Inter-particle force and stress models for wet and dry particulate flow

Inter-particle force and stress models for wet and
dry particulate flow at the intermediate flow regime
Xi Yu1, Raffaella Ocone3, Sotos Generalis2, Yassir Makkawi1
1 Chemical Engineering & Applied Chemistry, Aston University, Birmingham B4 7ET, UK
2 Mathematics, Aston University, Birmingham B4 7ET, UK
3 Chemical Engineering, Heriot-Watt University, Edinburgh EH14 4AS, UK
Outlines
1.
2.
3.
4.
5.
Granular material and regime map of granular flow
Objectives and big picture
Dry particle flow
Slightly wet particle flow
Summary and Acknowledgement
What’s granular material?
Granular material -a collection of a large number of discrete solid particles
may behave an elastic-solid or a fluid
Some examples of granular materials are nuts, coal, sand, rice, coffee, corn
flakes, fertilizer and ball bearings.
Regime map In granular flow
Fluid-like behaviour
Rapid flow regime
Binary-collision
KTGF (kinetic theory
of granular flow)
Solid-like behaviour
Particle packingEnduring contact
Coulomb frictional law
Intermediate regime of granular flow
Coexistence of frictional and collisional stress in dry flow
Less understood?
Regime map In granular flow
Friction
ignored
Continuous
shear field
(Tardos er al, 2003)
Three regimes are identified using a dimensionless shear rate
In a sense, shear rate is gradient of velocity in granular material
Example of problems at intermediate dry flow
Dense bubbling fludised bed
Particle-particle friction leading to limited bed
expansion, increased bubble size and solid slugging
(Makkawi et al, 2006)
Solid volume fraction
Pneumatic conveying
Excessive particle-wall friction leading
to pressure drop, wear and line blockage
(McGlinchey et al, 2012)
Solid volume fraction
Example of problems at intermediate wet flow
Coal/biomass gasification
Surface oil/tar leading to
agglomeration and sever
Degradation and fludisation
Simple Gasification Process Graphic
(Gas Technology Institute, Illinois, US)
Fluidised bed coating
Liquid presence leading to
undesired Agglomeration
and particles segregation
Schemes of fluidized bed spray granulator
(Fries et al, 2011)
Exothermic fludised reactor
Temperature control by liquid
injection leading to dead zones
And overheating at various
Parts Of the reactor
Fluidized Bed Systems, hitachi
Zosen Inova, Switzerland)
What’s popular approach to model dense granular flow?
Solid phase:
continuity equation:
momentum:
Gas phase:
continuity equation:
momentum:
Energy equation (granular temperature):
Well developed KTGF (kinetic theory of granular flow)
Intermediate stress in CFD commercial codes
solids shear viscosity
No friction
Particle packingEnduring contact
How to present friction shear stress in intermediate regime of
granular flow?
?
Friction
fluid shear resistance
Objective and big picture
1. How to incorporate shear stress in intermediate particle dry
flow?
2. How to incorporate shear stress in intermediate and slightly
wet particle flow?
user defined function (UDF)
Formula
Fluent (platform)
Experimental observation
ECT
Validate
Predicted flow behavior
(Solid concentration distribution)
Dry particle flow
Experiment results (ECT) in dry particle-flow
(Makkawi et al, 2006)
Solid volume fraction
ECT (electrical capacitance tomography) is a diagnostic imaging tool in the medical field
Unified solid stress model- Tardos et al (2003)
Simpler expression
Average particle stress
Standard deviation of the strain rate
Energy dissipation
Solid phase momentum:
Energy equation (granular temperature):
Specific shear stress（pascal）at the wall
user defined function written in C
language (approx. 600 lines)
Model setup for numerical experiment
Diffusion of granular temperature
Drag
Turbulence
Lun et al.
Syamlal and O’Brian
K-epsilon
Boundary/operating condition
Value
Gas inlet velocity, Ug[m/s]
0.26,0.54,0.8
Gas density, ρg [kg/m3]
1.2
Particle-particle restitution
0.9
Gas dynamic viscosity [kg/(m.s)]
1.8x10-5
Particle-wall restitution
0.9
Gas outlet pressure, Pgo [Pag]
0
Johnson et al
Apparent particle density, ρP
[kg/m3]
2500
Frictional Viscosity
Bulk viscosity
Lun et al
Solids pressure
Lun et al
Radial distribution function
Lun et al
Specularity coefficient
0.2
20
Particle size, Ds [µm]
350
14.3-18.1
Tardos et al (2003) friction model
0.61
0
Time averaged
Fluent friction model
Fluent KTGF without friction model
0.61
0.61
0
0
Time averaged
Time averaged
Tardos et al (2003) friction model
0.61
0
Time averaged
Fluent friction model
Fluent KTGF without friction model
0.61
0.61
0
0
Time averaged
Time averaged
Tardos et al (2003) friction model
0.61
0
Time averaged
Fluent friction model
Fluent KTGF without friction model
0.61
0.61
0
0
Time averaged
Time averaged
Prediction of bed height
Tardos et al (2003) friction model
Fluent friction model Fluent KTGF without friction model
Experimental and simulated bed height of gas velocity
Slightly wet particle flow
(on-going work)
In slightly wet and dense systems
Figure: the different states of saturation of liquid-bound granules
( Newitt and Conway-Jones,1958; York and Rowe,1994)
liquid saturation higher
Liquid bridges
merge
Frictional contact
continuous fluid network
Fluid shear resistance
Collisional contacts dissipate energy in both the liquid bridges
and particles.
Experimental results(ECT) in slight wet flow
air
packed particles
conventional
bubbling
0
bubbles splitting
0.03
0.06
solid slugs
slugging
0.09
0.12
Types of two-phase system
0.15
liquid weight % (kg/kg dry bed)
three-phase system: slightly wet system
Particle-particle interactions in slightly
wet suspension Hypothesis
Solid concentration
In wet particles flow, direct
solid-solid contacts are limited
Rapid flow
Transient contacts
dominated by
collisional stresses
Dense-intermediate flow
Enduring contacts
dominated by liquid
viscous stresses
Quasi-static flow
Enduring contacts
dominated by
particle frictional
stresses
Liquid bridge Stresses
 For this, we may start from the interparticle
force at single particle level:


3
u
F liquid   liquidd p2
8
h
Approach velocity
R
Interparticle gap
Normal stress
Equivalent shear viscosity
• For this, it is required to determine
the force per unit area:

Pliquid
h
3
2 u  6 s 
  liquidd p  3 
8
h  d 
• Analogue to Coulomb friction law
23
 wet 
2 Pliquid
S
“lubrication” coefficient
Conclusion and ongoing work
An unified shear stress (Tardos et al, 2003) model in 3D has been
implemented in numerically studying a bubbling fluidised bed and its
predicted results (solid distribution, bed height) have been compared with
experimental data (ECT) and two other stress models (Fluent friction model，
Fluent KTGF without friction model).
Ongoing work will be focused on developing a shear stress model for slightly
wet particle flow. The validation of the model will be done using
experimental data (ECT) in a fluidised bed.
Acknowledgement
Aston University
Dr Yassir T. Makkawi
Dr Sotos Generalis
Heriot Watt University
Professor Raffaella Ocone
Grant funding from
The Leverhulme Trust
(Makkawi et al, 2006)