Direct Numerical Simulation of Air Bubbles in Water/Glycerol Mixtures: Shapes and Velocity Fields

Abstract

In this paper results of direct numerical simulation (DNS) of bubbles rising in viscous Newtonian liquids with high-density ratio are presented. The simulations are carried out with the highly parallelized code FS3D, which employs the Volume-of-Fluid (VOF) method. The high degree of parallization of the code allows high resolution of the computational domain, such that the Kolmogorov length scale inside the liquid phase is resolved for the simulations. For validation of the numerical results the terminal rise velocities, bubble shapes and flow fields are compared to experimental data as well as to approximate analytical solutions. For high Morton numbers terminal rise velocities and aspect ratios agree very well with experimental values. For lower Morton numbers there is an increasing difference between experimental and numerical rise velocities. The aspect ratios of ellipsoidal bubbles match both with experimental measurements and with theoretical values of Taylor and Acrivos. At very low Reynolds numbers (ReB < 1) the velocity fields in and outside of the bubble show good semi-quantitative agreement with the analytical creeping flow solution of Hadamard and Rybczynski.

A Volume-of-Fluid-based numerical method for multi-component mass transfer with local volume changes

“…FS3D has been validated for fluid dynamics simulations, including droplet impacts and collisions [26,9,8], bubble flow [16] and falling films [1]. A detailed account of the numerical method for hydrodynamics simulations can be found in [25].…”

Numerical simulation of bubble rising in viscous liquid

“…There are only few quantitative comparisons about bubble terminal velocity, e.g. in the work of Koebe et al [14]. In this paper, the improved front tracking method is used to systematically investigate single air bubble rising in water solutions within wider flow regimes.…”

Multifield hybrid method applied to bubble rising and coalescence

“…Despite several theoretical [5], experimental [6] and over these recent years numerical [7,8] studies, this paradigm is still a topic of major interest.…”