computational and experimental study of the effect of

Research ArticleComputational and Experimental Study of the Effect ofOperating Parameters on Classification Performance ofCompound Hydrocyclone

Jin Jiang1 Rui Ying 1 Jingan Feng2 andWeibingWang2

1Key Lab of Hydraulic Machinery Transient MOE Wuhan University Wuhan 430072 China2College of Mechanical amp Electrical Engineering Shihezi University Shihezi 832003 China

Correspondence should be addressed to Rui Ying yrfhtd126com

Received 3 January 2018 Revised 3 March 2018 Accepted 15 March 2018 Published 29 April 2018

Academic Editor Xesus Nogueira

Copyright copy 2018 Jin Jiang et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Compound hydrocyclone is a kind of dynamic hydrocyclone also with the advantages of static hydrocyclone In this investigationthe effect of operating parameters on separation performance of compound hydrocyclone is studied using both CFD technique andexperimental method The flow field of compound hydrocyclone was simulated by the RSM turbulence model the particles withdifferent size were simplified to 6 phases and simulated by themixturemultiphasemodelThe central composite designmethodwasused to conduct the separation experiment of compound hydrocyclone The results indicated that compound hydrocyclone can beused for finer particles separation and the flow field of compound hydrocyclone can still achieve a higher centrifugal force in lowerinlet velocity When the minimum partition size is required the optimized operating condition of the compound hydrocyclone isk = 25ms n = 1865 rpm and c = 75 while when the maximum partition size is required the optimized operating condition isk = 25ms n = 905 rpm and c = 245

1 Introduction

Hydrocyclones are widely used for particle separation andclassification in chemical mineral and power industriesmainly due to their simple structure high capacity lowoperating and maintenance and small space occupation Fornormal static hydrocyclones there are still many problemsand limitations [1] such that (1) the kinetic energy of the flowfield is converted by pressure thus a higher inlet pressureis required to ensure the centrifugal intensity of the flowfield (2) the short-circuit flow in flow field can result inthe overflow with more coarse particles which seriouslyimpact the separation accuracy (3) for differentmaterials andrequirements the application scope of static hydrocyclone islimited A great number of improvements on static hydro-cyclone have been proposed and the corresponding researchworks have been carried out by the investigators Boadway [2]has improved the vortex finder pipe to a gradual expansionpipe so that the discharge ability of vortex finder pipe was

enhanced and the energy consumption was reduced by 20Larsson [3] has proposed the 3D spiral inlet This inlet struc-ture can effectively reduce the turbulence andfluctuationnearthe inlet region of hydrocyclone Chu et al [4] have inventedthe hydrocyclone which is the vortex finder pipe with annularteeth This improvement can effectively restrain the short-circuit flow and improve the separation accuracy Evans etal [5] and Sripriya et al [6] have designed a hydrocyclonewith insertion solid rod to eliminate the air core The solidrod can greatly reduce the kinetic energy dissipation andstabilizing the flow field Ghodrat et al [7 8] proposeda hydrocyclone with convex conical section Compared tothe conventional design the new hydrocyclone has largerseparation region and smaller pressure drop Ghodrat et al[7 8] also analyzed the performance of hydrocyclone withdifferent vortex finder and a compromised optimum con-figuration has been proposed The structure improvementsof hydrocyclones can reduce the energy consumption of theflow field to a certain extent and improve the efficiency

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 7596490 16 pageshttpsdoiorg10115520187596490

2 Mathematical Problems in Engineering

But these improvements have failed to break through thelimitations which are the hydrocyclone without energy inputwhile the dynamic hydrocyclone is a good solution to thisproblem Compared to the conventional static hydrocyclonethe dynamic hydrocyclone can also get a higher separationefficiency and a variable capacity

Compound hydrocyclone is a new form of dynamichydrocyclones which has structure characteristics of thenormal static hydrocyclone Because of the acceleration effectof rotating blades higher separation efficiency can still beobtained in compound hydrocyclone at lower inlet pressureLiu et al [9] carried out a test research on oil-water separationof compound hydrocyclone They found that higher rotatingspeed will result in seriously emulsification of oil phaseJiang et al [10] experimentally optimized the rotating bladestructure of deoiling compound hydrocyclone and raised theseparation performance They suggested that the advantagesof compound hydrocyclone in terms of flow field energyconsumption separation efficiency and application scopeare that the static hydrocyclone cannot be achieved Wang[11] investigated the influence of geometric and operationparameters of compound hydrocyclone to deoiling perfor-mance and suggested that appropriate rotating speed rangesfrom 1700 rpm to 2400 rpm Li et al [12] investigated theeffect of vibration behavior on the flow field and separationperformance They found that the flow rate and the electricmotor running not only cause the vibration but also affectthe separation accuracy Liu et al [13] investigated the radialpressure distribution of compound hydrocyclone flow fieldand determined the general equation of the unit productionability of compound hydrocyclones Ying et al [14] madean experimental prototype of compound hydrocyclone forparticle separation of which experimental result indicatedthat the compound hydrocyclone has a good performance forfiner particle separation So far the compound hydrocycloneismainly used for oil-water separation in petroleum industrywhile the investigation of the compound hydrocyclonesapplied in the field of particle separation are relatively fewIn this investigation the effect of operating condition oncompound hydrocyclone performance is studied using bothCFD technique and experimental method The compoundhydrocyclone with different operating parameters was sim-ulated by RSM turbulence model and the particle phase inthe flow field is simulated by mixture multiphase model Thecentral composite designwas used for the experiment and themathematical models of evaluation indexes were establishedby nonlinear regression method

2 Experimental Aspects

21 Experimental Equipment The internal structure of com-pound hydrocyclone is displayed in Figure 1(a) It can beseen that a driving device (rotation blade) is installed in thecompound hydrocyclone which is the main difference withstatic hydrocyclone The shaft of rotation blade is attached toan electricmotor so that the fluid in compoundhydrocyclonecan be accelerated Meanwhile the shaft of rotation blade isalso used as the vortex finder pipe of hydrocyclone so that thefluid can flow into the overflow chamber through the shaft

Table 1 Structure parameters of hydrocyclone

Parameters Symbols ValueInlet diameter Di 14mmVortex finder diameter Do 20mmApex diameter Du 10mmCylindrical diameter D 75mmRotating blade diameter d 65mmCylindrical length L 40mmRotating blade length l 55mmCone angle 120579 6∘

In this investigation the experimental system is a circu-lation loop mainly composed of water tank slurry pumpand compound hydrocyclone The details of experimentalsystem can be seen from Figures 1(c) and 1(d) A branchpipe is set before the inlet of compound hydrocyclone suchthat the inlet velocity can be regulated by changing the valveopening of branch pipe Electromagnetic flowmeters (EMF)and pressure gauges are installed on the inlet pipe and theoverflow pipe so that the data of flow rate and pressure canbe collected Rotating speed of electric motor is regulated bythe variable-frequency drive (VFD) and the value of rotatingspeed is measured by a laser tachometer In order to makethe liquid and solid in the water tank mix evenly a mixingmachine is installed above the water tank

Structure parameters of compound hydrocyclone usedin this investigation were determined in the literature [14]Details of structure parameters can be seen from Table 1and the symbols of structure parameters can be seen fromFigure 1(b) The main body of compound hydrocyclone ismade of wear-resistant polyurethane The rotating blade ismade of nylon and blades number is six Solid particlesused in this experiment are Ca(OH)2 particles which areslightly soluble in water (165 gL) and the vacuum densityof particles is 2234 kgm3 Before mixture preparation fewCa(OH)2 particles should be added to water to make theliquid saturated Particle size is normal distribution andranges from 6sim498 120583m (measured after mixing with water)The distribution of particle size is presented in Figure 2

22 Operating Parameters and Indexes Operating parame-ters are themain factors that affect the classification and sepa-ration performance of hydrocyclone including temperaturesolid density particle size distribution inlet velocity feedconcentration and setting angle [15] The previous studiesof static hydrocyclone show that inlet velocity and feedconcentration (in mass) are the two most influential factorstherefore the effect of these two parameters on compoundhydrocyclone needs to be considered in this paper On theother hand rotating blade is the important component ofcompound hydrocyclone and has a great influence on theflow field Thus the effect of rotating speed also needs to beconsidered

In order to reflect the effects of the operating condi-tions on the performance of compound hydrocyclone three

Mathematical Problems in Engineering 3

(1)

(2)

(3)

(4)

(5)

(6)(7)

(a)

Du

Do L

l

Di

D

d

휽

(b)

(1)

(2)

(3)(4)

(5)

(6)

(7)

(8)(9)

(10)(11)

(12)

M

M VFD

EMFEMF

PP

(c) (d)

Figure 1 Experimental device and system (a) Internal structure view of compound hydrocyclone ((1) inlet pipe (2) vertex finder pipe (3)apex pipe (4) rotating blade (5) overflow outlet (6) holes (7) overflow chamber) (b) The symbols of structure parameters (c) Diagramof experimental system ((1) slurry pump (2) split-flow valve (3) and (7) electromagnetic flowmeter (4) and (6) pressure gauge (5)compound hydrocyclone (8) water tank (9)mixing machine (10) variable-frequency drive (11) electric motor (12) laser tachometer) (d)The photo of experimental system

1 5 10 25 50 100 250 500

Particle Size (휇m)

0

10

20

30

40

50

60

70

80

90

100

Pass

ing

()

0

1

2

3

4

5

6

7

8

9

10

Chan

nel (

)

Figure 2 Distribution of particle size

evaluation indexes were selected according to the literature[16] the indexes are as follows

(a) Partition size (D50 the particle size which has 50grade efficiency) this is an important index to eval-uate the classification and separation performance ofcompound hydrocyclone This index was calculatedfrom the particle distribution of overflow and the par-ticle distribution was measured by the Laser ParticleSize Analyzer

(b) Split ratio (S the ratio of volume flow of overflow tovolume flow of inlet) this index directly reflects the

situation of flow distribution of compound hydrocy-clone

(c) Total efficiency (E the ratio of particle mass in theunderflow to the inlet) this is an important indexto evaluate the production capacity and efficiency ofcompound hydrocyclone

23 Experimental Method Central composite design is astatistical mathematical method widely used in engineeringproblem analysis and modeling It can be used for thenonlinear evaluation of between operating parameters andindexes and then operating conditions can be optimizedby the response surface [17] In this paper the classificationexperiment of compound hydrocyclone was carried out bycentral composite designmethodThemathematical relation-ship between operating parameters and evaluation indexeswas modeled by multivariate nonlinear regression analysisBased on the mathematical models the effect of operatingparameters and their interactions on the indexes can beanalyzed

The experiment scheme was designed by the commer-cial software Design-Expert According to the experimentalrequirements fifteen groups of the experiments should becarried out at least and the experiment matrix is comprisedof 4 factorial points 6 axial points and 5 center points Forthis compound hydrocyclone the inlet velocity range is from05 to 25ms the rotating speed range is 450 to 2950 rpmthe feed concentration (in mass) range is 75 to 245 Eachexperimental factor was set to five levels and the details arepresented in Table 2


