Viscous flow through particle assemblages at intermediate reynolds numbers — a cell model for transport in bubble swarms

Abstract

Abstract The fluid mechanical behaviour of a bubble swarm was simulated using a cell model. The Navier‐Stokes equations were solved numerically for the liquid flow in a uniform assemblage of circulating, spherical bubbles. Ranges of parameters studied included, Reynolds numbers, 0–1000 and porosities, 0.4–1. The numerical calculations show the effects of variations in Reynolds numbers and porosity on: surface vorticity and pressure distributions and form and friction drag coefficients. For all Reynolds numbers investigated a standing vortex ring was absent Predicted drag coefficients and Sherwood or Nusselt numbers agree with limiting analytical solutions for low and high Reynolds numbers. The theoretical results show good agreement with experimental data for porosity as a function of superficial gas velocity. Predicted and measured Sherwood and Nusselt Numbers were in substantial disagreement, making detailed comparison unwarranted The calculations should also be valid for dispersions of uniform, circulating, spherical droplets for the special case where the droplet viscosity is much less than the viscosity of the continuous fluid