numerical modeling of the flow field and performance in cyclones of different cone-tip diameters

Computers & Fluids 51 (2011) 48–59

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Computers & Fluids

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Numerical modeling of the flow field and performance in cyclones of differentcone-tip diameters

Khairy Elsayed ⇑, Chris LacorVrije Universiteit Brussel, Department of Mechanical Engineering, Research Group Fluid Mechanics and Thermodynamics, Pleinlaan 2, B-1050 Brussels, Belgium

a r t i c l e i n f o

Article history:Received 28 June 2010Received in revised form 12 May 2011Accepted 17 July 2011Available online 5 August 2011

Keywords:Cyclone separatorCone tip-diameterLarge eddy simulation (LES)Mathematical modelsDiscrete phase modeling (DPM)Grid convergence index (GCI)

0045-7930/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.compfluid.2011.07.010

⇑ Corresponding author. Tel.: +32 26 29 2368; fax:E-mail address: [email protected] (K. Elsayed).

a b s t r a c t

The effect of the cone tip-diameter on the flow field and performance of cyclone separator was investi-gated computationally and via mathematical models. Three cyclones with different cone tip diameterswere studied using large eddy simulation (LES). The cyclone flow field pattern has been simulated andanalyzed with the aid of velocity components and static pressure contour plots. In addition the cyclonecollection efficiency based on one-way discrete phase modeling has been investigated. The resultsobtained demonstrate that LES is a suitable approach for modeling the effect of cyclone dimensions onthe flow field and performance. The cone tip-diameter has an insignificant effect on the collection effi-ciency (the cut-off diameter) and the pressure drop. The simulation results agree well with the publishedexperimental results and the mathematical models trend.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Gas cyclone separators are widely used in industries to separatedust from gas or for product recovery because of their geometricalsimplicity and relative economy in power consumption. Cyclonesmay also be adapted for use in extreme operating conditions (hightemperature, high pressure, and corrosive gases). Since there areno moving parts, cyclones are relatively maintenance-free. There-fore, cyclones have found increasing utility in the field of air pollu-tion, the petrochemical and process industries.

Until now, a considerable number of investigations has beenperformed either on small sampling cyclones or larger industrialcyclone separators, for example; Buttner [1], Iozia and Leith [2],Kim and Lee [3], Zhu et al. [4], Elsayed and Lacor [5–7] and Safikh-ani et al. [8]. In these studies, almost all of the cyclone dimensionslisted in Table 1, were varied and the changes in cyclone perfor-mance characteristics brought about by these variations werestudied. However, very little information is available on the effectof changing the cone bottom (tip) diameter (which determines thecone shape if other cyclone dimensions are fixed [9]) on the flowpattern and performance. Regarding this effect, discrepancies anduncertainties exist in the literature. Bryant et al. [10] observed thatif the vortex touched the cone wall, particle re-entrainment oc-curred and efficiency decreased, so collection efficiency will belower for cyclones with a small cone opening (cone tip diameter).

ll rights reserved.

+32 26 29 2880.

While according to Stern et al. [11] (cited in Xiang et al. [9]), a coneis not an essential part for cyclone operation, although it serves thepractical purpose of delivering collected particles to the centraldischarge point. However, Zhu and Lee [12] stated that the coneprovides greater tangential velocities near the bottom for remov-ing smaller particles.

Although the understanding and knowledge of the flow field in-side a cyclone has been developed rapidly over the last few years,the exact mechanisms of removing particles are still not fullyunderstood. Therefore, most existing cyclone theories are basedon simplified models or depend upon empirical correlations [13].Xiang et al. [9] carried out experiments with cyclones of differentcone dimensions and evaluated a few models, namely Barth [14],Leith and Licht [15] and Iozia and Leith [16]. All these models wereable to simulate correctly the trend of Xiang’s experimental data.However, the quantitative agreement was not satisfactory. CFDhas a great potential to predict the flow field characteristics andparticle trajectories as well as the pressure drop inside the cyclone[17]. Chuah et al. [13] carried out a numerical investigation on thesame cyclone dimensions used by Xiang et al. [9] with the com-mercial finite volume code Fluent. Using different turbulence mod-els they proved that Fluent with Reynolds stress model (RSM)predicts well the cyclone collection efficiency and pressure drop.

The CFD simulation results from Chuah et al. [13] agree wellwith Xiang’s experimental results in that cyclones with a smallercone diameter result in a slightly higher collection efficiency com-pared to cyclones with a bigger cone tip diameter (only if the conetip diameter is not smaller than the gas exit tube diameter). Also

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Table 1The geometrical dimensions of the three cyclones.a

Dimension Length(mm)

Dimension ratio(dimension/D)

Body diameter, D 31 1Gas outlet diameter, Dx 15.5 0.5Inlet height, a 12.5 0.4Inlet width, b 5 0.16Cyclone height, Ht 77 2.5Cylinder height, h 31 1Gas outlet duct length, S 15.5 0.5Cone tip-diameter, Bc Cyclone I 19.4 0.625

Cyclone II 15.5 0.5Cyclone III 11.6 0.375

a The outlet section is above the cylindrical barrel surface by Le = 0.5D. The inletsection located at a distance Li = 0.75D from the cyclone center (cf. Fig. 1).

Sa

hD

b

H t

D x

L i

L e

B c

Fig. 1. Schematic diagram for the cyclone geometry and coordinate definition.

