Bernard Bunner

Dynamics of homogeneous bubbly flows Part 1. Rise velocity and microstructure of the bubbles

Direct numerical simulations of the motion of up to 216 three-dimensional buoyant bubbles in periodic domains are presented. The full Navier–Stokes equations are solved by a parallelized finite-difference/front-tracking method that allows a deformable interface between the bubbles and the suspending fluid and the inclusion of surface tension. The governing parameters are selected such that the average rise Reynolds number is about 12–30, depending on the void fraction; deformations of the bubbles are small. Although the motion of the individual bubbles is unsteady, the simulations are carried out for a sufficient time that the average behaviour of the system is well defined. Simulations with different numbers of bubbles are used to explore the dependence of the statistical quantities on the size of the system. Examination of the microstructure of the bubbles reveals that the bubbles are dispersed approximately homogeneously through the flow field and that pairs of bubbles tend to align horizontally. The dependence of the statistical properties of the flow on the void fraction is analysed. The dispersion of the bubbles and the fluctuation characteristics, or ‘pseudo-turbulence’, of the liquid phase are examined in Part 2.

Effect of bubble deformation on the properties of bubbly flows

Direct numerical simulations of the motion of 27 three-dimensional deformable buoyant bubbles in periodic domains are presented. The full Navier–Stokes equations are solved by a parallelized finite-difference/front-tracking method that allows a deformable interface between the bubbles and the suspending fluid and the inclusion of surface tension. The Eotvos number is taken as equal to 5, so that the bubbles are ellipsoidal, and the Galileo number is 900, so that the rise Reynolds number of a single bubble in an unbounded flow is about 26. Three values of the void fraction have been investigated: 2%, 6% and 12%. At 6%, a change in the behaviour of the bubbles is observed. The bubbles are initially dispersed homogeneously throughout the flow field and their average rise Reynolds number is 23. After the bubbles have risen by about 90 bubble diameters, they form a vertical stream and accelerate. The microstructure of the bubble suspension is analysed and an explanation is proposed for the formation of these streams. The results for the ellipsoidal bubbles are compared to the results for nearly spherical bubbles, for which the Eotvos number is 1 and the Galileo number is 900. The dispersion of the bubbles and the velocity fluctuations in the liquid phase are analysed.

Dynamics of homogeneous bubbly flows Part 2. Velocity fluctuations

Direct numerical simulations of the motion of up to 216 three-dimensional buoyant bubbles in periodic domains are presented. The bubbles are nearly spherical and have a rise Reynolds number of about 20. The void fraction ranges from 2% to 24%. Part 1 analysed the rise velocity and the microstructure of the bubbles. This paper examines the fluctuation velocities and the dispersion of the bubbles and the ‘pseudo-turbulence’ of the liquid phase induced by the motion of the bubbles. It is found that the turbulent kinetic energy increases with void fraction and scales with the void fraction multiplied by the square of the average rise velocity of the bubbles. The vertical Reynolds stress is greater than the horizontal Reynolds stress, but the anisotropy decreases when the void fraction increases. The kinetic energy spectrum follows a power law with a slope of approximately 3:6 at high wavenumbers.

Direct numerical simulations of three-dimensional bubbly flows

Direct numerical simulations of the motion of many buoyant bubbles are presented. The Navier–Stokes equation is solved by a front tracking/finite difference method that allows a fully deformable interface. The evolution of 91 nearly spherical bubbles at a void fraction of 6% is followed as the bubbles rise over 100 bubble diameters. While the individual bubble velocities fluctuate, the average motion reaches a statistical steady state with a rise Reynolds number of about 25.

Computations of Multiphase Flows

Abstract Computational studies of multiphase flows go back to the very beginning of Computational Fluid Dynamics. It is, however, only during the last decade that direct numerical simulations of multiphase flow have emerged as a major research tool. It is now possible, for example, to simulate the motion of several hundred bubbles and particles in simple flows and to obtain meaningful averaged-quantities that can be compared with experimental results. Much of this progress has been made possible by methods based on the ‘one-fluid’ formulation of the governing equations, in addition to rapidly increasing computational power. Here, we review computations of multiphase flows with particular emphasis on finite Reynolds number flows and methods using the ‘one-fluid’ approach. After an overview of the mathematical formulation and the various ‘one-fluid’ methods, the state-of-the-art is reviewed for three problems: Dispersed bubbly flows, microstructure formation during solidification, and boiling. For the first example numerical methods have reached the maturity where they can be used in scientific studies. For the second and third examples, major numerical development is still taking place. However, progress is rapidly being made and it is realistic to expect large-scale simulations of these problems to become routine within a few years.

