Mass Transport, Momentum

Transport and Fluidization in a

2D Bubbling Fluidized Bed

Alexander G. Mychkovsky and Steven L. Ceccio

University of Michigan

Dept of Mechanical Engineering

Deepak Rangarajan and Jennifer S. Curtis

University of Florida

Dept of Chemical Engineering

1

2

Overview

Background

Laser Doppler Velocimetry (LDV) Measurement Technique

Single Phase Gas Jet in Empty Bed

Gas Jets in Bubbling Bed

Turbulence Measurements

Effect of Emulsion Fluidization Level on Jet Dynamics

Conclusions

Modeling Effort

3

Background

High speed gas jets are injected into a bed emulsion, rapidly entraining and mixing bed particles and interstitial gas

4

Jets in Fluidized Beds

C. Xuereb, C. Laguerie, T. Baron. “Etude du comportement de jets continues horizontaux ou inclines introduits dans un lit

fluidise par un gaz Deuxieme partie: profiles de vitesse du gaz dans les jets horizontaux,” Powder Tech. 64 (3), 271-283

(1991)

Quantitative non-intrusive measurements of the mass and momentum transport in the jet plume are needed for characterization and modeling

Requires knowledge of the particulate and gas phase velocity profiles

Not widely reported in the literature

Jet dynamics are critical to the efficiency and design of the system

5

Our 2D Fluidized Bed

Vertical Gas Jet

(orifice flush with

distributor surface)

Dj = 9.2 mm, Vj = 92 m/s

Vfl /Vmf = 1.15

838 μm SMD HDPE micropellets

Quartz viewing windows

(102 mm x 153 mm x 5mm thick)

Acrylic walls

(457 mm wide x 12.7 mm gap)

Velocity profile scans at

y = 60, 70, 100, 130 mm

LDV Measurement Technique

6

7

LDV in Two Phase Gas-Particle flow

Particle speed

~ frequency of scattered light

Simultaneously measure bed particle (~1,000 μm)and jet gas (~1 μm tracers) velocity profiles (2 component)

Jet gas is seeded by rapidly condensing moisture in the air to produce ice crystals

(Tj = -5oC, ρj = 1.32 kg/m3)

Burst intensity subranging to distinguish the two phase measurements

7

8

Intensity Subranging

Bed particles (dp>>f)

produce larger amplitude

Doppler bursts than gas

tracer ice crystals (dp~ f)

R. S. Barlow & C. Q. Morrison. “Two-phase velocity measurements in dense

particle-laden jets,” Exp. Fluids. 9 (1-2) 93-104 (1990)

0 20 40 60 80 1000

200

400

600

800

1000

v (m/s)

I (m

V)

Bed Particles and Ice Crystals (0 s Coincidence)

Ice Crystals

Bed Particles

99% of bed particle bursts

> 200 mV

99% of ice crystal bursts

< 500 mV

Coincidence

Gas tracers: 0 μs

Bed Particles: 10 μs

Velocity Histogram Separation

0 20 40 60 80 1000

500

1000

1500

2000

v (m/s)

Co

un

ts

Bed Particles and Ice Crystals (0 s Coincidence)

Bed Particles

Ice Crystals

0 20 40 60 80 1000

500

1000

1500

2000

v (m/s)

Co

un

ts

Bed Particles Subranged (I >500 mV, 10 s Coincidence)

0 50 1000

500

1000

1500

2000

v (m/s)

Co

un

ts

Ice Crystals Subranged (I < 200 mV, 0 s Coincidence)

9

10

Single Phase Gas Jet

11

Empty Bed Transverse Velocity Profiles Single phase gas jet plume velocity profiles are self-similar with a Gaussian bell-

curve shape

Centerline axial velocity decay and velocity profile width expansion are consistent

with a free 2D turbulent jet

-2 -1 0 1 2

0.2

0.4

0.6

0.8

1

= x/xg,1/2

v g/v

g,m

Empty Bed, Vj = 90 m/s, V

fl = 0 cm/s

y =70 mm

y =100 mm

y =130 mm

exp[-ln(2)2]

1.6 1.8 2 2.21.6

1.8

2

2.2

log (y-yo), y

o = 2D

j

log

(v g

,m )

Empty Bed, Vj = 90 m/s, V

fl = 0 cm/s

vg,m

~ (y-yo)-1/2

1.6 1.8 2 2.2

0.7

0.8

0.9

1

1.1

1.2

log (y-yo), y

o = 2D

j

log

(xg

,1/2

)

Empty Bed, Vj = 90 m/s, V

fl = 0 cm/s

xg,1/2

~ (y-yo)1

12

Mass and Momentum Transport Calculations

Self-similar velocity profiles enable transport values to be calculated from velocity

centerline and half-point values.