Table 2The position of different plotting sections.

Section S1 S2 S3 S4

z (mm) 5 15 30 50z/D 0.16 0.48 0.97 1.61

K. Elsayed, C. Lacor / Computers & Fluids 51 (2011) 48–59 49

the change in pressure drop will not be significant when the conesize is varied. Both Xiang and Chuah did not give any results aboutthe effect of the cone tip diameter on the flow field inside the cy-clone separator, except some plots for axial and tangential velocityprofiles at two stations in the flow field for Chuah et al. [13].

Xiang and Lee [18] computationally investigated using the Rey-nolds stress turbulence model the effect of the cone tip diameteron the flow field. They did not present any contour plots for eitherthe static pressure, tangential and axial velocity. However, thecomparisons between the tangential and axial velocity profiles atdifferent sections indicating no valuable difference between thethree cyclones [18, Fig. 8, p. 216 and Fig. 9, p. 217], they mentionedthat the cone tip diameter has a significant effect on the flow field.No particle tracking study has been performed in the study ofXiang and Lee.

Currently a better understanding of the flow field inside cycloneseparators is an important concern, especially with the applicationof large eddy simulation (LES). The present study was undertakenin an effort to carry out a numerical study on the effect of the conetip diameter on the flow field and the cyclone performance usingLES available in Fluent commercial finite volume solver.

2. Numerical simulation

2.1. Configuration of the three cyclones

The cyclones used in this study had a reversed flow tangentialinlet. The geometry and dimensions are shown in Fig. 1 and Table 1.Three cyclones with different cone-tip diameters are used viz., Bc/D = 0.625, 0.5 and 0.375. The three cyclones are identical to thoseused by both Xiang et al. [9,19] and Chuah et al. [13]. Four plottingsections are used to investigate the effect of cone-tip diameter Bc

on the velocity profiles as given by Table 2.

2.2. Selection of turbulence model (RANS versus LES)

For the turbulent flow in cyclones, the key to the success of CFDlies with the accurate description of the turbulent behavior of theflow [17]. To model the swirling turbulent flow in a cyclone sepa-rator, there are different turbulence models available in Fluent.These range from the standard k–e model to the more complicatedReynolds stress model (RSM) and large eddy simulation (LES)methodology as an alternative for RANS models. The standard k–e, RNG k–e and Realizable k–e models were not optimized forstrongly swirling flows found in cyclones [13]. The Reynolds stressturbulence model (RSM) requires the solution of transport equa-tions for each of the Reynolds stress components and yields anaccurate prediction on swirl flow pattern, axial velocity, tangentialvelocity and pressure drop on cyclone simulation [20].

Large eddy simulation (LES) has been widely accepted as apromising numerical tool for solving the large-scale unsteadybehavior of complex turbulent flows. Encouraging results havebeen reported in recent literature and demonstrate the ability ofLES to capture the swirling flow instability and the energy contain-ing coherent motion of such highly swirling flows [21]. LES meth-odology has been used in many articles to study the highly swirlingflow in cyclone separators, [e.g., 20,22–26]. It will be used in thisstudy to reveal the effect of changing the cone-tip diameter onthe turbulent flow in the cyclone separator. For the governingequations of LES, we refer to Refs. [20,27,28] and for RSM, we referto Refs. [6,27].

2.3. Solver settings

2.3.1. The time stepThe simulation started with unsteady Reynolds stress model for

initialization with a time step of 1E�4 s using implicit coupledsolution algorithm. For the LES simulation, the time step is1E�5 s. The selected time step results in an average inlet Courantnumber of 2.3 for the three cyclones. But as the solver is a segre-gated implicit solver, there is no stability criterion that needs tobe met in determining the time step (and consequently the Cou-rant number) [27,29]. However, to model transient phenomenaproperly the Fluent manual [27] suggested using a time step ofat least one order of magnitude smaller than the smallest time con-stant in the system. In the cyclone separator studies, the averageresidence time (cyclone volume/gas volume flow rate) is widelyused to estimate the time step [6,13,30]. In this study, the cyclonevolumes (calculated by the Fluent solver) are 5.045387E�5 m3,4.738813E�5 m3 and 4.468306E�5 m3 for cyclones I–III respec-tively. For a flow rate of 30E�3 m3/s, the corresponding averageresidence time values are 0.00168 s, 0.00158 s and 0.001489 s forcyclones I–III respectively, i.e., the used time step is just a smallfraction of the average residence time. This confirms that the usedtime step can reveal the transient phenomena properly, however,

50 K. Elsayed, C. Lacor / Computers & Fluids 51 (2011) 48–59

the interest in this study lies in the simulation of averaged scalarsand vectors (the average velocities and pressures in order to esti-mate the cyclone performance). To resolve the high frequency phe-nomena in the time domain may be a time step smaller by twoorders of magnitude (tiny fraction) than the average residence timewould be required which is not the case in this study. Furthermore,to verify that the choice for the time step was appropriate after thecalculation is complete; Fluent manual [27] suggests to check themaximum value of Courant number at the most sensitive transientregions of the domain (in this study, it is the central region) shouldnot exceed a value of 20–40 [27]. For the three cyclones the max-imum values of courant number are 9.78, 12.1, 16.92 for cyclonesI–III respectively. This verifies again that the choice of the time stepwas proper.

