Numerical Simulations of Two-Phase Flow in a Dorr-Oliver Flotation Cell Model
Abstract: Two-phase (water and air) flow in the forced-air mechanically-stirred Dorr-Oliver machine has been investigated using computational fluid dynamics (CFD). A 6 m 3 model is considered. The flow is modeled by the Euler-Euler approach, and transport equations are solved using software ANSYS-CFX5. Unsteady simulations are conducted in a 180-degree sector with periodic boundary conditions. Air is injected into the rotor at the rate of 2.63 m 3 /min, and a uniform bubble diameter is specified. The effects of bubble diameter on velocity field and air volume fraction are determined by conducting simulations for three diameters of 0.5, 1.0, and 2.0 mm. Air volume fraction contours, velocity profiles, and turbulent kinetic energy profiles in different parts of the machine are presented and discussed. Results have been compared to experimental data, and good agreement is obtained for the mean velocity and turbulent kinetic energy profiles in the rotor-stator gap and in the jet region outside stator blades.
CFD MODELS OF MICROCEL AND JAMESON FLOTATION CELLS
Computational fluid dynamics (CFD) models of the Microcel column and Jameson cell have been developed for coal flotation. The models have been used to increase understanding of the cell hydrodynamics and to identify any opportunities to improve design and operation. The models incorporate micro-processes including particlebubble attachments and detachments. From CFD simulations, liquid velocities, turbulent dissipation rates, gas hold-up, particle-bubble attachment rates and detachment rates are obtained. The attachment and detachment rates per particle have been used for comparing cell performance. NOMENCLATURE As constant = 0.5 B buoyancy reduction force (N m) Bo bond number C1 constant = 2 d bubble or particle diameter (m) Di diffusivity of phase I (m s) F drag force (N m) g gravity vector (m s) k turbulent kinetic energy (m s) k1 rate constant (s) n particle number concentration (m) P pressure or probability (N m) Re Reynolds number Si mass source or sink (kg m s) S surface ratio t time (s) U velocity (m s) Z collision frequency (m s) α volume fraction β bubble loading parameter γ shear rate (s) ε turbulent eddy dissipation (m s) θ contact angle (degree) μ dynamic viscosity (Pa s) ν kinematic viscosity (m s) ρ density (kg m) σ surface tension (N m) INTRODUCTION Flotation is used by the minerals industry to separate valuable minerals from the ore in air-sparged flotation cells. Separation is achieved when particles of the valuable minerals preferentially attach to air bubbles and are floated to the surface, forming a froth layer. The particles are removed from the froth by means of an overflow launder. The remaining slurry is discharged from the cell. This paper describes an investigation using computational fluid dynamics (CFD) to increase understanding of the hydrodynamics in coal flotation and to identify any opportunities to improve the design and operation of both the Microcel column and Jameson cell. The flotation effect is included as three sub-processes involving collision, attachment and detachment. A turbulent collision model has been used (Koh et al., 2000) to estimate the rate of particle-bubble encounters. The probability of collision is due to the streamline effect of fine particles moving around a larger bubble. The CSIRO CFD model incorporates micro-processes from cell hydrodynamics that affect particle-bubble attachments and detachments. The issues facing coal flotation are two-fold: firstly, a drive to increase capacity of existing installations, and secondly, a need to increase the recovery of coarse coal. These issues are influenced by the flow conditions inside the cell. The conditions that affect coal recovery can be identified through an analysis of the CFD results in the tank. The effect of composite particles in coal flotation is considered by the spread of specific gravities and particle sizes. The application of CFD modelling can provide knowledge of the hydrodynamics involved in enhancing particle-bubble attachments while minimizing particle detachment from bubbles.
Flow in a branching open channel: a review
Branching channel flow refers to any side water withdrawals from rivers or main channels. Branching channels have wide application in many practical projects, such as irrigation and drainage network systems, water and waste water treatment plants, and many water resources projects. In the last decades, extensive theoretical and experimental investigations of the branching open channels have been carried out to understand the characteristics of this branching flow, varying from case studies to theoretical and experimental investigations. The objectives of this paper are to review and summarise the relevant literatures regarding branching channel flow. These literatures were reviewed based on flow characteristics, physical characteristics, and modeling of the branching flow. Investigations of the flow into branching channel show that the branching discharge depends on many interlinked parameters. It increases with the decreasing of the main channel flow velocity and Froude number at the upstream of the branch channel junction. Also it increases with the increasing of the branch channel bed slope. In subcritical flow, water depth in the branch channel is always lower than the main channel water depth. The flow diversion to the branch channel leads to an increase of water depth at the downstream of the main channel. From the review, it is important to highlight that most of the study concentrated on flow characteristics in a right angle branch channel with a rigid boundary. Investigations on different branching angles with movable bed have still to be explored.