Mathematical Model of Low-Concentration Disperse Suspension Fractionation in a Plane Vertical Hydroclassifier
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Mathematical Model of Low-Concentration Disperse Suspension Fractionation in a Plane Vertical Hydroclassifier A. V. Ryazhskikh Voronezh State Technical University, Voronezh, 394026 Russia e-mail: [email protected] Received January 9, 2020; revised February 18, 2020; accepted February 19, 2020
Abstract—A continuum mathematical model of low-concentration suspension transfer without mixing in a plane vertical gravitational classifier under conditions of phase flux balance is suggested. The flow of a carrier medium is assumed to be laminar, and no limitations on the particle sedimentation rate are imposed. Analytical relationships to calculate the local counting functions of the particle size distribution density have been derived. A computational experiment has confirmed the fractionation of a monodisperse suspension and the presence of fine particles in the “heavy” fractions of polydisperse suspensions. The latter fact is explained by a low velocity of the disperse medium at the “wetted” surfaces of the hydroclassifier. The results are in agreement with available experimental data and data calculated in terms of classical kinetic models. DOI: 10.1134/S1063784220080150
INTRODUCTION Phase separation in heterogeneous medium flows through vertical vessels is widely used in chemical technology and food manufacturing, the biochemical and oil-and-gas industries, metallurgy, and ecology [1, 2]. The key parameter influencing the productivity of equipment is the relative classification rate (classification rate of one phase relative to another) [3]. The difference in classification rates results in fractionation of suspension particles. Gravitational fractionation of suspensions is based on the sedimentation process, which exploits the gravity force and density difference of phases [4]. Sedimentation is implemented using various hydroclassifiers [5], the efficiency of which depends on the physicochemical properties of suspensions, geometry of equipment, and phase flux intensity. Simulation of transfer phenomena in hydroclassifiers usually uses two, Eulerian–Eulerian and Lagrangian–Eulerian, approaches. The former (which is most frequently used) is based on the continuum hypothesis: the motion of each phase is described by equations of continuity and motion [6, 7], the identification of interfacial interaction being considered a not fully solved problem. In the latter approach, the discrete model of disperse phase is used, which keeps track of the behavior of each particle, and the continuum hypothesis formalizes the hydrodynamics of disperse medium [8]. This approach can be applied if the concentration of a disperse phase is low, since the computation time grows in proportion to the amount of par-
ticles. In recent years, an approach based on statistical methods has begun to be used [9]. The above strategies require much effort for conducting multivariate computational experiments. Therefore, at the stage of designing hydroclassifiers, it is necessary to have alternative analytical tools to justify the range of
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