twoWayGPBEFoam: An open-source Eulerian QBMM solver for monokinetic bubbly flows

twoWayGPBEFoam is an open-source mesoscopic Eulerian QBMM solver for monokinetic bubbly flows. The solver is implemented within the OpenFOAM software framework. Unlike the existing macroscopic two-fluid model (TFM) solver twoPhaseEulerFoam, it can predict the size segregation phenomenon and the size-conditional velocities of the disperse phase, although it will not be able to predict the particle trajectory crossing (PTC). On theoretical grounds, the evolution of the disperse phase in multiphase flows is dictated by the generalized population balance equation (GPBE), which can be transformed into moment transport equations and solved using the finite-volume method with higher-order realizable spatial-discretization schemes and time-integration schemes. In order to address the closure problem of the size-conditional spatial flux, the size-conditional velocities need to be modeled. In many previous works, these are assumed to be identical with the disperse phase velocity predicted by the TFM. In this work, the size-conditional velocities were modeled using the velocity polynomial approximation (VPA), for which the velocity polynomial coefficients (VPCs) can be obtained from the moments themselves. By carrying out several test cases with both one-way and two-way coupling, we show that the results predicted by our solver agree well with the analytical solutions and the existing experimental data.