Lattice-Boltzmann vs. Navier-Stokes simulation of ...Workshop/... · November, 2013 1 Amir...
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Transcript of Lattice-Boltzmann vs. Navier-Stokes simulation of ...Workshop/... · November, 2013 1 Amir...
November, 20131
Amir Eshghinejadfard, Abouelmagd Abdelsamie, Dominique Thévenin
14th Workshop on Two-Phase Flow Predictions
Sept. 2015, Halle
University of Magdeburg, Germany
Lattice-Boltzmann vs. Navier-Stokes simulation of
particulate flows
November, 20132
• Lattice Boltzmann method (LBM)
• Navier Stokes Equation (NSE)
• LBM vs. NSE
Cavity flow
Flow over stationary cylinder
Turbulent channel flow
• LBM applications in two-phase flows:
Spherical particles
Ellipsoid particles
Particulate flows with heat transfer
CONTENT
November, 20133
• LBM is a mesoscopic method originated from LGA.
LATTICE BOLTZMANN METHOD (LBM)
( , ) ( , ) ( , ) ( , )eq
i i i i i
tf t t t f t f t f t
x c x x x
i
i
f i i
i
f u c
November, 20134
• ALBORZ: In-house code developed in LSS-OvGU, Magdeburg.
Particulate flows,
Turbulent flows,
Porous media,
Non-isothermal flows
• Single and Multi Relaxation time
• Parallelized on MPI.
• Particles: Immersed Boundary Method (IBM)
• Natural convection: Boussinesq approximation
ALBORZ
November, 20135
• Force at each Lagrangian node:
• Ud: desired Lagrangian node velocity;
• UnoF: velocity without force at each Lagrangian node.
• Interpolation:
• Spread:
IMMERSED BOUNDARY METHOD (IBM)
d noFn
t
U uF
, ,( )i j b i j b b
b
D s F F x x
3
, ,( )( ) ,noF
i j i j b
b
D h u u x X
November, 20136
• Lattice Boltzmann method (LBM)
• Navier Stokes Equation (NSE)
• LBM vs. NSE
Cavity flow
Flow over stationary cylinder
Turbulent channel flow
• LBM applications in two-phase flows:
Spherical particles
Ellipsoid particles
Particulate flows with heat transfer
CONTENT
November, 20137
DNS: with DINOSOARS (A. Abdelsamie)
• Low Mach (for reacting cases) number or incompressible (for
cold flow), 3-D parallel.
• 6th order in space (FDM) and 3rd/4th order in time (Runge-Kutta)
• Multiphase (Lagrangian) for spherical droplets/particles:
• Inert or Reactive (evaporation, burning)
• Point-particles or Resolved (Immersed Boundary, IBM)
• Includes Direct Boundary-IBM, for complex geometries
• Point-wise implicit integration for stiff chemistry
• Poisson equation solved by fully spectral method,
even for non-periodic boundaries
• Full reactions schemes or tabulated chemistry (FPI )
• Kinetics, transport & thermodynamics: coupled to Cantera1.8
and Eglib3.4
droplets of
n-heptane
November, 20138
Code Scaling (SuperMuc )
Strong scaling of DINOSOARS on SuperMUC for reactive
benchmark up to >104 cores. Flames
Complex
geometries
Channel
flow
November, 20139
• Lattice Boltzmann method (LBM)
• Navier Stokes Equation (NSE)
• LBM vs. NSE
Cavity flow
Flow over stationary cylinder
Turbulent channel flow
• LBM applications in two-phase flows:
Spherical particles
Ellipsoid particles
Particulate flows with heat transfer
CONTENT
November, 201312
TURBULENT CHANNEL FLOW
.Re 180 , wu H
u
.2Re 5600b
b
u H
Lx Ly Lz Nx Ny Nz Npoints
DINOSOARS
256 193 128 6.3 mil.
ALBORZ
512 256 256 33.6 mil.
November, 201313
TURBULENT CHANNEL FLOW
* Moser R., Kim J., Mansour N. N. (1999). Phys. Fluid, Vol. 11.
** Vreman A. W., and Kuerten J. G. M. (2014) Phys. Fluid, 2014, Vol. 26.
November, 201314
Flow over stationary cylinder at Re=20
• Domain: 768x768
• DINOSOARS, Cd = 2.14
• ALBORZ, Cd =2.16
November, 201315
• Lattice Boltzmann method (LBM)
• Navier Stokes Equation (NSE)
• LBM vs. NSE
Cavity flow
Flow over stationary cylinder
Turbulent channel flow
• LBM applications in two-phase flows:
Spherical particles
Ellipsoid particles
Particulate flows with heat transfer
CONTENT
November, 201316
• Dimensions of the box: 0.1×0.16×0.1 m3.
• The sphere starts its motion at a height
Hs=0.12m from the bottom of the box.
• Particle diameter: 15 mm
• Particle density: 1120 kg/m3.
•
SPHERICAL PARTICLE SEDIMENTATION
Re 1.5; 4.1;11.6; 32.2U D
*ten Cate, A., Nieuwstad, C. H., Derksen, J. J., & Van den Akker, H. E. A. (2002).. Phys. Fluids, Vol. 14.
