The two-phase flow resulting from the bottom injection of gas into a liquid bath, constrained to be axisymmetric, is modelled by governing equations that incorporate the virtual mass and particle lift forces and a diffusive interfacial force. The equations are solved numerically by using the transient, two-fluid-flow program K-FIX. Both the bath and the top space are included in the calculation domain, but attention is focused on the central plume. Inclusion of terms describing the virtual mass force together with a force due to microscopic bulk pressure differences are found to ensure formal stability of a simplified case for all admissible parameter values; this also ensures numerical stability in practice. The particle lift force, together with a diffusive interfacial force, is shown to account for the observed spreading of the plume, the vertical variation in the centerline void fraction, and the magnitude of the bubble rise velocity in the upper half of the plume; however, although the void fraction is adequately predicted away from the centerline, the off-center bubble velocity remains poorly determined despite only small errors in the calculated gas flow rate at different heights. © 1990.
Davidson, M. R. (1990). Numerical calculations of two-phase flow in a liquid bath with bottom gas injection: The central plume. Applied Mathematical Modelling, 14(2), 67–76. https://doi.org/10.1016/0307-904X(90)90074-F