Department of Energetics, Politecnico di Torino Pietro Asinari, Romano Borchiellini, Michele Calì MESOSCOPIC NUMERICAL MODELING OF REACTIVE MIXTURE FLOWS

Department of Energetics, Politecnico di Torino

Pietro Asinari, Romano Borchiellini, Michele Calì

MESOSCOPIC NUMERICAL MODELING OF REACTIVE MIXTURE FLOWS IN SOLID OXIDE FUEL

CELLS BY LATTICE BOLTZMANN METHOD AND HIGH PERFORMANCE PARALLEL COMPUTING

Politecnico di Milano sede Bovisa

15 - 16 Ottobre, 2007


Outline

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


Lattice Boltzmann Method – LBM

Microscopic Theory

Deterministic Newton’s Law

Molecular Dynamics

Statistical Mechanics

Liouville Equation

Boltzmann Equation

Kinetic Theory

Macroscopic Theory (Continuum) and Thermodynamics (Equilibrium)

Euler Equations

Hilbert and Chapman – Enskog Analysis (Singular Perturbation Analysis)

Navier – Stokes Equations

Lattice Gas Automata

Finite Moments Multiple Relaxation

Times

Lattice Boltzmann Equation

LBMDiscretized Distribution

Functions (DDFs)


Why Mesoscopic Modeling and LBM

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.


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.

Application to SOFC Electrodes


Self collisions involve particles of the same type while cross collisions involve particles of different type

Mixture Modeling


Collision Step (Internal Layer)

Collision Step (Core)

Streaming Step (Core)

Moment Calculation Step (Core)

Streaming Step (Internal Layer)

Moment Calculation Step (Internal Layer)

Non – Blocking Send (Internal Layer)

Calculations and communications at the same time !

Non – Blocking Receive (External Layer)

Parallel Algorithm


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.

LABORA Code @ POLITO


System X is a supercomputer assembled by System X is a supercomputer assembled by Virginia Tech faculty members, staff, and Virginia Tech faculty members, staff, and students in the summer of 2003, comprising students in the summer of 2003, comprising 1,100 Apple PowerMac G51,100 Apple PowerMac G5 computers. computers. System X is currently running at 12.25 System X is currently running at 12.25 Teraflops, (20.24 peak), and was last ranked Teraflops, (20.24 peak), and was last ranked #47 (November, 2006) in the #47 (November, 2006) in the TOP500TOP500 list of list of the world's most powerful supercomputers. At the world's most powerful supercomputers. At that time, it was still the that time, it was still the most powerful systemmost powerful system categorized by TOP500 as categorized by TOP500 as "self made""self made" at any at any university. university.

HPC Facility: System X @ Virginia Tech


““Politecnico di Torino” (Italy):Politecnico di Torino” (Italy): ClusterLinux, ClusterLinux, scalable grid computing facility, currently 64 scalable grid computing facility, currently 64 Pentium single processor nodes (64 CPUs, 2.8 Pentium single processor nodes (64 CPUs, 2.8 GHz, 512 MB RAM, 40 GB HD), LAN 100 Megabit GHz, 512 MB RAM, 40 GB HD), LAN 100 Megabit Ethernet, Ethernet, up to 102 CPUsup to 102 CPUs..

This facility is based on This facility is based on PC from student PC from student laboratorieslaboratories which are under-used during night which are under-used during night and/or vacations.and/or vacations.

The main goal is to fruitfully use computational The main goal is to fruitfully use computational resources which are already available in order resources which are already available in order to maximize the investment outcome.to maximize the investment outcome.

HPC (?) Facility: ClusterLinux @ POLITO


Scaling Performances of LABORA


Comparison on Different Facilities (1)


Comparison on Different Facilities (2)


EnerGRIDEnerGRID: design and development of a grid : design and development of a grid infrastructure for high performance computing in infrastructure for high performance computing in modeling energy networks based on widespread modeling energy networks based on widespread sources of heat and power generationsources of heat and power generation

On-going collaborations with research groups On-going collaborations with research groups of Computer Science Department at of Computer Science Department at Stuttgart Stuttgart (GE)(GE) in the framework of the program in the framework of the program HPC – EuropaHPC – Europa..

The (near) future: EnerGRID project


Non-destructiveNon-destructive X-ray computed X-ray computed micro-tomographymicro-tomography is not enough for is not enough for SOFC application,SOFC application, this resolution is this resolution is not sufficientnot sufficient reconstructions reconstructions from reliable 2D techniques, such from reliable 2D techniques, such asas standard and back scanning standard and back scanning electron microscopy (SEM/BSEM)electron microscopy (SEM/BSEM), , is the only viable alternative.is the only viable alternative.

(1) granulometry law (1) granulometry law grain grain shapes are assumed;shapes are assumed;

(2) multiple–point statistics(2) multiple–point statistics neighboring information are neighboring information are processed for more reliable processed for more reliable reconstruction.reconstruction.

