Solving the Nonstationary Problem of the Disperse Phase Concentration during the Pneumoclassification Process of Mechanical Mixtures

Author(s): Pavlenko I. V.1, Yukhymenko M. P.1*, Lytvynenko A. V.1, Bocko J.2

1 Sumy State University, 2 Rymskogo-Korsakova St., 40007 Sumy, Ukraine;
2 Technical University of Kosice, 1/9 Letna St., 040 01 Kosice, Slovak Republic

*Corresponding Author’s Address: [email protected]

Issue: Volume 6; Issue 1 (2019)

Paper received: July 10, 2018
The final version of the paper received: December 18, 2018
Paper accepted online: December 23, 2018

Pavlenko, I. V., Yukhymenko, M. P., Lytvynenko, A. V., Bocko, J. (2019). Solving the nonstationary problem of the disperse phase concentration during the pneumoclassification process of mechanical mixtures. Journal of Engineering Sciences, Vol. 6(1), pp. F1-F5, doi: 10.21272/jes.2019.6(1).f1

DOI: 10.21272/jes.2019.6(1).f1

Research Area: CHEMICAL ENGINEERING: Processes in Machines and Devices

Abstract. 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.

Keywords: pneumoclassifier, weighted layer, fine particles, agglomeration, mathematical modeling, Laplace transform, Heaviside step function.


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