FINDING THE TRAJECTORYOF MOVEMENT OF A MATERIAL PARTICLE ON THE INNER SURFACE OF A VERTICAL CYLINDER AT THE SIDE SUPPLY OF MATERIAL

Abstract

The movement of material particles on the inner surface of the cylinder takes place in cyclones. Due to the complexity of the aerodynamics of the process, theoretical developments can not be used as a basis for calculating the design and efficiency of their operation. Because of this, a number of simplifications are allowed in the theoretical provisions, as a result of which the calculated data do not coincide with the experimental data. The use of modern software products, which have great graphics capabilities, allows you to get new results in solving such problems in the form of high-quality graphic illustrations. The aim of the study is to determine the motion of a material particle that enters the inner surface of a vertical cylinder with a given initial velocity. A number of simplifications were introduced in the calculations: air resistance, the effect of particles on each other, their size, etc. were not taken into account. Accompanying Frenet and Darboux triangles were used to find the trajectory. Differential equations of motion of a material particle on the inner surface of a vertical cylinder are compiled. The equations are solved using the MatLab system. It is established that the velocity of particles that fall on the inner surface of the cylinder decreases to a certain value, and then begins to increase. For specific conditions (coefficient of friction and radius of the cylinder), the value of the minimum speed to which the movement of particles is slowed down is approximately the same and does not depend on the value of the initial speed. This means that there is a minimum value of the initial velocity at which the particle will not slow down when it hits the surface of the cylinder. Since particles with different coefficients of friction at the initial stage of their movement on the cylinder are poorly scattered on its surface, for the effective operation of the cyclone you need to make an inlet window of sufficient size in the vertical direction.