computational fluid mechanics of gas-solid systems€¦ · + gas phase flow field + drag force on...
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Chemical Engineering and Chemistry, Multiscale Modeling of Multiphase Flows
Frank Peters
COMPUTATIONAL FLUID MECHANICS OF GAS-SOLID SYSTEMS
Dense Gas-Particle Flowsfluidized 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
JMBC Particle Technology course - CFD fluid-solid systems2
Dense Gas-Particle Flowsclusters in co-current vertical gas-solid flows
JMBC Particle Technology course - CFD fluid-solid systems3
e = 1.0m = 0.0
e = 0.96m = 0.24
Dense Gas-Particle Flows with Coupled Mass Momentum and Heat Transport (spray granulation)
JMBC Particle Technology course - CFD fluid-solid systems4
Prof. Stefan Heinrich (TUHH)
Multiscale Modeling
JMBC Particle Technology course - CFD fluid-solid systems5
CFD-DEM
CFD-DEM
• grid cell size > particle diameter
• particle unresolved
• needs fluid-particle closure relations
DNS
• grid cell size ≪ particle diameter
• particle resolved
• no-slip boundary conditions at particle surface
JMBC Particle Technology course - CFD fluid-solid systems6
CFD-DEM vs DNS
or
Computational Fluid Dynamics
Discretize Navier-Stokes equation
Spatial discretization
• Finite difference on Cartesian staggered grid
• Viscous/diffusion terms: central differencing
• Convective term: second order total variation diminishing
Temporal discretization
• Convective terms explicit
• Viscous term and source term (semi) implicit
• Fractional step discretization: pressure correction by solving Poisson equation
JMBC Particle Technology course - CFD fluid-solid systems7
xy
z
scalar variables
x-velocity component
y-velocity component
z-velocity component
𝜙𝑊 𝜙𝐶 𝜙𝑒
𝜉
𝜙𝑆
𝜙𝑁
𝑥𝐵
solid
fluid
Particle-resolved Direct Numerical Simulation
Grid size ≪ particle size
After discretization general matrix equation for unknowns 𝜙𝑖: 𝑎c𝜙c = 𝑛𝑏 𝑎𝑛𝑏 𝜙𝑛𝑏 + 𝑏𝑐
Immersed Boundary Method: eliminate nodes inside solid by extrapolation
𝜙w =2
1 − 𝜉)(2 − 𝜉𝜙𝐵 −
2𝜉
1 − 𝜉𝜙C +
𝜉
2 − 𝜉𝜙E
JMBC Particle Technology course - CFD fluid-solid systems8
𝜉
solid
𝑑1 𝑑2
fluid 𝑛
𝑊 𝐶 𝐸
Results DNS/IB Modeltransport phenomena in packed bed reactors: DEM generated beds
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Results DNS/IB Model transport phenomena in packed bed reactors: velocity profiles (N=6)
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Red=1 Red=500
mm/s
phase fractions (left) and axial velocity map (right) for a packed bed of spheres with a diameter of 4 mm
Results DNS/IB Modelcomparison with experiment (MRI flow imaging)
JMBC Particle Technology course - CFD fluid-solid systems11
Rep = 50
radial porosity profile (left) and axial velocity profile (right)for a packed bed of spheres with a diameter of 5 mm
Results DNS/IB Modelcomparison with experiment (MRI flow imaging)
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Results DNS/IB Modeltransport phenomena in packed bed reactors: temperature profiles
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Results DNS/IB Modeltransport phenomena in packed bed reactors: temperature profiles
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Results DNS/IB Modeltransport phenomena in packed bed reactors: wall-to-bed heat transfer
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Results: Wet collisions
Snapshot sequence of a spherical particle (1.74 mm) impacting on a wet plate with 400 µm liquid layer at an impact velocity of 1.13 m/s: experimental measurements (top) and simulation
results (bottom).