2/1,

2

,2

2

2 5.1 gmgg

b

b

ggg xvwCdxvwCJ

2/1,,11 09.2 gmgg

b

b

ggg xvwCdxvwCm

Axial mass transport

-5 0 50

0.5

1

z (mm)

v g/v

g,p

eak

Empty Bed, Vj = 90 m/s, V

fl = 0 cm/s

7.0 )(1

1,1, CvCdzzvw

v peakg

w

avgg

55.0 )(1

2

2

,2

22

, CvCdzzvw

vw

peakgavgg

Axial momentum transport

The 3D nature of flow must be accounted for

13

Gas Jets in a Bubbling Bed

Bubbling Bed Vertical Jet Velocity Profiles

Jet gas and bed particle velocities obtained simultaneously

838μm HDPE particles

Fluidization: Vfl = 33.4 cm/s (Vfl /Vmf = 1.15)

Gas Velocity Profiles

-20 -10 0 10 200

5

10

15

x (mm)

v p (

m/s

)

838 m HDPE, Vj = 92 m/s, V

fl = 33.4 cm/s

y = 60 mm

y = 70 mm

y = 100 mm

y = 130 mm

Particle Velocity Profiles

-20 -10 0 10 200

10

20

30

40

50

60

70

x (mm)

v g (

m/s

)

838 m HDPE, Vj = 92 m/s, V

fl = 33.4 cm/s

y = 60 mm

y = 70 mm

y = 100 mm

y = 130 mm

14

Transverse Velocity Profile Self-Similarity

The gas and particulate phase velocity profiles appear

self-similar, thus they can be fully characterized by

Centerline velocity: vm(y)

Velocity profile width: x1/2(y)

Particulate Velocity Profiles

-2 -1 0 1 20

0.2

0.4

0.6

0.8

1

= x/xg,1/2

v g/v

g,m

838 m HDPE, Vj = 92 m/s, V

fl = 33.4 cm/s

y =60 mm

y =70 mm

y =100 mm

y =130 mm

exp[-ln(2)2]

Gas Velocity Profiles

-2 -1 0 1 20

0.2

0.4

0.6

0.8

1

= x/xp,1/2

v p/v

p,m

838 m HDPE, Vj = 92 m/s, V

fl = 33.4 cm/s

y =60 mm

y =70 mm

y =100 mm

y =130 mm

exp[-ln(2)2]

15

Centerline Velocity and Profile Width

16

The presence of bed particles significantly reduces the gas

phase velocity

60 80 100 120

20

40

60

80

100

y (mm)

v m (

m/s

)

838 m HDPE, Vj = 92 m/s, V

fl = 33.4 cm/s

gas

particle

slip

empty

Axial Velocity Profile Velocity Profile Expansion

Velocity profile width for the gas phase in the bubbling and

empty bed is very similar

60 80 100 1204

5

6

7

8

9

10

11

12

13

14

15

y (mm)

x 1/2

(m

m)

838 m HDPE, Vj = 92 m/s, V

fl = 33.4 cm/s

gas

particle

slip

empty

Volumetric Void Fraction (ε) Indirectly determined from a momentum balance using

the measured velocity profiles

pgj JJJ

b

b

ggg dxvwCJ 2

2

b

b

ppp dxvwCJ 2

2)1(

b

b

pp

b

b

gg

b

b

ppj

dxvdxvwC

dxvwCJ

22

2

2

2

0 20 40 60 80 100 120

0.96

0.98

1

y (mm)

838 m HDPE, Vj = 92 m/s, V

fl = 33.4 cm/s

vo

id f

ract

ion

Void Fraction > 95% in the dilute jet plume

17

Mass Flow and Momentum Transfer Bed particles are entrained into the jet plume while the

gas phase mass flow remains nearly constant for this fluidization level

Mass flow in jet plume Momentum transfer in jet plume

0 50 100

0

20

40

60

80

100

y (mm)

m (

g/s

)

