Models for predicting flow pattern transitions during steady gas-liquid flow in vertical tubes are developed, based on physical mechanisms suggested for each transition. These models incorporate the effect of fluid properties and pipe size and thus are largely free of the limitations of empirically based transition maps or correlations.

Modelling flow pattern transitions for steady upward gas-liquid flow in vertical tubes

This study describes the development and validation of Computational Fluid Dynamics (CFD) methodology for the simulation of dispersed two-phase flows. A two-fluid (Euler-Euler) methodology previously developed at Imperial College is adapted to high phase fractions. It employs averaged mass and momentum conservation equations to describe the time-dependent motion of both phases and, due to the averaging process, requires additional models for the inter-phase momentum transfer and turbulence for closure. The continuous phase turbulence is represented using a two-equation k − ε−turbulence model which contains additional terms to account for the effects of the dispersed on the continuous phase turbulence. The Reynolds stresses of the dispersed phase are calculated by relating them to those of the continuous phase through a turbulence response function. The inter-phase momentum transfer is determined from the instantaneous forces acting on the dispersed phase, comprising drag, lift and virtual mass. These forces are phase fraction dependent and in this work revised modelling is put forward in order to capture the phase fraction dependency of drag and lift. Furthermore, a correlation for the effect of the phase fraction on the turbulence response function is proposed. The revised modelling is based on an extensive survey of the existing literature. The conservation equations are discretised using the finite-volume method and solved in a solution procedure, which is loosely based on the PISO algorithm, adapted to the solution of the two-fluid model. Special techniques are employed to ensure the stability of the procedure when the phase fraction is high or changing rapidely. Finally, assessment of the methodology is made with reference to experimental data for gas-liquid bubbly flow in a sudden enlargement of a circular pipe and in a plane mixing layer. Additionally, Direct Numerical Simulations (DNS) are performed using an interface-capturing methodology in order to gain insight into the dynamics of free rising bubbles, with a view towards use in the longer term as an aid in the development of inter-phase momentum transfer models for the two-fluid methodology. The direct numerical simulation employs the mass and momentum conservation equations in their unaveraged form and the topology of the interface between the two phases is determined as part of the solution. A novel solution procedure, similar to that used for the two-fluid model, is used for the interface-capturing methodology, which allows calculation of air bubbles in water. Two situations are investigated: bubbles rising in a stagnant liquid and in a shear flow. Again, experimental data are used to verify the computational results.

Computational fluid dynamics of dispersed two-phase flows at high phase fractions

http://calliope.dem.uniud.it/CLASS/EPFL-COURSE/Tomyama-Zun-CES-2002.pdf

Transverse migration of single bubbles in simple shear flows

One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes

▪ Abstract Predicting the motion of bubbles in dispersed flows is a key problem in fluid mechanics that has a bearing on a wide range of applications from oceanography to chemical engineering. In this review we synthesize the recent progress made in describing bubble motion in inhomogeneous flow. A trident approach consisting of experimental, analytical, and numerical work has given a clearer description of the hydrodynamic forces experienced by isolated bubbles moving either in inviscid flows or in slightly viscous laminar flows. A significant part of the paper is devoted to a discussion of drag, added-mass force, and shear-induced lift experienced by spheroidal bubbles moving in inertially dominated, time-dependent, rotational, nonuniform flows. The important influence of surfactants and shape distortion on bubble motion in a quiescent liquid is highlighted. Examples of bubble motion in inhomogeneous flows combining several of the effects mentioned above are discussed.

The Motion of High-Reynolds-Number Bubbles in Inhomogeneous Flows

Simple but reliable correlations for a drag coefficient, CD, of single bubbles under a wide range of fluid properties, bubble diameter and acceleration of gravity were developed based on a balance of forces acting on a bubble in a stagnant liquid and available empirical correlations of terminal rising velocities of single bubbles. The proposed CD consists of three equations, each of which corresponds to pure, slightly contaminated and contaminated systems. The effect of a frictional pressure gradient due to a liquid flow is also taken into account by introducing a concept of an effective body acceleration. Terminal rising velocities of single bubbles were calculated using the proposed CD, and compared with measured data under the condition of 10-2<Eo<103, 10-14<M<107 and 10-3<Re<105 where Eo, M and Re are Eotvos, Morton and bubble Reynolds numbers, respectively. As a result, it was confirmed that the proposed CD gives better predictions than available drag coefficient models.

https://www.jstage.jst.go.jp/article/jsmeb1993/41/2/41_2_472/_pdf

Drag Coefficients of Single Bubbles under Normal and Micro Gravity Conditions

Experiments and numerical simulations on lateral migration of a single bubble in stagnant liquids and laminar flows were conducted in the present study to examine the effects of the Eotvos number Eo and dimensionless liquid volumetric flux on lateral forces. It was confirmed that (1) a lateral force due to the existence of the wall acts on a bubble and (2) a lift force due to the net circulation of liquid strongly depends on Eo. Empirical models for the wall and lift forces were also proposed and their validity was confirmed by comparing measured and calculated bubble trajectories.

Effects of Eötvös Number and Dimensionless Liquid Volumetric Flux on Lateral Motion of a Bubble in a Laminar Duct Flow

Numerical analysis of bubble motion with the VOF method

Flow instabilities in parallel-channel flow systems of gas-liquid two-phase mixtures

In order to examine the feasibility of direct simulation of bubbly flow, the applicability of the VOF (volume of fluid) method to analyses of a single rising bubble was examined in this study. Calculated bubble shapes and terminal velocities under wide ranges of Eotvos number and Morton number were compared with the experimental data summarized by Grace et al. Except for the cases in which bubble shapes were spherical-cap and skirted, the VOF method could predict them well by assigning only eight cells to the bubble diameter. Hence, it was confirmed that some modification of this method will enable us to simulate bubbly flow directly under a wide range of flow conditions. The relationship between bubble shape and velocity distribution was also examined within the ranges in which the VOF method is valid. It was found that the secondary vortex appearing in wobbling bubbles induces a velocity component normal to the bubble interface, and this velocity is one of the causes of the wobbling shape of the bubble.

https://www.jstage.jst.go.jp/article/jsmeb1993/36/1/36_1_51/_pdf

Tadashi Sakaguchi

Papers

Drag Coefficients of Single Bubbles under Normal and Micro Gravity Conditions

Effects of Eötvös Number and Dimensionless Liquid Volumetric Flux on Lateral Motion of a Bubble in a Laminar Duct Flow

Numerical analysis of bubble motion with the VOF method

Flow instabilities in parallel-channel flow systems of gas-liquid two-phase mixtures

Numerical Analysis of a Single Bubble by VOF Method.