CFD Modeling of Dense Medium Cyclone

CFD MODELING OF DENSE MEDIUM CYCLONE

RAJ K. RAJAMANI1, JOSE DELGADILLO2,UDAYA BHASKAR KODUKULA3, AND DILEK ALKAC4

1Metallurgical Engineering Department, University ofUtah, Salt Lake City, USA2Universidad Autonoma de San Luis Potosi,San Luis Potosi, Mexico3Global R&D Centre ArcelorMittal, Chicago,Illinois, USA4Metallurgical Engineering Department, University ofUtah, Salt Lake City, USA

A number of empirical models are in existence for the dense medium

cyclone (DMC) and in recent years this subject has been broached

with computational fluid dynamics (CFD). The dense medium pre-

sents a centrifugal field within the cyclone body. The coal particles

separate in this field due to various forces acting on them. Hence,

CFD is ideally suited for the modeling of the DMC. The Large Eddy

Simulation (LES) method for resolving the turbulence was used in the

CFD simulation of a 76mm dense medium cyclone. In particular,

the magnetite was modeled as three granular fluids. In the simulation

the diameter of the vortex finder and spigot are varied to compare

with the experimental data of P. A. Verghese and T. C. Rao. The

results obtained using LES turbulence model is found to be accurate

in terms of the cut density and the slope of the distribution curves.

Thus, the three granular fluid modeling of the magnetite stream

is a computationally simpler method for the analysis of DMC.

This article was presented at the 2010 International Coal Preparation Congress

(ICPC), Lexington, KY. ICPC 2010 conference proceedings published are by the Society

of Mining, Metallurgy, and Exploration, Inc. (SME), Littleton, CO (www.smenet.org;

Tel.: 303-948-4200). SME’s permission to republish the article is gratefully acknowledged.

Address correspondence to Raj K. Rajamani, Metallurgical Engineering Department,

University of Utah, Salt Lake City, UT 84112, USA. E-mail: [email protected]

International Journal of Coal Preparation and Utilization, 30: 113–129, 2010

ISSN: 1939-2699 print=1939-2702 online

DOI: 10.1080/19392699.2010.497089

Keywords: Computational fluid dynamics; Dense medium hydrocy-

clone; Large Eddy Simulation; Reynolds stress model

INTRODUCTION

In principle it is widely known that magnetite suspension in water

generates an intermediate density between the coal and the

ash-forming minerals and researchers have identified that a density

gradient naturally occurs within the separation chamber of heavy

medium cyclones. The gradient is due to the centrifugal forces on

the magnetite particles and their balance with the drag force at differ-

ent radial and axial positions in the cyclone body [1–3]. There exists

a density differential in the overflow and the underflow products of

the cyclone; both of which are different from that of the density

maintained in the feed. However, very limited information is available

on the segregation of magnetite and, hence, the slurry density distri-

bution at different radial and axial positions in the cyclone body. Stu-

dies on such behavior of medium will be useful both in terms of

engineering principles and in the design modifications for specific

applications.

The simulation of a dense medium cyclone (DMC) with computa-

tional fluid dynamics (CFD) is a leap forward based on the enormous

success of CFD in hydrocyclones. Recently, developments in computa-

tional systems enabled the simulation of hydrocyclone performance

using CFD techniques [4–40]. However, applying the CFD technique

learned in hydrocyclones to DMC may not produce correct results for

obvious reasons.

CFD simulation of heavy medium cyclones is a complex task and

numerically intensive. The direct Eulerian simulation for different

medium sizes, and size- and density-based coal classification is extremely

difficult to achieve in years to come. Toward this objective, Narasimha

et al. [28] presented the results of the Large Eddy Simulation (LES)

and Reynolds Stress Model (RSM) and compared them with density

distribution measured in a 350mm DMC. These authors presented the

discrepancies between the computations and experimental results as well

as the means to remedy these discrepancies. Though the simulated

results agree with values of density distribution within the cyclone

body, the computational effort is enormous and further the unsteady

114 R. K. RAJAMANI ET AL.

state simulation needs good expertise and judgment for solution

convergence. It is apparent that high concentration of magnetite in

water would exhibit non-Newtonian rheology. Hence, Suasnabar and

Fletcher [12] studied non-Newtonial rheology and turbulence of

DMC using CFD. They concluded that the turbulence effect is

more important than the rheology effect. The multiphase approach

by Brennan [31] produced nearly matching results in terms of density

distribution and coal-separation characteristics, that too with a reason-

able computational effort. However, medium segregation was found to

be overpredicted by CFD, and it was concluded that it might be caused

by the fact that turbulent mixing of the dispersed phase was more

significant for sizes typical to DMC (�30 mm).

