hydrocyclones for particle size separation

Figure 1 Principal features of the hydrocyclone.

Hydrocyclones for Particle Size Separation

J. J. Cilliers, UMIST, Manchester, UKCopyright^ 2000 Academic Press

Introduction

The hydrocyclone is a static, continuous particle sizeseparation device that can also be used for phaseseparations, including solid}liquid, liquid}liquid andliquid}gas separations and has been used for variousclassiRcation duties since the 19th century.

Hydrocyclones are attractive for industrial use asthey have no moving parts, a small footprint, relative-ly low capital and operating costs, and are simple tooperate. On the other hand, their operation is ratherinSexible once installed and single-stage efRcienciesmay be low, especially for particles Rner than 10 m.

This article describes the mode of operation ofhydrocyclones, and the motion of Suid and solidparticles in the classiRer. Quantifying the separationis followed by the effect of the major design andoperating variables on the efRciency.

Two modelling approaches are introduced: a fun-damentally based model, including computationalSuid dynamics (CFD), and empirical models, whichare still in general use.

The article concludes with aspects of furtherdevelopment.

Description

Hydrocyclones are cono-cylindrical in shape,with a tangential feed inlet into the cylindrical sectionand an outlet at each axis. The outlet at the cylin-drical section is called the vortex Rnder and extendsinto the cyclone to reduce short-circuit Sow directlyfrom the inlet. At the conical end is the second outlet,the spigot. For size separation, both outlets are gener-ally open to the atmosphere. Hydrocyclones are gen-erally operated vertically with the spigot at the lowerend, hence the coarse product is called the underSowand the Rne product, leaving the vortex Rnder, theoverSow. Figure 1 schematically shows the principalSow and design features of a typical hydrocyclone:the two vortices, the tangential feed inlet and theaxial outlets. Except for the immediate region of thetangential inlet, the Suid motion within the cyclonehas radial symmetry. If one or both of the outlets areopen to the atmosphere, a low pressure zone causesa gas core along the vertical axis, inside the innervortex.

The operating principle is simple: the Suid, carry-ing the suspended particles, enters the cyclone tangen-tially, spirals downward and produces a centrifugalReld in free vortex Sow. Larger particles movethrough the Suid to the outside of the cyclone ina spiral motion, and exit through the spigot witha fraction of the liquid. Due to the limiting area of thespigot, an inner vortex, rotating in the same directionas the outer vortex but Sowing upward, is establishedand leaves the cyclone through the vortex Rnder,carrying most of the liquid and Rner particles with it.If the spigot capacity is exceeded, the air core is closedoff and the spigot discharge changes from an um-brella-shaped spray to a rope and a loss of coarsematerial to the overSow.

The diameter of the cylindrical section is the majorvariable affecting the size of particle that can beseparated, although the outlet diameters can bechanged independently to alter the separationachieved. While early workers experimented with cyc-lones as small as 5 mm diameter, commercial hydro-cyclone diameters currently range from 10 mm to2.5 m, with separating sizes for particles of density2700 kg m3 of 1.5}300 m, decreasing with in-creased particle density. Operating pressure dropranges from 10 bar for small diameters to 0.5 bar for

II /PARTICLE SIZE SEPARATION /Hydrocyclones for Particle Size Separation 1819

large units. To increase capacity, multiple small hydro-cyclones may be manifolded from a single feed line.

Although the principle of operation is simple, manyaspects of their operation are still poorly understood,and hydrocyclone selection and prediction for indus-trial operation are largely empirical.

Liquid Velocity Distributions

Kelsall, in 1952, performed a classic series of experi-ments measuring axial and tangential Suid velocityproRles in a hydrocyclone using an ingenious experi-mental system with rotating objectives. The radial velo-city was calculated by continuity. The velocity proRlesare shown in Figure 2. More recently, velocity proRlesmeasured using laser Doppler velocimetry (LDV) werefound to correspond closely to those of Kelsall.

