moddeling of hydrocyclones

7/23/2019 moddeling of hydrocyclones

1/17

MODELLING OF HYDROCYCLONESMODELLING OF HYDROCYCLONES

CFD Modelling Group

Department of Mechanical Engineering

University of British Columbia

Process Simulations imited


2/17

OBJECTIVES

Feed

Reject

Accept

HYDROCYCLONESHYDROCYCLONES

Investigate the flow, particle, and fiberInvestigate the flow, particle, and fiber

separation occurring in hydrocyclonesseparation occurring in hydrocyclones

Use suitable turbulence models forUse suitable turbulence models forhigh swirl fluid flowshigh swirl fluid flows

Develop mathematical models toDevelop mathematical models to

compute fiber trajectories in complexcompute fiber trajectories in complex

flowsflows Model separation and fractionationModel separation and fractionation

according to properties in hydro-according to properties in hydro-

cyclonescyclones


3/17


3-D turbulent flow is solved in3-D turbulent flow is solved in

hydrocyclones using k -hydrocyclones using k - turbulence modelturbulence model

with curvature correctionwith curvature correction

Lagrangian method for tracking sphericalLagrangian method for tracking spherical

particles three-dimensionally inparticles three-dimensionally in

hydrocyclones to obtain separation curveshydrocyclones to obtain separation curves

Spherical particles are replaced inSpherical particles are replaced in

lagrangian model with rigid fibre, able tolagrangian model with rigid fibre, able to

swell, and ignoring fibre rotationswell, and ignoring fibre rotation

MODEL CHARACTERISTICS


4/17

HYDROCYCLONESHYDROCYCLONESNUMERICAL METHODSNUMERICAL METHODS

Develop 3D method using cylindrical curvilinear gridDevelop 3D method using cylindrical curvilinear grid

- combination of cylindrical co-ordinates and non-orthogonalgrids

Take advantage of the cylindrical co-ordinates to calculateTake advantage of the cylindrical co-ordinates to calculatethe physical geometrical quantities and curvature sourcethe physical geometrical quantities and curvature source

terms accuratelyterms accurately

Circular co-ordinates are used to account for the curvedCircular co-ordinates are used to account for the curved

surface of each control cell in the calculation of geometricalsurface of each control cell in the calculation of geometrical

quantitiesquantities

The centrifugal force is used to replace the curvature sourceThe centrifugal force is used to replace the curvature source

term in the angular momentum equationterm in the angular momentum equation


5/17

The standard k-The standard k-

model fails to producemodel fails to produce

reasonable solutionreasonable solution

Use modified k-Use modified k- model proposed by Laundermodel proposed by Launder

- model adds correction term in dissipation equation


r

ru

r

ukRi

kRiCCkC

t

tC

=

!!

!

!

!

!

! "#$%"

&it' (urbulent &ichardson number

u ' tangential velocity

r ' radial

TURBULENCE MODEL


6/17


Traced by numerical integration of the particleTraced by numerical integration of the particle

velocity calculated from the fluid velocity andvelocity calculated from the fluid velocity and

particle slip velocityparticle slip velocity Particle slip velocity is solved from the dynamicParticle slip velocity is solved from the dynamic

force balance in radial, tangential & axial directionsforce balance in radial, tangential & axial directions

u' tangential velocities

Us ' settling velocities

)p' particle volume

*p' pro+ected area

Particle Trajector

pDrslpl

l

p

p ACUVru

ru !

!!

!$#%

=

pDxslplp ACUgV!

!

