Transcript Lecture 8 - nus.edu.sg

Week 8
Dynamics of Particulate systems
– (1) Electrohydrodynamic atomization fabrication of
pharmaceutical particles, (2) bubble motion in Taylor
vortex, (3) vibrated granular bed system, (4) pneumatic
transport of granular material.
–Measurement techniques used in the study of such
systems include Electrical Capacitance Tomography
(ECT), Particle Image Velocimetry (PIV) and Phase
Doppler Particle Analyzer (PDPA).
Bubble Motion in Taylor
Vortex
Camera
Mineral Oil: (25C)
ρ=0.86g/cm3
η=29.67cp
Synchronizer
Outer cylinder
Laser Generator
Inner cylinder
Computer
Bubble Motion in Taylor
Vortex
1
8
5
9
6
2
3
Radius ratio (η=ri/ro) : 0.613
Aspect ratio (Γ=L/d): 5.17
Clearance ratio (c=d/ri): 0.63
Air bubble: (25C)
ρ=0.0012g/cm3
η=0.0185cp
4
Reynolds number:
7
10
Re 
Ri d

65 ~ 520
Taylor number:
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
Ta 
2 Ri d 3
2
1.1e4 ~ 6.8e5
Core bubble: ring structure
Ω =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
Ri
Ro
20.0 rpm
Ri
Ro
90.1 rpm
Ri
Ro
107.8 rpm
Ri
Ro
155.3 rpm
Ri
Ro
179.9 rpm
Ri
Ro Ri
Ro Ri
Ro Ri
Ro Ri
Ro Ri
Ro Ri
Ro
200.1 rpm 300.0 rpm 352.4 rpm 387.6 rpm 500.0 rpm 600.0 rpm 800.4 rpm
Ω
One-dimensional flow turns into Taylor vortex flow at about 95rpm, and no wavy
vortex is observed below 800rpm in the present system.
Two types of bubbles
R.S. Deng, C.H. Wang, and K. A. Smith, “Bubble behavior in a Taylor vortex”, P
hysical Review E, 73, 036306 (2006).
P3
P1
P4
P2
Ri
Core Bubble
Wall Bubble
Ro
Pressure distribution calculated
from CFD (Fluent 6.1)
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
1
5
3
A, f
4
2
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
Peak
Peak
Y
O
X
Free Space
Valley
Granular Layer
Detachment
Bottom Plate
Typical stages in a
vibrating cycle
(First Half)
(First Half)
Impact
Contact
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).
Free-flight
(Second Half)
Flow Stability Analysis
H
Taking average
over one period
Granular Layer M
t
A, f
X  A sin(t )
Vibrator
Example
VY
H
t
Granular Layer M
t
VY=0
Qt
Governing Equations



