Particle Image Velocimetry Study of the Turbulence Characteristics in

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Particle Image Velocimetry study of the turbulence characteristics in an aerated flotation cell Hossna Darabi, S. M. Javad Koleini, David A. Deglon, Bahram Rezai, and Mahmoud abdollahy Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b03648 • Publication Date (Web): 24 Oct 2017 Downloaded from http://pubs.acs.org on October 26, 2017

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Industrial & Engineering Chemistry Research

Particle Image Velocimetry study of the turbulence characteristics in an aerated flotation cell Hossna Darabi1; S.M.Javad Koleini*1; David Deglon2; Bahram Rezai3; Mahmoud Abdollahy1 1- Department of Mineral Processing, Tarbiat Modares University, Tehran, Iran 2- Mineral Processing Research Unit, Department of Chemical Engineering, University of Cape Town, Cape Town, South Africa. 3- Department of Mining & Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iran

Abstract The turbulence characteristics in the presence of bubbles is very important for multi-phase processes such as froth flotation. The turbulence characteristics in an aerated Denver flotation cell were investigated using high speed stereoscopic particle image velocimetry technique at single-phase (water) and two-phase (water and air) systems to provide insight into the change in liquid phase hydrodynamics. The effect of the gas flow rate (0.043-0.125 cms-1) and Reynolds number (107,000–154,000) on the fluid flow properties were investigated. The results showed that the flow pattern at the both systems was the radial-type flow. The presence of air bubbles changed the local turbulence characteristics (mean velocity, the root mean square velocity, turbulence kinetic dissipation energy and turbulence kinetic energy). The results obtained may be useful for deeper investigation about the effect of the turbulence properties on the hydrodynamic characteristics and sub-processes in the mechanical flotation cells.

Keywords Two-phase flow, Stereo-PIV, Rotor-stator mechanism, Turbulence kinetic dissipation energy

1-Introduction *Corresponding author: Tel: +98 2182883397 Fax: +98 2182884324 E-mail:[email protected]

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Mechanical flotation cells, which are widely employed in the mineral processing industry, essentially consist of a tank agitated by an impeller or rotor. The impeller is surrounded by a stator. Rotor–stator beside injected gas generate bubbles.1,2 Multiphase flows in a mechanical flotation cell are often fully turbulent and complex.3-6 The mean flow patterns and turbulence characteristics of the flow fields generated by rotor-stator mechanism have important effects on the hydrodynamic and metallurgical responses of a mechanical flotation cell.7-10 Bubbles play an important role in froth flotation process.11,12 Therefore, investigation of two- phase (water and air) flow characteristics and the effect of the presence of bubbles on turbulence characteristics of the flow fields is considerably demanded. There are few measurement techniques that have been employed to characterize turbulence in flotation cells.13-16 These techniques may be divided into single-point and whole flow field methods. The single-point methods give the flow velocity at a given point in the flow field, whereas the whole flow field methods are able to provide the spatially distribution of the flow velocity over a large region of the flow field.17 The group of single-point techniques include: the optical fiber probe, Hot Wire Anemometry (HWA), Laser Doppler Anemometry (LDA), Phase Doppler Anemometry (PDA), electrochemical probe and Piezoelectric Vibration Sensor (PVS).18,19 The class of whole flow field techniques include: Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV).17,18 PIV has been extensively utilized to flow measurements in a single and multiphase flow systems.10,15,20,21 With novel developments of camera and laser technology, as well as PIV software, the performance of the PIV systems have been improved for difficult flow measurements.18 In addition to the instantaneous measurement of the flow, high frequency lasers and high frame rate cameras opened the possibility for a time resolved measurement of the flow.18


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The turbulence properties in a standard tank (without rotor–stator mechanism) have received remarkable attention in different investigations.13,14,19-21 Only few studies are available on turbulence characteristics at the flotation cells with rotor-stator mechanism, especially in the twophase (water and air) flow systems.2,10,12,15 The general flow pattern and velocities in a flotation cell were investigated using a PIV method.22 Dong et al. (2013) studied the single phase flow pattern of the rotor–stator mechanism of a KYF (designed by BGRIMM company) flotation cell with different impeller angles by combining PIV measurements and Computational Fluid Dynamics (CFD) simulation. Their simulation results showed that high velocity region appears near the stator blades. The PIV results were in good agreement with CFD prediction results.15 These results were used for the structural design of impellers for KYF flotation cells.2 Amini et al. (2013) measured the turbulent kinetic energy (TKE) of two- phase (water and air) flow using a Constant Temperature Anemometer (CTA) in both a 5 L and a 60 L flotation cell with rotor– stator mechanism.12 They studied the effect of the average TKE on bubble Sauter mean diameter (d32). Their results showed that d32 initially decreased by increasing TKE and become constant above a critical TKE.12 The characteristics of the single phase flow field in an industrial Wemco flotation cell were studied using CFD and PIV by Kuang et al. (2015). Their results showed that there are two vortices in the flotation cell - one vortex above the impeller and another below the impeller.10 In this study, the turbulent hydrodynamics of a two- phase (water and air) and single-phase (water) flow in a lab-scale Denver flotation cell has been studied using high speed stereoscopic particle image velocimetry (stereo-PIV) technique. The turbulence properties have been estimated using all three velocity components (i.e. the flow velocity in x, y and z directions) from the PIV measurements. The experimental results obtained at two-phase compared with



