MODELLING OF HYDROCYCLONES CFD Modelling Group Department of Mechanical Engineering University of...

MODELLING OF HYDROCYCLONESMODELLING OF HYDROCYCLONES

CFD Modelling GroupDepartment of Mechanical EngineeringUniversity of British Columbia

Process Simulations Limited

OBJECTIVES

Feed

Reject

Accept

HYDROCYCLONESHYDROCYCLONES

Investigate the flow, particle, and fiber Investigate the flow, particle, and fiber separation occurring in hydrocyclones separation occurring in hydrocyclones

Use suitable turbulence models for Use suitable turbulence models for high swirl fluid flowshigh swirl fluid flows

Develop mathematical models to Develop mathematical models to compute fiber trajectories in complex compute fiber trajectories in complex flowsflows

Model separation and fractionation Model separation and fractionation according to properties in hydro-according to properties in hydro-cyclonescyclones


3-D turbulent flow is solved in 3-D turbulent flow is solved in hydrocyclones using k - hydrocyclones using k - turbulence model turbulence model with curvature correctionwith curvature correction

Lagrangian method for tracking spherical Lagrangian method for tracking spherical particles three-dimensionally in particles three-dimensionally in hydrocyclones to obtain separation curveshydrocyclones to obtain separation curves

Spherical particles are replaced in Spherical particles are replaced in lagrangian model with rigid fibre, able to lagrangian model with rigid fibre, able to swell, and ignoring fibre rotationswell, and ignoring fibre rotation

MODEL CHARACTERISTICS

HYDROCYCLONES HYDROCYCLONES NUMERICAL METHODSNUMERICAL METHODS

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

- combination of cylindrical co-ordinates and non-orthogonal grids

Take advantage of the cylindrical co-ordinates to calculate Take advantage of the cylindrical co-ordinates to calculate the physical geometrical quantities and curvature source the physical geometrical quantities and curvature source terms accuratelyterms accurately

Circular co-ordinates are used to account for the curved Circular co-ordinates are used to account for the curved surface of each control cell in the calculation of surface of each control cell in the calculation of geometrical quantitiesgeometrical quantities

The centrifugal force is used to replace the curvature The centrifugal force is used to replace the curvature source term in the angular momentum equationsource term in the angular momentum equation

The standard k-The standard k- model fails to produce model fails to produce reasonable solutionreasonable solution

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

- model adds correction term in dissipation equation


Rit = Turbulent Richardson number

u = tangential velocity

r = radial

TURBULENCE MODEL


Traced by numerical integration of the particle Traced by numerical integration of the particle velocity calculated from the fluid velocity and velocity calculated from the fluid velocity and particle slip velocityparticle slip velocity

Particle slip velocity is solved from the dynamic Particle 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

Vp= particle volume

Ap= projected area

Particle Trajectory

pDxslplp ACUgV 2

2

1)(


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

Modified k-Modified k- model is identified as a good model is identified as a good alternative for high swirl flowsalternative for high swirl flows

Model is accurate for both flow simulation Model is accurate for both flow simulation and separation predictionand separation prediction

Model can be used to analyse performance Model can be used to analyse performance of industrial hydrocyclonesof industrial hydrocyclones

- design, separation, optimisation

3 Different Hydrocyclones3 Different Hydrocyclones

Dimensions(in mm)

Cyclone 1 Cyclone 2 Cyclone 3

Cyclone Diameter 76 75 75

Inlet Diameter 21 25 25

Cylindrical Length 51 75 75

Vortex Finder Diameter 26 25 22

Vortex Finder Length 30 50 50

Spigot Diameter 12 15 11

Cone Angle 11 20 20

COMPARISON (PARTICLES)COMPARISON (PARTICLES)

FIBER FRACTIONATIONFIBER 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+071.42361E+071.32292E+071.22222E+071.12153E+071.02083E+079.20135E+068.1944E+067.18745E+066.1805E+065.17355E+064.1666E+063.15965E+062.1527E+061.14575E+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

0.04sw

2.845312.655632.465942.276252.086561.896881.707191.51751.327811.138130.9484380.758750.5690630.3793750.189688

(c)

(a) Velocity vectors, (b) pressure contours, and (c) swirl velocity contours in a hydrocyclone


10

20

30

40

50

60

70

0

20

40

60

80

100

carr

ied

ove

r(%

)

5

0

20

40

60

80

100

carrie

do

ver

(%)

