Solving the Nonstationary Problem of the Disperse Phase Concentration during the Pneumoclassification Process of Mechanical Mixtures - Pavlenko I. V.; Yukhymenko M. P.; Lytvynenko A. V.; Bocko J. (Журнал інженерних наук)
The article dials with studying of the gas-dispersed systems classification process in gravitation pneumoclassifiers of prismatic shape. The aim of the research is to determine operating parameters of the investigated process. Recent research is based on the previously developed mathematical model of hydrodynamics for a gas-dispersed flow in a vertical channel with variable cross-section. As a development of this study, a physical model based on the process of kinetic removal from the mixture was used. This process is caused by the removal of fine particles from the weighed layer in the case of theirs low velocities in comparison with the average gas flow velocity. This model also considers the inertial effect due to the kinetic energy of fine particles removed from the surface of the weighted later. The first order linear nonhomogeneous partial differential equation describing the unsteady process of changing the dispersed phase concentration in the gas-mechanical mixture by channel height was solved by mathematical modeling using the combination of direct and inverse Laplace transforms. As a result, for the first time the general solution was obtained for for non-trivial boundary and initial conditions. This fact allowed developing the mathematical model of the nonstationary problem for the disperse phase concentration during the pneumoclassification process of mechanical mixtures in pneumoclassifiers. The model allows determining the concentration of fine fraction of the gas-dispersed mixture by channel height in operating volume of the device, as well as evaluating time of the pneumoclassification process. Particularly, it was found that the dispersed phase concentration decreases by the height of the apparatus with respect to time. This fact proves the possibility of effective separation of components in gas-mechanical mixtures. Finally, the achieved results allow proposing the engineering technique for calculations of vertial-type gravitation pneumoclassifiers.