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7/30/2019 S3 0 Kuipers
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MULTI-SCALE MODELING OF DENSE
PARTICLE-LADEN FLOWS
J.A.M. KUIPERS
M.A. VAN DER HOEF
M. VAN SINT ANNALAND
N.G. DEEN
EINDHOVEN UNIVERSITY OF TECHNOLOGY
FACULTY OF CHEMICAL ENGINEERING AND CHEMISTRY
MULTIPHASE REACTORS GROUP
THE NETHERLANDS
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DENSE GAS-PARTICLE FLOWS
shifting sands (Tanzania)
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DENSE GAS-PARTICLE FLOWS
clusters in co-current vertical gas-solid flows
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DENSE GAS-PARTICLE FLOWS
clusters in co-current vertical gas-solid flows
e = 1.0
µ = 0.0
e = 0.96
µ = 0.24
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DENSE GAS-PARTICLE FLOWS
fluidized bed family of gas-solid contactors
1: bubbling bed
2: turbulent bed
3: circulating bed
4: riser
5: downer
6: lateral staged bed
7: vertical staged bed
8: spouted bed
9: floating bed 10: twin bed
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POLY-DISPERSE DENSE GAS-PARTICLE FLOWS
fluidized bed spray granulation
Prof. Stefan Heinrich (TUHH)
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DENSE GAS-PARTICLE FLOWS & MODELLING
• GAS-PARTICLE SYSTEMS
+ very broad range of applications and related equipment geometries
+ occurence of both dilute and dense particle-laden flows (poly-disperse)
+ display a great variety of (very complex) flow structures
+ flows are inherently unsteady (bubbles, clusters)
• IMPLICATIONS FOR MODELLING
+ development of a single universal model far to ambitious (irrealistic)
+ multi scale approach is appropriate
+ closures for gas-particle and particle-particle interaction required
+ model should account for the transient nature of the flow
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MULTI-SCALE MODELLING
Van der Hoef et al., Annu. Rev. Fluid M., 2008
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MULTI-SCALE MODELLING
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LATTICE BOLTZMANN MODEL
• BASIC FEATURES
+ fictitious particles propagate in a three-dimensional (3D) lattice and
collide at surface of real particles (or walls): momentum exchange
+ particle-particle collisions can be accounted for (hard sphere model)
• ADVANTAGES
+ all details of the flow field are obtained: drag closure is computed
• DISADVANTAGES
+ number of particles is (very) limited (CPU limitations)
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RESULTS OF LATTICE BOLTZMANN MODEL
static array of bi-disperse particles at low Re p
example of initial particle
configuration for
a bi-disperse system
generated with a
Monte Carlo procedure
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RESULTS OF LATTICE BOLTZMANN MODEL
static array of bi-disperse particles at low Re p
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RESULTS OF LATTICE BOLTZMANN MODEL
static array of particles with log-normal PSD
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RESULTS OF LATTICE BOLTZMANN MODEL
static array of particles with log-normal PSD
Re=0.1 Re=500
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RESULTS OF LATTICE BOLTZMANN MODEL
final drag closure for mono-disperse and poly-disperse particles
good fit (deviation less then 8%) of basic LB simulation data
generated over wide range of εg and Re
strictly valid for homogeneous arrays of particles
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IB-DP MODEL
• FEATURES
+ Eulerian grid and Lagrangian force points on solid boundaries
• ADVANTAGES
+ all details of continuous phase flow field are captured
+ arbitrary shape of solid particles can be accounted for
• DISADVANTAGES
+ IB-DP simulations are CPU-demanding (especially in 3D)
+ limited to relatively small number of solid bodies (typically 103)
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RESULTS OF IB-DP MODEL
single and simple cubic array of particles (3D)
Re p=100 Re p=1
1003 Eulerian grid
N=(d p/h)=20
Dimensionless drag
F=10.9 (computed)
F=10.2 (analytical)
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RESULTS OF IB-DP MODEL
fluidization of 1296 spherical particles (3D)
Fluid phase Density 1216 kg/m3
Viscosity 0.1 kg/(m.s)
Solid phase
Density 8000 kg/m3
Particle diameter 0.005 m
Collision parameters 0.9, 0.3, 0.10 (-)
U mf 1.2 cm/s
U t 40 cm/s
U 0 8.0 cm/s
Grid 400x12x800 (-)
Grid size 0.5 mm
∆t 0.2 ms
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RESULTS OF IB-DP MODEL
fluidization of 1296 spherical particles (3D)
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RESULTS OF IB-DP MODEL
fluidization of 1296 spherical particles (3D)
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DISCRETE PARTICLE MODEL
• BASIC FEATURES
+ individual particles are tracked in the computational domain taking
into account particle-particle and particle-wall encounters (collisions)
• ADVANTAGES
+ incorporation of arbitrary distribution of particle properties is easy
+ detailed particle-particle interaction models can be incorporated
• DISADVANTAGES
+ number of particles is (very) limited (CPU limitations)
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RESULTS DISCRETE PARTICLE MODEL
bubble formation in pseudo 2D bed
W=0.30 md p=1.5 mm
ρs=2526 kg/m3
U b=0.85 m/s
U j=15.0 m/s
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RESULTS DISCRETE PARTICLE MODEL
spouted bed
“CAPABILITIES” OF DPM
(COLLISION PARAMETERS!!!)
