A Particle Tracking Model for Sedimentation from Buoyant Jets

Abstract

Sediment-laden turbulent buoyant jets are commonly found in natural and engineered environments. Examples include volcanic eruptions, deep sea hydrothermal vents, discharge of partially-treated wastewater, and dredging operations. A horizontal sediment buoyant jet is characterized by a horizontal momentum jet, rising plume, and a horizontal surface gravity current. The settling of particles from a sediment buoyant jet depends on the complex interaction of particles with turbulent fluctuations and the mean flow—in particular particle re-entrainment due to the external irrotational flow induced by the jet. A three-dimensional (3D) stochastic particle tracking model is proposed to predict the sedimentation from an arbitrarily inclined sediment-laden buoyant jet in a stagnant ambient. The simple model predicts the entire 3D jet flow field via a coupling of semianalytical models for the mean flow as well as turbulent fluctuations. The mean flow for the turbulent buoyant jet and the surface gravity current are determined using well-validated integral models, while the external jet-induced irrotational flow field is computed by a distribution of point sinks along the jet trajectory. Turbulent velocity fluctuations are modeled by a Lagrangian particle velocity autocorrelation function that mimics the trapping and loitering of sediment particles in turbulent eddies. The turbulent fluctuations are stochastically generated from a self-similar profile of the turbulent kinetic energy derived from computational fluid dynamics (CFD) solution of jets and plumes. Predictions of the particle tracking model are in excellent agreement with experimental data over the entire jet-plume regime for a wide range of particle sizes (58–621 μm) and properties. The model provides physical insight in delineating the modes of sediment fall out. The fraction of sediment mass fall-out from the jet lower boundary is found to be a function of the ratio between the jet momentum–buoyancy length scale ls=Mo3/4/Bo1/2 and the momentum-settling length scale lm=Mo1/2/ws, where Mo and Bo are the source momentum and buoyancy fluxes, and ws is the particle settling velocity in quiescent fluid. The particle distribution in the vertical centerline plane of the buoyant jet is also well-predicted. The model does not require any a priori adjustment of sediment settling velocity or particle re-entrainment rate.