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Lecture CFD-3

CFD modelling of multiphase flows

Simon Lo CD-adapco

Trident House, Basil Hill Road Didcot, OX11 7HJ, UK

simon.lo@cd-adapco.com

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Multiphase models and applications

VOF Free surface flows

LMP Droplet flows Liquid film

DEM Particle flows

EMP Particle flows Bubbly flows Population balance Boiling heat and mass transfers Interphase mass transfer

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Volume of Fluid (VOF) model

Solve equation for volume fraction (based on conservation of mass) to identify location of gas and liquid.

Momentum equation for the gas-liquid mixture:

Properties of mixture:

( ) iii mut!=+

.

( ) ( ) Mgxpuu

xu

t imiijijm

jim ++

=

+

( )=

=N

iiim

1

( )=

=N

iiim

1

Gas flow

Liquid flow

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Slug flow in interconnected subchannels

150 mm

20 m

m

Calculation grid 204,512 cells 18.7 mm

1.7

mm

Water Inlet 0.23 m/s

Air Inlet 2.0 m/s Air Inlet 0.5 m/s

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Slug flow in interconnected subchannels

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Effects of surface tension

S. Tension = 0.072 S. Tension = 0.06

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Free surface flow in drink carton

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Lagrangian model for particle flows

Equation of motion for individual particle:

= force acting on particle

Fdtdum dd = dt

dxu dd =

F

Gas flow Particle

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Spray modelling

Modified Han et al atomisation model

Charalambos (2002)!

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Droplet collision and coalescence

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Spray coating

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Simulation of films and their evaporation on high temperature surfaces Walls above saturation temperature of droplet fluid Required multi-component film

Fluid film boiling

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DEM (Discrete Element Method)

Linear momentum of particle:

Angular momentum:

= rolling torque = rolling friction coefficient.

OtherContactDragi

i FFFdtvdm ++=

[ ]=

+=k

jijij

ii MdtdI

1

!!

iContactrollij FM !!!

=

ijM!

roll

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Pneumatic conveying of particles in pipe

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Spreading of particles by conveyor belts

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Eulerian multiphase model

Conservation of mass of phase k:

Conservation of momentum of phase k:

Gas flow Particle

( ) ( ) ( )=

=+

N

jkjjkkkkkk mmut 1

. !!

( ) ( )

ktkkkkkk

kkkkkkk

Mgp

uuut

++++=

+

)(.

.

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Forces on a particle

Forces acting on a particles: Buoyancy, B. Drag, D. Lift, L. Virtual mass, V. Turbulent dispersion, T. Basset force. And others.

Buoyancy and drag are the dominant ones.

Basset force is complicated and almost always ignored. Lift, virtual mass and other forces will be considered later.

g

L, T

D

B

uc

ud V

B

D

g

ud

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Slurry flow in horizontal pipe

Liquid velocity

Inlet Outlet Middle Particle volume fraction

Uniform inlet g

L=10m

V

1m

D

Measurement plane

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d=90 m, vf=0.19, D=103mm, V=3 m/s

d=165 m, vf=0.189, D=51.5mm, V=4.17 m/s

Uniform inlet g

L=10m

V

1m

D

Measurement plane

d=270 m, vf=0.2, D=51.5mm V=5.4 m/s

d=165 m, vf=0.0918 D=51.5mm V=3.78 m/s

d=480 m, vf=0.203, D=51.5mm V=3.41 m/s

d=165 m, vf=0.273, D=495mm V=3.46 m/s

Slurry flow horizontal pipe

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Particle suspension in stirred vessel

-0.5 -0.4 -0.3 -0.2 -0.1

0 0.1 0.2 0.3 0.4 0.5

0 0.2 0.4 0.6 0.8 1

U/U

tip

r/R

Liquid Velocities Uz Experimental

Uz Star-CCM+

Ur Experimental

Ur Star-CCM+

Utheta Experimental

-0.5 -0.4 -0.3 -0.2 -0.1

0 0.1 0.2 0.3 0.4 0.5

0 0.2 0.4 0.6 0.8 1

U/U

tip

r/R

Solids Velocities

Uz Experimental

Uz Star-CCM+

Ur Experimental

Ur Star-CCM+

Utheta Experimental

Measurement

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Gas dispersion in stirred vessel

U=0.0184 m/s

Gas superficial velocity: U=0.0448 m/s U=0.0835 m/s U=0.1175 m/s U=0.201 m/s

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Comparison of gas holdup

0 0.05 0.1 0.15 0.2 0.250

5

10

15

20

25

30

35

40

45

50

E xperimentalS tar-C C M+

S uperfic ial veloc ity [m/s ]

Gas

holdup

[%]

STAR-CCM+

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An Eulerian population balance method for poly-disperse multiphase flows.

Adaptive MUSIG Model

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1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8

Mass and number density are redistributed between neighbour groups

so that each group has the same mass but new diameters.

d

d

Adaptive MUSIG Model

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Droplet breakup through an orifice

Sauter Mean Diameter

Breakup Rate (log scale)

Turbulent-induced breakup

Shear-induced breakup

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Boiling heat and mass transfers

Conservation of energy for phase k:

Wall heat flux is modelled by three mechanisms:

eqcT qqqq ++= !!!!

cq ! qq ! eq !

Convective

heating Quenching

Evaporation

( ) ( ) kkh

tkkkkkkkkkk QhThuht

=

++

..

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Bartolomei (1982) 147 bar experiments

D = 0.012 m L = 2 m P = 147 bar Tsat = 613 K Q = 0.42 - 2.21 MW/m2 G = 1878 - 2012 kg/m2s Tsub = 16 - 145 K

L

g

Sub-cooled water

Water + steam

Wall heat

flux

Void fraction Condensation rate

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Bart 22-26 : Comparison of axial void profiles

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Multi-component multiphase model

General species transport equation for phase k is:

=mass fraction of species or other scalar quantity, =diffusion coefficient, =Schmidt number, =sources.

( ) ( ) kkY

tkkkkkkkkk SYDYuYt

=

++

..

YDS

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Oxygen transfer in aeration tank

Volume fraction of air Oxygen in air

Oxygen in water Oxygen level at water surface and exit

Water

Air injector

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Summary

VOF Free surface flows

LMP Droplet flows

DEM Particle flows

EMP Particle flows Bubbly flows Population balance Boiling heat and mass transfers Interphase mass transfer