A design method of hopper shape optimization with improved mass flow pattern and reduced particle segregation

A shape optimization method is presented in this paper to re-design hopper shapes for improving the flow patterns in silos. This method combines a continuum model of granular matter based on the Eulerian Finite Element Method, the optimization algorithms of genetic algorithm and the gradient descent method. Starting from a classic conical shape, the optimization method searches for the optimal shape of the hopper under given geometrical constraints. An optimized curve design can increase the mass flow zone in the hopper by more than 90%. The sensitivity of this method suggests that the shape optimization is of particular significance for initially funnel flow hoppers and granular materials with high internal friction. The optimized design was further characterized by using the Discrete Element Method. The DEM results demonstrate that the optimized hopper can also dramatically reduce particle segregation by around 70% during hopper discharge.