Özet:

The simplicity of design solutions of the drum type machines is paradoxically combined with the extremely difficult-to-describe behavior of the treated medium. The workflow efficiency of such equipment is determined by the dynamic activity of the shear part of the fill. The traditional hypothesis of the two-phase flow regime of the granular fill of the rotating chamber ignores the shear layer formation. However, recent numerical and experimental results approach the flow regimes of the studied medium only in terms of qualitative characteristics. The analytical model of the behavior of the shear layer of the granular fill near the free surface in the cross-section of the cylindrical chamber rotating around a horizontal axis is constructed. The equations for the mean value and the velocity distribution along the normal to the flow direction of the layer are obtained. They allow determining the shear velocity profile of the layer approximately, depending on the kinematic, geometric and rheological parameters of the system. Granular fill is considered as a continuous medium with the volume-averaged parameters. A plastic rheological model is adopted. Based on the performed simulation, the fields of stresses and velocities in the fill mass in the cross-section of the rotating chamber are formalized using the system of differential equations of the two-dimensional state of the flowing granular medium. It is shown that such gravitational flow arises from the conditional, additional to gravitational, vertical inertial acceleration, which is due to the previous growth of kinetic energy of the layer in the non-free-fall zone of the fill. It is found that the flow of the shear layer near the free fill surface is realized in the form of gravitational flow without slipping along the supporting boundary surface of the quasi-solid-state zone that is shifted up. It is found that the values of the average and maximum velocity of the shear layer of the fill depend on the chamber radius, the radial coordinate of the basis of the considered section of the layer, its thickness, filling degree and chamber rotation velocity, friction angle of the fill and angle of inclination of the layer to the horizontal. Author Biographies Yuriy Naumenko, National University of Water and Environmental Engineering Soborna str., 11, Rivne, Ukraine, 33028 Doctor of Technical Sciences, Associate Professor Department of construction, road, reclamation, agricultural machines and equipment

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