MODELLING OF MULTIPHASE FLOWS
FROM MICRO-SCALE TO MACRO-SCALE
Department of Applied Mechanics,Chalmers University of Technology,
Gothenburg, Sweden.
Siamuf Seminar October 2006
Group PhilosophyProjects and People
MultiFlowPhD students
Conclusions
OUTLINE
1 GROUP PHILOSOPHY
2 PROJECTS AND PEOPLE
3 MULTIFLOW
TheoryStatusExamples
4 PHD STUDENTS
Rasmus HemphVinay GopalaAldo BenavidesAndreas MarkJose Oliveira
5 CONCLUSIONS
Multiphase Flow Modelling Chalmers
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GROUP PHILOSOPHY
Understanding physical behaviour at various scales.
Combining knowledge obtained at one scale to improvemodelling at another.
Combination of fundamental projects and applied projects.
Employ MultiFlow (inhouse code), OpenFoam (OpenSource), Fluent, CFX.
Multiphase Flow Modelling Chalmers
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Conclusions
VARIOUS LENGTH AND TIME SCALES
eddy
particle
interactioncluster−turbulencewake
meso scaleturbulent structures
clustersbig
macro scalemeso scalemicro scale
Multiphase Flow Modelling Chalmers
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PROJECTS AND PEOPLE
Model and Solver Development - Berend van Wachem
Particle packing for Chromatography - Rasmus Hemph
Modeling and validation of Liquid-Liquid flows - VinayGopala
Numerical simulation of turbulent gas-solid two-phaseflows - Aldo Benavides
Direct numerical simulation of gas-solid flows - AndreasMark
Direct numerical simulation around objects - Jose Oliveira
Multiphase Flow Modelling Chalmers
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Conclusions
TheoryStatusExamples
MODEL AND SOLVER DEVELOPMENT: MULTIFLOW
MultiFlow is a fully coupled, parallel code for various setsof governing equations describing multiphase flows:
Eulerian-Lagrangian particle modelling.Volume of Fluid modelling.Direct Numerical Simulation around objects (IBM).Eulerian-Eulerian is underway.
Most algorithms employed to solve multiphase governingequations are based on single phase ideas and aretherefore time-consuming.
MultiFlow employs analytical weighting of the momentumequations at cell faces. The resulting equations areemployed to solve the continuity equation.
http://www.multiflow.org/
Multiphase Flow Modelling Chalmers
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Conclusions
TheoryStatusExamples
MULTIFLOW APPROACH I
The approach is shown on single phase type equations, forexample, used for VOF modelling.
EQUATIONS
∂
∂x i ui = 0
ρ∂u j
∂t+ ρ
∂
∂x i
(u iu j
)= −
∂p∂x j +
∂τij
∂x i − Ru j− Sj
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MULTIFLOW APPROACH II
DISCRETIZED EQUATIONS
By discretizing these equations, we can determine analyticalexpressions for the variables at both cell centers as well as facecenters.
∑
faces
u if s
if = 0
[1 + ce′ d (uj)
e′
]u j
e′ = u je′ − d (uj)
e′
[∂p∂x j
]
e′
+ ce′ d (uj)e′ u j ,O
e′
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TheoryStatusExamples
MULTIFLOW APPROACH III
SOLVER
The complete set of equations are put into matrix form, and theinverse of this matrix determines the solution.
... ... ... ...
... ... ... ...
... ... ... ...
... ... ... ...
... ... ... ...
... ... ... ...
u1
u2
u3
pα
. . .
=
RHu1
RHu2
RHu3
RHp
RHα
. . .
Solution is directly presented in unknowns; velocity, pressure,volume fraction, etc.
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TheoryStatusExamples
STATUS OF MULTIFLOW
⊲ VOF, Levelset⊲ FCT, Youngs, PLIC, CICSAM, Inter Gamma⊲ Mass transfer, Improve model for surface tension
⊲ Eulerian-Lagrangian⊲ Size distributions, LES, drag models⊲ Non-spherical objects, attrition, agglomeration.
⊲ Immersed Boundary Method⊲ Arbitrary shapes, non-stationairy bodies⊲ Deformable bodies, LES/RANS(?)
⊲ Eulerian-Eulerian⊲ Kinetic Theory, Turbulence Modulation
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LID DRIVEN CAVITY
To validate the approach, the solver is compared with the liddriven cavity data of Ghia et al (1982) (Results of Jose)
Re=100
Re=400
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TheoryStatusExamples
FLOW AROUND OBJECTS: IBM METHOD
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TheoryStatusExamples
LARGE-SCALE LAGRANGIAN PARTICLE MODELLING
Particles and gas velocity
Particles and averaged volume fraction
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TheoryStatusExamples
FLUIDIZED BED MODELLING
U = 2Umf , NP = 50, 000,∆t = 2 · 10−2 s
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PARTICLE FLOW MODELLING
Particle flow through tubes
Fluidized Bed 3Umf
WursterBed1
WursterBed2
Fines
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TheoryStatusExamples
VOF MODELLING (VINAY)
t = 0 t = 14P t = 5
8P
t = P
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20.04
0.045
0.05
0.055
0.06
Time (s)
Hei
ght a
t the
left
face
(m
)
PLICTheoretical
Period
0 0.5 1 1.5 2 2.5−0.01
−0.005
0
0.005
0.01
0.015
0.02
Time(s)E
rror
(%
)
PLIC
Error
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Rasmus HemphVinay GopalaAldo BenavidesAndreas MarkJose Oliveira
PARTICLE PACKING FOR CHROMATOGRAPHY
OpenFoam simulations of the emptying of a 3 dimensionalhopper.
