Exploration of hydrocyclone designs using computational fluid dynamics

84 (2007) 252–261www.elsevier.com/locate/ijminpro

Int. J. Miner. Process.

Exploration of hydrocyclone designs using computationalfluid dynamics

Jose A. Delgadillo ⁎, Raj K. Rajamani

Department of Metallurgical Engineering, University of Utah, Salt Lake City, Utah, USA

Received 9 May 2006; received in revised form 21 July 2006; accepted 26 July 2006Available online 1 September 2006

Abstract

The hydrocyclone has been widely used in the mineral industry for over hundred years, yet the standard geometry ofhydrocyclones has remained almost unchanged. The exploration of new designs is time-consuming and costly to do byexperimentation. In this paper, the computational fluid dynamics tool is used to explore alternative geometries in a way tomanipulate the hydrodynamics to achieve the desired classification. Fluent™ 6.0 was used to solve the governing equations. Thelarge-eddy simulation model was used for the turbulence closure and the Lagrangian particle-tracking method was used to predictthe particle classification. Six new geometries are explored and compared with the standard design. The mass balance and theclassification curve are the variables used to evaluate the performance of each of the novel designs.

The results show that the modification of the geometry in designs #1 and #2 did not improve the classification performance, andthey are not suitable for experimental validation. Designs #4 and #5 showed a similar performance achieved with the standarddesigns, whereas designs #3 and #6 were the most promising configurations to create a sharper particle classification. Designs #3and #6 will be excellent candidates for further experimental validation. The principal contribution of this paper is that thecomputational fluid dynamics is the right tool to study and explore novel designs of hydrocyclones.© 2006 Elsevier B.V. All rights reserved.

Keywords: Large-eddy simulation; Computational fluid dynamics; Hydrocyclone design

1. Introduction

The standard design, cone-cylinder hydrocyclonewith a single tangential inlet, shown in Fig. 1, is widelyused in the mineral processing industry. Here, the coneangle is taken as the main design variable because itproduces the upward spiraling flow (Campbell et al.,2005).

The hydrocyclone suffers from two inherent defi-ciencies. The first one is the coarse particle by-pass

⁎ Corresponding author.E-mail addresses: [email protected]

(J.A. Delgadillo), [email protected] (R.K. Rajamani).

0301-7516/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.minpro.2006.07.014

whereby coarse particles in the feed stream move alongthe boundary layer over the vortex finder and hencedirectly join the overflow stream. The second one is fineparticle by-pass. This is unavoidable in the sense thatvery fine particles do not possess sufficient drag force toresist moving with the fluid medium, in this case water.Thus, the amount of fines reporting to the underflow isnearly equal to the fraction of feed water reporting to theunderflow (Svarovsky, 1984). The only way to mini-mize the by-pass fraction is to reduce the amount ofwater passing through the underflow, which is accom-plished by increasing the centrifugal force so that theunderflow stream is highly concentrated with solids.Thus, in the design of hydrocyclone, the two by-pass

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http://dx.doi.org/10.1016/j.minpro.2006.07.014

Fig. 1. Standard hydrocyclone geometry with tangential inlet.

253J.A. Delgadillo, R.K. Rajamani / Int. J. Miner. Process. 84 (2007) 252–261

mechanisms must be minimized to realize higher per-formance efficiencies.

In a hydrocyclone, the cylindrical part gives someresidence time for the particles to experience centrifugalforce, so that coarse particles can migrate toward thewall. The cone constricts the downward flow, thus cre-ating a central spiraling upward flow. The division bet-ween upward and downward flow determines the mid-section of the classification curve. The centrifugal forcedetermines mostly the coarser side of the classificationcurve. Thus, it is possible to influence the classificationby changing the dimensions of the cylinder and thecone. It is readily apparent that by choosing narrowercone angles the cut size can be decreased. However, thischange comes at the expense of a higher pressure drop.

Higher pressure drop means greater energy spent onthe pump feeding the hydrocyclone. It would be ideal toimprove classification without unduly increasing pres-sure drop. Hence, a lot of effort is still needed to improvethe actual designs or explore novel designs to tune theperformance for a specific operation (Rietema, 1961).

