Direct numerical simulations of hydrodynamics and mass transfer in dense bubbly flows

Abstract

Bubbly flows belong to dispersed two-phase flows involving a gas and a liquid phase, which are brought into contact with each other such that the gas forms bubbles which rise through the liquid. Bubbly flows are often encountered in industrial environments, for instance in bubble columns in the (bio-)chemical or metallurgical industry. In chemical processes, (reacting) components are exchanged between a multitude of bubbles (’bubble swarms’) and the continuous liquid phase, while in metallurgical applications the (argon) bubbles are mainly used to induce a mixing current in large vessels of molten steel. The gas hold-up is an important parameter that determines the efficiency of operation in a bubble column. At high gas fractions, many bubbles are injected simultaneously, forming bubble swarms which adopt a behavior very different from single, undisturbed rising bubbles in an infinite liquid. Numerical studies on bubbly flows at industrial scales require detailed information on the effect of the gas fraction on the hydrodynamics and mass transfer characteristics, which can be obtained with dedicated numerical simulations resolving the physics occurring at small scales. This work focuses on the behaviour of bubbles rising in a swarm at small scales by numerical simulations. The results are presented in a form that can be used in larger-scale simulations which are performed both in academics and industry. The is work is a part of an industrial partnership programme, to scientifically investigate the hydrodynamic and mass transfer phenomena prevalent in bubbly flows in an industrially relevant context. A Front-Tracking model has been used to dynamically simulate the interaction between multiple phases (such as gas bubbles rising in a liquid), which tracks the interface between the phases by Lagrangian control points. The model is able to simulate multiple bubbles in a periodic domain, accounting for the surface tension force and deformations of the bubbles in great detail. In this work the model has been extended with the capability of simulating bubbly flows with very high gas loadings via improved remeshing techniques ensuring mass conservation. Thereafter, a species solver using an explicit immersed boundary technique was embedded in the model to investigate mass transfer between the phases, including chemical reactions. This model was employed to investigate several hydrodynamic and mass transfer characteristics of bubble swarms. The drag force is one of the dominant forces in bubbly flows. In this study, the drag force acting on bubbles rising in a mono-disperse swarm has been numerically determined as a function of the gas hold-up. It was shown that the normalized drag linearly increases with the gas fraction (hindered rise) and a correlation for the drag coefficient as a function of the gas hold-up and the Eotvos number has been developed, in which the Eotvos number accounts for the bubble size and shape deformations. The correlation matches the simulation results in a wide range, i.e. for Eotvos numbers between … and Reynolds numbers between …. Additionally, it was shown that the derived correlation can also be applied to bi-disperse bubble swarms. The computed turbulent energy spectrum induced by the rising bubbles shows an excellent agreement with experimental results obtained from literature. It was confirmed that the energy cascade follows a power-law with a slope of -3, and is independent of the gas fraction. The distribution of bubble velocities shows again good agreement with experimental results, and it was shown that for high gas fractions, the distribution of horizontal velocity fluctuations converges to a Gaussian distribution. Finally, simulations on mass transfer in bubble swarms have been performed. For accurate modelling of mass transfer in large-scale bubble column models, detailed knowledge on the liquid side mass transfer coefficient is required. Several interpretation methods to determine the liquid-side mass transfer coefficients in bubbly flows have been compared, and a closure relation for mass transfer in bubbly flows has been formulated. The insight and closure relations developed in this work can be used to improve existing numerical models, used by academics and industry, and allow for more efficient design and operation of bubble column reactors.