Enhancing silo discharge and energy efficiency with vibrated insert

• Novel use of vibrated inserts boosts silo discharge rates. • Discharge rate shows a non-monotonic dependence on vibration intensity. • Critical transition points for optimal discharge and energy efficiency are identified. • An effective Froude number unifies the description of vibrated flow behavior. • New mechanisms driving enhanced discharge and energy efficiency are revealed. The scenarios of particle flow through small orifices are ubiquitous in manufacturing, agriculture, and natural processes. Remarkably, the flow rate can be enhanced by inserting an obstacle above the orifice. In this study, the discrete element method (DEM) is employed to investigate a novel paradigm for modulating particle flow—namely, by applying vibration to the inserted obstacle. Our results demonstrate significant increases in flow rate under vibratory excitation, driven primarily by the interplay between vibration frequency and particle descent dynamics. Granular temperature analysis reveals a localized concentration of kinetic energy near the insert, thereby requiring less energy input compared to conventional wall vibration methods. The effects of insert shape, size, position, as well as vibration amplitude and frequency, are systematically examined. Furthermore, an effective Froude number ( Fr *) is introduced to unify the diverse vibrated flow conditions, enabling accurate prediction of discharge rates and identification of critical transitions in energy efficiency. This paradigm offers a practical, energy-efficient solution for optimizing granular flows with wide-reaching implications for bulk solids handling industries.