Essay: Simulation of the multiphase flow in dense medium cyclone with high orientation angle containing ‎ferrosilicon medium: a CFD study

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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)‎

Transient flow: When water begins to flow into DMC, it takes some time (~3-4 s) until ‎flow properties (such as velocity) at a given point become stable. Although in reality this ‎period of time is very short, simulating such a transient course of operation takes a ‎considerable amount of computer time (~ 3 hour). Due to importance of having ‎computation stability and accuracy, choice of proper time steps is very important. The ‎results are not sensitive to the time step for the considered DMC flows. Based on the ‎experiences acquired the overall simulation time and other works (Chu et al., 2015; Chu et ‎al., 2009; Wang et al., 2009; Wang et al., 2007; Narasimha et al., 2007a; Narasimha et al., ‎‎2007b; Narasimha et al., 2006), for observing the computation stability as well as the ‎accuracy of the results, the simulations were performed with a time step of 0.001 s. ‎
Boundary conditions: Inlet area of the DMC is considered as location for entry water and air ‎to the DMC (velocity inlet). Outlets (overflow and underflow) of the DMC are defined as ‎pressure outlet. The applied velocity values were computed based on the inlet surface area ‎and the pump volume-flow rate. The relationships used to calculate water and medium pulp ‎velocity are as follows: According to Table 2, the DMC has a rectangle and tangential inlet ‎and its surface area of the DMC is calculated via: A_inlet=l×w=0.0054 m^2‎
Also, in the DMC separation circuit, volume-flow rate of DMC pump is equal to 70-250 ‎m^3⁄h that in practice equal to~ 100 m^3⁄h So, ‎
volume flow rate (m^3/s) = A_inlet (m^2)×〖vlocity〗_inlet (m⁄s), 〖vlocity〗‎‎_inlet ~ 5 m⁄s.‎
The DMC considered in this work is used in industrial scale, different with that used in the ‎previous experimental and numerical studies so far. Because the feed, which is a mixture of ‎ferrosilicon medium and Zinc ore pumped to the DMC. The flow is a multi-phase ‎‎(Newtonian fluids: air, water, fine particles of ferrosilicon medium and Zinc ore’s solids ‎particles), forming a strong swirling, Rotational, High speed, Twists, Turbulence, Transient, ‎Incompressible, dense, Immiscible and iso-thermal flow. When the inlet pressure changes, ‎the total computational domain density varies but the density of each phase is constant. ‎Centrifugal effect causes the Zinc particles to move towards the outer wall of the DMC, ‎where the axial velocity points predominantly downward, and to discharge through the ‎spigot. The lighter gangue particles, driven by the pressure gradient force and radial fluid ‎drag force, move towards the longitudinal axis of the DMC, where there is usually an air ‎core, and the predominant axial velocity points upward and the gangue particle exits ‎through the vortex finder. The pressure at the two outlets (vortex finder and spigot) is set to ‎one atmosphere (101.325 kPa). The best necessary conditions of medium into DMC, such as ‎its suitable density, are gotten based on industrial data in three years (from medium density ‎‎2300 kg⁄m^3 (minimum) to 2640 kg⁄m^3 (maximum)). The CFD simulations were run ‎different concentrations of ferrosilicon and the results are similar. The best medium density ‎is 2640 kg⁄m^3 , d80 of ferrosilicon particles is 50 μm and pump head of the DMC feed is ‎‎15 m. In DMC, different particle sizes of ferrosilicon are used. Simulations are all unsteady, ‎undertaken by the unsteady solver in the ANSYS Fluent CFD software package (v18.2). ‎Runs of numerical calculations are carried out to reduce the computational cost, under ‎dense flow, mono-sized particles (the shape of ferrosilicon particles to be spherical), ‎uniform particle density distribution and gravity acceleration was considered to be equal to ‎‎9.81 m⁄s^2 . ‎
The water–air flow is firstly solved with VOF model to reach its macroscopically steady ‎state that is defined as the steady state when the flow properties just fluctuate around their ‎respective average values, not varying with time. Then, the mixture flow of air, water and ‎ferrosilicon particles is solved with Mixture model to reach its macroscopically steady ‎state. The convergence strategy uses the Transient solver of Pressured-Based. Spatial ‎Discretization method of the second-order up-winding and pressure-velocity coupling ‎algorithm of SIMPLE are used. The centrifugal acceleration induced by swirl causes ‎medium segregation inside the cyclone body and the medium concentration is larger in the ‎underflow than in the overflow. Excessive medium segregation causes a reduction in ‎cyclone efficiency and this is believed to be because the increased medium concentration ‎near the underflow traps ore particles because of the increase in particle drag due to the ‎increase in viscosity.‎

‎4. Results and Discussion‎

In this work to understand the flow and its optimization, the contours of static pressure, ‎velocity magnitude, axial velocity, tangential velocity, radial velocity and density ‎distribution of medium of central section and the sections normal to Y-axis with different ‎heights are shown that the contours are similar to the previous works (Wang et al., 2009). ‎The predicted air core shape and its diameter were found (Figure 6). The rotation origin in ‎the middle of the intersection of the cylindrical and conical parts is located. ‎

