Scale-up of gas-liquid stirred tanks using coupled computational fluid dynamics and population balance modelling

The main aim of the work was to produce scale-up methods for the design of aerated stirred tanks using a combined computational fluid dynamics (CFD) and population balance approach. First a modeling study of single phase stirred tanks was performed to evaluate the best model features (turbulence model, impeller's model, discretisation, grid etc). Good agreement was obtained between the CFD simulation and the LDA measurement on the time-averaged mean velocities and turbulence quantities. The angle-resolved mean velocities and turbulence quantities were also predicted very well as were the power number and the positions of the vortex cores. The next stage involved the development of a population balance model (PBM) which was carried out first using a well-mixed single compartment implemented in MATLAB to reduce the modeling complexity. The algorithm was validated for various mechanisms, namely breakage, aggregation, nucleation and growth which have an analytical solution available from literature. Tests using realistic models for bubble coalescence and breakage were also carried out with the results showing a reasonable agreement with the Sauter mean bubble sizes obtained from empirical correlations. The algorithm also responded well to changes in the turbulence dissipation rate, the initial bubble size distribution and the local gas hold-up, which suggest that the final bubble size is not affected by the initial bubble size. A fully predictive model must combine both the fluid mechanics and bubble dynamics models which can be performed either by a four-way or three-way coupling simulation. The disadvantage of the latter is that is does not consider the effect of the bubble dynamics in- the two-phase modelling. A four-way coupling (CFD-PBM) method was carried out by implementing the PBM within the CFD code. Various drag models which take into account the effect of distorted bubbles and dense gas dispersion are also considered. Mass transfer models are also implemented using the bubble sizes obtained from the PBM. The CFD-PBM model showed a reasonable prediction of the power number, local bubble sizes, gas hold-up, dissolved oxygen concentration and the mean velocities of the two-phase flow in comparison to experimental data taken from the literature. Finally, the CFD-PBM model was employed to evaluate the consequences of scale-up on the mass transfer rate in aerated stirred tanks agitated either by Rushton turbine or CD-6 impeller with operating volume ranged from 14L to 1500L. Three scale-up rules, namely a constant P IV combined with either constant Fig, Vg and VVM were studied. The simulation results suggest, that a successful scale-up may be achieved by keeping the P IV and VVM constant, which led to a slightly higher (kLa) representing a more conservative approach. In contrast, constant P/V and Vg led to a slight reduction in the rate of mass transfer at larger scale which is in agreement with experimental measurement . from the literature. Results from the CFD-PBM simulation also suggest a similar scale-up rule may be applicable for an advanced gas dispersion impeller such as the CD-6 which yielded a similar scale-up trend to that of a Rushton turbine.