Efficient simulation of gas-liquid pipe flows with the population balance model

The inhomogeneous population balance equation for the bubble size distribution (BSD) in a vertical pipe flow is solved with the Direct Quadrature Method of Moment (DQMOM) and predictions are compared with those obtained with a classical approach, where bubbles are characterized by a constant mean size. The turbulent two-phase flow field, solved within a RANS formulation, is assumed to be in local equilibrium and the relative gas and liquid velocities are therefore calculated with the algebraic slip model (ASM) taking into account the drag, lift and lubrication forces. The non-linear relationship between bubble size and resulting forces is accurately described through DQMOM: each quadrature node represents a class of bubbles with characteristic size (and velocity) dynamically changing in time and space and accurately representing the first moments of BSD. The obtained results are validated against experiments (Szalinski et al., 2010) demonstrating the validity of the approach an suggesting the possibility of extending it to long piping systems and to more complex geometries.