2.3.2. Selection of the discretization schemesThe choice of the discretization schemes has a tremendous

influence on the simulation results and the Fluent solver offersmany different schemes for pressure–velocity coupling, pressure,momentum, kinetic energy, rate of kinetic energy dissipation dis-cretization [27]. Both Kaya and Karagoz [31] and Shukla et al.[32] investigated the performance of different discretizationschemes in the steady and unsteady simulation of cyclone separa-tors. The schemes used in this study are given in the followingparagraphs together with an explanation of the reasons behindtheir selection.

Kaya and Karagoz [31] reported the advantages of SIMPLECalgorithm for pressure–velocity coupling in terms of convergence.For the pressure discretization they stated that the PRESTO pres-sure interpolation scheme only can predict precisely the meanvelocity profiles static pressure distribution and the pressure dropin the cyclone separator with good agreement with the experimen-tal values. This scheme is also recommended by the Fluent manual[27] for highly swirling flows.

For momentum, QUICK scheme has been recommended by bothKaya and Karagoz [31] and Fluent manual [27] for the flow in cy-clone separators. From the authors’ experience in simulatinghighly swirling flows using the Reynolds stress turbulence model,the QUICK scheme is the best scheme for the momentum discret-ization. It always gives good agreement with experimental mea-surements. For the discretization of kinetic energy and itsdissipation rate equation, the second order upwind scheme hasbeen used [32]. The first order upwind scheme has been used forthe discretization of the Reynolds stress equations [31,32]. ForLES simulations the bounded central difference scheme is the de-fault and the recommended convection scheme by the Fluent man-ual [27]. The temporal discretization starts with the first orderimplicit scheme and after 10 time steps the second order implicitscheme has been used.

2.3.3. Boundary conditions and other settingsVelocity inlet boundary condition is applied at inlet, outflow at

gas outlet and wall (no-slip) boundary condition at all otherboundaries. The air inlet velocity Uin equals 8 m/s, correspondingto air inlet volume flow rate Qin = 30 l/s, air density 1.0 kg/m3 anddynamic viscosity of 2.11E�5 Pa s, leading to a Reynolds numberof 1.17E4 based on the cyclone diameter and the area averaged in-let velocity. The turbulence intensity I equals 5% and the turbu-lence characteristic length equals 0.07 times the inlet width [33].At the cyclone inlet, the Reynolds stress specific method in Fluentsolver is the Reynolds stress components. The diagonal compo-nents of the the Reynolds stress tensor (normal stresses) are as-signed to 2kin/3, kin ¼ 3

2 ðIU2inÞ, where kin is the kinetic energy at

the inlet [27,34]. The shear stresses (non-diagonal components)at the inlet are set to zero. To take into account the stochastic com-ponent of the turbulent flow at the inlet for the LES simulation,

artificial perturbations have been generated using the spectral syn-thesizer method available in the Fluent solver [27,35,36], wherethe fluctuation velocity components are computed by synthesizinga divergence-free velocity-vector field from the summation of 100Fourier harmonics [27]. The fluctuations are added to the mean in-let velocity. The reason for introducing these artificial perturba-tions instead of selecting the no-perturbation option in theFluent solver, is that the unperturbated flat turbulent profiles at in-let generates unrealistic turbulent eddies [27]. For the near-walltreatment, the enhanced wall function [27] has been used in theRSM simulation. For subgrid scale model, the dynamic Smagorin-sky–Lilly model [27,37,38] has been used. The Smagorinsky modelconstant is dynamically computed instead of given as an input tothe solver, but clipped to zero or 0.23 if the calculated model con-stant is outside this range to avoid numerical instabilities [27]. Thesecond advantage of the dynamic Smagorinsky–Lilly model overthe Smagorinsky model is the treatment near the wall. In the dy-namic Smagorinsky–Lilly model, a damping function for the eddyviscosity near the wall is not required, since the model constantgoes to zero in the laminar region just near the wall [39].

2.3.4. The grid independency studyThe grid independence study has been performed for the three

tested cyclones. Three levels of grid for each cyclone have beentested, to be sure that the obtained results are grid independent.The hexahedral computational grids were generated using GAMBITgrid generator and the simulations were performed using Fluent6.3.26 commercial finite volume solver on a eight nodes CPUOpteron 64 Linux cluster.

The computational results of the three grid types are presentedin Table 3. As seen the maximum difference between the resultsobtained from the fine and medium meshes is 1% for the calcula-tion of cut-off diameter Euler number which is in the range ofexperimental error [29,6]. It has been observed that even mediumgrids provide a sufficient grid independency. However, for exclud-ing any uncertainty, computations have been performed using thefine grid, where the total number of grid points was not that crit-ical with respect to the computation overhead [40]. So the usedgrid produces grid independent results (the authors only checkedthe mean values, so for future studies with unsteady phenomenalike vortex-core precession (cf. Ref. [22]), the effect of the grid onthe Strouhal number associated with the simulated vortex-coreprecession [22] should be included in the grid independency studyprobably requiring finer grids, but this is not part of the presentstudy). Moreover, to accurately evaluate the numerical uncertain-ties in the computational results (especially because of the largedifference between the results obtained on the coarse and the finemesh which is about 7%), the concept of grid convergence index(GCI) was adopted using three grid levels per cyclone.