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single-phase data and discussed for gaining insight into the effect of the existence of bubbles on the flow characteristics in the cell. Experimental investigations of the two- phase flow characteristics in the mechanical flotation cells may be useful for providing further insight into the system behavior and for deeper investigating the effect of the turbulence properties on metallurgical responses of a flotation cell.

2. Materials and methods 2.1 Turbulence characteristics Typically in a turbulent flow the instantaneous velocity is divided into a time-average ( u ) and fluctuating components (u'), u = u + u ′ . Turbulent flow is characterized by fluctuating velocity, the root mean square (RMS) velocity, the turbulent kinetic energy (TKE) and the turbulence kinetic dissipation energy (TKDE). The velocity is denoted u, v and w in the x, y and z directions respectively. The RMS in each direction can be defined as follows: 23 = = ( − ) , = = ( − ̅ ) , = = ( − )

(1)

The TKE is calculated from its full definition, using the RMS of the fluid velocity in three velocity components, as follows: 23 =

1 ( + + ) 2

(2)

The turbulence dissipation rate, ɛ, is a principal variable in the flotation process and its local values may have an important effect on the performance of many processes in flotation cells. Moreover, ɛ is used to calculate sub-processes such as collision and detachment based on different models. Various approaches have been employed to estimate the turbulence dissipation rate. Some investigations have used dimensional analysis to estimate the TKED as follows: 24, 25 4 ACS Paragon Plus Environment

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ɛ=

()/ !

(3)

Where L is an integral length scale and A is a constant 0.85 for a standard cylindrical vessel. 24 The integral length scale is assumed to be constant and close to half an impeller blade width.25 However, L varies from region to region in a flotation cell. 26 The equation (3) is applicable only to flows or regions where the turbulence is homogeneous, isotropic, and in spectral; however in practice, it is rather difficult to meet these conditions. Moreover, the TKED can be estimated directly from the following definition: 27

$%́ ) $%́ $%́ ɛ = ʋ #$( ' + $( * $( ' )

'

)

(4)

Where ʋ is the kinematic viscosity and ́ + is instantaneous fluctuating velocity component in the

ith direction. Direct estimate of ɛ from this definition would require high spatial resolution.26, 27

The spatial resolution has to be smaller than Kolmogorov length scale. According to Saarenrinne et al. (2001), a spatial resolution of 2λ (where λ is Kolmogorov length scale) is required to estimate approximately 90% of the true ɛ from equation (4).

28

The spatial resolution of PIV

usually is insufficient to determine the dissipation rate directly from equation (4).19, 26, 28 With such limitations, Sheng et al. (2000) developed a large eddy simulation (LES) PIV method to estimate the TKED.26 The LES PIV method was developed based on a dynamic equilibrium assumption for the sub-grid scale flux between the spatial scale that can be resolved by PIV and the sub-grid scales (SGS).26 Thus, it is possible to calculate the global distribution of TKED over a large flow region by using the LES PIV approach. This method has been used in several studies to determine the TKED in stirred tanks by different impellers. 26, 29-33 It was reported that LES PIV approach is a useful method for calculation of the local dissipation energy. study, LES PIV method was employed to calculate the turbulent dissipation rate.


26, 29-33

In our


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In the LES method, the dissipation energy rate can be estimated by calculating the Reynolds averaged SGS dissipation rate: 26

, ≈ ,./. = −20 12 312

(5)

3+4 = # $( + $( 7 *

(6)

The sij is the resolved scale strain rate tensor that is calculated as follows: 26 5 $%6 7

%$6

The SGS stress tensor τij cannot be calculated directly and must be modelled by a SGS turbulence model.

