Ryuichi IWATA１Takeo KAJISHIMA１Takeo KAJISHIMA１Shintaro TAKEUCHI 2

1 Osaka university2 The university of Tokyo

ex. Three-phase fluidized bed, flotation, air lift

Microscopic

Interface phenomena– Bubble deformation, surface tension

Three-phase flows include

Microscopic,– Particle rotation, vortex shedding

– Interface phenomena– Collective behavior Mesoscopic

◎ Multi-fluid model (Tomiyama1994)◎ Euler/Lagrange Calculations ( Bourloutski, Sommerfeld 2002) ◎Turbulent structure (Kitagawa 2000)◎Front Tracking-DEM coupling

h d (A l d 2005)

(Kitagawa 2000) (Annaland 2005)

method (Annaland 2005)

– Fluid-Solid Interaction: Immersed boundary method of body force type (Kajishima 2001)

– Gas-Liquid Interface Capturing: Volume of fluid method – Cartesian coordinate system– Finite difference method – Dispersed-phases described by volumetric fraction

in each computational cell.

Multiple bubbles and particle interaction

• Fluids-Solid Interaction ：– Clusterization of 1024-particle system (Kajishima and co-workers, 2001,2002)– Hindered settling in 105-particle system (Hidaka and co-workers, 2006)

Particle of arbitrarily (time dependent) geometry (Yuki and co workers 2007)– Particle of arbitrarily (time dependent) geometry (Yuki and co-workers 2007)

gg

Particle distribution Induced vortices Sedimentation Deformable particles

Unified velocity field

The equation of continuity and N-S equation based on one-fluid formulation

Interaction force

Momentum and angler momentum equations

No leakage of momentum

Basic equationsBasic equations0.10 0.300.00

1.000.820.22

1.00 1.000.61

Interface reconstruction

Mixed Youngs-centered method(by Aulisa 2007)(by Aulisa, 2007)

Advection scheme Split Lagrangian-explicit scheme (by Gueyffier 1999)(by Gueyffier 1999)

Surface tension Continuum Surface Force Model

Start

Set up

Time increment

Start

Fluids interface

Advection term,Viscous term

VOF StepFluids interfacecapturing phaseAdvection of VOF

VOF Step

Prediction of fluid velocity

Degitize interface(volumetoric fraction)

Interactionphase

Momentum exchange

Solve momentum eq. Solid phaseIBM Step

Solve poisson eq.C ti St

Update of displacement

Correction Step

37.8D

D

w t

Periodic

12.6

D

Inle

t flo

w

Out

let

Re=200

x

y 6.3D Periodic

N i l diti

Computational domainSt

Numerical conditions

Re

axis

n out

let

on

rm in

let

cond

ition

nvec

tive

ow

con

ditioa

b

Fixed particleU

nifo

rflo

w c

Con

flow

Ellipticity

Free slip condition

p y

Reynolds number y

L w

Dp

Re=100, Dp/Dx=10

Numerical conditionsgas

liquid

Free slip condition

particle

A floating object A floating object g jg j

IB-VOF coupling method for three-phase flow◦ Validated by comparison with other solutions◦ Applicability for non-spherical objects◦ Capability for large scale simulation involving multiple◦ Capability for large-scale simulation involving multiple

dispersed-phases