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

▪ 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

The formation of gas bubbles and their subsequent rise due to buoyancy are very important fundamental phenomena that contribute significantly to the hydrodynamics in gas−liquid reactors. The rise o...

Bubble Formation and Bubble Rise Velocity in Gas−Liquid Systems: A Review

While experts in various fields discuss the potential of carbon capture and storage (CCS) technologies, the utilization of carbon dioxide as chemical feedstock is also attracting renewed and rapidly growing interest. These approaches do not compete; rather, they are complementary: CCS aims to capture and store huge quantities of carbon dioxide, while the chemical exploitation of carbon dioxide aims to generate value and develop better and more-efficient processes from a limited part of the waste stream. Provided that the overall carbon footprint for the carbon dioxide-based process chain is competitive with conventional chemical production and that the reaction with the carbon dioxide molecule is enabled by the use of appropriate catalysts, carbon dioxide can be a promising carbon source with practically unlimited availability for a range of industrially relevant products. In addition, it can be used as a versatile processing fluid based on its remarkable physicochemical properties.

Chemical Technologies for Exploiting and Recycling Carbon Dioxide into the Value Chain

Several aspects of the growth and departure of bubbles from a submerged needle are considered. A simple model shows the existence of two different growth regimes according to whether the gas flow rate into the bubble is smaller or greater than a critical value. These conclusions are refined by means of a boundary-integral potential-flow calculation that gives results in remarkable agreement with experiment. It is shown that bubbles growing in a liquid flowing parallel to the needle may detach with a considerably smaller radius than in a quiescent liquid. The study also demonstrates the critical role played by the gas flow resistance in the needle. A considerable control on the rate and size of bubble production can be achieved by a careful consideration of this parameter. The effect is particularly noticeable in the case of small bubbles, which are the most difficult ones to produce in practice.

Dynamics of bubble growth and detachment from a needle

Bubble formation under constant-flow conditions

The phenomena of the bubble formation from an orifice submerged in a liquid is classified according to their formation mechanisms and the estimation expressions of the bubble volume are reviewed The revised two-stage model of bubble formation accompanied by the pressure fluctuation in the gas chamber is presented and the results computed by this model are compared with the experimental results obtained for relatively wider range of gas chamber volume. Effects of some factors on the bubble volume, such as, gas chamber volume, orifice diameter, physical properties of gas and velocity of surrounding liquid are discussed

Bubble formation from an orifice submerged in liquids

Induced air flotation (IAF) was developed using a rotating-flow microbubble generator for water treatment. This newly-developed generator can produce fine microbubbles with diameters on the order of micrometers, whereas it has to use a large quantity of water as propulsion, especially when surfactant-free water is used. That is to say, if the microbubble generator is utilized in flotation, the recycle ratio in IAF will be very high. To overcome this problem, we applied a centrifugal pump and altered the air-induced way of the generator. Microbubble size, microbubble concentration and particle removal efficiency of the improved microbubble generating method were compared with those of traditional ones.The best performance occurred in the improved method where gas and water were simultaneously induced and mixed by the pump, and dispersed through the rotating-flow microbubble generator. Microbubble size was decreased, while microbubble concentration was increased by the improved method. Particle removal efficiency of over 95% was achieved by recycling only 10% of treated water.Batch experiments were carried out under various flocculation and flotation conditions to evaluate the improved IAF process. A slight overdose achieved better removal efficiency and no or less flocculation time performed very well. Lower water flow rates achieved better removal efficiency due to the increase of the bubble concentration and the decrease of the bubble size. The air flow rate showed little effect on removal efficiency.

Water Treatment by Induced Air Flotation Using Microbubbles

Bubble formation at an orifice submerged in highly viscous liquid was studied. The volume and shape of the bubble formed at an orifice and the pressure fluctuation in the gas chamber were measured experimentally. A revised nonspherical bubble formation model is proposed to describe the bubble formation mechanism and to estimate the bubble volume and shape and the pressure change in the gas chamber. The bubble volume, bubble shape and gas chamber pressure calculated by the present model agreed relatively well with the values obtained experimentally in a wide range of viscosity: μ = 0.001 to 1.1 Pas.

Hideki Tsuge

Papers

Bubble formation under constant-flow conditions

Bubble formation from an orifice submerged in liquids

Water Treatment by Induced Air Flotation Using Microbubbles

Bubble Formation at a Single Orifice in Highly Viscous Liquids

Bubble formation at a nozzle submerged in viscous liquids having yield stress