An Examination of the Flow Induced by the Motion of Many Buoyant Bubbles

The results of direct numerical simulations of the motion of many three-dimensional buoyant bubbles in periodic domains are examined. The bubble motion is computed by solving the full Navier-Stokes equations by a parallelized finite difference/front tracking method that allows a fully deformable interface between the bubbles and the ambient fluid and the inclusion of surface tension. The governing parameters are selected such that the average rise Reynolds number is about 25. Two cases are examined. In one, the bubbles are nearly spherical; in the other, the bubbles rise with an ellipsoidal shape. The ellipsoidal bubbles show a much larger fluctuation velocity and by visualizing the flow field it is possible to show that the difference is due to larger vorticity generation and stronger interactions of the deformable bubbles. The focus here is on the early stage of the flow, when both the spherical and the deformable bubbles are nearly uniformly distributed.

Direct Numerical Simulation of Bubble Swarms with a Parallel Front-Tracking Method

Direct numerical simulations are performed to study the behaviour of an important class of dispersed multiphase flows, namely gas bubbles rising in a liquid. The numerical method combines a finite difference scheme for solving the Navier-Stokes equations with a front tracking method for following the gas-liquid interfaces. The size of the problem as well as the simulation time requirements necessitate the use of large parallel computers. Sample simulation results are presented illustrating the evolution of such systems and the dependence of statistical quantities on the gas volume fraction. The goal of these numerical experiments is to gain insight into fundamental properties of bubbly flows and support the development of simplified models

Simulation of Bubbly Gas-Liquid Flows by a Parallel Finite-Difference/Front-Tracking Method

Bubbly gas-liquid flows represent a prototype of dispersed multiphase flow systems, which appear in many natural phenomena and industrial applications. It is of fundamental interest to understand how the dispersed elements in such systems interact with each other and the ambient fluid field, and the collective motion and induced turbulence that arise from these interactions. The special challenges of simulating bubbly flows are to follow the motion of deformable phase boundaries and to accurately account for the stress boundary conditions at the interfaces. A parallel version of a finite difference/front tracking method is used to perform direct numerical simulations of mono- and bidisperse bubble size distributions rising in a stagnant liquid. The Navier-Stokes equations are solved on a fixed, regular, three-dimensional grid, while the interfaces between the gas and the liquid are tracked by two-dimensional surface-fitted moving meshes.

Simulation of Bidisperse Bubbly Gas-Liquid Flows by a Parallel Finite-Difference/Front-Tracking Method

Three-dimensional direct numerical simulations of bidisperse bubbly gas-liquid flows in a triply-periodic cubic domain are carried out. The numerical method utilizes a finite difference scheme for the solution of the Navier-Stokes equations for the flow field and a front tracking method for the resolution and movement of the deformable bubble interfaces. These numerical experiments aim at evaluating the dependency of bubble interactions, bubble rise velocities, and bubble-induced liquid turbulence on parameters like bubble size, interface deformability, bubble size distribution, and gas volume fraction in order to gain insight into these dispersed multiphase flows. The temporal evolutions of bubble velocities and liquid turbulent kinetic energies in various bidisperse bubble systems with spherical and deformable bubbles are presented for comparison. Also given are some details about the requirements and performance of these simulations on a parallel computer platform.

Microstructure of a Bidisperse Swarm of Spherical Bubbles

Three-dimensional simulations of bidisperse bubble swarms rising in a liquid have been carried out. This article describes the microstructure of a swarm of mostly spherical bubbles representing 6% void fraction. The swarm consists of an equal number of large and small bubbles with volume ratio 2. While the behavior of the large bubbles is similar to that in a comparable monodisperse system, the behavior of the small bubbles is different.Copyright