Prediction of magnetite segregation in dense medium cyclone using computational fluid dynamics technique

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Abstract

Multi-phase simulations of turbulent driven flow in a dense medium cyclone with magnetite medium have been conducted in Fluent, using the Algebraic Slip Mixture model to model the dispersed phases and the air-core, and both the Large Eddy Simulation turbulence model (LES) and Reynolds Stress Models (RSM) for turbulence closure. The predicted air-core shape and diameter were found to be close to the experimental results measured by gamma ray tomography. It is possible to use the LES turbulence model with ASM multi-phase model to predict the air/slurry interface accurately. Multi-phase simulations (air/water/medium) show appropriate medium segregation effects but over-predict the level of segregation compared to that measured by gamma ray tomography near the wall. This is believed to be because of unaccounted back-mixing of the dispersed phase due to turbulence in the basic Algebraic Slip Mixture model. The predictions of accurate axial segregation of magnetite medium are investigated using the LES turbulence model in conjunction with the multi-phase mixture model and viscosity corrections according to the feed particle loading factor. At higher feed densities the agreement between the Dunglison [Dunglison, M.E., 1999, A general model of the dense medium cylone, PhD thesis, JKMRC, University of Queensland] correlations and experimental measurements and the CFD is reasonably good, but the overflow density is lower than the model predictions. It is believed that the excessive underflow volumetric flow rates are responsible for under prediction of the overflow density. The effect of size distribution of the magnetite has been fully studied. As expected, the ultra-fine magnetite sizes (i.e. 2 and 7 microns) are distributed uniformly throughout the cyclone. As the size of magnetite increases, more segregation of magnetite occurs close to the wall.

Introduction

A dense medium cyclone (DMC) effects a sharper separation than can be obtained in other types of coal-washing equipment handling the same size range, usually 50–0.5 mm size range. For hard-to-clean coal (+ 10% near gravity material) in the size range of 50 mm to 0.5 mm, DMCs are very effective. In a typical DMC, illustrated in Fig. 1(a) mixture of medium and raw coal enters tangentially near the top of the cylindrical section, thus forming a strong swirling flow. The refuse or high ash particles move along the wall of the cyclone due to the centrifugal force, where the velocity is least and is discharged through the underflow orifice or the spigot. The lighter washed coal moves towards the longitudinal axis of the cyclone due to the drag force where a high velocity zone exists and passes through the overflow orifice, or vortex finder, also termed as overflow chamber.

The flow behavior in DMC is quite complex. This complexity of fluid flow in DMCs is basically due to the existence of the medium, the dominance of particle turbulence and the density effect on separation. The complexity of flow processes has led designers to rely on empirical equations for predicting the cyclone performance. These empirical relationships are derived from an analysis of experimental data and include the effect of operational and geometric variables. Different sets of experimental data lead to different equations for the same basic parameters. However, these models suffer from the inherent deficiency of any empirical models — they can only be used within the extremes of the experimental data from which the model parameters were determined. In view of this shortcoming, mathematical models based on fluid mechanics are highly desirable.

Computational Fluid Dynamics (CFD) is a versatile means to predict velocity profiles under a wide range of design and operating conditions. The numerical treatment of Navier–Stokes equations the back-bone of any CFD technique, gradually crept into the analysis of hydrocyclones in the early 1980s. This resulted from the rapid improvement in computers and a better understanding of the numerical treatment of turbulence.

Detailed studies in regard of experimental, empirical and analytical modeling and computational modeling of the fluid flow pattern, pressure drop, and solids motion in hydrocyclones have been widely carried out by many researchers (Kelsall, 1952, Pericleous and Rhodes, 1986, Hsieh, 1988, Davidson, 1988) however, for DMCs such information is very limited. DMCs have been mainly subjected to experimental and analytical studies (Davis, 1994, Napier-Munn, 1990, Wood, 1990). Within the experimental studies, only parametric studies analyzing the influence of geometrical and operating variables on the efficiency of separation are reported. The utility of this information is limited. There is an extensive literature on the performance of dense medium separation (DMS) processes in both coal (low density) and mineral (high density) applications (Napier-Munn, 1990). However, very few workers have grappled successfully with the problem of developing effective mathematical models of DMS processes for simulation, other than the trivial option of using partition curves with arbitrary parameter selection.