Computational fluid dynamics (CFD) is a magnifi-cent tool to explore novel designs (Olson and VanOmmen, 2004; Delgadillo and Rajamani, 2005a). In thispaper, six different designs of hydrocyclones are testedwith the methodology described by Delgadillo and Ra-jamani (2005a,b). The dimensions are held nearly equalto the standard 75-mm hydrocyclone so that the CFDcomputations do not steer too far away from the appli-cable large-eddy simulation (LES) regime. LES turbu-lence closure has been proved to be successful to predict

hydrodynamics in both the 75-mm and 250-mm hydro-cyclones (Slack et al., 2000; Delgadillo and Rajamani,2005a,b). By extension, it is presumed that the fluiddynamics and turbulent transport of momentum aresimilar in the novel designs explored here.

In an effort to make the CFD tool easily accessible toanyone for hydrocyclone simulations, Slack et al. (2003)describe a custom interface for their CFD package. Infact, Slack et al. claim that such a tool would provide thecapability to develop “designer cyclones” optimized forthe specific operating conditions of a particular process.Thus, it is readily apparent that the CFD tool is mucheasier to use today than in the past.

The coarse particle by-pass and fine particle by-passare discussed in detail by Kawatra and Eisele (2005). Asan illustration of the design modification, Campbellet al. (2005) studied by experimentation the deslimingcapacity. A 100-mm hydrocyclone was compared to astandard 250-mm hydrocyclone. In each device, thevortex finder and spigot dimensions were varied toachieve the best cut size and low partition imperfection.This work is a clear illustration where CFD study iscapable of reducing the experimental work load, al-though it is not expected to make all experimentationunnecessary.

2. Model description

In the description of the fluid dynamics of the hy-drocyclone, the key component is the turbulence clo-sure model. A number of models including the κ–εmodel (Hargreves and Silvesters, 1990; Dyakowski andWilliams, 1992; Malhotra et al., 1994; He et al., 1999)and the Reynolds stress model (Lu et al., 1999; Cul-livan et al., 2004; Slack et al., 2000) have been tried inthe past. In recent years, the availability of computingpower has stepped up this analysis to three-dimensionalcomputations which avoid a few assumptions inherentto two-dimensional analysis. It appears that large-eddysimulation is a leading candidate for the description ofturbulence encountered here (Derksen and Van denAkker, 2000; Slack et al., 2000; Delgadillo and Raja-mani, 2005a). In a recent manuscript (Delgadillo andRajamani, 2005a), the present authors compared renor-malization group (RNG) κ–ε model, the Reynoldsstress model and the large-eddy simulation model, andshowed that LES leads in the description of massbalance, velocity profile, air-core dimension and evenroot-mean-square velocity prediction. In a second paper(Delgadillo and Rajamani, 2005b), it was shown thatLES predicts measured tangential and axial velocityprofiles in 75-mm and 250-mm hydrocyclones. For

254 J.A. Delgadillo, R.K. Rajamani / Int. J. Miner. Process. 84 (2007) 252–261

these reasons, LES was chosen for the CFD solutionpresented here.

2.1. Turbulence closure model

In LES, velocity profiles are resolved by a filteringoperation of the velocity field, and the smaller scalesare modeled with the eddy viscosity model. In otherwords, the eddies up to the size of the computationalmesh are solved and the eddies below the mesh sizeare modeled. Therefore, the velocity field is defined asthe sum of the filtered velocity ūi and the residualcomponent ū′,

ui ¼ ui þ ui V ð1Þ

Eq. (1) is applied to the governing Navier–Stokesequations (Pope, 2000). From this transformation, a newterm arises, containing the stress tensor of the residualmotions τij

sgs. The filtered Navier–Stokes equations aregiven in Eqs. (2) and (3).

AqAt

þ qA uiAxi

¼ 0 ð2Þ

A uiAt

þ Að ui ujÞAxj

¼ −1qA pAxi

þ A

AxjlA uiAxj

� �−Assgsij

Axjþ gi

ð3Þ

The new term that arises from the filtering operation,called the residual stress tensor, τij

sgs, is modeled as theproduct of the eddy viscosity and the strain rate (Sma-gorinsky, 1963) as shown in Eq. (4). The eddy viscosityis resolved using the RNG model. The RNG model isvery effective to model the transitional flows and near-wall regions where the molecular viscosity has moresignificance (Yakhot et al., 1989).