Figures 6. The predicted air core shape and its diameter.‎

The static pressure decreases rapidly from wall to center (Figure 7). The pressure gradient is ‎the largest along the radial direction. In comparison the cylinder and conical regions of ‎DMC, the pressure gradient is the largest along the radial direction in the cylinder region.‎

Figures 7, Distribution (contour) of static pressure in a central section normal to Z-axis.‎

The axial velocity near internal wall of the vortex finder represents the upward flow and its ‎magnitude is more than the flows in other regions (Figure (8-A)). As shown in this Figure, ‎two types of the upward (yellow) and downward (blue) are created into cylinder region. Into ‎conical region, the upward flow is being decreased and the downward flow is increased and ‎the flow in apex region near wall is just downward. According to the flow around the air ‎core in the bottom of the cylinder and in the conical region, the upward flow into the DMC ‎is a helical twisted cylinder, but the flow into vortex finder of the DMC is just upward and ‎without turbulence and its value is maximum but in down the vortex finder, the flow is ‎turbulent (Figure (8-B)) because the short circuit flow is created, so velocity magnitude into ‎vortex finder is increased. As well as creating a bypass opportunity, this behavior called the ‎short circuit flow would increase the loss of energy and separation efficiency in the DMC ‎‎(Narasimha et al., 2006).‎

Figure 8. A) Contour of axial velocity in a central section normal to Z-axis, B) Comparison ‎between predicted axial-velocity on X-axis in different heights for different sections normal ‎to Y-axis.‎

Figure (9-A) shows the simulated distribution of the tangential velocity in central section ‎normal to Z-axis into the DMC. The value of the tangential velocity at near the wall and the ‎center of the flow field (red) is zero but it is maximum between the wall and center axis ‎‎(Figure 9-B).‎

Figure 9. A) contour of tangential velocity in a central section normal to Z-axis, B) ‎Comparison between predicted tangential-velocity on X-axis for sections in different ‎heights.‎

Figure 10. shows the simulated radial velocity distribution. This result is similar to that ‎reported in the literature because the distribution is like a helical twisted cylinder and the ‎main reason for this phenomenon is the internal flow collisions, which may cause instability ‎in the DMC (Narasimha et al., 2006).‎

Figure 10. Distribution of radial velocity in a central section normal to Z-axis.‎

‎4.1. The optimum separation density of Zinc ore

Based on particles density including smithsonite mineral (3430 kg⁄m^3 ) and gangue ‎particles (2710 kg⁄m^3 ) in ANGOURAN mine-Iran (case study), gravity concentration of ‎Zinc ore with ferrosilicon medium is carried out from medium density 2300 kg⁄m^3 ‎‎(minimum) to 2640 kg⁄m^3 (maximum). Using medium density 2300 kg⁄m^3 , zinc ‎concentrate was gotten with low grade (20-25%) and high recovery. For increasing grade up ‎to 35%, medium density was increased up to 2640 kg⁄m^3 . So, to get the flow pattern of ‎medium and density distribution into DMC, the CFD simulation was done based on medium ‎properties in industrial data. Figure 11. shows the density distribution of medium into the ‎DMC normal to Z-axis in two densities. Generally, the density distribution decreases ‎radially from wall to center and the density at the conical region is higher than the cylinder ‎region. The peak value occurs at near the wall and the bottom of the DMC. Moreover, a ‎high-density ring exists around the air core with a diameter larger than that of the vortex ‎finder (red). The instantaneous variation of density on three-phases flow ‎‎(air/water/ferrosilicon) vs. time with mixture model (second step of simulation) are shown ‎in Figure 12. The industrial (medium and ore) and predicted (medium) densities in the ‎DMC are shown in Table 6.‎

Figure 11. the density distribution of medium into central section normal to Z-axis A) ‎medium density(minimum) =2300 kg⁄m^3 , B) medium density(maximum) =2640 kg⁄‎m^3 ‎

Figure 12, The instantaneous variation of density on three-phases flow ‎‎(air/water/ferrosilicon) vs. time with Mixture model (second step of simulation from 11s to ‎‎16s), A) medium density 2300 kg⁄m^3 and B) medium density 2640 kg⁄m^3 .‎

Table 6. The industrial and predicted densities of the DMC
Separation ‎density, kg⁄‎m^3 ‎ Overflow, ‎kg⁄m^3 ‎ Underflow, ‎kg⁄m^3 ‎
Industrial density
‎(medium + ore)‎ ‎4255‎ ‎3100‎ ‎5410‎
predicted density
‎(medium)‎ ‎2300-2640‎ ‎2287-2440‎ ‎2290-2480‎