26

Various SGS turbulence models have been employed for estimating the

stress tensor such as the Smagorinsky model,

34

gradient model,

35

similarity model

36

and

Dynamic model.26 Sheng et al. (2000) tested these models and concluded that the choice of the SGS model has no effect on the estimation of TKDE by the LES PIV method.26 They used the Smagorinsky model: 0+4 = −89 ∆ ;3+4 ;3+4

(7)

Where Cs is the Smagorinsky constant, equal to 0.17, ∆ is the filter width (or IA size) and ;3+4 ; is

the characteristic filtered strain rate, defined as >C $% $% $F $F $H $H B+ D E + D E + D E + D E + D E + D E M , = 89 ∆ B $G $I $( $I $( $G M ?B MP $% $F $% $H $F $H > > +2 JD$GE D$(E + D $I E D $( E + D$I E D $G EK =A LO

(8)

The tangential velocity can be provided by Stereo-PIV, although it does not supply information of derivatives in the out-of-plane direction.18, 19 Khan (2005) found that the cross-product term

D$GE D$(E can be very close to zero for a Pitch Blade Turbine using 2D PIV system.30 Unadkat

%$$F


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(2011), also found D E D E and D E D

%$$F

$G

$(

$F $I

$H $G

E can be negligible for a Sawtooth impeller using 3D

PIV system.33 In our study, the gradient cross product term D$GE D$(E took very close to zero. The gradient cross product term D E D $F $I

$H $G

%$$F

E evaluated from data at position 2 (see Figure 1), was

also found that can be negligible. The third cross-product term D E D

trend similar to D E D E and D E D $% $G

$F

$(

$F $I

$H $G

$% $I

$H $(

E is assumed to follow a

E terms. Consequently, a scaling factor of 12/10 was

employed to estimate the remaining squared gradients. The details of this approach have been described by Unadkat et al., (2010).19 The final relationship may be written as: R/ $% $F $H 2 #D$( E + D$GE + D $I E * 5 VW , = 89 ∆ S5T U $% $F $H $H + D$GE + D$(E + D $( E + D $G E

(9)

2.2 Flotation test This study was conducted on a 10.5 L laboratory Denver flotation cell. The cell bottom had a square shape with 200 mm by 200 mm dimensions. The impeller consisted of eight blades with a diameter of 90 mm, and the stator consisted of twelve blades with a diameter of 120 mm. The impeller speed in revolutions per minute, N, was fixed at 700, 850 and 1000 corresponding to impeller tip speed, Vtip (where Vtip=πND is the impeller tip speed), 3.30, 4.00 and 4.71 ms-1, respectively. Furthermore, off-bottom clearance was 20 mm (0.1T). Clearance is defined as the distance between the impeller and the bottom of the cell. The gas and liquid turbulent flow fields were measured at gas flow rate 0.041, 0.083 and 0.125 cm/s. The Reynolds number (Re) of the flow is calculated using the impeller diameter as characteristic length scale, XY =

Z[\ ]

, where, d

is impeller diameter in m, ^ is fluid density in kg/m3 and µ is dynamic viscosity of fluid in 7

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kg/(s.m). All the considered flows have Re equal to 107,000 and over; therefore, the flows fall under fully turbulent regime. In the two- phase system the 22.4 ppm methyl isobutyl carbinol (MIBC) was used as a frother. The PIV system (Dantec Dynamics Company, Denmark) consisted of two SpeedSense M110 CMOS cameras (1280×800 pixels) synchronized with a double cavity Nd:YAG laser (frequencydoubled laser generating laser light at a wavelength of 532 nm) that was capable of pulsing at 110 kHz with energies of 15 mJ/pulse. An optical system transformed the cylindrical laser beam into a vertical plane of 1.6 mm thick. In PIV measurements, tracer particles should be small enough to follow the flow and particle concentration should be high enough to give reliable velocity measurements.18,

37

For high quality of PIV data a particle concentration of about 15

particles per interrogation area (IA) is necessary.37 Moreover, the presence of particles in high concentration may changes the flow properties and reduces quality of PIV records.19, 30, 37 Based on these requirements the water flow was seeded with spherical fluorescent particles (Rhodamine-B) of 15 µm diameter and 1100 kg/m3density. The volume fraction of the particles was 7×10-4. These particles scattered light at a wavelength of 575 nm which is greater than the wavelength of light diffused by the air bubbles, 550 nm. The cameras were equipped with orange light filters which enables only light with a wavelength greater than 550 nm to be captured. The commercial Dynamic Studio software developed by the Dantec Dynamics Company was used to analyze the test data. The IA was set at 32×32 pixels and the cross-correlation of the image pairs was performed on a rectangular grid with 50% overlap between adjacent cells to provide a spatial resolution of 16×16 pixels. The shaft and the impeller were painted matt black to minimize light reflection. The two cameras were arranged in a Scheimpflug configuration that is the optimum configuration for accurate measurements of the out-of-plane (z) and in-plane (x and


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y) components of velocity. The measurements of local velocity by PIV were carried out at two positions that were shown in Figure 1 (positions 1 and 2 corresponding to the impeller region and in front of the stator blade, respectively). The single phase flow fields was also measured at the same conditions, for comparison purposes. The power input (P) by the impeller was calculated as follows, 38 P=

(10)

2 π TN 60

Where T is the stirring shaft torque. The stirring shaft torque was measured by using the torque sensor at unloaded and loaded (single-phase and two- phase) systems. Then the power was calculated by using Equation (10) for each condition. The effective power (Peffective) was estimated by subtracting the unloaded power from the loaded power. The mean energy dissipation rate, ,̅, was calculated as shown in Equation (11), where M is the total mass of liquid.39, 40 ε =

(11)

Peffective M

Figure 1. Schematic showing the Denver flotation cell. The green area represents measurement positions.



