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Traditionally, bubble shapes have been assumed to be spherical in breakup models such as the one developed by Luo and Svendsen in 1996. This particular breakup model has been widely accepted and implemented into computational fluid dynamics (CFD) modeling of gas–liquid two-phase flows. However, simulation results from this model usually provide unreliable predictions about the breakage of very small bubbles. The incorporation of bubble shape variation into breakup models has rarely been documented in literature but the bubble shape plays an important role in the interactions with the surrounding eddies, especially when the effects of bubble deformation, distortion, and bubble internal pressure change are considered during the events of eddy-bubble collision. Thus, the assumption of spherical bubbles seems to be no longer appropriate in reflecting this phenomenon. This study proposes and implements a modified bubble breakup model, which accounts for the variation of bubble shapes when solving the population balance equations for CFD simulation of gas–liquid two-phase flows in bubble columns. The key parameters predicted by the modified breakup model have been compared with the ones predicted by the original model. The simulation results of interfacial area and mass transfer coefficient for larger bubbles have been greatly enhanced by the modified breakup model. [ABSTRACT FROM AUTHOR]

• Considering the effects of bubble induced turbulence in the bubble breakage model. • κ −3 scaling has been identified on bubble induced turbulence kinetic energy spectrum. • Mean turbulent velocity and number density of turbulent eddies have been modified. • Influence of characteristic length scale on daughter bubble PDF is illustrated. • Effect of eddy-bubble contact on mass transfer in the bubble column is demonstrated. A quantitative description of the interaction between the turbulence eddies and bubble groups is crucial for the prediction of the bubble size distribution in bubble columns when adopting the population balance model (PBM) to estimate the heat and mass transfer across the interfaces between bubbles and carrier liquid. The majority of breakage kernels that are currently adopted focus on the shear turbulence in the liquid phase and model the kinetic energy contained in the arrival eddies that hit the bubbles by using the classical single-phase turbulence Kolmogorov −5/3 scaling law. In bubble columns, eddies that collide with bubbles and cause the bubble breakage are mainly generated by bubble-induced turbulence (BIT). The present work focuses on the influence of κ −3 scaling of the bubble-induced turbulence energy spectrum on the bubble breakage due to the eddy-bubble collision in bubble columns. A modified breakage model accounting for the bubble-induced turbulence is proposed. The proposed breakage model considers the mean turbulent velocity of eddies under the influence of bubble-induced turbulence and the characteristic wavenumber/length scale that corresponds to BIT. A comparison of the simulation results with the experimental data clearly demonstrate that the modified breakage model appropriately describes the bubble breakage events occurring under the influence of bubble-induced turbulence in bubble columns. It is also shown that the interaction of bubbles with the bubble-induced turbulence eddies has an impact on prediction of the mass transfer in bubble column flows. [ABSTRACT FROM AUTHOR]

For the simulation of industrial-scale bubble column reactors, while modelling the gas distributor as uniform inlets oversimplifies the inhomogeneity introduced by inlets, the direct simulation of the full geometry of gas distributor or sparger brings about enormous pre-processing work and huge computational cost. A new inlet model is therefore proposed in this paper to simplify the modelling of gas distributor and meanwhile maintain the simulation accuracy. The new inlet model is validated by the comparison of the model prediction with experiments and the CFD simulation incorporating the full geometry of gas distributor for bubble columns of small or large diameters. Comparisons of three different inlet boundary conditions, i.e., the direct simulation of gas distributor, the uniform inlet, and the new inlet model, are made in the simulation of the total gas holdup, the radial profiles of gas holdup at different cross-sections along the column height, and the axial velocity of liquid at various superficial gas velocities. The results indicate that the new inlet model is capable of achieving a good balance between simulation accuracy and computational cost for the CFD simulation of large-scale bubble column reactors. [ABSTRACT FROM AUTHOR]

In the study of meso-scale structures of multi-phase flow in bubble columns, accurate modelling of the interaction between the turbulence eddies and particle/bubble groups is crucial for capturing the heat and mass transfer occurring between the bubbles and surrounding carrier fluid. This work focuses on the influence of bubble shape variations on bubble breakage due to the eddy collision with the bubbles in bubble column flows. An improved breakage model accounting for the variation of bubble shapes was proposed. The improved breakage model coupled with the widely adopted isotropic, homogeneous turbulence kinetic energy spectrums, that are currently available from the open literature, takes into account the different energy requirements in forming the daughter bubbles, i.e. the increase of in surface energy and the pressure head difference of the bubble and its surrounding turbulent eddies. The simulation results compared with experimental data have clearly demonstrated that the improved model effectively describes the various shapes of bubble breakage events, which may consequently have a strong impact on the interfacial area estimation that is crucial for calculation of the transfer rates of mass and heat transfer in the bubble columns. [ABSTRACT FROM AUTHOR]

• A modified SGS model was proposed to account for the effect of bubble response to turbulent eddies • The modified SGS LES can effectively capture the transient bubbly flow in the bubble column • Both Kolmogorov -5/3 scaling law and -3 scaling law were recovered in LES turbulent kinetic energy spectrum • Strong spatial correlation between the cross-sectional averaged gas hold-up and local vorticity of turbulent eddies The Eulerian–Eulerian Large-eddy simulations (LES) of gas–liquid two-phase flow in a cylindrical bubble column reactor have been conducted. When considering the turbulent eddy viscosity in LES, apart from the well-accepted contributions from shear turbulence and bubble induced turbulence (BIT), the effect of the interaction between entrained bubbles and eddies with a similar turbulence length scale to the sub-grid scale (SGS) cannot be neglected. With the consideration of the bubble response to the eddies on the induced sub-grid stresses, a modified SGS model, which incorporates the Stokes number, St, was proposed. The results of LES clearly indicate that the use of the modified SGS model can effectively capture the transient bubbly flow in the cylindrical bubble column. The power turbulent kinetic energy spectrum obtained in LES indicates that a slope similar to Komogorov -5/3 scaling law and the -3 scaling law can still be identified for a critical frequency f =10.70 Hz. Image, graphical abstract [ABSTRACT FROM AUTHOR]