Effect of Drag Modeling on the Prediction of Critical Regime Transitions in Agitated Gas-Liquid Reactors With Bubble Size Distribution Modeling

A study on liquid‐liquid dispersions in a continuous mixer via computational fluid dynamics (CFD) simulation combined with population balance model (PBM)

“…The two‐fluid model is one of the most popular methods for the investigation of a liquid‐liquid multiphase system . The Reynolds‐averaged Navier‐Stokes equation (RANS) approach was found to be a good trade‐off between accuracy and computational costs for multiphase systems . The Eulerian‐Eulerian approach and standard k‐ϵ model were adopted in the present work.…”

“…[23] The Reynolds-averaged Navier-Stokes equation (RANS) approach was found to be a good trade-off between accuracy and computational costs for multiphase systems. [24,25] The Eulerian-Eulerian approach and standard k-e model were adopted in the present work. In the Eulerian two-fluid model, each phase is treated as an interpenetrating continuum, though in reality, one phase is implicitly assumed as a continuous phase, whereas the other one is a dispersed phase.…”

Bubble size distribution modeling in stirred gas–liquid reactors with QMOM augmented by a new correction algorithm

“…Different turbulent models were tested in preliminary investigations (in which a fixed bubble diameter has been considered) and the one that proved to be a good trade off between accuracy and reasonable computational cost was the k ‐ε model for the gas–liquid mixture 50, 51. In this approach, the turbulent viscosity in all phases is considered equal to the turbulent viscosity of the mixture (i.e., μ t,c = μ t,d = μ t ) that in turn is defined as follows: where k is the turbulent kinetic energy, ε is the turbulence dissipation rate, ρ m is the density of the mixture: …”

“…It is important to remind here that in this work a unique internal coordinate was used in the PBM so all the bubbles are assumed to be spherical, a reasonable assumption in the investigated bubble size range (i.e., between 2 and 10 mm); moreover, this bubble size range is consistent with the choice of a unique value for the terminal velocity for all the bubbles. An isolated air bubble, included in the considered size range (corresponding to the plateau region of Mendelsons' law65) and rising in still water presents a terminal velocity of about 26 cm/s, but this value must be corrected to take into account the effect of turbulence, as suggested by Montante et al66 The effect of turbulence on the value of bubbles terminal velocity was studied in a previous work,51 where a modified Bakker's correction was proposed: different values of the fitting constant of Bakker's correction were tested and good agreement with empirical correlations, and experimental data was achieved for those corresponding to a bubble terminal velocity of 12–13 cm/s about. Although this correction should be applied and calculated with the local turbulence intensity and gas hold‐up, in this work a simplified approach was used, and a constant terminal velocity of 13 cm/s was adopted throughout the entire reactor.…”

“…Instead their increased concentration causes interactions between them, which interfere with their rising motion, leading to a lower terminal velocity. Extensive validation based on comparison with correlations derived from experimental data resulted in a further reduction to about 8.5 cm/s 51. Therefore, a terminal velocity of 13 cm/s, throughout the entire reactor, was considered for global hold‐ups smaller than 5% and of 8.5 cm/s for global gas hold‐ups larger than 5%.…”