838 m HDPE, Vj = 92 m/s, V

fl = 33.4 cm/s

gas

particle

empty

0 50 100

0

0.2

0.4

0.6

0.8

y (mm)

J (k

g.m

/s2)

838 m HDPE, Vj = 92 m/s, V

fl = 33.4 cm/s

gas

particle

Momentum is rapidly transferred from the jet gas to the entrained particles

18

Effect of Emulsion Fluidization

State

19

20

Fluidization level varied from spouted bed to 50% beyond minimum

fluidization

838 μm HDPE micropellets

Vj = 92 m/s

Effect of Fluidization on Jet Dynamics

Vfl/Vmf = 0 Vfl/Vmf = 1 Vfl/Vmf = 1.5

21

Effect of Fluidization on Velocity Profiles Increasing the fluidization velocity decreases the maximum

centerline velocity and widens the velocity profiles for both phases Gas Phase Particulate Phase

60 80 100 1208

9

10

11

12

13

14

y (mm)

v p,m

(m

/s)

838 m HDPE, Vj = 92 m/s

Vfl/V

mf = 0

Vfl/V

mf = 0.7

Vfl/V

mf = 1

Vfl/V

mf = 1.15

Vfl/V

mf = 1.3

Vfl/V

mf = 1.5

Cente

rlin

e V

elo

city

Pro

file

Wid

th

60 80 100 120

30

40

50

60

70

y (mm)

v g,m

(m

/s)

838 m HDPE, Vj = 92 m/s

60 80 100 1208

9

10

11

12

13

y (mm)v p

,m (

m/s

)

838 m HDPE, Vj = 92 m/s

60 80 100 120

5

10

15

20

25

y (mm)

xg

,1/2

(m

m)

838 m HDPE, Vj = 92 m/s

60 80 100 1205

10

15

20

25

y (mm)

xp

,1/2

(m

m)

838 m HDPE, Vj = 92 m/s

22

Effect of Fluidization on Void Fraction

Void fraction in the jet plume increases with emulsion fluidization

Void Fraction

60 80 100 1208

9

10

11

12

13

14

y (mm)

v p,m

(m

/s)

838 m HDPE, Vj = 92 m/s

Vfl/V

mf = 0

Vfl/V

mf = 0.7

Vfl/V

mf = 1

Vfl/V

mf = 1.15

Vfl/V

mf = 1.3

Vfl/V

mf = 1.5

0 50 1000.92

0.94

0.96

0.98

1

y (mm)

838 m HDPE, Vj = 92 m/s

23

Effect of Fluidization on Mass Transport

60 80 100 1208

9

10

11

12

13

14

y (mm)

v p,m

(m

/s)

838 m HDPE, Vj = 92 m/s

Vfl/V

mf = 0

Vfl/V

mf = 0.7

Vfl/V

mf = 1

Vfl/V

mf = 1.15

Vfl/V

mf = 1.3

Vfl/V

mf = 1.5

Gas Phase Mass Flow

As the fluidization rate increases, the gas phase mass flow increases Below minimum fluidization, jet gas diffuses into the emulsion to locally fluidize

the particles

Above minimum fluidization, interstitial gas and bubbles in the emulsion are

entrained into the jet plume

0 50 100

5

10

15

20

y (mm)

mg (

g/s

)

838 m HDPE, Vj = 92 m/s

24

60 80 100 1208

9

10

11

12

13

14

y (mm)

v p,m

(m

/s)

838 m HDPE, Vj = 92 m/s

Vfl/V

mf = 0

Vfl/V

mf = 0.7

Vfl/V

mf = 1

Vfl/V

mf = 1.15

Vfl/V

mf = 1.3

Vfl/V

mf = 1.5

Particulate phase mass flow in the plume decreases with

increasing fluidization due to competition with the interstitial gas

entrainment

Effect of Fluidization on Mass Transport

Particulate Phase Mass Flow

0 50 1000

50

100

150

y (mm)

mp (

g/s

)