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Results: Wet collisionscollision of particle with a flat plate with thin liquid layer
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Results: Wet collisionscollision of particle with a flat plate with thin liquid layer
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Particle dynamics
Translation of center-of-mass
Rotation around c.o.m.
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generallya complexproblem
Forces and Torques on Particles
Fluid-induced forces & torques
Gravity force
Direct contact forces & torques
Other particle-particle forces & torques, such as Van der Waals and charge interactions
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Contact Models
Contact model = a model specifying the forces and torques on granular particles due to direct collisions
Usually approximated as pair sums:
• Short ranged interactions
• Momentum is conserved
• Energy is not conserved (or lost as heat): dissipation
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Contact Forces: Soft Sphere Model
• Spheres can partly overlap (up to few %)
• Normal spring and dashpot
• Tangential spring and dashpot
• Friction slider forstick slip transition
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Fluid-particle Forces in DNS
• Forces exerted on particle by fluid
• Integrate computed stresses and pressure on particle surface
𝐅𝑓𝑙𝑢𝑖𝑑,𝑖 = 𝛕 ⋅ 𝐧 − 𝑝 𝐧 𝑑𝐴
• Use values defined on staggered grid to approximate this integral
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Results: Particle-resolved DNS Fluidized Bed
Pseudo-2D fluidized bed with 3000 particles
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Sim.
Exp.
Dynamics in a Small Pseudo-2d Fluidized BedFlow regime
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Dynamics in a small pseudo-2D fluidized bedTime-averaged solids flux
PIV/DIAIBM
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Dynamics in a small pseudo-2D fluidized bedGranular temperature
PIVIBM
Characteristic frequency𝑓 = 2 ±0.3 s-1
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Multiscale approach: DNS to CFD-DEM
Clossure relations obtained from DNS
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Drag Correlations
DNS: measure average drag force as a function of
solids volume fraction f
particle Reynolds number Re
non-dimensionalize with Stokes drag in dilute limit
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Drag correlation from DNS/IBM
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𝐹𝑑 𝜙, Re = 10𝜙(1 − 𝜙)−2+ 1− 𝜙 2 1 + 1.5 𝜙
+Re ⋅ 0.11𝜙 1 + 𝜙 − 0.00456 1 − 𝜙 −4 + 0.169 1 − 𝜙 + 0.0644 1 − 𝜙 −4 ∙ Re−0.343
low-Re flow inertial effects
+2.98Re𝑇𝜙 1 − 𝜙−2 mobility effect
with
𝜙: solids volume fraction
Re =𝜌𝑔𝑑𝑝𝑈
𝜇𝑔, Re𝑇 =
𝜌𝑔𝑑𝑝 Θ
𝜇𝑔
O(105) particlesO(102) particles
2 3
1 0.343
2 1/2
3 (1 4 )/22 2
0.064 ( ,Re) with
3 8.4Re10 0.413( ,Re) (1 1.5 )
24 1 10 Res s
ii g i s i g i s i
g s gss g s
g g
dF y y y F y
d
F
Drag in Binary Mixtures of Particlesmultiscale approach to segregation in binary system
