Horio's 2004 Sino German meeting pp slides on lubrication force paper
-
Upload
masayuki-horio -
Category
Technology
-
view
173 -
download
1
Transcript of Horio's 2004 Sino German meeting pp slides on lubrication force paper
Evaluation of lubrication force on colliding particles
for DEM simulation of fluidized beds
Wenbin Zhang , R. Noda and Masayuki Horio
Tokyo University of Agri. and Tech.
Koganei, Tokyo 184-8588, Japan
Sino-German Workshop, Beijing
Oct. 25, 2004
Come & Visit Tokyo Univ. A&T
at Koganei (25min from Shinjuku)
Green Technologies in the
October 19, 2004
APPChE 2004
Tuesday October 19 9:00~12:00
Plenary Session II Chair: Masayuki Horio, Prof., TUAT
Co-chair: Yasuhiko Arai, Prof., Kyushu U
Sustainable Future through Green Technologies in the Growing Asian Pacific Region -Chemical Engineers’ Challenges-
TUA&T Group “ESTeC”: Evolution and Survival of Technology based Civilization; organized in 2002
Collaboration of 28 Members from:
Energy Technologies, Chemical
Engineering, Agronomy,
Agricultural Civil & Mechanical Eng.
with ESTeC Industrial Innovation
Consortium and associating NPOs Backcasting from 100yrs ahead
Our decision for survival
For the last three years I have been involved in a new program:
We are aiming at developing bonds between
1. Agriculture and Engineering,
City and Country
2. Material and Energy Metabolism
3. Development/Market Economy and Control/Community Collaboration
4. Natural and Social Sciences ■ PEGASUS, LCA and GIS
(PEGASUS is an web based Energy/environment Public Giga-analyzer
for Sustainable Society)
■ Innovative Systems for Renewable Energy and Waste Management
■ Revitalization And Partnership Development for Regional
Communities and Mountainous Areas
■ N, P Circulation and Precision Farming
PEGASUS A web-based Knowledge Platform for Evolution and Survival of Civilization
Public Energy/Environment Giga-Analyzer for Sustainable Society
To reconstruct our town & village
A regional society design tool for everyone
Tokyo Univ. Agri. & Tech. ESTeC Group
20C Sequelae(20世紀後遺症): Climate changes,
Resources exhaustion, Waste flooding, Food crisis,
Water crisis, Spiritual crises
21C should be the period of control action for coming sustainable millennia.
Energy consump-tion
time
A Japanese proverb: ‘The plan for a year should be made on New Year’s Day.’ (一年的計在元旦) Then: ‘The plan for coming 3000yrs should be made in 21C.’
20C 21C20C 21C
China
Hope we chemical engineers can organize an effective collaboration for sustainability development.
Hope Chinese Chemical Engineers can introduce Seeds of Sustainability into the
Society from Now as much as possible
for our Future Soft Landing!
TUA&T VBL Entrance Hall Objet
(Opening Ceremony: Nov. 9)
I am also working on: Technology and Art Linkage
SAFIRE is an extended
Tsuji-Tanaka model
developed by TUAT
Horio group.
Surface/bridge force
Rupture joint h c
Attractive force F c
No tension joint
Normal elasticity k n
Normal dumping h n
Tangential dumping h t
k t Tangential elasticity
Friction slider m
SAFIRE (Horio et al.,1998~)
(Non-linear spring)
w/wo Tangential Lubrication
w/wo Normal Lubrication
DEM in the 1990s
Evaluation of lubrication force on colliding particles for DEM simulation of fluidized beds
SAFIRE
Achievements
I-H
1998
Ash
Melting
Olefine
Polymerization
PP, PE
Kaneko et al.
1999
Scaling Law
for DEM
Computation
Kajikawa-Horio
2000~
Natural Phenomena
Catalytic Reactions
CHEMICAL REACTIONS
Structure of
Emulsion Phase
Kajikawa-Horio
2001
FUNDAMENTAL LARGE SCALE SIMULATION
OTHER
AGGLOMERATIONCOMBUSTION
Coal/Waste
Combustion
in FBC
Spray
Granulation/Coating
Agglomerating
Fluidization
FB of
Solid Bridging
Kuwagi-Horio
1999
Tangential
Lubrication
Effect
Kuwagi-Horio
2000
Particles w/
van der Waals
Interaction
Iwadate-Horio
1998
Single Char
Combustion
in FBC
Rong-Horio
1999
Parmanently
Wet FB
Mikami,Kamiya,
Horio
1998
FB w/
Immersed
Tubes
Rong-Horio
1999
FB
w/ Immersed
Tubes :
Pressure Effect
Rong-Horio
2000
Particle-Particle
Heat Transfer
Rong-Horio
1999
Fluidized Bed DEM
Started from
Dry-Noncohesive Bed
Tsuji et al. 1993
Scaling Law
for DEM
Computation
Kuwagi-Horio
2002~
Lubrication
Force Effect
Noda-Horio
2002
I-H
1998
Ash
Melting
Olefine
Polymerization
PP, PE
Kaneko et al.
