modelling of multiphase flows - from micro-scale to macro ... · micro scale meso scale macro scale...

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



Conclusions

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.




Conclusions

VARIOUS LENGTH AND TIME SCALES

eddy

particle

interactioncluster−turbulencewake

meso scaleturbulent structures

clustersbig

macro scalemeso scalemicro scale




Conclusions

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




Conclusions


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/




Conclusions


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




Conclusions


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′




Conclusions


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.




Conclusions


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




Conclusions


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




Conclusions


FLOW AROUND OBJECTS: IBM METHOD




Conclusions


LARGE-SCALE LAGRANGIAN PARTICLE MODELLING

Particles and gas velocity

Particles and averaged volume fraction




Conclusions


FLUIDIZED BED MODELLING

U = 2Umf , NP = 50, 000,∆t = 2 · 10−2 s




Conclusions


PARTICLE FLOW MODELLING

Particle flow through tubes

Fluidized Bed 3Umf

WursterBed1

WursterBed2

Fines




Conclusions


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




Conclusions


PARTICLE PACKING FOR CHROMATOGRAPHY

OpenFoam simulations of the emptying of a 3 dimensionalhopper.




Conclusions


PARTICLE PACKING FOR CHROMATOGRAPHY

Particle packing due to flow

and gravity in a 5 mm wide column.




Conclusions


MODELLING OF INTERFACIAL FLOWS

Youngs Method (*)

Flux Corrected Transport

Lagrangian PLIC (*)

CICSAM

Inter-Gamma Scheme

Experimental result




Conclusions


RAYLEIGH-TAYLOR INSTABILITY

t = 0s t = 0.2s t = 0.4s t = 0.6s t = 0.8s t = 0.95sMultiFlow, CICSAM




Conclusions


IMPROVING COALESCENCE MODELS




Conclusions


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




Conclusions


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




Conclusions


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




Conclusions


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




Conclusions



Separation, Re=500 10 spheres interacting with the flow




Conclusions



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




Conclusions


FULLY IMPLICIT IBM: FLOW AROUND PARTICLES

Solution after 1 iteration!




Conclusions

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.


modelling of multiphase flows - from micro-scale to macro ... · micro scale meso scale macro scale...

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