Empirical drag closure for polydisperse gas-liquid systems in bubbly flow regime: Bubble swarm and micro-scale turbulence

Gas-liquid systems in the bubbly flow regime can be successfully simulated by considering that gas bubbles are polydisperse, namely a population of bubbles characterized by different sizes and velocities. Phase coupling issues can be properly overcome by considering the evolution in space and time of such distribution, which is dictated by the so-called Generalized Population Balance Equation (GPBE). Therefore, the development of reliable meso-scale models is crucial for its solution. This work focuses on meso-scale models for momentum coupling, namely the drag force coefficient, with particular attention to the so-called bubble swarm and micro-scale turbulence effects present in the turbulent bubbly flow regime. The proposed empirical methodology is here adopted for the simulation of very different gas-liquid systems, such as rectangular and circular bubble columns, as well as aerated stirred tank reactors, and simulation results are eventually compared with the available experimental data, resulting in very good agreement.