Mathematical Description of the Process of Impact Interaction of a Flow of Catalyst Particles with a Breaking Element in a Cyclone Device with a Coaxial Arrangement of Purification Stages

Processes for cleaning solid particles from gases are used in many modern enterprises. Among the main requirements for gas-cleaning equipment are high purification degree, small overall dimensions, low hydraulic resistance, and ease of maintenance. All these requirements are met by a cyclone apparatus with a coaxial arrangement of cleaning stages, developed at Yaroslavl State Technical University. In this apparatus, three stages of purification of the dust and gas flow are arranged sequentially. At the first and third stages, the separation of solid particles from the gas flow occurs due to centrifugal force, and at the second stage, inertial settling of particles is effectuated. In addition, the first stage of the apparatus is equipped with a baffle element, which not only increases the efficiency of solid-phase separation, but also makes it possible to destroy the formed agglomerates due to the organization of impact interaction. The processes of centrifugal and inertial separation, implemented at the second and third stages of the apparatus, are currently studied almost completely, whereas the impact interaction of the particle flow with the baffle element remains poorly understood. In this paper, on the basis of a probabilistic approach, expressions are obtained for the differential distribution function of the number of particles of the solid phase captured by the centrifugal-impact stage of the cyclone apparatus with a coaxial arrangement of purification stages. Experimental studies have confirmed the adequacy of the formulated expressions for the average particle size. Thus, the obtained expressions for the differential distribution function of the number of particles make it possible to estimate the composition of the solid phase separated at the first stage and carried away with the gas flow to the second and third, which is necessary when drawing up an engineering method for calculating the apparatus.