Influence of insert position in the hopper on powder stream mass flow rate and morphology

Hoppers are essential for the storage and transport of granular materials in industries such as chemicals, pharmaceuticals, mining, and food processing. Precise control of both mass flow rate and stream morphology is critical in their design. This study demonstrates that strategically placing inserts at various positions within the hopper enables regulation of the granular mass flow rate and powder stream characteristics. Experimental results indicate that mass flow rate variation with insert position occurs in two distinct regimes: an annular gap restriction regime and an outlet restriction regime, where flow is primarily governed by gap dimensions and exit pressure, respectively. Theoretical models were developed to predict mass flow rates in both regimes with high accuracy, showing strong quantitative agreement with experimental data and allowing precise flow regulation through insert position adjustments. Furthermore, high-speed imaging reveals a regime evolution in powder stream morphology, where the beam width transitions from being dominated by peripheral particle contributions to being controlled by overall mass flow rate as the insert is raised. Complementary high-resolution imaging and discrete element modeling further elucidate the formation mechanism of the highly convergent powder stream, demonstrating that a reduction in transverse particle velocity following collisions is the key factor driving high convergence. These findings establish a novel theoretical framework for optimizing hopper flow design and improving the controllability of granular material transport.