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DOI: 10.1243/09544089JPME225 2009 223: 1Proceedings of the
Institution of Mechanical Engineers, Part E: Journal of Process
Mechanical Engineering
D A Egarr, M G Faram, T O'Doherty and N SyredExperimental study
of a hydrodynamic vortex separator
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1Experimental study of a hydrodynamic vortex separatorD A
Egarr1,M G Faram2,T ODoherty1, and N Syred11Cardiff University, The
Parade, Cardiff, UK2Hydro International plc, Clevedon Hall Estate,
North Somerset, UK
The manuscript was received on 20 June 2008 and was accepted
after revision for publication on 3 October 2008.
DOI: 10.1243/09544089JPME225
Abstract: A hydrodynamic vortex separator (HDVS) has been
studied under laboratoryconditions by using a specically designed
rig. Pressure tapping points placed at eight loca-tions, six
external and two internal, have revealed an even radial pressure
distribution on theouter walls and central shaft. The ability of
the HDVS to separate particulates has been stud-ied. The
particulates have been characterized by measurements of particle
diameter and settlingvelocity, which have allowed efciency cusps to
be plotted against dimensionless groups used byother researchers.
Owing to an unsatisfactory reduction of the data to a single curve
by plottingthe efciency against dimensionless groups, an efciency
law has been determined based on thelogistic equation and describes
the separation efciency in terms of the inlet owrate, volume ofthe
separator, and particle diameter and density.
Keywords: combined sewer overow, hydrodynamic vortex separator,
retention, separation,efciency
1 INTRODUCTION
Older urban drainage systems, particularly in Europe,consist of
combined sewers that are used to carry foulsewage and storm water.
This can result in a largequantity of grit requiring removal at the
prelimi-nary stage of treatment, necessary to avoid damageto
machinery such as pumps and valves, and accu-mulation in downstream
process chambers [1]. Onemethod of performing this is through the
use of ahydrodynamic vortex separator (HDVS), whereby gritsettles
due to the force of gravity [2]. Sufcient resi-dence time for this
to take place is provided by therotary nature of the path of the
grit through theseparator.
Figure 1 shows a schematic of a Grit King, a form ofHDVS
analysed in this study, which is used for sewagegrit removal [3].
The uid enters the HDVS througha tangential inlet, marked in Fig. 1
by A, and uponentering the main chamber strikes a deector plateB.
The uid tends to take a path through the HDVSsuch that it rotates
down around the outer part of theseparator and upon reaching the
bottom of the cone
Corresponding author: School of Engineering, Cardiff
Univer-sity, The Parade, PO Box 925, Cardiff CF24 3AA, UK.
email:
[email protected]
F it rotates up through the central region between thedip plate
E and the central shaft G before leavingthrough the overow J.
Separated solids are collectedin the grit pot H, which are removed
either by anunderow component through the central underowI or by
the use of a submersible pump, typically onan intermittent batch
basis. Hence, in this study, theHDVS is considered operating
without an underowcomponent. The vent box C allows the air
trappedbetween the dip plate and the vessel wall D toescape when
the uid level within the device lls theseparator.
The operation of these systems to date has beendifcult to
quantify such that a single equation maybe applied to predict the
separation performance ofsuch a device operating without an
underow. Manyresearchers have used dimensionless groups to
reducethe spread of efciency cusps, but few report onthe successful
t of a function to the data. Freder-ick and Markland [4] related
the efciency to thedimensionless group VsC0.5d /U , where Vs is the
ter-minal settling velocity of the particle, Cd is the
dragcoefcient, andU is themean velocity at the inlet.Thiswas used
while plotting retention efciency curvesfor the particles entering
a stilling pond a form ofcombined sewer overow (CSO) treatment
chamber.This dimensionless group can be computed directlyin
combination with equation (1), when the particle
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2 D A Egarr,M G Faram,T ODoherty, and N Syred
Fig. 1 Schematic of a 0.75m diameter Grit King
properties are known and the particles are assumed tobe
spherical
Vs =
4dg(p f )3Cdf
(1)
where d is the particle diameter, m; g is the acceler-ation due
to gravity, m/s2; p is the particle density,kg/m3; and f is the uid
density, kg/m3.
