Detailed 3D Modeling of Mass Transfer Processes in Two‐Phase Flows with Dynamic Interfaces

Abstract

A model is presented which allows a priori computation of mass transfer coefficients for bubbles (droplets) rising in quiescent Newtonian fluids. The proposed model is based on the front tracking technique and explicitly accounts for the bubble-liquid mass transfer process. The dissolved species concentration in the liquid phase is computed from a species conservation equation while the value of the concentration at the interface is imposed via an immersed boundary technique. Simulations are carried out to demonstrate the capabilities of the model to predict bubble shape, flow field as well as transport of a species from the bubble to the liquid phase.

An improved Front-Tracking technique for the simulation of mass transfer in dense bubbly flows

“…The numerical solution method presented here is globally based on the description in Darmana et al (2006). The model presented here provides a number of improvements and subtle changes, such as an improved velocity interpolation method, additional validation cases, and the use of special boundaries to simulate "infinite" bubble swarms in periodic domains.…”

“…Radl et al (2008) performed simulations of single and multiple bubbles with a Schmidt number of = Sc 50, which allowed them to show that the interaction between bubbles causes very fine structures in the concentration field, after which molecular diffusion quickly spreads them out. Simulations of mass transfer from single rising bubbles using a 3D Front-Tracking model have been performed by Darmana et al (2006), who use a constant refined mesh for the species balance, with Schmidt…”

Effect of bubble interactions on mass transfer in bubbly flow

“…Most of those studies focused on two-dimensional or axisymmetric flow. Because of the large disparity between the length and time scale for the mass transfer compared to the momentum transfer, fully resolved three-dimensional calculations of mass transfer are challenging undertakings and those available in the literature are done for very low Schmidt number, Sc ¼ Oð1Þ, [8,22]. In order to resolve the mass transfer at the interface of moving bubbles, and make the computational requirement of simulation of high Schmidt number bubbly flows manageable, several authors have presented different approaches; [3] computed the evolution of a soluble surfactant by incorporating a singular perturbation analysis of the fluid next to the interface into a numerical solution of the interface motion for Stokes flow, [4] used the exact solution of a one-dimensional diffusion problem, fitted to the computational results close to the bubble, to find the mass flux at the surface, and [2,1] solved a mass boundary layer equation at the interface for the evolution of the mass concentration next to the bubble and transferred the mass to the surrounding fluid when the boundary layer grew over a certain limit.…”

One‐Dimensional Modeling and Simulation of Bubble Column Reactors

“…those reactions that run completely under kinetic influence and therefore in the core space of the liquid. In the literature, a three-dimensional CFD model, such as in Darmana [1] or Krishna [2], is often implemented in as much detail as possible for the simulation of bubble columns. The complex modeling and computational time required, however, are extremely time-consuming and costly.…”