week 8 dynamics of particulate...

Week 8 Dynamics of Particulate systems

– (1) Electrohydrodynamic atomization fabrication ofpharmaceutical particles, (2) bubble motion in Taylorvortex, (3) vibrated granular bed system, (4) pneumatictransport of granular material.

–Measurement techniques used in the study of suchsystems include Electrical Capacitance Tomography(ECT), Particle Image Velocimetry (PIV) and PhaseDoppler Particle Analyzer (PDPA).

Bubble Motion in Taylor Vortex

Laser Generator

Camera

Inne

r cylin

der

Ou

ter

cylin

de

r

Synchronizer

Computer

Mineral Oil: (25C)

ρ=0.86g/cm3

η=29.67cp

Bubble Motion in Taylor Vortex

Figure 1 Schematic diagram of experimental apparatus (1) motor (2) outer cylinder (3) working liquid (4) inner cylinder (5) needle (6) lamp (7) camera (8) computer for viscosimeter (9) syringe pump (10) computer for high-speed video camera

1

2 3 4

5

6

7

8

9

10

dRiRe

Radius ratio (η=ri/ro) : 0.613Aspect ratio (Γ=L/d): 5.17Clearance ratio (c=d/ri): 0.63

Reynolds number:

Taylor number:

2

32

dRTa i

Air bubble: (25C)

ρ=0.0012g/cm3

η=0.0185cp

65 ~ 520

1.1e4 ~ 6.8e5

Core bubble: ring structureΩ =300rpm, Side View

68 Bubbles 110 Bubbles

R.S. Deng, C.H. Wang, and K. A. Smith, “Bubble behavior in a Taylor vortex”, Physical Review E, 73, 036306 (2006).

Flow pattern in pure liquid system

20.0 rpm 200.1 rpm179.9 rpm155.3 rpm107.8 rpm90.1 rpm

Ri Ro RiRiRiRiRi RoRoRoRoRo

800.4 rpm600.0 rpm500.0 rpm387.6 rpm352.4 rpm300.0 rpm

RoRi Ri RiRi Ro Ro Ro RoRo RiRi

One-dimensional flow turns into Taylor vortex flow at about 95rpm, and no wavy vortex is observed below 800rpm in the present system.

Ω

Two types of bubbles

P1

P2

P3

P4

Core Bubble Wall Bubble Pressure distribution calculated from CFD (Fluent 6.1)

Ri Ro

R.S. Deng, C.H. Wang, and K. A. Smith, “Bubble behavior in a Taylor vortex”, Physical Review E, 73, 036306 (2006).

Application of Particle Image Velocimetry (PIV) for Pattern Characterization in a Vertically Vibrated Granular Layer

High-speed video camera, 1,000fps Discrete Element Simulation

Experimental apparatus

A, f

1

2

3

4

5

6

7 8

(1) Synchronizer (2) Computer (3) Laser generator (4) CCD camera

(5) Vessel (6) Vibrator (7) Function generator (8) Power amplifier

Image captured by PIV camera

X

Y

O

Free Space

Granular Layer

Detachment

Bottom Plate

Peak Peak

Valley

Typical stages in a vibrating cycle

Impact

Free-flight

Contact

(First Half)

(First Half)

(Second Half)

R.S. Deng and C.H. Wang, "Particle Image Velocimetry Study on the Pattern Formation in a Vertically Vibrated Granular Bed", Phys. Fluids, 15(12) 3718-3729 (2003).

Flow Stability Analysis

)sin( tAX

H Mt

Vibrator

Granular Layer

A, f

H MtGranular Layer

Qt

Taking average over one period

tVY

VY=0Example

Governing Equations

Continuity

Momentum

Energy

0)(

u

t

JuqDt

DT :

2

3

gDt

uD

Perturbation Form

)exp()exp()(

)exp()exp()(

)exp()exp()(

)exp()exp()(

XiKYTT

XiKY

XiKY

XiKYuu

xe

xe

xe

xe

Where:

ir iAnd

Perturbations:

0

0 uuu

TTT

0

0

Stability Analysis

Stability Diagram

Stability Analysis

Mt

Qt

Stable

Unstable

A

B

r

Layer

Mode

Stationary

Mode

S-C margin

L-C margin

R.S. Deng and C.H. Wang, "Instabilities of Granular Materials under Vertical Vibrations", J. Fluid Mechanics, 492, 381-410 (2003).