Halliwell and Saul [5] by studying CSO chambers,related
theefciency to thedimensionlessgroupVs/U .Application of this group
requires either knowledge ofthe particle settling velocity or
knowledge of the par-ticle properties such that the particle
settling velocitymay be computed theoretically [6].
Fenner and Tyack [7] proposed a hybrid scalinglaw for particle
retention efciency that combinedFroudian and Hazen scaling. The
Froude number isgiven by Q2/D5Sg , where DS is the diameter of
theHDVS, and the Hazen number, (Q/AS)/Vs, where ASis the plan area
of the separator and Q is the inletowrate. A drawback of the
scaling law proposed byFenner and Tyack [7] is that the efciency is
calcu-lated based on prior knowledge of the efciency ofa separator
of a scaled size.
Researchers have found a relationship to describethe efciency of
an HDVS while operating with a con-stant underow component [8].
This took the form ofequation (2)
= 1 (1 q
Q
)exp
(k Vs
U
)(2)
where q is the underow discharge, m3/s, and k isa constant.
This function demonstrated that the efciency wasonly dependent
on the ow ratio q/Q and the ratioVs/U . One limitation of this work
was that it onlyconsidered particles of a single density.
2 EXPERIMENTAL SETUP
Figure 2 shows a schematic of the custom-built rigused for
testing the 0.75m diameter HDVS.
Water is pumped to a header tank, marked A inFig. 2, where a
constant head is maintained by thevertical pipe marked B. Pipe C is
used for feedingwater to the HDVS via a vertical section that
comprisesa buttery valve D chosen for ease of controllingthe ow. A
horizontal distance of 45 diameters ofstraight pipe precedes the
inlet to the separator so thata reasonably developed ow is allowed
to establish.Particles are released into pipe C in the header
tank,where access can be gained by the stand E. Releaseof the
particles at this point was preferable to a standpipe that would be
positioned relatively close to theseparator and would not allow a
reasonable distancefor the particles to settle before entering the
separator,as it has been shown that the position of the particle
atentry to an HDVS may affect the efciency [9]. Hence,the particles
enter the separator at what is thought tobe a realistic position in
the vertical plane of the inletpipe. Flow measurement was via an
electromagneticowmeter marked F. Once water passes through theHDVS,
marked G in Fig. 2, it discharges into a tank Hconnected to tank I
below the header tank. Hence,the ow circulates through the pumped
system.
2.1 Retention efciency testing
The particulate used for testing the HDVS includeda pre-expanded
polystyrene (Styrocell) and an ionexchange resin used in water
treatment applications(Purolite). Both types of particles are
generally spher-ical, and hence, a sphericity of 1 can be assumed.
Thesphericity is dened as the surface area of a spherewith the same
volume as the particle divided by the
Fig. 2 Schematic of the experimental rig used for testingthe
0.75m diameter HDVS
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Experimental study of an HDVS 3
surface area of the particle [6], which is given by
= 4(3Vp/4)2/3
Ap(3)
where is the sphericity, Vp is the volume of sphere,m3, and Ap
is the surface area of particle, m2.