Table 2 List of factors and different levels

Number Factors LevelsMin (minus168) Low (minus1) Center (0) High (+1) Max (+168)

1 Inlet velocity ms (k) 05 08 15 22 252 Rotating speed rpm (n) 450 800 1700 2600 29503 Feed concentration (c) 75 10 16 22 245

3 Numerical Simulation Method

31 Numerical Model With the development of com-puter technology the computational fluid dynamics (CFD)approach is widely used in the investigation of the flowfield in hydrocyclone and the accurate predictions can beobtained In this investigation the mixture model is adoptedto simulate the solid-liquid multiphase flow in compoundhydrocyclone Mixture model is a simplified TFM modelwhich allows the interpenetrating and the relative slidingbetween solid phase and liquid phase [18] This multiphasemodel is applicable to simulating the flow flied with anextensive particle distribution The equations of continuityand momentum for mixture model as follows

120597120588119898120597119905 + 120597 (120588119898119906119898119894)120597119909119894 = 0 (1)

120597 (120588119898119906119898119894)120597119905 + 120597 (120588119898119906119898119894119906119898119895)120597119909119895= minus 120597119875120597119909119894 +

120597119875119904120597119909119894 +120597120591119898119894119895120597119909119895 +

120597 (minus12058811989811990610158401198981198941199061015840119898119895)120597119909119895

+ 120597120597119909119895 (119899sum119896=1

120588119896119906dr119896119894119906dr119896119895) + 119892120588119898

(2)

where 120588119898 119906119898 120583119898 and 119875119904 represent the density velocity andviscosity of the mixture and the pressure of total solid phaserespectively

In (2) the viscous stress of mixture 120591119898 and the driftvelocity of the 119896th phase 119906dr119896 are respectively given by

120591119898119894119895 = 120583119898 (120597119906119898119895120597119909119894 +120597119906119898119894120597119909119895 )

119906dr119896119894 = (120588119896 minus 120588119898) 119889211989618120583119908119891 119886119896119894 minus 41205781199053 (nabla120572119896120572119896 minus

nabla120572119908120572119908 )minus 119899sum119896=1

(120572119896120588119896119906119908119896119894120588119898 ) (3)

where 120583119908 120572119908 represent the viscosity and volume fraction ofthe primary phase (water) 120588119896 120572119896 119889119896 and 119886119896 represent thedensity volume fraction diameter and acceleration of phasek 119906119908119896119894 is the velocity of water phase relative to the velocity ofphase k 120578119905 is the turbulent diffusivity

When the volume fraction of solid phase is under 08 thedrag force onparticles119891 is determined byErgun [19] andWenand Yu [20] given by following equation

119891 = 11986211986324120583119908120572minus165119908 120588119908119889119896 1003816100381610038161003816119906119908 minus 1199061198961003816100381610038161003816 (4)

In previous studies of hydrocyclone Reynolds stressmodel (RSM) and large eddy simulation (LES) are widelyused in the turbulence simulation of hydrocyclone [21] ForLES method a sufficient number of boundary layer gridsneeds to be meshed to ensure the 119884+ le 1 in the near wallarea which is the necessary condition for LES [22] Howeverthe LES needs a large number of meshes to produce validresults More importantly in Fluent software the mixturemodel cannot be adopted for LES simulation [23]

In this investigation the turbulence flow in compoundhydrocyclone is modeled by RSM model thus the stressterm minus12058811990610158401198941199061015840119895 in (2) is closed by the Reynolds stress transportequation in

120597 (12058811990610158401198941199061015840119895)120597119905 + 120597 (12058811990611989611990610158401198941199061015840119895)120597119909119896= 119863119879119894119895 + 119866119894119895 + 120601119894119895 minus 120576119894119895 + 119875119894119895

(5)

where 119863119879119894119895 119866119894119895 120601119894119895 120576119894119895 and 119875119894119895 respectively represent theturbulent diffusion term the buoyancy production termthe pressure strain term the dissipation term and stressproduction term

32 Meshing and Boundary Conditions In this study thecommercial softwareGAMBITwas used formeshing the flowfield model of compound hydrocyclone The computationaldomain of compound hydrocyclone consists of the ldquostablezonerdquo and the ldquodynamic zonerdquo where the rotation bladesare located as shown in Figure 3 Block-structured gridgeneration method was applied to mesh the computationaldomain and the grids near the central region were refinedto capture the evolution of pressure and velocity gradientin addition the grid size of the conical part was graduallyreduced in a certain ratio which can avoid a larger residual ofcontinuity equation caused by higher grids aspect ratio Sincethe grid nodes of dynamic and stable zone cannot bematchedthese two zones were connected by ldquointerface boundaryrdquo

The quality and number of CFD meshes are very impor-tant for obtaining meaningful numerical results Thereforethe entire flow field of compound hydrocyclone was dis-cretized by hexahedral grids so that the grid quality canget a higher level Meanwhile the grid-independent test was


Dynamic region Pressure-outlet

Velocity-inlet

Cylindrical section

Conical section

Pressure-outlet

Figure 3 Mesh representation of compound hydrocyclone

performed by gradually decreasing the grid size which canexclude the impact of grids number on simulation resultsTaking into account the length of calculation time thenumber of grids was eventually set to 15 million

33 Simulation Strategy The simulation model in this workwas developed by Kuang et al [18] A two-step work wasconducted in this simulation In step 1 only air and waterwere considered the turbulent flow in compound hydrocy-clone was modeled by RSMmodel and the interface betweenwater and air core was modeled by Volume of Fluid (VOF)model The primary air core shape and velocity distributioncan be gained in this step In step 2 the simulation startswith the results from step 1 and the multiphase model waschanged fromVOF tomixture so that the liquid-particle flowin compoundhydrocyclone can be simulatedThis simulationmodel has already been proved to be valid for hydrocyclone[18 24]

In the setting of boundary conditions the ldquovelocity inletrdquowas used for hydrocyclonersquos inlet and the inlet velocity was05 15 and 25ms respectively the ldquopressure outletrdquo wasused for hydrocyclonersquos overflow and underflow and thepressure at the two outlets was 1 atm (standard atmosphericpressure) the ldquoMoving meshrdquo model was used to simulatethe rotation of dynamic zone and the rotating speed was450 1700 and 2950 rpm respectively the inlet speed ofsolid phase is the same as that of liquid phase and theconcentration of solid phase was 75 16 and 245respectively In order to ensure the numerical stability thenumber of solid phase sizes was simplified to 6 types (1025 50 100 150 and 250120583m the proportion is 25 15 22 1214 and 12 resp) In the setting of solution controls theSIMPLE-Consistent (SIMPLEC) algorithm was used for the

AB

Figure 4 Two representative positions

pressure-velocity coupling the PRESTO scheme was takenfor spatial discretization of the pressure term the quadraticupwind interpolation (QUICK) scheme was taken for spatialdiscretization of the advection terms The convergence strat-egy uses the unsteady solver and the time step is 10minus3 s

4 Results and Discussion

For better describing the effect of each operating parameterson the flow field of compound hydrocyclone two represen-tative positions in compound hydrocyclone were selected toillustrate the evolution of flow field As shown in Figure 4ldquoposition Ardquo is the interface between the cylindrical part andthe conical part and ldquoposition Brdquo is the middle cross-sectionof the conical part

41 CFD Model Validation It is necessary to validate theaccuracy and rationality of the CFD model At present thevelocity distribution of multiphase flow field in hydrocycloneis difficult to be obtained by experiment So that only splitratio and total efficiency were discussed here for modelvalidation Figure 5(a) compares the split ratio observedin classification experiment and CFD simulation results indifferent inlet velocities It can be seen that the split ratio ofsimulation is higher than experiment results In the conditionof lower inlet velocity a bigger prediction error is observedand the maximum error is 11 However the split ratiovariation trend of CFD simulation is basically the samewith classification experiment Figure 5(b) compares theexperimental results and simulation results of total efficiencyat different rotating speeds It can be seen that the totalefficiency of simulation is lower than experiment resultswhile the variation trend of total efficiency can be correctlypredicted by simulation The maximum error is observed atthe rotating speed of 2950 rpm and the value of maximumerror is about 7 The above results indicate that this CFDmodel can at least make a qualitative analysis of compoundhydrocyclonersquos performance However the solid phase wassimplified by mixture model and the particle distributioncannot be presented exactly Therefore an accurate quantita-tive analysis of compoundhydrocyclone is difficult to achieve

42TheEffect of Inlet Velocity (v) on Flow Field Theevolutionof tangential velocity in different inlet velocities is shown inFigures 6(a) and 6(b) It can be seen that with the increase ofinlet velocity the tangential velocity of inner vortex (forcedvortex) is gradually increased while the tangential velocityof outer vortex (free vortex) has no obvious changes Thisindicates that the outer vortex is accelerated to the same speedas the rotating blade and is not affected by inlet velocity


v = 1700 rpmc = 16

observedsimulated

05

06

07

08

09Sp

lit ra

tio

15 2505Inlet velocity (ms)

(a) Split ratio (119899 = 1700 rpm 119888 = 16)

observed simulated

v = 15 msc = 16

40

50

60

70

Tota

l effi

cien

cy (

)

1700 2950450Rotating speed (rpm)

(b) Total efficiency (V = 15ms 119888 = 16)

Figure 5 Comparison of experimental results and simulation results

On the other hand the centrifugal intensity of the innervortex is enhanced which is beneficial to coarse and heavyparticles in inner vortex move toward to outer vortex so thatthe partition size will be decreased Tangential velocity ofhydrocyclone flowfield is the basis for classification and sepa-rationwork and the effect of tangential velocity on separationefficiency is significant [25] For static hydrocyclone a higherinlet velocity is usually required to achieve a better separationwork However in the flow field of compound hydrocyclonethe outer vortex can still achieve a higher centrifugal force atlower inlet velocity which ismore favorable for the heavy andcoarse particles which accumulate near the cyclone wall

Figures 6(c) and 6(d) show the evolution of axial velocityin different inlet velocities It is observed that the axialvelocity of inner vortex is gradually increased as the inletvelocity rising while the axial velocity of outer vortex andthe relative space of inner and outer vortex have no obviouschanges This indicates that increasing the inlet velocitycan make the discharge of the overflow increase while thedischarge of the underflow is essentially unchangedThe axialvelocity directly determines the residence time of the fluidin hydrocyclone and higher axial velocity will reduce theresidence time which results in the insufficient separation[26] Therefore an excessive inlet velocity should not beadopted in compound hydrocyclone

Figures 6(e) and 6(f) show the evolution of radial velocityin different inlet velocities It is observed that with theincrease of inlet velocity the radial velocity of inner vortexis increased significantly while the radial velocity of outervortex has no obvious regular varieties This indicates thatincreasing the inlet velocity can enhance the movement ofparticles in inner vortex toward the wall

