swirling flows in a cylindrical separator

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Strongly swirling flows in a cylindricalseparator

Article in Minerals Engineering April 2008

Impact Factor: 1.6 DOI: 10.1016/j.mineng.2007.10.012

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Hitham Tlilan

Hashemite University

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Ahmad Alshyyab

Jordan University of Science and Technology

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Strongly swirling flows in a cylindrical separator

Ali M. Jawarneh *, Hitham Tlilan, Ahmad Al-Shyyab, Amer Ababneh

Department of Mechanical Engineering, The Hashemite University, Zarqa 13115, Jordan

Received 12 June 2007; accepted 9 October 2007Available online 3 December 2007

Abstract

This paper describes a numerical study of two-phase, strongly swirling flow in a cylindrical separator with double vortex generators topredict the separation efficiency of a mixture consisting of oil as the primary phase and sand, with a specific diameter, as the secondaryphase. The mixture-granular multiphase and RNGketurbulence models are implemented in this study. The analytical predictions arecompared against experimental data; i.e., the mean tangential velocity and the mean radial pressure profiles. The overall agreementbetween the experimental data and the predictions obtained with the RNG ke model are reasonably good. The numerical procedurehas the ability to capture a narrow localized residence zone for the solid particles at a periphery location near the mid-separator wherethe two vortices merge and the suspension process occurs. Moreover, the analysis has proven to be useful in predicting the internal flowstructure of the primary phase, thereby, the separation of the particulate phase. The separated particles are forced to remain near theperiphery of the cylindrical separator and being concentrated at the mid-separator as a result of the strong centrifugal force. 2007 Elsevier Ltd. All rights reserved.

Keywords: Two vortices; Separator; Centrifugal force; Two-phase flow; Turbulence

1. Introduction

Separation technology has a dominant role in many pro-cess industries; e.g., is that of a crude and shale oil industry.The cylindrical separator is a newly technology for solidliquid separation and is increasingly attracting attentionin the oil and sand industry. There are many reasons forthe importance of quality separation; e.g., the increasingdemand on product purity, the gradual reduction in thequality of raw materials and the growing environmentalconstraints for the acceptability of waste materials. Separa-tion of oil and sand is therefore vital in the oilsand pro-duction and processing. Solids may be separated insettling tanks/basins or by mechanical devices. A wide vari-ety of commercial separators are used. Some of the morecommonly used types are static inclined screens, vibratingscreens, rotary screens, belt presses, perforated roll pressesand screw presses. Each of these separator types has one or

more disadvantages, such as high initial cost, high operat-ing cost, high maintenance cost and/or inadequate degreeof separation.

Swirl and vortex technologies have been developed dur-ing the last three decades with their major applicationshave been found in the vortex combustor, liquid atomizer,vortex flow meter, Hilsch vortex tube and many others. Avariety of opinions have been developed regarding theireffectiveness in the applications of these technologies,which vary from overwhelming support to conservative.Design and performance of swirl/vortex devices dependon the understanding of their characteristics, such as thevelocity and the pressure distributions, the strength of thecentrifugal forces, the vortex tube geometry and the sizeof the solid particles.

The separation action of the cylinder separator is basedon the effects of the centrifugal forces where the necessaryvortex action is produced by directing the fluid tangen-tially into the vortex generators. The vortex action distrib-utes the solid particles over the radius of the separator.The larger particles are forced near the periphery of the

0892-6875/$ - see front matter 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.mineng.2007.10.012

* Corresponding author.E-mail address:[email protected](A.M. Jawarneh).

This article is also available online at:

www.elsevier.com/locate/mineng

Available online at www.sciencedirect.com

Minerals Engineering 21 (2008) 366372
mailto:[email protected]:[email protected]


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separator, while the smaller ones remain closer to the cen-tral-axis. Investigation was conducted on the performanceof a vortex-separation system, regarding the particle sizeand its ability to retain the solid particles, through thework of Roberts (1968) and Barnhart and Laurendeau(1979). An experimental work in a cylindrical double vor-tex chamber was conducted byGeorgantas et al. (1987)in

order to predict the flow pattern of the inserted solid par-ticles. The minimum particle size retained in a vortexchamber was established in relation to different operatingparameters.