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In the following, the origin of the coordinate system is placed at the center of the base of the cell, and x, y and z are the axial, radial and tangential coordinates, respectively. The axial velocity, U, is positive if directed upwards, the radial velocity, V, is positive if directed towards the cell wall and the tangential velocity, W, is positive if directed towards the out-of-plane.

4. Results and discussion 4.1 Power input The gas flow rate was varied from 0.041 to 0.125 cms-1 at different Reynolds numbers in order to investigate its effect on the power consumption. Figure 2 shows the power input increased by increasing the impeller speed (based on Reynolds number). As it can be observed, the power input decreased by increasing the presence of air bubbles. These results can be due to the reduction of fluid density and the formation of air cavities behind the impeller blades.20, 41, 42

Figure 2. Power input versus the gas flow rate at different Reynolds numbers

4.2 Mean flow field 10 ACS Paragon Plus Environment

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The flow pattern at both the two-phase flow and single phase flow fields at Re of 154,000 are shown in Figure 3(a) and (b). It can be clearly seen that the flow pattern is radial-type (double loop) for both systems. This result shows that the presence of gas does not change the type of the flow pattern. Results demonstrate that the upper circulation loop for the two-phase case is slightly smaller than the ungassed case. This phenomenon could be due to the drop in the power input and forming gas cavities around the impeller upon aeration. By decreasing the power input, the rate of liquid pumped by the impeller decreased.

Figure 3. Experimental (a) single -phase and (b) two -phase (Jg=0.083 cm/s) liquid velocity vector plot at position 1, Re = 154,000

According to Figure 3, the liquid mean velocity is decreased with the presence of air bubbles. The normalized mean radial (v/Vtip), axial (u/Vtip) and tangential (w/Vtip) velocity components of ungassed and gassed systems are compared at two radial locations of 63.2 and 82.4 mm (Figure



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4). The profiles indicates a slightly lower liquid velocity at both radial locations in the two-phase system than the single phase case. Results demonstrates that the flow rate pumped by the impeller in gassed system is lower than the ungassed system. The action of impeller blades rotation applies tangential velocity component to fluid and causes shearing of flow close to the impeller blades. The drop in the power input and forming gas cavities around the impeller upon aeration, makes a significant decrease in the shear stress exerted to the fluid. Therefore, normalized tangential velocities are decreased at the both of radial locations, similar to the radial velocity measurements. The mean radial and tangential velocity components are very similar for both the single-phase and two-phase cases in the upper part of the cell. This result indicated that the mean radial and tangential velocity components is not affected by the bubbles in the upper part of the cell.


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Figure 4. Vertical profiles of the mean axial, radial, and tangential velocity components normalized in single phase and two-phase at position 1, Re = 154,000.

At radial location of 63.2 mm, the axial velocity component is positive below the impeller disc due to the upward movement of the liquid. As the liquid is moving downwards above the impeller disc, the axial velocity component is negative. At x=63.2mm, the axial velocity in the gassed system is lower than the ungassed system below the impeller disc. This phenomenon can 13 ACS Paragon Plus Environment


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be related to the force of the bubbles when they are discharged around the rotor. Due to the upward rising of bubble in the aeration system at radial location of 63.2 mm, the axial liquid velocity is lower negative than the ungassed case above the impeller disc. At x=82.4mm, the liquid is moving downwards in the part below the impeller disc and upwards in the upper region. Below the impeller level, the axial velocity is lower negative for the aerated case than the ungassed case at x=82.4 mm. This interaction may be due to the upward moving of bubbles. In the impeller discharge region, the magnitude of the axial velocity components for both the single-phase and two-phase cases are very similar. Similar results of liquid velocity profiles have been reported by a Rushton turbine (RT) impeller in a two-phase system.43-45 The gas flow rate was varied from 0.041 to 0.125 cms-1 in order to investigate its effect on the liquid phase hydrodynamics. The effects of the gas flow rate on the mean radial, axial and tangential velocity of the liquid phase at a fixed radial location x=63.2 mm can be seen in Figure 5. The radial velocity profiles are almost identical for the investigated flow rates in the impeller level, while the difference becomes noticeable in the upper part. The effects of the gas flow rate on tangential velocity are very similar to that on radial velocity. The radial and tangential velocities decreased by increasing the gas flow rate. These results can be due to the lower liquid rate pumped by the impeller for the higher gas flow rate at fixed rotational impeller speed. The axial velocity shows notable behavior by increase of gas flow rate. The axial velocity does not show considerable variation in the impeller level. Above the impeller level the lower negative velocities are associated to the higher gas flow rate conditions, whereas higher axial velocity values are achieved below the impeller for the higher gas flow rates. Therefore, when the bubbles and water move upwards, the axial velocity is increased by increasing the bubble


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concentration, while the opposite behavior is observed due to the upward rising of bubble when the flow travels downwards.

