Investigation of CFD-PBM simulations based on fixed pivot method: Influence of the moment closure

• Published in: Chemical engineering journal (Lausanne, Switzerland : 1996) Switzerland : 1996), 2020-02, Vol.382, p.122882, Article 122882
• Main Authors: Shang, Xiaopeng, Ng, Bing Feng, Wan, Man Pun, Ding, Shirun
• Format: Article
• Language: English
• Subjects: CFD-PBM; Moment closure; Oscillating bubble plume; Population balance modeling; Rectangular bubble columns
• ISSN: 1385-8947; 1873-3212
• DOI: 10.1016/j.cej.2019.122882

•CFD-PBM solver with different conserved moments to be selected at program execution.•A rectangular bubble column simulated by CFD-PBM models with two moment closures.•Oscillating bubble plume of the gas-liquid flow inside the column is well captured.•Moment closure is essential to predictions of hydrodynamics and population balance.•CFD-PBM-SV model shows better accuracy for hydrodynamics and population balance. 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.