Week 8 Dynamics of Particulate systems · PDF fileWeek 8 Dynamics of Particulate systems...
Transcript of Week 8 Dynamics of Particulate systems · PDF fileWeek 8 Dynamics of Particulate systems...
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
Inn
er
cylin
de
r
Oute
r cylin
der
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)
R.S. Deng and C.H. Wang, "Instabilities of Granular Materials under Vertical Vibrations", J. Fluid Mechanics, 492, 381-410 (2003).
Surface Patterns (II) Square
Z
X
x / D
z /
D
(a) (b) (c)
2-Perturbations Simulation(This work)
Experiment (Umbanhowar, Nature, 389, 1997)
R.S. Deng and C.H. Wang, "Instabilities of Granular Materials under Vertical Vibrations", J. Fluid Mechanics, 492, 381-410 (2003).
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
tt
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).
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
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) (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
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).
(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
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).
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
iji
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
iiii
2
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).
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
• 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
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
• 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
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
• 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
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
• 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
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).