1-s2.0-S0263876212002432-main

chemical engineering research and design 9 0 ( 2 0 1 2 ) 21352147

Contents lists available at SciVerse ScienceDirect

Chemical Engineering Research and Design

r .co

Comp arasepar oc

GuofengSchool of En T 26

a

T devic

u a con

c ap si

h and

e D) m

re uen

mini-hydrocyclone at a low Reynolds number (Rein = 300) because of the onset of centrifugal instability. The centrifu-

gal instability offered an insight into the ow transition and the development of turbulent ow in hydrocyclones

which have not been studied. The centrifugal instability in the mini-hydrocyclone begins as Grtler vortices devel-

oping in the boundary layer and they subsequently affect the ow eld. Particle motion tracing showed that improved

separation with ner cut size, d50, and steeper separation sharpness were obtained as the inlet velocity was increased.

T

K

1. Int

Although tgressed sigmicro-devilagged behsolids in thmicro-reactions (Robefrom the dequipmenting parts. Tuidsolid ment in thmicro-devible solution

A typicabody with with an unticles is inj

CorresponE-mail aReceived

0263-8762/$http://dx.dohe improvement can be explained by the ow characteristics when the ow transits to turbulent ow.

2012 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

eywords: Mini-hydrocyclone; CFD; Centrifugal instability; Grtler vortex; Particle separation

roduction

he development of the micro-reactor has pro-nicantly in recent years, the development of

ces for separating out the products and wastes hasind. The lack of useful micro-devices for handlinge product streams has limited the application oftor technology to a wider range of industrial reac-rge et al., 2005). The dearth of investigations stemsifculty in miniaturising conventional separation

due to the complex internals and extensive mov-herefore, the development of a simple and feasibleseparation device is critical to further advance-e use of micro-technology in a large number ofces. The mini-hydrocyclone is proposed as a possi-

for its simple geometry and lack of moving parts.l hydrocyclone (Fig. 1) consists of a cylindricala central tube (vortex nder) and a conical bodyderow orice. The uid containing the solid par-ected tangentially through the feed inlet into the

ding author.ddress: [email protected] (J.-L. Liow).

7 December 2011; Received in revised form 23 May 2012; Accepted 30 May 2012

hydrocyclone giving rise to outer and inner swirling ows andgenerating centrifugal force within the device. This centrifugalforce eld brings about a rapid classication of particles basedon particle size difference. Large particles are centrifugedoutwards to the hydrocyclone wall and leave through theunderow orice with the outer swirling ow. Fine particlesdragged in by the uid ow are removed by the inner swirlingow through the overow in the vortex nder (Hoffmann andStein, 2007). The particle size at which 50% separation ef-ciency to a hydrocyclone underow occurs is dened as thecut size, d50. As the majority of particles ner than the cutsize will be collected from the overow, a smaller cut size rep-resents the hydrocyclones ability to separate ner particles(Svarovsky, 1984).

An important dimensionless number for hydrocycloneoperation is the Stokes number based on the cut size, Stk50,dened as:

Stk50 = F

= vchd250

18D(1)

see front matter 2012 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.i.org/10.1016/j.cherd.2012.05.020j ourna l ho me page: www.elsev ie

utational study of the ow chation efciency in a mini-hydr

Zhu, Jong-Leng Liow , Andrew Neelygineering and Information Technology, UNSW@ADFA, Canberra, AC

b s t r a c t

he development of a simple and feasible uidsolid separation

se of micro-technology. The mini-hydrocyclone, which possesses

ess, has been proposed as a promising solution to bridge this g

ydrocyclone diameter. In this work, we investigated the uid ow

ter mini-hydrocyclone through computational uid dynamics (CF

sults with CFD have shown that the ow transition and subseqm/locate /cherd

cteristics andyclone

00, Australia

e is critical to further advancement in the

cise geometry and simple operational pro-

nce the cut-size decreases with decreasing

particle separation ability of a 5 mm diam-

odelling. Direct numerical simulation (DNS)

t unsteady state behaviour occurred in the

2136 chemical engineering research and design 9 0 ( 2 0 1 2 ) 21352147

a

b

CDd50D DdDxEuf(d)

FcFpFvg HHcMiMoP P

Qr

ReinRepS Stk50u(d)

utv vchvinw x z

Greek sym

m

p

F(d)(d50) x

where density () a

yclo 2

ased

D the ctime bhydrocyclone feed inlet dimension (vertical),mmhydrocyclone feed inlet dimension (horizontal),mmdrag coefcientparticle cut size, mhydrocyclone diameter, mmhydrocyclone underow diameter, mmhydrocyclone overow diameter, mmEuler numbertotal number of a certain size particle countedin the feedcentrifugal force, kg m/s2

pressure gradient force, kg m/s2

viscous effects force, kg m/s2

gravitational force, kg m/s2

hydrocyclone total height, mmhydrocyclone conical section height, mmmass ow rate of the inlet, kg/smass ow rate of the overow, kg/sstatic pressure, Papressure drop across the hydrocyclone inletand outlet, Pavolumetric ow rate, m3/sradial position from hydrocyclone central axis,mmReynolds number based on inlet velocityReynolds number based on relative velocityhydrocyclone vortex nder length, mmStokes number based on the cut sizenumber of a certain size particle counted at theunderowlocal azimuthal or tangential velocities, m/svelocity in the y-direction, m/scharacteristic velocity, m/sinlet velocity, m/svelocity in the z-direction, m/sdownstream distance from the inlet, mmaxial distances measure from the top of thecyclone, mm

bolsdensity difference between the uid and parti-cle, kg/m3

uid viscosity, Pa sangular momentum per unit mass of a uidelement, m2/smomentum thickness of a Blasius boundarylayer, mmkinematic viscosity, m2/suid density, kg/m3

particle density, kg/m3

particle relaxation time based on the densitydifference, scharacteristic timescale of the uid, sseparation efciency of a certain size particleseparation efciency at the cut sizeX-vorticity, 1/s

is the density difference between the uid phasend particle phase density (p,), the uid viscosity,

timescale.

vch =4Q

D2

where Q iscan be viewform. As anit is a meas

Anothernumber, Eucyclone inlunit volum

Eu = P(1/2)