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Conclusions
Rasmus HemphVinay GopalaAldo BenavidesAndreas MarkJose Oliveira
PARTICLE PACKING FOR CHROMATOGRAPHY
Particle packing due to flow
and gravity in a 5 mm wide column.
Multiphase Flow Modelling Chalmers
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Conclusions
Rasmus HemphVinay GopalaAldo BenavidesAndreas MarkJose Oliveira
MODELLING OF INTERFACIAL FLOWS
Youngs Method (*)
Flux Corrected Transport
Lagrangian PLIC (*)
CICSAM
Inter-Gamma Scheme
Experimental result
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Rasmus HemphVinay GopalaAldo BenavidesAndreas MarkJose Oliveira
RAYLEIGH-TAYLOR INSTABILITY
t = 0s t = 0.2s t = 0.4s t = 0.6s t = 0.8s t = 0.95sMultiFlow, CICSAM
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Rasmus HemphVinay GopalaAldo BenavidesAndreas MarkJose Oliveira
IMPROVING COALESCENCE MODELS
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Rasmus HemphVinay GopalaAldo BenavidesAndreas MarkJose Oliveira
TURBULENT GAS-SOLID FLOWS
A carrier fluid (gas-phase) which is loaded with particles(solid-phase)
An turbulent interstitial fluid is present.
Applications: fluidized beds, inhalers, pneumatic transportof powders, dispersion of pollutants, so forth
Need to model the interaction (including turbulence)between phases
Multiphase Flow Modelling Chalmers
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Conclusions
Rasmus HemphVinay GopalaAldo BenavidesAndreas MarkJose Oliveira
EULERIAN OR TWO-FLUID MODEL
EQUATION SET
∑
k
αk = 1
∂αk
∂t+ ∇ ·
(αk
~Uk
)= 0
∂
∂t
(ρkαk
~Uk
)+ ∇ ·
(ρkαk
~Uk~Uk
)= ∇ ·
[αk
(¯Tk + ¯Rk
)]+
− αk∇P + ~Mk + ρkαk~Bk
∂
∂t(ρkαkKk ) + ∇ ·
(ρkαk
~UkKk
)=
∇ ·
[αk
~Jk
]+ αk (Pk − ǫk ) + Ek
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Rasmus HemphVinay GopalaAldo BenavidesAndreas MarkJose Oliveira
FULLY DEVELOPED TURBULENT PIPE FLOW
r
U
V
g
z
dz
dP
R
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.2
0.4
0.6
0.8
1
1.2
1.4
rR
GasSolidsGas (experiments)Clear gas
Normalized mean velocity profiles, comparison with Tsuji et al. data
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Rasmus HemphVinay GopalaAldo BenavidesAndreas MarkJose Oliveira
SECOND ORDER IMPLICIT IBM
The IB is a triangulation of anarbitrary surface
Reversed velocity field overthe IB
An implicit immersedboundary condition constrainsthe velocity of the fluid to theIB velocity exactly at the IB
Implemented for both movingand stationairy IBs with threeway coupling
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Rasmus HemphVinay GopalaAldo BenavidesAndreas MarkJose Oliveira
SECOND ORDER IMPLICIT IBM
Separation, Re=500 10 spheres interacting with the flow
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Rasmus HemphVinay GopalaAldo BenavidesAndreas MarkJose Oliveira
SECOND ORDER IMPLICIT IBM
10−2
10−1
100
101
102
10−1
100
101
102
103
104
Re
Cd
Cd value for medium Re
Immersed Flow 1Immersed Flow 2Stoke DragShiller and NaumannLappleLangmuir and Blodgett
Drag coefficient for a sphereFlow around a non-spherical object
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Rasmus HemphVinay GopalaAldo BenavidesAndreas MarkJose Oliveira
FULLY IMPLICIT IBM: FLOW AROUND PARTICLES
Solution after 1 iteration!
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CONCLUSIONS
Multiphase Flow Modelling: approach at various scales.
Couple the knowledge obtained at the various scales.
Work on physical modelling from a fundamental and anapplied viewpoint.
Modelling work done in MultiFlow, OpenFoam, Fluent,CFX.
Development of novel solver and physics: MultiFlow.
Multiphase Flow Modelling Chalmers