Reported computational modeling of DMCs is very limited (Zughbi et al., 1991, Suasnabar, 2000, Brennan et al., 2003). CFD studies on cyclone separators have been reviewed by Brennan et al. (2003), Suasnabar (2000) and also by Slack et al. (2000). The seminal CFD study is that of Hsieh (1988) with further publications by co-workers (Hsieh and Rajamani, 1991, Monredon et al., 1992). These studies used 2D-axisymmetric grids with an imposed air-core position. However even with these limitations the work demonstrated the effect of swirl and flow reversal on turbulence behavior. It is now generally accepted that k-ε turbulence models are not suitable for modeling the swirling flows that occur in cyclone separators. The more complex Reynolds Stress Turbulence model (Launder et al., 1975), which solves a set of transport equations for each individual component in the Reynolds Stress tensor is recognized as being more suitable and has been used successfully in recent CFD studies of cyclones (Brennan et al., 2003, Suasnabar, 2000, Slack et al., 2000).

In this paper, the numerical simulations in a 350 mm Dutch State Mine (DSM) dense medium cyclone using FLUENT 6.2 multi-phase models with RSM (Reynolds Stress Model) and LES (large eddy simulation) turbulence models are presented. Air-core diameter, magnetite segregation and overflow and underflow densities are predicted.

Section snippets

Particle behavior and segregation phenomena in cyclone: a review

Experimental investigations of particle separation for dense medium cyclones and hydrocyclones are abundant. However, only external variables such as separation efficiency and evaluation of the slurry properties have been determined. Experimental measurements within the cyclone such as density or concentration gradients are very limited. Galvin and Smitham (1994) measured the radial segregation of particles in terms of density profiles in a dense medium cyclone using X-ray tomography and found

Turbulence modeling in cyclones

Turbulence models for prediction of very high swirl flow contain empirical constants and are still being developed. The computational cost of such simulations is also very high. Most authors note that the standard k-ε turbulence model is unsuitable for the highly swirling flows that exist in cyclones. This has been dealt with in a number of ways. Hsieh and Rajamani (1991) and Devullapalli (1994) used a modified mixing length model for the turbulence with a different mixing length for each

Model formulation

Fluid flow and particle interaction in DMCs are very complex phenomena. Broadly speaking, three phases can be distinguished: water, solids (magnetite, coal and waste particles) and air. However, from a numerical point of view different density and size particles must be considered as separate phases. Under normal operation, the vortex flow within the cyclone body generates an air-core along the entire axis of the body. The air-core has been modeled to be approximately cylindrical in shape and

Theoretical considerations of LES turbulence model and mixture model

In these studies, the LES turbulence model was used to predict air-core and water splits in cyclone apart from RANS turbulence models. The air-core interface has been modeled using volume of fluid (VOF) method.

CFD methodology

The equations of motion do not have general analytical solutions and are solved numerically by CFD packages using finite volume approximations in a 350 mm dense medium cyclone of standard DSM design, angled at 15° to a horizontal plane. This was the model target, as a DSM cyclone of this dimension was being studied using gamma ray tomography at the JKMRC. The grid is a numerical model of the flow domain, which defines the size, shape, and orientation of the finite volumes for the CFD solver. A

Velocity field inside dense medium cyclone

As expected the flow field inside dense medium cyclone is similar to hydrocyclones. The CFD simulations predict velocities at different positions inside the cyclone; however, data do not exist to validate this information at present. Typical flow patterns at plane xz are shown in Fig. 4. Similar to hydrocyclone, in dense medium cyclones, a recirculation zone exists beneath the inlet region which is seen clearly in the velocity vector plot (Fig. 4). The fluid is seen flowing downward along the

Conclusions

Multi-phase simulations of a dense medium cyclone with magnetite medium have been conducted using Fluent. The predicted air-core shape and diameter were found to be close to the experimental results measured by gamma ray tomography. The LES turbulence model together with ASM multi-phase model can be used to predict the air/slurry interface accurately (within 2% error). Multi-phase simulations (air/water/medium) show appropriate medium segregation effects but over-predict the level of

Acknowledgements

The authors would like to express their sincere thanks to Prof. Tim-Napeir Munn, Ex-director of JKMRC, University of Queensland, Australia, Dr Debashish Battacharjee and Dr S Chandra, R&D management, TATA Steel, for their keen interest and encouragement for undertaking these studies.

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