Lattice Boltzmann Simulation of Fluid Flows

M.J. Pattison & S. Banerjee

MetaHeuristics 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) ( , )

eqi i

i i i

f t f tf t f t

x x

x e x

29 31 3

2 2eq

i 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 F

u

*2 1nP

t

u

1 *11

0n

nPt

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

[m

m]

LBM

Exp

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

Tu

rbu

len

t in

ten

sity 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

Co

mp

uta

tio

n s

pee

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)