1999
Scaling Law
for DEM
Computation
Kajikawa-Horio
2000~
Natural Phenomena
Catalytic Reactions
CHEMICAL REACTIONS
Structure of
Emulsion Phase
Kajikawa-Horio
2001
FUNDAMENTAL LARGE SCALE SIMULATION
OTHER
AGGLOMERATIONCOMBUSTION
Coal/Waste
Combustion
in FBC
Spray
Granulation/Coating
Agglomerating
Fluidization
FB of
Solid Bridging
Kuwagi-Horio
1999
Tangential
Lubrication
Effect
Kuwagi-Horio
2000
Particles w/
van der Waals
Interaction
Iwadate-Horio
1998
Particles w/
van der Waals
Interaction
Iwadate-Horio
1998
Single Char
Combustion
in FBC
Rong-Horio
1999
Parmanently
Wet FB
Mikami,Kamiya,
Horio
1998
FB w/
Immersed
Tubes
Rong-Horio
1999
FB
w/ Immersed
Tubes :
Pressure Effect
Rong-Horio
2000
Particle-Particle
Heat Transfer
Rong-Horio
1999
Fluidized Bed DEM
Started from
Dry-Noncohesive Bed
Tsuji et al. 1993
Scaling Law
for DEM
Computation
Kuwagi-Horio
2002~
Lubrication
Force Effect
Noda-Horio
2002
SAFIRE 21
Contact force models
Normal force:Hertz model
Tangential force: Mindlin, Deresiewicz(1953)’s
‘no-slip’ solution
Particle size: PSD
Drag force: Extended Ergun CD
Model and Computing Conditions with PSD
23
/ pp dd
Run1 Run2 Run3 Particle size [mm] 3.00 4.50/3.00/2.25 4.50/2.25 Particle number [#] 30000 2963/10000/23703 4444/35556 Volume fraction [-] 1 0.333/0.333/0.333 0.500/0.500
Sauter mean dsv=Σ(Ndp3)/Σ(Ndp
2) = 3.00 mm
Particle vol. = 4.24×10-4m3,
Total particle surface area = 8.48×10-1m2
Young’s modulus: 80GPa, Poisson
ratio: 0.3, friction coefficient: 0.3
(Glass beads)
Computed Examples
Run 1
3.00mm
Run 2
4.50 / 3.00 / 2.25
mm
Run 3
4.50 / 2.25 mm
u0 = 1.438→2.938m/s (t<1sec), u0 = 2.938m/s (t≧1sec)
Now, Looking for
a Realistic Collision Process Description
Spring constant ?
Restitution coefficient ?
Field force: Electrostatic
force
Contact forces: •Van der Waals
force •Liquid and solid bridge
force •Impact force
Near Contact force:
Lubrication force
Looking for a solid basis for heat transfer & agglomeration modeling
Inter-particle forces
Let’s revisit the Classical lubrication theory (e.g. R. Davis)
basically for Liquid-solid systems
Stokes Paradox: Two solid surfaces can never make contact
in a finite time in any viscous fluid due to the infinite lubrication force when surface distance approaches zero
How shall we get along with the Stokes paradox, practically or essentially?
htvRdrtrrptFL /)(2
3),(2)( 2
0, m
Lubrication force, FL
When h 0, FL infinity
v1
v2
H(r,t) h(0,t) r
p(r,t)
analytical solution with paraboloid approximation
What about the Lubrication Force in Gas-solid systems?
Lubrication force negligible ? Can we overcome “Stokes Paradox” ?
Gas
Examining classical lubrication theory from gas-solid systems’ view point
v1
v2
H(r,t) h(0,t) r
p(r,t)
)()( 21 vvtvdt
dh
LFtFdt
dvm )(
Assumptions in classical lubrication theory are invalid in gas solid systems
Initial gap size h0 is assumed to be much smaller than particle radius Upper limit of integration of pressure for lubrication force is extended to infinity Paraboloid approximation of un-deformed surface Fluid is treated as a continuum
RrthtrH /),0(),( 2
rotated paraboloid approximation
htvRdrtrrptFL /)(2
3),(2)( 2
0, m
Breakdown of classical theory in gas-solid systems
• h0 as lubrication effect area
• Adoption of h0=R
• lubrication effect area is much larger in gas-solid systems than in liquid-solid systems
R
RL drtrrpF0
, ),(2
0
, ),(2 drtrrpFL
Classical theory is valid only for very small h0.