Chu et al. [32] took the DMC simulation one level above what

is possible with CFD. They combined the discrete element method

for particle behavior with CFD. With this approach they proved

the existence of surging phenomena in DMC. While this approach is a

leap forward, the computations would be prohibitive for reasonable use.

The understanding of the effect of magnetite particles on the

changes in fluid characteristics in the centrifugal field via fluid dynam-

ics is the key aspect of LES simulations. The simulation methodologies

that are relatively less computationally expensive and yet produce

reasonable results would be attractive for the analysis and design

of DMC. The present study is an attempt to develop such a CFD

methodology.

MODEL DESCRIPTION

Geometry

The 76mm diameter hydrocyclone geometry used in the experimental

studies of Verghese and Rao [1] was simulated in the present study.

The dimensions of the DMC are shown in Figure 1. In particular

four different spigots were used in this study. These authors report

25 experiments conducted with magnetite as the heavy medium.

The experiments were performed with the aim of understanding the

effects of design variables and operating variables. These authors

presented detailed size and specific gravity for all the streams in

each of the 25 experiments. Hence, the data set is valuable for model

verification.

CFD MODELING OF DENSE MEDIUM CYCLONE 115

Boundary and Initial Conditions

Water, air, and magnetite particles were defined as fluids with density

values corresponding to 1000, 1, and 5100 kg=m3, respectively. Magnetite

is defined as a granular phase with a suitable particle size. Water was the

primary phase for simulation; air and three different phases of magnetite

granular fluids were used as secondary phases. Feed inlet was designated

as mass flow inlet. The necessary values of mass flow rates (taken from

Verghese and Rao [1]) were assigned for the water and magnetite phases

at the feed inlet. The vortex finder and spigot outlets were designated as

pressure outlets. At both the outlets, the backflow volume fraction of air

was assigned as unity for air entry into the cyclone body.

Simulation. Simulation was carried out using a 3-D double precision,

unsteady state, and segregated solver under Cartesian coordinate

systems. In order to enhance the capture of flow features, at critical

regions such as cyclone walls, around the air-core, in the vicinity of the

vortex finder and at the spigot, methods like boundary layer mesh

adjacent to the outer cyclone wall, block-structured mesh at the air

core, and a larger number of meshes near the spigot were adopted.

The computational domain is divided into about 150,000 elements, a

reasonably optimum mesh domain for such CFD problems.

The mixture density and viscosity that are calculated based on the

concentration of the magnetite and water phases will effectively enable

Figure 1. Dense medium cyclone design used in the CFD simulation.


the phases to act as a true dense liquid within the system. In a heavy

medium cyclone, volumetric concentration of coal in proportion to the

mixture of water and magnetite can be presumed to be reasonably dilute

to simulate the path of coal particles using the Lagrangian tracking

approach.

This assumption though is far off from the actual condition and

would reduce the computational effort to a great extent. It is also

reported that using this method partition curves can be generated with

reasonable accuracy in both sharpness and cut density [28, 31, 33].

In the LES approach for turbulence closure modeling, eddies larger

than the mesh size are resolved and eddies of smaller scales are modeled.

Thus the equations of motion are filtered, which results in an additional

stress tensor term in the filtered Navier Stokes equations that account for

the transfer of momentum by subgrid scales of turbulence. The subgrid

scale (SGS) stresses are usually modeled using a simple eddy viscosity

model known as Smagorinsky-Lilly SGS model. The SGS model pre-

sumes that the eddy viscosity is related to the local average grid spacing

and the mean strain rate. In the mixture model with granular flow, the

granular viscosity, the granular temperature, and the drag law formula-

tions are the important parameters. Granular viscosity is comprised of

collisional viscosity and kinetic viscosity. In the present work granular

viscosity was set as a constant in the calculations. The drag law formula-

tions incorporated in phase interactions, as per available in Fluent model

library, were respectively Schiller-Naumann model [34] for air-water and

the Syamlal-Obrien model for magnetite-water. The slip velocity for air

was modeled with Manninen et al. [35] law. In the present study, the

use of five fluids required a reasonable computational time. A typical

value of mass flow inlet of water was set at 0.71 kg=s. The magnetite fluid

inlet flow was set at 0.41 kg=s with 33.5, 33.9, and 32.6 weight percents

apportioned to the three granular fluids, i.e., 7.0 mm, 19.4 mm, and 38 mmsizes. Specific experimental values were taken from Table 3 of Verghese

and Rao [1].