Reconstruction Techniques


Multiple-point statisticsMultiple-point statistics were used, based on two- were used, based on two-dimensional (2D) thin sections as training images, to dimensional (2D) thin sections as training images, to generate 3D pore space representations (Okabe & Blunt, generate 3D pore space representations (Okabe & Blunt, Journal of Petroleum Science & Engineering, 2005).Journal of Petroleum Science & Engineering, 2005).

AA 3D image can be generated that 3D image can be generated that preserves typical patterns preserves typical patterns of the void spaceof the void space seen in the thin sections seen in the thin sections..

The use of multiple-point statistics predicts The use of multiple-point statistics predicts long-range long-range connectivity of the structuresconnectivity of the structures better than granulometry law better than granulometry law..

Essentially the algorithm is based on three steps:Essentially the algorithm is based on three steps:– Borrowing multiple-point statistics from Borrowing multiple-point statistics from training imagestraining images,,– Pattern reproductionPattern reproduction,,– Image Image processing-noise reductionprocessing-noise reduction and smoothing and smoothing..

Multiple-point Statistics


Reconstructed Domain


Hexahedral mesh Hexahedral mesh 25625633=16.7 MCell=16.7 MCell 134.2 MDof134.2 MDof for for binary mixture binary mixture (H(H22O/HO/H22) in 3D ) in 3D porous medium.porous medium.

100,000 collisions.100,000 collisions. Wall clock time Wall clock time 57 57

hours hours with a 64 with a 64 CPU cluster.CPU cluster.

Parallelization Parallelization efficiency efficiency 85 %85 % with non-optimized with non-optimized domain domain decomposition.decomposition.

Fluid Flow at the Bottom


Surface averagedSurface averaged quantities must be introduced for quantities must be introduced for comparing the mesoscopic fluid flow with the comparing the mesoscopic fluid flow with the macroscopic macroscopic measurementsmeasurements and and user-level expectations.user-level expectations.

<Concentration> <Mass Flux>

/eff

uD

n

Surface Averaged Quantities


IIn order to recover the desired accuracy (<3%), the finest n order to recover the desired accuracy (<3%), the finest computational mesh, i.e. computational mesh, i.e. 25625633 (refinement X8) (refinement X8) must be must be considered. Unfortunately, this means to simulate a considered. Unfortunately, this means to simulate a portion portion too smalltoo small of the anode of the anode,, which is not representative of the which is not representative of the whole electrode. whole electrode.

Optimal Refinement: Fluid Flow


eff

D

D

Fortunately the tortuosity has a Fortunately the tortuosity has a small dependencesmall dependence on the on the mesh resolution (<5%). It depends on the mesh resolution (<5%). It depends on the path of the path of the considered speciesconsidered species flowing in the porous medium and even flowing in the porous medium and even very coarse meshesvery coarse meshes allow one to at least estimate the path of allow one to at least estimate the path of the species with acceptable accuracy. the species with acceptable accuracy. This means that This means that larger physical domains can be simulatedlarger physical domains can be simulated..

Optimal Refinement: Tortuosity


eff

D

D

Spatial Dependence of Tortuosity


Conclusions

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


P. Asinari, M.R. von Spakovsky, M. Calì, B.V. Kasula, “P. Asinari, M.R. von Spakovsky, M. Calì, B.V. Kasula, “Direct Direct numerical calculation of the kinematic tortuosity of reactive mixture numerical calculation of the kinematic tortuosity of reactive mixture flow in the anode layer of solid oxide fuel cells by the Lattice flow in the anode layer of solid oxide fuel cells by the Lattice Boltzmann MethodBoltzmann Method”, ”, Journal of Power SourcesJournal of Power Sources, 170, pp. 359-375, , 170, pp. 359-375, 2007.2007.

P. Asinari, “P. Asinari, “Semi-implicit-linearized Multiple-relaxation-time Semi-implicit-linearized Multiple-relaxation-time formulation of Lattice Boltzmann Schemes for Mixture Modelingformulation of Lattice Boltzmann Schemes for Mixture Modeling”, ”, Physical Review EPhysical Review E, 73, 056705, 2006., 73, 056705, 2006.

P. Asinari, “P. Asinari, “Viscous coupling based Lattice Boltzmann model for Viscous coupling based Lattice Boltzmann model for binary mixturesbinary mixtures”, ”, Physics of FluidsPhysics of Fluids, 17, 067102, 2005., 17, 067102, 2005.

P. Asinari, “P. Asinari, “Asymptotic analysis of multiple-relaxation-time lattice Asymptotic analysis of multiple-relaxation-time lattice Boltzmann schemes for mixture modelingBoltzmann schemes for mixture modeling”, ”, Computers and Computers and Mathematics with ApplicationsMathematics with Applications, 2007 (in press)., 2007 (in press).

Further Documentation

Documents

Department of Energetics, Politecnico di Torino Pietro Asinari, Romano Borchiellini, Michele Calì MESOSCOPIC NUMERICAL MODELING OF REACTIVE MIXTURE FLOWS