As the Epressure drand is a me

For geoconcentrattionship foStk50 and E

Stk50 Eu =

The Eulcyclone desthe Euler nber, resultinpower greaing on the the above e

Stk50 Eu

From the abstant, in ag(1984) of d5

From thvolumetric

Stk50 Eu

Therefore, which is sby Svarovshydrocycloa smaller c

Currentindustry ancyclones hsize around(dominant centration and Harriso(diameter: ery (>97%) 2008). A recaration of ne diameter, = d50/(18) the particle relaxation the density difference, F = D/vch the characteristicThe characteristic velocity, vch, is dened as

Q

D2(2)

the feed volumetric owrate. The Stokes numbered as representing the cut size in a dimensionless

increasing Stk50 means an increasing cut size d50,ure of the separation quality.

important dimensionless number is the Euler, dened as the pressure drop across the hydro-et and outlet, P, divided by the kinetic energy pere:

v2ch

(3)

uler number is normally used in problems whereop is important, it is also called pressure coefcientasure of the cost of separation.metrically similar hydrocyclones at low solidsion, Svarovsky (1984) found that the following rela-r particle separation in a hydrocyclone involves theu as:

d250P

9Dvch d

250P

Dvch= constant (4)

er number of a gas cyclone is constant for a givenign (Hoffmann and Stein, 2007). For hydrocyclones,umber increases slightly with the Reynolds num-g in the pressure drop increasing with velocity to ater than 2, typically to 2.4, i.e., P v22.4

chdepend-

hydrocyclone design (Svarovsky, 1984). Therefore,quation can be rewritten as

d250v(11.4)ch

D d

250P

(0.50.58)

D= constant (5)

ove equation, d50 D0.5 when P or vch is kept con-reement with the relationship given by Svarovsky

0 D0.420.5.e relationship between characteristic velocity and

owrate, the above equation can be rewritten as

d250Q(11.4)

D(33.8)= constant (6)

d50 D1.51.9, at a constant volumetric owrate,imilar to the relationship of d50 D1.51.69 givenky (1984). The above analysis shows a mini-ne with smaller diameter should be able to provideut size.ly, the smallest hydrocyclone regularly used ind research is 10 mm in diameter. The 10 mm hydro-ave been used to dewater quartz slurry with a cut

3 m (Pasquier and Cilliers, 2000), dewater yeastcell diameter: 4.55.5 m) with a high cell con-ratio of 2.0 and absence of cell breakage (Cilliersn, 1997), and separate Chinese hamster ovary cells

840 m) from exhausted medium with high recov-and low cell viability losses (

chemical engineering research and design 9 0 ( 2 0 1 2 ) 21352147 2137

Fig. 1 (A) ovskcharacteris

diameter mow at 30 mThey foundseparation Clearly, thegest that to investigaoperations,enced by pa

A consiusing compows in hyding from 10in the lamiwith inlet not found iand Parks mini-hydrotion rather velocity conof the uidhydrocycloa steady lam

In this wcyclone wafor two inlmation of (Zhu et al., lished for tinlet velocimodelling tvelocities c3) suggestsstate behavReynolds nity. The cenas Grtler van importafor differenshowed imThe improvwhen the

Nution

onsitordernumuatir inc

= 0

) =

u is ts stretenso

u +

equA typical hydrocyclone conguration and ow pattern (Svartic dimensions in the vertical plane.

ini-hydrocyclone producing a 27% decanol over-l/min at an overow to underow ratio of 0.375.

that increasing the feed pressure improved theefciency but at the cost of higher pressure drops.

current studies on small hydrocyclones do sug-ne particle separation is achievable, but studieste the parameters controlling small hydrocyclone

especially how ne particle separation is inu-rticle interaction, are lacking.

derable amount of research has been performedutational uid dynamics (CFD) to model turbulentrocyclones with the inlet Reynolds numbers rang-5 to 106, but there are few computational studiesnar/transitional ow region in mini-hydrocyclonesReynolds numbers of 102103 as this regime isn conventional hydrocyclones. Early work by Petty(2004) of a 5 mm oil/water cylindrical shapedcyclone modelled only the liquidliquid separa-than particle separation, and only provided overalltours without further exploring the characteristics

structure. Zhu et al. (2010) modelled a 5 mm mini-ne with an inlet velocity of 0.1 m/s and showed that

inar ow was developed.ork, the uid ow in the 5 mm diameter hydro-

s modelled by direct numerical simulation (DNS)

2.condi

As thenar/traof the direct ow eqance fo

(u)

(uu

whereviscoustress by

= (

Theet velocities (0.2 and 0.4 m/s) focusing on the for-centrifugal instabilities. Although the early work2010) showed that a steady laminar ow was estab-he inlet velocity of 0.1 m/s (Rein = 150 based on thety and inlet pipe dimension), this study extends theo the 0.2 m/s (Rein = 300) and 0.4 m/s (Rein = 600) inletases. The centrifugal instability criterion (Section

that the ow transition and subsequent unsteadyiour arises in concave ow regions at quite low

umbers because of the onset of centrifugal instabil-trifugal instability in the mini-hydrocyclone beginsortices developing in the boundary layer and playsnt role in determining the uid ow characteristicst inlet velocities. Particle motion simulation alsoproved separation results at a higher inlet velocity.ement can be explained by the ow characteristicsow transits into turbulence.

dup

dt= FD(u

which is a tion for parside of the the gravitagroup IV is(force/unit

The ui

FD = 18d2pp

C

Rep is the re

Rep =dp

uy, 1984); (B) schematic of a hydrocyclone with the

merical model and simulations

w in the mini-hydrocyclone falls in the lami-ional ow regime with an inlet Reynolds number

of 102103, this study used a ne mesh to obtain aerical simulation (DNS) of the ow eld. The uidons for mass (Eq. (7)) and momentum (Eq. (8)) bal-ompressible ow in a mini-hydrocyclone are:

(7)

P + ()

+ g (8)

he uid velocity vector, P the static pressure, thess tensor, and g is the gravitational body force. Ther for a constant viscosity Newtonian uid is given

uT) (9)

ation for the particle velocity vector, up, is given by

( )

up)I

+ g p pII

+ 12

p

d(u up)dt

III

+ PpIV

(10)

simplied BassetBoussinesqOseen (BBO) equa-ticle motion (Crowe et al., 2011). On the right handequation, group I is the uid drag force, group II istional force, group III is the virtual mass force and

the pressure gradient force per unit particle massparticle mass).d drag force factor, FD, is given by

DRep

24(11)

lative Reynolds number, dened as:

p u

(12)


Table 1

Geometri

Diameter, DTotal heighConical secOverow dVortex ndFeed inlet dUnderow

CD is the (Haider and

CD = 24Rep

(1

where b1, b0.6459, 0.42

The minhydrocycloles have bby a numbRajamani, 5 mm minilier comparfound in Zh

The minnates withand coupleThe CFD codouble precthe pressurto steep prpressure-imused for caccurate qu(QUICK) scadvection tat the inleset with presure was sethe liquid pvelocity prtions were inlet pipe fed by theare not strocentral regimini-hydro

The accvergence cpendence. discrepancall the scaldence tests2.6 millionrate of the sity of 1.3 m0.5% of thastep tests w0.0001 s, anstep as the0.5%.

