Abstract
The efficiency of working processes of machines of the drum type is determined by the mode of flow of the fill in a rotating chamber. But the numerical and experimental results obtained over a recent period approach the actual behavior of the examined medium only in terms of qualitative characteristics. A mathematical model is built for a three-phase flow mode of granular fill in the cross section of a cylindrical chamber that rotates around the horizontal axis. The analytical-experimental research method is applied. A calculation algorithm is derived that approximately establishes position of the flow regions and the distribution of velocities in the cross sections normal to the flow direction, depending on the kinematic, geometrical, inertial, and rheological parameters of the system. Based on the performed modeling, the effect of rotation velocity of the chamber on the characteristics of a three-phase flow mode of the fill was determined. We established conditions when mass fractions of the active sliding layer and the region of a non-free fall reach maximal values, while mass fraction of the passive quasi-solid-body region acquires a minimum value. The conditions are determined when thickness and mean velocity of the sliding layer reach a maximum. We revealed a predominant reduction in thickness, in the average velocity and the shear rate gradient in the normal cross section along the length of the layer. A decrease in the thickness and an increase in the average velocity and the gradient of shear rate of the sliding layer were registered with a decrease in the relative size of the chamber granular fill’s element. Visualization of flow patterns confirmed a convergence of the calculation results and experimental data within a range of 11–13 %
Highlights
Various drum-type machines remain basic equipment for the multi-tonnage processing of granular materials in many industrial sectors
In [27], authors investigated geometrical and velocity characteristics of flow patterns of granular fill of the rotating chamber, a wide range of variations of parameters of the system, which were obtained when applying the Euler’s multiphase model of the discrete elements method (DEM) method and by running a visual analysis of data acquired from high-speed video recording
The aim of present work is to construct a mathematical model for the pattern of a steady flow of granular fill in the cross section of a cylindrical chamber that permanently rotates around a horizontal axis
Summary
Various drum-type machines remain basic equipment for the multi-tonnage processing of granular materials in many industrial sectors. This is predetermined by a number of ope rational and economic advantages of such equipment. The joint action of the gravitational and distorted centrifugal force fields results in the increased complexity of the flow of granular fill of a rotating chamber, which considerably complicates modeling of characteristics. The lack of a gene rally accepted technique for predicting the behavior of filling substantially limits effectiveness of the implementation of technological processes when using such equipment. Performing the working processes of machines of the drum type is predetermined by the character of the flow mode of granular fill in the cross section of a rotating chamber. That is why establishing the regularities of change in the geometric and kinematic pattern of such a flow appears to be a rather relevant task
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