43 The Effect of Rotating Speed (n) on Flow Field Theevolution of tangential velocity in different rotating speeds

is shown in Figures 7(a) and 7(b) It can be seen that withthe increase of rotating speed the tangential velocity ofboth inner and outer vortex are gradually increased and thetangential velocity increment of outer vortex is significantlylarger than that of inner vortexThis indicates that increasingthe rotating speed can enhance the centrifugal intensity ofboth inner and outer vortex Furthermore the acceleratingeffect of rotating blade on the outer vortex is obvious moreIn the flow field of hydrocyclone a stronger centrifugal forcein outer vortex is favorable for heavy and coarse particles to beconfined in the outer vortex which can avoidmore heavy andcoarse particles flowing into inner vortex while a strongercentrifugal force in inner vortex is favorable for heavy andcoarse particles which move toward outer vortex whichcan decreases the partition size and increases the separationefficiency Therefore a higher rotating speed is necessary toimprove the performance of compound hydrocyclone It alsocan be seen that the tangential velocity is increasing fromthe wall to the center of hydrocyclone in the rotating speedof 450 rpm This phenomenon can be explained as the inletvelocity larger than the rotating speed so that the rotationof outer vortex is hindered by the rotating blade Thus therotating speed should reach a certain level to ensure theclassification performance of compound hydrocyclone

Figures 7(c) and 7(d) show the evolution of axial velocityin different rotating speeds It is observed that the axialvelocity of inner vortex is gradually increased as the rotatingspeed increasing and the boundary between inner and outervortex moves toward the cyclone wall This indicates that thespace volume of inner vortex is expanded by increasing therotating speed and the discharge of overflow is increasedIt is also observed that increasing the rotating speed canalso improve the axial velocity of outer vortex This can beexplained as the radial compression of outer vortex in ahigher rotating speed which enhances the axial movement


v = 05 ms v = 15 ms v = 25 ms

minus1

0

1

2

3

4

5

6Ta

ngen

tial V

eloci

ty (m

s)

20100 30 40minus20minus30 minus10minus40Position (mm)

Position A

(a) Tangential velocity

v = 05 msv = 15 msv = 25 ms

minus1

0

1

2

3

4

5

Tang

entia

l Velo

city

(ms

)

minus10 0 10 20minus20Position (mm)

Position B

(b) Tangential velocity

v = 05 msv = 15 msv = 25 ms


minus1

0

1

2

3

Axi

al V

eloci

ty (m

s)

Position A

(c) Axial velocity

v = 05 msv = 15 msv = 25 ms


minus1

0

1

2

3A

xial

Velo

city

(ms

)Position B

(d) Axial velocity

v = 05 msv = 15 msv = 25 ms


minus08

minus04

00

04

08

Radi

al V

eloci

ty (m

s)

Position A

(e) Radial velocity

v = 05 msv = 15 msv = 25 ms

minus08

minus04

00

04

08

Radi

al V

eloc

ity (m

s)

minus10 100 20minus20Position (mm)

Position B

(f) Radial velocity

Figure 6 Evolution of velocity-field in different inlet velocities (119899 = 1700 rpm 119888 = 16)


n = 450 rpmn = 1700 rpmn = 2950 rpm


minus1

2

5

8Ta

ngen

tial V

eloci

ty (r

pm)

Position A


n = 450 rpmn = 1700 rpmn = 2950 rpm

minus1

1

3

5

7

Tang

entia

l Velo

city

(rpm

)


Position B

0


n = 450 rpmn = 1700 rpmn = 2950 rpm


minus2

minus1

0

1

2

3

Axi

al V

eloci

ty (r

pm)

Position A

0

(c) Axial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm


minus1

0

1

2

3A

xial

Velo

city

(rpm

)Position B

0

(d) Axial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm


minus08

minus04

00

04

08

Radi

al V

eloc

ity (r

pm)

Position A

0

(e) Radial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm

minus08

minus04

00

04

08

Radi

al V

eloc

ity (r

pm)


Position B

0

(f) Radial velocity

Figure 7 Evolution of velocity-field in different rotating speed (V = 15ms 119888 = 16)


Table 3 Experimental conditions and results

Number Factors D50 (120583m) S E ()k n c Observed Predicted Observed Predicted Observed Predicted

1 +1 +1 minus1 176 178 0875 0877 652 6492 +1 minus1 +1 291 295 0712 0710 514 5163 minus1 +1 +1 238 242 0711 0707 599 5964 minus1 minus1 minus1 217 219 0338 0336 799 8015 minus168 0 0 242 238 0538 0534 774 7756 +168 0 0 195 191 0795 0798 683 6847 0 minus168 0 268 264 0607 0607 630 6288 0 +168 0 238 235 0830 0822 575 5809 0 0 minus168 172 165 0838 0841 654 65610 0 0 +168 274 265 0772 0775 449 45111 0 0 0 214 215 0815 0808 614 60412 0 0 0 207 215 0801 0808 605 60413 0 0 0 215 215 0806 0808 617 60414 0 0 0 209 215 0813 0808 591 60415 0 0 0 216 215 0812 0808 599 604

of the fluid in outer vortex Due to the decrease of flow areain outer vortex the increase of axial velocity cannot indicatethat the discharge of underflow is increased

Figures 7(e) and 7(f) show the evolution of radial velocityin different rotating speeds It is observed that with theincrease of rotating the radial velocity of both inner andouter vortex is increased This indicates that increasing therotating speed can enhance themovement of particles towardthe cyclone wall

44 The Effect of Feed Concentration (c) on Flow Field Theevolution of tangential velocity in different feed concen-trations is shown in Figures 8(a) and 8(b) It can be seenthat increasing the feed concentration has a certain levelof decelerating effect on tangential velocity This indicatesthat the centrifugal intensity of flow field is decreased withthe feed concentration increasing so that the movementof particles toward the hydrocyclone wall is weakened Onthe other hand with the increasing of feed concentrationthe particle spacing in the flow field is decreased and theinteracting between particles is increased This may hinderthe centrifugal sedimentation of particles and reduce theseparation efficiency Literature [27] suggested that thereis a critical value for the effect of feed concentration onseparation efficiency When the feed concentration is lessthan the critical value the interaction between particles canbe ignored so that the separation efficiency can be increasedwith the increasing of feed concentration However whenthe feed concentration is greater than the critical value theinteraction between particles is significant This seriouslyhinders the centrifugal sedimentation and results in a sharpdecrease of separation efficiency

Figures 8(c) and 8(d) show the evolution of axial velocityin different feed concentrations It is observed that withthe increasing of feed concentration the axial velocity ofouter vortex is increased while the axial velocity of inner

vortex is decreased In addition the boundary between innerand outer vortex moves toward the center line slightly Thisindicates that in the condition of higher feed concentrationa lower discharge of overflow and a higher discharge ofunderflow can be obtained

Figures 8(e) and 8(f) show the evolution of radial velocityin different feed concentrations It is observed that with theincrease of feed concentration the radial velocity of innervortex is gradually decreased while the radial velocity ofouter vortex has no obvious regular varieties This indicatesthat increasing the feed concentration will hinder the cen-trifugal sedimentation of particles which are in inner vortex

45 Regression Model The results of the observation andprediction for each evaluation index in different operatingparameters are summarized in Table 3 Nonlinear regressionanalysis was used to establish the prediction models toexpress the partition size (D50) split ratio (S) and totalefficiency (E) as function of inlet velocity rotating speed andfeed concentration In order to investigate the validity andsignificance of the predictionmodels the analysis of variance(ANOVA) was carried out

The prediction model of partition size (D50) obtained bynonlinear regression analysis is as follows

D50 = 2158 minus 721V minus 293 lowast 10minus3119899 + 075119888 minus 031V119888minus 363 lowast 10minus4119899119888 + 222 lowast 10minus61198992 (6)

The analysis of variance results for partition size (D50)prediction model are shown in Table 4 It can be seen thatthe ldquoModel 119865-valuerdquo is 6931 and ldquoModel 119901 valuerdquo is less than00001 This implies that the model is very significant andthere is only a 001 chance that a ldquoModel 119865-valuerdquo of thislarge may occur due to noise On the other hand the ldquoLackof Fit 119865-valuerdquo is 245 and ldquoLack of Fit 119901 valuerdquo is 01081 This


c = 75c = 16c = 245


minus1

0

1

2

3

4

5Ta

ngen

tial V

eloci

ty (

)Position A

0


c = 75c = 16c = 245

minus1

0

1

2

3

4

5

Tang

entia

l Velo

city

()


Position B

0


c = 75c = 16c = 245


minus2

minus1

0

1

2

3

Axi

al V

eloci

ty (

)

Position A

0

(c) Axial velocity

c = 75c = 16c = 245


minus1

0

1

2

3A

xial

Velo

city

()

Position B

0

(d) Axial velocity

c = 75c = 16c = 245


minus08

minus04

00

04

08

Radi

al V

eloc

ity (

)

Position A

0

(e) Radial velocity

c = 75c = 16c = 245

minus08

minus04

00

04

08

Radi

al V

eloc

ity (

)


Position B

0

(f) Radial velocity

Figure 8 Evolution of velocity-field in different feed concentration (V = 15ms 119899 = 1700 rpm)


Table 4 Variance analyses for partition size (D50) prediction model

Term Sum of squares Mean square 119865-value 119901 valueModel 15981 2663 6931 lt00001k 1104 1104 2874 00007n 450 450 1171 00091c 9817 9817 25547 lt00001kc 317 317 824 00208nc 770 770 2003 00021n2 2364 2364 6152 lt00001Residual 307 038Lack of fit 245 061 390 01081Pure error 063 016

Table 5 Variance analyses for split ratio (S) prediction model

Term Sum of squares Mean square 119865-value 119901 valueModel 029 0032 82208 lt00001k 0033 0033 85619 lt00001n 0025 0025 64464 lt00001c 0002 0002 5647 00007kn 0012 0012 29819 lt00001kc 0006 0006 14693 lt00001nc 0004 0004 9873 00002k2 0031 0031 80585 lt00001n2 0012 0012 32202 lt00001knc 0002 0002 5165 00008Residual 0001 0001Lack of fit 0001 0001 054 05040Pure error 0001 0001

implies the lack of fit term is not significant relative to the pureerror and there is a 1081 chance that a ldquoLack of Fit 119865-valuerdquoof this largemay occur due to noise All these results indicatedthat the model described in (6) is effective for partition size(D50) prediction

If the 119901 value is lt005 the corresponding term of themodel is significant at 5 level While the 119901 value gt 01means that the model term is not significant Thereforethe main factors such as inlet velocity rotating speed andfeed concentration as well as square of rotating speed havesignificant effects on the partition size Among the interac-tional effects the interaction between inlet velocity and feedconcentration and the interaction between rotating speed andfeed concentration have significant effects on partition sizeOther effects which are lack of fit terms (kn k2 c2 knc) havenegligible effect on partition size

The prediction model of split ratio (S) is expressed asfollows

S = minus116 + 122V + 798 lowast 10minus4119899 + 005119888 minus 263lowast 10minus4V119899 minus 003V119888 minus 214 lowast 10minus5119899119888 minus 014V2minus 552 lowast 10minus81198992 + 895 lowast 10minus6V119899119888

