Department of Energetics,
Politecnico di Torino
MESOSCOPIC NUMERICAL MODELING OF
REACTIVE MIXTURE FLOWS IN SOLID OXIDE FUEL
CELLS BY LATTICE BOLTZMANN METHOD AND
HIGH PERFORMANCE PARALLEL COMPUTING
Pietro Asinari, Romano Borchiellini, Michele Calì
Politecnico di Milano
sede Bovisa
15 - 16 Ottobre, 2007
Department of Energetics,
Politecnico di Torino
Outline
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Mesoscopic modeling of SOFC electrodes by
Lattice Boltzmann Method (LBM)
Mixture modeling: MRT Gross & Krook model
Numerical scheme: semi-implicit linearized
backward Euler formulation (SILBE)
LABORA Code
Cluster facilities and scaling performances
Reconstruction techniques
Gas permeation and diffusion: direct numerical
simulation of tortuosity
Department of Energetics,
Politecnico di Torino
Lattice Boltzmann Method – LBM
Microscopic
Theory
Kinetic
Theory
Deterministic
Newton’s Law
Statistical
Mechanics
Molecular
Dynamics
Liouville
Equation
Boltzmann
Equation
Discretized
Distribution
Functions (DDFs)
Macroscopic Theory (Continuum) and
Thermodynamics (Equilibrium)
Euler
Equations
Navier – Stokes
Equations
Hilbert and Chapman – Enskog Analysis
(Singular Perturbation Analysis)
Lattice Boltzmann
Equation
Finite Moments
Multiple Relaxation Times
Lattice Gas
Automata
LBM
Department of Energetics,
Politecnico di Torino
Why Mesoscopic Modeling and LBM
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No linear system of algebraic equations must be solved 
no need of iterative procedures.
Explicit time numerical process  transient simulations
can be naturally performed.
No need for staggered grids  unphysical solutions are
automatically avoided.
Additional local information are available  the computed
variables of a single cell are enough to estimate higher
order derivatives.
Complex topologies can be efficiently included  the
models are stable for quite rough meshes.
Department of Energetics,
Politecnico di Torino
Application to SOFC Electrodes
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Mesoscopic Modeling is a very powerful tool for SOFC
technology because
 it allows one to go deeply in the reaction core for
investigating fuel cell portions, which are actually not
accessible by direct measurement (spatial distribution
of the concentration polarization, local fluid flow,…).
However the reliability of numerical results strongly
depends on
 the reliability of the microscopic structure used in the
simulations,
 the reliability of the input parameters, particularly the
transport coefficients effecting the reaction rate.
Department of Energetics,
Politecnico di Torino
Mixture Modeling
Self collisions involve
particles of the same type
while cross collisions
involve particles of
different type
Department of Energetics,
Politecnico di Torino
Parallel Algorithm
Collision Step (Internal Layer)
Non – Blocking Send (Internal Layer)
Collision Step (Core)
Streaming Step (Core)
Moment Calculation Step (Core)
Calculations and
communications
at the same time !
Non – Blocking Receive (External Layer)
Streaming Step (Internal Layer)
Moment Calculation Step (Internal Layer)
Department of Energetics,
Politecnico di Torino
LABORA Code @ POLITO
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The LABORA code (Lattice Boltzmann for Raster
Applications) was developed from scratch at “Politecnico
di Torino” (Italy), for solving mainly the fluid flow of reactive
mixtures in porous media.
The project started in 2003 (now 10,000 lines in C++).
Main code features are:
– fully three dimensional formulation (D3Q19 lattice);
– optimized memory storage;
– parallelization based on automatic and arbitrary
domain decomposition (open source MPI package);
– different tuning strategies.
Department of Energetics,
Politecnico di Torino
HPC Facility: System X @ Virginia Tech
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System X is a supercomputer assembled by
Virginia Tech faculty members, staff, and
students in the summer of 2003, comprising
1,100 Apple PowerMac G5 computers.
System X is currently running at 12.25
Teraflops, (20.24 peak), and was last ranked
#47 (November, 2006) in the TOP500 list of
the world's most powerful supercomputers. At
that time, it was still the most powerful system
categorized by TOP500 as "self made" at any
university.
Department of Energetics,
Politecnico di Torino
HPC (?) Facility: ClusterLinux @ POLITO
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“Politecnico di Torino” (Italy): ClusterLinux, scalable
grid computing facility, currently 64 Pentium single
processor nodes (64 CPUs, 2.8 GHz, 512 MB RAM,
40 GB HD), LAN 100 Megabit Ethernet, up to 102
CPUs.
This facility is based on PC from student
laboratories which are under-used during night
and/or vacations.