2.3.4.1. Grid convergence index (GCI). Roache [41–43] suggested aquantitative measure for the grid convergence; the grid conver-gence index (GCI). The GCI can be computed using two levels ofgrid; however, three levels are recommended in order to accu-rately estimate the order of convergence and check that the solu-tion is within the asymptotic range of convergence [44]. For aconsistent numerical analysis the discretized equations will ap-proach the solution of the actual equations as the grid resolutionapproaches zero [44]. The appropriate level of grid resolution is asignificant issue in numerical investigations. It is a function ofmany variables including the flow condition, type of analysis,geometry and many other variables.

The GCI is based upon a grid refinement error estimator derivedfrom the theory of the generalized Richardson extrapolation [44].The GCI is a measure of how far the computed value is away fromthe value of the asymptotic numerical value. Consequently, it

Table 3The details of the grid independence study for cyclones I–III.a

Cyclone I II III

N Eu X50 N Eu X50 N Eu X50

Coarse 632153 2.48 1.396 513021 2.36 1.335 513991 2.869 1.24Medium 861077 2.405 1.355 863852 2.28 1.257 712576 2.712 1.21Fine 1021616 2.39 1.35 1025778 2.27 1.25 1027982 2.687 1.2% differenceb 3.76 3.4 3.96 6.8 6.77 3.33

% differencec 0.63 0.37 0.44 0.56 0.93 0.83

a N is the number of hexahedral cells, Eu is the Euler number (dimensionless pressure drop = pressure drop/average kinetic energy at inlet) and X50 is the cut-off diameter;the particle diameter that will produce 50% collection efficiency (cf. Section 3.3).

b The percentage absolute difference between the coarse and fine grid values for Euler number and cut-off diameter.c The percentage absolute difference between the medium and fine grid values for Euler number and cut-off diameter.


indicates how much the solution would change with a furtherrefinement of the grid. A small value of GCI indicates that the com-putation is within the asymptotic range.

The GCI on the fine grid is defined as:

GCIfine ¼ Fsjejðrp � 1Þ ð1Þ

where Fs is a factor of safety. Fs = 3 for comparison of two grids and1.25 for comparison over three grids or more.

For the coarse grid:

GCIcoarse ¼ Fsjejrp

ðrp � 1Þ ð2Þ

e is a relative error measure of the key variable f between the coarseand fine solutions,

e ¼ f2 � f1

f1ð3Þ

where f2 is the coarse-grid numerical solution obtained with gridspacing h2. f1 is the fine-grid numerical solution obtained with gridspacing h1. r is the grid refinement ratio (r = h2/h1 > 1). For compli-cated geometries r is replaced by the ratio of the number of controlvolumes in the fine and coarse mesh [45] which is the case in thisstudy,

r12 ¼N1

N2

� �1D

ð4Þ

where D = 2 and 3 for two-dimensional and three-dimensionalgeometries respectively [41, pp. 410]. N1 and N2 are the numberof control volumes in the fine and coarse mesh respectively.

p is the order of the discretization method. p equals two if thesecond order discretization is used for all terms in space [45].(However, Slater [44] stated that if all discretization in space wasof second order, p will be less than 2. The difference is due to gridstretching, grid quality, non linearity in the solution, presence ofshocks, turbulence modeling and perhaps other factors.) For thegrid refinement study, three meshes have been used with N1, N2

and N3 cells for the fine, medium and coarse three-dimensionalmesh.

r12 ¼N1

N2

� �13

; r23 ¼N2

N3

� �13

; e12 ¼ f2 � f1; e23 ¼ f3 � f2;

where ei, i+1 = fi+1 � fi is the difference in the key variable f resultingfrom the use of different grids. If r12 = r23 then,

p ¼ lne23

e12

� ��lnðrÞ ð5Þ

If r12 – r23 which is the case in this study, Roache [42] proposedto solve Eq. (6)

e23

rp23 � 1

� � ¼ rp12

e12

rp12 � 1

� �" #

ð6Þ

Eq. (6) is transcendental in p. Using the iterative technique withrelaxation factor introduced in Roache [42,43]

p ¼ xqþ ð1�xÞ lnðbÞlnðr12Þ

ð7Þ

where b ¼ rp12�1ð Þe23

rp23�1ð Þe12

, x = 0.5 and q is the previous iteration of p. The

authors suggest to use q ¼ ln e23e12

� �=lnðr12Þ as a first guess. The itera-

tion will stop if j p�qp j < 1E� 5.

Now one can calculate, e12 ¼ f2�f1f1

, e23 ¼ f3�f2f2

, GCIfine12 ¼

1:25je12 jrp

12�1ð Þ and

GCIfine23 ¼

1:25je23 jrp

23�1ð Þ. GCIfine12 should be smaller than GCIfine

23 .

