Numerical simulation of 3D bubbles rising in viscous liquids using a front tracking method

10.1016/j.jcp.2007.12.002Journal of Computational Physics22763358-3382JCTP

Dynamics of an initially spherical bubble rising in quiescent liquid

The beauty and complexity of the shapes and dynamics of bubbles rising in liquid have fascinated scientists for centuries. Here we perform simulations on an initially spherical bubble starting from rest. We report that the dynamics is fully three-dimensional, and provide a broad canvas of behaviour patterns. Our phase plot in the Galilei–Eötvös plane shows five distinct regimes with sharply defined boundaries. Two symmetry-loss regimes are found: one with minor asymmetry restricted to a flapping skirt; and another with marked shape evolution. A perfect correlation between large shape asymmetry and path instability is established. In regimes corresponding to peripheral breakup and toroid formation, the dynamics is unsteady. A new kind of breakup, into a bulb-shaped bubble and a few satellite drops is found at low Morton numbers. The findings are of fundamental and practical relevance. It is hoped that experimenters will be motivated to check our predictions

Dynamics of rising bubble inside a viscosity-stratified medium

The rising bubble dynamics in an unconfined quiescent viscosity-stratified medium has been numerically investigated. This is frequently encountered in industrial as well as natural phenomena. In spite of the large number of studies carried out on bubbles and drops, very few studies have examined the influence of viscosity stratification on bubble rise dynamics. To the best of our knowledge, none of them have isolated the e ff ects of viscosity-stratification alone, even though it is known to influence the dynamics extensively, which is the main objective of the present study. By conducting time-dependent simulations, we present a library of bubble shapes in the Galilei and the Eötvös numbers plane. Our results demonstrate some counter-intuitive phenom- ena for certain range of parameters due to the presence of viscosity stratification in the surrounding fluid. We found that in a linearly increasing viscosity medium, for certain values of parameters, bubble undergoes large deformation by forming an elongated skirt, while the skirt tends to physically separate the wake region from the rest of the surrounding fluid. This peculiar dynamics is attributed to the migration of less viscous fluid that is carried in the wake of the bubble as it rises, and thereby creating an increasingly larger viscosity contrast between the fluid occupied in the wake region and the surrounding fluid, unlike that observed in a constant viscosity medium. It is also observed that the e ff ect of viscosity stratification is qualitatively di ff erent for di ff erent regimes of the dimensionless parameters. In future, it will be interesting to investigate this problem in three-dimensions

Numerical Simulation of High-Density Ratio Bubble Motion with interIsoFoam

The breeding blanket is one of the fundamental components of a nuclear fusion reactor and is responsible for the fuel production, generating tritium through neutronic capture reaction between lithium and neutrons. Lithium is a liquid PbLi alloy and the helium formed as reaction by-product can coalesce into bubbles, generating a two-phase mixture with a high-density ratio (¿¿ ~ O5 ). These bubbles can accumulate and stagnate within the blanket channels with potentially harmful consequences. In this work, the interIsoFoam solver of OpenFOAM v2012 is used to simulate bubble motion for a two-phase mixture representative of the He-PbLi system to test its potential for future developments in the field of fusion. In a first phase, several traditional benchmarks were carried out, both 2D and 3D, and considering the two variants of the VOF method implemented in the solver, isoAdvector and plicRDF. Subsequently, He bubbles of different diameters rising in liquid PbLi (¿¿ = 1.2 × 105 ) were analysed to investigate different regimes. For a Eötvös number (Eo) greater than 10, it was possible to recreate the axisymmetric, skirted, oscillatory regimes and the peripheral and central breakup regimes. For Eo < 10, non-physical deformations of the interface are observed, probably generated by spurious velocities that have a greater impact on the solution for very small bubbles and rising velocities.Peer ReviewedPostprint (published version

Experimental Studies on Regime Mapping of a Rising Bubble

An experimental study on shape variation of an initially spherical rising bubble in different liquids is presented, which validates the results from a paper by Tripathi et al.[2]. They had presented numerical simulation of an initially spherical gas bubble rising in a viscous fluid by Volume of Fluid method with a finite volume open source code, Gerris. They put forward the existence of a phase plot in Eotvos - Galilei plane having five different regimes of bubble behavior with well-defined boundaries. The regimes are characterized by differences in the shape of rising bubble (for example ellipsoidal, axisymmetric cap with a skirt and a doughnut like shape) as well as the path traversed by it (for example straight, zigzag and spiral path). The regime a bubble falls in depends on both its Eotvos and Galilei numbers. In the present study an experimental setup was developed to create an initial bubble of different sizes in a liquid and observe its rise behavior using a high-speed camera. This setup enabled us to get a 2D image of shape and path oscillation through high-speed video recordings. Aqueous glycerol solutions of different volume concentrations were used to obtain the range of Eotvos and Galilei numbers as presented by Tripathi et al [2]. The results indicate that at low Ga and Eo, the bubbles show similar path and shape behavior and show the demarcation of regime boundaries as the numerical simulation. But at high Ga and Eo, there is a mismatch in terms of the regime demarcation boundary indicating that initial condition of the bubble is a critical parameter