Studies of the turbulent flow field in cyclones are neededfor improving the cyclone performance. Experimentally,Deotte (1990)studied the velocity field in a small-size cylin-drical cyclone; Hoekstra et al. (1999) measured flow fieldparameters in a cyclone of industrial dimensions. Derksenand van den Akker (2000), utilizing the Reynolds stressmodel, found that velocities fluctuations near the centerare much higher than those close to the wall; Lu et al.(1999) measured the Reynolds stresses in a liquidliquid

hydrocyclone and reported that the turbulence is aniso-tropic.Boysan et al. (1982)simulated the two dimensionalturbulent flow in a cyclone using an algebraic stress model.Zhou and Soo (1990)predicted the time-averaged axial andtangential velocities and the pressure distributions usingthe ke model and compared them with Laser DopplerVelocimetry (LDV) measurements. Lu et al. (2001) simu-lated the turbulent flow in hydrocyclones using the ke,renormalization group of ke, and the Reynolds stressmodel and compared them with LDV. Hu et al. (2005)studied the 3D strongly swirling turbulent flows in acyclone separator using a Reynolds stress model and mea-

sured the velocities using LDV. Erdal et al. (1997) pre-

sented CFD simulation utilizing a commercial code CFX,whereby they used axis-symmetric assumption for thetwo-phase flow, and for the inlets, which are tangentiallyinclined, were simulated via specifying the rotational veloc-ity along with the axial and radial components. In addition,an expression was developed for the equivalent inlet tan-gential velocity for the axis-symmetric model, and the

effects of the inlet swirl velocity to the axial velocity onthe flow behavior was also carried out. Motta et al.(1997)presented a CFD model in the case of an axis-sym-metric flow for rotational two-phase flow in a gasliquidcylindrical separator.Jawarneh et al. (2005)have generateda swirling flow by using a single vortex generator and uti-lizing an expression that was developed for the pressuredrop.

An understanding of the mechanism of the double vor-tex separator to concentrate the dispersed phase using twostrong vortices is still insufficient. Therefore, this paper isconcerned with the ability of the double vortex cylinderto separate the oil from sand and to create a localized res-

idence zone for the solid particles at some distance from theend walls of the vortex cylinder using a numerical tech-nique based on the ke turbulent and the two-phase flowmodels. The mixture-granular multiphase and the RNG-based ke turbulence models are implemented in theCFD code Fluent 6.1 (Fluent Inc., 2003).

2. Numerical method

Since the flow simulation involved the combined effectsof turbulence and the two-phase flow, the mixture-granularmultiphase model and the RNG-based ke turbulence

model are implemented in this study.

Nomenclature

A inlet areaCp radial pressuredo diameter of the separator

dp diameter of the particlef drag functionL separator lengthp static pressureQin volumetric flow rateq velocity vectorr* normalized radius, r/Rer normalized radius, r/RoRe radius of exit portReo Reynolds numberRo radius of the separatorS swirl numberui, uj, uk velocity components in Cartesian coordinates

Vu Vz, Vr mean tangential, axial and radial velocitycomponents

v velocity

Greek symbols

a volume fractione turbulence dissipation ratel

dynamic viscosityk turbulent kinetic energyq densityt kinematics viscosityu inlet angle

Subscripts

f fluidin swirler inletp particler, u, z radial, tangential and axial coordinate, respec-

tivelyt turbulent

A.M. Jawarneh et al. / Minerals Engineering 21 (2008) 366372 367
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2.1. Geometry and materials

Fig. 2schematically shows the geometry for the presentsimulation, which was described in a previous study byJawarneh and Vatistas (2005). The double vortex separatorhas a cylindrical configuration with constant cross-sec-

tional area (Ro = 7 cm), circumferential inlets and a cen-tral-axis outlet. A swirl is imparted to the fluid via thetwo vortex generators shown inFig. 1. Each of the vortexgenerators has four perpendicular inlets through which thecompressed fluid enters. A number of passages with a cir-cular cross-section (din) are drilled at a specified angleu= 30. As the flow passes through the swirlers, it isguided to enter the vortex chamber in a tangential directionso that a vortex is formed inside the cylindrical chamber.The two vortex generators are placed at the opposite endsof the vortex chamber. Each generator has eight passageswith a diameter din= 1.267 cm and an inlet areaA1,2= 10 cm

