Gravity Flow of Granular Materials in Conical Hoppers
نویسنده
چکیده
This paper presents an approximate solution to the flow of a cohesionless granular material in a conical hopper. This is a problem which has received considerable attention in the past though much of the work was directed toward developing an empirical relation of the mass flow rate from experimental data (for example (1,211. In the early 1960's Jenike and Johanson [23] applied the basic principles of plasticity to study the behavior of bulk solids; the material was treated as a perfectly plastic solid which yields according to the Mohr-Coulomb condition. Jenike [3] solved the equilibrium equations in a hopper with a "radial stress field;" that is to say the mean stress in the material was assumed to vary linearly with the radial distance from the apex of the hopper. However, no unique velocity field can he derived from such a quasi-static analysis; the addition of inertia is necessary in order to obtain a unique velocity field. Unfortunately, the resulting nonlinear equations of motion are considerably more difficult to solve. Brown [4] studied the problem using an energy approach. He assumed that the material would flow when the total kinetic and potential energies are at a minimum. From this, he derived an expression for the mass flow rate. Savage [5] used a perturbation scheme based on the wall friction angle to solve the problem of flow in a hopper. Up to the order presented, the velocity and stress field are weak functions of the angular position 8 (see Fig. 1). Brennen and Pearce [6] solved the problem for a two-dimensional hopper. They used a perturbation scheme based on the angular position 0, introduced modified
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تاریخ انتشار 2004