$#% =


7/17


Turbulence model is proven to be criticalTurbulence model is proven to be critical

Modified k-Modified k- model is identified as a goodmodel is identified as a good

alternative for high swirl flowsalternative for high swirl flows Model is accurate for both flow simulationModel is accurate for both flow simulation

and separation predictionand separation prediction

Model can be used to analyse performanceModel can be used to analyse performanceof industrial hydrocyclonesof industrial hydrocyclones

- design, separation, optimisation


8/17

3 Different Hydrocyclones3 Different Hydrocyclones

Di!e"#io"#

$i" !!%

Cclo"e & Cclo"e ' Cclo"e (

Cclo"e Dia!eter )* )+ )+

I"let Dia!eter '& '+ '+

Cli"drical Le",t- +& )+ )+

Vorte. Fi"der Dia!eter '* '+ ''

Vorte. Fi"der Le",t- (/ +/ +/

Spi,ot Dia!eter &' &+ &&

Co"e A",le && '/ '/


9/17

COMARISON !ARTICLES"COMARISON !ARTICLES"


10/17

FI#ER FRACTIONATIONFI#ER FRACTIONATION

x

r

0 0.1 0.2 0.3 0.40

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

(a)

x

r

0 0.1 0.2 0.3 0.40

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

p1.52431E+07

1.42361E+071.32292E+071.22222E+071.12153E+071.02083E+07

9.20135E+068.1944E+06

7.18745E+066.1805E+065.17355E+064.1666E+063.15965E+062.1527E+06

1.14575E+06

(b)

x

r

0 0.1 0.2 0.3 0.40

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

sw

2.845312.65563

2.465942.27625

2.086561.89688

1.707191.5175

1.327811.13813

0.9484380.75875

0.569063

0.379375

0.189688

(c)

$a% Velocit 0ector#1 $2% pre##3re co"to3r#1 a"d $c% #4irl 0elocit co"to3r# i"a -drocclo"e


11/17


10

20

30

40

50

60

70

0

20

40

60

80

100

carriedover(%)

5

0

20

40

60

80

100

carriedover(%)

5

10

20

30

40

50

60

70

cov

89.625

77.675

65.725

53.775

41.825

29.875

17.925

5.975

densityrel=1.04

densityrel=1.14

densityrel=1.42

densityrel

carriedover(%)

1

1

1.1

1.1

1.2

1.2

1.3

1.3

1.4

1.4

0 0

10 10

20 20

30 30

40 40

50 50

60 60

70 70

80 80

90 90

100 100

Adensityrel

Bdensityrel

*

*

FiberB

FiberA

I"5l3e"ce o5 t-e particle de"#it o"

5ractio"atio"

Separatio" o" dia!eter a"d le",t- a# 53"ctio" o5 t-e

particle de"#it


12/17


diameter(microns)

carriedover(%)

10

10

20

20

30

30

40

40

50

50

60

60

70

70

0 0

10 10

20 20

30 30

40 40

50 50

60 60

70 70

80 80

90 90

100 100

AdiameterBdiameter

FiberA

*

*

FiberB

20

40

60

0

50

100

carriedover(%)

1.2

1.4

0

50

100

carriedover

(%)

1.2

1.4

20

40

60

cov

22.2

20.3857

18.5714

16.7571

14.9429

13.1286

11.3143

9.5

7.68571

5.87143

4.05714

2.24286

0.428571

-1.38571

-3.2

10 20 30 40 50 60 70

diameter(microns)

10 20 30 40 50 60 70

diameter(microns)

1.1

1.2

1.3

1.4

density

rel

1.1

1.2

1.3

1.4

density

rel

1.1

1.2

1.3

1.4

density

rel

10 20 30 40 50 60 70

diameter(microns)

T-e di55ere"ce 2et4ee" particle# carried o0er at t 6 '/7C a"d t

6 8+7C9 T-e ello4 ,rid repre#e"t# particle# carried o0er at t 6

'/7C

I"5l3e"ce o5 t-e particle dia!eter o"

5ractio"atio"


13/17


T-e co!2i"ed i"5l3e"ce o5 coar#e"e## a"d #peci5ic #3r5ace o"

#eparatio"