The Suid velocity in the cyclone has tangential,axial and radial components. The axial velocity isnegative (downward) close to the walls in the coneand positive (upward) near the air core, increasingtowards the spigot. This results in a locus of zerovertical velocity between the two vortices, whichroughly follows the proRle of the cyclone. Toroidalrotation in the inlet Sow and interaction between thevortices result in multiple Sow reversals.

The tangential velocity increases toward the axis,reaching a maximum near the air core, thereafterdecreasing in a forced vortex region. It is the tangen-tial velocity component that generates the centrifugalforce, which separates coarser particles from Rnerones. The radial velocity, which is two orders ofmagnitude smaller than the axial or tangential vel-ocities, is directed toward the centre of the cycloneand increases toward the apex.

Particle Motion

Particles entering the cyclone move radially, depend-ing on their mass, either outward due to tangentialliquid motion, or inward due to radial Suid motion.In the radial and axial directions, the particle motionis assumed to equal the Suid motion.

Direct measurement of particle motion and solidsconcentrations at positions in the hydrocyclone canbe performed using phase Doppler anemometry.Electrical impedence tomography has been used tomeasure the position of the air core and the solidsconcentration proRle in a plane through industrialhydrocyclones.

Classi\cation Performance and the PartitionCurve

The partition curve (also called a performance curve,efRciency curve or Tromp curve) is used to quantify

hydrocyclone particle size separation performance. ItquantiRes the weight fraction (or percentage) of eachparticle size fraction in the feed reporting to theunderSow product. For any particle size d, the parti-tion number, p(d), is calculated from:

p(d)"U.u(d)F.f (d)

[1]

U and F are the mass Sow rates of solids (in the sameunits) and u(d) and f(d) are the weight fractions ofparticle size d in the feed and underSow streams,respectively. The size at which the partition numberequals 0.5 (or 50%) is called the cut size (d50).

A fraction of Rne particles always report tothe underSow, hence experimentally observed parti-tion curves do not asymptote to zero but to a min-imum, called the bypass. This can be interpreted asa fraction of all particles in the feed bypassing classi-Rcation and reporting directly to the underSowstream. Short-circuiting of feed material to the over-Sow stream may cause the partition curve not toreach a partition value of 1 (100%): this is not com-mon. The effect of bypass on classiRcation perfor-mance is taken into account by correcting the parti-tion value:

c(d)"p(d)!r(d)1!r(d) [2]

where c(d) is the corrected partition value and r(d) thefraction of material of size d bypassing classiRcation.The particle size at which the corrected partitionnumber is 0.5 (50%) is called the corrected cut size(d50c). It is often found that the bypass equals thewater recovery from the feed to the underSow (RF),although there is no fundamental reason why thisshould be so.

Figure 3 schematically shows an observed and cor-rected partition curve.

A so-called Rshhook may occur in the observedpartition curve when, for particle sizes Rner than thatat the minimum partition value, progressively higherpartition numbers are observed. This is more com-monly observed for smaller diameter hydrocyclonesand is thought to be the result of turbulent dispersion.In such cases the water recovery may be signiRcantlylower than the lowest partition value observed. Ap-plying the correcting concept to such partition curvesis meaningless.

Mathematically Describing the Partition Curve

Corrected partition curves have a sigmoidal shapethat can be represented using two-parameter

1820 II /PARTICLE SIZE SEPARATION /Hydrocyclones for Particle Size Separation

Figure 2 (A) Axial, (B) tangential and (C) radial velocity profiles in a hydrocyclone. (Reproduced with permission from Kelsall(1953).)

functions such as the exponential sum, the Rosin}Rammler and the log-logistic expressions. The twoparameters determine the cut size and the sharpnessof separation, respectively. The Rshhook partitioncurve can be modelled using the sum of a corrected

partition curve and an inverted partition curve multi-plied by a bypass fraction.

The observed partition curve gives a complete de-scription of the selective separation of all sizes ofsolids entering a cyclone and can be used to predict


Figure 3 The observed (continuous line) and corrected (dashedline) partition curves of a hydrocyclone with a bypass of 20%.