To check if the solution is in the asymptotic range, a � 1 (cf. Eq.(8))

a ¼ rp12GCIfine

12

GCIfine23

ð8Þ

The Richardson extrapolation can be used to obtain the value off when the grid spacing h vanishes (h ? 0) [41,46].

fexact ¼ f1 þ ðf1 � f2Þ=ðrp12 � 1Þ ð9Þ

Table 4 presents the grid convergency calculations using GCI meth-od and three grid levels for cyclones I–III. The following conclusionshave been obtained from the GCI analysis:

� The results are in the asymptotic range for the three cyclones,because the obtained values for a are close to unity.� The ratio R is less than unity this means monotonic convergence

[46].� There is a reduction in the GCI value for the successive grid

refinements ðGCIfine12 < GCIfine

23 Þ for the two variables (Eu andX50). This indicates that the dependency of the numerical resultson the cell size has been reduced. Also, a grid independent solu-tion has been achieved. Further refinement of the grid will notgive much change in the simulation results. For the two vari-ables (Eu and X50), the extrapolated value is only slightly lowerthan the finest grid solution. Therefore, the solution has con-verged with the refinement from the coarser grid to the finergrid [46]. Fig. 2 presents a qualitative proof that the obtainedresults are in the asymptotic range.

2.3.5. Convergence criteriaWith regard to the convergence criteria, two aspects should be

considered. Firstly, the scaled residuals should be below 1E�5(The default convergence criterion of Fluent is that scaled residualsof all equations fall below 1E�3). Secondly, some representativequantities such as velocity and pressure should be monitored until

Table 4Grid convergency calculations using GCI method and three grid levels for cyclones I–III.

i Ni fi ri,i+1 ei,i+1 ei,i+1 GCIfinei;iþ1% Ra ab

I Eu 0c 2.37501 1021616 2.3900

1.0586 0.0150 0.0063 0.78492 861077 2.4050 0.2013 1.0063

1.1085 0.0750 0.0312 1.55973 632153 2.4800

X50 0 1.34711 1021616 1.3500

1.0586 0.0050 0.0037 0.26492 861077 1.3550 0.1224 1.0037

1.1085 0.0410 0.0303 0.72523 632153 1.3960

II Eu 0 2.25231 1025778 2.2700

1.0589 0.0100 0.0044 0.97542 863852 2.2800 0.1256 1.0044

1.1897 0.0800 0.0351 1.51943 513021 2.3600

X50 0 1.24131 1025778 1.2500

1.0589 0.0070 0.0056 0.87402 863852 1.2570 0.0902 1.0056

1.1897 0.0780 0.0621 1.56523 513021 1.3350

III Eu 0 2.68351 1027982 2.6870

1.1299 0.0250 0.0093 0.16192 712576 2.7120 0.1607 1.0093

1.1150 0.1570 0.0579 1.31273 513991 2.8690

X50 0 1.19621 1027982 1.2000

1.1299 0.0100 0.0083 0.39132 712576 1.2100 0.3361 1.0083

1.1150 0.0300 0.0248 1.42113 513991 1.2400

a R = e12/e23.b a= rp

12GCI12� �

=GCI23.c The value at zero grid space (h ? 0). i = 1, 2 and 3 denote the calculations at the fine medium and coarse mesh respectively.

N -1

Eule

r num

ber

Cut

-offd

iam

eter

0 5E-07 1E-06 1.5E-062

2.2

2.4

2.6

2.8

3

1.15

1.2

1.25

1.3

1.35

1.4

1.45

1.5CycloneI(Eu)CycloneI(X50)CycloneII(Eu)CycloneII(X50)CycloneIII(Eu)CycloneIII(X50)

(h-->0)

Fig. 2. Qualitative representation of the grid independency study. The Eulernumber and the cut-off diameter for each cyclone at the three grid levels. N�1 isthe reciprocal of the number of cells, h ? 0 means the value at zero grid size (cf.Table 4). To obtain a smooth curve; the spline curve fitting has been applied inTecplot post-processing software.


they are constant [29]. Although the present simulations were con-verged at about (t = 1.5–1.6 s), they were only terminated at t = 2 sto get more accurate time averaged values. After achieving constanttangential velocity with time at a certain point in the middle of thecyclone domain, Fluent begins the data sampling for time statisticsfor the whole domain (the velocity components and the static pres-sure) each time step for sufficiently long time (t = 1.5 s untilt = 2.0 s). From this step, the following time averaged values areavailable; the mean and the root mean square values of the staticpressure p, the velocity magnitude v, the x-velocity vx, the y-velocityvy and the z-velocity vz. The mean z-velocity �vz is identical to themean axial velocity �vaxial. The mean tangential velocity �vh can be ob-tained using Fluent custom field function [27] according to Eq. (10).

�vh ¼ �vx cos hþ �vy sin h ð10Þ

where �vx is the time averaged x-velocity, �vy is the time averaged y-velocity and h is the angular coordinate.

3. Results and discussion

3.1. Validation of results

The obtained numerical results are compared with the LDAvelocity measurements of Boysan et al. [47] measured using laser

Dimensionless radial position

Dim

ensi

onle

ss ta

ngen

tial v

eloc

ity

-1 -0.5 0 0.5 10

0.5

1

1.5

2

2.5LDALES

Dimensionless radial position

Dim

ensi

onle

ss a

xial

vel

ocity

-1 -0.5 0 0.5 1-0.5

-0.25

0

0.25

0.5LDALES

Fig. 3. Comparison of the time averaged axial and tangential velocity between LDA measurements [47] and the LES simulations at section z = 564 mm from bottom. From leftto right: tangential and axial velocity.


doppler anemometry (LDA) system. Fig. 3 shows the comparisonsbetween the LES simulation and the measured axial and tangentialvelocity profiles at axial station z = 564 mm from the cyclone bot-tom [20]. The LES simulation predicts a similar trend as observedexperimentally although the maximum tangential velocity isunderestimated whereas the axial velocity is overestimated inthe central region. The non exact matching between experimentaland LES simulation has been reported in some other literatures[e.g., 20,22]. Considering the complexity of the turbulent swirlingflow in the cyclones, the agreement between the simulations andmeasurements is considered to be quite acceptable. Another com-parison between the current LES results and Reynolds stress turbu-lence model (RSM) results of Xiang and Lee [19] for cyclone III isgiven by Fig. 4 which indicates LES can also depict the main flowfeatures of cyclonic flow as Reynolds stress turbulence model cando.

