Analysis of granule layer impact interaction on vibrating 2D prism

Abstract

The impact of granules which are of various form, size and densities against a vibrating prism is analyzed. The analysis is performed in a two-dimensional plane (2D), assuming that the prism perpendicular to the plane is symmetric with the given constant height. In the description of the interactions, classical mechanics are used to describe the impact of granules or granule flow against a moving obstacle (vibrating prism). The air viscosity is not taken into account and thereby the present work offers simplified analytical solutions for engineer calculations through a straight forward mathematical model. In the interaction of granules with the obstacle, the impulse restitution coefficient is applied in the normal direction. The no-slip rule or the dry friction coefficient for slip, respectively, is applied to the interaction in the tangential direction. The analysis uses the superposition principle for individual airflow and for each granule fraction. As a result, for a continuous environment, it is possible to divide the interaction by the center of mass of several layers in the region of motion. The results obtained show the distribution of fractional flows, taking into account that there is a suction zone just behind the prism. Despite the complicated interactions of the components of the environmental fractions, the developed analytical method allows analytical prediction and calculation of the separation motions. The equipment for the experiments is 3D printed, and the experiments were performed to measure the flow speed of the medium using a bottom open cone container.