The thickening of the dense medium towards the apex of the cyclone has been ‎postulated as a cause for the observed fact that separations in a cyclone always ‎occur at a specific gravity higher than the specific gravity of the feed medium ‎‎(Gupta and Yan, 2016). In this work, a medium made up to a density of 2640 kg⁄‎m^3 produces a separation equivalent to a specific gravity of 4255 kg⁄m^3 in the ‎cyclone. Therefore, it is apparent that there is some other factor contributing to the ‎effect of centrifugal forces on gravity separation. Nevertheless, the zone near the apex ‎of the cyclone is important when using an unstable suspension as the medium (Gupta and ‎Yan, 2016). At first, the VOF model is used for two fluids (air and water), the velocity of ‎water is 5 m/s, then in the second step, the mixture model is used for three fluids (air, water ‎and ferrosilicon), the velocity must be increased to 10 m/s or inlet gauge pressure should be ‎increased to provide separation conditions (suitable density of separation (2640 kg⁄m^3 )) ‎and to increase the inlet flow rate of the DMC, and this would be caused the improvement ‎density distribution in the simulations, as shown in Figure 11. As a result, it is important ‎that the velocity and pressure of the DMC is different for the two fluids of water and ‎ferrosilicon medium
The density should be reduced from the wall to the middle of the DMC and the lowest ‎density is created on overflow, so the blue zone relates to the air core. To validate the ‎simulation results, increasing velocity and improving the density distribution can be one of ‎the criteria for industrial validation.‎

‎4.2. The effects of length of vortex finder and the orientation angle on the flow pattern
In order to study the effect of length of vortex finder on the flow pattern such as turbulence ‎and short circuit flow caused by collision the inflow with upward flow in the lower part of ‎the vortex finder, length of vortex finder is decreased from 21 to 15 cm as shown in Figure ‎‎13, But distributions of static pressure and axial velocity don’t change.‎

Figure 13. contours in a central section normal to Z-axis with length of vortex finder 15 cm, ‎A) static pressure, B) axial velocity.‎

Also, the orientation angle of the DMC is decreased from 25° to 10° as shown in Figure 14. ‎So, distributions of static pressure, axial velocity don’t change but density distribution is ‎false, because overflow density is more than underflow.‎

Figure 14. contours in a central section normal to Z-axis in orientation angle 10°, A) static ‎pressure, B) axial velocity, C) density 2640 kg⁄m^3 with length of vortex finder 21 cm.‎

‎5. Conclusions‎

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 ‎segregation using ferrosilicon medium different with previous cases. The DMC orientation ‎angle with horizontal level is 25°. ‎
In first step of simulation using VOF model, the results shown to be generally comparable ‎to those reported in the literature, such as, the initial shape and position of the air core, ‎static pressure and velocity distribution. The tangential velocity increases between the wall ‎of the DMC and air core up to its maximum value. This velocity decreases near the wall and ‎into air core. The axial velocity points down at the wall and gradually decreases toward the ‎bottom. The axial velocity increases in the inner wall of the vortex finder and reaches up to ‎maximum. In the cyclone’s central zone, the pressure is negative and the suction of air ‎allows an air column to be formed therein. At the center of the radial negative zone the ‎pressure drops to its lowest value phenomenon that has been verified by theoretical ‎analysis. ‎
In second step of simulation using mixture model, the medium density is 2640 kg⁄m^3 ‎and orientation angle is 25°, the results including medium segregation and medium density ‎distribution are appropriate and it decreases from wall to DMC center, but under-predicting ‎the level of segregation compared to the data reported in the literature. ‎
For both of simulation steps, the velocity of entrance flow is different and it is determined ‎based on the flow rate of DMC pump. In first step of simulation for two-phases (air and ‎water) flow, the velocity of entrance flow is 5 m⁄s, but in second step of simulation for ‎three-phases (air, water and ferrosilicon) flow, the velocity of entrance flow is 10-12 m⁄s ‎because medium segregation is optimized. It is important the velocity and entrance pressure ‎of the DMC is different for the two types of fluids of water and ferrosilicon medium! That ‎is, when using the medium pulp, we must increase the input velocity (the same inlet gauge ‎pressure in operation) to reach the desired separation density and then injecting the ore. this ‎would be caused the improvement density distribution in the simulations.‎
The effects of geometry parameters and operating conditions on flow pattern were studied. ‎At different medium densities (2300-2640 kg⁄m^3 ), the results of the CFD are similar. ‎By changing the length of vortex finder from 21 (0.6*cyclone diameter = standard) to 15 cm ‎‎(0.4*cyclone diameter), distributions of pressure, axial velocity, tangential velocity and ‎density wasn’t changed.‎
The orientation angle of the DMC was decreased from 25° to 10° with different length of ‎vortex finder 21 cm and different density 2640 kg⁄m^3 . Distributions of static pressure, ‎axial velocity don’t change but density distribution is false, because overflow density is ‎more than underflow. So, for medium with high density, the orientation angle of 25° is ‎proposed.‎

Acknowledgements ‎
The authors thank Mr. Yousef Moradloo as chairman of the board of directors of Aria Kaneh-Araie ‎plant for financial support this research. ‎

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