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



• LBM vs. NSE

Cavity flow




Spherical particles

Ellipsoid particles


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



• LBM vs. NSE

Cavity flow




Spherical particles

Ellipsoid particles


CONTENT

November, 201310

Lid driven cavity at Re=1000, 5000

November, 201311

Lid driven cavity at Re=1000, 5000

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



• LBM vs. NSE

Cavity flow




Spherical particles

Ellipsoid particles


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, 201317

SPHERICAL PARTICLE SEDIMENTATION RESULTS

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, 201323

ELLIPSOID PARTICLE IN COUETTE FLOW

November, 201324

SPHEROID ROTATION

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, 201326

Multiple particles

November, 201327

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


•

•

•

•

•

•


8D

16D D

1.1r

, 1P rC

Re 40

1000Gr

1Q

Pr 0.7

* Wachs A., (2011). Comput. Chem. Eng. Vol. 3511.

November, 201332


November, 201333

• 60 Catalyst particles are located in an enclosure


• Domain: 8D×8D×19D

•

•

•

•

•

•

60 Catalyst particles with varied temperature

1.1r

, 1P rC

Re 40

1000Gr

3.88Q

Pr 0.7

November, 201334




•

•

•

•

•

•


1.1r

, 1P rC

Re 40

1000Gr

3.88Q

Pr 0.7

November, 201335




•

•

•

•

•

•


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!

Lattice-Boltzmann vs. Navier-Stokes simulation of ...Workshop/... · November, 2013 1 Amir...

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