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Standard drag model
Bi-disperse drag modelR
ela
tive s
egre
gation (
-)
5 s 10 s 15 s 25 s
Relative size particle class i
Re
lati
ve d
rag
par
ticl
e cl
ass i
+ particle collision dynamics
+ gas phase flow field
+ drag force on particles
+ bed voidage and source terms in momentum equation gas phase
particle moves due to externalforces while collisions withother particles and/or confiningwalls may occur
gas flow
gravity drag
Eulerian cell
CFD-DEM: Key Ingredients
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• Gas phase conservation equations
• Volume-averaged Navier-Stokes equations
+ continuity equation𝜕
𝜕𝑡1 − 𝜙 𝜌𝑔 + 𝛁 ⋅ 1 − 𝜙 𝜌𝑔 𝐮 = 0
+ momentum equation
+ interaction with solids phase
𝜙: solids volume fraction, 𝐒𝑝: - drag of solids on fluid
equations formulated and solved at length scalewhich is large compare to the particle size but small compared to the macroscopic system size
L
CFD-DEM: Gas phase Hydrodynamics
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CFD-DEM: Fluid-particle interactions
fluid-induced force on particle:
• buoyant force
• effective drag force:
• 𝐅𝑓𝑙𝑢𝑖𝑑,𝑖 = −𝑉𝑖𝛁P +𝑉𝑖𝛽𝑖
𝜙𝐮 − 𝐯𝑖
• local gas velocity, 𝐮
• local solid volume fraction, 𝜙
• local inter-phase momentum transfer coefficient, 𝛽
solids-induced force on fluid (action = - reaction)
𝜙 = 𝑖=1
𝑁
𝑉𝑖 𝛿ℎ 𝐫 − 𝐫𝑖
𝑺𝑝 = 𝑖=1
𝑁 𝑉𝑖𝛽𝑖𝜙𝐮 − 𝐯𝑖 𝛿ℎ 𝐫 − 𝐫𝑖 ≝ 𝛽𝐮 − 𝜶
regularized delta function
𝛿ℎ 𝐫 − 𝐫𝑖 𝑑𝑉 = 1
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CFD-DEM: Force Distribution & Velocity Interpolation
Exchange information between Lagrangian points, 𝐫𝑖, and Eulerian mesh, 𝐫𝑘
𝛿ℎ 𝐫 − 𝐫𝑖 →1
𝑉𝑐𝑒𝑙𝑙𝐷 𝐫𝑘 − 𝐫𝑖 ,
𝑘𝐷 𝐫𝑘 − 𝐫𝑖 = 1
Particle-fluid forces at Lagrangian points,𝐫𝑖, distributed to Eulerian grid positions, 𝐫𝑘
𝐒𝑝 𝐫𝑘 =𝟏
𝑉𝑐𝑒𝑙𝑙 𝑖=1
𝑁 𝑉𝑖𝛽𝑖𝜙𝐮 − 𝐯𝑖 𝐷 𝐫𝑘 − 𝐫𝑖
Velocities known at Eulerian positions needed at Langrangian points
𝒖 𝐫𝑖 = 𝑖=1
𝑁
𝒖 𝐫𝑘 𝐷 𝐫𝑘 − 𝐫𝑖
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CFD-DEM: Volume Weighing
Simplest approach: volume weighing = tri-linear interpolation
JMBC Particle Technology course - CFD fluid-solid systems
velocity nodes
particle
xx
x
y
yy
zz
z
2 3
41
6 7
5
y
x
z
xy
z
1
2
3
4
5
6
7
8
( ) (1 )(1 )(1 )
( ) (1 )(1 )
( ) (1 )
( ) (1 ) (1 )
( ) (1 )(1 )
( ) (1 )
( )
( ) (1 )
p x y z
p x y z
p x y z
p x y z
p x y z
p x y z
p x y z
p x y z
D
D
D
D
D
D
D
D
r r
r r
r r
r r
r r
r r
r r
r r
36
Larger scale CFD-DEM simulations
Uses correlations from DNS
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Results CFD-DEMspouted bed
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Results CFD-DEMspouted bed
JMBC Particle Technology course - CFD fluid-solid systems
/ 16.0 / 1.2sf mf bf mfu u u u
particle configuration particle velocity map
39
Results CFD-DEMspouted bed
JMBC Particle Technology course - CFD fluid-solid systems
experimental simulated
/ 16.0 / 1.2sf mf bf mfu u u u
40
Results CFD-DEMspouted bed
JMBC Particle Technology course - CFD fluid-solid systems
“CAPABILITIES” OF CFD-DEM(COLLISION PARAMETERS!!!)