(7)

According to the variance analysis results shown inTable 5 it can be seen that the model is very significant andthe lack of fit term is not significant relative to the pure errorTherefore the model described in (7) is very effective for splitratio (S) prediction It also can be seen from Table 5 that themain factors such as inlet velocity rotating speed and feedconcentration as well as square of inlet velocity and square ofrotating speed have significant effects on split ratio Amongthe interactional effects the interaction between any twofactors and the interaction of the three factors have significanteffect on split ratio Only the square of feed concentration hasnegligible effect on split ratio

The prediction model of total efficiency (E) is expressedas follows

E = 11783 minus 4597V minus 001119899 + 031119888 + 191 lowast 10minus3V119899+ 478 lowast 10minus4119899119888 + 1271V2 minus 0071198882 (8)

According to the variance analysis results shown inTable 6 it can be seen that the model is very significant andthe lack of fit term is not significant relative to the pure errorTherefore themodel described in (8) is very effective for totalefficiency (E) prediction It also can be seen from Table 6that the main factors such as inlet velocity rotating speed


Table 6 Variance analyses for total efficiency (E) prediction model

Term Sum of squares Mean square 119865-value 119901 valueModel 105794 15113 20927 lt00001k 4140 4140 5733 00001n 2437 2437 3375 00007c 21013 21013 29096 lt00001kn 289 289 400 00855nc 1334 1334 1847 00036k2 29966 29966 41494 lt00001c2 5308 5308 7350 lt00001Residual 506 072Lack of fit 049 016 014 09295Pure error 457 114

and feed concentration as well as square of inlet velocity andsquare of feed concentration have significant effects on totalefficiency Among the interactional effects the interactionbetween rotating speed and feed concentration has significanteffect on total efficiency Other effects which are lack offit terms (kc n2 and knc) have negligible effect on totalefficiency

46 The Effect of Operating Parameters on Partition Size(D50 ) For better understanding the prediction models ofeach evaluation index are described by 2D response surfaceplots which show the significant interaction of differentcombination factors The effect of inlet velocity and feedconcentration on D50 of compound hydrocyclone is shownin Figure 9(a) It is observed that finer particles can beobtained from the vertex finder at higher level of inlet velocityand lower level of feed concentration This can be explainedas the centrifugal intensity of flow field is enhanced sothat the quantity of coarse particles suspended in the innervortex is decreased On the other hand decreasing the feedconcentration can make the particle spacing in the flow fieldincreased and the interaction between particles decreasedthese lead to the decreasing resistance during the particlescentrifugal sedimentation and the quantity reducing of theparticles in axial central region It also can be seen fromFigure 9(a) the effect of inlet velocity on D50 is graduallyweakened with the feed concentration increasing This isdue to the fact that in the higher concentration flow fieldthe effect of sedimentation resistance on particles is moreobvious

The effect of rotating speed and feed concentration onD50 of compound hydrocyclone is shown in Figure 9(b) It isobserved that the partition size of compound hydrocyclonewill be decreased with the increasing of rotating speedThis is also due to the enhancement of centrifugal intensityin the flow field However in the condition of lower feedconcentration an excessive high rotating speed can makethe overflow particles coarser This can be explained as theturbulence and fluctuation of the flow field is enhancedwhich seriously disturb the centrifugal sedimentation of par-ticles and finally result in the overflow with coarse particlesWith the increasing of feed concentration the coarsening

phenomenon in overflow caused by excessive high rotatingspeed is gradually eliminatedThis can be explained as higherfeed concentration increases the fluid viscosity of flow fieldwhich has suppression effect on the unstable flow caused bythe rotating blade with high speed

According to the response surfaces of partition size (D50)it can be concluded that in the condition of k = 05ms n =450 rpm and c=245 this compoundhydrocyclone gets themaximum partition size of 355 120583m while in the conditionof k = 25ms n = 1275 rpm and c = 75 this compoundhydrocyclone gets the minimum partition size of 113 120583m

47 The Effect of Operating Parameters on Split Ratio (S) Theeffect of inlet velocity and rotating speed on S of compoundhydrocyclone is shown in Figure 10(a) It is observed thatgreater split ratio can be obtained at higher level of inletvelocity and higher level of rotating speed so that a biggerdischarge of overflow can be achieved This can be explainedas the pressure energy of the flow field is increased withinlet velocity and rotating speed increasing which enhancethe resistance of the cyclonersquos conical part to outer vortexand expand the volume of inner vortex However the splitratio of compound hydrocyclone is decreased slightly in thecondition of excessive high inlet velocity and rotating speedThis is due to the fact that the axial velocity of outer vortex isincreased significantly which enhances the discharge abilityof the apex pipe

The effect of inlet velocity and feed concentration on Sis shown in Figure 10(b) It is observed that greater splitratio can be achieved at higher level of inlet velocity andlower level of feed concentration This can be explained asthe effect of gravity on outer vortex is weakened with thedecreasing of feed concentration In addition decreasingthe feed concentration reduces the flow viscosity which candecrease the kinetic energy loss and increase the pressure inhydrocyclone so that the flow resistance in cyclonersquos conicalpart is increased It is also noted that in the condition of lowerinlet velocity raising the feed concentration can make thesplit ratio increased slightlyThis is due to the fact that higherfeed concentration causesmore particles to accumulate in theapex zone of conical part and then impedes the discharge ofthe overflow


D50 (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

25

20

15

(a)

D50 ( = 15 ms)

450 1075 1700 2325 2950

Rotating speed (rpm)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

30

25

20

(b)

Figure 9 Response surface plot showing the effect of operating parameters on D50

S (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

04

0608

(a)

S (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

06 07

08

09

(b)

S ( = 15 ms)

450 1075 1700 2325 2950


245

203

160

118

75

Feed

conc

entr

atio

n (

)

07

08

09

(c)

Figure 10 Response surface plot showing the effect of operating parameters on S


E (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

70 65 60 65

(a)

E ( = 15 ms)245

203

160

118

75

Feed

conc

entr

atio

n (

)

70

50

60

450 1075 1700 2325 2950


(b)

Figure 11 Response surface plot showing the effect of operating parameters on E

The effect of rotating speed and feed concentration on Sis shown in Figure 10(c) It is observed that in the conditionof higher rotating speed and lower feed concentration higherlevel of split ratio can be achieved Moreover the interactionbetween rotating speed and feed concentration is similar tothat between inlet velocity and feed concentration

The response surfaces of split ratio (S) show that themaximum split ratio of compound hydrocyclone is 094 andthe corresponding operating condition is k = 20ms n= 2200 rpm and c = 75 while the minimum split ratioof compound hydrocyclone is 002 and the correspondingoperating condition is k=05msn=450 rpm and c= 105

48 The Effect of Operating Parameters on Total Efficiency(E) The effect of inlet velocity and rotating speed on Eof compound hydrocyclone is shown in Figure 11(a) It isobserved that higher total efficiency can be obtained in thecondition of lower rotating speed and lower inlet velocityso that the underflow has a bigger discharge This can beexplained as the space volume of inner vortex is in a lowerlevel decreasing the quantity of the particles suspended ininner vortex Nevertheless the effect of inlet velocity ontotal efficiency has two sides It can be seen that when theinlet velocity is at a higher level the total efficiency willalso be increased This is because the centrifugal force onparticles is greater than the sedimentation resistance so thatthe radial equilibrium position of particles is closer to thehydrocyclonersquos wall

The effect of rotating speed and feed concentration onE is shown in Figure 11(b) It is observed that higher totalefficiency can be obtained at lower level of feed concentrationThis can be explained as the sedimentation resistance ofparticles is weakened with the feed concentration decreasingso that the number of particles which radial equilibriumpositions in inner vortex is decreased It also can be seenthat in the condition of higher feed concentration there isa negligible effect on total efficiency as the rotating speedchangesThis is because the effect of sedimentation resistanceon particles is much greater than that of the centrifugal force

The response surfaces of total efficiency (E) show thatin the condition of k = 05ms n = 450 rpm and c =99 this compound hydrocyclone gets the maximum totalefficiency of 908 while in the condition of k = 17ms n =1060 rpm and c = 245 this compound hydrocyclone getsthe minimum total efficiency of 429

5 Conclusion

The effect of operating parameters on compound hydrocy-clone performance is studied using CFD numerical simula-tion and experimental method According to the responsesurfaces of three performance indexes and the simulationresults of flow field some conclusions can be obtained asfollows

(1) As the key component of compound hydrocyclonerotating blade has significant effects on the flow field andperformance indexes Because of the accelerating function ofrotating blade the centrifugal intensity of hydrocyclonersquos flowfield can get a higher level so that compound hydrocyclonecan be used for separation of finer particles On the otherhand the flow field of compound hydrocyclone can stillachieve a higher centrifugal force in the condition of lowerinlet velocity This is the advantage that static hydrocyclonecannot be compared However an excessive higher speed ofrotating blade will cause strong fluctuations in the flow fieldwhich seriously disturb the particles centrifugal sedimenta-tion Therefore excessive high level of rotating speed shouldnot be adopted

(2) For this compound hydrocyclone the results ofresponse surfaces indicate that the partition size range is113sim355 120583m the split ratio range is 002sim094 and thetotal efficiency range is 429sim908 In the application ofcompound hydrocyclone higher inlet velocity and feedconcentration should be adopted to achieve a greater yieldcapacity meanwhile rotating speed should be set to a lowerlevel to reduce the energy consumptionOn the other hand inorder to get more particles from the overflow the compoundhydrocyclone should be operated in the condition which


can achieve higher level of split ratio and lower level oftotal efficiency According to the above requirements tooptimize the operating parameters for partition size less than12 120583m the optimized operating condition is k = 25ms n =1865 rpm and c = 75 The corresponding total efficiencyis 728 and split ratio is 0928 For partition size less than35 120583m the optimized operating condition is k = 25ms n =905 rpm and c = 245The corresponding total efficiency is498 and split ratio is 0638

Nomenclature

Di Inlet diameter (mm)Do Vortex finder diameter (mm)Du Apex diameter (mm)D Cylindrical diameter (mm)d Rotating blade diameter (mm)L Cylindrical length (mm)l Rotating blade length (mm)120579 Cone angle (∘)k Inlet velocity (ms)n Rotating speed (rpm)c Feed concentration by mass ()DS Partition size of overflow (120583m)S Split ratio of overflowR Recovery rate ()

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The authors would like to express their sincere thanks to theNational Natural Science Foundation of China (Grant no51264034)

References

[1] P-K Liu L-Y Chu J Wang and Y-F Yu ldquoEnhancement ofhydrocyclone classification efficiency for fine particles by intro-ducing a volute chamber with a pre-sedimentation functionrdquoChemical Engineering amp Technology vol 31 no 3 pp 474ndash4782010

[2] J D Boadway ldquoA hydrocyclone with recovery of velocityenergyrdquo in Proceedings of the Second International Conferenceon Hydrocyclones pp 99ndash108 Bath England 1984