Velocity profile prediction is the most ubiquitous method of verifi-

cation; although predicting Reynolds’s stresses is more advanced in

characterizing modeled turbulence if such measurement is available.

The velocity field can be resolved into three components: tangential,

radial, and axial. The tangential velocity determines the distribution of

centrifugal force that constitutes the major contribution to the total

pressure drop. The tangential velocity increases rapidly in the radial


direction in a free vortex zone. In the central part of the hydrocyclone,

the vortex and the air-core force the tangential velocity to decrease cre-

ating a force vortex zone. The axial velocity sets the boundary between

the inner spiral, which is moving upward, and outer spiral, which is mov-

ing downward. The accurate prediction of this component is the key to

predicting particle size classification.

Delgadillo and Rajamani [23] compared the LES model with RSM

and j-e model for the prediction of 75mm and 250mm hydrocyclones.

Figure 2 shows the comparison between computed axial and tangential

velocity profiles against experimental values in a 250mm hydrocyclone.

The trends in the experimental data are extremely well predicted.

Likewise, the velocity predictions made at various heights within the

body of the hydrocyclone compared well with experimental data.

Since the velocity profiles along the axial and tangential direction

are well described by LES, the conclusion is that the anisotropy of

turbulence is well captured.

In the same study [23], it was demonstrated that once the velocity

profiles are accurately described, the particle size classification can also

be predicted by following the path of each size class of particles in the

computed velocity field. The particle path is traced by what is known

as the Lagrangian tracking method. Indeed such success with the LES

method shows its promise for application in the dense medium hydrocy-

clone. More fundamental verification of fluid dynamics in the DMC field

was shown by Narasimha et al. [25] in their computer tomography

verification of predicted density profiles.

Figure 2. Axial (a) and tangential (b) velocity predictions with LES in a 250mm hydro-

cyclone (Delgadillo and Rajamani, 2005).


The typical computation for five fluids takes over 20 to 40 days on

2.6GHz single CPU processor. Upon convergence of flow conditions

of the primary and secondary phases, a constant number of coal particles

of different sizes and densities were injected into the fluid body and the

percentage reporting to the overflow and underflow products were

generated.

RESULTS AND DISCUSSIONS

In the present study, validation of the CFD with experimental results is

shown for 22.5mm vortex finder and at 15.0mm diameter spigot opening

design. Verghese and Rao [1] present the distribution of coal particles as

a function of reduced specific gravity. Furthermore, they present a func-

tional form for the mean value of the experimentally obtained data

points. In other words, the experimental data points are nearly clustered

around this mean distribution curve. Therefore, in the present study, the

mean curve is taken as the experimental response and the CFD simula-

tions are compared with it.

An attempt was made in the modeling of the phases to reduce com-

putational time. First, the fluid phase was modeled as three phases:

water, air, and magnetite, where magnetite was modeled as a single

granular fluid. The size of the single granular phase was varied from

5 mm to 10 mm to 15 mm. These approaches, although an order of

magnitude less in computing time, did not produce the ideal density

distribution within the cyclone body. Finally, the five-fluid LES

model discussed earlier produced meaningful density distributions

that led to reasonable predictions of partition curves. The CFD pre-

dicted values of cut densities of coal particles with LES simulation

are 1510 kg=m3, 1520 kg=m3, 1530 kg=m3, and 1520 kg=m3 corres-

ponding to coal particle sizes 1673, 1285, 1086, and 550 microns,

respectively.

Air Core

The air core was nearly 10mm in diameter at or near the spigot open-

ing. With increasing vertical heights from the spigot opening, the

diameter of the air core broadens and the fractional volume of air

in this region decreases. Figure 3 shows the volume fraction of air

profiles throughout the 75mm DMC. The central air-core has a


parabolic contour shape. However, the air-core in the vortex finder is

nearly cylindrical. The decrease in the volume fraction of air at

increased vertical heights from the spigot opening is due to entrap-

ment of water and the magnetite particles reporting to the overflow

product through the vortex finder.

Figure 4 shows the results of CFD computations compared with

experimental data. As shown in Figure 4, the results indicate that

single granular fluid systematically fall short of experimental results.

Figure 3. Volume concentration of air in the central core of the 75mm DMC.


