Lattice-Boltzmann vs. Navier-Stokes simulation of particulate flows Amir Eshghinejadfard, Abouelmagd Abdelsamie, Dominique Thévenin University of Magdeburg, Germany 14th Workshop on Two-Phase Flow Predictions Sept. 2015, Halle 1
CONTENT 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 2
LATTICE BOLTZMANN METHOD (LBM) LBM is a mesoscopic method originated from LGA. t eq fi( x ci t, t t) fi( x, t) fi(, t) fi (, t) x x fi u cifi i i 3
ALBORZ 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 4
IMMERSED BOUNDARY METHOD (IBM) Force at each Lagrangian node: F n U d u t nof U d : desired Lagrangian node velocity; U nof : velocity without force at each Lagrangian node. Interpolation: Spread: nof 3 u ui, jd( xi, j Xb)( h), b F F D( x x ) s i, j b i, j b b b 5
CONTENT 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 6
DNS: with DINOSOARS (A. Abdelsamie) Low Mach (for reacting cases) number or incompressible (for cold flow), 3-D parallel. 6 th order in space (FDM) and 3 rd /4 th 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 droplets of n-heptane 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 7
Code Scaling (SuperMuc ) Channel flow Complex geometries Strong scaling of DINOSOARS on SuperMUC for reactive benchmark up to >10 4 cores. Flames 8
CONTENT 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 9
Lid driven cavity at Re=1000, 5000 10
Lid driven cavity at Re=1000, 5000 11
TURBULENT CHANNEL FLOW u. H w Re 180, u ub.2h Reb 5600 Lx Ly Lz Nx Ny Nz Npoints DINOSOARS 256 193 128 6.3 mil. ALBORZ 512 256 256 33.6 mil. 12
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. 13
Flow over stationary cylinder at Re=20 Domain: 768x768 DINOSOARS, C d = 2.14 ALBORZ, C d =2.16 14
CONTENT 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 15
SPHERICAL PARTICLE SEDIMENTATION Dimensions of the box: 0.1 0.16 0.1 m 3. The sphere starts its motion at a height H s =0.12m from the bottom of the box. Particle diameter: 15 mm Particle density: 1120 kg/m 3. U D Re 1.5; 4.1;11.6; 32.2 *ten Cate, A., Nieuwstad, C. H., Derksen, J. J., & Van den Akker, H. E. A. (2002).. Phys. Fluids, Vol. 14. 16
SPHERICAL PARTICLE SEDIMENTATION RESULTS 17
ELLIPSOID PARTICLES Differences with spherical particles: Lagrangian points distribution Rotational velocity calculation Particle-Particle and Particle-Wall collision force 18
CREATING AN ELLIPSOID Lagrangian points distribution and area calculation x y z a b b 2 2 2 1 2 2 2 1 x2 2 a b a b x S 2 b 1 dx 4 a x 19
EQUATIONS OF MOTION 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. dup M P Fb dv ( P f ) VP dt g F dx I xx y z ( Iyy I zz ) T x dt dy Iyy z x ( I zz I xx) T Body-fixed coordinate y dt dz I zz x y ( I xx Iyy ) T z dt Inertial coord. T MT, q0 q0 q1 q2 q3 0 2 2 2 2 q0 q1 q2 q3 2( q0q1 q 2 3) 2( q1q3 q0q2) q 1 1 q1 q0 q3 2 2 2 2 q 2 x M 2( q1q2 q0q3) q0 q q 1 q2 q q 3 2( q2q3 q0q1 ) 2 2 q2 q3 q0 q1 y 2 2 2 2 2( q1q3 q0q2) 2( q2q3 q0 1) q0 q1 q2 q 3 3 q3 q2 q1 q0 z c 1 M 20
COLLISION FORCE Particle-Particle collision: Spring force model* P 2 i, j cij dij Ri R j i j F x x, p d ij 0, d R R ij i j R R d R R i j ij i j d ij A B 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. 21
SPHEROIDAL PARTICLE IN COUETTE FLOW Computational domain: 120 120 60 lattice nodes. U Reynolds number=0.5 Neutrally buoyant Particle radii: 6.0 ; 4.5; 4.5 Shear rate is G=2U/N y =1/8640 Re 4 GD. 2 U 22
ELLIPSOID PARTICLE IN COUETTE FLOW 23
SPHEROID ROTATION 24
Multiple particles Dimensions of the box: 0.1 0.16 0.1 m 3. The upper particle is at height H s =0.12m from the bottom of the box. Particle major diameter: 15 mm Particle minor diameter: 7.5 mm Particle density: 1120 kg/m 3. Fluid density: 960 kg/m 3 Fluid viscosity: 58e-3 Pa.s 25
Multiple particles 26
Multiple particles 27
Hot circular cylinder in a square enclosure Hot eccentric cylinder in a square box D 0.4L g ( ) h c L Gr 2 Pr 10 3 100,000 y 0 Θ=0 D Θ=1 0.1L Θ=0 Θ=0 y 0 28
Hot circular cylinder in a square enclosure Hot eccentric cylinder in a square box D 0.4L g ( ) h c L Gr 2 Pr 10 3 100,000 y 0 Θ=0 D Θ=1 0.1L Θ=0 Θ=0 y 0 29
Catalyst particle with varied temperature Catalyst particle is located in an enclosure Particle temperature changes with time 1.1 r C Pr, 1 Re 40 8D Gr 1000 Pr 0.7 16D D Q 1 * Wachs A., (2011). Comput. Chem. Eng. Vol. 3511. 30
Catalyst particle with varied temperature Catalyst particle is located in an enclosure Particle temperature changes with time 1.1 r C Pr, 1 Re 40 8D Gr 1000 Pr 0.7 16D D Q 1 * Wachs A., (2011). Comput. Chem. Eng. Vol. 3511. 31
Catalyst particle with varied temperature 32
60 Catalyst particles with varied temperature 60 Catalyst particles are located in an enclosure Particle temperature changes with time Domain: 8D 8D 19D 1.1 r C Pr, 1 Re 40 Pr 0.7 Gr 1000 Q 3.88 33
60 Catalyst particles with varied temperature 60 Catalyst particles are located in an enclosure Particle temperature changes with time Domain: 8D 8D 19D 1.1 r C Pr, 1 Re 40 Pr 0.7 Gr 1000 Q 3.88 34
60 Catalyst particles with varied temperature Z / D 60 Catalyst particles are located in an enclosure Particle temperature changes with time Domain: 8D 8D 19D 1.1 r C 20Pr, 1 Re 40 16 Pr 0.7 12 Gr 1000 Present study 8 Q 3.88 4 0 0 20 40 60 80 35
CONCLUSIONS & OUTLOOK 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 6 th order NSE code can capture the vortices structure and predict fluctuations better than LBM. THANK YOU FOR YOUR ATTENTION! 36