Surface Patterns (I) Stripe

X

Z

z /

D

x / D

(a) (b) (c)

1-Perturbation Simulation(This work)

Experiment (Umbanhowar, Nature, 389, 1997)


Surface Patterns (II) Square

Z

X

x / D

z /

D

(a) (b) (c)

2-Perturbations Simulation(This work)

Experiment (Umbanhowar, Nature, 389, 1997)


J. Fluid Mech., 435,

217-246 (2001).

Chem. Eng. Sci., 53(22),

3803-3819 (1998)

J. Fluid Mech., 435,

217-246 (2001).

Schematic Diagram of ECT SystemSchematic Diagram of ECT System

Multiplexing

Circuit

Capacitance

to Voltage

Transfer

A/D

Converter

Insulating Pipe

Components

C1

C2

Data

Image Reconstruction

Algorithm

Control Signals

Capacitance Measurement

Data Acquisition Unit

Post-processing

Electrode

Twin plane ECT system(Velocity measurement)

LPlane 1 Plane 2

V

(a) (a)

(b)(b)

Homogeneous flow (a) typical flow

pattern (b) time averaged particle

concentration profile (c) particle

concentration contours.

Moving Dunes (a) typical flow pattern (b)

time averaged particle concentration

profile (c) particle concentration

contours.

t

X YX

Y

t

S.M. Rao, K. Zhu, C.H. Wang, and S. Sundaresan, “Electrical Capacitance Tomography Measurements on the Pneumatic Conveying of Solids”, Ind. Eng. Chem. Res. 40(20) 4216-4226 (2001).

Flow over settled layer (a) typical

flow pattern (b) time averaged

particle concentration profile (c)

particle concentration contours.

Plug Flow (a) typical flow pattern

(b) time averaged particle

concentration profile (c) particle

concentration contours.

(a) (a)

(b) (b)

X YX

Y

t t


0 1 2 3 4 500.020.040.060.08

Sec

0 2 4 6 8 1002468x 10

-5

Hz

S

0 1 2 3 4 500.050.10.150.2

Sec

0 1 2 3 4 501234x 10

-4

Hz

S

Homogeneous Moving dunes

Eroding dunes Plug flow

Polypropylene particles ( - average solid concentration, S –

power spectrum density)

10 15 20 250

0.20.40.60.8

1

0 1 2 3 4 50

1

2

Hz

Sec

S

x 10 -2

0 1 2 3 4 500.005

0.010.015

Sec

0 2 4 6 8 100246x 10

-6

Hz

S

Power spectra of solid concentration fluctuations from

single plane data can characterize various flow regimes

of pneumatic conveying.

s s

ss


(a) (b)

N

S

W E

(d)

W

N

S

E

(c)

Distribution of polypropylene particles in a vertical riser flow –dispersed flow

Ug = 15.6 m/s

Gs = 31.4 kg/(m2.s).

Left: z = 0.47 m

Right: z = 2.05 m

K. Zhu, S.M. Rao , C.H. Wang, and S.

Sundaresan “Electrical Capacitance

Tomography Measurements on the

Vertical and Inclined Pneumatic

Conveying of Granular Solids“, Chem.

Eng. Sci. 58(18) 4225-4245 (2003).

t

(a)(b)

0

0.1

(c)

Slugging flow

Ug = 14.3 m/s

Gs = 21.7 kg/(m2.s)

Z = 2.05 m

Distribution of polypropylene particles in a vertical riser flow –slugging flow






Eng. Sci. 58(18) 4225-4245 (2003).

(a)

(b)

t

(d)

(c )

N

S

EW

Slugging flow

Ug = 13.0 m/s

Gs = 7.0 kg/(m2.s)

Z = 2.05 m

Distribution of polypropylene particles in a vertical riser flow –annular capsule flow






Eng. Sci. 58(18) 4225-4245 (2003).

Summary for Horizontal & Vertical Conveying

Using single plane data - time averaged particle concentration.

Using twin plane cross correlation – pattern velocity.

Single plane particle concentration data vs time data– (a) Homogeneous is not homogeneous. – (b) Moving dunes and eroding dunes with multiple

characteristic peaks in the lower frequency region.– (c ) Plug flow with a single largest peak at near zero

frequency. Cross sectional variation of time averaged density

distribution in different flow regimes.

Electrostatic Characterization

J. Yao, Y. Zhang, C.H. Wang, S. Matsusaka, H. Masuda, “Electrostatics of the Granular Flow in a Pneumatic Conveying System“, Ind. Eng. Chem. Res., 43, 7181-7199 (2004).

