Estimate of solids rate in air-impeded silo discharge with a novel calculation procedure

During the discharge of fine powders from a hopper, an experimentally observed negative pressure gradient often emerges close to the outlet. This reduction in pressure counteracts the natural gravitational motion of particles, resulting in a discharge flow rate lower than the expected value. In this study, this phenomenon is addressed by defining a systematic sequence of steps and equations to estimate the solids discharge rate more accurately in air-impeded silos. Specifically, the analysis focuses on cylindrical bins followed by conical hoppers; the effect of hopper diameter on the discharge rate of different materials was evaluated. The experimental results and procedure outputs were compared to verify algorithm reliability. The procedure involves the following key steps: first, material properties such as bulk density, effective internal friction angle, etc., were collected and expressed as functions of stress state; next, the unit was discretized to trace stress and pressure profiles along its length. Using well-known equations by Janssen and Walters, stress distribution within the unit is predicted, and a recent equation proposed in the literature to estimate the pressure gradient is applied. Material properties are updated incrementally to refine stress and pressure profiles. Finally, starting from the Brown and Richards equation for discharge rate estimation, the pressure gradient is accounted for by introducing a reduction in gravitational acceleration. As proposed in the existing literature, the discharge rate can be linked to the region where the pressure gradient reaches a zero value. By combining information regarding the material stress state near the outlet with the observed pressure gradient trend, we achieved a more accurate estimation of the discharge flow rate than conventional methods. This approach underscores the significance of developing a predictive model for pressure profile trends and assessing the efficacy of the proposed approach.