics of a two-phase flow inside the grinding chamber of a disintegrator, with the help of which it is possible to determine the speed characteristics of its operating modes for materials with different physical and mechanical properties. The nature of the change in the tangential components of the velocities of the two-phase flow has been established: the range of the current radius of the grinding chamber Ri has been determined, at which the radial components of the velocities of the carrier flow and particles of the ground material continue to increase. As a result of mathematical modeling, it was confirmed that with an increase in the concentration of dust particles in the increasing volume of the grinding chamber, the value of the tangential component of the velocity of a dynamic two-phase flow decreases in relation to the maximum parameters at Ri = 0.15 m by an average of 15.5%. It has been determined that the maximum velocity values for the tangential component are in the limit of Ri = 0.1-0.15 m and are 131 m/s for air, and 127.5 m/s for an average suspended particle with dsr = 40 μm. In the process of developing a mathematical description, it was established that in the range Ri = 0.15 - 0.3 m the increase in the radial components of the velocities of the air carrier medium and the weighted average particle flow is about 14.5%, which, in turn, indicates an increase in the kinetic energy of the crushed particles during the movement of a dynamic two-phase flow from the center to the periphery of the grinding chamber of the disintegrator.