Figure 5. Influence of the gas flow rate on the mean radial, axial and tangential velocities normalized. Re = 154,000, x=62.4 mm.

4.3 RMS and Turbulent kinetic energy (TKE)



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Effect of the bubbles on the turbulence characteristics in the cell can be investigated by comparing the RMS velocities in the ungassed and gassed systems. Contour plots of the ratio of the RMS velocities in ungassed and gassed systems are shown in Figure 6. Turbulence is dampened when this ratio is higher than 1 and turbulent is reinforced in the opposite case. Results demonstrate that the radial RMS velocity is decreased around the stator in the gassed system compared to ungassed system. Figure 6 shows that the radial and tangential RMS velocities have similar distributions in the cell. The axial RMS velocities are dampened above the impeller disc, due to the upward rising of bubble when the flow travels downward. But below the impeller level, the axial RMS velocities are reinforced, because the flow and bubbles move upwards. Above the impeller disc at x>82.4mm, the axial RMS velocities in the gassed system are higher than the ungassed system. It was found that the RMS components are not equal in the impeller zone. This result indicates that the flow is anisotropic at both systems. Figure 7(a) and (b) show the spatial distribution of TKE normalized by the square of the impeller tip speed (Vtip2) in the single-phase and two-phase systems. The maximum TKE is found in the impeller discharge for both the single-phase (0.080Vtip2) and two-phase (0.068Vtip2) systems. In addition, the low levels of TKE are localized in the region far from the stator. The intensity of TKE is decreased with the existence of air bubbles in the impeller region, similar to radial and tangential RMS velocities. This result indicated that the kinetic energy of the fluid was mainly controlled with power input by the impeller in the impeller zone. Therefore, TKE of the fluid is reduced in the impeller zone due to decrease of the power input with the presence of bubbles as shown in Figure 2. In the bulk region, the TKE is increased with the presence of bubbles. It can be concluded that the bubbles can facilitate kinetic energy transfer of the fluid in regions with the low levels of TKE.


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Figure 6. Contour plots of the ratio of the RMS velocities in ungassed and gassed systems. (Re = 154,000 and Jg=0.083cms-1)



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Figure 7. Normalized TKE at Re = 154,000. (a). Single - phase flow, (b). Two - phase flow (Jg=0.083cms-1)

The TKE profiles normalized by Vtip2 at different Re in the single-phase and two-phase systems are shown in Figure 8(a) and (b). The normalized profiles are identical for all Re used (107,000– 154,000) in the single-phase flow. Montante et al.(1999) and Li et al. (2011, 2012) indicated that the normalized TKE profiles do not change by increasing the RT impeller speed in a fully turbulent system.46-48 Although, in aerated case the TKE/ Vtip2 is slightly increased by increasing Reynolds number above the impeller level. This phenomenon can be due to the increase in bubble rise speed and its effect on kinetic energy transfer.


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(a)

10

(b)

10 Re=107000 Re=130000 Re=154000 Re=107000 Re=130000 Re=154000

8 7

Re=107000 Re=130000 Re=154000 Re=107000 Re=130000 Re=154000

9

z, axial distance (cm)

9

z, axial distance (cm)

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6 5 4 3 2 1

8 7 6 5 4 3 2 1

0

0 0

0.02

0.04

0.06

0.08

0.1

0

TKE/Vtip2

0.02

0.04

0.06

0.08

TKE/Vtip2

Figure 8. Normalized TKE at different Re in (a). Single phase and (b). Two-phase (Jg=0.083cms-1) at position 1. Solid symbols: x=63.2mm; open symbols: x=82.4 mm.

4.4 Turbulence dissipation energy rate The mean Kolmogorov length scale (from the mean dissipation rate at N=1000rpm), was estimated to be around 22 µm at the both systems. The mean Kolmogorov length scale values indicate that the PIV resolution (1.6 mm) is insufficient to determine the dissipation rate directly from its fundamental definition. Moreover, the RMS velocities indicates that the flow is anisotropic at both systems. Thus, the dimensional analysis method is not applicable. Consequently, the large eddy simulation (LES) analogy of Sheng et al. (2000) was used for the calculation of ɛ, which was assumed to be the best method compared to dimensional analysis and the direct estimation. The distribution of turbulence dissipation rates normalized by the mean dissipation rate at 1000 rpm in the single-phase and two-phase systems are presented in the Figure 9(a) and (b). Results demonstrate that the maximum dissipation rate occurs very close to stator blade at x=63.2 mm.