[3] T Larsson ldquoA new type of hydrocyclonerdquo in Proceedings ofthe First International Conference on Hydrocyclones pp 83ndash97Cambridge UK 1980

[4] L Chu W Chen and Q Luo ldquoSeparation characteristicsof the hydrocyclone with a central cone and annular teethrdquoTransactions of Nonferrous Metals Society of China vol 6 no4 pp 11ndash15 1996

[5] W K Evans A Suksangpanomrung and A F NowakowskildquoThe simulation of the flow within a hydrocyclone operatingwith an air core and with an inserted metal rodrdquo ChemicalEngineering Journal vol 143 no 1-3 pp 51ndash61 2008

[6] R Sripriya M D Kaulaskar S Chakraborty and B C MeikapldquoStudies on the performance of a hydrocyclone and modeling

for flow characterization in presence and absence of air corerdquoChemical Engineering Science vol 62 no 22 pp 6391ndash64022007

[7] MGhodrat S B Kuang A B Yu AVince GD Barnett and PJ Barnett ldquoNumerical analysis of hydrocyclones with differentconical section designsrdquo Minerals Engineering vol 62 pp 74ndash84 2014

[8] MGhodrat S B Kuang A B Yu AVince GD Barnett and PJ Barnett ldquoNumerical analysis of hydrocyclones with differentvortex finder configurationsrdquoMinerals Engineering vol 63 pp125ndash138 2014

[9] X M Liu F Li M H Jiang et al ldquoTest research on oil-waterseparation of the compound hydrocyclonerdquo China PetroleumMachinery vol 30 pp 1ndash3 2002

[10] M H Jiang Z C Wang X M Liu et al ldquoStructural designof compound hydrocyclones for oil-water separationrdquo FluidMachinery vol 30 pp 17ndash19 2002

[11] Z C Wang ldquoNumerical simulation of internal flow field incompound hydrocyclonerdquo Acta Petrolei Sinica vol 26 pp 125ndash128 2005

[12] S Li Z Wang F Lv Y Xu and J Zhang ldquoStudy on separa-tion performance of the compound hydrocyclone under self-vibration conditionrdquo in Proceedings of the 28th InternationalConference on Ocean Offshore and Arctic Engineering OMAErsquo09 pp 71ndash77 USA June 2009

[13] C Liu L I Feng and Y U Yonghong ldquoRadial PressureDistribution and Unit Production Ability Determination ofCompound Hydrocyclonesrdquo Chemical Engineering amp Machin-ery vol 80 pp 125ndash130 2009

[14] R Ying J Yu W Wang T Zhang J Feng and S Du ldquoOpti-mization of Structural and Process Parameters for Fine ParticleClassifying Hydrocyclonerdquo Jixie Gongcheng XuebaoJournal ofMechanical Engineering vol 53 no 2 pp 124ndash134 2017

[15] J Huang L An and Z Wu ldquoStudy on Application and Opera-tion Optimization of Hydrocyclone for Solid-liquid Separationin Power Plantrdquo Lecture Notes in Engineering amp ComputerScience vol 2178 pp 297ndash299 2009

[16] L Svarovsky ldquoHydrocyclonesrdquo in Solid-Liquid Separation chap-ter 7 pp 191ndash245 Elsevier 4th edition 2001

[17] P Dixit R Tiwari A K Mukherjee and P K BanerjeeldquoApplication of response surfacemethodology formodeling andoptimization of spiral separator for processing of iron ore slimerdquoPowder Technology vol 275 pp 105ndash112 2015

[18] S B KuangKWChuA B Yu andAVince ldquoNumerical studyof liquid-gas-solid flow in classifying hydrocyclones Effect offeed solids concentrationrdquoMinerals Engineering vol 31 pp 17ndash31 2012

[19] S Ergun ldquoFluid flow through packed columnsrdquo ChemicalEngineering Progress vol 48 pp 89ndash94 1952

[20] C Y Wen and Y H Yu ldquoMechanics of fluidizationrdquo Chem EngProg Symp Series vol 62 pp 100ndash111 1966

[21] M Narasimha M Brennan and P N Holtham ldquoLarge eddysimulation of hydrocyclone-prediction of air-core diameter andshaperdquo International Journal of Mineral Processing vol 80 no1 pp 1ndash14 2006

[22] M Saidi R Maddahian B Farhanieh and H Afshin ldquoModel-ing of flow field and separation efficiency of a deoiling hydro-cyclone using large eddy simulationrdquo International Journal ofMineral Processing vol 112-113 pp 84ndash93 2012

[23] M Ghodrat Z Qi S B Kuang L Ji and A B Yu ldquoCom-putational investigation of the effect of particle density on the


multiphase flows and performance of hydrocyclonerdquo MineralsEngineering vol 90 pp 55ndash69 2016

[24] M Ghodrat S B Kuang A B Yu A Vince G D Barnett andP J Barnett ldquoComputational study of the multiphase flow andperformance of hydrocyclones Effects of cyclone size and spigotdiameterrdquo Industrial amp Engineering Chemistry Research vol 52no 45 pp 16019ndash16031 2013

[25] S R Knowles D R Woods and I A Feuerstein ldquoThe velocitydistribution within a hydrocyclone operating without an aircorerdquoTheCanadian Journal of Chemical Engineering vol 51 no3 pp 263ndash271 2010

[26] Z Stegowski and J-P Leclerc ldquoDetermination of the solidseparation and residence time distributions in an industrialhydrocyclone using radioisotope tracer experimentsrdquo Interna-tional Journal of Mineral Processing vol 66 no 1-4 pp 67ndash772002

[27] J S Qiu W M Chen Y Du et al ldquoEffects of solid contentparticle size and setting angle on separation performance of ahydrocyclonerdquo Journal of Filtration amp Separation vol 5 pp 3ndash6 1995

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Submit your manuscripts atwwwhindawicom


But these improvements have failed to break through thelimitations which are the hydrocyclone without energy inputwhile the dynamic hydrocyclone is a good solution to thisproblem Compared to the conventional static hydrocyclonethe dynamic hydrocyclone can also get a higher separationefficiency and a variable capacity

Compound hydrocyclone is a new form of dynamichydrocyclones which has structure characteristics of thenormal static hydrocyclone Because of the acceleration effectof rotating blades higher separation efficiency can still beobtained in compound hydrocyclone at lower inlet pressureLiu et al [9] carried out a test research on oil-water separationof compound hydrocyclone They found that higher rotatingspeed will result in seriously emulsification of oil phaseJiang et al [10] experimentally optimized the rotating bladestructure of deoiling compound hydrocyclone and raised theseparation performance They suggested that the advantagesof compound hydrocyclone in terms of flow field energyconsumption separation efficiency and application scopeare that the static hydrocyclone cannot be achieved Wang[11] investigated the influence of geometric and operationparameters of compound hydrocyclone to deoiling perfor-mance and suggested that appropriate rotating speed rangesfrom 1700 rpm to 2400 rpm Li et al [12] investigated theeffect of vibration behavior on the flow field and separationperformance They found that the flow rate and the electricmotor running not only cause the vibration but also affectthe separation accuracy Liu et al [13] investigated the radialpressure distribution of compound hydrocyclone flow fieldand determined the general equation of the unit productionability of compound hydrocyclones Ying et al [14] madean experimental prototype of compound hydrocyclone forparticle separation of which experimental result indicatedthat the compound hydrocyclone has a good performance forfiner particle separation So far the compound hydrocycloneismainly used for oil-water separation in petroleum industrywhile the investigation of the compound hydrocyclonesapplied in the field of particle separation are relatively fewIn this investigation the effect of operating condition oncompound hydrocyclone performance is studied using bothCFD technique and experimental method The compoundhydrocyclone with different operating parameters was sim-ulated by RSM turbulence model and the particle phase inthe flow field is simulated by mixture multiphase model Thecentral composite designwas used for the experiment and themathematical models of evaluation indexes were establishedby nonlinear regression method

2 Experimental Aspects

21 Experimental Equipment The internal structure of com-pound hydrocyclone is displayed in Figure 1(a) It can beseen that a driving device (rotation blade) is installed in thecompound hydrocyclone which is the main difference withstatic hydrocyclone The shaft of rotation blade is attached toan electricmotor so that the fluid in compoundhydrocyclonecan be accelerated Meanwhile the shaft of rotation blade isalso used as the vortex finder pipe of hydrocyclone so that thefluid can flow into the overflow chamber through the shaft

Table 1 Structure parameters of hydrocyclone

Parameters Symbols ValueInlet diameter Di 14mmVortex finder diameter Do 20mmApex diameter Du 10mmCylindrical diameter D 75mmRotating blade diameter d 65mmCylindrical length L 40mmRotating blade length l 55mmCone angle 120579 6∘

In this investigation the experimental system is a circu-lation loop mainly composed of water tank slurry pumpand compound hydrocyclone The details of experimentalsystem can be seen from Figures 1(c) and 1(d) A branchpipe is set before the inlet of compound hydrocyclone suchthat the inlet velocity can be regulated by changing the valveopening of branch pipe Electromagnetic flowmeters (EMF)and pressure gauges are installed on the inlet pipe and theoverflow pipe so that the data of flow rate and pressure canbe collected Rotating speed of electric motor is regulated bythe variable-frequency drive (VFD) and the value of rotatingspeed is measured by a laser tachometer In order to makethe liquid and solid in the water tank mix evenly a mixingmachine is installed above the water tank

Structure parameters of compound hydrocyclone usedin this investigation were determined in the literature [14]Details of structure parameters can be seen from Table 1and the symbols of structure parameters can be seen fromFigure 1(b) The main body of compound hydrocyclone ismade of wear-resistant polyurethane The rotating blade ismade of nylon and blades number is six Solid particlesused in this experiment are Ca(OH)2 particles which areslightly soluble in water (165 gL) and the vacuum densityof particles is 2234 kgm3 Before mixture preparation fewCa(OH)2 particles should be added to water to make theliquid saturated Particle size is normal distribution andranges from 6sim498 120583m (measured after mixing with water)The distribution of particle size is presented in Figure 2

22 Operating Parameters and Indexes Operating parame-ters are themain factors that affect the classification and sepa-ration performance of hydrocyclone including temperaturesolid density particle size distribution inlet velocity feedconcentration and setting angle [15] The previous studiesof static hydrocyclone show that inlet velocity and feedconcentration (in mass) are the two most influential factorstherefore the effect of these two parameters on compoundhydrocyclone needs to be considered in this paper On theother hand rotating blade is the important component ofcompound hydrocyclone and has a great influence on theflow field Thus the effect of rotating speed also needs to beconsidered

In order to reflect the effects of the operating condi-tions on the performance of compound hydrocyclone three


(1)

(2)

(3)

(4)

(5)

(6)(7)

(a)

Du

Do L

l

Di

D

d

휽

(b)

(1)

(2)

(3)(4)

(5)

(6)

(7)

(8)(9)

(10)(11)

(12)

M

M VFD

EMFEMF

PP

(c) (d)


1 5 10 25 50 100 250 500


0

10

20

30

40

50

60

70

80

90

100

Pass

ing

()

