CFD-PBM simulations on hydrodynamics and gas-liquid mass transfer in a gas-liquid-solid circulating fluidized bed

Further developments of the extended quadrature method of moments to solve population balance equations

Developing numerical methods to solve polydispersed flows using a Population Balance Equation (PBE) is an active research topic with wide engineering applications. The Extended Quadrature Method of Moments (EQMOM) approximates the number density as a positive mixture of Kernel Density Functions (KDFs) that allows physical source terms in the PBEs to compute continuous or point-wise form according to the moments. The moment-inversion procedure used in EQMOM has limitations such as the inability to calculate certain roots even if it is defined, absence of consistent result when multiple roots exist or when the roots are nearly equal. To address these limitations, the study proposes a modification of the moment-inversion procedure to solve the PBE based on the proposed Halley-Ridder (H-R) method. Although there is no significant improvement in the extent of variability relative to the mean of the tested shape parameter σ values, an increase in the number of floating point operations (FLOPS) is observed which the proposed algorithm responds in limitations mentioned above. The total number of FLOPS for all the kernels used for the approximation increased by around 30%. This is an improvement towards the development of a more reliable and robust moment-inversion procedure.

Transferring Bubble Breakage Models Tailored for Euler-Euler Approaches to Euler-Lagrange Simulations

Most bubble breakage models have been developed for multiphase simulations using Euler-Euler (EE) approaches. Commonly, they are linked with population balance models (PBM) and are validated by making use of Reynolds-averaged Navier-Stokes (RANS) turbulence models. The latter, however, may be replaced by alternate approaches such as Large Eddy simulations (LES) that play a pivotal role in current developments based on lattice Boltzmann (LBM) technologies. Consequently, this study investigates the possibility of transferring promising bubble breakage models from the EE framework into Euler-Lagrange (EL) settings aiming to perform LES. Using our own model, it was possible to reproduce similar bubble size distributions (BSDs) for EL and EE simulations. Therefore, the critical Weber (Wecrit) number served as a threshold value for the occurrence of bubble breakage events. Wecrit depended on the bubble daughter size distribution (DSD) and a set minimum time between two consecutive bubble breakage events. The commercial frameworks Ansys Fluent and M-Star were applied for EE and EL simulations, respectively. The latter enabled the implementation of LES, i.e., the use of a turbulence model with non-time averaged entities. By properly choosing Wecrit, it was possible to successfully transfer two commonly applied bubble breakage models from EE to EL. Based on the mechanism of bubble breakage, Wecrit values of 7 and 11 were determined, respectively. Optimum Wecrit were identified as fitting the shape of DSDs, as this turned out to be a key criterion for reaching optimum prediction quality. Optimum Wecrit values hold true for commonly applied operational conditions in aerated bioreactors, considering water as the matrix.

CFD-PBM Simulation on Bubble Size Distribution in a Gas-Liquid-Solid Flow Three-Phase Flow Stirred Tank

The bubble size distribution, location distribution, and gas holdup in a gas-liquid-solid flow three-phase stirred tank were numerically simulated by the Eulerian-Eulerian method and the population balance model (PBM). The Euler-Euler method combined with the PBM model included the influence of bubble aggregation and fragmentation on the interfacial force, which can better predict the bubble size distribution and phase holdups. The simulation results show that there are some differences in the fluid morphology and gas dispersion characteristics in the stirred tank under different rotating speeds. With the increase of rotating speed, the content of small-diameter bubbles increases obviously, and they are mainly concentrated in areas with higher speeds. The higher the rotational speed, the more the bubbles with small diameters, but the content of bubbles with large diameters is less affected by the rotational speed. Small-size bubbles mainly exist in the region of high fluid velocity, while large-size bubbles mainly exist in the region of low hydrostatic pressure. Compared with the change of the bubble content at different speeds, the content of bubbles with diameters of 0.50-1.90 mm is largest at 2000 rpm, while the content of bubbles with diameters of 2.65-10.09 mm is largest at 1500 rpm. The simulation work has certain guiding significance for the research and development of the forced mineralization device and the understanding of the dispersion characteristics of bubbles in the stirred tank.