Tthe mass movement of fine particles and changes in their trajectories under the effect of centrifugal, gravitational, and aerodynamic forces is studied by numerical modeling of turbulent swirling flow. The effect of turbulent migration of solid particles due to pulsating gas flow velocities on the aerodynamics of particles and, consequently, on the efficiency of the process of separation of particles by size is analyzed. The studies revealed the behavior laws of probability curve of separation of particles by size and showed the effect of regime and geometric parameters on the process of classification of fine powders.There are various methods of separating finely dispersed media, the most promising of which are centrifugal pneumatic methods, allowing a significant improvement in production intensity and a reduction of energy consumption and making the process of producing powder products more environmentally friendly.Centrifugal air separation of particles is a very complex process that depends on a number of physical, structural, and operational characteristics. In general, the motion of an ensemble of polydisperse particles is determined by the force interaction of the particles with gas flow, the exchange of momentum in collisions of particles with each other, the effect of the geometry and walls of the device, the effect of pulsations of the carrier medium due to turbulence, and other physicomechanical phenomena. It is known that such motion of two-phase flow is both deterministic and random in nature.The most important parameter affecting the process of centrifugal separation of particles by size is the volume concentration of the solid phase in the gas flow. Experimental and theoretical studies have shown that high efficiency of size separation of particles can be achieved only at small volume concentrations of the solid phase. This allows one to simplify the mathematical formulation of the problem under study. Indeed, the interaction of solid particles and the force effect of the particles on the carrier flow can be neglected at small concentrations of the solid phase [1]. At the same time, fine particles are involved in the pulsating motion of the gas phase in turbulent swirling flow. This phenomenon of turbulent migration of particles violates the deterministic nature of their motion and causes a stochastic distribution of particles in the vortex chamber, thereby reducing the efficiency of their separation by size [2]. Therefore, these effects should be taken into account when constructing a mathematical model for the centrifugal separation of fine solid particles.
PHYSICAL FORMULATION OF THE PROBLEMThe process of separation of particles by size can be described by Tromp's separation curve, which characterizes the probability of particles falling into the fine or coarse fractions. The critical particle size δ * , which controls