5

10

20

30

40

50

60

70

cov89.62577.67565.72553.77541.82529.87517.9255.975

densityrel = 1.04

densityrel = 1.14

densityrel = 1.42

densityrel

carr

ied

ove

r(%

)

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

A densityrel

B densityrel

*

*

Fiber B

Fiber A

Influence of the particle density on fractionation

Separation on diameter and length as function of the particle density


diameter (microns)

carr

ied

ove

r(%

)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

A diameterB diameter

Fiber A

*

*

Fiber B

20

40

60

0

50

100

carr

ied

ove

r(%

)

1.2

1.4

0

50

100

carrie

do

ver

(%)

1.2

1.4

20

40

60

cov22.220.385718.571416.757114.942913.128611.31439.57.685715.871434.057142.242860.428571-1.38571-3.2

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

de

nsi

tyre

l

1.1

1.2

1.3

1.4

de

nsi

tyre

l

1.1

1.2

1.3

1.4

de

nsi

tyre

l

10 20 30 40 50 60 70

diameter (microns)

The difference between particles carried over at t = 20°C and t = 45°C. The yellow grid represents particles carried over at t = 20°C

Influence of the particle diameter on fractionation


The combined influence of coarseness and specific surface on separation

Influence of the particle coarseness on separation based on specific surface

0

10

20

30

40

50

60

00.1

0.20.3

0.4200

400

600

800

1000

57.754.350.847.444.040.637.133.730.326.923.420.016.613.29.8

Coarseness and Specific surface influence on separation

coarseness (mg/m)

specific surface (m2/kg)

carried over (%)carried over (%)

specific surface (m2/kg)ca

rrie

do

ver

(%)

200 400 600 800 10000

10

20

30

40

50

60

70

80

90

100

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

Influence of coarsenesson separation based on specific surface

Particle length = 2 mmShape factor s3 = 1.5


Influence of particle length on separation based on diameter

Influence of the particle length on fractionation

diameter (m)

carr

ied

un

de

r(%

)

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

10

20

30

40

50

60

70

80

90

100

density = 1100 kg/m3, L = 1 mmdensity = 1100 kg/m3, L = 6 mmdensity = 1050 kg/m3, L = 1 mmdensity = 1050 kg/m3, L = 6 mm

Influence of particle length on separation based on diameter

length (mm)ca

rrie

do

ver

(%)

1 2 3 4 5 60

10

20

30

40

50

60

70

80

90

100

Influence of particle length on fractionation

Reference data:

Fiber A: L = 3.1 mm; density = 1050 kg/m3; d = 48 micronsFiber B: L = 3.5 mm; density = 1100 kg/m3; d = 39 microns

Reference lines:

(a) density = 1050 kg/m3; d = 48 microns(b) density = 1100 kg/m3; d = 39 microns(c) density = 1140 kg/m3; d = 12 microns(d) density = 1140 kg/m3; d = 45 microns

Fiber A

**

Fiber B


Influence of entry particle position on separation and fractionation (Fibre A - Early Wood, Fibre B - Late Wood) for an entry feed at the top of hydrocyclone (z = 0)

ytangential (mm)

x axi

al(m

m)

0 10 20 30 400

5

10

15

20

downward

upward

Separation as function of entry position for fiber B (z = 0 mm)- Tangential feed -

ytangential (mm)

x axi

al(m

m)

0 10 20 30 400

5

10

15

20

downward

upward

Separation as function of entry position for fiber A (z = 0 mm)- Tangential feed -

ytangential (mm)

x axi

al(m

m)

0 10 20 30 405

10

15

20

25

downward

upward

Separation as function of entry position for fiber A (z = 5 mm)- Tangential feed -

ytangential (mm)x a

xia

l(m

m)

0 10 20 30 405

10

15

20

25

downward

upward

Separation as function of entry position for fiber B (z = 5 mm)- Tangential feed -

Influence of entry particle position on separation and fractionation (Fibre A - Early Wood, Fibre B - Late Wood) for a 5 mm downward entry feed (z = 5 mm)

BENEFITSBENEFITS

Increase operating efficiency for hydrocyclonesIncrease operating efficiency for hydrocyclones

Optimize the hydrocyclones designOptimize the hydrocyclones design

Evaluate the influence on fractionation of fiber Evaluate the influence on fractionation of fiber wet density, fiber diameter, fiber length, and wet density, fiber diameter, fiber length, and fiber specific surfacefiber specific surface

Evaluate the influence of the fluid temperature on Evaluate 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

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