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The high turbulent region is evident around the stator .The highest values of dissipation energy

are 39.447ε (5.480N2D3) in the single phase system and 31.36ε 1 (4.161N2D3) in the two phase

system, which are in a good agreement with those reported in the literature by a RT impeller.13,

29, 49

It should be noted that there is no reported value of ,à( /,̅ in a Denver flotation cell with

rotor- stator mechanism. The dissipation rate is very low in the bulk zone and has a magnitude of less than the mean dissipation rate. In fact, the magnitudes of ɛ are very different from region to

may provide an unreliable estimation region. Consequently, a mean energy dissipation rate (,)

for ɛ throughout the cell. The comparison of the plots indicates that the presence of bubbles

reduces the turbulence dissipation rate in the impeller region. Moreover, the dissipation rate is slightly lower for the ungassed case than the gassed case in the bulk zone.

Figure 9. Dissipation rate at Re = 154,000. (a). Single - phase flow, (b). Two - phase flow (Jg=0.083cms-1)

5. Conclusions


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The turbulent conditions of single-phase and two-phase flow in a lab-scale Denver flotation cell were studied using high speed stereoscopic Particle Image Velocimetry (stereo-PIV) technique. The effects of bubbles on the flow patterns in the cell were investigated. It was found that the flow pattern of the rotor–stator mechanism at single and two phase systems was the double-loop flow. At the both systems, the axial component of mean flow velocity was negligible close to stator at the impeller disc. Furthermore, the gas flow rate was varied from 0.041 to 0.125 cms-1 in order to study their effects on the normalized flow characteristics. The result indicated that the radial and tangential velocities decreased by increasing the gas flow rate due to the lower liquid rate pumped by the impeller for the higher gas flow rate at fixed rotational impeller speed. The axial velocity did not show much variation in the impeller level. Generally, when the bubbles and water moved upward, the axial velocity component was increased by increasing the bubble concentration, while the reverse term was observed due to the upward rising of bubble when the flow was shifted downward. The presence of bubbles decreased the radial and tangential RMS velocity around the stator, but in the upper part of the cell they would increase in the aerated system compared to when there was no bubble. The effect of bubbles on the axial RMS velocities was related to the direction of flow and bubbles movement. When the flow moved downward, the axial RMS velocities were dampened by the bubbles. However, the axial RMS velocities were increased where the flow and bubbles moved in the same direction. The RMS velocities indicated that the flow was anisotropic in the impeller region at the both systems. The turbulent kinetic energy (TKE) was calculated from its full definition, using all three velocity components. The TKE was decreased in the gassed system around the stator, similar to radial and tangential RMS velocities. The result indicated that the normalized TKE did not change with increasing Re in the single-phase flow.



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Although, in aerated case the normalized TKE slightly increased by increasing Reynolds number above the impeller level. The maximum of dissipation rate was found along impeller in single phase and two phase flow systems. It should be mentioned that the PIV experiments were done outside the stator blades and it is possible that the maximum TKDE occurred within the gap between impeller and stator, where turbulent dissipation rate could be significantly higher. The presence of bubbles reduced the turbulence dissipation rate in the impeller region. Moreover, the dissipation rate was slightly lower for the ungassed system than the gassed case in the bulk zone. The study of local dissipation energy rate and other turbulence properties may be useful for deeper investigation about the effect of the turbulence properties on the hydrodynamic characteristics and subprocesses in the mechanical flotation cells.

Acknowledgments The authors would like to thank the Tarbiat Modares University (TMU) and the Amirkabir University of Technology (AUT) for financial supports. We would also like to thank the Centre for Minerals Research (CMR) and the Crystallisation and Precipitation Unit (CPU) at the University of Cape Town for providing the Particle Image Velocimetry (PIV) system and their assistance supplied throughout the period of the test work. The authors wish to acknowledge the contribution by Jemitias Chivavava, Department of Chemical Engineering at the University of Cape Town, for his help with the PIV system.

References (1)

Shi, S.X.; Yu, Y.; Yang, W.W., and Zhou, H.X. Flow Field test and analysis of KYF flotation cell by PIV. in Applied Mechanics and Materials. Trans Tech Publ. 2013.