ssgsij ¼ −ltA uiAxj

þ A ujAxi

� �ð4Þ

The turbulent viscosity μt is defined as the effectiveturbulent viscosity μs or molecular viscosity μ as shownhere:

lt ¼ l 1þ Hl2sleffl3

−100� �� 1=3

−l ð5Þ

where the effective viscosity, μeff, is defined as,μeff=μ[1+H(x)]

1/3 and H(x) is the Heaviside function,

defined asH(x)=x for x≥0 and 0 for x≤0. The turbulentviscosity, μs, depends on the strain rate defined as:

ls ¼ CRNGV1=3

� �2ffiffiffiffiffiffiffiffiffiffiffiffiffi2 Sij Sij

qð6Þ

In Eq. (6), V is the volume of the computational celland S ij is the filtered strain rate. A typical value of theconstant CRNG is 0.157 (Yakhot et al., 1989).

2.2. Multiphase model

The tangential acceleration applied to the flowcreates a high centrifugal force that pushes the fluid tothe wall, creating a low pressure in the central axis. Thelow pressure in the core of the hydrocyclone gives theright conditions to suck air into the system, forming anair-core. The interface is modeled with the volume-of-fluid model (VOF). The VOF model, whose modelequations are shown below, tracks the location of suchan interface at every time step.

AapAt

þ apAuiAxi

¼ 0 ð7Þ

AðquiÞAt

þ AðquiujÞAxj

¼ −ApAxi

þ A

Axjl

AuiAxj

þ AuTiAxj

� ��

þ qgi ð8Þ

Based on the local value of volume fraction αp,which ranges from 0 to 1. In the air-core region, thevolume fraction αp is nearly zero.

2.3. Particle classification

The additional model used in the hydrocycloneproblem is the particle trajectory prediction. Particles areclassified due to the drag force and diffusion of particlesdue to the fluid turbulence. The trajectory of particles iscomputed by Lagrangian tracking of particles upon theEulerian continuous-phase predictions. The balancebetween the drag, gravity, buoyancy and centrifugalforces, shown in Eq. (9), determines the trajectory of theparticles in the continuous phase (Haider and Leven-spiel, 1989).

dupdt

¼ FD u−up þ gxðqp−qÞ

qpð9Þ


where

FD ¼ 18lqpd2p

CDRe24

ð10Þ

Re ¼ qdpjup−ujl

ð11Þ

where up is the particle velocity, u is the fluid velocity, ρis the fluid density, ρp is the density of the particle, FD isthe drag force, dp is the particle diameter and CD is thedrag coefficient.

3. Description of novel designs

The aim of this computational study is to optimize theclassification performance through the modification ofthe standard geometry shown in Fig. 1. The standardgeometry adopted by Hsieh and Rajamani (1988) wasused as a reference to compare the performance of noveldesigns. The experiment chosen for comparison was the75-mm hydrocyclone for which the flow rate of water inthe inlet was 1.2 kg/s and the solid concentration was4.8% by wt. Six novel designs are presented in this paper.

3.1. Novel design #1: modification of the cylinder in thestandard hydrocyclone

Design #1, shown in Fig. 2(a), is a modification ofthe standard cylindrical section. The cylinder flares outfrom the top and then contracts back. This modificationis proposed to reduce the by-pass of coarse particlesthrough the vortex finder. The coarse particles have atendency to reach the vortex finder wall directly fromthe feed inlet. Then, they travel downward along thevortex finder wall and are caught in the upward flowthrough the vortex finder. Thus, coarse particles take ashorter path to the overflow. The expectation is that thewidening cylinder would distance the coarse particlesfrom the vortex finder. The dimensions are nearlyidentical to the standard geometry of the 75-mmdiameter hydrocyclone.

3.2. Novel design #2: change on vortex finder length

The geometry for design #2 is shown in Fig. 2(b).This design is a slight modification of design #1. Thevortex finder length was reduced from 50 mm to37.5 mm. This modification creates an increase in thetangential velocity at the top section. Hence, particlesentering the hydrocyclone are immediately classified.

The expected result is an improvement in the classifi-cation process.

