Spreading Hypothesis of a Particle Plume

Integral models of single-phase plumes are often closed using the entrainment hypothesis, which assumes the entrainment velocity is proportional to a characteristic plume velocity, but the corresponding theoretical development for modeling particle plumes has received less attention. In this paper an integral model is developed by proposing a new spreading hypothesis for particle plumes, in which the fluid phase spreading rate is taken as that of a single-phase plume, whereas the particle phase spreading rate is a function of the particle phase and fluid phase average vertical velocity. The change in momentum flux of the particle and fluid phases are calculated by considering the cross-sectional integrated buoyant and drag forces acting on the particles, and their reaction force acting on the fluid. Mixing characteristics of the particle plume can then be determined. The model was validated by laboratory particle plume experiments conducted for various particle sizes and initial plume-to-particle-settling velocity ratios, as well as experiments in the literature. Centerline particle and fluid velocities, as well as particle concentrations were generally well predicted. The inferred entrainment coefficient for a particle plume and the importance of lift force are also discussed. (C) 2016 American Society of Civil Engineers.