Although the density of the particles is supplied bythe
manufacturer/supplier of the particles, the gureis not exact. In
the case of Styrocell, it is thought thatpores of air may be
trapped in the particle duringthe manufacturing process, which
would explain whya fraction of particles oat inwater, despite the
densitybeing stated as being in the range 10201050 kg/m3.Purolite
expands when wet, and since it is an ionexchange resin, the density
varies depending on whations the particles have come into contact
with. Theparticles were therefore characterized by taking
drysamples that were sieved to reduce the size range. Thevolume of
particles used in retention efciency testingranged from 100 to
900ml, depending on the vol-ume of particles available after
sieving. Since Puroliteexpands when wet, it was left in water for
approx-imately a week after sieving. Settling velocity testswere
then carried out on a random sample of typi-cally 50 individual
particles in a sieved size range. Thediameter of the settling
column used was 0.25m, andthe maximum particle diameter can be
assumed tobe no more than 5.6mm from the sieve sizes used.Hence,
from a gure adapted from Fidleris and Whit-more [10], which
accounts for wall effects on theterminal settling velocity of a
particle, the diameterof the settling column is sufcient to neglect
these.The temperature of the uid was taken before andafter the
settling tests so that the density and viscos-ity of the water
could be determined. Each settlingtest allowed the particle to
settle in an adequate dis-tance to allow the terminal settling
velocity to beachieved. Using a stop watch, the particle would
thenbe timed to fall a predetermined distance. The diam-eter of a
random sample of typically 50 individualwater soaked particles in a
sieved size range was alsomeasured by using Vernier callipers,
taking care notto squash the particle while measuring its
diameter.Ideally the diameter of all the particles in the sam-ple
used in the settling velocity tests would be taken,but due to the
size of the particles, ease of handlingdid not allow this. Assuming
the sphericity to be 1and with the mean settling velocity and mean
parti-cle diameter known, as well as the uid density andviscosity,
a mean particle density can be calculated.This involves calculating
the particle Reynolds num-ber, equation (4), which is then used to
calculate thedrag coefcient from an equation proposed by Tur-ton
and Levenspiel [11]. The drag coefcient is thenused in equation (1)
to calculate the particle density.This has been done for all the
particle sieve size ranges
used in retention efciency testing
Rep = dVsf
(4)
where Rep is the particle Reynolds number and is theabsolute
viscosity of uid, kg/ms.
Faram et al. [12] have shown through experimen-tation that the
efciency of such devices is time-dependent since particles captured
in the grit pot maybe re-entrained into the ow. Each retention
efciencytest was therefore carried out for 10min, and the
tem-perature of the uid was taken at the start and end ofeach test.
At the end of each test, the buttery valvemarked D, in Fig. 2, was
closed before switching offthe pump to prevent the particulates
remaining in theHDVS from being ushed out by the water remainingin
the header tank. The HDVS efciency is dened byequation (5) and was
determined by measuring thevolume of particles, instead of
measurement by mass,as this would include excess water held between
theparticles by surface tension. Drying the particles aftereach
testwouldhavebeenextremely time-consuming,particularly in the case
of Purolite as each samplewould have to be soaked for at least a
week to allowthe particles to expand
= 100VGPVT
(5)
where is the efciency, per cent, VGP is the volume ofparticles
remaining in the HDVS at the end of a test,and VT is the volume of
particles released into thesystem.
Comparisons of efciency by using different vol-umes of particles
have been made and it has beendetermined that the efciency is
independent of theparticle loading for the volumes used in
testing.
2.2 Pressure tapping measurements
Theuseof pressure tappingmeasurements tomeasurethe static
pressure at the walls has revealed an insightinto the pressure
distribution within the HDVS. BS ENISO 5167 [13] outlines the
guidelines for placing pres-sure tapping points on Venturi tubes,
and whereverappropriate, these were applied in this study. Figure
3shows the location of each pressure tapping point.Points 14 at the
inlet were placed in a plane, i.e.0.375m from the centre-line of
the HDVS and werearranged such that each was positioned 90 from
eachother on the circumference of the inlet pipe. Points58 are
located on the same plane as points 2 and 4at the inlet. Points 9
and 10 on the central shaft areplaced opposite points 5 and 7,
respectively, and thestatic pressure on the outside of the shaft is
measured.Points 11 and 12 are located half way down the grit pot,in
the same plane as points 5 and 7.
