Numerical study of bubbly flows using direct quadrature method of moments

To model the macroscopic bubble interactions (e.g. coalescence and breakage), the two-fluid model in conjunction with the population balance equation (PBE) approach has been considered as a practical and accurate formulation of handling bubbly flow systems. Recently, the MUltiple SIze Group (MUSIG) model appears to be one of the most direct solution methods which solves the PBE with discrete class approach and fuses seamlessly with the computational fluid dynamics (CFD) framework. Nonetheless, for complex bubbly flow structures with wide range of bubble size, large number of classes must be used to attain sufficient resolution for the bubble size distribution (BSD). This poses severe limitations on both computational time and resources. This paper focuses on introducing an alternative direct quadrature method of moments (DQMOM) (Marchisio and Fox, 2005) where the BSD is tracked through its moments by integrating out the internal coordinate. The main advantage of DQMOM is that the number of scalars to be solved is very small (i.e. usually 4-6). To assess the performance of DQMOM in measure-up with the MUSIG model, predictions of both models are validated against two experimental data by Hibiki et al. (2001) and Lucas et al. (2005). In general, the model predictions compared very well against the measured data. Associated
numerical issues and drawbacks for the DQMOM model are also discussed.