A computational fluid dynamics (CFD) numerical study of the multiphase flow in a dense medium cyclone (DMC) have been conducted to predict the flow pattern and medium (defined as the mixture of water and the ferrosilicon) segregation containing ferrosilicon. The volume of fluid (VOF) model is used to show the initial shape and position of the air core (defined as the region with volume fraction of air larger than 90%), static pressure and velocity distribution. These results shown to be generally comparable to those reported in the literature. The mixture model is used to show medium segregation. Medium density distribution is appropriate and it decreases from wall to DMC center, but under-predicts the level of segregation compared to the data reported in the literature. The turbulence is described by the Reynolds stress model (RSM). For both the VOF and the mixture models, the velocity of entrance flow is different and it is determined based on the flow rate of DMC pump. The effects of length of vortex finder (15-21 cm), medium density (2300-2640 kg⁄m^3 ) and orientation angle (10-25°) with horizontal level on flow pattern are studied.

Keywords: smithsonite; ferrosilicon; orientation angle; dense medium cyclone (DMC); Reynolds stress model (RSM); medium segregation

1. Introduction

The dense medium cyclone (DMC) is a high-tonnage device that has been widely used to upgrade the run-of-mine coal, in the 0.5-50 mm size range, in modern coal industry by separating gangue from product coal (Narasimha et al., 2006). The DMC is also used in other mineral processing plants for treating iron ore, dolomite, diamonds, potash, and lead–zinc ores (Chu et al., 2015). Normally, the feed slurry including water, magnetite, and nonmagnetic particles is named “medium” (defined as the mixture of water and the ferrosilicon) in practice. In the past decade or so, significant experimental research has been carried out with hydrocyclones where dense medium is absent and where the measurements are relatively easy to make (Wang et al., 2009). Hsieh, 1988; Hsieh and Rajaamani, 1991, reported a comprehensive experimental study of the fluid flow pattern, pressure drop, and solids motion in a 75 mm hydrocyclone using laser doppler velocimetry (LDV). The density distribution of medium in a DMC has been reported by Galvin and Smitham, 1994 using X-ray tomography and by Subramanian, 2002 using gamma ray tomography (GRT).

The DMC is simple in design and geometry but the flow pattern within it is very complex due to the presence of the turbulent vortex formed, the air-core, and the size and the density distributions of the feed and process medium solids (Chu et al., 2009). Segregation of medium and ore particles with the size and density to physically separate solid particles using the strong centrifugal force field generated by the internal rotational motion is another complicated phenomenon in DMC devices (Chu et al., 2009; Kuang et al., 2013; Wang et al., 2009). The computational fluid dynamics (CFD) analysis of the DMC flow using only magnetite medium was performed, and a mathematical model was proposed to describe the multiphase flow in the DMC. In this model, the volume of fluid (VOF) multiphase model is first used to determine the shape and position of the air core (defined as the region with volume fraction of air larger than 90%), and the pressure and velocity distributions. Then the mixture multiphase model was employed to describe the flow of the dense medium and the density distribution, where the turbulence was described by the Reynolds stress model (RSM) (Narasimha et al., 2006; Kuang et al., 2013; Wang et al., 2009). Of course, as related literature indicate that to simulate a complicated multiphase flow a LES model is more adaptable than a RSM model but this model suffers from some drawbacks, such as utilization of more resources and slower computation speed, and it may need a finer grid (Narasimha et al., 2007a; Narasimha et al., 2007b; Shen et al., 2009).

All previous CFD investigations have only been done on coal in special density range (1200-2200 kg⁄m^3 ) and medium has been created by magnetite with density 1500 kg⁄m^3 .

The ferrosilicon medium rheology such as viscosity, stability and its other properties were studied and were compared with magnetite medium. Ferrosilicon has a fast settling rate in dense suspension, attributed to its very high solids density, coarser particle size distribution, more spherical particle shape and low medium viscosity at the same medium density (Dunglison et al., 2000; Svoboda, 2004; Shi, 2016). A characteristic curve between apparent viscosity and medium density was established, which can be used in FeSi selection for dense medium separation. Medium stability was determined from the FeSi sedimentation rate measurement. It shows that medium stability was closely correlated with medium viscosity (Shi, 2016).

