On the numerical study of isothermal vertical bubbly flow using two population balance approaches

Abstract

Two population balance approaches based on the MUltiple-SIze-Group (MUSIG) model and one-group Average Bubble Number Density (ABND) model for handling the bubble size distribution of gas-liquid bubbly flows under isothermal conditions are assessed. Three forms of coalescence and breakage mechanisms by Wu et al. (1998), Hibiki and Ishii (2002) and Yao and Morel (2004) are incorporated in the ABND model. To examine the relative merits of both approaches, local radial distributions of five primitive variables in bubbly flows: void fraction, Sauter mean bubble diameter, interfacial area concentration, and gas and liquid velocities, are compared against the experimental data of Liu and Bankoff (1993a,b) and Hibiki et al. (2001). In general, both of the ABND model and MUSIG model predictions yield close agreement with experimental results. To account for the range of different bubble sizes in the gas-liquid bubbly flows, the resolution required is achieved through the application of the MUSIG model. Nevertheless, computational times increase by a factor of two when compared to applying the simpler ABND model. To further exploit the models' capabilities, investigations are carried out by extending the two population approaches beyond the bubbly flow regime of higher void fraction, particularly in the transition regime. The numerical results are found to be grossly over-predicted, which expose the inherent limitations of the models. It is known that bubbles in this regime are generally highly distorted and closely packed instead of spherically shape and allowed to move freely in bubbly flow regime.

A Second‐Order Turbulence Model Based on a Reynolds Stress Approach for Two‐Phase Flow—Part I: Adiabatic Cases

“…Figures 3 and 4 show that the simulation results are in quite good agreement with the experimental data. In [31], computations performed with a K-ε turbulence model for the liquid produced comparable results. Our main objective in this paper is to check that the simulation with the R i j -ε turbulence model gives satisfactory results in a simple geometry, which is crucial before calculating industrial geometries, where the K-ε turbulence model is susceptible to fail.…”

“…Other forces, like the turbulent dispersion force, have also a crucial effect on the void fraction distribution. These forces depend on uncontrolled parameters like the bubble shape, the liquid turbulence, the bubbles collective effects, and so on [31]. [32] investigated experimentally several upwards bubbly flows in a vertical pipe with a sudden expansion.…”

Two-Phase Bubble Columns: A Comprehensive Review

“…Comparisons between the k-ε model and LES simulations have shown that similar performances are obtained in terms of average quantities; conversely, more accurate fluctuating quantities are achievable through LES [436][437][438][439], owing to the isotropic turbulence hypothesis of the k-ε model. The SST k-ω model has proven to be slightly superior to the k-ε model for simulating upward bubbly flow [440,441] and vertical pipes [10,430,[442][443][444][445][446][447]. It is worth noting that suitable prediction and selection of inlet turbulent boundary conditions are needed for reliable predictions [448].…”

“…Rzehak et al [459] compared various formulations applied to vertical bubbly flow in a pipe and concluded that the inclusion of this force into the model is fundamental. The virtual mass force arises from the relative acceleration of an immersed moving object to its surrounding fluid; this force is often found to be negligible in bubble column simulations [421,428,437,439,449,460], and different studies have neglected it [420,430,440,441,446,450,458,[461][462][463][464][465][466][467][468][469]. Recently, Ziegenhein et al [10] demonstrated that the virtual mass force has an influence on the prediction of the turbulence intensity at higher flow rates.…”

“…In the latter approach, the gas phase is subdivided into different bubble size classes along with a single ("homogeneous population balance model") or multiple ("inhomogeneous population balance model") gas velocity fields, depending on the desired level of distinction between small and large bubbles [465]. Homogeneous population balance models have been applied to bubble column simulations and upward bubbly flows by several authors [428,433,440,441,[461][462][463]466,475,483]. On the other hand, Krishna et al [484] introduced one of the first uses of two velocity groups to distinguish the dynamics of small and large bubbles.…”