Experimental Study of a Hydrodynamic

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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

JPME225 IMechE 2009 Proc. IMechE Vol. 223 Part E: J. Process Mechanical Engineering


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

Proc. IMechE Vol. 223 Part E: J. Process Mechanical Engineering JPME225 IMechE 2009


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.




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




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




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.




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




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


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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2 Andoh, R. Y. G. and Smisson, R. P. M. High ratesedimentation in hydrodynamic separators. In 2ndInternational Conference on Hydraulic ModellingDevelopmentand Application of Physical and Mathe-matical Models, Stratford, UK, 1416 June 1994, pp. 341358.

3 Faram,M. G., James,M. D., and Williams, C. A.Wastew-ater treatment using hydrodynamic vortex separators. InCIWEM/AETT 2nd National Conference, Wakeeld, UK,1315 September 2004, pp. 7987.

4 Frederick, M. R. and Markland, E. The performance ofstilling ponds in handling solids. Paper 5: ICE Sympo-sium on Storm Sewage Overows, London, UK, 1967, pp.5161.

5 Halliwell, A. R. and Saul, J. The use of hydraulic modelsto examine the performance of storm-sewage overows.Proc. Inst. Civ. Eng., Part 2, 1980, 69, 245259.

6 Brown, N. P. and Heywood, N. I. Slurry handling designof solidliquid systems, 1991 (Elsevier Science PublishersLtd, England).

7 Fenner, R. A. and Tyack, J. N. Scaling laws for hydro-dynamic separators. J. Environ. Eng., 1997, 123(10),10191025.

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9 Egarr, D. A., Faram, M. G., ODoherty, T., and Syred, N.An investigation into the factors that determine theefciency of a hydrodynamic vortex separator. In 5thInternational Conference, Sustainable Techniques andStrategies in UrbanWater Management, Novatech, Lyon,France, 711 June 2004, pp. 6168 (ISBN 2-9509337-5-0).

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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)



Experimental Study of a Hydrodynamic

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