check the integration limit
FL,0/G
FL,0/Fd
0.01 0.1 1
0
2
4
6
8
10
Ra
tio
of
F L,0
to
oth
er
forc
es
h 0 / R
0.0 0.2 0.4 0.6 0.8 1.0
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Ratio of lubrication force FL
,R
/FL
,¡Þ
Relative initial distance
h0/R
Classical theory
Check h0 effect in Classical Theory for dp=50 mm, FCC
Numerical solutions for pressure distribution on a colliding sphere compared with classical theory
Pre
ssu
re
Relative radial distance r/R
h0=0.01R h0=0. 1R h0=R
numerical for a sphere analytical with paraboloid approximation
• Pressure decays to zero much faster with paraboloid approximation • Contribution of pressure in the outer region to the lubrication force may play an important role
2222),0(),( rRRthtrH RrthtrH /),0(),( 2
Case studies on minimum approaching distance
• Assuming that minimum surface distance equals to surface roughness
• Whether the fluid remains as a continuum is determined by the relative
magnitude of surface distance to mean free path of fluid molecules
Surface
roughness 1/10 R 1/1000 R smooth
Fluid
treatment Continuum Non-continuum Non-continuum
Adhesive
Force Neglected Neglected Important
Typical
particles FCC GB Ideal smooth GB
Case 2: hmin<l0 Case 3: hmin ~ Z0 Case 1: hmin>l0
Collision process with lubrication effect
• Physical contact happens when hmin equals to surface roughness • Energy dissipation in both approaching and separating stages • Lubrication force increases quickly when surfaces approach closer
Force:
FL/FL0 Velocity: v/v0
Even with Lubrication force we can avoid “Stokes Paradox”
Case 1: hmin>l0
l0=mean free
path
Increase of lubrication force stops when roughness makes contact
To realistic particles with surface roughness, stokes paradox is practically avoided
Case 2: hmin<l0
l0=mean free
path
Increase of lubrication force is slowed down in close approaching distance
Treatment of fluid as a non-continuum helps us avoid the infinite lubrication force
Avoidance of “Stokes Paradox”
Avoidance of “Stokes Paradox”
Case 3: hmin ~ Z0
Z0=repulsi ve
molecular distance
Magnitude of van der Waals force increases more rapidly when h -> 0 A critical collapse distance hcollaplse is defined to indicate the adhesive force dominant region (~10-9m) Consideration of adhesive force in the last approaching stage saves us again from Stokes Paradox essentially
Van der Waals force: important!!
collapse distance hcollaplse
0.0
Collapse distance contours
The collapse distance decreases with increase of Stokes number It increases with the increase of Hamaker constant A
)3.16
ˆlnˆ
4
1(
ˆ
6lnˆ
4
1ˆ 00
2
0
02 hhSt
hh
Z
lStE
collapse
collapse
0
ˆl
hh ,
2
0
6 R
mvSt
m ,
2
002
0
6
2
1ˆ
mvZ
AR
mv
EE
Effective Restitution Coefficient
• Lubrication effect is actually a kind of damping effect, causing kinetic energy dissipation during both approaching and separating stage
• Restitution coefficient can be regarded as a criterion for evaluating the lubrication effect on collision process
St
Ste e
*
1
2
0
6 R
mvSt
mStokes Number:
Ratio of particle inertia
to viscous force
Critical Stokes Number
2
**
6 R
mvSt c
cm
2
**
6 R
mvSt e
em
• vc* is called “critical contact velocity”. If initial velocity v0 <vc*, particles
cannot make contact in the approaching stage
• ve* is called “critical escape velocity” . If v0 <ve*, particles cannot escape
from the lubrication effect area and will stop during the separation stage
*
2
1e
cc St
St
eee
ec: restitution coefficient due
to deformation. Suppose ec=1
Calculated examples and discussions Case 1: FCC
Under the same approaching velocity v0, the effect of lubrication force on larger particles is less significant than on smaller particles
surface roughness: 1/10 R
Case 1: FCC w/ different roughness
Collisions with Stokes numbers less than Ste* result in a
restitution coefficient to be zero, consequently causing cluster and agglomeration to occur.
Calculated examples and discussions
Ste*
The independent effects of particle size and approaching velocity on the coefficient of restitution can be included in the consideration of Stokes numbers
Calculation examples and discussions Case 2: GB
Consideration of non-continuum fluid weakens the lubrication effect and thus increases the values of the restitution coefficient
GB, surface roughness:
1/1000 R
Case 3: smooth GB
Lubrication effect is most significant in case 3 since particles can approach much more closely and the effect of non-continuum fluid is more significant.
Calculation examples and discussions
Concluding Remarks
By numerically extending classical lubrication theory into gas-solid systems, semi-empirical expressions for lubrication force are proposed.
Evaluation of lubrication effect on collision process are made in terms of restitution coefficient.
Stokes Paradox is avoided by considering surface roughness, non-continuum fluid and van der Waals force.
Further research should be aiming at incorporating lubrication force and an effective restitution coefficient into DEM simulation in the near contact area.
year
Cap
acit
y i
n w
orl
d t
ota
l [%
]
year
Cap
acit
y i
n w
orl
d t
ota
l [%
]
From Burton to Fluid Cat. Cracking
Chemical Engineers’ Unforgettable
Memory
The FCC Development (1940-50)