The main goal is to fruitfully use computational
resources which are already available in order to
maximize the investment outcome.
Department of Energetics,
Politecnico di Torino
Scaling Performances of LABORA
Department of Energetics,
Politecnico di Torino
Comparison on Different Facilities (1)
Department of Energetics,
Politecnico di Torino
Comparison on Different Facilities (2)
Department of Energetics,
Politecnico di Torino
The (near) future: EnerGRID project
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EnerGRID: design and development of a grid
infrastructure for high performance computing in
modeling energy networks based on widespread
sources of heat and power generation
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On-going collaborations with research groups
of Computer Science Department at Stuttgart (GE)
in the framework of the program HPC – Europa.
Department of Energetics,
Politecnico di Torino
Reconstruction Techniques
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Non-destructive X-ray computed
micro-tomography is not enough for
SOFC application, this resolution is
not sufficient  reconstructions
from reliable 2D techniques, such
as standard and back scanning
electron microscopy (SEM/BSEM),
is the only viable alternative.
(1) granulometry law  grain
shapes are assumed;
(2) multiple–point statistics 
neighboring information are
processed for more reliable
reconstruction.
Department of Energetics,
Politecnico di Torino
Multiple-point Statistics
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Multiple-point statistics were used, based on twodimensional (2D) thin sections as training images, to
generate 3D pore space representations (Okabe & Blunt,
Journal of Petroleum Science & Engineering, 2005).
A 3D image can be generated that preserves typical patterns
of the void space seen in the thin sections.
The use of multiple-point statistics predicts long-range
connectivity of the structures better than granulometry law.
Essentially the algorithm is based on three steps:
– Borrowing multiple-point statistics from training images,
– Pattern reproduction,
– Image processing-noise reduction and smoothing.
Department of Energetics,
Politecnico di Torino
Reconstructed Domain
Department of Energetics,
Politecnico di Torino
Fluid Flow at the Bottom
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Hexahedral mesh
2563=16.7 MCell 
134.2 MDof for
binary mixture
(H2O/H2) in 3D
porous medium.
100,000 collisions.
Wall clock time 57
hours with a 64 CPU
cluster.
Parallelization
efficiency 85 % with
non-optimized
domain
Department of Energetics,
Politecnico di Torino
Surface Averaged Quantities
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Surface averaged quantities must be introduced for
comparing the mesoscopic fluid flow with the macroscopic
measurements and user-level expectations.
<Concentration>
<Mass Flux>
Deff
 u

 / n
Department of Energetics,
Politecnico di Torino
Optimal Refinement: Fluid Flow
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In order to recover the desired accuracy (<3%), the finest
computational mesh, i.e. 2563 (refinement X8) must be
considered. Unfortunately, this means to simulate a portion
too small of the anode, which is not representative of the
whole electrode.
Department of Energetics,
Politecnico di Torino
Optimal Refinement: Tortuosity
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Fortunately the tortuosity has a small dependence on the
mesh resolution (<5%). It depends on the path of the
considered species flowing in the porous medium and even
very coarse meshes allow one to at least estimate the path of
the species with acceptable accuracy.  This means that
larger physical domains can be simulated.

D
Deff
Department of Energetics,
Politecnico di Torino
Spatial Dependence of Tortuosity
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D
Deff
Department of Energetics,
Politecnico di Torino
Conclusions
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Direct numerical simulation of tortuosity for SOFC
application is promising for comparing the
performances of different materials and highlighting
the possible ways to improve them
The required mesh resolution for solving the fluid flow
with regards to the tortuosity calculation is not too
demanding
The simulation of the local electro-chemical reaction
must be improved  the ion and electron flows in the
solid phases must be accurately solved too
Different sintering technologies can be compared
Department of Energetics,
Politecnico di Torino
Further Documentation
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P. Asinari, M.R. von Spakovsky, M. Calì, B.V. Kasula, “Direct
numerical calculation of the kinematic tortuosity of reactive mixture
flow in the anode layer of solid oxide fuel cells by the Lattice
Boltzmann Method”, Journal of Power Sources, 170, pp. 359-375,
2007.
P.
Asinari,
“Semi-implicit-linearized
Multiple-relaxation-time
formulation of Lattice Boltzmann Schemes for Mixture Modeling”,
Physical Review E, 73, 056705, 2006.
P. Asinari, “Viscous coupling based Lattice Boltzmann model for
binary mixtures”, Physics of Fluids, 17, 067102, 2005.
P. Asinari, “Asymptotic analysis of multiple-relaxation-time lattice
Boltzmann schemes for mixture modeling”, Computers and
Mathematics with Applications, 2007 (in press).