1 Turbulence Characteristics in a Rushton & Dorr-Oliver Stirring Vessel: A numerical investigation...

1

Turbulence Characteristics in a Rushton & Dorr-Oliver Stirring

Vessel: A numerical investigation

Vasileios N Vlachakis

06/16/2006

2

Outline of the Presentation

Introduction/Motivation

Background of the Flotation process

Mechanically agitated vessels

The Rushton Stirring TankComputational Model

Comparisons between them

The Dorr-Oliver Stirring Tank

Conclusions

Future Work

3

Introduction/Motivation

The objectives of the thesis are to:study the hydrodynamics of two stirring tanks

The Rushton mixing tankThe Dorr-Oliver

estimate accurately the velocity distributiondiscuss which turbulent model is the most suitable for this type of flow (validation with the experiments)determine the effect of the clearance of the impeller on the turbulence characteristics

VorticityTurbulent kinetic energyDissipation rate

4

Significance of the Dissipation rate

Dissipation rate controls:

Collisions between particles and bubbles in flotation cells

bubble breakup

coalescence of drops in liquid-liquid dispersions

agglomeration in crystallizers

5

Background

Flotation is carried out usingMechanically agitated cells

Widely Used in Industries to separate mixtures

MiningChemicalEnvironmentalPharmaceuticalBiotechnological Principles of Froth-Flotation

6

The flotation process

The flotation technique relies on the surface properties of the different particles

Two types of particles: hydrophobic (needs to be separated and floated)

hydrophilic

Particles are fed from a slurry located in the bottom

While the impeller rotates air is passing through the hollow shaft to generate bubbles

Some particles attach to the surface of the air bubbles and some others fall on the bottom of the tank

The floated particles are collected from the froth layer

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The Rushton Stirring Tank

Cylindrical Tank

Diameter of the Tank

Diameter of the Impeller

Four equally spaced baffles with width

Thickness of the baffles

Blade height

Blade width

Liquid Height = Height of the Tank

/ 3I TD D

0.1524TD

0.1bf Tw D

/ 40bf Ith D

0.2bl Ih D

/ 4bl Iw D

8

Governing Equations

0ut

22

3

uuu p S u F

t

' ' and u u u p p p

' and 0u u u

0u

' '22

3uu p S u g u u

Unsteady 3D Navier-Stokes equations

Continuity

Momentum

Decomposition of the total velocity and pressure

Time-averaged Navier-Stokes equations

Averaging rules

Continuity

Momentum

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Dimensionless ParametersScaling Laws

/ 1/ 4 and N 6b I bw D

ReuD uD

The Reynolds number:

22tip

Du r N DN

2

ReND

Laminar flow: Re<50Transitional: 50<Re<5000Turbulent: Re>10000

The Power number: 3 5

PPo

N D

b5 N

6

b

bwPo aD

Where a=5 and b=0.8 in the case of radial-disk impellers

In our case where 6.25oP

This Power number is hold for unbaffled tanks

10

Power number versus Re number

0.4bb

wNT

0.33D

T 1.05Po

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Dimensionless ParametersScaling Laws

2 2 2 2u N D N DFr

Dg Dg g Froude number:

The Froude number is important for unbaffled tanks

It is negligible for baffled tanks or unbaffled with Re<300

In unbaffled tanks for Re>300 log Re

b Pof

a Fr

Flow number: 3

QFl

ND

6

6

0.7

0.3

b c

b bladeN w DFl a

D T

a

b

c

In the case of the radial-disk impellers

In our case (Rushton turbine) : Fl=1.07

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Computational Grid

The computational grid consists of 480,000 cells

View from the top3Dimensional View

Grid surrounding the impeller (The unsteady Navier - Stokes equations are solved)

Outside grid (The steady Navier - Stokes equations are solved)

The grid surrounding the impeller is more dense from the outside

Two frames of reference:The first is mounted on the Impeller and the second is stationary (MRF)

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Simulation Test matrix

/ 1/ 2TC D

310 Re/ 1/15TC D

310 Re

/ 1/ 3TC D

20 25 35 40 45

Standard k-e 1a 2a 3a 4a 5a

RNG k-e 1b 2b 3b 4b 5b

Reynolds Stresses

1c 2c 3c 4c 5c

20 25 35 40 45

Standard k-e 6 7 8 9 10

Standard k-e 11 - 12 13 -

Three different configurations

Three turbulent models

Five Reynolds numbers

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Normalized radial velocity contours

