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, $U_c$ , in relation to the terminal settling velocity of each individual particle, $u_{st}$ . When $u_{st}>U_c$ , 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 $u_{st}\leqslant U_c$ , particle re-entrainment behaviour changes significantly and the plume dynamics becomes independent of $P$ . When $u_{st}\approx U_c$ , 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 $u_{st}< U_c$ , 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 $u_{st}\ll U_c$ , or in the case of these experiments, when $U_c\geqslant 1\ \text{cm s}^{-1}$ , 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.