A coupled volume-of-fluid/level-set method for simulation of two-phase flows in unstructured meshes

This paper presents a methodology for simulation of two-phase flows with surface tension in the framework of unstructured meshes, which combines volume-of-fluid with level-set methods. While the volume-of-fluid transport relies on a robust and accurate polyhedral library for interface advection, surface tension force is calculated by using a level-set function reconstructed by means of a geometrical procedure. Moreover the solution of the fluid flow equations is performed through the fractional step method, using a finite-volume discretization on a collocated grid arrangement. The numerical method is validated against two- and three-dimensional test cases well established in the literature. Conservation properties of this method are shown to be excellent, while geometrical accuracy remains satisfactory even for the most complex flows.This paper presents a methodology for simulation of two-phase flows with surface tension in the framework of unstructured meshes, which combines volume-of-fluid with level-set methods. While the volume-of-fluid transport relies on a robust and accurate polyhedral library for interface advection, surface tension force is calculated by using a level-set function reconstructed by means of a geometrical procedure. Moreover the solution of the fluid flow equations is performed through the fractional step method, using a finite-volume discretization on a collocated grid arrangement. The numerical method is validated against two- and three-dimensional test cases well established in the literature. Conservation properties of this method are shown to be excellent, while geometrical accuracy remains satisfactory even for the most complex flows.Postprint (author's final draft

A three-dimensional non-orthogonal multiple-relaxation-time phase-field lattice Boltzmann model for multiphase flows at large density ratios and high Reynolds numbers

This study proposes a three-dimensional non-orthogonal multiple-relaxation-time (NMRT) phase-field multiphase lattice Boltzmann (PFLB) model within a recently established unified lattice Boltzmann model (ULBM) framework [Luo et al., Phil. Trans. R. Soc. A 379, 20200397, 2021]. The conservative Allen-Cahn equation and the incompressible Navier-Stokes (NS) equations are solved. In addition, a local gradient calculation scheme for the order parameter of the Allen-Cahn equation is constructed with the non-equilibrium part of the distribution function. A series of benchmark cases are conducted to validate the proposed model, including the two-phase Poiseuille flow, Rayleigh-Taylor instability, binary liquid/metal droplet collision, and a bubble rise in water. The present simulation results are in good agreement with existing simulation and experimental data. In the simulation of the co-current two-phase Poiseuille flow, the present model is proven to resolve the discontinuity at the phase interface and provide accurate results at extremely high density ratios (i.e., up to ). Finally, the proposed model is adopted to simulate two challenging cases: (1) water droplet splashing during its impacting on a thin liquid film and (2) liquid jet breakup. The simulation results demonstrate an excellent agreement with previous experimental results, both qualitatively and quantitatively. In these simulations, the Weber number and Reynolds number reach 105 and 6000, respectively, and the viscosity can be as low as , in the lattice unit

Experimental and simulation studies of the shape and motion of an air bubble contained in a highly viscous liquid flowing through an orifice constriction

This paper reports an experimental and computational study on the shape and motion of an air bubble, contained in a highly viscous Newtonian liquid, as it passes through a rectangular channel having a constriction orifice. The magnitude of the viscosity ratios, $\lambda$, and capillary numbers, CA, explored is high: 5.5 x 10$^{5}$ < $\lambda$ < 3.9 x 10$^{6}$ and 2.9 < Ca < 35.9 respectively. A multipass rheometer is used for the experimental work: air bubbles are suspended in 10 Pa s and 70 Pa s polybutene viscosity standards and passed through an orifice-plate geometry constructed within an optical flow-cell. High levels of bubble distortion are observed, including bubbles that resemble ‘crescent moons’. Simulation work is carried out using an implementation of the volume of fluid method in the freely-available finite-volume computational fluid dynamics code OpenFOAM. Quantitative data pertaining to the motion and shape of the bubble was extracted from both the experimental and simulation work. Initially, a good match between numerical simulation and experimental work could not be obtained: this problem was alleviated by changing the viscosity averaging method from an arithmetic mean to a logarithmically-weighted arithmetic mean. Medium- and high-resolution simulations using this new viscosity averaging method were able to match experimental data with coefficients of determination, R$^{2}$, typically 0.898 < R$^{2}$ < 0.985.Funding is gratefully acknowledged from the EPSRC, grant EP/N00230X/1