November, 201318
• Differences with spherical particles:
Lagrangian points distribution
Rotational velocity calculation
Particle-Particle and Particle-Wall collision force
ELLIPSOID PARTICLES
November, 201319
• Lagrangian points distribution and area calculation
CREATING AN ELLIPSOID
2 2 2
2 2 21
x y z
a b b
2
1
2
42 1
x
x
a b a b xS b dx
a
November, 201320
Newton’s equation of motion for moving particle
• For the simulation of a moving particle, we have to consider the
equations of motion of the particle.
( )xxx y z yy zz x
dI I I T
dt
( ) cPP b P f P
dM F dV V
dt
Ug F
EQUATIONS OF MOTION
2 2 2 2
0 1 2 3 0 1 2 3 1 3 0 2
2 2 2 2
1 2 0 3 0 1 2 3 2 3 0 1
2 2 2 2
1 3 0 2 2 3 0 1 0 1 2 3
2( ) 2( )
2( ) 2( )
2( ) 2( )
q q q q q q q q q q q q
M q q q q q q q q q q q q
q q q q q q q q q q q q
( )zzz x y xx yy z
dI I I T
dt
( )y
yy z x zz xx y
dI I I T
dt
,T MT 0 0 1 2 3
1 1 0 3 2
2 2 3 0 1
3 3 2 1 0
0
1
2
x
y
z
q q q q q
q q q q q
q q q q q
q q q q q
q1M
Body-fixed coordinate
Inertial coord.
November, 201321
• Particle-Particle collision: Spring force model*
• Each Lagrangian point may have collision with one or more points
of other particles.
*Feng, Z. G., & Michaelides, E. E. (2004) J. Comput. Physi., Vol. 195.
COLLISION FORCE
2
,
0,
,
ij i j
P
i j ij ij i j i j
i j ij i j
p ij
d R R
c d R RR R d R R
d
F x x
A B
dij
November, 201322
• Computational domain: 120×120×60 lattice
nodes.
• Reynolds number=0.5
• Neutrally buoyant
• Particle radii: 6.0 ; 4.5; 4.5
• Shear rate is G=2U/Ny=1/8640
•
SPHEROIDAL PARTICLE IN COUETTE FLOW
U
U
24 .Re
G D
November, 201325
• Dimensions of the box: 0.1×0.16×0.1 m3.
• The upper particle is at height Hs=0.12m
from the bottom of the box.
• Particle major diameter: 15 mm
• Particle minor diameter: 7.5 mm
• Particle density: 1120 kg/m3.
• Fluid density: 960 kg/m3
• Fluid viscosity: 58e-3 Pa.s
Multiple particles
November, 201328
• Hot eccentric cylinder in a square box
•
•
•
Hot circular cylinder in a square enclosure
Θ=1 Θ=0Θ=0
0y
0y
D
Θ=0
0.1L
3
2
( )100,000h cg L
Gr
0.4D L
Pr 10
November, 201329
• Hot eccentric cylinder in a square box
•
•
•
Hot circular cylinder in a square enclosure
Θ=1 Θ=0Θ=0
0y
0y
D
Θ=0
0.1L
3
2
( )100,000h cg L
Gr
0.4D L
Pr 10
November, 201330
• Catalyst particle is located in an enclosure
• Particle temperature changes with time
•
•
•
•
•
•
Catalyst particle with varied temperature
8D
16D D
1.1r
, 1P rC
Re 40
1000Gr
1Q
Pr 0.7
* Wachs A., (2011). Comput. Chem. Eng. Vol. 3511.
November, 201331
• Catalyst particle is located in an enclosure
• Particle temperature changes with time
•
•
•
•
•
•
Catalyst particle with varied temperature
8D
16D D
1.1r
, 1P rC
Re 40
1000Gr
1Q
Pr 0.7
* Wachs A., (2011). Comput. Chem. Eng. Vol. 3511.
November, 201333
• 60 Catalyst particles are located in an enclosure
• Particle temperature changes with time
• Domain: 8D×8D×19D
•
•
•
•
•
•
60 Catalyst particles with varied temperature
1.1r
, 1P rC
Re 40
1000Gr
3.88Q
Pr 0.7
November, 201334
• 60 Catalyst particles are located in an enclosure
• Particle temperature changes with time
• Domain: 8D×8D×19D
•
•
•
•
•
•
60 Catalyst particles with varied temperature
1.1r
, 1P rC
Re 40
1000Gr
3.88Q
Pr 0.7
November, 201335
• 60 Catalyst particles are located in an enclosure
• Particle temperature changes with time
• Domain: 8D×8D×19D
•
•
•
•
•
•
60 Catalyst particles with varied temperature
1.1r
, 1P rC
Re 40
1000Gr
3.88Q
Pr 0.7
0
4
8
12
16
20
0 20 40 60 80
Z /
D
t* = t Uref / Dp
Present study
November, 201336
• LBM is a promising approach for multiphase flow simulation.
• Motion of particles of different shapes is successfully modeled by LBM
• Thermal effect can be considered by IB-LBM.
• LBM required less memory and computational time for lid-driven cavity flow.
• In case of turbulent flow the current 6th order NSE code can capture the
vortices structure and predict fluctuations better than LBM.
CONCLUSIONS & OUTLOOK
THANK YOU FOR YOUR ATTENTION!