Page 23 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(2) (3) (4) (5) (6)

(7) (8) (9)

(10)

(11) (12) (13) (14) (15) (16) (17) (18) (19)

Shi, Sh.; Zhang, M.; Fan, X.; Chen, D. Experimental and computational analysis of the impeller angle in a flotation cell by PIV and CFD. Int. J. Miner. Process. 2015, 142, 2. Lane, G.; Schwarz, M., and Evans, G.M.; Numerical modelling of gas–liquid flow in stirred tanks. Chem. Eng. Sci. 2005, 60 , 2203. Evans, G.; Doroodchi, E.; Lane, G.; Koh, P., and Schwarz, M.; Mixing and gas dispersion in mineral flotation cells. Chem. Eng. Res. Des. 2008, 86,1350. Karimi, M.; Akdogan, G., and Bradshaw, S.; A computational fluid dynamics model for the flotation rate constant, Part I: Model development. Miner. Eng. 2014, 69, 214. Schwarz, M.P.; Koh, P.T.; Verrelli, D.I., and Feng, Y.; Sequential multi-scale modelling of mineral processing operations, with application to flotation cells. Miner. Eng. 2016, 90, 2. Koh, P.T.L.; Schwarz, M.P. CFD modelling of bubble–particle collision rates and efficiencies in a flotation cell. Miner. Eng. 2003, 16, 1055. Koh, P.T.L.; Schwarz, M.P. CFD modelling of bubble–particle attachments in flotation cells. Miner. Eng. 2006, 19, 619. Yianatos, J.B. Fluid flow and kinetic modelling in flotation related processes: columns and mechanically agitated cells — a review. Chem. Eng. Res. Des. 2007, 85, 1591. Kuang, J.; Feng, Y.; Yang, W.; Witt, P.J.; Schwarz, M.P.; Qiu, T. CFD modelling and PIV validation of flow field in a flotation cell, In: Eleventh International Conference on CFD in the Minerals and Process Industrie, 2015. Ahmed, N.; Jameson, G. The effect of bubble size on the rate of flotation of fine particles. Int. J.Miner. Process. 1985, 14, 195-. Amini, E.; Bradshaw, D.J.; Finch, J.A.; Brennan, M. Influence of turbulence kinetic energy on bubble size in different scale flotation cells. Miner. Eng. 2013, 45,146. Deglon, D.; O'connor, C.; Pandit, A. Efficacy of a spinning disc as a bubble break-up device. Chem. Eng. Sci. 1998, 53, 59. Pyke, B.; Fornasiero, D.; Ralston, J. Bubble particle heterocoagulation under turbulent conditions. J. Colloid Interface Sci. 2003, 265, 141. Dong, G.G.; Zhang, M.; Yang, L.J., and Wu, F. Analysis of flow field in the KYF flotation cell by CFD. in Applied Mechanics and Materials. Trans Tech Publ, 2013. Meng, J.; Xie, W.; Brennan, M.; Runge, K., and Bradshaw, D. Measuring turbulence in a flotation cell using the piezoelectric sensor. Miner. Eng. 2014, 66, 84. Bachalo, W. D. Experimental methods in multiphase flows. Int. J. Multiphase Flow. 1994, 20, 261. Jensen, K.D. Flow measurements, J. Braz. Soc. Mech. Sci. Eng. 2004, 26, 400. Unadkat, H. Investigation of Turbulence Modulation in Solid–Liquid Suspensions Using FPIV and Micromixing Experiments. Ph.D. Thesis. Loughborough University, Loughborough, UK, 2010.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(20)

(21)

(22)

(23) (24) (25)

(26) (27) (28) (29) (30)

(31)

(32)

(33) (34) (35) (36)

