The dominant underlying parameters controlling the dispersion of falling particle curtains

Abstract

A new analytical model of a free-falling curtain of heavier-than-fluid particles from a wedge-shaped hopper in a quiescent medium is presented and used to determine the key underlying–non-dimensional parameters that control its dispersion. The model calculates the particle velocity and the volumetric flow rate of the induced air into the particle stream, using an Eulerian approach based on the momentum transfer between the two phases. It employs a new drag model to account for the sphericity of the particles over a wide range of Reynolds numbers to achieve a root mean square error of less than 10% in the predicted drag coefficient relative to available data over a wide range of sphericities (ψ = 0.023 − 1), even including granular particles. The solid-phase is modelled as a stream of particles, with the dynamics of the stream approximated by a stream coefficient determined from the published experimental data. The effects of particle size, mass flow rate, sphericity, and particle density on the particle velocity, entrained air, curtain thickness, and solid fraction are incorporated into the model. The model is used to provide new method of characterising the evolution of falling particle curtains onto a single regime map, which collapses all previous data. The velocity in near-field is controlled by the flow in the hopper. It then transitions to a similarity regime in which the mean velocity of particle stream normalised by the terminal velocity of single particle scales with the axial distance from the nozzle exit normalised by the product of the particle diameter and Froude number. Further downstream again the particles asymptote toward the settling velocity of the individual particles, which is greater when particles are decelerated from above than when accelerated from below. Other insights, such as the role of non-sphericity, are also reported.