Entrainment into particle-laden turbulent plumes

We use laboratory experiments to investigate the entrainment of ambient fluid into an axisymmetric turbulent plume containing dense particles with a settling velocity that is considerably smaller than the plume velocity. We consider the effect of particle size, particle concentration, and the orientation of the plume buoyancy flux-in either the same or opposite direction to the particle buoyancy flux. When the plume buoyancy flux is in the opposite direction to the particle buoyancy flux, entrainment into the plume increases by up to 40%. The rate of entrainment increases linearly with the ratio of particle buoyancy flux to fluid buoyancy flux but does not depend on the particle size for the range of particle sizes investigated here. In contrast, when the plume buoyancy flux is in the same direction as the particle buoyancy flux, entrainment into the plume is unaffected by the addition of particles. The observed increase in entrainment, when the plume and particle buoyancy fluxes are in opposite directions, is consistent with inertial clustering whereby particles are ejected from regions of relatively high vorticity and accumulate in regions of relatively high strain rate within the turbulent flow field. Regions with high particle concentration can then experience convective instabilities that affect the entrainment of ambient fluid into the plume. The differing behavior observed based on the plume buoyancy flux orientation is also consistent with the above mechanism. Finally, based on the laboratory findings, we propose an expression for the entrainment coefficient to take into account the effect of suspended particles of opposing buoyancy flux to the plume buoyancy flux.