lattice boltzmann simulation of fluid flows m.j. pattison & s. banerjee metaheuristics llc santa...
DESCRIPTION
Objectives – Phase 1 NSTX Lithium Free Surface Module (ORNL) Complex geometry Multiphase flow Heat transport Turbulence Fluid-wall interactions Parallelisation capabilityTRANSCRIPT
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)