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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 (
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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)
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2138 chemical engineering research and design 9 0 ( 2 0 1 2 )
21352147
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
-
chemical engineering research and design 9 0 ( 2 0 1 2 )
21352147 2139
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)
-
2140 chemical engineering research and design 9 0 ( 2 0 1 2 )
21352147
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.
-
chemical engineering research and design 9 0 ( 2 0 1 2 )
21352147 2141
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
-
2142 chemical engineering research and design 9 0 ( 2 0 1 2 )
21352147
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
-
chemical engineering research and design 9 0 ( 2 0 1 2 )
21352147 2143
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.
-
2144 chemical engineering research and design 9 0 ( 2 0 1 2 )
21352147
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
-
chemical engineering research and design 9 0 ( 2 0 1 2 )
21352147 2145
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
-
2146 chemical engineering research and design 9 0 ( 2 0 1 2 )
21352147
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.
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Brennacoresec505
Cilliersminsus
CriminComUni
Crowe,Mu
Delgadthrepro
Dueck,s64
Dueck,the
FesslerconPhy
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Guo, Y.of sFlui
HaiderveloTec
HoffmaPrin
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Hsieh, hyd
KraipeSuktheow197
Majumopecyc
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NarasimoApp
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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