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4 D A Egarr,M G Faram,T ODoherty, and N Syred
Fig. 3 Location of pressure tapping points on the 0.75m diameter
HDVS
3 RESULTS
3.1 Pressure tapping
An observation during the reading of the static pres-surewas
that theuctuationswerevery low, suggestingthat the pressures at the
walls are fairly stable. Threeseries of static pressure data were
read from the fourindividual pressure tapping points at the inlet,
whichrevealed negligible, if any, variation of the pressurearound
the circumference of the wall due to the lengthof the inlet pipe,
which implied that a reasonablydeveloped ow had been established.
Figure 4 com-pares the static pressure readings taken in the
HDVS.The data are the combined set of three series ofreadings and
the repeatability of the data is consistent.
Points 58 are located around the central drum ofthe separator
and the readings shown in Fig. 4 indi-cate that there is
anequalpressuredistributionaroundthe outer circumference of the
device, which is slightlyhigher than the pressure at the inlet.
This could be
due to the reduced velocity of the uid upon expan-sion from the
inlet into the HDVS. The static pressurereadings taken at points 9
and 10 are located on thecentral shaft, which is at the centre of
the separa-tor. Here, the static pressure is low compared withthe
pressure on the central drum of the separator,as would be expected
from a vortex ow where thepressure increases radially outwards
[14], and the rota-tion of the uid creates a low-pressure axial
core [15].At points 11 and 12, situated on the grit pot, thestatic
pressure is lower than at the inlet. This may beexpected due to the
diameter of the grit pot being lessthan the vessel. Hence, due to a
pressure distribution,which increases radially outwards, the
pressure at thewall of the main vessel would be expected to be
higherthan in the grit pot.
At owrates of 3 l/s and lower, the pressure at eachtapping point
is almost identical. This implies that upto 3 l/s, the vortex ow is
not fully developed due tothe pressure on the central shaft and the
vessel wallsbeing identical.
Fig. 4 Comparison of the static pressure readings in the 0.75m
diameter HDVS
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Experimental study of an HDVS 5
3.2 Retention efciency results
An observation during retention efciency testing isthat
particles are drawn towards the centre of the sep-arator. This
would imply that the vortex generatedwithin theHDVS tendsmore
towards a free vortex thana forced one, where particles would be
forced outsidethe device.
Plotting the retention efciency against the inletowrate gives a
series of efciency cusps as shown inFig. 5. Each efciency cusp
follows a denite trendand the repeatability of the data is
consistent. Thedata for the Purolite 500710m sieve range were
notrepeated due to the time required to collect all theparticulate.
Efciencies for Styrocell 1.42.0mmbelow4.25 l/s cannot be achieved
because at lower owrates,the particles tend to occulate and begin
to oat. Athigher owrates, the turbulence in the ow preventsthe ocs
forming. Flowrates >12 l/s cannot currentlybe achieved due to
facility constraints. Initially, thetrend in the efciency cusps
appears tobewith settlingvelocity of the particles, but upon closer
inspection itcan be seen that the particles, Purolite 500600m,have
the highest efciency despite having a settlingvelocity lower than
Styrocell 2.85.6mm, as detailedin Table 1.
Figure 6 shows the efciency as a functionofQ2/D5Sg(Froude
number), VsC0.5d /U , and Vs/U .
From Fig. 6, where the efciency has been plottedas a function of
the Froude number, it may be impliedthat the ratio of the inertia
to gravity forces in the sep-arator has negligible effect on the
efciency due to thelack in reduction of the spread of data. This
result hasalso been observed by Luyckx et al. [8] who studiedan
HDVS operating with a constant underow. Thedimensionless
groupVsC0.5d /U brings the curves closertogether, implying that the
particle properties have
Table 1 Particle properties
Mean Mean settling MeanParticle type settling velocity
particleand sieve velocity standard surface loadsize range (m/s)
deviation (%) (kg/m2)
Purolite 500600m 0.026 27 6.9 0.2112Styrocell 2.85.6mm 0.034 29
9.1 0.1009Styrocell 2.02.8mm 0.029 25 11.7 0.0843Styrocell 1.42.0mm
0.020 87 6.9 0.0625Purolite 7101000m 0.009 66 9.8 0.0408Purolite
500710m 0.006 86 13.3 0.0350
a greater impact on the efciency.When the efciencyis expressed
as a function of Vs/U , the efciency cuspsare brought closer
together again suggesting that theefciency is more strongly linked
with the settlingvelocity of the particle.