Figure 4 Cut size and throughput for different cyclone diameters.

the product size distribution and solids recovery forchanges in feed size distribution. If the bypass isassumed to equal the water recovery, the liquid andvolumetric balances can also be estimated.

Hydrocyclone Geometry

The hydrocyclone diameter is the main design vari-able, and affects both capacity and cut size. Thebroad operating range available for any hydrocyclonediameter is narrowed down by Rxing the inlet andoutlet dimensions. It is not generally possible to selectindependently all the design variables; however, thereare reasonable ranges in relation to the hydrocyclonediameter, Dc. Figure 4 shows the approximate cutsize and throughput range that can be achieved usingcyclones of different diameters.

The cone angle for classiRcation of hydrocyclonesis 15}303, with smaller angles for Rner cut sizes, andlarger angles for coarser cut sizes, respectively. Thefree vortex height is the distance between the bottomof the vortex Rnder and the spigot. Increasing hydro-cyclone height improves both capacity and separationefRciency, and generally varies between 3 and 8Dc.

The inlet opening is usually rectangular witha height to width ratio of 2 and an equivalent circulardiameter of 0.14}0.33 Dc. The inner wall, outer wallor centre of the hydrocyclone inlet may be designed tobe tangential to the cyclone body, and may also scrolldownwards.

The outlet dimensions are the most importantphysical parameters used to alter the operation. Vor-tex Rnder diameters of 0.13}0.43 Dc are commonlyused. Spigot diameters in the range 0.1}0.2 Dc areused, but the ratio to the vortex Rnder is more impor-tant. In general, the vortex Rnder diameter is greaterthan that of the spigot. Equal diameters should beavoided.

The Effect of Operating andDesign Variables

Table 1 summarizes the effect that changes to themajor design and operating variables have on thecapacity, cut size and sharpness of classiRcation.

The effect of pressure drop on the sharpness ofseparation depends on the operating range, as anincrease in pressure drop increases the throughputand hence the separation efRciency, but decreases thevolumetric Sow to the underSow. Of particular inter-est is the effect of feed solids concentration, which hasa signiRcant effect on the classiRcation. Figure 5shows clearly that an increase in solids concentrationincreases the cut size and reduces the sharpness ofseparation.

Hydrocyclone Models

The modelling of hydrocyclones is performed byeither describing the Suid Sow and particle motionwithin the cyclone, or by developing empirical


Table 1 Cyclone design and operating variable effectsa

Increasing Throughput(Q)

Cut size(d50)

Sharpness ofclassification

Cyclone diameter, Dc Vortex finder diameter,Do

Spigot diameter, Du Feed inlet, Di Cone angle Not comparable Free vortex height, h Pressure drop, P or Volumetric feed solidsconcentration,

a increase; decrease.

Figure 5 Effect of feed solids concentration on hydrocyclone separation. Circles, 2.68 vol%; squares, 11.11 vol%; triangles, 17.54vol%; diamonds, 23.75 vol%. (Reproduced with permission from Braun and Bohnet (1989). Copyright: Wiley-VCH.)

(or semi-empirical) relationships between operatingvariables and measured responses. Fundamentalmodels are appealing from a rigorous standpoint buthave difRculty in describing satisfactorily the com-plex particle}particle and particle}Suid interactionsfor hydrocyclones operating at higher solids concen-trations.

Empirical or semi-empirical models, which relatethe parameters of the partition curve to cyclone de-sign and operating variables, are generally used forindustrial hydrocyclone modelling and simulation.A number of general models, particularly for largerdiameter hydrocyclones, have been developed (seeFurther Reading).

Fundamentally Based Hydrocyclone Models

Early attempts at understanding the physical prin-ciples that govern size separation in hydrocyclonesyielded theories based on equilibrium, residence timeand crowding. More complete simulations in which

Suid and particle motion is estimated from solutionof the Navier}Stokes equations have been developedmore recently.

