Investigation of CFD-PBM simulations based on fixed pivot method : influence of the moment closure - Shang, Xiaopeng (2019)
The fixed pivot method can only conserve two moments while other moments suffer from inherent errors caused by internal inconsistency. In this work, we present a comprehensive investigation regarding the influence of moment closure on population balance and hydrodynamics in the coupled CFD-PBM simulations. The CFD-PBM model, which conserves the surface area and volume (second and third moment, i.e. CFD-PBM-SV model), and the number and volume (zeroth and third moment, i.e. CFD-PBM-NV model), has been developed based on a two-fluid model. To assess the accuracy of Sauter Mean Diameter (SMD) with different moment closures, a transient and homogeneous case is first simulated by the single PBM model, which conserves the surface area-volume (i.e. PBM-SV model) and number-volume (i.e. PBM-NV model), respectively. It shows that in comparison with the analytical solution, the SMD predicted by the PBM-SV model shows higher accuracy than the PBM-NV model with identical sectioning resolution, and the PBM-NV model can give satisfactory results only on very fine sectioning grids. A rectangular bubble column is then simulated by the CFD-PBM-SV and CFD-PBM-NV model, respectively. It is found that both models can capture the oscillating bubble plume of the gas-liquid flow inside the column reactor. The flow features predicted by the CFD-PBM-SV model show better agreement with experimental data, in terms of the time-averaged vertical liquid velocity, gas hold-up and plume oscillation period, than the CFD-PBM-NV model. It is speculated that the better performance of the CFD-PBM-SV model is ascribed to more accurate predictions of interfacial forces and momentum transfer between the two phases due to internal consistency of the local SMD compared to the CFD-PBM-NV model.