Lattice Boltzmann Simulation of Fluid Flows

M.J. Pattison & S. BanerjeeMetaHeuristics LLC

Santa Barbara, CA 93105

Main Topics

• Objectives• Lattice Boltzmann method• Complex geometry• Multicomponent flow• Turbulence modelling• Parallelisation

Objectives – Phase 1

NSTX Lithium Free Surface Module (ORNL)

• Complex geometry• Multiphase flow• Heat transport• Turbulence• Fluid-wall interactions• Parallelisation capability

Objectives – Phase II

• MHD• Chemical reactions• Parallel code• Input/output

processing

Lattice Boltzmann Method

Solve for velocity distribution

( , ) ( , )( , 1) ( , )eq

i ii i i

f t f tf t f t

x xx e x

29 31 32 2

eqi i i if w

e u a e u a u a u a

( ) ( )ii

f x x ( ) ( )x ix ii

u e fx x

is a relaxation time (function of viscosity) a is force term

ie

Projection Method

*

2n n

n nNLt

u u Fu

*2 1nP

t

u

1 *11 0

nnP

t

u u

1.

2.

3.

Predictor

Poisson eqn

Corrector

Poisson equation is elliptic. Can solve using spectral method (FFT)for simple geometry or by iterative method. Methods use non-local data so making parallel processing less efficient.

Capabilities of LB code

• Can handle complex geometry easily• Multicomponent/multiphase flows• Turbulence models – LES or algebraic• Well suited to parallel processing – almost

linear scaling with number of CPUs

Complex Geometry

a

b

Fluid

Wall( )af x( )bf x

No need for body-fitted grid

but need distributionsat point b

*( ) (1 ) ( ) ( )b a bf f f x x x

is function of distance from wall

is an equilibrium distribution*( )bf x

Flow over Cylinder

Backward Facing Step

0

2

4

6

8

10

-50 50 150 250Velocity [cm/s]

Hei

ght

[mm

]

LBMExp

0

2

4

6

8

10

-50 0 50 100 150 200Velocity [cm/s]

Hei

ght [

mm

]

LBM

Exp

Velocity profiles downstream of step. Left at x/S = 6, right at at x/S = 20

Multicomponent Flows

Model interactions between components using a force term

( ) ( ) ( )i i ii

G

F x x x e

Where summation is over nearest neighbours and the different components. is a function of density

Can model effects of: - surface tension - phase change (i.e. condensation) - immiscible fluids

( ) x

Movement of Droplet down Wall

Drop is initially semi-circular, with surrounding fluid stationaryDrop spreads due to surface tension, then moves down wall

Penetration of Dense Fluid into Light Fluid

Turbulence Modelling

• Use Baldwin-Lomax algebraic model• Smagorinski type LES model• Models use an “eddy viscosity” to account

for effects of turbulence• Both models only require local data, so are

suited for parallel processing

Turbulence in Shear Flow

0

0.5

1

1.5

2

2.5

3

0 10 20 30 40 50 60

Distance from wall

Turb

ulen

t int

ensi

ty Streamw ise

Spanw ise

Wall normal

Parallelisation

Split domain up into slabsor blocks

Assign each one to a different processor

Speed of computation for different numbers of CPUsused – plane Poiseuille flowproblem 0

1

2

3

4

5

6

7

0 2 4 6 8 10 12

Number of CPUs

Com

puta

tion

spee

d

480x40x28120x40x28

Conclusions

• 3-D transient Lattice Boltzmann code with following capabilities developed:

• Multicomponent flow• Complex geometry• Turbulence modelling• Efficient parallel processing with almost

linear scaling

NSTX Lithium Free Surface Module (ORNL)