Therefore, in the rest of this article the discussions are about the

five-fluid LES model predictions.

Mixture Density Distribution in the Cyclone Body

The slurry density is the most important variable that decides the separ-

ation efficiency inside a DMC. Because of the range of particle sizes of

the media used in the feed slurry, a natural segregation of the media

within the cyclone occurs. The coarser size particles tend to report

toward the walls while layers of relatively finer particles are found at

smaller radial distance from the cyclone axis. Ideally, the fines below

the cut size of the cyclone mostly report into the overflow product while

the size coarser than the cut size mostly report to the underflow pro-

duct. Therefore, the density that is maintained in the feed slurry to

the cyclone will be always lower than the cut density. It is widely

reported that most of the magnetite pumped to cyclones reports into

the underflow product. Realizing the importance of density distribution

due to media segregation on the separation behavior, attempts were

Figure 4. Comparison of single granular fluid and three granular fluid LES results with

experimental data for size fractions of coal particles.


made to understand the mixture density at different radial and axial

positions in the cyclone body.

The density distribution characteristics are presented in Figure 5.

The maximum value of mixture densities are observed more at

the lower conical portions of the cyclone body. For example, at a

distance of 50mm from the cyclone roof, the maximum value of

mixture density observed at the walls is 1787 kg=m3 while the

maximum value of mixture density at 225mm axial distance is

2820 kg=m3. Within the central core region, the density is predomi-

nantly that of air.

Figure 5. Mixture density distribution in the hydrocyclone body.


Figure

6.Volumefractiondistributionofmagnetitegranularfluids.

123

Figure 7. Predicted partition curve compared with experimental data for case 18, 19, and 6

(percentage of feed to overflow versus relative density, SG=SG50).


Media Segregation Behavior in the Cyclone Body

The behavior of the three different sizes of the magnetite granular fluid is

helpful in understanding how the overall density gradation is established

within the cyclone. The distribution behavior of these fluids in terms of

the volume fraction contours is presented in Figure 6. The magnetite

granular fluid of 38 mm is mostly segregated along the walls of the cyc-

lone body, preferentially in the cylindrical and upper conical regions.

The fluid of a grain size of 19.4 mm also segregates along the walls of

the cyclone body. However, this fluid segregates in the lower conical por-

tions of the cyclone body indicating preferential discharge of this fluid

into the underflow. The fluid of grain size of 7.0 mm is mostly distributed

around the cylindrical and upper conical portions of the cyclone body.

Lower values of the fractional volume concentration of this phase can

be observed at lower conical heights indicating that this fraction of

the fluid essentially decides the density distribution in the cylindrical

portion of the cyclone body, where most of the classification effects

are anticipated to occur.

Figure 7 compares the LES predictions for each coal particle

size class with the experimental data. Table 1 shows the experimental

conditions used in three cases. The solid line in the figure is the fitted

line to the large volume of experimental data, and the results from

CFD simulation are marked by small circles. It is readily apparent

that CFD predictions compare well with experiments. Both the slope

and the cut density is well predicted for 550 to 1673 mm sizes. How-

ever, it was noted that the predictive quality diminished at smaller

particle sizes. It is believed that the force balance done by the Lagran-

gian tracking method may not accurately describe the drag forces act-

ing on the coal particle especially in a very small size range. While

much is known in dilute fluid systems, accurate descriptions of

the flow characteristics of highly concentrated fluid-particle systems

are not yet available.

Table 1. Experimental conditions

Case no.

Vortex finder

diameter (mm)

Medium

density

Feed slurry

flowrate (L=min)

18 12.4 1.38 40.0

19 12.4 1.39 52.5

6 9.7 1.39 55.1


CONCLUSIONS

A CFD simulation methodology is described for simulating the classi-

fication of dense medium cyclone. The methodology included multiphase

mixture modeling using five different fluids. Water being the primary fluid,

and air and three different granular magnetite fluid particles are used as

the secondary phases. The turbulence is resolved using the LES method.

The classification behavior of 76mm dense medium cyclone is evaluated.

The distribution characteristics were generated using particle injection

using the discrete particle modeling technique. The results show that the

cut density of different size coal particles and the slopes of the distribution

curves match with the published results. The simulation method using

LES turbulence and five-phase simulation is found to have improved

matching characteristics than the multiphase simulations generated using

just three phases (water, air, and single granular magnetite fluids), and two

phases (pure high-density water 1400 kg=m3 density and air) with an RSM

method for resolving the turbulence.