Mini-hydrocyclone mesh and the prole position ofrtical plane used for presenting the results.

iews of turbulence ow and particle separation stud-ydro

2007an gFD mparmerydrot anda.

bettne atn thevertiand

Re

Un

howini-hdy bs ovoverus in

4

6

8

time-averaged

0.0 0.5 1. 0 1. 5 2. 02

4

6

8

A

BDimensional details of the mini-hydrocyclone.

cal properties Dimensions (mm)

5.00t, H 16.82tion height, Hc 11.82iameter, Dx 1.67er length, S 3.34imensions, a b 1.67 1.34

diameter, Dd 0.84

drag coefcient for spherical particles given by Levenspiel, 1989) as:

+ b1Reb2p ) +b3Rep

Rep + b4 (13)

2, b3 and b4 are constants with values of 0.1806,51 and 6880.95 respectively.i-hydrocyclone simulated is a 1:15 scale of a 75 mmne (Hsieh, 1988) where experimental velocity pro-een reported and have been studied numericallyer of researchers (Brennan, 2006; Delgadillo and2005; Wang et al., 2007). The dimensions of the-hydrocyclone are shown in Table 1 while an ear-ison with the original 75 mm hydrocyclone can beu et al. (2010).i-hydrocyclone was meshed in Cartesian coordi-

structured meshes in the bulk of the ow domaind to unstructured meshes around the vortex nder.de FLUENT V13.0 was used to model the ow inision. The pressure interpolation scheme used wase staggered option (PRESTO), which is well-suitedessure gradients involved in swirling ows. Theplicit with splitting of operators (PISO) algorithm wasoupling the pressure and velocity. A third-orderadratic upstream interpolation convective kinematics

heme was used for spatial discretisation of theerms. A velocity inlet boundary condition was usedt, while the overow and underow outlets weressure outlet conditions. The reference gauge pres-t to 0 Pag at the outlets. The physical properties ofhase are those of water at 20 C. Fully developed

oles used as the inlet velocity boundary condi-obtained separately from the simulation of a longor the three velocity components, and are identi-

average inlet velocity. The velocities in this studyng enough to generate a negative pressure in theon to form an air core, so water completely lls thecyclone.uracy of the simulation depends on the con-riteria, mesh independence and time step inde-The convergence criteria used were that the

Fig. 2 the ve

Revies in het al., tions cThe Cby comous numini-hpresental dat

For2D plainlet. Ias the radial

3.

3.1.

Fig. 3 sthe munsteasionlesof the previo

0.7

0.7

0.7

0.7

0.7

0.7

0.7

nle

ss o

ve

rflo

w r

atey in the global mass balance was below 0.1% anded residuals were below 1 105. Mesh indepen-

were conducted for mesh densities of 0.7, 1.3 and cells by monitoring the time-averaged mass owoverow, and this was achieved with a mesh den-illion as the deviation of the ow rate was below

t from the 2.6 million cells case. In addition, timeere carried out at time steps of 0.001, 0.0005 andd time independence was achieved at 0.001 s per

difference from the smallest time step was within

0.72

0.74

0.76

0.78

0.72

Dim

en

sio

Fig. 3 Dimhistories o0.1 m/s (Re(Rein = 600).cyclones (Mousavian and Naja, 2009; Narasimha; Wang et al., 2007) have shown that CFD simula-ive excellent agreement with experimental results.odel used in this study was previously validated

ing a 75 mm hydrocyclone simulation with previ-ical and experimental results (Zhu et al., 2010). Thecyclone simulation cannot be directly validated at

work is currently in progress to obtain experimen-

er visualisation, results are presented for a vertical specied azimuthal angles of 0 and 180 facing the

rest of the paper, this plane is simply referred tocal plane. The resolved directions of positive axial,tangential velocities are shown in Fig. 2.

sults and discussion

steady ow and centrifugal instability

s the dimensionless overow rate time histories ofydrocyclone for the three inlet velocities, and theehaviour begins with the 0.2 m/s case. The dimen-erow rate, Mo/Mi, is the ratio of the mass ow rateow, Mo, to the mass ow rate of the inlet, Mi. Avestigation by Zhu et al. (2010) of the 0.1 m/s case

instantaneous0.0 0.5 1.0 1.5 2.0

0.0 0.5 1. 0 1. 5 2. 0

Flow time (s)

C

ensionless overow rate, Mo/Mi versus timef mini-hydrocyclone for three inlet velocities: (A)

in = 150), (B) 0.2 m/s (Rein = 300) and (C) 0.4 m/s


Fig. 4 Con azi(A) 0.1 m/s, neostatistically

showed thaHowever, thlation whic0.4 m/s casof unsteadynumber, artime-averatistically stand 0.4 m/s

Fig. 4 shhydrocyclovelocities, walls to a radius of thcentral axisa ow eldtial velocitythe inlet toincrease in

A uid pcyclone wathe wall. Pnumber inclayer on a Martinez aThese secocan lead toturbulent ow over a