3.3. Novel design #3: two-cone design

The logic behind design #3 is to create the oppositeeffect created in designs #1 and #2. Design #3 is anexploration of the cone-angle effect on the classificationprocess. The cylindrical section is replaced with atapered cone of angle 30° (Rong and Napier-Munn,2003). This modification changes the flow field and theclassification process, creating a smooth classificationand probably creating a lower turbulence in the fluid.The reduction of fluid turbulence improves the classi-fication efficiency. The angle of the lower cone was keptto 20°. The geometry and dimensions proposed fordesign #3 are shown in Fig. 2(c).

3.4. Novel design #4: modification of cone angle

The double-cone configuration used in design #3depends on the combination of cone angles. Design #4,shown in Fig. 2(d), is an improvement of design #3 andan exploration of the cone-angle effect on the classifi-cation process. The angle of the cone tip was changedfrom 30° to 20° so that the main body is made up of asingle cone. In this design there are no abrupt changes inthe outer walls, and hence the velocity field transitionssmoothly. The velocity field directly affects the clas-sification efficiency. The angle of the lower cone waskept constant at 20°.

3.5. Novel design #5: modification of the conical section

The standard geometry was modified in the cylin-drical and conical sections of design #5. The cylinderlength was reduced from 75 mm to 50 mm. Next, a coneangle of 30° was placed followed by a second cone of10° angle. Here, the configurations of design #3 and thestandard geometry are mixed to form a unique design.The dimensions and geometry are shown in Fig. 2(e).This modification will create a more aggressive clas-sification process, and also the residence time will in-crease enormously.

3.6. Novel design #6: change of cone angles

Novel design #6, shown in Fig. 2(f), is a modificationof design #5. Here, the angles of the two cones werechanged from 30° and 10° to 20° and 6°, respectively.The angle change is expected to produce a sharp classi-fication process and an increase in the residence time.


4. Computer simulations

The flow problems for the novel designs were solvedusing three-dimensional unstructured meshes. Thecomputations were run until a steady state was reached.

Fig. 2. Dimensions for

The residuals for momentum, velocity components andflow rate at the outlet streams were monitored for con-vergence. Fluent™ 6.0 code was used to perform thesimulations with the large-eddy simulation model asturbulence closure.

six new designs.

Table 1Cumulative size distributions for the standard design

Size (μm) Feed (%) Overflow (%) Underflow (%)

42.2 100 100 10035.3 88 99.2 67.925.1 70.3 94.9 31.917.7 50.5 74.3 1312.6 37.5 56.4 7.48.9 28.4 43 5.26.3 19.6 29.9 3.34.4 12.8 19.7 1.93.1 8.7 13.4 1.12.1 5.6 8.7 0.81.3 2.8 4.3 0.40.8 1 1.5 0.20.5 0 0 0


Steady state was achieved after 1000 iterations, atwhich time the residuals and flow rates were constant.After the steady state was reached, a real time of 1 s wassimulated with time steps of 0.0005 s. An average ofover 1000 time steps were taken to record the velocityprofiles, mass balance and flow rates. A sample of 1560particles in each size fraction was injected at the inletand tracked down the flow until each particle leftthrough the outlets. The slurry used is one of 4.8% by wtof limestone ore (density 2700 kg/m3) with a particlesize distribution shown in Table 1. From the particletrajectory the cumulative distributions were computedas the split ratio for each size class. The low solidcontent chosen here is in the very dilute flow regime.This regime is devoid of interparticle interactions andviscosity effects. Hence the simulations reveal totallythe effect of the shapes of the cylinder and cone.

The mass balance is primary in the analysis of thehydrocyclone performance. In the exploration of noveldesigns, these values determine the improvement of theprocess. The mass balance was computed from theparticle trajectory for each size fraction. The split ratioof each size fraction was calculated by sampling theoverflow and underflow streams. With the feed sizedistribution and solid split ratio, the size distributions of

Table 2Computed mass balance, pressure drop and air-core diameter for the six des

Design

Standard #1

Split ratio to underflow, water (%) 4.46 18.66Split ratio to underflow, solids (%) 39.34 27.77Pressure drop (kPa) 39.70 29.07Air-core diameter (mm) 11.0 8.0Inlet pressure (kPa) 141.0 130.4

overflow and underflow were calculated. The mass ba-lance results are shown in Table 2.

The air-core is another part of the performance eva-luation. The prediction of the air-core profile is funda-mental to the description of the flow dynamics. Thetangential velocity pushes the water to the wall, creatingthe air-core. Hence, a reduction in the tangential velocityreduces the diameter of the air-core (Williams et al.,1994).