3.2. The flow pattern in the three cyclones

3.2.1. The pressure fieldFig. 5 shows the time-averaged static pressure contours plots at

section Y = 0. In the three cyclones the static pressure decreasesradially from the wall to the center. A negative pressure zone ap-

Dimensionless distance

Dimensionless

tangential

velocity

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 10

0.25

0.5

0.75

1

1.25Present studyXiang and Lee (2005)

Fig. 4. Comparison of the time averaged tangential and axial velocity between RSM resuD = 0.375). From left to right tangential and axial velocity. (Note, the dimensionlessvelocity/inlet velocity.)

pears in the forced vortex region (central region) due to high swirl-ing velocity. The pressure gradient is largest along the radialdirection, while the gradient in axial direction is very limited. Thecyclonic flow is not symmetrical as is clear from the shape of thelow pressure zone at the cyclone center (twisted cylinder). The staticpressure contour plots for the three cyclones are almost the same.

3.2.2. The velocity fieldBased on the contours plots of the time averaged tangential

velocity (Fig. 5) and the radial profiles at sections S1, S2, S3 andS4 shown in Fig. 6, the following comments can be drawn. Themaximum tangential velocity equals around 1.25 times the aver-age inlet velocity and occurs in the annulus cylindrical part. Thetangential velocity distribution for the three cyclones are nearlyidentical at the corresponding sections. The tangential velocityprofile at any section is composed from two regions, inner and out-er. In the inner region the flow rotates approximately like a solidbody rotation (forced vortex), where the tangential velocity in-creases with radius. After reaching its peak the tangential velocitydecreases with radius in the outer part of the profile (free vortex).This profile is so-called Rankine type vortex which include a quasi-forced vortex in the central region and a quasi free vortex in theouter region.


Dimensionless

axial

velocity

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1-0.5

-0.25

0

0.25

0.5Present studyXiang and Lee (2005)

lts of Xiang and Lee [19] and the current LES results at z/D = 1.29 for Cyclone III (Bc/radial distance = the distance/the cyclone radius, the dimensionless velocity = the


The radial profiles given in Fig. 6 represent the time averagedtangential velocity in the lower part of the cyclone. The tangentialvelocity distributions at the bottom sections show good axis-sym-metrical distribution. The tangential velocity for the three cyclonesare identical in the inner region, where the maximum tangentialvelocity nearly equals the inlet velocity and occurs at a position0.25–0.45 of the cyclone radius as given in Table 5.

The axial velocity contours (Fig. 5) indicate the existence of twoflow streams. Downward flow directed to the cyclone bottom (neg-ative axial velocity), and upward flow directed to the vortex finderexit. The axial velocity plots for the three cyclones are nearly iden-tical at the corresponding sections in the conical part. The axialvelocity equals zero at the walls and maximum close to the posi-tion of maximum tangential velocity. The axial velocity profilesshown in Fig. 6 exhibit a severe asymmetrical feature.

3.2.3. Comparison of the velocity profiles in the three cyclonesHowever, from the previous discussion it is clear that, the effect

of the cone tip diameter on the flow field in the conical section isinsignificant, in comparison with other geometrical parameterssuch as the vortex finder diameter. But in this section a comparison

Cyclone I Cyc

The

stat

icpr

essu

reN

/m2

The

tang

enti

alve

loci

tym

/sT

heax

ialv

eloc

ity

m/s

Fig. 5. The contours plots for the time averaged flow variables at Y = 0. From top to bottcyclones I, II and III respectively.

between the axial and tangential velocity profiles at four sections(Table 2) will be analyzed as presented in Fig. 7.

The tangential velocity profiles in the forced vortex region arenearly identical in the three cyclones at each sections. While inthe free vortex region, the tangential velocity increases as the conetip diameter is reduced. The tangential velocity profiles for thethree cyclones are almost the same.

The axial velocity profile has the shape of an inverted W for allcyclones. The highest axial velocity occurs at 0.25–0.5 of the cy-clone radius down the vortex finder till the cyclone bottom, andbetween 0.25 and 0.5 of the cyclone radius in the annulus andthrough the vortex finder. No considerable difference exist in theaxial velocity profiles for the three cyclones. Since the axial veloc-ity profiles is almost the same for the three cyclones so the averageresidence time of particles is nearly the same. Also the position ofthe highest axial velocity moves inward in the conical part as thecone tip diameter reduced.

