Modeling of hydrodynamics, heat transfer, and averaging of granular media in a pneumatic circulation apparatus

The mathematical modeling of hydrodynamics, heat transfer, and averaging of a highly concentrated granular medium in the working area of a vertical pneumatic circulation apparatus is performed. The hydrodynamics of a dense layer of the granular medium is described by a non-Newtonian model with partial slip conditions on solid walls. Such a representation of the granular medium dynamics allows one to approve theoretical calculations with available experimental data for a steady flow in a flat channel. The numerical applicability of the partial slip condition for a non-Newtonian fluid is confirmed by the analytical dependences obtained by the authors for a steady flow in a circular tube and a flat channel, which are transformed into the known analytical formulas under no-slip conditions for a non-Newtonian medium. On the basis of the proposed model, the heat exchange intensity is analyzed when setting the constant heat flux density or the constant temperature on the annular shelves in the apparatus. The intensity of the granular mixture averaging in the bunker with the introduction of additional annular shelves is studied, and the efficiency of granular mixture mixing during rotation is considered. A method for analyzing the mixing of a granular medium in dynamics in each local area of the apparatus is proposed, which is based on the determination of the inhomogeneity coefficient. The results of this study can be used when developing powder technology devices for drying, mixing, dosing, and transport.