The flow for the first two cases can be described as a radial jet with two recirculation regions in each side of the tank

In the case of the low clearance, a low speed jet and only one large recirculation area is observed

15

Normalized dissipation rate contours

In the first two cases the dissipation rate has high values around and nextto the impeller’s blade while in the last is extended to the region below them too

16

Normalized TKE contours

Slices that pass through the middle plane of the impeller / 0Tz D

The TKE is lower in the case of the low configuration

17

Normalized X-vorticity contours

Re=35000

In the first two cases the tip vortices that form at the end of the moving blades can be observed while in the third case only one big vortex ring forms.

18

Y- Vorticity

Trailing Vortices at y/Dtank=0.167(exactly at the end of the blades)

Trailing vortices at the 1st bladeTrailing vortices at the next blade Time-averaged experimental

results

19

Vorticity superimposed with streamlines for Re=35000

Flow can be described as a radial jet with convecting tip vortices

20

Normalized Z-vorticity contours

In the first two cases the presence of the trailing vortices that form behind the rotating blades can be seen. In all cases small vortices also form behind the baffles

21

Grid Study

0.2 0.25 0.3 0.35 0.4 0.45 0.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7Plot of the normalized Radial velocity at the centerline of the impeller

r/Dtank

Vr/

Utip

Finest grid using the K-e modelFine grid using the K-e modelCoarse grid using the K-e modelFinest Grid using the RNG K-e modelFine grid RNG K-e modelCoarse grid RNG K-e modelFinest grid using the Reynolds StressesExperimental results

0.2 0.25 0.3 0.35 0.4 0.45 0.50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4Plot of the normalized TKE at the centerline of the impeller

r/Dtank

TK

E/(

Utip

2 )


0.2 0.25 0.3 0.35 0.4

5

10

15

20

25

30

Plot of the normalized Dissipation rate at the centerline of the impeller

r/Dtank

/(N

3 Dim

p2 )


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Radial Plots for Re=35000 along the centerline of the impeller

0.2 0.25 0.3 0.35 0.40

0.1

0.2

0.3

0.4

0.5

0.6

Plot of the normalized Radial velocity at the centerline of the impeller

r/Dtank

Vr/

Utip

CFD results using the K-e model for C/T=1/2CFD results using the RNG K-e model for C/T=1/2CFD results using the Reynolds Stresses for C/T=1/2Experimental resultsCFD results using the K-e model for C/T=1/3CFD results using the K-e model for C/T=1/15

0.2 0.25 0.3 0.35 0.40

0.1

0.2

0.3

0.4

0.5

0.6

r/DtankV

mg

n/U

tip)


Normalized radial velocity Normalized velocity magnitude

The velocity magnitudes consists only of the axial and radial components in order to be validated by the experimental results where the tangential component Is not available.

The low speed jet in the case of the low configuration is confirmed but astrong axial component is present as it is shown in the second plot

/ 0Tz D

23


0.2 0.25 0.3 0.35 0.4-4

-3

-2

-1

0

1

2

3

4

5

r/Dtank

Vo

rtic

ity/(

Utip

/Dim

p)


0.2 0.25 0.3 0.35 0.4

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

r/Dtank

Vth

eta

/Utip

)

CFD results using the K-e model for C/T=1/2CFD results using the RNG K-e model for C/T=1/2CFD results using the Reynolds Stresses for C/T=1/2CFD results using the K-e model for C/T=1/3CFD results using the K-e model for C/T=1/15

Normalized tangential velocity Normalized X-VorticityRe=35000

Experimental vorticity seems to be oscillating due to the periodicity and due to the fact that trailing vortices are present. Clearly none of the turbulent models can capture what is happening

/ 0Tz D

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0.2 0.25 0.3 0.35 0.4

5

10

15

20

25

30

r/Dtank

/(N

3 Dim

p2 )


0.2 0.25 0.3 0.35 0.4

0.05

0.1

0.15

0.2

0.25

0.3

0.35

r/DtankT

KE

/(U

tip2 )

CFD results using the K-e model for C/T=1/2CFD results using the RNG K-e model for C/T=1/2CFD results using the Reynolds Stresses for C/T=1/2Experimental results with periodicityExperimental results without periodicityCFD results using the K-e model for C/T=1/3CFD results using the K-e model for C/T=1/15

Normalized Dissipation rate Normalized Turbulent Kinetic Energy

The apparent discrepancy in TKE is due to the periodicity that characterizes the flow, since with every passage of a blade strong radial jet is created.