The study was about finding the minimum fluid configuration in the

FLUENT solver code that would accurately describe the DMC perform-

ance. The five-fluid configuration was adequate for this purpose, yet it

should be mentioned that for solution convergence CPU time was in

the range of 20 to 40 days.

REFERENCES

1. Verghese, P. A., and T. C. Rao. 1994. Modelling of a 76mm dense medium

cyclone. Coal Preparation 15:71–91.

2. Davis, J. J. 1994. A study on coal washing dense medium cyclone. PhD

Thesis, JKMRC, University of Queensland.

3. He, Y. B., and J. S. Laskowski. 1994. Effect of dense medium properties on

the separation performance of a dense medium cyclone. Minerals Engineering

7: 209–221.

4. Hsieh, K. T., and K. Rajamani. 1988. Phenomenological model of the

hydrocyclone: Model development and verification for single-phase flow.

International Journal of Mineral Processing 22(1–4): 223–237.

5. Monredon, T. C., K. T. Hsieh, and R. K. Rajamani. 1992. Fluid flow model

of the hydrocyclone: An investigation of device dimensions. International

Journal Mineral Processing 35(1–2): 65–83.

6. Rajamani, R. K., and L. Milin. 1992. Fluid flow model of the hydrocyclone

for concentrated slurry classification. Hydrocyclones: Analysis and Appli-

cation: 4th Intentional Conference 12: 95–108.


7. Devulapalli, B., and R. K. Rajamani. 1996. A comprehensive CFD model

for particle-size classification in industrial cyclones. In Hydrocyclones ‘96,

83–104. Cambridge, UK: Mechanical Engineering Publications, Ltd.

8. Griffths, W. D., and F. Boysan. 1996. Computational fluid dynamics (CFD)

and empirical modeling of the performance of a number of cyclone samples.

Journal of Aerosol Science 27(2): 281–304.

9. Slack, M. D., and A. E. Wraith. 1997. Modelling the velocity distribution

in a hydrocyclone. Fourth International Colloquium on Process Simulation:

65–83.

10. Slack, M. D., and F. Boysan. 1998. Advances in cyclone modelling using

unstructured grids, Scandinavian FLUENT UGM, Gothenburg: 1–9.

11. Stoven, V. R., and A. J. Saul. 1998. A computational fluid dynamics (CFD)

particle tracking approach to efficiency prediction. Water Science and

Technology 37: 285–293.

12. Suasnabar, D. J., and C. A. Fletcher. 1999. A CFD model for dense medium

cyclones. In Second International Conference on CFD in the Minerals and

Process Industries. Melbourne, Australia: CSIRO, 199–204.

13. Slack, M. D., R. O. Prasad, A. Bakker, and F. Boysan. 2000. Advances in

cyclone modeling using unstructured grids. Trans. IchemE 78: 1098–1104.

14. Ma, L., D. B. Ingham, and X. Wen. 2000. Numerical modelling of the fluid

and particle penetration through small sampling cyclones. Journal of Aerosol

Science 31: 1097–1119.

15. Nowakowski, A. F., W. Kraipech, R. A. Williams, and T. Dyakowski. 2000.

The hydrodynamics of a hydrocyclone based on a three-dimensional multi-

continuum model. Chemical Engineering Journal 80: 275–282.

16. Nowakowski, A. F., J. C. Cullivan, R. A. Williams, and T. Dyakowski. 2004.

Application of CFD to modelling of the flow in hydrocyclones. Is this a

realizable option or still a research challenge? Minerals Engineering 17:

661–669.

17. Grady, S. A., G. D. Wesson, M. M. Abdullah, and E. E. Kalu. 2002.

Prediction of flow field in 10-mm hydrocyclone using computational fluid

dynamics. Fluid and Particle Separations Journal 14: 1–11.

18. Grady, S. A., G. D. Wesson, M. M. Abdullah, and E. E. Kalu. 2003. Predic-

tion of 10mm hydrocyclone separation efficiency using computational fluid

dynamics. Research article, Dept. of Chemical and Civil Engineering,

FAMU-FSU College of Engineering, Tallahassee, FL, USA.

19. Nowakowski, A. F., and T. Dyakowski. 2003. Investigation of swirling flow

structure in hydrocyclones. Transactions of the Institution of Chemical

Engineers, Chemical Engineering Research and Design 81(A): 862– 873.