Disperse flow – pattern observed in the vertical pipe

Initial condition

Two hours later

The clusters were located fairly high up in the pipe and traveled along a curved path by the pipewall. These clusters appeared and disappeared intermittently in an unpredictable manner.

J. Yao, Y. Zhang, C.H. Wang, S. Matsusaka, H. Masuda, “Electrostatics of the Granular Flow in a Pneumatic Conveying System“,Ind. Eng. Chem. Res., 43, 7181-7199 (2004).

Ring flow - vertical granular pattern

Initial condition

Fifteen minutes later

Particles were observed totravel in a spiral fashion up the vertical pipe along thepipe wall. This resulted in a ring or annulus structure with high particle concentrations adjacent to the wall and a relatively empty core region

J. Yao, Y. Zhang, C.H. Wang, S. Matsusaka, H. Masuda, “Electrostatics of the Granular Flow in a Pneumatic Conveying System“,Ind. Eng. Chem. Res., 43, 7181-7199 (2004).

Induced current measurement

Test station B

Polymer film

electrometer

Pipe wallSections A & C

Aluminum foil

K. Zhu, S.M. Rao , Q.H. Huang, C.H. Wang, S Matsusaka, and H. Masuda, “On the Electrostatics of Pneumatic

Conveying of Granular Materials Using Electrical Capacitance Tomography“, Chem. Eng. Sci., 59(15) 3201-3213 (2004).

t, sec

0 5 10 15 20

i, m

icro

A

-40

-20

0

20

40

60

80

(a)

time, sec

0 5 10 15 20

s

0.0

0.2

0.4

0.6

0.8

1.0

plane1

plane 2(b)

(a) MPCT measurement

(b) ECT Measurement

U = 14.3 m/s, Gs = 0.08 kg/s

Moving capsule flow

K. Zhu, S.M. Rao , Q.H. Huang, C.H. Wang, S Matsusaka, and H. Masuda, “On the Electrostatics of Pneumatic Conveying of Granular Materials Using Electrical Capacitance Tomography“, Chem. Eng. Sci., 59(15) 3201-3213 (2004).

Time(second)

I(A

)

2000 4000 6000 8000

0

5E-08

1E-07

1.5E-07

2E-07

2.5E-07

Disperse flow

Half-ring flow

Ring flow

Negative

Induced current – vertical pipe

Time(second)

Ch

arg

eQ

(C)

0 2000 4000 6000

0

2E-05

4E-05

6E-05

8E-05

Disperse flow

Half-ring flow

Ring flow

Negative

(a) Comparison of the current value (negative) for the three flows. (b) Comparison of the charge accumulation for the three flows.

J. Yao, Y. Zhang, C.H. Wang, S. Matsusaka, H. Masuda, “Electrostatics of the Granular Flow in a Pneumatic Conveying System“, Ind. Eng. Chem. Res., 43, 7181-7199 (2004).

Summary: Electrostatics in Pneumatic Conveying

Air flow rate is a key factor determining the electrostatic behavior of granularflow. The lower the air flow rate, the higher the induced current and particlecharge density. These in turn lead to particle clustering and the formation ofsuch structures as half-ring and ring in the vertical conveying pipe.

Electrostatic effects increase with time. The charge accumulated at the pipewall increases with time and the rate of increase seems constant for each ofthe three types of flow. Particle charge density also increases with time andthis may account for clustering behavior occurring at the vertical pipe walleven when a high air flow rate is used and the dominant flow regime is that ofdisperse flow. Pipe wall material has an obvious effect on the electrostatics ofthe granular flow.

Electrostatic effects depend on composition for particle mixture. Thecommercially available anti-static agent, Larostat-519 powder, was found toreduce electrostatic effects within the system effectively.

The mechanism of electrostatic charge generation for the granular flow in thepneumatic conveying system mainly depends on tribroelectrification due tostrong force effect on the surface when the particles slide on the pipe wall.

DEM Simulation

• Newton’s Laws of Motion

• Force-displacement Model

N

1j

i,fiij,dij,ci

i mdt

dm fgff

v

N

1j

ij

i

idt

dI T

ω

ij,ni,nij,cn δf

ij,ti,tij,ct δf

iiri,nij,dn nnvf jjiiiiri,tij,dt RωRωttvf

Reversed flow in pneumatic conveying in an inclined pipe

g

DEM Simulation

• Fluid Drag Force Model 1

ii,0fi,f

ff

iiii2

i

2

ifi,0di,0f Rc5.0 vuvuf

2

Relog5.1exp65.07.3

2

i,p10

2

5.0

i,p

i,0dRe

8.463.0c

f

iiiif

i,p

R2Re

vu

Di Felice, R. The voidage function for fluid-particle interaction systems. Int. J. Multiph. Flow 1994, 20, 153.

