lattice boltzmann simulation of fluid flows
DESCRIPTION
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. NSTX Lithium Free Surface Module (ORNL). - PowerPoint PPT PresentationTRANSCRIPT
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)