Mathematical Model of Vortex Motion of Two-Phase Flow in a Disintegrator Mill

Abstract

Mathematical models and the results of their numerical calculations play an important role at the modern level of automation of technological processes. The development of mathematical models to determine the design-technological or energy-power parameters of the operation of grinding equipment allows to obtain numerical information about the rational modes of its operation. In this study, numerical results were obtained from calculating a mathematical model of the vortex motion of a two-phase flow for the second stage of grinding depending on the physical and mechanical characteristics of the material being ground (ρp) and the current radius Rk of the grinding chamber of the unit. A method for numerically determining the speed characteristics of unit operating modes for materials with different physical and mechanical properties is presented. In the work, using the analysis of graphs of the sought functions of the mathematical model of the vortex motion of a two-phase flow, the velocity fields are presented in the form of diagrams of the radial, circumferential (tangential) and axial velocity components, which characterize the intensity of the flow dynamics inside the original design of the grinding chamber of the mill. In the process of mathematical modeling, it was established that the radial and circumferential (tangential) components of the two-phase flow velocities at current radii in the range Rk = 0.1–0.2 m reach their maximum values, both for solid particles of the crushed material and for the carrier phase – air. It has been determined that for the circumferential component of the velocity of a two-phase flow in a vortex at Rk = 0.3 m, its maximum is observed for both solid particles and the carrier phase – up = uo = 112.1 m/s.