Althougmechanismclassied atours of tangential velocity in the vertical plane (0 and 180 (B) 0.2 m/s and (C) 0.4 m/s inlet velocities (B and C instanta

steady state).t it laid in the steady laminar ow regime (Fig. 3A).e Mo/Mi for the 0.2 m/s case shows a small oscil-h increases and becomes more irregular for thee (Fig. 3B and C). These results suggest that onset

state behaviour occurred at a low inlet Reynoldsound 300, in the mini-hydrocyclone. Furthermore,ged analysis of the overow data shows that a sta-eady ow is reached after 0.5 s and 1 s for the 0.2

cases respectively.ows the tangential velocity contours in the mini-ne for the three inlet velocities. The tangentialut, vary from zero at the cyclone or vortex ndermaximum at a position approximately half thee cyclone diameter. The tangential velocity at the

is either zero or slightly negative as there exists asymmetry of the central uid core. The tangen-

decreases in magnitude as the ow moves from the underow with the energy transferred to an

the axial velocity and pressure losses.article moving with the tangential ow near thell is strongly inuenced by the boundary layer atrevious studies have shown that as the Reynoldsrease, secondary ows are formed in the boundaryconcave surface (Mangalam et al., 1985; Navarro-nd Tutty, 2005; Peerhossaini and Wesfreid, 1988).ndary ows result in centrifugal instabilities that

the breakdown of laminar ow and a transition toow at lower Reynolds numbers to that found for

at surface (Guo and Finlay, 1994).h centrifugal instabilities share the same physical

of the secondary ow formation, they have beenccording to the different geometries they appear

due to diffethree majobetween twbility of oow on consurface arelayer on the

The onssimilar meary layers. increases wthe hydrocywall, a mawhere d|rutticle in thethe pressurcentrifugalshown in Fijected to anpressure grmotion. Thgal force exviscous effe

Criminainviscid casr (with an in radial diut + ut). Afresisting th

Fp Fc = 2rmuthal positions) of the mini-hydrocyclone forus results one time-step after the ow reached arences in the ow eld generated (Saric, 1994). Ther groups are the TaylorCouette instability of owo rotational concentric cylinders, the Dean insta-w in concave ducts, and the Grtler instability ofcave surfaces. As the cyclone wall has the largesta, Grtler instability generated at the boundary

cyclone wall is the main source of uid instability.et of secondary ows for a concave wall followschanisms found in the transition of planar bound-For a concave surface, the angular momentumith increasing radial distance from the centre ofclone. Since the angular momentum is zero at the

ximum in the angular momentum with a region|/dr < 0 must exist. The force balance for a uid par-

boundary layer experiences competition amonge gradient force, Fp, viscous effects force, Fv, and

force, Fc (Criminale et al., 2003; Saric, 1994). Asg. 5A, a uid element close to a concave wall is sub-

outward centrifugal force and a combined inwardadient and viscous force opposing the direction ofe element will ow outwards once the centrifu-ceeds the resultant force from the pressure andcts (Fig. 5B).le et al. (2003) gave an instability analysis for thee by describing a uid element at a radial position,original velocity ut) displaced to a small distancerection to new position, r + r (with a new velocityter displacement, the pressure gradient force, Fp,e centrifugal force, Fc is given by

(r

r

) (u2t + ut r

utr

)(14)


Fig. 5 Simple concave wall ows: (A) force analysis of uid element; (B) secondary movement; and (C) secondary toroidalvortices (Saric, 1994).

The last bracketed term is also the radial rate of change of thesquare of the angular momentum per unit mass, (Rayleigh,1917), and the ow becomes unstable when

d 2

drFp Fc

(u2t + ut r

dutdr

)< 0 (15)

which means the uid will not return to its original locationonce it is displaced.

Fig. 6I sin Eq. (15). between thand a negaovercome tties forminare observetex nder the area thvelocity inchence the ber; howev

inertia forces is very large, the viscous effect will not restrainthe instability. These results are consistent with the unsteadystate behaviour observed only for the overow mass ow ratesof the 0.2 and 0.4 m/s inlet velocities studied.

Fig. 6II shows the pressure gradient contours, dp/dr. Thepositive contours indicate that the pressure gradient has alocal minimum at the cyclone and vortex nder walls andincreases towards the central axis. Hence the pressure gradi-ent force at the cyclone wall is small and is unable to resist the

ugalility o

Flo

Grticeperimo-MThe r a all

Fig. 6 I: Cmini-hydroplane (0 ahows the contours of the stability criterion givenIt can also be seen as representing the differencee pressure gradient, Fp, and centrifugal force, Fctive value indicates that the centrifugal force hashe pressure gradient which will result in instabili-g in the boundary layer. Although negative valuesd for every inlet velocity at the cyclone and vor-

walls, the occurrences increase dramatically andey cover extends further downwards as the inletreases. Viscosity acts to provide some stability andow will be stable below a small Reynolds num-er, when the imbalance between the viscous and

centrifinstab

3.2.

3.2.1. The voied exNavarr1988). that fothe smontours of the stability criteria (Eq. (15)) in the vertical plane (0

cyclone for (A) 0.1 m/s and (B) 0.4 m/s inlet velocities. II: Contournd 180 azimuthal positions) of the mini-hydrocyclone for (A) 0.1 force, Fc, resulting in the likelihood of centrifugalccurring.

w characteristics in the mini-hydrocyclone

rtler vortices and tangential velocitiess caused by the Grtler instability have been stud-entally and numerically (Mangalam et al., 1985;

artinez and Tutty, 2005; Peerhossaini and Wesfreid,early and pioneering work (Grtler, 1941) showedreal uid, although the viscous force stabilisesnegative imbalance given in Eq. (15), centrifugaland 180 azimuthal positions) of thes of the pressure gradient (dp/dr) in the vertical

m/s and (B) 0.4 m/s inlet velocities.


Fig. 7 Con al po0.2 and (C) r thetime-avera

instability din the streaGrtler vor

As showNavarro-Mation of Grtand velocitused, the vewith the YZx, on the v

x = wy

where v anX-vorticity and negativclockwise rvelocity (Fivortices in ues of vortinside wall(Fig. 7B), thing in the ithe negativdevelopmethe vortex For the 0.4 mthe presenregions closvortices. Aof the cycloFig. 8. In cona more uniinstantanetheir positi

The Grtrifugal for

f the

m(

m isnd ickntream

writl Grtours of vorticity in the vertical plane (0 and 180 azimuth0.4 m/s inlet velocities (B and C1 one time-step results afteged results).

oes occur giving rise to Grtler vortices stretchedmwise direction. For a closed concave surface, thetices take on a toroidal shape (Fig. 5C).n by previous studies (Guo and Finlay, 1994;rtinez and Tutty, 2005), the existence and distribu-ler vortices can be shown by the vorticity contoursy vectors plots. For the Cartesian coordinate systemrtical plane of the mini-hydrocyclone is coincident

plane and the vorticity contours are the X-vorticity,ertical plane, dened as:

v(16)

onset o1994)