0

1

2

3

4

5

6

7

8

9

10

Chan

nel (

)















120597120588119898120597119905 + 120597 (120588119898119906119898119894)120597119909119894 = 0 (1)

120597 (120588119898119906119898119894)120597119905 + 120597 (120588119898119906119898119894119906119898119895)120597119909119895= minus 120597119875120597119909119894 +

120597119875119904120597119909119894 +120597120591119898119894119895120597119909119895 +

120597 (minus12058811989811990610158401198981198941199061015840119898119895)120597119909119895

+ 120597120597119909119895 (119899sum119896=1

120588119896119906dr119896119894119906dr119896119895) + 119892120588119898

(2)



120591119898119894119895 = 120583119898 (120597119906119898119895120597119909119894 +120597119906119898119894120597119909119895 )


nabla120572119908120572119908 )minus 119899sum119896=1

(120572119896120588119896119906119908119896119894120588119898 ) (3)



119891 = 11986211986324120583119908120572minus165119908 120588119908119889119896 1003816100381610038161003816119906119908 minus 1199061198961003816100381610038161003816 (4)



120597 (12058811990610158401198941199061015840119895)120597119905 + 120597 (12058811990611989611990610158401198941199061015840119895)120597119909119896= 119863119879119894119895 + 119866119894119895 + 120601119894119895 minus 120576119894119895 + 119875119894119895

(5)






Velocity-inlet

Cylindrical section

Conical section

Pressure-outlet





AB








v = 1700 rpmc = 16

observedsimulated

05

06

07

08

09Sp

lit ra

tio


(a) Split ratio (119899 = 1700 rpm 119888 = 16)

observed simulated

v = 15 msc = 16

40

50

60

70

Tota

l effi

cien

cy (

)











v = 05 ms v = 15 ms v = 25 ms

minus1

0

1

2

3

4

5

6Ta

ngen

tial V

eloci

ty (m

s)


Position A


v = 05 msv = 15 msv = 25 ms

minus1

0

1

2

3

4

5

Tang

entia

l Velo

city

(ms

)


Position B


v = 05 msv = 15 msv = 25 ms


minus1

0

1

2

3

Axi

al V

eloci

ty (m

s)

Position A

(c) Axial velocity

v = 05 msv = 15 msv = 25 ms


minus1

0

1

2

3A

xial

Velo

city

(ms

)Position B

(d) Axial velocity

v = 05 msv = 15 msv = 25 ms


minus08

minus04

00

04

08

Radi

al V

eloci

ty (m

s)

Position A

(e) Radial velocity

v = 05 msv = 15 msv = 25 ms

minus08

minus04

00

04

08

Radi

al V

eloc

ity (m

s)


Position B

(f) Radial velocity



n = 450 rpmn = 1700 rpmn = 2950 rpm


minus1

2

5

8Ta

ngen

tial V

eloci

ty (r

pm)

Position A


n = 450 rpmn = 1700 rpmn = 2950 rpm

minus1

1

3

5

7

Tang

entia

l Velo

city

(rpm

)


Position B

0


n = 450 rpmn = 1700 rpmn = 2950 rpm


minus2

minus1

0

1

2

3

Axi

al V

eloci

ty (r

pm)

Position A

0

(c) Axial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm


minus1

0

1

2

3A

xial

Velo

city

(rpm

)Position B

0

(d) Axial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm


minus08

minus04

00

04

08

Radi

al V

eloc

ity (r

pm)

Position A

0

(e) Radial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm

minus08

minus04

00

04

08

Radi

al V

eloc

ity (r

pm)


Position B

0

(f) Radial velocity

















c = 75c = 16c = 245


minus1

0

1

2

3

4

5Ta

ngen

tial V

eloci

ty (

)Position A

0


c = 75c = 16c = 245

minus1

0

1

2

3

4

5

Tang

entia

l Velo

city

()


Position B

0


c = 75c = 16c = 245


minus2

minus1

0

1

2

3

Axi

al V

eloci

ty (

)

Position A

0

(c) Axial velocity

c = 75c = 16c = 245


minus1

0

1

2

3A

xial

Velo

city

()

Position B

0

(d) Axial velocity

c = 75c = 16c = 245


minus08

minus04

00

04

08

Radi

al V

eloc

ity (

)

Position A

0

(e) Radial velocity

c = 75c = 16c = 245

minus08

minus04

00

04

08

Radi

al V

eloc

ity (

)


Position B

0

(f) Radial velocity











(7)
















D50 (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

25

20

15

(a)

D50 ( = 15 ms)

450 1075 1700 2325 2950


245

203

160

118

75

Feed

conc

entr

atio

n (

)

30

25

20

(b)


S (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

04

0608

(a)

S (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

06 07

08

09

(b)

S ( = 15 ms)

450 1075 1700 2325 2950


245

203

160

118

75

Feed

conc

entr

atio

n (

)

07

08

09

(c)



E (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

70 65 60 65

(a)

E ( = 15 ms)245

203

160

118

75

Feed

conc

entr

atio

n (

)

70

50

60

450 1075 1700 2325 2950


(b)







5 Conclusion






Nomenclature




Acknowledgments


References






































Journal of












Journal of







Volume 2018






Volume 2018









(1)

(2)

(3)

(4)

(5)

(6)(7)

(a)

Du

Do L

l

Di

D

d

휽

(b)

(1)

(2)

(3)(4)

(5)

(6)

(7)

(8)(9)

(10)(11)

(12)

M

M VFD

EMFEMF

PP

(c) (d)


1 5 10 25 50 100 250 500


0

10

20

30

40

50

60

70

80

90

100

Pass

ing

()

0

1

2

3

4

5

6

7

8

9

10

Chan

nel (

)















120597120588119898120597119905 + 120597 (120588119898119906119898119894)120597119909119894 = 0 (1)

120597 (120588119898119906119898119894)120597119905 + 120597 (120588119898119906119898119894119906119898119895)120597119909119895= minus 120597119875120597119909119894 +

120597119875119904120597119909119894 +120597120591119898119894119895120597119909119895 +

120597 (minus12058811989811990610158401198981198941199061015840119898119895)120597119909119895

+ 120597120597119909119895 (119899sum119896=1

120588119896119906dr119896119894119906dr119896119895) + 119892120588119898

(2)



120591119898119894119895 = 120583119898 (120597119906119898119895120597119909119894 +120597119906119898119894120597119909119895 )


nabla120572119908120572119908 )minus 119899sum119896=1

(120572119896120588119896119906119908119896119894120588119898 ) (3)



119891 = 11986211986324120583119908120572minus165119908 120588119908119889119896 1003816100381610038161003816119906119908 minus 1199061198961003816100381610038161003816 (4)



120597 (12058811990610158401198941199061015840119895)120597119905 + 120597 (12058811990611989611990610158401198941199061015840119895)120597119909119896= 119863119879119894119895 + 119866119894119895 + 120601119894119895 minus 120576119894119895 + 119875119894119895

(5)






Velocity-inlet

Cylindrical section

Conical section

Pressure-outlet





AB








v = 1700 rpmc = 16

observedsimulated

05

06

07

08

09Sp

lit ra

tio


(a) Split ratio (119899 = 1700 rpm 119888 = 16)

observed simulated

v = 15 msc = 16

40

50

60

70

Tota

l effi

cien

cy (

)











v = 05 ms v = 15 ms v = 25 ms

minus1

0

1

2

3

4

5

6Ta

ngen

tial V

eloci

ty (m

s)


Position A


v = 05 msv = 15 msv = 25 ms

minus1

0

1

2

3

4

5

Tang

entia

l Velo

city

(ms

)


Position B


v = 05 msv = 15 msv = 25 ms


minus1

0

1

2

3

Axi

al V

eloci

ty (m

s)

Position A

(c) Axial velocity

v = 05 msv = 15 msv = 25 ms


minus1

0

1

2

3A

xial

Velo

city

(ms

)Position B

(d) Axial velocity

v = 05 msv = 15 msv = 25 ms


minus08

minus04

00

04

08

Radi

al V

eloci

ty (m

s)

Position A

(e) Radial velocity

v = 05 msv = 15 msv = 25 ms

minus08

minus04

00

04

08

Radi

al V

eloc

ity (m

s)


Position B

(f) Radial velocity



n = 450 rpmn = 1700 rpmn = 2950 rpm


minus1

2

5

8Ta

ngen

tial V

eloci

ty (r

pm)

Position A


n = 450 rpmn = 1700 rpmn = 2950 rpm

minus1

1

3

5

7

Tang

entia

l Velo

city

(rpm

)


Position B

0


n = 450 rpmn = 1700 rpmn = 2950 rpm


minus2

minus1

0

1

2

3

Axi

al V

eloci

ty (r

pm)

Position A

0

(c) Axial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm


minus1

0

1

2

3A

xial

Velo

city

(rpm

)Position B

0

(d) Axial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm


minus08

minus04

00

04

08

Radi

al V

eloc

ity (r

pm)

Position A

0

(e) Radial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm

minus08

minus04

00

04

08

Radi

al V

eloc

ity (r

pm)


Position B

0

(f) Radial velocity

















c = 75c = 16c = 245


minus1

0

1

2

3

4

5Ta

ngen

tial V

eloci

ty (

)Position A

0


c = 75c = 16c = 245

minus1

0

1

2

3

4

5

Tang

entia

l Velo

city

()


Position B

0


c = 75c = 16c = 245


minus2

minus1

0

1

2

3

Axi

al V

eloci

ty (

)

Position A

0

(c) Axial velocity

c = 75c = 16c = 245


minus1

0

1

2

3A

xial

Velo

city

()

Position B

0

(d) Axial velocity

c = 75c = 16c = 245


minus08

minus04

00

04

08

Radi

al V

eloc

ity (

)

Position A

0

(e) Radial velocity

c = 75c = 16c = 245

minus08

minus04

00

04

08

Radi

al V

eloc

ity (

)


Position B

0

(f) Radial velocity











(7)
















D50 (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

25

20

15

(a)

D50 ( = 15 ms)

450 1075 1700 2325 2950


245

203

160

118

75

Feed

conc

entr

atio

n (

)

30

25

20

(b)


S (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

04

0608

(a)

S (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

06 07

08

09

(b)

S ( = 15 ms)

450 1075 1700 2325 2950


245

203

160

118

75

Feed

conc

entr

atio

n (

)

07

08

09

(c)



E (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

70 65 60 65

(a)

E ( = 15 ms)245

203

160

118

75

Feed

conc

entr

atio

n (

)

70

50

60

450 1075 1700 2325 2950


(b)







5 Conclusion






Nomenclature




Acknowledgments


References






































Journal of












Journal of







Volume 2018






Volume 2018














120597120588119898120597119905 + 120597 (120588119898119906119898119894)120597119909119894 = 0 (1)

120597 (120588119898119906119898119894)120597119905 + 120597 (120588119898119906119898119894119906119898119895)120597119909119895= minus 120597119875120597119909119894 +

120597119875119904120597119909119894 +120597120591119898119894119895120597119909119895 +