Continuity
Momentum
Energy

   (  u)  0
t
Du

  g   
Dt
3 DT

   q   : u  J
2 Dt
Stability Analysis
Perturbation Form
Perturbations:
Where:
u  u0  u 
  0   
   0  
T  T0  T 
u   ue (Y ) exp( ) exp(iK x X )
    e (Y ) exp( ) exp(iK x X )
    e (Y ) exp( ) exp(iK x X )
T   Te (Y ) exp( ) exp(iK x X )
And
  r  ii
Stability Analysis
Stability Diagram
L-C
margin
Unstable
Qt
S-C
margin
Stationary
Mode
r
B
Layer
Mode
Stable
A
Mt
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
R.S. Deng and C.H. Wang, "Instabilities of Granular Materials under Vertical Vibrations",
J. Fluid Mechanics, 492, 381-410 (2003).
(a)
(b)
(c)
X
z/D
Z
x/D
1-Perturbation
Simulation
(This work)
Experiment
(Umbanhowar, Nature, 389, 1997)
Surface Patterns (II) Square
R.S. Deng and C.H. Wang, "Instabilities of Granular Materials under Vertical Vibrations",
J. Fluid Mechanics, 492, 381-410 (2003).
(a)
(b)
(c)
X
z/D
Z
x/D
2-Perturbations
Simulation
(This work)
Experiment
(Umbanhowar, Nature, 389, 1997)
Chem. Eng. Sci., 53(22),
3803-3819 (1998)
J. Fluid Mech., 435,
217-246 (2001).
J. Fluid Mech., 435,
217-246 (2001).
Components
Capacitance Measurement
Data Acquisition Unit
C2
C1
Multiplexing
Capacitance
A/D
Circuit
to Voltage
Converter
Transfer
Insulating Pipe
Control Signals
Data
Electrode
Post-processing
Image Reconstruction
Algorithm
Schematic Diagram of ECT System
Plane 1
L
Plane 2
V
Twin plane ECT system
(Velocity measurement)
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).
(a)
(a)
(b)
(b)
t
t
X
Y
Homogeneous flow (a) typical flow
pattern (b) time averaged particle
concentration profile (c) particle
concentration contours.
X
Y
Moving Dunes (a) typical flow pattern (b)
time averaged particle concentration
profile (c) particle concentration
contours.
(a)
(a)
(b)
(b)
t
t
X
Y
Flow over settled layer (a) typical
flow pattern (b) time averaged
particle concentration profile (c)
particle concentration contours.
X
Y
Plug Flow (a) typical flow pattern
(b) time averaged particle
concentration profile (c) particle
concentration contours.
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).
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).
Homogeneous
s
Moving dunes
0.015
0.01
0.005
S
s
0
-6
x0
10
6
4
2
0 0
1
2 Sec
3
4
5
2
4
6
8
10
Hz
0.08
0.06
0.04
0.02
0 0 -5
x 10
8
6
S
4
2
0 0
Eroding dunes
s
0.2
0.15
0.1
0.05
0
0 -4
x 10
4
3
S
2
1
0 0
1
2 Sec
3
4
5
2
4
6
8
10
Hz
Plug flow
0.8
0.6
0.4
0.2
s
1
2Sec
3
4
5
1
2 Hz
3
4
5
1
0
10
-2
2 x 10
15
20
Sec
25
1
S
0
0
1
2
Hz
3
4
Polypropylene particles ( - average solid concentration, S –
power spectrum density)
Power spectra of solid concentration fluctuations from
single plane data can characterize various flow regimes
of pneumatic conveying.
5
Distribution of polypropylene particles in a vertical riser flow –dispersed flow
Ug = 15.6 m/s
(a)
(b)
Gs = 31.4 kg/(m2.s).
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.
N
N
Eng. Sci. 58(18) 4225-4245 (2003).
(d)
(c)
Left: z = 0.47 m
W
E
W
E
Right: z = 2.05 m
S
S
Distribution of polypropylene particles in a vertical riser flow –
slugging flow
0.1

0
(b)
(a)
Slugging flow
Ug = 14.3 m/s
Gs = 21.7 kg/(m2.s)
t
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).
(c)
Distribution of polypropylene particles in a vertical riser flow –
annular capsule flow
N
(a)
W
E
(b)
(c )
S
Slugging flow
Ug = 13.0 m/s
Gs = 7.0 kg/(m2.s)
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
(d)
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
The clusters were located fairly
high up in the pipe and traveled
along a curved path by the pipe
wall. These clusters appeared and
disappeared intermittently in an
unpredictable manner.
Two hours later
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
Particles were observed to
travel in a spiral fashion up the
vertical pipe along the
pipe wall. This resulted in a ring or
annulus structure with high particle
concentrations adjacent to the wall
and a relatively empty core region
Fifteen minutes later
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
Polymer film
Sections A & C
Pipe wall
Test station B
Aluminum foil
electrometer
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).
80
(a)
(a) MPCT measurement
60
(b) ECT Measurement
i, microA
40
20
0
-20
U = 14.3 m/s,
Gs = 0.08 kg/s
-40
0
10
15
20
t, sec
1.0
Moving capsule
flow
(b)
plane1
plane 2
0.8
0.6
s
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).
5
0.4
0.2
0.0
0
5
10
time, sec
15
20
2.5E-07
Disperse flow
Half-ring flow
Ring flow
vertical pipe
Charge Q (C)
I(A)
Induced current –
Negative
2E-07
Disperse flow
Half-ring flow
Ring flow
8E-05
Negative
6E-05
1.5E-07
4E-05
1E-07
5E-08
2E-05
0
0
2000
4000
6000
8000
0
2000
4000
Time(second)
6000
Time(second)
(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 granular
flow. The lower the air flow rate, the higher the induced current and particle
charge density. These in turn lead to particle clustering and the formation of
such structures as half-ring and ring in the vertical conveying pipe.