Based on the CFD and CFD-DEM simulated data, a PC-based mathematical model is formulated to predict the performance of DMCs under various conditions. Then, the effects of some key variables related to DMC geometry (dimensions of different parts of the DMC), operational conditions (medium to coal volumetric ratio and medium feed density (RD)) and materials properties (Coal averaged relative density (RD)) were examined. With increasing length of vortex finder the operational head was slightly decreased but with increasing orientation angle, the operational head dropped further (Chen et al., 2012). The PC-based model has been used to design and optimize DMC. In order to achieve high capacity, the change of length of vortex finder had no effect, so standard Lv was used (0.6*cyclone diameter) but in order to achieve high separation efficiency or lower Ep, length of vortex finder should be decreased (Lv=0.4*cyclone diameter) (Chen et al., 2014). Of course, the effects of these geometry parameters of length of vortex finder and orientation angle on other variables of DMC performance such as the flow pattern and medium segregation weren’t studied. A computational fluid dynamics (CFD) model is proposed to describe the multiphase flow in a dense medium cyclone (DMC). The results reveal that when vortex finder or spigot diameter is varied at the same U:O ratio, the offset and medium split nearly remain the same, however, the coal feed rate and Ep are different under the conditions considered. It is also shown that the fish-hook phenomenon is observed when spigot diameter is equal to or slightly larger than vortex finder diameter, and a normal operation becomes less stable with decreasing U:O ratio (Kuang et al., 2013). Different designs of the outlet geometry of the vortex finder are used to achieve different purposes. This phenomenon is studied numerically by use of a combined approach of CFD–DEM with reference to the effect of the pressure at the vortex finder. It is shown that a relatively small change of the vortex finder pressure can cause significant variations of both the medium-coal flow and DMC performance (Chu et al., 2012). The wear rate of DMC walls due to the impact of coal particles is predicted by a combined computational fluid dynamics and discrete element method (CFD-DEM) approach, using the Finnie wear model from the literature. The numerical results show that the severe wear locations are generally the inside wall of the spigot and the outside wall of the vortex finder. The specific wear pattern depends on operational conditions and particle properties or particle type. The wear rate generally increases with a decrease of M:C ratio. The wear of the inner spigot wall is found to affect the DMC performance significantly. It is shown that as the life of the spigot wall increases, operational head, medium split and cut density decrease, Ep increases, and medium differential decreases to a minimum and then increases slightly (Chu et al., 2014).

All numerical studies of CFD and coupled CFD-DEM of the DMC, were done by magnetite medium to preparation Coal with the orientation angle of DMC is equal to 10-15° (Chu et al., 2015; Kuang et al., 2013; Wang et al., 2009).

In this work, the CFD study of the multiphase flow into the DMC used for pre-concentration of Smithsonite ore. The VOF model to determine the shape and position of the air core and the pressure and velocity distributions is used and the mixture model to describe the flow of the dense medium and the density distribution is employed. To validate the results achieved, the literatures is used.

The density of employed ore in this work is 3090 kg⁄m^3 , it is more than coal density in previous investigations, so the ferrosilicon medium with high density is used. A comparison between magnetite and ferrosilicon is done that ferrosilicon medium has more stability and lower viscosity than the magnetite.

Finally, the effects of the length of vortex finder, high orientation angle of the DMC and high density of the medium on flow pattern are studied.

2. Mathematical Modelling

Recognizing that the incompressible fluid flow in a DMC is quite complicated, the CFD modelling was divided into two steps, as shown in Figure 1. These two steps are devoted to solving the medium slurry flow. The continuum medium flow is calculated from the continuity and the Navier–Stokes’ equations based on the local mean variables defined over a computational cell. These are given by

(∂(ρ_f))/∂t+∂/(∂X_i ) (ρ_f u_i )=0 (1)

∂(ρ_f u_i )/∂t+∂/(∂X_j ) (ρ_f u_i u_j )=-∂p/(∂X_i )+∂/(∂X_j ) [μ((∂u_i)/(∂X_j )+(∂u_j)/(∂X_i ))]+∂/(∂X_j ) (〖-ρ〗_f (〖u^’〗_i 〖u^’〗_j ) ̅ ) (2)

where the velocity components are decomposed into the mean (u_i ) ̅ and fluctuating 〖u^’〗_i velocities (i =1, 2, 3). They are related, as given by

u_i=(u_i ) ̅+〖u^’〗_i (3)

-ρ(u^’ u^’ ) ̅ is the Reynolds stress term in eq. (2) due to the turbulence and is modelled by the Reynolds Stress Model (RSM) provided in the ANSYS-Fluent software (Wang et al., 2009).

In the first step, only the air and the water are considered. In the VOF model is used to describe the interface between the medium and the air core. The two-phases are modelled by solving a single set of momentum equations and tracking the volume fraction of each of the fluids throughout the domain. Also, the turbulence is modelled using the RSM model (Wang et al., 2009). At this stage, the position of the air core and the initial velocity and pressure distribution is obtained. The method is similar to that used for modelling multiphase flow in hydro-cyclones (Wang et al., 2007). In step 2, one additional phase is introduced to describe the behavior of ferrosilicon particles with average sizes. The multiphase model is changed from the VOF to the Mixture model. Medium density distribution is obtained at the end of this step.