Page 24 of 26

Ranade, V.V.; Perrard, M.; Xuereb, C.; Le Sauze, N. and Bertrand, J. Influence of gas flow rate on the structure of trailing vortices of a Rushton turbine: PIV measurements and CFD simulations. Chem. Eng. Res. Des. 2001, 79, 957. Aubin, J.; Le Sauze, N.; Bertrand, J.; Fletcher, D.F. and Xuereb, C. PIV measurements of flow in an aerated tank stirred by a down-and an up-pumping axial flow impeller. Exp. Therm Fluid Sci. 2004, 28, 447. Zachos, A.; Kaiser, M., and Merzkirch, W. Particle dynamics during froth flotation of hardcoal determined by means of particle image velocimetry. in Fifth International Conference on Laser Anemometry: Advances and Applications. 1993. Nguyen, A. and Schulze, H.J., Colloidal science of flotation. Vol. 118. 2003: CRC Press. Wu, H.; Patterson, G. K. Laser-Doppler measurements of turbulent-flow parameters in a stirred mixer, Chem. Eng. Sci. 1989, 44, 2207. Jenne, M.; Reuss, M. A critical assessment on the use of k–ε turbulence models for simulation of the turbulent liquid flow induced by a Rushton-turbine in baffled stirredtank reactors. Chem. Eng. Sci. 1999, 54, 3921. Sheng, J.; Meng, H.; Fox, R.O. A large eddy PIV method for turbulence dissipation rate estimation. Chem. Eng. Sci. 2000, 55, 4423. Hinze, J., Turbulence, 2nd. 1975, Edition, McCraw Hill Book Company. Saarenrinne, P.; Piirto, M.; Eloranta, H. Experiences of turbulence measurement with PIV. Meas. Sci. Technol. 2001, 12, 1904. Sharp, K.V.; Adrian, R.J. PIV study of small-scale flow structure around a Rushton turbine. AIChE J. 2001, 47, 766. Khan, F.R. Investigation of Turbulent Flows and Instabilities in a Stirred Vessel Using Particle Image Velocimetry. Ph.D. Thesis. Loughborough University, Loughborough, UK, 2005. Gabriele, A.; Nienow, A.W.; Simmons, M.J.H. Use of angle resolved PIV to estimate local specific energy dissipation rates for up- and down-pumping pitched blade agitators in a stirred tank. Chem. Eng. Sci. 2009, 64, 126. Delafosse, A.; Marie-Laure, C.; Michel, C.; and Dominique, T. Estimation of the turbulent kinetic energy dissipation rate from 2D-PIV measurements in a vessel stirred by an axial Mixel TTP impeller. Chem. Eng. Sci., 2011, 8, 1728. Unadkat, H. PIV study of the flow field generated by a sawtooth impeller. Chem. Eng. Sci. 2011, 66, 5374. Smagorinsky, J. General Circulation experiments with the primitive equation I the basic experiment. Monthly Weather Review. 1963, 91, 99. Clark, R. A.; Ferziger, J. H.; Reynolds, W. C. Evaluation of sub grid-scale models using an accurately simulated turbulent flow. J. Fluid Mech. 1979, 91, 1. Liu, S.; Meneveau, C.; Katz, J. On the properties of similarity sub grid-scale models as deduced from measurements in a turbulence jet. J. Fluid Mech. 1994, 275, 83.


Page 25 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(37) (38) (39) (40) (41)

(42) (43) (44) (45) (46) (47) (48)

(49)

Melling, A. Tracer particles and seeding for particle image velocimetry. Meas. Sci. Technol. 1997, 8 , 1406. Gui, X.; Cheng, G.; Liu, J.; Cao, Y.; Li, S. and He, Q. Effects of energy consumption on the separation performance of fine coal flotation. Fuel Process. Technol. 2013, 115, 192. Schubert, H. On some aspects of the hydrodynamics of flotation processes. In: Forssberg, E. (Ed.), Flotation of Sulphide Minerals, 337–352, 1984. Schubert, H. On the optimization of hydrodynamics in fine particle flotation. Miner. Eng. 2008, 21, 930. Dohi, N.; Takahashi, T.; Minekawa, K., and Kawase, Y. Power consumption and solid suspension performance of large-scale impellers in gas–liquid–solid three-phase stirred tank reactors. Chem. Eng. J. 2004, 97, 103. Van der Westhuizen, A.; Deglon, D. Evaluation of solids suspension in a pilot-scale mechanical flotation cell: The critical impeller speed. Miner. Eng. 2007, 20, 233. Ranade, V.V.; Deshpande, V.R. Gas-liquid in stirred reactors: trailing vortices and gas accumulation behind impeller blades. Chem. Eng. Sci. 1999, 54, 2305. Deen, N.D.; Hjertager, B.H. Particle Image Velocimetry measurements in an aerated stirred tank. Chem. Eng. Commun. 2002, 189, 1208. Montante, G.; Paglianti, A.; Magelli, F. Experimental analysis and computational modelling of gas–liquid stirred vessels. Chem. Eng. Res. Des. 2007, 85, 647. Montante, G.; Brucato, A.; Lee, K.C.; Yianneskis, M. An experimental study of doubleto-single-loop transition in stirred vessels. Can. J. Chem. Eng. 1999, 77, 649. Li, Z.; Bao, Y., and Gao, Z. PIV experiments and large eddy simulations of single-loop flow fields in Rushton turbine stirred tanks. Chem. Eng. Sci. 2011, 66, 1219. Li, Z.; Hu, M.; Bao, Y., and Gao, Z. Particle image velocimetry experiments and large eddy simulations of merging flow characteristics in dual Rushton turbine stirred tanks. Ind. Eng. Chem. Res. 2012, 51, 2438. Zhou, G.; Kresta, S.M. Impact of tank geometry on the maximum turbulence energy dissipation rate for impellers. AIChE J. 1996, 42, 2476.



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Particle Image Velocimetry Study of the Turbulence Characteristics in

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