2. The chamber length L is set to 42 cm and

the radius of the exit opening Reis set to 1.75 cm. The mix-ture flow rate Qin through each generator is 0.014 m

3/s.The density of the engine-oil qf, was used for the primaryor the continuous phase 889 kg/m3 while the density ofsand particlesqp, defined as the secondary phase or the dis-persed phase, was set at 2500 kg/m3. The particle size dpwas chosen 250 lm according to a recommendation out-lined byGeorgantas et al. (1987). The feed volume fractionap at the two inlets is 0.1.

2.2. Governing equations

2.2.1. Mixture modelThe swirling flow was considered to be turbulent, incom-

pressible, steady and axis-symmetric The mixture modeluses a single-fluid approach and allows the phases to beinterpenetrating. The continuity and the momentum equa-tions are solved for the mixture while the volume fractionequation is used for the secondary phase, in addition toalgebraic expressions for the relative velocities if the phasesare moving at different velocities.

The continuity equation for the mixture is

r qv 0:0 1

where v is the velocity of the mixture,

vafqfvf apqpvp

q 2

and qis the mixture density,

q afqf apqp 3

The momentum equation for the mixture can be obtainedby summing the individual momentum equations for allphases. It can be expressed as

r qvv rp r lrv rvT qg r

afqfvdfvdf apqpvdpvdp 4

wherel is the viscosity of the mixture as defined byBatch-elor (2000),

l lf 152ap

5

vdp is the drift velocity for the solid phase,

vdp vp v 6

The relative velocity or the slip velocityvpfis defined as thevelocity of the solid phase p relative to the velocity of thefluid phase f,

vpfvpvf 7

The drift velocity and the slip velocity are related through,

vdp vpf

afqf

q

apqp

q

vfp 8

Manninen et al. (1996) suggested the form of the relativevelocity as,

vpfqpqd

2p

18lff a 9

where dp is the diameter of the particles of the secondaryphase and a is the acceleration of the secondary phase.

Fig. 1. Schematic of the vortex chamber (Jawarneh and Vatistas, 2005).

368 A.M. Jawarneh et al. / Minerals Engineering 21 (2008) 366372
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The drag function f is taken from Schiller and Naumann(1935),

f 0:0183Reo 10

The Reynolds number Reo is defined based on the averageaxial velocity as,

Reo 4QinmpDo

11

and the accelerationa is of the form,

a g v rv 12

From the continuity equation for the secondary phase p,the volume fraction equation for secondary phase can beobtained,

r apqpv rapqpvdp 13

2.2.2. RNG ke model

The RNG-based ke turbulence model is derived fromthe instantaneous NavierStokes equations using a mathe-matical technique called renormalization group (RNG)methods. The analytical derivation results in a model withconstants different from those in the standard ke model,and additional terms and functions appear in the transportequations forkande, seeChoudhury (1993). The RNGkemodel is similar in form to the standard ke model, but ithas shown substantial improvements over the standardkemodel where the flow features of strong streamline cur-

vature, vortices, and rotation are included. So, the effect ofswirl on turbulence is included in the RNG model, enhanc-ing the solution accuracy for swirling flows.

Transport equations for the RNG ke model,

oqkui

oxi

o

oxj akleff

ok

oxj

qu0iu

0j

ouj

oxiqe 14

oqeui

oxi

o

oxj aeleff

oe

oxj

C1

e

k qu0iu

0j

ouj

oxi

C2q

e2

kRe

15

The quantities ak and ae are the inverse effective Prandtlnumbers for kand e and for high Reynolds number their

values are ak= ae1.393. The effective viscosity leff is

the sum of the laminar l and turbulent viscosities lt ofthe mixture,

ltqClk2

e

16

The model constants; C1, C2 and Cl are 1.42, 1.68 and0.0845, respectively. The main difference between theRNG and standard ke model lies in the additional termin the e equation given by

Re Clqg

31g=g0

1bg3e2

k 17

whereg=Sk/e,g0= 4.38,b= 0.012. The swirl numberSisdefined as the ratio of the axial flux of angular momentumto the axial flux of axial momentum:

SRRo

0

qVzVur2dr

RoRRo

0 qVzr2dr

18

whereRois the separator radius,Vuand Vzare the tangen-tial and axial velocities components.