The RNG k-e model has a superior behavior among the studied turbulent models in predicting the Turbulent Dissipation Rate (TDR)

/ 0Tz D

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Normalized Maximum Dissipation rate

0

2

4

6

8

10

12

15000 20000 25000 30000 35000 40000 45000 50000 55000

Re

εma

x/(N

3 D2 )

Our experimental study for C/T=1/2

CDD Standard k-e model for C/T=1/2

CFD RNG k-epsilon model for C/T=1/2

CFD Reynolds Stresses model for C/T=1/2

CFD Standard k-e model for C/T=1/15

0

2

4

6

8

10

12

10000 15000 20000 25000 30000 35000 40000 45000

Re

εmax

/(N

3 D2 )

S.Baldi, M.Yianneskis experimental results for C/T=1/3

CFD Standard K-e model for C/T=1/3

For C/T=1/2 and C/T=1/15 For C/T=1/3

As the Re number increases the maximum TDR decreases for the first two configurations (agreement with the experimental data)

For case of the low clearance configuration the line of the maximum dissipationlevels off.

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Velocity Profiles

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Vr/Utip

z/w

bl

CFD results using the K-e modelCFD results using the RNG K-e modelCFD results using the Reynolds Stresses modelExperimental results

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Vr/Utip

z/w

bl


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Vr/Utip

z/w

bl


r/T=0.19

r/T=0.256

r/T=0.315

0.2 0.25 0.3 0.35 0.40

0.1

0.2

0.3

0.4

0.5

0.6

Plot of the normalized Radial velocity at the centerline of the impeller

r/Dtank

Vr/

Utip

CFD results using the K-e model for C/DT=1/2CFD results using the RNG K-e model for C/DT=1/2CFD results using the Reynolds Stresses for C/DT=1/2Experimental results for C/DT=1/2CFD results using the Standard K-e model for C/DT=1/3CFD results using the Standard K-e model for C/DT=1/15

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Dissipation rate profiles

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1.5

-1

-0.5

0

0.5

1

1.5

/(N3Dimp2)

z/w

bl


0 0.5 1 1.5 2 2.5 3-1.5

-1

-0.5

0

0.5

1

1.5

/(N3Dimp2)

z/w

bl


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

/(N3Dimp2)

z/w

bl


r/T=0.19

r/T=0.256

r/T=0.315

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Reynolds Stresses & Isosurfaces

0.2 0.25 0.3 0.35 0.4-10

-8

-6

-4

-2

0

2x 10

-3

r/Dtank

uw

/(u

tip2 )

FLUENT Simulations for C/DT=1/3S.Baldi & M.Yianneskis experimental results for C/DT=1/3

u’w’ normalized component of the RSC/T=1/3

h u

Helicity

Isosurfaces of vorticity

Isosurfaces of helicity

The higher the helicity the more the vorticity vector is closer to the velocity vector (swirl)

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Conclusions

The turbulent kinetic energy and dissipation have the highest values

in the immediate neighborhood of the impeller Good agreement with the experimental data is succeed

Most of the times the Standard k-e model predicts better the flow velocities and the turbulent quantities while in some others has poor performance and the RNG k-e is better

In the case of the low configuration model:

there is a strong tendency to skew the contours downward the dominant downward flow is diverting the jet-like flow that leaves the tip of the impeller downward, and it convects with the turbulent features of the flow. The axial component of the velocity has high values

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Future Work

Experimental predictions for the Dorr-Oliver Flotation cell

Comparisons of the studied cases with the experiments

More Re numbers and clearances for the Dorr-Oliver Cell

Higher Re numbers for both Tanks (100000-300000)

Unsteady calculations

Extension to two-phase or three phase flows

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1 Turbulence Characteristics in a Rushton & Dorr-Oliver Stirring Vessel: A numerical investigation...

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