G = utv

wherelayer atum thdownscan becriticaz

d w are the Y and Z velocities. Fig. 7 shows thecontours on the vertical plane, with the positivee contours representing the counter-clockwise andotational ows respectively. For the 0.1 m/s inletg. 7A), the vorticity contours show a pair of largethe centre of the mini-hydrocyclone with large val-icity at the walls of the underow outlet and the

of the vortex nder. For the 0.2 m/s inlet velocityere is the possibility of a Grtler vortex develop-nner surface of the vortex nder, as indicated bye and positive contours occurring together but itsnt may have been hampered by the short length ofnder as well as the strong swirling ow present./s inlet velocity, the instantaneous contours show

ce of positive and negative vorticity occurring ine to one another resulting in numerous secondary

n alternating pattern, observed in the lower partne wall as highlighted in Fig. 7C1, is magnied intrast, the time-averaged contours of Fig. 7C2 showform distribution of vorticity, indicating that theous Grtler vortices are randomly distributed andons are time-dependent.tler number, G, representing the ratio of the cen-ce to the viscous force provides a criteria for the

occur for a has shownnumbers.

For the 0as the magincreasing sectional aensure maof alternaticone sectiofurther doworice.

The velotions of ththe 0.4 m/sby a countof the walinto the paPeerhossaintices are smwall while their centrvortex pairthe wall (vowall (vortexby the Grtsitions) of the mini-hydrocyclone for (A) 0.1, (B) ow reached a statistically steady state and C2

Grtler vortices and is dened as (Guo and Finlay,

mr

)0.5(17)

the momentum thickness of a Blasius boundary is the kinematic viscosity. For m r, the momen-ess can be estimated from m (vx/ut)0.5 (x is the

distance from the inlet), so the Grtler numberten as G u0.25t x0.75r0.5. Although there is no xedtler number above which the Grtler instability will

wide range of concave surface problems, research

that the instability is more likely at higher Grtler

.4 m/s inlet velocity, the centrifugal force is largernitude of the tangential velocity, ut, increases withinlet velocity. Moreover, the decrease in the crossrea at the cone requires the velocity to increase toss balance. A signicant increase in the numberng positive and negative vortices is found in then and the presence of Grtler vortices can be foundn the mini-hydrocyclone towards the underow

city vector plot of Fig. 8 shows the size and posi-e Grtler vortices in the mini-hydrocyclone for

inlet velocity. Each clockwise vortex is balanceder-clockwise vortex along the vertical directionl, which is in agreement with previous researchttern of the Grtler vortices (Guo and Finlay, 1994;i and Wesfreid, 1988). The counter-clockwise vor-aller in diameter and their centres are closer to thethe clockwise vortices are larger in diameter andes are further away from the wall. Between each, the uid motion alternates between ow towardsrtex pairs ab, cd and ef) and ow away from the

pairs bc, de and fg). The ow patterns formedler vortices result in uid transfer that will affect


Fig. 8 VelFig. 7C1 shconcave wavelocity.

particle sepprole is smby the resu

The vartion at the Fig. 9 showinstability. for the inleprole is areduce thedistance dehydrocyclo

For an showed thventional hThe bounddened forle (Fig. 9Bpresence o

3.2.2. AxThe axial vdistance be

of the mini-hydrocyclone reverses its axial direction an

der. tes that teloci

liked th

insidthe s the

expthe idowy ocgimecomesulencetion.the Lds inresucentreto formtex nseparafrom tinlet vshapedwall anwhile

As towardC). Thetia of of the velocitow retour bLZVV rtion, hsepara

As upwarnder ocity vector plot of the dotted square region inowing the paired vortices arising from thell of the mini-hydrocyclone for the 0.4 m/s inlet

aration. The usual assumption that the velocityooth from the centre to the wall is not supported

lts from the uid ow simulations.iation of the tangential velocities with radial posi-axial distances of z = 5, 6 and 7 mm are plotted ining the changes under the inuence of the GrtlerFig. 9A shows smooth tangential velocity prolest velocity of 0.1 m/s. The almost parabolic velocity

consequence of the laminar ow. Viscous effects velocity with the maximum velocity at each axialcreasing as the ow progresses down the mini-

ne.inlet velocity of 0.4 m/s, the tangential velocitye free/force vortex proles usually found in con-ydrocyclones operating in the turbulent region.

ary layer on the cyclone wall is much more clearly the z = 5 and 6 mm positions with a free vortex pro-). The velocity proles for z = 5 mm also shows thef velocity inections in the free vortex region.

ial velocityelocity is initially directed downwards and at somelow the vortex nder, part of the ow near the

the vortex the 0.2 m/srecirculatinand cyclonhas shownsized particrecirculatinthat are recne particl

3.2.3. RaIt has beenand can beimportant rcentre of thmain radiathe inwardity distribuRecent wovelocity maesis encoun

The radthe three inity vectors drawn in Fan inward tre (Fig. 11Avelocities aimmediatewith a cornno-slip wathe vorticittop cover win Fig. 12. Tin the axiaing 180 arregions I athe uid isthat a counbut can be Fig. 11A. As upward swirling ow that exits through the vor-The locus of the zero axial velocity vectors (LZVV)he portions of the uid that ows to the underowo the overow. Fig. 10A shows that for the 0.1 m/sty, the LZVV is located around the vortex nder and

a long balloon. In the region between the cyclonee LZVV, the uid ows downwards to the underow,e the LZVV uid ows upwards.velocity is increased, the LZVV contour expands

wall and extends further downwards (Fig. 10B andansion and extension arise from the increased iner-nlet ow leading to an increase in the magnitudenward swirling uid velocity. Thus, the reversal ofcurs further away from the vortex nder. As thee transits to turbulence, the tip of the LZVV con-es sharper. The expansion and extension of thets in an increased volume for ne particle separa-

a higher inlet velocity should promote ne particle

ZVV zone expands, the amount of uid directedcreases and part of it does not enter the vortexlting in an annulus of recirculating ow betweennder outer wall and the cyclone wall as evident for

and 0.4 m/s inlet velocities (Fig. 10B and C). In thisg ow, the uid moves between the vortex ndere wall and then down the walls. Previous research

that the recirculating ow is rich in intermediateles (Renner and Cohen, 1978). The existence of theg ow may help retain intermediate sized particlesycled for further separation, thus assisting in thee separation through the vortex nder.