Turbulence is affected by the swirl in the mean flow. TheRNG model provides an option to account for the effectsof swirl by modifying the turbulent viscosity appropriately.The modification takes the following functional form,

ltltof W; S;k

e

19

where lto is the value of the turbulent viscosity calculated

without the swirl modification using Eq. (16), and W is aswirl constant that takes on different values depending onwhether the flow is swirl-dominated or only mildly swirling.For strongly swirling flows as in the present work a valueof 0.08 was used.

2.3. Boundary conditions and numerical schemes

At the two inlets to the vortex chamber uniform velocitycomponents are used. The same velocity is specified forboth the fluid and particulate phases. The total inlet veloc-ity vector qin at both inlets has two components Vr in and

Vuin and they are related to each other by,

Fig. 2. Schematic diagram for the geometry used for the simulation.

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Vu in q in cosu 20

Vr in q in sinu 21

where qin= Qin/Ain.It should be noted that the vortex at the right end acts

clockwise while the left one acts in the counter clockwise.

At the outlet boundary there is no information about thevariables and some assumptions have to be made. The dif-fusion fluxes in the direction normal to the exit plane areassumed to be zero. At the solid walls, the no-slip conditionwas applied where the velocities at the walls were specifiedto be zero. The centerline boundary was considered axis ofsymmetry.

A phase-coupled SIMPLE algorithm for the pressurevelocity coupling is adopted. The second order upwindschemes were used for the momentum and the swirl veloc-ity while first order upwind schemes were used for the tur-bulence kinetic energy, turbulence dissipation rate, and

volume fraction. Convergence was assumed when the resid-ual of the equations dropped more than three orders ofmagnitude. Triangular mesh elements and an unstructuredgrid were used for the separator. The mesh is sufficientlyrefined in order to resolve the expected large flow parame-ter gradients. The under-relaxation parameters for thevelocities were selected 0.30.5 for the radial and axial,and 0.9 for the swirl velocity components. The segregatedimplicit solver, which is well suited for the sharp pressureand velocity gradients, has been applied for the solutionof the separator. When using the present models it is nec-essary to run the simulation for a significant number ofiterations beyond normal convergence criteria. Experience

has shown that typically 6000 iterations are needed beforethe peak tangential velocity in the simulation stabilizes. Anindependent grid sensitivity study was conducted by per-forming simulations for three different grids consisting of

33,000, 37,000 and 48,000 nodes. It was observed that therewas no significant variation in the solutions utilizing thelater two grid sizes; therefore a grid size of 37,000 wasadopted.

3. Results and discussion

In order to gain confidence of the modeling methodol-ogy, that is required to adequately simulate the separatorflow, the experimental work ofGeorgantas et al. (1986)was used for comparison purposes of the modeling resultspresented in this paper. Fig. 3 compares the tangentialvelocity and the radial pressure distributions. The resultspresented inFig. 3a where obtained using the renormaliza-tion group ofke model. The tangential velocity increasessharply with the radius in the central core region then itdecreases. This is a typical radial transition between a freeand a forced vortex regions. The two vortex modes areclearly captured and compares well with the measured val-ues. The mean pressure coefficient Cp is defined as,

Cp2 pr pr 1

qV2in; wherer

r

Ro22

It is obvious fromFig. 3b that the renormalization groupofkemodel can capture the experimental points. It is evi-dent that the maximum pressure occurs at the longitudinalwall of the separator due to the action of the centrifugalforces. The pressure decreases at a progressively higher rateas the center of the separator is approached.