From the previous analysis the region of downward flow isnearly the same, for the three cyclones, while the tangential veloc-ity slightly increases as the cone tip diameter reduced, so the par-ticles will experience a higher tangential velocity for cyclone III

lone II Cyclone III

om: the static pressure, the tangential velocity and axial velocity. From left to right


Dimensionless

tangential

velocity

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 10

0.25

0.5

0.75

1

1.25S1S2S3S4


Dimensionless

axial

velocity

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1-0.5

-0.25

0

0.25

0.5S1S2S3S4


Dimensionless

tangential

velocity

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 10

0.25

0.5

0.75

1

1.25S1S2S3S4


Dimensionless

axial

velocity

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1-0.5

-0.25

0

0.25

0.5S1S2S3S4


Dimensionless

tangential

velocity

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 10

0.25

0.5

0.75

1

1.25S1S2S3S4


Dimensionless

axial

velocity

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1-0.5

-0.25

0

0.25

0.5S1S2S3S4

Fig. 6. The radial profile for the time averaged tangential and axial velocity at different sections on the X–Z plane (Y = 0) for each cyclone. From left to right tangential velocityand axial velocity. From top to bottom: Cyclones I, II and III respectively.

Table 5Comparison between the maximum tangential velocity value and its position at different sections.

Section S1 S2 S3 S4

Cyclone I II III I II III I II III I II III

vhmax =v ina 1.08 0.97 1.02 1.02 0.95 1.05 0.96 0.89 1.04 0.94 0.88 1.035

x/Rb 0.3 0.28 0.26 0.3 0.33 0.33 0.32 0.37 0.41 0.35 0.43 0.425

a The ratio between the maximum tangential velocity and the area average inlet velocity.b The dimensionless distance between the centerline and the point of maximum velocity, R is the cyclone radius.



Dim

ensi

onle

ssta

ngen

tial

velo

city

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 10

0.25

0.5

0.75

1

1.25 Cyclone ICyclone IICyclone III


Dim

ensi

onle

ssax

ial

velo

city

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1-0.5

-0.25

0

0.25



Dim

ensi

onle

ssta

ngen

tial

velo

city

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 10

0.25

0.5

0.75

1



Dim

ensi

onle

ssax

ial

velo

city

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1-0.5

-0.25

0

0.25



Dim

ensi

onle

ssta

ngen

tial

velo

city

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 10

0.25

0.5

0.75

1



Dim

ensi

onle

ssax

ial

velo

city

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1-0.5

-0.25

0

0.25



Dim

ensi

onle

ssta

ngen

tial

velo

city

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 10

0.25

0.5

0.75

1



Dim

ensi

onle

ssax

ial

velo

city

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1-0.25

0

0.25


Fig. 7. Comparison between the radial profile for the time averaged tangential and axial velocity at different sections on the X–Z plane (Y = 0). From top to bottom: section S4–S1. From left to right tangential velocity and axial velocity respectively.


than in other cyclones for the same time (as the region of down-ward axial velocity is nearly equal). Which results in a slightlyhigher collection efficiency. This is consistent with the measured

results reported by Xiang et al. [9] and simulation by Xiang andLee [19] and Chuah et al. [13]. The change of cone tip diameter af-fect the flow field in the cyclone separator but this change is so

Table 6The cut-off diameter and pressure drop for the three cyclones.

Cyclone I II III

Bc/D 0.625 0.5 0.375Cut-off diameter (lm) 1.35 1.25 1.2Cut-off diameter (lm) (Chuah et al. [13]⁄) 1.65 1.45 1.1Pressure dropDP (N/m2) 76.5 72.7 86

Euler numberEu (DP=ð0:5qV2inÞ) 2.39 2.27 2.687

⁄ Qin = 60 l/min.

Bc /D

Eule

r num

ber [

-]

Cut

-off

diam

eter

[mic

ron]

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.70

1

2

3

4

5

1

1.2

1.4

1.6

1.8Eulernumber [-] (Exp.)Eulernumber [-] (LES)Cut-offdiameter [micron] (LES)

Fig. 8. The effect of cone-tip diameter on the pressure drop (Euler number) and cut-off diameter (with spline curve fitting to get a smooth curve).


limited, i.e., the reduction of cone tip diameter enhance the collec-tion efficiency but with small percentage, as the flow field patternis so close for the three cyclones.

3.3. Discrete phase modeling (DPM)

The Lagrangian discrete phase model in Fluent follows the Eu-ler–Lagrange approach. The fluid phase is treated as a continuumby solving the time-averaged Navier–Stokes equations, while thedispersed phase is solved by tracking a large number of particlesthrough the calculated flow field. The dispersed phase can ex-change momentum, mass, and energy with the fluid phase.

A fundamental assumption made in this approach is that thedispersed second phase occupies a low volume fraction (usuallyless than 10–12%, where the volume fraction is the ratio betweenthe total volume of particles and the volume of fluid domain), even

Table 7The cyclone performance parameters using CFD, Experimentalc [9] and different seven ma

Cyclone CFD Barth MM

Euler number Eu [–] I 2.39 6.94 4.88II 2.27 7.40 4.95III 2.687 7.43 4.95

Cut-off diameter X50 [lm] I 1.35 1.22 2.13II 1.25 1.22 2.089III 1.2 1.28 2.089

a The mathematical model used for estimation of the pressure drop only.b The mathematical model used for estimation of the cut-off diameter only.c Different particle density.

though high mass loading is acceptable. The particle trajectoriesare computed individually at specified intervals during the fluidphase calculation. This makes the model appropriate for the mod-eling of particle-laden flows.

