Eulerian–Lagrangian modeling of turbulent liquid–solid slurries in horizontal pipes

Abstract

Computations of liquid–solid slurries in horizontal pipes are performed to investigate the complex multiphase flow dynamics associated with operating conditions above and below the critical deposition velocity. A high-fidelity large eddy simulation framework is combined with a Lagrangian particle tracking solver to account for polydispersed settling particles in a fully developed turbulent flow. The two phases are fully coupled via volume fraction and momentum exchange terms, and a two-step filtering process is employed to alleviate any dependence of the liquid-phase mesh size on the particle diameter, enabling the capture of a wide range of spatial turbulent scales. A fully conservative immersed boundary method is employed to account for the pipe geometry on a uniform Cartesian mesh. Two cases are simulated, each with a pipe geometry and particle size distribution matching an experimental study from Roco & Balakrishnam, which considers a mean volumetric solid concentration of 8.4%, corresponding to just over 16 million particles. The first case considers a Reynolds number based on the bulk flow of the liquid of 85,000, resulting in a heterogeneous suspension of particles throughout the pipe cross-section. Statistics on the concentration and velocity of the particle phase for this case show excellent agreement with experimental results. The second case considers a lower Reynolds number of 42,660, leading to the formation of a stationary bed of particles. Three distinct regions are identified in the second case, corresponding to a rigid bed at the bottom of the pipe, a highly-collisional shear flow just above the bed, and a dilute suspension of particles far from the bed. Computational results indicate segregation in particle size along the vertical direction, with the smallest particles located at the top, increasing monotonically until the bed surface, where the largest particles are located. The covariance of concentration and velocity of each phase is presented, giving further insight on the multiphase dynamics. Statistics on the individual mechanisms that contribute to the motion of each particle, namely forces due to drag, the pressure gradient and viscous stresses of the surrounding fluid, and collisions, are provided for each case. It is observed that for the majority of the pipe cross-section, the drag force dominates for each case, which is balanced by inter-particle collisions in the streamwise direction, and by gravity in the vertical direction. Simulation results are also used to investigate closures from Reynolds average modeling of multiphase flows.