(Link et al., CES, 2005)
REGIME PREDICTION
GAS BUBBLES BEHAVIOUR
PRESSURE FLUCTUATIONS
SOLIDS MOTION
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RESULTS DISCRETE PARTICLE MODEL
spouted bed
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RESULTS DISCRETE PARTICLE MODEL
spouted bed
/ 16.0 / 1.2sf mf bf mf u u u u= ↔ =
particle configuration particle velocity map
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RESULTS DISCRETE PARTICLE MODEL
spouted bed
experimental simulated
/ 16.0 / 1.2sf mf bf mf u u u u= ↔ =
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RESULTS DISCRETE PARTICLE MODEL
spouted bed
DPM PEPT
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1 bar 2 bar 4 bar 8 bar 16 bar 32 bar 64 bar
RESULTS DISCRETE PARTICLE MODEL
effect of operating pressure
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RESULTS DISCRETE PARTICLE MODEL
effect of operating pressure
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Porosity
P D F
1 bar
2 bar
4 bar
8 bar
16 bar
32 bar
Dense emulsion Intermediate Bubbles
p p
p
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RESULTS DISCRETE PARTICLE MODEL
Courtesy: Prof. Heinrich (TUHH)
• wide residence time distribution
• stochastic flow profile
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RESULTS DISCRETE PARTICLE MODEL
Courtesy: Prof. Heinrich (TUHH)
• wetting cycles
• narrow residence time distribution
• stationary flow profile in spray zone
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TWO-FLUID MODEL BASED ON KINETIC THEORY
• BASIC FEATURES
+ statistical mechanical description of particle-particle encounters
• ADVANTAGES
+ based on more fundamental description of particle-particle interaction
compared to classical two-fluid model and the discrete bubble model
• DISADVANTAGES
+ incorporation of different particle properties (polydispersity) is quite
difficult and leads to (many) additional equations (CPU limitations)
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TWO-FLUID MODEL BASED ON KINETIC THEORY
• DEFINITION OF PARTICLE VELOCITIES
+ instantaneous particle velocity:
+ ensemble averaged particle velocity:
+ fluctuating particle velocity:
• DISTRIBUTION OF FLUCTUATING VELOCITIES (KTG)
vcC −=
v
c
)2
exp()2
(2
2/3
kT
mC
kT
mn f −
π
= Maxwell’s velocity distribution
Boltzmann constantnumber density
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RESULTS TWO-FLUID MODEL
bubble formation: 15 cm bed
W=0.15 m
d p=1.5 mm
ρs=2526 kg/m3
U b=0.85 m/s
U j=15.0 m/s N p=120000
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RESULTS TWO-FLUID MODEL
bubble formation: 30 cm bed
W=0.30 m
d p=2.5 mm
ρs=2526 kg/m3
U b=1.20 m/s
U j=20.0 m/s N p=60000
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TWO-FLUID MODEL BASED ON KINETIC THEORY
Geldart A type fluidization
grid size
0.8 mm
grid size0.2 mm
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SEGREGATION IN BIDISPERSE SYSTEMS
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SEGREGATION IN BIDISPERSE SYSTEMS
experimental technique
DIGITAL IMAGE ANALYSIS
USING TWO PARTICLE TYPES
WITH DIFFERENT COLORS
COLOR INTENSITY MEASURE
FOR PARTICLE FRACTION
CAREFUL CALLIBRATION
ESSENTIAL
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RESULTS DPM MODEL
segregation in bidisperse systems
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RESULTS DPM MODEL
segregation in bidisperse systems
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RESULTS DPM MODEL
segregation in bidisperse systems
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MULTI-FLUID MODEL (MFM) BASED ON KINETIC THEORY
• BASIC FEATURES OF CURRENT MFM
all particle species are assumed to possess a nearly Maxwellian
velocity distribution with respect to the particle mixture velocity
and the particle mixture granular temperature
in the corresponding equilibrium situation (no external forces and
absence of gradients in porosity, velocity and granular temperature)
interaction between different particle species already exists
differences in the mean velocities and granular temperatures of the
particle species result from higher order perturbation terms in theChapman-Enskog solution method of the Boltzmann equations
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SEGREGATION IN BIDISPERSE SYSTEMS
simulation with multi-fluid model
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RESULTS MFM MODEL
segregation in bidisperse systems
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RESULTS MFM MODEL
segregation in bidisperse systems
New MFMOld MFM
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RESULTS MFM MODEL
segregation in bidisperse systems
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CONCLUSIONS
• MULTI –SCALE SIMULATION APPROACH
+ closures for gas-particle and particle-particle interaction are critical
+ LBM provides closures for gas-particle interaction
+ DPM essential………but should be viewed as a “learning model”
+ incorporation of friction in kinetic theory models (encounter model)
• EXPERIMENTAL VALIDATION
+ important role for non-invasive monitoring (CARPT, MRI, PEPT)
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FUTURE WORK
• MULTI-SCALE SIMULATION APPROACH
+ readily applicable to non-spherical particles
+ extension to mass and heat transport (ERC Advanced Grant)
+ incorporation of liquid phase (droplets) (Prof. Heinrich TUHH)
+ filtered two-fluid models (Geldart A)
+ other multiphase flows (gas-liquid + gas-liquid-solid)
+ hybrid models (particle based + continuum)
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EXTENSION TO BUBBLY FLOW
O(105) bubblesO(102) bubbles
( ),
( , )1 25.88 exp( / 2)
D g
g l
D
C Eo Eo
C
ε ε ε
∞
= + −
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ACKNOWLEDGEMENTS
PhD’s + PD’s
Renske BeetstraAlbert Bokkers
Maureen van Buitenen
Willem Godlieb
Matthijs Goldschmidt
Bob HoomansJeroen Link
Daneshwar Patil
Junwu Wang
Mao Ye
Funding
Akzo NobelCorus
DSM
FOM
NWO-CW
SabicShell
STW
Unilever
Yara