20. Schuetz, S., G. Mayor, M. Bierdel, and M. Piesche. 2004. Investigations on

the flow and separation behavior of hydrocyclones using computational fluid

dynamics. International Journal of Mineral Processing 73(2–4): 229–237.


21. Cullivan, J. C., R. A. Williams, T. Dyakowski, and C. R. Cross. 2004. New

understanding of a hydrocyclone flow field and separation mechanism from

computational fluid dynamics. Minerals Engineering 17: 651–660.

22. Cullivan, J. C., R. A. Williams, and C. R. Cross. 2003. Understanding the

hydrocyclone separator through computational fluid dynamics. Transactions

of the IchemE, Part A, Chemical Engineering, Research and Design 81(A4):

455–466.

23. Delgadillo, A. J., and R. K. Rajamani. 2005. A comparative study of

three turbulence-closure models for the hydrocyclone problem. International

Journal of Mineral Processing 77: 217–230.

24. Delgadillo, A. J., and R. K. Rajamani. 2007. Large-Eddy Simulation (LES)

of large hydrocyclones. Particulate Science and Technology 25: 227–245.

25. Narasimha, M., M. S. Brennan, P. N. Holtham, T. J. Napier–Munn, 2007. A

comprehensive CFD model of dense medium cyclone performance. Minerals

Engineering 20: 414–426.

26. Narasimha, M., R. Sripriya, and P. K. Banerjee. 2005. CFD modeling of

hydrocyclone—Prediction of cut size. International Journal Mineral Proces-

sing 75(1–2): 53–68.

27. Udaya Bhaskar, K., Y. Rama Murthy, N. Ramakrishnan, J. K. Srivastava,

Supriya Sarkar, and Vimal Kumar. 2007. CFD validation for flash classi-

fication in hydrocyclones. Minerals Engineering 20: 290–302.

28. Narasimha, M., M. Brennan, and P. N. Holtham. 2006. Large eddy simula-

tion of hydrocyclone; prediction of air core diameter and shape. International

Journal of Mineral Processing 80: 1–14.

29. Udaya Bhaskar, K., Y. Rama Murthy, M. Ravi Raju, Sumit Tiwari, J. K.

Srivastava, and N. Ramakrishnan. 2007. CFD simulation and experimental

validation studies on hydrocyclone. Minerals Engineering 20: 60–71.

30. Udaya Bhaskar, K., S. Tiwari, and N. Ramakrishnan. 2005. Simulation

studies of a 76mm hydrocyclone. CMC Journal 2: 13–21.

31. Brennan, M. S. 2003. Multiphase CFD simulations of dense medium and

classifying hydrocyclones. Paper presented at the Third International

Conference on CFD in the Minerals and Process Industries, CSIRO,

Melbourne, Australia.

32. Chu, K. W., B. Wang, A. Vince, and A. B. Yu. 2009. CFD - DEM modeling of

multiphase flow in dense medium cyclones. Powder Technology 193: 235–247.

33. Suasnabar, D. J. 2000. Dense Medium Cyclone Performance, enhancements

via computational modeling of the physical process. PhD Thesis, University

of New South Wales.

34. Schiller, L., and Z. Z. Naumann. 1935. Ver. Deutsch. Ing. 77: 318.

35. Manninen, M., V. Taivassalo, and S. Kallio. 1996. On the mixture model for

multiphase flow. VTT Publications 288. Technical Research Centre of

Finland.


36. Brennan,M. S.,M.Narasimha, and P. N.Holtham. 2007.Multiphasemodeling

of hydrocyclones – Prediction of cut size. Minerals Engineering 20: 395–406.

37. Hsieh, K. T. 1988. A Phenomenological model of hydrocyclone. PhD Thesis,

University of Utah.

38. King, R. P., and A. H. Juckes. 1984. Cleaning of fine coals by dense-medium

hydrocyclone. Powder Technology 40: 147–160.

39. Smagorinsky, J. 1963. General circulation experiments with the primitive

equations. I. The Basic Experiment Month. Wea. Rev. 91: 99–164.

40. Syamlal, M. 1987. The Particle-Particle Drag Term in a Multiparticle Model of

Fluidization. DOE=MC=21353-2373, NTIS=DE87006500. Springfield, VA:

National Technical Information Service.


Copyright of International Journal of Coal Preparation & Utilization is the property of Taylor & Francis Ltd and

its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's

express written permission. However, users may print, download, or email articles for individual use.

Documents

CFD Modeling of Dense Medium Cyclone