The details of the calculation of the dense medium flow can be found in Refs. (Chu et al., 2009; Wang et al., 2009; Wang et al., 2007).

Figure 1. Steps used in the present simulation.

3. Operation conditions and details of numerical methods

3.1. Concentration circuit of Smithsonite mineral in DMC

The DMC is applied to concentrate a low-grade smithsonite ore using ferrosilicon medium, as is shown in Figure 2. In this work, simulation data are used based on the industrial data. Simulation’s parameters such as medium density and viscosity are also calculated. The particles size distribution of smithsonite ore in this dense medium separation is equal to 0.5 mm ≤ d≤20 mm, and the range of variation of the dense medium’s density is 2300 kg⁄m^3 ≤ ≤ 2640 kg⁄m^3 . The pulp specifications of the ferrosilicon medium are shown in Table 1.

Figure 2. The DMC operated for low-grade Smithsonite ore that is used to simulate in present study (Located in the Kane-Araie Aria Co., Zanjan, Iran).

Table 1. The pulp specifications of the ferrosilicon medium

The parameters of medium Units Value

FeSi Pump Qv m3/h 97.2-194.4

Averaged FeSi Density kg/ m3 6808

Pulp Density (max) kg/ m3 2640-2300

% solid (X): FeSi sump % 72.8-66.3

Qmp: FeSi Pulp t/h 256.6-223.6

Qms: FeSi Solid t/h 186.9-148.1

3.2. Geometry and meshing

The details of geometry which is considered based on the industrial DMC, are shown in Table 2. The solution geometry (the DMC’s internal volume) is used for the CFD simulation. The DMC meshes were generated using the Hexahedral cells due to the accuracy of the numerical results obtained based on these cells. In present study, the whole computational domain is divided into 88881 hexahedron cells. A view of generated mesh in the DMC is shown in Figure 3-A. In some parts of the DMC, such as the vicinity of the walls and vortex finder, due to turbulent flow the grid is finer than its other parts.

For better understanding the flow, such as, tangential velocity and axial velocity on entire domain, the sections normal to Z-axis and Y-axis on the DMC are shown in Figure 3-B. The DMC is operated at high orientation angle. In the present simulations, the orientation angle (is defined as the angle between the DMC central axis and the horizontal plane) is 〖25〗^°.

Table 2. Geometry dimensions of the DMCs considered

Parameter symbol value

Diameter of the body Dc 34 cm

Type of inlet - Tangential

Shape of inlet - Square

Side length of inlet Li 9 cm

Side width of inlet W 6 cm

Hydraulic diameter of inlet (4A/P) Dhyd. 7.2 cm

Length of vortex finder Lv 50-56 cm

Diameter of vortex finder Do 20 cm

Length of cylindrical part Lc 50 cm

Height of conical part Lp 78 cm

Spigot diameter Du 10 cm

Orientation angle 25 degrees

Figure 3. A) a view of generated mesh of the DMC and B) the sections normal to Z-axis and Y-axis on the DMC.

3.3. Steady state and convergence criteria

It is assumed that the steady-state operating condition is achieved when the variables variation such as, the pulp flow rate over time should be negligible on entire domain of the DMC. Required simulation time must be determined in order to guarantee the convergence to a reliable solution. During the two-phases CFD simulation with the VOF model, the instantaneous variation of the volume flow rate and velocity through these cross sections on entire domain are checked. When the variations versus time approached zero, the steady state conditions have been achieved. The time needed to achieve the steady state for the DMC is 3-4s.

3.4. Selection of the suitable media

3.4.1. Media types and sizes

The most common medium for separation is a suspension in water of fine Magnetite, ferrosilicon (FeSi), or a mixture of the two, depending on the separation density required. Ferrosilicon alone for 2900 to 3700 kg⁄m^3 (Svoboda, 2004). In all previous papers, Magnetite has been used in coal preparation but in this work, Smithsonite ore is concentrated and the range averaged density of ore different particles is 2890 – 3090 kg⁄m^3 , so ferrosilicon medium is used. Ferrosilicon is invariably used, for instance, for the concentration of diamonds, Lead & Zinc ores, for the recovery of aluminum in recycling plants, and for beneficiation of iron and manganese ores. Ferrosilicon containing between 14% to 16% silicon has a density ranging from 6700 to 7100 kg⁄m^3 . It is non-rusting and strongly magnetic. With concentrations of silicon greater than 22% the material is feebly magnetic, while with concentrations of silicon lower than 15%, it is prone to rusting (Svoboda, 2004). In this work, particle size distribution of used ferrosilicon and its other characterizations in Figure 4 and Table 3 are shown, respectively.

Figure 4. Particle size distribution of used ferrosilicon medium.