For modeling of heavily loading cyclones, particle–particle andparticle turbulence interaction should be considered. The particleloading in this study is small, and therefore, it can be safely as-sumed that the presence of the particles does not affect the flowfield (one-way coupling).

In terms of the Eulerian–Lagrangian approach (One Way cou-pling), the equation of particle motion is given by [48]

dupi

dt¼ 18l

qpd2p

CDRep

24ðui � upiÞ þ

giðqp � qÞqp

ð11Þ

dxpi

dt¼ upi ð12Þ

where the term 18lqpd2

p

CDRep

24 ðui � upiÞ is the drag force per unit particle

mass [48]. q and l are the gas density and dynamic viscosityrespectively, qp and dp are the particle density and dimeter respec-tively, CD is the drag coefficient, ui and upi are the gas and particlevelocity in i direction respectively, gi is the gravitational accelera-tion in i direction, Rep is the relative Reynolds number.

Rep ¼qpdpju� upj

lð13Þ

In Fluent, the drag coefficient for spherical particles is calcu-lated by using the correlations developed by Morsi and Alexander[49]. The equation of motion for particles was integrated along thetrajectory of an individual particle. Collection efficiency statisticswere obtained by releasing a specified number of mono-dispersedparticles at the inlet of the cyclone and by monitoring the numberescaping through the outlet. Collisions between particles and thewalls of the cyclone were assumed to be perfectly elastic (coeffi-cient of restitution is equal to 1).

3.3.1. The DPM resultsIn order to calculate the effect of the vortex finder diameter on

the cut-off diameter, 16800 particles were injected from the inletsurface with zero velocity and a mass flow rate _mp of 0.001 kg/s(corresponding to inlet dust concentration Cinð _mp=QinÞ ¼2:0 gm=m3) for each of the three cyclones. The particle density is860 kg/m3 and the maximum number of time steps for each injec-tion was 900,000 steps. The DPM analysis results for the three cy-clones are shown in Table 6 and Fig. 8. It is found that the cut-offdiameter decreases slightly with decreasing the cone-tip diameterwhile the pressure drop is increasing slightly. Consequently, the ef-fect of cone-tip diameter on the cyclone performance is insignificant.

The trend of changing the cut-off diameter with the cone-tipdiameter given by Chuah et al. [13] (Qin = 60 l/min) supports theconclusion of the slightly decrease of cut-off diameter by

thematical models.

Stairmanda Sphereda Casala Ioziab Ritemab Exp.

6.68 4.1 4.07 – – 2.86.69 4.1 4.07 – – 2.86.69 4.1 4.07 – – 3.25

– – – 1.44 1.4 3.01– – – 1.44 1.4 2.60– – – 1.44 1.4 2.36


decreasing the cone-tip diameter and the insignificant effect of thecone-tip diameter on cut-off diameter (Table 6).

4. Comparison with mathematical models

Table 7 presents a comparison between the Euler number(dimensionless pressure drop) and the cut-off diameter obtainedfrom CFD, experimental investigation [9] and seven mathematicalmodels, viz. (the Barth model [14], the Muschelknautz method ofmodeling (MM) [50,51], the Stairmand model [52], the Casal andMartnez-Benet model [53] and the Shepherd and Lapple model[54], the Iozia and Leith model [16], the Ritema model [55] (cf.Hoffmann and Stein [56]).

The Euler numbers obtained from the models of Sphered andLapple, Casal and Martnez-Benet are constant, because these mod-els do not include the effect of Bc in their formulas. The three othermodels (Barth, MM and Stairmand) indicate less effect on Eulernumber or cut-off diameter by changing the cone-tip diameter.The models of Iozia and Leith in addition to that of Rietma indicateno change in cut-off diameter with changing the cone-tip diameter.The results of mathematical models and the experimental investi-gation support the CFD results that the cone tip diameter is insig-nificant factor on the cyclone separator performance.

5. Conclusion

Large eddy simulation has been used to study the effect of cone-tip diameter on the cyclone flow field and performance. Three cy-clones with different values of Bc/D viz. 0.625, 0.5 and 0.375 (atconstant vortex finder diameter Dx/D = 0.5) have been investigated.The following conclusion can been drawn:

� The cone-tip diameter has an insignificant effect on the flowpattern and performance.

� As the cone-tip diameter decreases, the maximum tangentialvelocity increases slightly, while its position is almost thesame.

� The flow pattern and performance parameters of the threecyclones are almost the same.

� Decreasing the cone-tip diameter increases the pressuredrop slightly. The reverse trend is obtained for the cut-offdiameter.

� Seven mathematical models used for estimation of the effectof cone-tip diameter on the cyclone performance, and all ofthem support the CFD results for the insignificance of vary-ing the cone-tip diameter on the cyclone performance.

� However, the main finding of the current study is the insig-nificant effect of the cone-tip diameter on the cyclone perfor-mance, in comparison to the the other geometricalparameters like the vortex finder diameter Dx or the inletdimensions [cf. 5,6], the cone is an essential part for cycloneoperation. If the cone would be removed from the cyclone, itwill be only cylindrical part and that one will have anothergeometry (not the conventional cyclone). Also the particlesare collected over the cone wall and then moved to thecyclone bottom. Consequently, a very low collection effi-ciency will be expected for cyclone separator without cone.

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numerical modeling of the flow field and performance in cyclones of different cone-tip diameters

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