dial velocity generally accepted that radial velocities are small

neglected. However, the radial velocities play anole in the transport of the ne particles towards thee hydrocyclone. Hsieh (1988) has shown that the

l velocity is directed inwards to the centre driven by pressure force. Thus, the plot of the radial veloc-tion indicates how the ne particles are separated.rk (Hreiz et al., 2011) has shown that the radialgnitude is not negligible contrary (to) the hypoth-tered in the literature.

ial velocity contours in the mini-hydrocyclone forlet velocities are shown in Fig. 11, while the veloc-for the mini-hydrocyclone cylindrical section areig. 12. For the inlet velocity of 0.1 m/s, there isradial velocity from the cyclone wall to the cen-). Two regions (regions I and II) of outward radialre present. Fig. 12A shows that region I is locatedly below the cyclone top cover and is associateder vortex. The corner vortex originates from the

ll condition. As the pressure gradient is positive,y associated with it is negative near the cycloneall resulting in a clockwise rotation as observedhis corner vortex is then advected with the owl direction and appears at region II after travers-ound the cyclone. The vertical distance betweennd II provides a visual indication of how rapidly

entering and exiting the mini-hydrocyclone. Noteter-rotating vortex below region I is rather weak

identied by the positive radial velocity contour in the inlet velocity is increased (Fig. 12B and C), the


Fig. 9 The tangential velocities on the vertical plane (0 and 180 azimuthal positions) varying with radial position at axialdistances of z = 57 mm of the mini-hydrocyclone for (A) 0.1 m/s and (B) 0.4 m/s inlet velocities. Values for B areinstantaneous result at one time-step after the ow reaches steady state; (C) the locations of the axial distances in themini-hydrocyclone as measured downwards from the top of the cyclone.

Fig. 10 Contours of the axial velocity in the vertical plane (0 and 180 azimuthal positions) of the mini-hydrocyclone for(A) 0.1 m/s, (B) 0.2 m/s and (C) 0.4 m/s inlet velocities. A positive value indicates upward axial velocity and a negative valueindicates downward axial velocity; B and C1 instantaneous results one time-step after the ow reached a statisticallysteady state and C2 time-averaged results.


Fig. 11 Co zimu0.1 m/s, (B) catesindicates in timestate and C

corner vortary layer bvortex becocorner vort

The cornaffected byAs the inletowing upof the owentrains inand vortexand an incinlet velociing of the cvortex, regiinlet veloci

For the iat the bounshow a cleafrom the foin the coneinlet velocicontours aGrtler vor

The raddirection agesting thafor all the inthe ow is be inuenc

3.3. Sep

The particcle tracking

ose g/m3

racke 25, 3h siow cy,

ed atntours of radial velocity in the vertical plane (0 and 180 a 0.2 m/s and (C) 0.4 m/s inlet velocities. A positive value indiward radial velocity; B and C1 instantaneous results one 2 time-averaged results.

ex (region I) becomes smaller in size as the bound-ecomes thinner. The counter-clockwise rotatingmes stronger and leads to more ow bypassing theex region.er and advected vortices (regions I and II) are also

the upward ow of uid towards the vortex nder. velocity increases, so too does the volume of uidwards to the vortex nder. An increasing amount

are th2600 kwere t15, 20,for eacunderefciencollect does not enter the vortex nder but bypasses and the region between the mini-hydrocyclone wall

nder outer wall. This sets up a recirculating zonereasingly larger secondary vortex with increasingty. The secondary vortex contributes to the squeez-orner and advected vortices. The advected corneron II, thus moves closer to the inlet position as thety is increased.nlet velocity of 0.4 m/s, the radial velocity contoursdary layer down the cyclone conical body (Fig. 11C1)r pattern of alternating radial direction. They arisermation of Grtler vortices on the boundary layer

section. The time-averaged results for the 0.4 m/sty show that most of the alternating radial velocityt the boundary layer disappears (Fig. 11C2) as thetices are time-dependent.ial velocity shows a series of alternating radiallong the centreline of the mini-hydrocyclone, sug-t the ow is not symmetrical about the central axislet velocities studied. This asymmetry means that3-D in nature and the ne particle separation caned by the distribution of radial velocities.

aration efciency of mini-hydrocyclone

le motion was simulated by a Lagrangian parti- method. The physical properties of the particles

sum of par

(d) = u(d)f (d)

Fig. 13 sthe three inthe 0.4 m/sleads to anslope of thsharpness separation

The impment of thevortices, patured by thgreater thaet al., 1994)of Grtler vtheir distribody towarhigher Stokthe Grtlercles, with sow and beThe Grtlerary layer tothal positions) of the mini-hydrocyclone for (A) outward radial velocity and a negative value-step after the ow reached a statistically steady

of spherical silica particles with the density of. Equal number of particles (8000 per size fraction)d for the following particle diameters: d = 1, 5, 10,0, 35, 40, 45, 50, 55, 60, 70 and 90 m. The particlesze range that pass through the overow and theorices are recorded to obtain the grade separation(d), which is the ratio of the number of particles

the mini-hydrocyclone underow, u(d), to the total

ticles of diameter d, f(d), dened as:

(18)

hows the separation efciency curves obtained forlet velocities. The nest cut size, d50, is obtained for

inlet velocity. An increase in the inlet velocity also increased sharpness of separation, which is thee separation curve at the cut size. The increasedof separation indicates a more complete particlearound the cut size.rovement in separation is linked to the develop-

Grtler vortices. For ows controlled by large-scalerticles with a Stokes number less than 1 can be cap-e vortices, while particles with a Stokes numbern 10 are only accelerated past the vortices (Fessler. In the mini-hydrocyclone separation, the presenceortices increases as the inlet velocity increases andbution tends to be concentrated down the cycloneds the underow orice. The larger particles, withes numbers, are accelerated and transported past

vortices towards the cyclone wall. The ne parti-maller Stokes numbers, can be captured with the

transported into the core of the Grtler vortices. vortices are unstable and moving from the bound-wards the centre of the cyclone and simultaneously


Fig. 12 Velocity vector plot in the vertical plane (0 and180 azimuthal positions) for the cylindrical part for (A)0.1 m/s, (B) 0.2 m/s and (C) 0.4 m/s inlet velocities (B and C instantaneous results one time-step after the ow reacheda statistically steady state. The inlet position is highlightedby a blue square.). (For interpretation of the references tocolour in this gure legend, the reader is referred to theweb version of the article.)

