The inhomogeneous generalized population balance equation, discretized
with the Direct Quadrature Method of Moment (DQMOM), is solved to
predict the bubble size distribution (BSD) in a vertical pipe flow. The
proposed model is compared against a more classical approach, in which
bubbles are characterized by a constant mean size. The turbulent
two-phase flow field, modeled with a Reynolds-Averaged Navier-Stokes
equation approach, is assumed to be in local equilibrium, so that the
relative gas and liquid (slip) velocities can be calculated with the
algebraic slip model, accounting for the drag, lift and lubrication
forces. The complex relationship between the bubble size distribution
and the resulting forces is accurately described through DQMOM. Each
quadrature node and weight represent a class of bubbles with
characteristic size and number density dynamically changing in time and
space to preserve the first moments of the bubble size distribution. The
obtained predictions are validated against experiments from the
literature, demonstrating the advantages of the approach for large-scale
systems and suggesting a future extension to long piping systems and to
more complex geometries.