On the dynamics of stratified particle-laden plumes

Abstract

An experimental study on stratified particle-laden plumes is presented and five steady-state flow regimes have been identified. The steady-state behaviour of the plume is directly related to the magnitude of the convective velocity associated with particle-induced instabilities, Uc, in relation to the terminal settling velocity of each individual particle, ust. When ust > Uc, the ratio of particle to fluid buoyancy flux at the source, P, becomes important. For P < 0.2, the plume dynamics appears very similar to a single-phase plume as particle recycling has minimal impact on the steady-state plume height. When P > 0.2, the plume height decreases significantly, creating an anvil-shaped intrusion similar to those associated with explosive volcanic eruptions. Importantly, the measured steady-state heights of plumes within this settling regime validate the collapse model of Apsley & Lane-Serff (J. Fluid Mech., vol. 865, 2019, pp. 904.927). When ust ≤ Uc, particle re-entrainment behaviour changes significantly and the plume dynamics becomes independent of P. When ust ≈ Uc, a trough of fluid becomes present in the sedimenting veil due to a significant flux of descending particles at the edge of the plume. Once ust < Uc, the particles spreading in the intrusion become confined to a defined radius around the plume due to the significant ambient convection occurring beneath the current. For ust ≪ Uc, or in the case of these experiments, when Uc ≫ 1 cm s-1, ambient convection becomes so strong that intrusion fluid is pulled down to the plume source, creating a flow reminiscent of a stratified fountain with secondary intrusions developing between the original current and the tank floor. Through an extension of the work of Cardoso & Zarrebini (Chem. Engng Sci., vol. 56, issue 11, 2001a, pp. 3365-3375), an analytical expression is developed to determine the onset of convection in the environment beyond the edge of the plume, which for a known particle settling velocity, can be used to characterise a plume's expected settling regime. In all plume regimes, the intrusion fluid is observed to rise in the environment following the sedimentation of particles and a simple model for the change in intrusion fluid height has been developed using the steady-state particle concentration at the spreading level.