Although thedatahavebeenbrought closer togetherwhile plotting
Vs/U , at a value of Vs/U equal to 0.4 avariation in efciency of 50
per cent exists, where theefciency of Styrocell 2.85.6mm is 30 per
cent andthe efciency of Purolite 500600m is 80 per cent.Hence, a
satisfactory single curve has not beenachieved.
Figure 5 shows a series of curves that are in the formof a
backward S. Plotting efciency as a function ofV /Q, where V is the
volume of uid in the separatorand Q is the inlet owrate, inverts
the S curve andalso takes into account the size of the separator.
AnS curve may be described by the logistic function, asin equation
(6), which was developed for modellingpopulation growth [16,
17]
f (x) = A 1 + BeCx
1 + DeCx (6)
Fig. 5 Efciency versus owrate for the 0.75m diameter HDVS
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6 D A Egarr,M G Faram,T ODoherty, and N Syred
Fig. 6 HDVS efciency as a function of various dimensionless
groups
Equation (6) is a four-parameter model, i.e. it requiresfour
constants to be specied; but by examination ofthe function,
thismaybe reduced. First, the termBeCx
applies negative growth in that when B D the func-tion
approaches a straight line; therefore B = 0. Now,when x , f (x) A.
Obviously, A = 100 as the ef-ciency does not exceed 100 per cent.
The function cannow be written as
= 1001 + DeCx (7)
Equation (7) is a two-parameter model. The coef-cients that give
the best t in a two-parametermodel may be determined by using an
optimization
technique by Guymer [18]. This involves determiningthe R2t value
[19] for a matrix of values of C and D, andreducing the range
between the constants that givethe highest R2t value until a
satisfactory accuracy hasbeen achieved for each. This has been done
for eachefciency cusp, when plotted against V /Q.
By plotting various quantities for the full range ofparticles
used, it has been found that the quantitythat appears to be
controlling the efciency is massdiffusion, which is given by
md = d(p f ) (8)
where md is the particle surface load, kg/m2.
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Experimental study of an HDVS 7
Table 1 lists the average particle settling velocity,
thestandard deviation of the settling velocity expressedas a
percentage of the mean, and also particle sur-face load based on
the mean particle diameter anddensity.
Hence, the larger the mass diffusion the higherthe expected
efciency. Thus, by plotting C and Din the logistic equation against
the mass diffusion,it can be seen that a function exists as
illustrated inFig. 7. (These constants have been normalized onlyfor
the purpose of publication.) In Fig. 7, those pointsthat have been
circled are dummy points, used toaid tting a trend line and are
justied in that they
aid the function to consistently predict the efciencycusps that
increasewhen themass diffusion increases,as observed with the
experimental data. The func-tions that best describe the
relationship between Cand D are polynomials. Hence, the efciency of
the0.75m diameter HDVS may be predicted for any par-ticle with a
mass diffusion in the range for whichexperimental testing has been
carried out. The modelis thus dependent on the inlet owrate, which
is thesame as the overow owrate, the volume of uidwithin the
separator, and the particle density anddiameter. Figure 8 shows a
good t by the model toa range of efciency cusps.
