Simulation of polydisperse multiphase systems using population balances and example application to bubbly flows

In this work the relationship between multiphase computational fluid dynamics models and population balance models is illustrated by deriving the main governing equations from the generalized population balance equation. The resulting set of equations, consisting of the well known two-fluid model coupled with a bivariate population balance model, is then implemented in the CFD code OpenFOAM. The implementation is used to simulate a particular multiphase problem: bubbly flow in a rectangular column. Results show that, although the different mesoscale models for drag force, coalescence, breakup and mass transfer, can be improved, the agreement with experiments is nevertheless good. Moreover, although the problem investigated is quite complex, as the evolution of bubbles is solved in real-space, time and phase-space (i.e. bubble size and composition) the resulting computational costs are reasonable. This is due to the fact that the bivariate population balance model is solved here with the so-called conditional quadrature method of moments, that very efficiently deals with these problems. The overall approach is demonstrated to be efficient and robust and is therefore suitable for the simulation of many polydisperse multiphase flows.