4.1. Results for design #1

A reduction in pressure drop of 36% was achievedwith design #1. The pressure drop is closely related tothe distribution of the centrifugal force. The reduction oftangential velocity results in an increase in the by-passof coarse and fine particles in the overflow. This reduc-tion is reflected in the modification of the water split.The water rate to the underflow increases by 76%,which creates more by-pass of fine particles. The massbalance shows that this new design is not much betterthan the standard design.

The hydrocyclone efficiency is reflected by the clas-sification curve, which is defined as the percentage ofcoarse particles reporting to the underflow stream. Thepredicted classification curve is compared with thestandard design in Fig. 3. The modification in the geo-metry did not improve the classification performance.The by-pass of fine and coarse particles increases. Thisdesign will not be useful for further experimental vali-dation. The weak point in design #1 is the lower tan-gential velocity in the vortex finder region due to theexpansion of the cylinder. The weaker tangential velo-city field reduces the upward spiraling stream, andhence the increase in underflow by-pass results.


The reduction in the vortex finder length in design #2creates a change in the water split ratio. The flow rate tothe underflow is reduced from 18.7% to 9.6%. This

igns

#2 #3 #4 #5 #6

9.55 7.41 4.64 11.61 13.5748.21 53.92 33.27 42.39 44.1330.11 59.64 40.09 37.63 27.039.0 10.0 10.0 11.0 8.4

131.4 161.0 141.4 138.9 128.3

Fig. 3. Design #1: Size classification compared with standard design at4.8% wt slurry and inlet flow rate of 1.12 l/s.


decrease in the flow rate is a signal that the velocityprofiles have changed. Furthermore, the reduction ofwater reporting to the underflow reduces the by-pass offine particles. The modification of the vortex finderlength improves the performance of this design.

The computed air-core profile is expected to besmaller than the standard air-core diameter. The reduc-tion in the tangential velocity reduces the centrifugalforce needed to maintain a larger diameter. The air-corediameter for design #2 is 2 mm less in diameter than inthe standard mean hydrocyclone.

The modification of the cylindrical section is thefocus of this effort because most of the by-pass occurs inthis region of the hydrocyclone body. The classificationcurve is shown in Fig. 4. The increase in the tangentialvelocity leads to a better classification. The by-pass ofcoarse particles is reduced. There is a slight improve-ment over the standard design. Design #2 exhibits someimprovement in the size classification, but it is not anoverall improvement in the classification process. There-


fore, with these simulation results, it can be concludedthat there is no more room for improving the flared-cylinder design.


The conical design of design #3 increases the pres-sure drop compared to the standard design. The waterreporting to the underflow in this design is 7.4%, com-pared to the 4.5% in the standard design. The by-pass offines is very closely related to the amount of water in theunderflow. The computed conditions show that the by-pass of solids increases in the underflow. The rise in thepressure drop can lead to a better classification process,particularly in the coarse sizes, which are driven to thewall at higher centrifugal forces.

The tangential velocity profile at 120 mm from thetop wall is compared with the velocity profiles of thestandard design in Fig. 5. The increase in the tangentialvelocity creates the centrifugal force needed to classifythe coarse particles and remove medium size particlesfrom the overflow stream. The analysis of the flow fieldshow that this profile will lead to a better classificationprocess with a finer cut size and a reduction of the by-pass of coarse particles.

Fig. 6 shows the classification curve compared withthe standard design values. There is a small increment inthe by-pass of the very fine sizes, but the classificationof coarse particles is greatly improved. The overallclassification process has been improved with the noveldesign. However, it should be noted that the pressuredrop increased by 50% over the standard design, whichmeans more energy per unit mass of slurry is spent onthis design. The fine cut size allows a better classifica-tion for mineral-processing circuits with low mineral-liberation sizes.

Fig. 5. Design #3: Tangential velocity predictions at 120 mm from thetop.





The pressure drop for design #4 is very similar to thepressure drop for the standard design. The reduction inthe pressure drop is attributed to the straight cone designfrom the tip to the bottom, which reduces turbulencetransitions due to contracting walls. The flow rate re-mains very similar to the standard design values in allthe streams with a small change in the solid concentra-tion at the underflow. The change in the mass balanceshows that top cone has very little effect on the clas-sification process.