Equilibrium orbit theory It can be postulated thatparticles will Rnd an equilibrium orbit in the hydro-cyclone where their terminal settling velocity radiallyoutward is equal to the radial velocity of the liquidinward. A particle will report to the spigot if itsequilibrium orbit is in the downward axial liquid Sowand to the vortex Rnder if in the upward axial Sow.The cut size is deRned by particles that have anequilibrium orbit that coincides with the locus of zerovertical velocity and therefore have an equal prob-ability of reporting to either product streams. Anequilibrium orbit may not be achieved due to theshort residence times and high solids concentrationsin the hydrocyclone.

Residence time theory This theory determineswhether the residence time in the hydrocycloneallows a particle entering the cyclone at the centre ofthe inlet to settle to the cyclone wall and enter theboundary layer Sow to the underSow.

Crowding theory At higher feed concentrations, it isfound that the separation size is primarily determinedby the discharge capacity of the spigot and the feedsize distribution. By controlling the outlet dimen-sions, it is thought that any cut size within the feedsize distribution can be obtained.

Computational Wuid dynamics (CFD) solutionsThis is the preferred approach for fundamentallybased modelling of hydrocyclone performance.Complete Sow modelling of the hydrocyclone


involves predicting the liquid-phase velocities, theslurry concentration proRle, the turbulent viscositiesand the slip velocities of particles with respect to theliquid phase for a range of particle sizes before predic-ting the partition curve. The solution is complex,because the governing Suid Sow equations arenonlinear, simultaneous partial differential equa-tions.

Chakraborti and Miller (1992) have published anextensive review of Suid Sow modelling in hydrocy-clones. They describe the Sowmodels in detail, givingparticular attention to models based on theNavier}Stokes equation and the treatment of Suidturbulence. They further discuss techniques for Sowmeasurement and visualization and give a brief sum-mary of pressure drop correlations and measure-ments. This paper is an essential reference for theSuid Sow modelling approach.

The general approach to develop a completeCFD-based model of a hydrocyclone must includea wide range of components. If it is assumed thatvariations of local density and viscosity are smallfor dilute slurries and that particle}particleinteractions are negligible, the Suid and particlemodelling can be decoupled. Liquid velocities arepredicted by combining the Suid transport equationsfor vorticity, stream function and angular spinvelocity with a modiRed Prandtl mixing lengthmodel, which varies both radially and axially, forthe turbulent viscosity. The set of simultaneous,nonlinear partial differential equations are solved byoverlaying the hydrocyclone dimensions with a rec-tangular grid and using appropriate boundary condi-tions at the solid walls and liquid}air interface, tosolve for conditions within each cell of the grid. Bybalancing all the forces on the particle, the particlemotion with respect to the Suid can be computed.The particle trajectories are found by calculatingaxial and radial slip velocities with respect to theSuid. Size classiRcation performance is determined byfollowing a particle of a given size from the inlet untilit exits. This computation is repeated for each particlesize across the inlet diameter yielding the partitioncurve.

For concentrated slurries, liquid-phase velocitiesare affected by local density and viscosity, which inturn are affected by local solid concentration andparticle size distribution. Since particle motion deter-mines the concentration and size distribution at eachlocation, this being determined from liquid velocities,an iterative solution is required so that local slurryproperty changes can be estimated and liquid-phasevelocities recalculated.

Advances in CFD methods such as computationgrid generation, numerical methods and computing

resources are increasing the applicability of this mod-elling technique to improve designs.

Empirical Models

At present, empirical models are the most commonlyused technique for hydrocyclone selection and perfor-mance prediction. Empirical hydrocyclone modelsuse the partition curve as a basis for describing sizeseparation. Suitable equations are developed fromexperimental results to relate the parameters of thecorrected partition curve to physical variables. Ingeneral, empirical hydrocyclone models consist offour relationships that describe the cut size, the sharp-ness of separation, the water balance around thehydrocyclone and the throughput}pressure droprelationship.

An empirical hydrocyclone model was described in1976 that is still commonly used to predict separationperformance. This model was the Rrst to documentan empirical form for the sharpness of separation andtherefore allow direct simulation of expected perfor-mance without any testwork. This model form isoften used as a basis for the development of modelsthat include further variables, such as, for example,angle of inclination, or for an operating range inwhich the model has not been tested.