20

30

40

50

60

70

80

90

100

Se

pa

ratio

n e

ffic

ien

cy (

%)

Fig. 13 Sevelocities s

transport ththe ne par

The cenparticle sizvelocity, Fcat the highthe centrifuthem to thtial velocitbody at hiacquire moincreased mtices to trapas the inletthe LZVV band increashortens thne particlfor trappinGrtler voraries as theand sharpeannular regis assisted particles arentering tha sharper s

Previousefciency oow increasize of 10 Pasquier anis known aseparation separation.ciency curvsize and nogest that ththe causes

In this sdifferent sitracking mcause of thNeesse, 200Villasana etis to deterhydrocyclo1 10 100

Particle diameter ( m)

0.1 m/s

0.2 m/s

0.4 m/s

paration efciency curves for three inlettudied.

e ne particles towards the LZVV boundary whereticles then move to the overow.trifugal force is proportional to the cube of thee, Fc d3 and to the square of the tangential v2t . Thus, an increase in the tangential velocityer inlet velocity leads to signicant increases ingal forces acting on the large particles transportinge cyclone wall. Moreover, higher levels of tangen-ies are also maintained throughout the cyclonegher inlet velocities. The smaller particles alsore momentum as the inlet velocity increases. Theomentum reduces the ability of the Grtler vor-

particles and hence smaller particles are trapped velocity increases. As the inlet velocity increases,oundary extends further outwards and downwardsses the region of upward swirling ow. This alsoe distance for the Grtler vortices to transport thees back to the overow stream. The preferenceg smaller particles, the increase in the number oftices found and the extension of the LZVV bound-

inlet velocity all contribute to the smaller cut-sizer separation. The recirculating ow occurring in theion between the cyclone wall and the vortex nderby the expanded LZVV region. Intermediate sizede more likely to be recycled and prevented frome vortex nder directly and this can contribute toeparation around the particle cut-size.

experiments have reported that the separationf very ne particles to the hydrocyclone under-ses with decreasing of particle size below a particle

m (Majumder et al., 2003, 2007; Neesse et al., 2004;d Cilliers, 2000; Schubert, 2004). This phenomenons the shhook effect and it interferes with theefciency of the ne particles resulting in poor

However, Fig. 13 shows that all the separation ef-es decrease monotonically with decreasing particle

shhook effect is found. The modelling results sug-e unsteady state behaviour and turbulence are notfor the onset of shhook effect.tudy, the hydrodynamic interaction of particles ofzes is not accounted for by the current particleethod. The interaction has been proposed as thee shhook effect (Dueck et al., 2007; Dueck and3; Kraipech et al., 2005; Neesse et al., 2004; Roldan-

al., 1993). An important question for future studiesmine if the shhook effect occurs in the mini-ne operation. If the shhook effect does occur, it


will be necessary to include a particle hydrodynamic interac-tion model

4. Co

In this papwith a Lagrtigate the 5 mm minithe laminaRein, of 102

A stead0.1 m/s (Reioccurs for of 300. Thethe centrifugal instabilthe ow. Thof the Grtsection wa

As the the tangenfree/force vand the lotowards thculating owall growsis increaseannular reg

Improveand steepeinlet velociof higher tGrtler vorzero verticathe recircuwall.

Althougdoes not leworking atthe develoenables thto be undebeen studieare assumstudy has pties give risrole playedcurves decand suggesare not the

The mincle separaton experimthe occurreoperation.

Acknowl

Guofeng ZhScholarshipaward undeFacility at t

ence

n, M co

ond m., J.J., i-hydpensale, Wputa

versi C.T.,ltiphaillo, Je turblem

J., Mh-hoo73.

J., Ne ultra, J.R.,centrs. Flu, H., 1kaverunge, Finlpatiad Me, A., Lcity hnol.nn, ciple., Ge

rling 1253K.-T.rocycch, Wsang

parti with

.der, ratinlonesder, h-hooticleslam, tler i2.vian,liqul. Me

mha,dellinl. Coo-Matler vds 34, T., Dticles696.er, S.,g hyssainamw., Parrocyc to comprehensively study the shhook effect.

nclusion

er, direct numerical simulation (DNS) combinedangian multiphase ow model was used to inves-uid ow and particle separation efciency of a-hydrocyclone. The mini-hydrocyclone operates inr/transition regime with an inlet Reynolds number,103.y laminar ow was found for an inlet velocity of

n = 150) and the onset of unsteady state behaviourthe inlet velocity of 0.2 m/s at a Reynolds number

formation of vortices on the concave walls andgal instability criterion suggest that the centrifu-ity in the form of the Grtler vortices develops ine computed vorticity contours show the existenceler vortices at the vortex nder inner and conicalll for an inlet velocity of 0.2 m/s.ow transits to turbulence for higher inlet velocities,tial velocity proles take on a form similar to theortex description for a conventional hydrocyclone,cus of the zero vertical velocity (LZVV) expandse wall and the underow orice. The annular recir-w between the vortex nder wall and the cyclone

stronger as the amount of upward swirling owd resulting in increased uid entrainment in theion.d separation efciency with a ner cut size, d50,r separation sharpness were obtained for higherties. This improvement is effected by a combinationangential velocities resulting in larger number oftices being generated, expansion of the locus of thel velocity (LZVV) and an increase in the strength oflating ow between the vortex nder and cyclone

h the inlet velocities cases studied by current workad to very small cut sizes, the mini-hydrocyclone

low velocities nevertheless offer an insight intopment of turbulent ow in hydrocyclones whiche physical processes affecting particle separationrstood. The turbulent ow development has notd previously as most conventional hydrocyclones

ed to be operating in the turbulent region. Thisrovided a physical basis as to why higher veloci-e to better separation and smaller cut sizes and the

by turbulence. The modelled separation efciencyrease monotonically with decreasing particle sizet that the unsteady state behaviour and turbulence

cause for the onset of the shhook effect.i-hydrocyclone is a promising tool for ne parti-

ion in micro-technology and future work will focusental validation of the CFD model, particularly fornce of the shhook effect in the mini-hydrocyclone

edgements

u acknowledges the nancial support of the China Council. This work was also supported by anr the Merit Allocation Scheme on the NCI Nationalhe Australian National University.

