INVESTIGATION OF PARTICLE MOVEMENT IN A CENTRIFUGAL APPARATUS WITH VERTICAL BLADES BY MEANS OF A MOVING COORDINATE SYSTEM

Abstract

Centrifugal devices for separating various environments are widely used in the chemical, pharmaceutical, food industries. Centrifugal devices can have working bodies of different designs. The shape of the working bodies of the devices and their design parameters affect the kinematic characteristics of the movement of the material. Thus, the study of the laws of motion of a material particle along the working bodies of different shapes and design parameters makes it possible to improve the design of the apparatus.

Working bodies of such devices can have different designs. The paper investigates the parameters of particle movement in a centrifugal scattering device, which consists of a conical disk with a cut bottom and vertically installed rectilinear blades, by means of a movable coordinate system that rotates with the disk with a given angular velocity around the vertical axis.

Since the vertex of a moving coordinate system describes a circle, such a system can be taken as the accompanying Frenet trihedron, widely known in differential geometry. This allows us to find the components of the absolute acceleration of the particle in the projections on the orts of the trihedron.

In addition, the forces applied to the particle have a constant direction in the system of the trihedron, which does not depend on its rotation. All this makes it possible to simplify the compilation of differential equations in the projections on the orts of the triangle. The system of differential equations of particle movement is compiled and solved by numerical methods in the article. The kinematic characteristics and regularities of the relative movement of a particle on a conical surface are found. Analytical description of the movement of a particle makes it possible to investigate its acceleration and find the relative and absolute velocity at the time of descent of the particle from the disk. With the obtained analytical dependencies, it is possible to determine the influence of technological and constructive parameters of the scattering apparatus on the process of particle acceleration.

Keywords: differential equations, Frenet trihedron, angular velocity, radius vector, acceleration.