Fluidized bed simulation using DEM

DEM Simulation

• Computational Fluid Dynamics

0t

u

Fguuu

u

fff

f Pt

Pneumatic Conveying simulations using DEM

V2

V1

0 0.25 0.5 0.75 10

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

V2

V1

0 0.25 0.5 0.75 10

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

V2

V1

0 0.25 0.5 0.75 10

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Simulation Conditions

Material Properties and System ParametersShape of particles Spherical

Type of particles Polypropylene

Number of particles 500, 1000, 1500, 2000

Particle diameter, d 2.8 10-3

m

Particle density, p 1123 kg m-3

Spring constant in force model, 5.0 103 N m

-1

Viscous contact damping coefficient, 0.35

Coefficient of friction 0.3

Gas density, f 1.205 kg m-3

Gas viscosity, f 1.8 10-5

N s m-2

Pipe diameter 0.04 m

Pipe length 1.0 m

Computational cell size 4 mm 4 mm

Simulation time step, t 10-7

s

Rao, S. M.; Zhu, K.; Wang, C. H.; Sundaresan, S. Electrical capacitance tomography measurements on the pneumatic

conveying of solids. Ind. Eng. Chem. Res. 2001, 40, 4216.

Simulation Conditions

• Particles first allowed to settle under gravity for 0.5 s

before gas flow was initiated

• Periodic boundary conditions applied to the solid phase

to simulate an open flow system

• Solid concentration, , defined as overall volume

fraction of particles divided by volume fraction of

particles at maximum packing (0.64)

Results and Discussion

Dispersed Flow

= 0.08

Gas velocity 14 m s-1

Plug Flow

= 0.32

Gas velocity 14 m s-1

W.C. Lim, C.H. Wang, and A.B. Yu, “Discrete Element Simulation for Pneumatic Conveying of Granular Material” AIChE Journal, 52, 496-509 (2006).


Stratified Flow

= 0.08, Gas velocity 10 m s-1

Moving dunes


Slug Flow


Homogeneous Flow




• The different flow regimes in vertical

pneumatic conveying are represented

in the form of phase diagrams

• Dashed lines separate regions

representing different flow regimes

while dashed circles enclose regions

where transition between two adjacent

flow regimes might be taking place

• In vertical pneumatic conveying, the

dispersed flow regime is dominant at

high gas velocities and low solid

concentrations while the plug flow

regime is dominant otherwise

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

12 14 16 18 20 22 24 26

Gas velocity (m s-1

)

So

lid

flo

w r

ate

(k

g s-

1)

= 0.32

= 0.24

= 0.16

= 0.08

Plug Flow

Dispersed Flow



• Similarly, the homogeneous flow

regime is dominant at high gas

velocities and low solid concentrations

while the slug flow regime is dominant

otherwise in horizontal conveying

• At low gas velocities and solid

concentrations, effects of gravitational

settling result in the formation of the

moving dunes and stratified flow

regimes

• Intermediate values of gas velocities

involve transitions between moving

dunes and homogeneous flow and

between stratified and homogeneous

flow

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

8 12 16 20 24 28 32

Gas velocity (m s-1

)

So

lid

flo

w r

ate

(k

g s-

1)

= 0.32

= 0.24

= 0.16

= 0.08

Slug Flow

Homogeneous Flow

Moving dunes

MD/H

S/H



• The solid concentration profile for

dispersed flow in vertical pneumatic

conveying shows that solid

concentrations are higher near the

walls than in the center of the pipe

• This trend is similar for all gas

velocities simulated

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.00 0.01 0.02 0.03 0.04

Radial position (m)

So

lid

co

nce

ntr

ati

on

Gas velocity

14 m s-1

16 m s-1

18 m s-1

20 m s-1

24 m s-1



• The solid concentration profiles in

horizontal pneumatic conveying show

quantitatively the effects of

gravitational settling which results in

higher solid concentrations along the

bottom wall of the pipe

• As before, the solid concentration

profiles are quantitatively similar for

different gas velocities used

0.00

0.01

0.02

0.03

0.04

0.00 0.10 0.20 0.30 0.40 0.50

Solid concentration

Ra

dia

l p

osi

tio

n (

m)

Gas velocity

14 m s-1

18 m s-1

22 m s-1

26 m s-1

30 m s-1


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