120597 (minus12058811989811990610158401198981198941199061015840119898119895)120597119909119895

+ 120597120597119909119895 (119899sum119896=1

120588119896119906dr119896119894119906dr119896119895) + 119892120588119898

(2)



120591119898119894119895 = 120583119898 (120597119906119898119895120597119909119894 +120597119906119898119894120597119909119895 )


nabla120572119908120572119908 )minus 119899sum119896=1

(120572119896120588119896119906119908119896119894120588119898 ) (3)



119891 = 11986211986324120583119908120572minus165119908 120588119908119889119896 1003816100381610038161003816119906119908 minus 1199061198961003816100381610038161003816 (4)



120597 (12058811990610158401198941199061015840119895)120597119905 + 120597 (12058811990611989611990610158401198941199061015840119895)120597119909119896= 119863119879119894119895 + 119866119894119895 + 120601119894119895 minus 120576119894119895 + 119875119894119895

(5)






Velocity-inlet

Cylindrical section

Conical section

Pressure-outlet





AB








v = 1700 rpmc = 16

observedsimulated

05

06

07

08

09Sp

lit ra

tio


(a) Split ratio (119899 = 1700 rpm 119888 = 16)

observed simulated

v = 15 msc = 16

40

50

60

70

Tota

l effi

cien

cy (

)











v = 05 ms v = 15 ms v = 25 ms

minus1

0

1

2

3

4

5

6Ta

ngen

tial V

eloci

ty (m

s)


Position A


v = 05 msv = 15 msv = 25 ms

minus1

0

1

2

3

4

5

Tang

entia

l Velo

city

(ms

)


Position B


v = 05 msv = 15 msv = 25 ms


minus1

0

1

2

3

Axi

al V

eloci

ty (m

s)

Position A

(c) Axial velocity

v = 05 msv = 15 msv = 25 ms


minus1

0

1

2

3A

xial

Velo

city

(ms

)Position B

(d) Axial velocity

v = 05 msv = 15 msv = 25 ms


minus08

minus04

00

04

08

Radi

al V

eloci

ty (m

s)

Position A

(e) Radial velocity

v = 05 msv = 15 msv = 25 ms

minus08

minus04

00

04

08

Radi

al V

eloc

ity (m

s)


Position B

(f) Radial velocity



n = 450 rpmn = 1700 rpmn = 2950 rpm


minus1

2

5

8Ta

ngen

tial V

eloci

ty (r

pm)

Position A


n = 450 rpmn = 1700 rpmn = 2950 rpm

minus1

1

3

5

7

Tang

entia

l Velo

city

(rpm

)


Position B

0


n = 450 rpmn = 1700 rpmn = 2950 rpm


minus2

minus1

0

1

2

3

Axi

al V

eloci

ty (r

pm)

Position A

0

(c) Axial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm


minus1

0

1

2

3A

xial

Velo

city

(rpm

)Position B

0

(d) Axial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm


minus08

minus04

00

04

08

Radi

al V

eloc

ity (r

pm)

Position A

0

(e) Radial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm

minus08

minus04

00

04

08

Radi

al V

eloc

ity (r

pm)


Position B

0

(f) Radial velocity

















c = 75c = 16c = 245


minus1

0

1

2

3

4

5Ta

ngen

tial V

eloci

ty (

)Position A

0


c = 75c = 16c = 245

minus1

0

1

2

3

4

5

Tang

entia

l Velo

city

()


Position B

0


c = 75c = 16c = 245


minus2

minus1

0

1

2

3

Axi

al V

eloci

ty (

)

Position A

0

(c) Axial velocity

c = 75c = 16c = 245


minus1

0

1

2

3A

xial

Velo

city

()

Position B

0

(d) Axial velocity

c = 75c = 16c = 245


minus08

minus04

00

04

08

Radi

al V

eloc

ity (

)

Position A

0

(e) Radial velocity

c = 75c = 16c = 245

minus08

minus04

00

04

08

Radi

al V

eloc

ity (

)


Position B

0

(f) Radial velocity











(7)
















D50 (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

25

20

15

(a)

D50 ( = 15 ms)

450 1075 1700 2325 2950


245

203

160

118

75

Feed

conc

entr

atio

n (

)

30

25

20

(b)


S (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

04

0608

(a)

S (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

06 07

08

09

(b)

S ( = 15 ms)

450 1075 1700 2325 2950


245

203

160

118

75

Feed

conc

entr

atio

n (

)

07

08

09

(c)



E (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

70 65 60 65

(a)

E ( = 15 ms)245

203

160

118

75

Feed

conc

entr

atio

n (

)

70

50

60

450 1075 1700 2325 2950


(b)







5 Conclusion






Nomenclature




Acknowledgments


References






































Journal of












Journal of







Volume 2018






Volume 2018










Velocity-inlet

Cylindrical section

Conical section

Pressure-outlet





AB








v = 1700 rpmc = 16

observedsimulated

05

06

07

08

09Sp

lit ra

tio


(a) Split ratio (119899 = 1700 rpm 119888 = 16)

observed simulated

v = 15 msc = 16

40

50

60

70

Tota

l effi

cien

cy (

)











v = 05 ms v = 15 ms v = 25 ms

minus1

0

1

2

3

4

5

6Ta

ngen

tial V

eloci

ty (m

s)


Position A


v = 05 msv = 15 msv = 25 ms

minus1

0

1

2

3

4

5

Tang

entia

l Velo

city

(ms

)


Position B


v = 05 msv = 15 msv = 25 ms


minus1

0

1

2

3

Axi

al V

eloci

ty (m

s)

Position A

(c) Axial velocity

v = 05 msv = 15 msv = 25 ms


minus1

0

1

2

3A

xial

Velo

city

(ms

)Position B

(d) Axial velocity

v = 05 msv = 15 msv = 25 ms


minus08

minus04

00

04

08

Radi

al V

eloci

ty (m

s)

Position A

(e) Radial velocity

v = 05 msv = 15 msv = 25 ms

minus08

minus04

00

04

08

Radi

al V

eloc

ity (m

s)


Position B

(f) Radial velocity



n = 450 rpmn = 1700 rpmn = 2950 rpm


minus1

2

5

8Ta

ngen

tial V

eloci

ty (r

pm)

Position A


n = 450 rpmn = 1700 rpmn = 2950 rpm

minus1

1

3

5

7

Tang

entia

l Velo

city

(rpm

)


Position B

0


n = 450 rpmn = 1700 rpmn = 2950 rpm


minus2

minus1

0

1

2

3

Axi

al V

eloci

ty (r

pm)

Position A

0

(c) Axial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm


minus1

0

1

2

3A

xial

Velo

city

(rpm

)Position B

0

(d) Axial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm


minus08

minus04

00

04

08

Radi

al V

eloc

ity (r

pm)

Position A

0

(e) Radial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm

minus08

minus04

00

04

08

Radi

al V

eloc

ity (r

pm)


Position B

0

(f) Radial velocity

















c = 75c = 16c = 245


minus1

0

1

2

3

4

5Ta

ngen

tial V

eloci

ty (

)Position A

0


c = 75c = 16c = 245

minus1

0

1

2

3

4

5

Tang

entia

l Velo

city

()


Position B

0


c = 75c = 16c = 245


minus2

minus1

0

1

2

3

Axi

al V

eloci

ty (

)

Position A

0

(c) Axial velocity

c = 75c = 16c = 245


minus1

0

1

2

3A

xial

Velo

city

()

Position B

0

(d) Axial velocity

c = 75c = 16c = 245


minus08

minus04

00

04

08

Radi

al V

eloc

ity (

)

Position A

0

(e) Radial velocity

c = 75c = 16c = 245

minus08

minus04

00

04

08

Radi

al V

eloc

ity (

)


Position B

0

(f) Radial velocity











(7)
















D50 (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

25

20

15

(a)

D50 ( = 15 ms)

450 1075 1700 2325 2950


245

203

160

118

75

Feed

conc

entr

atio

n (

)

30

25

20

(b)


S (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

04

0608

(a)

S (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

06 07

08

09

(b)

S ( = 15 ms)

450 1075 1700 2325 2950


245

203

160

118

75

Feed

conc

entr

atio

n (

)

07

08

09

(c)



E (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

70 65 60 65

(a)

E ( = 15 ms)245

203

160

118

75

Feed

conc

entr

atio

n (

)

70

50

60

450 1075 1700 2325 2950


(b)







5 Conclusion






Nomenclature




Acknowledgments


References






































Journal of












Journal of







Volume 2018






Volume 2018









v = 1700 rpmc = 16

observedsimulated

05

06

07

08

09Sp

lit ra

tio


(a) Split ratio (119899 = 1700 rpm 119888 = 16)

observed simulated

v = 15 msc = 16

40

50

60

70

Tota

l effi

cien

cy (

)











v = 05 ms v = 15 ms v = 25 ms

minus1

0

1

2

3

4

5

6Ta

ngen

tial V

eloci

ty (m

s)


Position A


v = 05 msv = 15 msv = 25 ms

minus1

0

1

2

3

4

5

Tang

entia

l Velo

city

(ms

)


Position B


v = 05 msv = 15 msv = 25 ms


minus1

0

1

2

3

Axi

al V

eloci

ty (m

s)

Position A

(c) Axial velocity

v = 05 msv = 15 msv = 25 ms


minus1

0

1

2

3A

xial

Velo

city

(ms

)Position B

(d) Axial velocity

v = 05 msv = 15 msv = 25 ms


minus08

minus04

00

04

08

Radi

al V

eloci

ty (m

s)

Position A

(e) Radial velocity

v = 05 msv = 15 msv = 25 ms

minus08

minus04

00

04

08

Radi

al V

eloc

ity (m

s)


Position B

(f) Radial velocity



n = 450 rpmn = 1700 rpmn = 2950 rpm


minus1

2

5

8Ta

ngen

tial V

eloci

ty (r

pm)

Position A


n = 450 rpmn = 1700 rpmn = 2950 rpm

minus1

1

3

5

7

Tang

entia

l Velo

city

(rpm

)


Position B

0


n = 450 rpmn = 1700 rpmn = 2950 rpm


minus2

minus1

0

1

2

3

Axi

al V

eloci

ty (r

pm)

Position A

0

(c) Axial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm


minus1

0

1

2

3A

xial

Velo

city

(rpm

)Position B

0

(d) Axial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm


minus08

minus04

00

04

08

Radi

al V

eloc

ity (r

pm)

Position A

0

(e) Radial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm

minus08

minus04

00

04

08

Radi

al V

eloc

ity (r

pm)


Position B

0

(f) Radial velocity

















c = 75c = 16c = 245


minus1

0

1

2

3

4

5Ta

ngen

tial V

eloci

ty (

)Position A

0


c = 75c = 16c = 245

minus1

0

1

2

3

4

5

Tang

entia

l Velo

city

()


Position B

0


c = 75c = 16c = 245


minus2

minus1

0

1

2

3

Axi

al V

eloci

ty (

)

