Direct quadrature method of moments for isothermal bubbly flows

Currently, the two-fluid model is one of the most practical and accurate macroscopic formulations for handling bubbly flow systems. Nevertheless, in order to rigorously account for bubble-bubble interactions (e.g. coalescence and breakage), the population balance equation (PBE) must be solved along with the continuity and momentum balance equations. Recently, the MUltiple SIze Group (MUSIG) model appears to be one of the most common and direct methods to solve the PBE with a finite series of discrete classes. Nonetheless, a large number of classes must be used posing severe limitations on the computational resources for complex bubbly flows. An attractive alternative is represented by the direct quadrature method of moments (DQMOM) (Marchisio and Fox, 2005) where the particle size distribution (PSD) 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). The objectives of this present study are: (1) to implement the DQMOM model to accommodate coalescence and breakage of bubbles, and (2) to validate the model against measurements of bubbly flows by Hibikiet al. (2001) for a range of flow conditions. Preliminary computed results compared very well against the experimental data.