838 m HDPE, Vj = 92 m/s

25

Effect of Fluidization on Momentum Transport

As the fluidization rate increases, the gas phase momentum

increases due to increased interstitial gas entrainment

Particulate phase momentum decreases with increasing fluidization

60 80 100 1208

9

10

11

12

13

14

y (mm)

v p,m

(m

/s)

838 m HDPE, Vj = 92 m/s

Vfl/V

mf = 0

Vfl/V

mf = 0.7

Vfl/V

mf = 1

Vfl/V

mf = 1.15

Vfl/V

mf = 1.3

Vfl/V

mf = 1.5

Gas Phase Momentum Particulate Phase Momentum

pgj JJJ

0 50 1000

0.2

0.4

0.6

0.8

y (mm)

J g (

kg

.m/s

2)

838 m HDPE, Vj = 92 m/s

0 50 100

0

0.2

0.4

0.6

0.8

y (mm)

J p (

kg

.m/s

2)

838 m HDPE, Vj = 92 m/s

Turbulence Measurements

26

Importance

The jet plume of a bubbling bed is a region of turbulent

mixing

Experimental measurements have been restricted to

plume size, plume shape, gas mean velocity, solids

mean velocity and solids concentration

Turbulence data will help in developing fundamentally

rigorous models to describe momentum transport in

bubbling beds

Fluctuating velocity data will be valuable in validating

gas-solid turbulence equations used in Eulerian

framework

27

M. Filla, L. Massimilla, and S. Vaccaro. “Gas jets in fluidized beds and spouts: A comparison of experimental

behaviour and models,” Can. J. Chem. Eng. (61): 370, 1983.

Experimental Procedure

The same LDV technique used for mean velocities is employed to measure fluctuating velocities in each phase

To be conservative, only measurements with Doppler burst counts greater than 1000 are considered

28

v

N

vvv

2' )(

500 1000 1500 2000 2500 30008

10

12

v' g (

m/s

)

500 1000 1500 2000 2500 30002

3

4

Burst Count

v' p (

m/s

)

Single Phase Turbulence

Data lies in the non-self similar or potential core region of turbulence

Shows good agreement with literature

Negligible influence of bounding walls seen

29

D.R. Miller, and E.W. Comings, “Static pressure distribution in the free turbulent jet,” J. Fluid Mech. (3): 1, 1957.

E. Gutmark, and I. Wygnanski, “The planar turbulent jet,,” J. Fluid Mech. (73): 465, 1976.

D. Rangarajan , and J. S. Curtis, “Effect of spanwise width on rectangular jets with sidewalls,” J. Fluids. Eng. T. ASME, submitted 2011.

-2 -1.5 -1 -0.5 0 0.5 1 1.5 20

0.05

0.1

0.15

0.2

0.25

0.3

x/x1/2

v' /v

m

Self-similar region

Bubbling Bed Fluctuating Velocity Profiles

Particle fluctuations are ~50% greater than gas fluctuations

Profile shapes for both phases similar to single phase turbulence

Deviation in shape at higher fluidization state due to plume boundary

fluttering

30

-2 -1 0 1 20.1

0.15

0.2

0.25

0.3

0.35

x/xg,1/2

vg'/v

g,m

-2 -1 0 1 20.1

0.15

0.2

0.25

0.3

0.35

x/xp,1/2

vp'/v

p,m

Empty Bed

Vfl/V

mf=0

Vfl/V

mf=0.7

Vfl/V

mf=1

Vfl/V

mf=1.15

Vfl/V

mf=1.3

Vfl/V

mf=1.5

y/Dj= 7.61

Effect of Fluidization on Turbulence

There is an increase in gas turbulence in Spouted Bed compared to Empty Bed

Effect of increasing distributor velocity is to initially decrease and then increase

fluctuations in both phases

Particle and gas fluctuations complement each other

31

Empty Bed 0 0.7 1.0 1.15 1.3 1.50.22

0.24

0.26

0.28

0.3

0.32

0.34

0.36

0.38

Vfl/V

mf

vp

,cl

'/v

p,m

y/Dj= 6.52

y/Dj= 7.61

y/Dj= 10.87

y/Dj= 14.13

Empty Bed 0 0.7 1.0 1.15 1.3 1.50.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