(Link et al., CES, 2005)
REGIME PREDICTION
GAS BUBBLES BEHAVIOUR
PRESSURE FLUCTUATIONS
SOLIDS MOTION
41
Results CFD-DEMmultiple spouts with interaction
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RATIONAL DESIGN OF FLUID BED GRANULATORS:
OPTIMAL DISTANCE BETWEEN SPOUTS ?
Results CFD-DEMmultiple spouts with interaction (?)
JMBC Particle Technology course - CFD fluid-solid systems
simulation experiment
43
Results CFD-DEMeffect of operating pressure
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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
PD
F
1 bar
2 bar
4 bar
8 bar
16 bar
32 bar
Dense emulsion Intermediate Bubbles
pp
p
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Results CFD-DEMeffect of operating pressure
CFD-DEM: Extension To Heat Transfer
Relevance: in many fluidized beds particles catalytic with large heat effects
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CFD-DEM: Extension To Heat Transferlab-scale experiments for validation
Cooling of a hot fluidized bed by injection of a cold gas
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Simulations Experiments
Quantitative Comparison
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CFD-DEM
CFD-DEM Modelling of Heat Transfer in Gas-fluidized Beds
experiment (l) versus simulation (r)
JMBC Particle Technology course - CFD fluid-solid systems
experimental system
CO2 absorption on Zeoliteparticles in pseudo 2D
gas-fluidized bed to representheat liberation due to
exothermicchemical reaction
PIV +DIA
IR-thermography fortemperature distribution
in particulate phase
EXP-IRCO2/N2 (60% CO2)qe=0.15 [g/g]
49
CFD-DEM Modelling of Heat Transfer in Gas-fluidized Bedsexperiment (top) versus simulation (bottom)
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CFD-DEM Modelling of Heat Transfer in Gas-fluidized BedsPDF of particle temperature
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Riser Flowinfluence of particle clusters on mass transfer
CFD-DEM simulations of riser flow
JMBC Particle Technology course - CFD fluid-solid systems
porosity mass fraction
52
Experimental Validation of Lab-scale CFB
JMBC Particle Technology course - CFD fluid-solid systems
CPU
computational domainexperimental setup
53
Experimental Validation of Lab-scale CFBtime-averaged results
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.1 0.2
Hei
ght(
m)
5.55 m/s
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.1 0.2
Hei
ght
(m)
5.95 m/s
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.1 0.2
Hei
ght(
m)
6.35 m/s
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.1 0.2
Hei
ght(
m)
6.74 m/s
1.0
휀𝑔𝑎𝑠
0.4
Solids volume fractions: experiments & simulations
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Wet Collisions In Fluid Bed Granulation Processes
JMBC Particle Technology course - CFD fluid-solid systems
dry wet
air air + water
Particulate flows involving liquid:
• Granulation• Agglomeration• Coating
Particle interactions:
• Different from dry particles• Liquid bridge formation
After
dryin
g
air
Antonyuk et al., 2009
Particuology
CFD-DEM
55
Acknowledgements
JMBC Particle Technology course - CFD fluid-solid systems
Kuipers groupPhD’s + PD’s
Renske BeetstraAlbert Bokkers
Maureen van BuijtenenWillem Godlieb
Zizi LiJeroen LinkSaju OlaofeAmit Patil
Vinayak SutkarYali Tang
Alvaro Carlos VarasJunwu Wang
Mao Ye
Funding
Akzo NobelCorus
DPIDSMERCFOM
NWO-CWSabicShellSTW
UnileverYara
56
Take home messagesMulti-scale approach fruitful
Experimental validation of numerical models important
Particle-resolved DNS can simulate small fluid-particle systems
Provides closure relation for coarser models
CFD-DEM numerical laboratory for fluidized systems
Can simulate lab-scale gas-solid systems
Suited for investigating influence meso-scale structures (bubbles, particle clusters)
Developments: towards realistic (reactor) systems
Heat & mass transfer, wet collisions
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