Position A

0

(c) Axial velocity

c = 75c = 16c = 245


minus1

0

1

2

3A

xial

Velo

city

()

Position B

0

(d) Axial velocity

c = 75c = 16c = 245


minus08

minus04

00

04

08

Radi

al V

eloc

ity (

)

Position A

0

(e) Radial velocity

c = 75c = 16c = 245

minus08

minus04

00

04

08

Radi

al V

eloc

ity (

)


Position B

0

(f) Radial velocity











(7)
















D50 (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

25

20

15

(a)

D50 ( = 15 ms)

450 1075 1700 2325 2950


245

203

160

118

75

Feed

conc

entr

atio

n (

)

30

25

20

(b)


S (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

04

0608

(a)

S (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

06 07

08

09

(b)

S ( = 15 ms)

450 1075 1700 2325 2950


245

203

160

118

75

Feed

conc

entr

atio

n (

)

07

08

09

(c)



E (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

70 65 60 65

(a)

E ( = 15 ms)245

203

160

118

75

Feed

conc

entr

atio

n (

)

70

50

60

450 1075 1700 2325 2950


(b)







5 Conclusion






Nomenclature




Acknowledgments


References






































Journal of












Journal of







Volume 2018






Volume 2018









v = 05 ms v = 15 ms v = 25 ms

minus1

0

1

2

3

4

5

6Ta

ngen

tial V

eloci

ty (m

s)


Position A


v = 05 msv = 15 msv = 25 ms

minus1

0

1

2

3

4

5

Tang

entia

l Velo

city

(ms

)


Position B


v = 05 msv = 15 msv = 25 ms


minus1

0

1

2

3

Axi

al V

eloci

ty (m

s)

Position A

(c) Axial velocity

v = 05 msv = 15 msv = 25 ms


minus1

0

1

2

3A

xial

Velo

city

(ms

)Position B

(d) Axial velocity

v = 05 msv = 15 msv = 25 ms


minus08

minus04

00

04

08

Radi

al V

eloci

ty (m

s)

Position A

(e) Radial velocity

v = 05 msv = 15 msv = 25 ms

minus08

minus04

00

04

08

Radi

al V

eloc

ity (m

s)


Position B

(f) Radial velocity



n = 450 rpmn = 1700 rpmn = 2950 rpm


minus1

2

5

8Ta

ngen

tial V

eloci

ty (r

pm)

Position A


n = 450 rpmn = 1700 rpmn = 2950 rpm

minus1

1

3

5

7

Tang

entia

l Velo

city

(rpm

)


Position B

0


n = 450 rpmn = 1700 rpmn = 2950 rpm


minus2

minus1

0

1

2

3

Axi

al V

eloci

ty (r

pm)

Position A

0

(c) Axial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm


minus1

0

1

2

3A

xial

Velo

city

(rpm

)Position B

0

(d) Axial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm


minus08

minus04

00

04

08

Radi

al V

eloc

ity (r

pm)

Position A

0

(e) Radial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm

minus08

minus04

00

04

08

Radi

al V

eloc

ity (r

pm)


Position B

0

(f) Radial velocity

















c = 75c = 16c = 245


minus1

0

1

2

3

4

5Ta

ngen

tial V

eloci

ty (

)Position A

0


c = 75c = 16c = 245

minus1

0

1

2

3

4

5

Tang

entia

l Velo

city

()


Position B

0


c = 75c = 16c = 245


minus2

minus1

0

1

2

3

Axi

al V

eloci

ty (

)

Position A

0

(c) Axial velocity

c = 75c = 16c = 245


minus1

0

1

2

3A

xial

Velo

city

()

Position B

0

(d) Axial velocity

c = 75c = 16c = 245


minus08

minus04

00

04

08

Radi

al V

eloc

ity (

)

Position A

0

(e) Radial velocity

c = 75c = 16c = 245

minus08

minus04

00

04

08

Radi

al V

eloc

ity (

)


Position B

0

(f) Radial velocity











(7)
















D50 (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

25

20

15

(a)

D50 ( = 15 ms)

450 1075 1700 2325 2950


245

203

160

118

75

Feed

conc

entr

atio

n (

)

30

25

20

(b)


S (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

04

0608

(a)

S (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

06 07

08

09

(b)

S ( = 15 ms)

450 1075 1700 2325 2950


245

203

160

118

75

Feed

conc

entr

atio

n (

)

07

08

09

(c)



E (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

70 65 60 65

(a)

E ( = 15 ms)245

203

160

118

75

Feed

conc

entr

atio

n (

)

70

50

60

450 1075 1700 2325 2950


(b)







5 Conclusion






Nomenclature




Acknowledgments


References






































Journal of












Journal of







Volume 2018






Volume 2018









n = 450 rpmn = 1700 rpmn = 2950 rpm


minus1

2

5

8Ta

ngen

tial V

eloci

ty (r

pm)

Position A


n = 450 rpmn = 1700 rpmn = 2950 rpm

minus1

1

3

5

7

Tang

entia

l Velo

city

(rpm

)


Position B

0


n = 450 rpmn = 1700 rpmn = 2950 rpm


minus2

minus1

0

1

2

3

Axi

al V

eloci

ty (r

pm)

Position A

0

(c) Axial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm


minus1

0

1

2

3A

xial

Velo

city

(rpm

)Position B

0

(d) Axial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm


minus08

minus04

00

04

08

Radi

al V

eloc

ity (r

pm)

Position A

0

(e) Radial velocity

n = 450 rpmn = 1700 rpmn = 2950 rpm

minus08

minus04

00

04

08

Radi

al V

eloc

ity (r

pm)


Position B

0

(f) Radial velocity

















c = 75c = 16c = 245


minus1

0

1

2

3

4

5Ta

ngen

tial V

eloci

ty (

)Position A

0


c = 75c = 16c = 245

minus1

0

1

2

3

4

5

Tang

entia

l Velo

city

()


Position B

0


c = 75c = 16c = 245


minus2

minus1

0

1

2

3

Axi

al V

eloci

ty (

)

Position A

0

(c) Axial velocity

c = 75c = 16c = 245


minus1

0

1

2

3A

xial

Velo

city

()

Position B

0

(d) Axial velocity

c = 75c = 16c = 245


minus08

minus04

00

04

08

Radi

al V

eloc

ity (

)

Position A

0

(e) Radial velocity

c = 75c = 16c = 245

minus08

minus04

00

04

08

Radi

al V

eloc

ity (

)


Position B

0

(f) Radial velocity











(7)
















D50 (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

25

20

15

(a)

D50 ( = 15 ms)

450 1075 1700 2325 2950


245

203

160

118

75

Feed

conc

entr

atio

n (

)

30

25

20

(b)


S (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

04

0608

(a)

S (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

06 07

08

09

(b)

S ( = 15 ms)

450 1075 1700 2325 2950


245

203

160

118

75

Feed

conc

entr

atio

n (

)

07

08

09

(c)



E (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

70 65 60 65

(a)

E ( = 15 ms)245

203

160

118

75

Feed

conc

entr

atio

n (

)

70

50

60

450 1075 1700 2325 2950


(b)







5 Conclusion






Nomenclature




Acknowledgments


References






































Journal of












Journal of







Volume 2018






Volume 2018























c = 75c = 16c = 245


minus1

0

1

2

3

4

5Ta

ngen

tial V

eloci

ty (

)Position A

0


c = 75c = 16c = 245

minus1

0

1

2

3

4

5

Tang

entia

l Velo

city

()


Position B

0


c = 75c = 16c = 245


minus2

minus1

0

1

2

3

Axi

al V

eloci

ty (

)

Position A

0

(c) Axial velocity

c = 75c = 16c = 245


minus1

0

1

2

3A

xial

Velo

city

()

Position B

0

(d) Axial velocity

c = 75c = 16c = 245


minus08

minus04

00

04

08

Radi

al V

eloc

ity (

)

Position A

0

(e) Radial velocity

c = 75c = 16c = 245

minus08

minus04

00

04

08

Radi

al V

eloc

ity (

)


Position B

0

(f) Radial velocity











(7)
















D50 (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

25

20

15

(a)

D50 ( = 15 ms)

450 1075 1700 2325 2950


245

203

160

118

75

Feed

conc

entr

atio

n (

)

30

25

20

(b)


S (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

04

0608

(a)

S (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

06 07

08

09

(b)

S ( = 15 ms)

450 1075 1700 2325 2950


245

203

160

118

75

Feed

conc

entr

atio

n (

)

07

08

09

(c)



E (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

70 65 60 65

(a)

E ( = 15 ms)245

203

160

118

75

Feed

conc

entr

atio

n (

)

70

50

60

450 1075 1700 2325 2950


(b)







5 Conclusion






Nomenclature




Acknowledgments


References






































Journal of












Journal of







Volume 2018






Volume 2018

















(7)
















D50 (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

25

20

15

(a)

D50 ( = 15 ms)

450 1075 1700 2325 2950


245

203

160

118

75

Feed

conc

entr

atio

n (

)

30

25

20

(b)


S (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

04

0608

(a)

S (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

06 07

08

09

(b)

S ( = 15 ms)

450 1075 1700 2325 2950


245

203

160

118

75

Feed

conc

entr

atio

n (

)

07

08

09

(c)



E (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

70 65 60 65

(a)

E ( = 15 ms)245

203

160

118

75

Feed

conc

entr

atio

n (

)

70

50

60

450 1075 1700 2325 2950


(b)







5 Conclusion






Nomenclature




Acknowledgments


References






































Journal of












Journal of







Volume 2018






Volume 2018



















D50 (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

25

20

15

(a)

D50 ( = 15 ms)

450 1075 1700 2325 2950


245

203

160

118

75

Feed

conc

entr

atio

n (

)

30

25

20

(b)


S (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

04

0608

(a)

S (n = 1700 rpm)

10 15 20 2505

Inlet velocity (ms)

245

203

160

118

75

Feed

conc

entr

atio

n (

)

06 07

08

09

(b)

S ( = 15 ms)

450 1075 1700 2325 2950


245

203

160

118

75

Feed

conc

entr

atio

n (

)

07

08

09

(c)



E (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

70 65 60 65

(a)

E ( = 15 ms)245

203

160

118

75

Feed

conc

entr

atio

n (

)

70

50

60

450 1075 1700 2325 2950


(b)







5 Conclusion






Nomenclature




Acknowledgments


References






































Journal of












Journal of







Volume 2018






Volume 2018









E (c = 16)

10 15 20 2505

Inlet velocity (ms)

2950

2325

1700

1075

450

Rota

ting

spee

d (r

pm)

70 65 60 65

(a)

E ( = 15 ms)245

203

160

118

75

Feed

conc

entr

atio

n (

)

70

50

60

450 1075 1700 2325 2950


(b)







5 Conclusion






Nomenclature




Acknowledgments


References






































Journal of












Journal of







Volume 2018






Volume 2018










Nomenclature




Acknowledgments


References






































Journal of












Journal of







Volume 2018






Volume 2018





















Journal of












Journal of







Volume 2018






Volume 2018








computational and experimental study of the effect of

Documents