Refer

Brennacoresec505

Cilliersminsus

CriminComUni

Crowe,Mu

Delgadthrepro

Dueck,s64

Dueck,the

FesslerconPhy

GrtlerkonSt

Guo, Y.of sFlui

HaiderveloTec

HoffmaPrin

Hreiz, Rswi252

Hsieh, hyd

KraipeSuktheow197

Majumopecyc

Majumspar

MangaGr12

MousagasApp

NarasimoApp

NavarrGrFlui

Neessepar689

Pasquiusin

Peerhostre

Petty, Chyds

., 2006. CFD simulations of hydrocyclones with an airmparison between large eddy simulations and aoment closure. Chem. Eng. Res. Des. 84, 495

Harrison, S.T.L., 1997. The application ofrocyclones in the concentration of yeast

ions. Chem. Eng. J. 65, 2126..O., Jackson, T.L., Joslin, R.D., 2003. Theory andtion of Hydrodynamic Stability. Cambridge

ty Press, Cambridge. Schwarzkopf, J.D., Sommerfeld, M., Tsuji, Y., 2011.se Flows with Droplets and Particles. CRC Press..A., Rajamani, R.K., 2005. A comparative study ofbulence-closure models for the hydrocyclone. Int. J. Miner. Process. 77, 217230.inKov, L., Pikushchak, E., 2007. Modeling of thek effect in a classier. J. Eng. Phys. Thermophys. 80,

esse, T., 2003. The hydrocyclones separation curve in-nes range. Aufbereitungstechnik 44, 1725.

Kulick, J.D., Eaton, J.K., 1994. Preferentialation of heavy particles in a turbulent channel ow.ids 6, 3742.941. Instabilitt laminarer Grenzschichten ann Wnden gegenber gewissen dreidimensionalenn. Z. Angew. Math. Mech. 21, 250252.ay, W., 1994. Wavenumber selection and irregularitylly developing nonlinear Dean and Grtler vortices. J.ch. 264, 140.evenspiel, O., 1989. Drag coefcient and terminalof spherical and nonspherical particles. Powder

58, 6370.A., Stein, L., 2007. Gas Cyclones and Swirl Tubes:s, Design and Operation. Springer Verlag, Berlin.ntric, C., Midoux, N., 2011. Numerical investigation ofow in cylindrical cyclones. Chem. Eng. Res. Des. 89,9., 1988. A phenomenological model of thelone. Ph.D. Thesis. The University of Utah.., Nowakowski, A., Dyakowski, T.,panomrung, A., 2005. An investigation of the effect ofcleuid and particleparticle interactions on thein a hydrocyclone. Chem. Eng. J. 111, 189

A.K., Shah, H., Shukla, P., Barnwal, J.P., 2007. Effect ofg variables on shape of sh-hook curves in. Miner. Eng. 20, 204206.A.K., Yerriswamy, P., Barnwal, J.P., 2003. Thek phenomenon in centrifugal separation of ne. Miner. Eng. 16, 10051007.S., Dagenhart, J., Hepner, T., Meyers, J., 1985. Thenstability on an airfoil. AIAA Paper 85-0491, pp.

S., Naja, A., 2009. Numerical simulations ofidsolid ows in a hydrocyclone separator. Arch.ch. 79, 395409.

M., Brennan, M., Holtham, P., 2007. A review of CFDg for performance predictions of hydrocyclones. Eng.mput. Fluid Mech. 1, 109125.rtinez, S., Tutty, O.R., 2005. Numerical simulation ofortices in hypersonic compression ramps. Comput., 225247.ueck, J., Minkov, L., 2004. Separation of nest

in hydrocyclones. Miner. Eng. 17,

Cilliers, J.J., 2000. Sub-micron particle dewateringdrocyclones. Chem. Eng. J. 80, 283288.i, H., Wesfreid, J.E., 1988. On the inner structure ofise Grtler rolls. Int. J. Heat Fluid Flow 9, 1218.ks, S., 2004. Flow structures within miniaturelones. Miner. Eng. 17, 615624.


Pinto, R.C.V., Medronho, R.A., Castilho, L.R., 2008. Separation ofCHO cells using hydrocyclones. Cytotechnology 56, 5767.

Rayleigh, L., 1917. On the dynamics of revolving uids. Proc. R.Soc. Lond. 93, 148154.

Renner, V., Cohen, H., 1978. Measurement and interpretation ofsize distribution of particles within a hydrocyclone. Trans.Inst. Min. Metall. 87, C139C145.

Roberge, D., Ducry, L., Bieler, N., Cretton, P., Zimmermann, B.,2005. Microreactor technology: a revolution for the nechemical and pharmaceutical industries? Chem. Eng.Technol. 28, 318323.

Roldan-Villasana, E.J., Williams, R.A., Dyakowski, T., 1993. Theorigin of the sh-hook effect in hydrocyclone separators.Powder Technol. 77, 243250.

Saric, W., 1994. Gortler vortices. Annu. Rev. Fluid Mech. 26,379410.

Schubert, H., 2004. On the origin of anomalous shapes of theseparation curve in hydrocyclone separation of ne particles.Particul. Sci. Technol. 22, 219234.

Svarovsky, L., 1984. Hydrocyclones. Holt, Rinehart and Winston,London.

Wang, B., Chu, K.W., Yu, A.B., 2007. Numerical study ofparticleuid ow in a hydrocyclone. Ind. Eng. Chem. Res. 46,46954705.

Wengeler, R., Nirschl, H., Herbstritt, F., Ehrfeld, W., 2006. Studieson a micro hydrocyclone for liquidliquid separation. J.Filtration 6, 2125.

Zhu, G.F., Liow, J.L., Neely, A.J., 2010. Computational study of owin a micro-sized hydrocyclone. 17th Australasian FluidMechanics Conference, Auckland, New Zealand, Paper 75, pp.14.

Computational study of the flow characteristics and separation efficiency in a mini-hydrocyclone1 Introduction2 Numerical model and simulation conditions3 Results and discussion3.1 Unsteady flow and centrifugal instability3.2 Flow characteristics in the mini-hydrocyclone3.2.1 Grtler vortices and tangential velocities3.2.2 Axial velocity3.2.3 Radial velocity

3.3 Separation efficiency of mini-hydrocyclone

4 ConclusionAcknowledgementsReferences

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