Quantitative measurements of flow dynamics in 3D hoppers using MRI

This work uses a recently developed MRI method to measure the solid fraction and velocity in three-dimensional (3D) hoppers quantitatively. We demonstrate that the measurements are quantitative by calculating the mass flow rate within the hopper using MRI and show good agreement with the mass flow rate measured gravimetrically. We study the velocity and solid fraction in hoppers with various angles and outlet sizes. We show that the solid fraction decreases smoothly from the bulk value above the outlet, indicating that the assumption of a “free-fall arch” used in some mass flow correlations is invalid. Furthermore, we show that the solid fraction, velocity and vertical evolution of the acceleration are all self-similar when normalised by the value at the centre of the outlet in a 3D hopper, in agreement with recent studies of 2D hoppers. Thus, these quantitative measurements enable evaluation of phenomenological models describing the flow rate from hoppers. [Display omitted] •We present quantitative measurements of solid fraction and velocity in 3D hoppers.•The velocity and solid fraction profiles scale with outlet size.•There is no “empty annulus” at the outlet of a hopper.•Acceleration increases towards the outlet and there is no “free fall arch”.