Method for calculating the upper velocity range of dispersed particles in centrifugal accelerators
The introduction provides a justification for the relevance of research. It is noted that devices of the centrifugal type, also called centrifugal accelerators, are widely used in various fields of engineering and technology. However, many issues related to their performance are not sufficiently studied, which is due to the complexity of tribomechanical and aerodynamic dynamic phenomena occurring in the working area. The aim of the work is to develop a mathematical modeling technique and use it to calculate the effect of the combined action of friction forces and aerodynamic drag on the range of changes in the transport speeds of dispersed particles along the accelerator rotor blade. The research methodology included a theoretical analysis of the forces acting on the particle and the accelerations caused by them. The analysis proceeded from the assumption that a particle in the radial direction of the centrifugal force of inertia that causes the acceleration, and directed toward the movement and braking force acceleration friction and aerodynamic drag force is perpendicular to the velocity vector direction of the force of gravity, the Coriolis force, and reactions on the part of the blade and the rotor disc. In this case, the friction force is equal to the product of the coefficient of friction and the clamping force. The laminar, transient, and self-similar modes of particle motion in the air flow are analyzed. It is shown that the self-similar mode is typical for centrifugal accelerators. The upper bound method is used to analyze the speed-limiting case of particle motion along the accelerator blade, when the aerodynamic drag force acting on the parachute effect, together with the friction force, balances the calculated centrifugal force of inertia. Analytical dependences are obtained for calculating the maximum radial and total velocity of the particle in the accelerator, as well as for calculating the angle of departure of the particle from the blade in this mode. On the example of mineral quartz particles, the limit values of the range of particle velocities, as well as the calculated values of the angles of departure of particles from the rotor, are numerically estimated.