Abstract
The study of motion and mixing of a highly concentrated loose granular medium in a vertical mixing hopper in the inertial motion mode within the framework of the of fast granular flows are shown. This paper presents the study of motion and mixing of a highly concentrated loose granular medium in a vertical mixing hopper in the inertial motion mode (1) within the framework of the of fast granular flows. To describe the flow, a differential model based on continuum mechanics concepts and rheological properties of granular materials with an additional equation of chaotic energy transfer caused by pulsation of the granules (2) is used. Simulation of the mixing process is based on the transport equation of concentration of the primary and key components of the granular mixture. Energy of the stochastic motion of granules in the inertial flow regime is modeled by analogy with the theory of turbulence (3). Energy dissipation of the stochastic motion of the granular medium and determination of the viscosity of the model in the equations of momentum and energy transport are written by means of the Kolmogorov-Prandtl formula. Granular motion in the pulsating mode is limited due to the high concentration of the granular medium that allows, in the first approximation, to consider the length scale of the chaotic pulsation of the granules as a constant value. This paper focuses on the steady gravity flow of a highly concentrated granular medium in a vertical silo with horizontal plates inside for intensive mixing of the primary and key components of the mixture. A scheme of such a bunker is shown in Fig. 1. At the entrance to the channel an unmixed homogeneous (by its physical properties) granular medium is fed at a constant speed from the top. The process of averaging is due to convection and diffusion phenomena caused by the chaotic pulsation of the granules in the inertial flow mode when moving through the bunker. To describe the hydrodynamics and the averaging process of a highly concentrated granular medium in the inertial flow regime, a set of equations consisting of those of momentum transport, the continuity equation, the equation of stochastic energy of pulsating granular motion and the transport equation of
Highlights
This paper presents the study of motion and mixing of a highly concentrated loose granular medium in a vertical mixing hopper in the inertial motion mode [1] within the framework of the “theory of fast granular flows”
Simulation of the mixing process is based on the transport equation of concentration of the primary and key components of the granular mixture
This paper focuses on the steady gravity flow of a highly concentrated granular medium in a vertical silo with horizontal plates inside for intensive mixing of the primary and key components of the mixture
Summary
This paper presents the study of motion and mixing of a highly concentrated loose granular medium in a vertical mixing hopper in the inertial motion mode [1] within the framework of the “theory of fast granular flows”. A differential model based on continuum mechanics concepts and rheological properties of granular materials with an additional equation of chaotic energy transfer caused by pulsation of the granules [2] is used.
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