Table 3. Ferrosilicon characterizations used in this work.

d,

micron Retained,

G Retained, % Density, kg⁄m^3 Dynamic viscosity, kg/m/s (Pa.s) Fe,

%

75 48.4 9.7 6812 0.004287 55.33

45 60.4 12.1 6937 0.004362 66.74

38 43 8.6 7105 0.004463 74.83

25 36 7.2 6958 0.004375 78.09

-25 309.4 62.2 6723 0.004234 78.38

Total 497.2 100 - - -

Averaged - - 6808 0.004285 74.39

3.4.2. Viscosity of dense medium suspensions

Magnetite media are characterized by high apparent viscosities, extremely sensitive to rate of shear. Viscosities of the magnetite medium ranging from 700 cP (0.7 Pa×s) at the shear rate of 1000 s-1 to 2740 cP (2.74 Pa×s) at 1000 s-1 were reported at the operating density of 2800 kg⁄m^3 . Viscosities of ferrosilicon under similar conditions ranged from 84 cP (0.084 Pa×s) to 200 cP (0.2 Pa×s). Similar results were obtained for various grades of ferrosilicon (Svoboda, 2004). Therefore, according to the above description about magnetite and ferrosilicon, FeSi has greater solids density, coarser particle size distribution, more spherical particle shape and smaller medium viscosity at the same medium density, so, in this work ferrosilicon medium is used. Medium viscosity is an important parameter describing the behavior of the medium flow and the separation of particles in DMCs. Its determination is complicated, because it depends on many variables, such as ferrosilicon particle size distribution, particle shape, medium density, medium contamination, and so on (Svoboda, 2004). Medium dynamic viscosity in Inlet boundary conditions, is calculated by the solid fraction of ferrosilicon on proposed model by Ishii and Mishima, 1984 that was corrected by Wang et al., 2009 (eq. 4).

μ_m=3.8μ_c (1-α_d/0.62)^(-1.55) (4)

Ferrosilicon medium dynamic viscosity (μ_m) has been reduced for increasing the density to 2640 kg⁄m^3 and grinding type of ferrosilicon particles to milled (coarse).

3.4.3. Calculation of “ferrosilicon particles” Viscosity as fluid phase

Based on simulation approach (Figure 1), the first and second stages are related to CFD simulation, so ferrosilicon particles are considered as fluid phase. The ferrosilicon powder dynamic viscosity was measured based on equation derived from linear trendline of dynamic viscosity of air, water and magnetite fluids vs. density (Table 4 and Figure 5).

Table 4. The viscosity and density of fluids.

Dynamic Viscosity,

Kg/m/s Density,

kg⁄m^3 Type of fluids

0.000017894 1.225 Air

0.001003 998.2 Water

0.0033 4945 Magnetite

Figure 5. The relationship between the fluid dynamic viscosity vs. density.

According to the linear relationship in Figure 5. and ferrosilicon powder density (6808 kg⁄m^3 ), ferrosilicon dynamic viscosity is gotten 0.004285 Pa.s. Also, air is considered as primary continuous phase and water and ferrosilicon as secondary continuous phases. The characterization of used fluids in DMCs considered is shown in Table 5.

Table 5. The characterization of used fluids in DMCs considered.

Phase Parameters Symbol(Units) Value

Air Density ρ_g (kg⁄m^3 ) 1.225

Dynamic Viscosity μ_g (kg/m/s) 0.000017894

Velocity at inlet U_ig (m/s) 0

Water Density ρ_w (kg⁄m^3 ) 998.2

Dynamic Viscosity μ_w (kg/m/s) 0.001003

Velocity at inlet U_iw (m/s) 5 – 12

Volume of fraction at inlet % 71.8 and 22.4

Ferrosilicon Density ρ_m (kg⁄m^3 ) 6808

Dynamic viscosity μ_m(kg/m/s) 0.004285

Velocity at inlet U_im(m/s) 5 -12

Size d_m(μm) 50

Volume of fractions

at inlet (%) 28.2 and 22.4

Medium Density (and volume of fractions of ferrosilicon into medium) ρ_m(kg⁄m^3 ) 2640 (28.2%), 2300 (22.4%)

Density (dynamic viscosity) μ_m (kg/m/s) 2640 (0.009775), 2300 (0.007632)

Surface tension stress (sigma) Water – Air 0.072 -

Particles – Air 0.072 -

Water – Particles 0 -

3.4.4. Media losses

In DMS plants that use ferrosilicon, the loss amount is from 20% to 40% of the DMS plant operating costs and used range may widely be, from 0.1 to 2.8 kg/t, although in modern plants they do not exceed 0.25 kg⁄t (Svoboda, 2004). In this DMC plant of Zinc Carbonate ore, the ferrosilicon losses are equal to 0.4-0.6kg⁄t.

3.4.5 Simulation and Boundary Conditions (BC)

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