# Current Limitations for Predicting Liquid Dispersion in Continuous Flow Bubble Columns Using CFD
## 1 Introduction
The mesh size for VOF models must be sufficiently small so that a smooth interface can be constructed for the bubble. In the E-E model, the dispersed phase is treated as a virtual continuous fluid. As a consequence, one set of N-S equations is needed for each phase to separately describe the virtual continuous fluid and the real continuous fluid. Both fluids occupy the whole space. Interaction forces between the two fluids are needed to connect them. Numerous CFD simulations of the air-water system in bubble columns have been reported, showing acceptable predictions of the average magnitudes of the fluid dynamics and mass transfer parameters [12; 21; 22; 23]. The majority of them, especially for pilot-scale systems, have been conducted using Reynolds-averaged Navier-Stokes (RANS) models. RANS models (e.g., kinetic energy-dissipation rate (\(k\)-\(\epsilon\)) turbulent model) and large eddy simulation (LES) models have been compared for describing flow in a rectangular bubble column [24]. RANS models overestimated the turbulent viscosity and were unable to provide estimation in the sparger area. LES, on the other hand, allowed better predictions of both flow and turbulent viscosity [24]. RANS models have been shown to overestimate the size of the bubbles, and better estimates are obtained using the renormalization group (RNG) methods [25]. The bubble size is of critical importance in bubble columns as it affects the coalescence and breakup of bubbles and also the gas-liquid interfacial area for mass transfer. If bubble coalescence and breakup are poorly modeled, the simulated flow pattern deviates from the actual one [25; 26]. Transient three-dimensional LES of a bubble column for a wide range of gas velocities best predicted the flow pattern of bubble plumes [26]. A comparison of the predictive performance of different turbulence models (\(k\)-\(\epsilon\), \(k\)-\(\omega\), RNG, Reynolds stress model (RSM),and LES) showed that the RSM predictions of liquid velocities, gas holdup, and energy dissipation rates were comparable to the LES results but required less computational time [27]. RSM models can account for flow instabilities while maintaining good predictions of average magnitudes and computational economy [22]. A combination of the baseline model (\(k\)-\(\omega\) for walls and \(k\)-\(\varepsilon\) for the other domains) with the explicit algebraic Reynolds stress model (EARSM) has been found to be effective in the simulation of flow fields and local turbulence [22]. The use of LES in relation to dispersed bubble flows has been comprehensively reviewed [20]. A failure to correctly select values for key parameters (e.g., time-step, total time, grid size, etc.) limits the performance of LES. Although LES is conceptually simple, its application is not because several parameters need to be specified and their selection is not straightforward. LES predictions have agreed well with experimental data, mainly at low values of superficial gas velocities and gas holdups [20]. This is thought to be caused by the limitations of E-E schemes for representing interphase forces and bubble-induced turbulence [28]. Simulations of a large bubble column using an E-E approach (\(k\)-\(\varepsilon\) turbulence model with an additional term for bubble turbulence) achieved good predictions of the phase velocities and mixing times [29; 30], but the model overpredicted the local holdup, particularly in the center of the column. Although for batch bubble columns several CFD models have been studied, liquid-phase dispersion in two-phase continuous-flow bubble columns has not been previously examined using CFD. Therefore, the present study focused on the use of CFD to characterize mixing in a large bubble column with continuous flows of the phases (air and water). Two sets of conditions combining high and low flows were assessed by simulations and experiments.