Fig. 7 Relationship between C and D in the logistic function and
the particle surface load
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8 D A Egarr,M G Faram,T ODoherty, and N Syred
Fig. 8 Comparison of the model and experimental retention
efciency results for the 0.75mdiameter HDVS
4 DISCUSSION
An experimental study has been carried out to inves-tigate the
operational and performance attributes ofan HDVS by using a
custom-built rig to attain accu-rate separation efciencies of
particulates. Pressuretappingdatahave revealed aneven radial
pressuredis-tribution on the outer walls and central shaft, and it
is
observed that the vortex ow within the HDVS is notfully
developed at a owrate
-
Experimental study of an HDVS 9
by previous researchers, has not resulted in a sat-isfactory
single-efciency cusp. The efciency hastherefore been dened by the
logistic function, wherethe constants are described as a function
of the parti-cle surface load. A limitation of the model is that
thepredicted efciency is never 0 per cent as the logisticequation
in the form of equation (7) is asymptotic toy = 0. However, the
offset is fairly small and when siz-ing a separator the required
efciency tends to be ofthe order of 95 per cent, where it can be
seen thatthe model gives an adequate prediction. The func-tions
that best t the constants in the logistic equationare polynomials.
This means that the model is onlyvalid for particles with a mass
diffusion within therangeused in testing. Furtherwork is required
to attaina more complete relationship for the constants. Themodel
does not take into account the shape factor ofthe particle, since
it is assumed that the particles usedin testing are spherical. The
viscosity of the uid is alsonot taken into account, depending on
the nature andconcentration of contaminants in the water and
itstemperature. Although the model does consider thesize of the
HDVS in that it takes into account the vol-ume of uid in the
separator, the application of themodel to HDVSs larger or smaller
than 0.75m has tobe validated.
A possible limitation of the testing is that the resultsare for
a specic test period, and therefore does notaccount for particle
re-entrainment that could occurover a longer duration. However,
HDVSs of the inves-tigated form have been demonstrated by others to
berelatively resistant to this phenomenon compared toother
deviceswith exposed particle collection regions[12]. A straight
pipe of 45 diameters upstream of theinletmaybeunlikely,where these
systemsare installedin practice. However, efciency predictions with
adeveloped velocity prole at the inlet to the HDVSare a basis for
comparisons with different congura-tions of upstream pipe work. The
method behind thederivation of the efciency model is a building
blockfor further studies on large scale HDVSs.
5 CONCLUSIONS
1. The pressure distribution within an HDVS hasfound to be an
even radial distribution on the wallsand the central shaftwhere the
vortexowbecomesdeveloped at a owrate of 3 l/s.
2. Retention efciency has been plotted as a func-tion of
dimensionless groups used by previousresearchers, none of which has
reduced the ef-ciency to a single cusp.
3. Retention efciency testing has revealed that ef-ciency cusps
are dependent onparticle surface loadand not particle settling
velocity.
4. A model for predicting the efciency of an HDVShas been
developed by using the logistic equation.
ACKNOWLEDGEMENTS
The authors would like to acknowledge Hydro Inter-national Plc
and EPSRC for funding.
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APPENDIX
Notation
A constant (dimensionless)Ap surface area of particle (m2)AS
plan area of the HDVS (m2)
B constant (dimensionless)C constant (dimensionless)Cd drag
coefcient (dimensionless)d particle diameter (m)D constant
(dimensionless)DS diameter of the HDVS (m)g acceleration due to
gravity (m/s2)k constant (dimensionless)md particle surface load
(kg/m2)q underow discharge (m3/s)Q inlet owrate (m3/s)Rep particle
Reynolds number (dimensionless)U mean velocity at the inlet (m/s)V
volume of uid (m3)VGP volume of particles remaining in the HDVS
at
the end of a test (m3)Vp volume of sphere (m3)Vs particle
terminal settling
velocity (m/s)VT volume of particles released into the
system
(m3)
efciency (per cent) absolute viscosity of uid (kg/ms)f uid
density (kg/m3)p particle density (kg/m3) sphericity
(dimensionless)
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