Electrostatic effects increase with time. The charge accumulated at the pipe
wall increases with time and the rate of increase seems constant for each of
the three types of flow. Particle charge density also increases with time and
this may account for clustering behavior occurring at the vertical pipe wall
even when a high air flow rate is used and the dominant flow regime is that of
disperse flow. Pipe wall material has an obvious effect on the electrostatics of
the granular flow.

Electrostatic effects depend on composition for particle mixture. The
commercially available anti-static agent, Larostat-519 powder, was found to
reduce electrostatic effects within the system effectively.

The mechanism of electrostatic charge generation for the granular flow in the
pneumatic conveying system mainly depends on tribroelectrification due to
strong force effect on the surface when the particles slide on the pipe wall.
DEM Simulation
• Newton’s Laws of Motion
N
dv i
mi
  f c,ij  f d ,ij   m i g  f f ,i
dt
j1
N
dω i
Ii
  Tij
dt
j1
g
• Force-displacement Model
f cn,ij   n ,i δ n ,ij
f ct,ij   t ,i δ t ,ij
f dn ,ij  n,i v r  ni ni
f dt ,ij  t ,i v r  t i t i  ωi  R i  ω j  R j 


Reversed flow in pneumatic conveying in an inclined pipe
DEM Simulation
• Fluid Drag Force Model
f f ,i  f f 0,i i1
f f 0,i  0.5cd0,i f R i2 i2 ui  v i ui  v i 
 1.5  log10 Re p ,i 2 
  3.7  0.65exp

2


2


4.8
cd 0,i   0.63  0.5 

Re p,i 

2 f R i  i u i  v i
Re p,i 
f
Fluidized bed simulation using DEM
Di Felice, R. The voidage function for fluid-particle interaction systems. Int. J. Multiph. Flow 1994, 20, 153.
DEM Simulation
• Computational Fluid Dynamics

   u   0
t
 f u 
    f uu  P     f u    f g  F
t
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
0
0.25
0.5
0.75
1
0.75
1
0.75
1
V2
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
0
0.25
0.5
V2
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
0
0.25
0.5
V2
Pneumatic Conveying simulations using DEM
Simulation Conditions
Material Properties and System Parameters
Shape of particles
Type of particles
Number of particles
Particle diameter, d
Particle density, p
Spring constant in force model, 
Viscous contact damping coefficient, 
Coefficient of friction
Gas density, f
Gas viscosity, f
Pipe diameter
Pipe length
Computational cell size
Simulation time step, t
Spherical
Polypropylene
500, 1000, 1500, 2000
2.8  10-3 m
1123 kg m-3
5.0  103 N m-1
0.35
0.3
1.205 kg m-3
1.8  10-5 N s m-2
0.04 m
1.0 m
4 mm  4 mm
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).
Results and Discussion
Stratified Flow
 = 0.08, Gas velocity 10 m s-1
Moving dunes
 = 0.16, Gas velocity 10 m s-1
Slug Flow
 = 0.32, Gas velocity 10 m s-1
Homogeneous Flow
 = 0.16, Gas velocity 30 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).
Results and Discussion
1.6




-1
Solid flow rate (kg s )
1.4
1.2
= 0.32
= 0.24
= 0.16
= 0.08
1.0
0.8
Plug Flow
0.6
Dispersed Flow
0.4
0.2
0.0
12
14
16
18
20
22
Gas velocity (m s-1)
24
26
• 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
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).
Results and Discussion
1.8




-1
Solid flow rate (kg s )
1.6
1.4
1.2
= 0.32
= 0.24
= 0.16
= 0.08
Slug Flow
1.0
0.8
Homogeneous Flow
0.6
0.4
MD/H
Moving dunes
0.2
S/H
0.0
8
12
16
20
24
Gas velocity (m s-1)
28
32
• 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
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).
Results and Discussion
Solid concentration
0.18
• 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
Gas velocity
0.16
14 m s-1
0.14
16 m s-1
18 m s-1
0.12
20 m s-1
0.10
24 m s-1
0.08
0.06
0.04
0.02
0.00
0.00
0.01
0.02
0.03
0.04
Radial position (m)
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).
Results and Discussion
0.04
• 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
Gas velocity
14 m s-1
Radial position (m)
18 m s-1
0.03
22 m s-1
26 m s-1
30 m s-1
0.02
0.01
0.00
0.00
0.10
0.20
0.30
0.40
0.50
Solid concentration
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).