The most important feature of the double vortex systemis its ability to create a localized residence zone for the solid

particles, as shown inFigs. 4 and 5, at some distance fromthe end walls of the vortex chamber, whereby in that regionthe suspension process can take place. Upon the introduc-tion of the mixture through the two swirlers, the particles

0

5

10

15

20

25

30

0 0.2 0.4 0.6 0.8 1

Experiment Georgantas et al (1986)

Vt, x=35 cm, Re=2.8 cm fluent

MeanSwirlVelocity

(m/s)

Present Prediction

r

V

-10

-8

-6

-4

-2

0

2

0 0.2 0.4 0.6 0.8 1

Experiment georgantas et al (1986)

Presenrt Prediction

r

Cp

a b

Fig. 3. Comparison of the flow field at a plane ofz = 300 mm obtained from the measurements and the CFD simulation: (a) mean swirl velocity and (b)

mean pressure coefficient.

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are suspended by the action of the axial drag force pro-duced by the right swirl generator meanwhile they are pre-vented from leaving the exit opening by the action of theleft swirl generator. So, the two axial drag forces actingin opposite directions at the periphery of the chamber arehigh enough to confine the particles in a narrow zone wherethe two vortices merge. The tangential drag forces acceler-ate the particles toward the periphery while the radial dragforces retard the particles toward the center of the cham-ber. For particle equilibrium in the horizontal plane thecentrifugal forces must balance the radial drag forces. Anadditional feature of the double vortex flow system is thatthe residence zone of the solid particles can be shiftedalong the height of the chamber by altering the flow ratesfrom the two inlet ports. The best performance is obtainedwhen the bottom to top mixture flow ratio is equal to unitywhere the strength of both vortices are the same, and theresidence zone is formed at the middle level of the separa-tor. From the numerical simulation the volume fractioncontours for the two-phases are shown in Figs. 4 and 5.The distributions of the volume fractions are evaluatedover the cross-sectional (rz) plane of the cylindrical sepa-rator using the contour maps. The portion shown in warmcolors such as red and orange indicate high concentrationscompared with those shown in cold colors such as blue and

sky blue.Fig. 4shows the liquid volume fraction distribu-

tion whereby it is seen that the flow field in the separatorconsist of strong swirling flow of high velocity aroundthe center (forced vortex region) and weak swirling flowof low velocity near the wall (free vortex region). Thestrong swirling flow in the center results in centrifugalforces that propel the solid particles to the outer free-vortexregion, where particles are collected and reside in the weakswirling intensity region. Thus pure liquid-phase will flowthrough the exit port; meanwhile some solid particles willescape at the periphery of the exit port. Solid particles of250 lm in size are shown inFig. 5. The particles are morelikely to be collected at the mid-separator because theyexchange more momentum and energy during the collisionand hence the majority of the particles do not trace theliquid flow, so the solid particles are trapped at the mid-separator.

4. Conclusions

The numerical methodology presented herein establishesthat the double vortex separator technology is potentiallyof a significant value in the area of designing and utilizingseparators. The mixture-granular multiphase model andRNG-based ke turbulence model are able to predict theflow features inside the separator such as the tangential

velocity and the radial pressure profiles. The results of

Fig. 4. Contours of the volume fraction of the liquid phase.

Fig. 5. Contours of the volume fraction of the particulate phase.

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the numerical simulation were compared with the experi-mental data and were found in reasonable agreement.The analyses reveal from the behavior of the mean tangen-tial velocity distribution that the flow of the vortex separa-tor is of a forced-vortex inside the core and a free-vortexoutside the core. The maximum pressure was observed to

occur along the longitudinal wall of the separator as aresult of the strong action of the centrifugal forces and itdecreases sharply as the center of the separator isapproached. The collected solid particles at the mid-separa-tor are predicted using the present models and the best per-formance is obtained when the bottom to top mixture flowratio is equal to unity where the strength of both vorticesare the same. As a result of the strong centrifugal force,two vortices are formed causing the solid particles andliquid to separate. The solid particles move toward thewall, while the liquid flows to the center and leaves fromthe exit opening. The majority of the particles are forcedto remain near the periphery of the separator, while fewer

ones escape from the outer exit annulus.

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swirling flows in a cylindrical separator

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