Vfl/V

mf

vg

,cl

'/v

g,m

y/Dj= 6.52

y/Dj= 7.61

y/Dj= 10.87

y/Dj= 14.13

Relationship with mean quantities

32

Empty Bed 0 0.7 1.0 1.15 1.3 1.50.5

1

1.5

2

2.5

Vfl/V

mf

xg

,1/2

/Dj

Empty Bed 0 0.7 1.0 1.15 1.3 1.5

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

vg

,m/V

j

Vfl/V

mf

Empty Bed 0 0.7 1.0 1.15 1.3 1.50.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

Vfl/V

mf

vg

,cl

'/v

g,m

y/Dj= 6.52

y/Dj= 7.61

y/Dj= 10.87

y/Dj= 14.13

Empty Bed 0 0.7 1.0 1.15 1.3 1.5

0.8

1

1.2

1.4

1.6

1.8

2

2.2

Vfl/V

mf

xp

,1/2

/Dj

Empty Bed 0 0.7 1.0 1.15 1.3 1.50.05

0.1

0.15

0.2

vp

,m/V

j

Vfl/V

mf

Empty Bed 0 0.7 1.0 1.15 1.3 1.50.22

0.24

0.26

0.28

0.3

0.32

0.34

0.36

0.38

Vfl/V

mf

vp

,cl

'/v

p,m

y/Dj= 6.52

y/Dj= 7.61

y/Dj= 10.87

y/Dj= 14.13

Coupling via Fluctuating Velocity

High St suggests particle motion is unlikely to be affected by gas-phase turbulence

High Rep suggests gas turbulence enhancement due to vortex shedding caused by particles

33

000,21~18

2

jg

jpp

g

p

D

Vd

t

tSt

30001500~)(

Re

g

gppg

p

dvv

Hestroni, G., “Particles-turbulence interaction”, Int. J. Multiphase Flow, 15 (1989) 5

34

Modeling Effort

Modeling Framework Eulerian two-fluid modeling

Solved using MFIX code

Inclusion of friction and turbulence

interaction terms from existing

works

35

Dilute region dominated by turbulent

and collisional/kinetic stresses

Dense region dominated by

frictional stress

www.mfix.netl.doe.gov

Dgggg

g

g FgPVVt

V

ssDss

s

s gFPVVt

V

Use of Experimental Data for

Validation

36

Experimental data Compare with Validate

Minimum fluidization

velocity

Minimum fluidization velocity Frictional pressure

Plume size and shape

from photograph

Solids fraction contour Frictional viscosity

Gas and particle mean

axial velocity

Gas and solids axial velocity Overall performance of

model

Gas phase axial

fluctuating velocity

Turbulent kinetic energy

assuming same anisotropy as

planar single phase jet

Gas-particle turbulence

interaction

Particle axial fluctuating

velocity

Granular temperature

assuming isotropy

Gas-particle turbulence

interaction

x (m)

y (

m)

-0.135 -0.045 0.045 0.135 0.225

0.429

0.386

0.343

0.3

0.257

0.214

0.171

0.128

0.085

Spouted Bed: Srivastava-Sundaresan friction and no turbulence

interaction

37

0 0.002 0.004 0.006 0.008 0.013

4

5

6

7

8

9

10

y/Dj= 7.61

x (m)

T (

m2/s

2)

Experiment

Simulation

0 0.002 0.004 0.006 0.008 0.0120

40

60

80

100

120

140

y/Dj= 7.61

x (m)

k (

m2/s

2)

Experiment

Simulation

0 10 20 30 40 505

6

7

8

9

10

11

12

13

y/Dj

vp

,m (

m/s

)

Experiment

Simulation

x (m)

y (

m)

0 0.1 0.20

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Srivastava, A., and Sundaresan, S., “Analysis of a frictional-kinetic model for gas-particle flow,” Powder Technol., 129 (2003) 72

Bulk FlowParticle mean velocity decay

Gas turbulence Granular temperature

Improvement in friction and turbulence interaction models required

Conclusions

A procedure has been developed to simultaneously

measure gas and particulate phase velocities based on

LDV burst intensity and coincidence subranging

Mass and momentum transport of the two phases inside

the jet plume of a bubbling bed was calculated from the

measured velocity profiles

Maintaining constant gas jet inlet conditions changes in

mean and fluctuating quantities were investigated for

varying emulsion fluidization states

The use of experimental data to validate the Eulerian

two-fluid model is presently being studied

38