(30a) Modeling of Heat and Momentum Transfer in the Context of Moving Particles By a Double MRT Lattice Boltzmann Scheme

Kruggel-Emden, H., Ruhr-Universitaet Bochum

Modeling of Heat and
Momentum Transfer in the Context of Moving Particles by a Double MRT Lattice
Boltzmann Scheme Bogdan Kravets, Harald

Mechanical Process Engineering and Solids
Processing (MVTA)

Technical University Berlin (TU Berlin)

Ernst-Reuter-Platz 1, 10587 Berlin, Germany

e-mail: kravets@tu-berlin.de, kruggel-emden@tu-berlin.de, web
page: http://www.mvta.tu-berlin.de


Dynamic particle/fluid systems - like in fluidized
beds, in pneumatic conveying or in rotary kilns passed through by a fluid - occur in many areas of technical processes in chemical industry and
in energy technology. Modeling of the named systems gained in significance
during the past years [1–5]. The most common applicable approach
is the discrete element method (DEM) coupled with computational fluid dynamics
(CFD), where the solid phase is described by Newton's laws of motion and the
fluid phase by the Navier-Stokes equations. However, coupled DEM/CFD usually does
not resolve the fluid phase spatially around individual particles.

Particle resolved flow simulations can rely on Navier-Stokes (NS)
based approaches like finite volume method (FVM) or finite difference method
(FDM) or more alternative schemes like the Lattice-Boltzmann method (LBM). Unlike other direct
numerical simulation (DNS) methods, LBM is not solving Navier-Stokes equations
but is based on kinetic theory and the discrete Boltzmann equation. LBM
utilizes a Cartesian mesh and hence does not require a complex mesh derivation
or a re-meshing when boundaries are moving. To address coupled heat transfer
and fluid flow conventional LBM can be extended by thermal LBM (TLBM). The
resulting scheme relies on a set of two distribution functions, the so called
double distribution function (DDF) approach [6];
one for the fluid density and one for the internal energy.

For the carried out numerical investigations an
existing 3D TLBM framework which was utilized for static particle packing
simulations [7,8]
in the past is extended for moving particles. Both, the fluid field and the
temperature field are represented by a multiple-relaxation-time (MRT) [9–11]
collision operator.
For the hydrodynamic boundary conditions, a scheme introduced by Bouzidi et al.
is applied with quadratic interpolation. Thermal
boundary conditions are prescribed according to Li et al. [13] with linear interpolation. The used
boundary conditions are superior to the standard half way bounce back and are
suitable for curved boundaries. Particle interactions are taken care of in the
context of the DEM. The numerical TLBM framework is applied to moving particles
and is validated against available analytical solutions and results obtained
from the scientific literature. It is shown that the derived framework offers a
highly accurate and efficient approach for the analysis of moving particles
considering heat transfer problems under resolved flow.


[1]      H. Kruggel-Emden, T. Oschmann, Numerical study of rope formation
and dispersion of non-spherical particles during pneumatic conveying in a pipe
bend, Powder Technol. 268 (2014) 219–236. doi:10.1016/j.powtec.2014.08.033.

[2]      T. Oschmann, K. Vollmari, H. Kruggel-emden, S. Wirtz,
Numerical Investigation of the Mixing of Non-Spherical Particles in Fluidized
Beds and during Pneumatic Conveying, Procedia Eng. 102 (2015) 976–985.

[3]      T. Oschmann, J. Hold, H. Kruggel-Emden, Numerical
investigation of mixing and orientation of non-spherical particles in a model
type fluidized bed, Powder Technol. 258 (2014) 304–323.

[4]      K. Vollmari, R. Jasevi, H. Kruggel-emden, Experimental and
numerical study of fl uidization and pressure drop of spherical and
non-spherical particles in a model scale fl uidized bed, 291 (2016) 506–521.

[5]      K. Vollmari, T. Oschmann, Mixing quality in mono- and
bidisperse systems under the in fl uence of particle shape : A numerical
and experimental study, Powder Technol. 308 (2017) 101–113.

[6]      X. He, S. Chen, G.D. Doolen, A Novel Thermal Model for the
Lattice Boltzmann Method in Incompressible Limit, J. Comput. Phys. 146 (1998)
282–300. doi:10.1006/jcph.1998.6057.

[7]      H. Kruggel-Emden, B. Kravets, M.K. Suryanarayana, R.
Jasevicius, Direct numerical simulation of coupled fluid flow and heat transfer
for single particles and particle packings by a LBM-approach, Powder Technol.
294 (2016) 236–251. doi:10.1016/j.powtec.2016.02.038.

[8]      B. Kravets, H. Kruggel-Emden, Investigation of local heat
transfer in random particle packings by a fully resolved LBM-approach, Powder
Technol. 318 (2017) 293–305. doi:10.1016/j.powtec.2017.05.039.

[9]      D. D’Humières, I. Ginzburg, M. Krafczyk, P. Lallemand, L.-S.
Luo, Multiple-relaxation-time lattice Boltzmann models in three dimensions.,
Philos. Trans. A. Math. Phys. Eng. Sci. 360 (2002) 437–451.

[10]    H. Yoshida, M. Nagaoka, Multiple-relaxation-time lattice
Boltzmann model for the convection and anisotropic diffusion equation, J.
Comput. Phys. 229 (2010) 7774–7795. doi:10.1016/j.jcp.2010.06.037.

[11]    L. Li, R. Mei, J.F. Klausner, Lattice Boltzmann models for the
convection-diffusion equation: D2Q5 vs D2Q9, Int. J. Heat Mass Transf. 108
(2017) 41–62. doi:10.1016/j.ijheatmasstransfer.2016.11.092.

[12]    M. Bouzidi, M. Firdaouss, P. Lallemand, Momentum transfer of a
Boltzmann-lattice fluid with boundaries, Phys. Fluids. 13 (2001) 3452–3459.

[13]    L. Li, R. Mei, J.F. Klausner, Boundary conditions for thermal
lattice Boltzmann equation method, J. Comput. Phys. 237 (2013) 366–395.



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