The Rosin}Rammler function describes the re-duced partition curve:

ci"1!exp (!0.693xmi ) [3]

where m indicates the sharpness of separation andxi is:

xi"did50c

[4]

In SI units, and using the symbols in Table 1, the Plittequation for the cut size is:

d50c"50.5 D0.46c D

0.6i D

1.21o exp[6.3]

D0.71u h0.38Q0.45(s!l)0.5

[5]

where s, l and p are the densities of the solid, liquidand pulp, respectively.

To describe the water balance, Plitt develops a rela-tionship for the volumetric Sow split between theoverSow and underSow streams, S, rather than thebypass:

S"3.28(Du/Do)3.31h0.54(D2u#D2o)0.360.24p exp[0.54]

P0.24D1.11c

[6]


The relationship for the sharpness of separation isgiven by:

m"1.94 exp[!1.58 Rv] D2chQ

0.15

[7]

where Rv, the recovery of slurry to the underSow, isrelated to the Sow split by:

Rv"S

1#S [8]

The relationship between the pressure drop across thecyclone and the throughput is given by:

P" 1.88 Q1.78exp[0.55]

D0.37c D0.94i h

0.28(D2u#D2o)0.87[9]

Roping is affected by the spigot diameter and thevolumetric solids concentration in the underSow;however, there is no satisfactory method for predic-ting operating limit.

It must be emphasized that empirical models, al-though developed from an extensive database, shouldbe used with caution.

Future Developments

The extremely wide range of hydrocyclones availableand separation applications for which they can beused assures their future role in particle classiRcation.However, signiRcant obstacles remain before theycan be used to replace more efRcient methods for RneclassiRcation purposes, such as centrifuges. ClassiRca-tion inefRciencies, in particular the large bypass, limittheir application. The potential of very small dia-meter hydrocyclones for sub-micron particle separ-ation, especially in multistage conRguration, is enor-mous, if these inefRciencies can be reduced.

Hydrocyclone modelling has advanced signiR-cantly with the use of CFD. Empirical hydrocyclonemodels are convenient ways of describing experi-mental data but do not enhance the understanding ofthe separation and CFD models will play a greaterrole in hydrocyclone simulation. Nonintrusivemeasurement techniques such as laser Doppler anem-ometry (LDA), laser Doppler velocimetry (LDV) andtomography have indicated the source of hydrocyc-lone inefRciencies. With increased resolution andcombined with CFD models, this will improve hydro-cyclone unit design.

Hydrocyclone operations will beneRt from novelmethods for monitoring which are currently beingdeveloped. Industrial tomography is becoming af-fordable, and the potential of visual and sonic tech-niques has been illustrated.

See also: II/Particle Size Separation: ElectrostaticPrecipitation.

Further Reading

Bradley D (1965) The Hydrocyclone. Oxford: PergamonPress.

Braun T and Bohnet M (1990) InSuence of feed solidsconcentration on the performance of hydrocyclones.Chem. Eng. Technol. 13: 15}20.

Chakraborti N and Miller JD (1992) Fluid Sow in hydro-cyclones: a critical review. Mineral Processing andExtractive Metallurgy Review 11:

Heiskanen K (1993) Particle ClassiTcation. London:Chapman & Hall.

Kelsall DF (1953) A study of the motion of solid particles ina hydraulic cyclone. Transactions of the Institution ofChemical Engineers 30: 87}104.

Plitt LR (1976) A mathematical model of the hydrocycloneclassiRer. CIM Bulletin December 114}122.

Svarovsky L (1984) Hydrocyclones. London: Holt,Rinehart and Winston.

Instrumentation of Field Flow Fractionation

See II /PARTICLE SIZE SEPARATION/Theory and Instrumentation of Field Flow Fractionation

Sedimentation

See II /PARTICLE SIZE SEPARATION/Split Flow Thin Cell (SPLITT) Separation


hydrocyclones for particle size separation

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