I"5l3e"ce o5 t-e particle coar#e"e##

o" #eparatio" 2a#ed o" #peci5ic

#3r5ace

0

10

20

30

40

50

60

00.1

0.20.3

0.4200

400

600

800

1000

57.7

54.3

50.8

47.444.0

40.6

37.1

33.7

30.3

26.9

23.4

20.0

16.613.2

9.8

CoarsenessandSpecificsurfaceinfluenceonseparation

coarseness(mg/m)

specificsurface(m2/kg)

carriedover(%)carriedover(%)

specificsurface(m2/kg)

carriedover(%)

200 400 600 800 10000

10

20

30

40

50

60

70

80

90

100

coarseness=0.1mg/mcoarseness=0.2mg/mcoarseness=0.3mg/mcoarseness=0.4mg/mcoarseness=0.5mg/m

Influenceofcoarsenessonseparationbasedonspecificsurface

Particlelength=2mmShapefactors

3=1.5


14/17


I"5l3e"ce o5 particle le",t- o" #eparatio" 2a#ed o" dia!eter

I"5l3e"ce o5 t-e particle le",t- o"

5ractio"atio"diameter(m)

carriedunder(%)

2E-05 4E-05 6E-05 8E-05 0.00010

10

20

30

40

50

60

70

80

90

100

density=1100kg/m3,L=1mm

density=1100kg/m3,L=6mm

density=1050kg/m

3

,L=1mmdensity=1050kg/m3,L=6mm

Influenceofparticlelengthonseparationbasedondiameter

length(mm)

carriedover(%)

1 2 3 4 5 60

10

20

30

40

50

60

70

80

90

100

Influenceofparticlelengthonfractionation

Referencedata:

FiberA:L=3.1mm;density=1050kg/m3;d=48microns

FiberB:L=3.5mm;density=1100kg/m3;d=39microns

Referencelines:

(a) density=1050kg/m3;d=48microns

(b) density=1100kg/m3;d=39microns

(c)density=1140kg/m3;d=12microns

(d) density=1140kg/m3;d=45microns

FiberA

* *

FiberB


15/17


I"5l3e"ce o5 e"tr particle po#itio" o" #eparatio" a"d

5ractio"atio" $Fi2re A : Earl ;ood1 Fi2re B : Late ;ood% 5or

a" e"tr 5eed at t-e top o5 -drocclo"e $< 6 /%

ytangential

(mm)

xaxial(mm)

0 10 20 30 400

5

10

15

20

downward

upward

SeparationasfunctionofentrypositionforfiberB(z=0mm)-Tangentialfeed-

ytangential

(mm)

xaxial(mm)

0 10 20 30 400

5

10

15

20

downward

upward

SeparationasfunctionofentrypositionforfiberA(z=0mm)-Tangentialfeed-

ytangential(mm)

xaxial(mm)

0 10 20 30 405

10

15

20

25

downward

upward

SeparationasfunctionofentrypositionforfiberA(z=5mm)-Tangentialfeed-

ytangential(mm)

xaxial(mm)

0 10 20 30 405

10

15

20

25

downward

upward

eparatonasunctono entryposton or er z= mm-Tangentialfeed-

I"5l3e"ce o5 e"tr particle po#itio" o" #eparatio" a"d

5ractio"atio" $Fi2re A : Earl ;ood1 Fi2re B : Late ;ood% 5or a

+ !! do4"4ard e"tr 5eed $< 6 + !!%


16/17

#ENEFITS#ENEFITS

Increase operating efficiency for hydrocyclonesIncrease operating efficiency for hydrocyclones

Optimize the hydrocyclones designOptimize the hydrocyclones design

Evaluate the influence on fractionation of fiberEvaluate the influence on fractionation of fiber

wet density, fiber diameter, fiber length, andwet density, fiber diameter, fiber length, andfiber specific surfacefiber specific surface

Evaluate the influence of the fluid temperature onEvaluate the influence of the fluid temperature on

fractionationfractionation

Predict the fractionation performance of a hydro-Predict the fractionation performance of a hydro-

cyclone for given fiber propertiescyclone for given fiber properties


17/17

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moddeling of hydrocyclones