The computed classification curve, shown in Fig. 7,is very similar compared with the classification curvefor the standard design. There is a slight increase incoarse particle by-pass. This by-pass can be attributed tothe lack of a high tangential velocity field. Hence,design #4 is not an improvement of the classificationprocess. It should be noted that this design required thesame pressure drop as the standard design, yet it pro-duces slightly inferior size classification.



Predicted operational conditions for design #5 arevery similar to those for the standard design operation.The main difference is the split to the underflow. Theincrease in the water flow rate in the underflow increasesby-pass of fine particles. The pressure drop shows asmall reduction, which results in the increase of coarseparticle by-pass.

Fig. 8 shows the classification curve that predictedfor design #5 and the standard design. The classificationcurves are very similar. The only difference is the in-crease of fine particles to the underflow. This newdesign performs very similarly to the standard design.The combination of different cone angles could make adifference in the classification process.


A reduction of the pressure drop in design #6 wasexpected due to the reduction of diameter in the lower



cone. This characteristic is an advantage because moreslurry can be processed at the same pressure drop as inthe standard design. The increase in water reporting tothe underflow is also due to the pressure drop. If theflow rate at the inlet is increased, the amount waterreporting to the underflow is reduced. The air-core dia-meter was reduced because the fluid is not moving asfast as in the standard design.

The predicted classification curve, shown in Fig. 9,shows that the slope of the classification curve is steeperthan that for the standard design. Since the pressure dropis lower, the flow rate to this design can be increased atthe same level of pumping energy. Thus, when thepressure drop is increased, one expects more improve-ment in size classification. This design is a real improve-ment in the classification process, and can be furtheroptimized by focusing on the combination of differentcone angles and inlet flow rate. In particular, the locationof the second cone would influence this design greatly.

5. Conclusions

The optimization of the classification performancethrough the modification of the standard geometry iseasily achieved with the CFD methodology shown here.The modification in the geometry in designs #1 and #2did not improve the classification performance. The by-pass of fine and coarse particles increases. These designswill not be useful for further experimental validation.The weak point in these designs is the lower tangentialvelocity in the vortex finder region.

With the modifications in designs #3 and #4, there isa small increase in the by-pass of the very fine sizes, butthe classification of coarse particles is greatly improved.The overall classification process was improved in thesetwo novel designs. However, it should be noted that thepressure drop increased over the standard design, whichmeans more energy per unit mass of slurry is spent withthis design. The fine cut size allows a better classifica-tion for mineral-processing circuits with low mineralliberation sizes.

In designs #5 and #6, the classification curves showthat even with a lesser tangential velocity field a slightlybetter efficiency was achieved. The slope of the classifi-cation curve is steeper than that of the standard classifi-cation curve. Since the computed pressure drop is lower,the flow rate can be increased to match the pressure dropof the standard hydrocyclone. Thus, when the pressuredrop is increased, one expects more improvement in sizeclassification.

The design of new geometries opens a new chapter inthe hydrocyclone optimization. It is possible to evaluate

changes in the standard geometry to manipulate thedynamics achieving the desired classification. The pro-posed designs showed that a double cone is the solutionto improve classification. Designs #3 and #6 are prom-ising configurations to create a sharper particle classi-fication. These designs must be tested in experimentalwork. The principal contribution of this paper is thatCFD is the right tool to study and explore the fluiddynamics of novel designs of hydrocyclones.

NomenclatureCD Drag coefficientdp Particle diameter (m)FD Drag force (N)gi Gravitational force component (m/s)H(x) Heaviside functionp Pressure (Pa)Re Reynolds numberSij Strain rate (m2/s)t Time (s)ui Velocity component (m/s)ū Filtered velocity (m/s)ū′ Subgrid-scale velocity (m/s)up Particle velocity (m/s)V Volume cell (m3)xi Dimensional component (m)αp Volume fractionμ Molecular viscosity (P)μeff Effective viscosity (P)μs Subgrid scale viscosity (P)μt Turbulent viscosity (P)ρ Density (kg/m3)τijsgs Subgrid stress tensor (Pa)

Acknowledgements

The authors would like to thank the National Councilfor Science and Technology (CONACyT), Mexico forsupport of this work.

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Exploration of hydrocyclone designs using computational fluid dynamics

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