Shape optimization of conical hoppers to increase mass discharging rate

Abstract

Mass discharging rate (MDR) is a critical aspect of hopper’s performance in bulk solids handling. A shape optimization method is established in this study to increase the MDR of cohesionless granular materials from hoppers. This method is based on a continuum model of granular matter and the Eulerian Finite Element Method (FEM) which can efficiently simulate the discharging process and predict the MDR. In this work with the focus on conical hoppers, the widths of silo and hopper outlet as well as the vertical height of hopper are fixed. The meridian of the hopper, however, evolves from a straight line to some optimal curve, guided by a combined genetic algorithm (GA) and gradient descent method (GDM). Cubic spline function is employed to parametrize the hopper shape. The effectiveness of the shape optimization is examined by comparing the MDRs of the optimal hopper and conventional conical hopper, obtained by both FEM and discrete element method (DEM) respectively. It is shown that this shape optimization method can automatically search the optimal shape of the hopper in a given range of constraints, and increase the MDR substantially. In a typical hopper with an initial half angle of 45°, the MDR is increased by over 130% after the shape optimization. Notably, the optimal shape depends mainly on the geometrical factors, i.e. the allowed width and height for the hopper, whilst insensitive to the material properties, which favors its general use for different particles. Such curved hoppers are particularly useful for increasing the discharge rate of hoppers ranging from 30° to 50°, which, facilitated with advanced manufacturing technology, will find wide potential applications in bulk solids handling.