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Modelling multiphase flows in the Chemical and Process IndustrySimon Lo 9/11/09Simon Lo 9/11/09

Contents

Breakup and coalescence in bubbly flows• Breakup and coalescence in bubbly flows

• Particle flows with the Discrete Element Modelling approachParticle flows with the Discrete Element Modelling approach

• Multiphase flows in pipelines

STAR Konferenz Deutschland 2009, Nürnberg 9-10 Nov. 2009 2

Bubbly flows in pipes and pipe bends


Bubble size distribution models

•Population balance equation:

, , , ,i

i br i br i cl i clDn

B D B DDt

= − + −

•Interfacial area concentration transport (e.g. Ishii’s model):

iDaφ φ= +br clDtφ φ= +


Moments of particle size distribution

• 0th moment is the particle number density:Sn =

• 2nd moment is related to interfacial area density:

∫∞

2 )( SdddPdA

0Sn =

• 3rd moment is related to dispersed phase volume fraction:

∫ ==0

22 )( SdddPdnAi ππ

30

3

6)(

6SdddPdn ππα == ∫

∞

• The Sauter mean diameter is:3

3216SS

Sd

πα

==22 SS π


Transport equation

S∂

•The transport equation:

.( )d br cl

SS s s

tγ

γ

∂+∇ = +

∂u

•Breakup:•Breakup:3

3

0

( ( ) 1)( ) ( )

( )f

br

d N ds nP d d d

d

γγ

−

∞ −= ∫

•Coalescence:

0 ( )br dτ∫

, , 2,0 0

( ) ' ( ) ( )d d d dcl cl cls K S n P d dd P d d dγ

∞ ∞ ′ ′ ′= Δ∫ ∫


Hibiki bubble column (2001)

– Air/Water Cylindrical Test Section50 8 mm ID 3 06 m Height50.8 mm ID, 3.06 m Height

– Ideal Gas Law for Air (297K)– Inlet B.C. at z/D=6

Air/Water Velocities, Void Fraction– Atmospheric Exit (pressure boundary)– Two-dimensional axisymmetricTwo dimensional axisymmetric

simulation (20×150 cells)– Steady state flow

0 3– CL = -0.3– CVM = 0.5– CD = 1.071CD 1.071


Fields distribution

bubble size interfacial area density gas phase volume fractiony g p


Radial void and velocity distributions

2 0

1.5

2.0

)1.5

2.0

s)

0.3

0.4

-)

0.5

1.0

axial velocity profile sim. with star-CD exp. Hibiki et al., 2001

jG=0.321 m/s, jL=0.986 m/s, z/D=53.5

v L (m

/s)

1.0

axial velocity profile sim. with star-CD exp. Hibiki et al., 2001

jG=0.321 m/s, jL=0.986 m/s, z/D=53.5

v G

(m/s

0.1

0.2

a G

(-

voidage radial distribution sim. with star-CD exp. Hibiki et al., 2001

jG=0.321 m/s, jL=0.986 m/s, z/D=53.5

0.0 0.2 0.4 0.6 0.8 1.00.0

r/R (-)

0.0 0.2 0.4 0.6 0.8 1.0

r/R (-)

Void fraction

0.0 0.2 0.4 0.6 0.8 1.00.0

r/R (-)

Liquid velocity Gas velocityVoid fraction Liquid velocity Gas velocity


Bubble size distributions

3

4

5

4

5

6

)3

4

5

m)

1

2bubble size radial distribution

sim. with star-CD exp. Hibiki et al., 2001

jG=0.471 m/s, jL=2.01 m/s, z/D=53.5

d B (m

m)

1

2

3

bubble size radial distribution sim. with star-CD exp. Hibiki et al., 2001

jG=0.624 m/s, jL=2.01 m/s, z/D=53.5

d B

(mm

)

1

2 bubble size radial distribution sim. with star-CD exp. Hibiki et al., 2001

jG=0.321 m/s, jL=0.986 m/s, z/D=53.5

d B (

mm

0.0 0.2 0.4 0.6 0.8 1.00

r/R (-)0.0 0.2 0.4 0.6 0.8 1.00

r/R (-)0.0 0.2 0.4 0.6 0.8 1.00

r/R (-)

jG and jL .

Bubble size distribution in radial direction. Different gas and liquid fluxes are investigated with S modelliquid fluxes are investigated with Sγ model.


Nottingham – Multiphase flow in bend pipes

Bubble accumulate at top of the bend

Gas vol. fraction

Bubble size

2 phase model2-phase model + S-gamma

Uniform bubble distribution in vertical section

11STAR Konferenz Deutschland 2009, Nürnberg 9-10 Nov. 2009

Nottingham – Multiphase flow in bend pipes

L b bblLarge bubbles

Medium bubbles

Small bubbles

Liquid

4-phase model


DEM – Rotating drum


DEM – Calculation scheme

Solve continuous phase on “flow” grid. Solve particle tracks accounting for particle-Solve particle tracks accounting for particleparticle and particle-wall interactions.

Calculate porosity and sources from particles over a “DEM” grid.

Apply porosity and sources from “DEM” grid to “flow” grid.


DEM – Particle equations

• Linear momentum of particle:

OtherContactDragi

i FFFdtvdm ++=

• Angular momentum:

[ ]∑k

i MdIrrω [ ]∑

=

+=j

ijiji

i Mdt

dI1

rτω

iContactrollij FM ωμrrr

−=

• = rolling torque opposes particle rotation= rolling friction coefficient

iContactrollij μ

ijMr

μ• = rolling friction coefficient.rollμSTAR Konferenz Deutschland 2009, Nürnberg 9-10 Nov. 2009 15

DEM – Multiple inlets


DEM – Buoyant particles


DEM – Particle transport in pipe


DEM – Non-spherical particles


DEM - Break-off of cohesive particle


10m riser section of a 100m long pipeline


OLGA-STAR coupled model

To study 3D effects in in-line equipment: valve, junction, elbow, obstacle, jumper, separator, slug catcher, compressor, ...

Fl t f OLGA t STAR

Flow rates from STAR to OLGA

InletOutlet

Flow rates from OLGA to STAR

Outlet

Pressure from STAR to OLGA Pressure from OLGA to STAR


Summary

• Active development of advanced models for multiphase flows found in the chemical and process industryfound in the chemical and process industry.

• Breakup and coalescence of bubbles in bubbly flows.• Particle-particle, particle-wall collision modelling using the p p g g

Discrete Element Model (DEM).• Modelling of multiphase flows in long pipelines.

C li 3D CFD t 1D i li d• Coupling 3D CFD to 1D pipeline codes.


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