Transient RANS/Lagrange calculations of two-and three-phase flows in bubble columns

Abstract

This chapter illustrates mathematical model based on Euler/Lagrange approach for time-dependent calculations of gas-liquid and gas-liquid-solid flows in a bubble column. The fluid phase flow is calculated based on the Euler approach solving the three-dimensional unsteady Reynolds-Averaged Navier-Stokes (RANS) equations in a time-dependent way. The conservation equations are closed using the standard k- ɛ turbulence model. Two-way coupling is also accounted by adding dispersed phase source terms in all conservation equations of the continuous phase and additionally considering wake-induced turbulence. Bubble motion is calculated by solving the equations of motion and by taking into account drag force, pressure, added mass force, transverse lift force, and buoyancy and gravity. It is noted that the forces, such as drag force, pressure, added mass force, Saffman force and gravity were taken into account in the equations of motion for the tracking of solid particles. The introduction of the effective density in the continuous phase conservation equations permitted to perform the calculations with high void fraction values for bubbles and solid particles. The comparison of the predicted results with experimental data showed a good agreement for the cases of two-phase and three-phase flows. In the three-phase flow the liquid velocity can be predicted reasonably well by extending the drag force of solids and bubbles and by simple correlations which describe an interaction between particles and bubbles.