Swiss Fuel Cell Symposium, Yverdon-les-bains, 19./20. May 2003 Numerical Modeling of PEM Fuel Cells in 2½D M. Roos, P. Held ZHW-University of Applied Sciences.

Swiss Fuel Cell Symposium, Yverdon-les-bains, 19./20. May 2003

Numerical Modeling of PEM Fuel Cells in 2½D

M. Roos, P. HeldZHW-University of Applied Sciences Winterthur

Switzerland

F. Büchi, St. FreunbergerPSI-Paul Scherrer Institut

Switzerland

Fuel Cell Research Symposium, Modeling and exp. Validation, 18./19. March 2004

Outline

• PEM Modeling Issues

• Modeling Goals

• 2½D Modeling Approach

• 1D Interaction Model

• Implementation

• Preliminary Results

• Conclusions

Fuel Cell Research Symposium, Modeling and exp. Validation, 18./19. March 2004

PEM Modeling Issues

Large variation of important length scales

• Electrochemistry at nm

• Porous Flow at um

• Flow Fields at mm

• Balance of Plant at m

Multi-domain physical modeling mandatory for many technical important applications

• Electrochemistry and Water transport

• Flow and heat generation and transport

• Charge transport, diffusion and reaction

Complexity of geometrical structure

• Layered structures

• Repeated sub systems

Fuel Cell Research Symposium, Modeling and exp. Validation, 18./19. March 2004

Modeling Goals

Understanding local processes in detail

• reaction mechanisms in electrochemistry, e.g., by state space models

Investigation coupled part processes

• interaction of mass transport and electrochemical reaction in PEM flow field structures

Understanding cell / stack behavior

• water management in PEM systems: strong dependence on operation conditions. Influence of processes in distant parts of a cell / stack.

Dynamic behavior of full stacks including auxiliary systems

• Setting up control systems

• Performance optimization

Flexibility with respect to Interactions

Demanding Geometries

Fast Calculation

How to realize?

Fuel Cell Research Symposium, Modeling and exp. Validation, 18./19. March 2004

2½D Modeling Approach 1

Basic Idea HEXIS Stack Modeling:Calculating effective transport parameters and deploying them in rotational symmetric 2D models

→ large reduction in computational effort,→ justified method

Application to PEM

Problem: there is no dimension to map form 3D to 2D (if full stacks or cells are in the focus)

→ Resort to two or more interacting 2D models describing the cathode and anode flow fields

→ Volume Averaging Method works in this case

x

yz

x

y

nact(jq)=nnernst-Vext-jqRsurfH2O jq

Fuel Cell Research Symposium, Modeling and exp. Validation, 18./19. March 2004

Single (repeated) fuel cell decomposed into 3 parts:

• Anode Flow Field

• Membrane Electrode Assembly (MEA)

• Cathode Flow Field

Modeling of flow fields by two 2D domains, Discretisation of Transport Equations with FEM and Volume Averaging Method (VAM)

El. chem. Reactions treated as non-local interaction of the 2D part models

2½D Modeling Approach 2

Flow Field

Bipolar Plate

x

z

MEA

y

x

Fuel Cell Research Symposium, Modeling and exp. Validation, 18./19. March 2004

The models of the 2D part domains can be tailored to describe transport phenomena

• Fluid Flow

• Diffusion (Channels)

• Heat Transport

Method of choice for the determination of effective material parameters is the volume averaging method, preferably its numerical variant.

Mass transport in flow fields, expressed by anisotropic Darcy tensor. → Different pressure drops for flow parallel or perpendicular to the channels (underneath the rims).

2½D Modeling Approach 3

2D Anode Flow Field

2D Cathode Flow Field

Local Interaction (1D)

yy

xx

0

0

Pv

Fuel Cell Research Symposium, Modeling and exp. Validation, 18./19. March 2004

1D Interaction Model 1

CathodeAnodeMembrane

z

Φ

The electrochemical interaction within the MEA is 1D

• low in-plane electrochemical interaction and associated transport processes

• coupling of different positions in the MEA plane is effected by the gas composition of the 2D domains and by the (per bipolar plate) constant electric potential.

PEM transport properties (water concentration dependence) does not allow for analytic expressions of the electrical current density in terms of partial pressures, potentials and temperatures of the corresponding points in flow fields.

Modeling the 1D interaction by a set of ordinary differential equations (ODE)

Fuel Cell Research Symposium, Modeling and exp. Validation, 18./19. March 2004

1D Interaction Model 2

The 1D interaction model accounts for

• Darcy flow in the gas diffusion layer

• Diffusion (Maxwell-Stefan for multi species)

• Heat transport

• Charge Transport

• Electrochemical reactions at the anode and cathode (including the kinetics)

• Water transport in the PEM (drag and diffusion)

• Interactions: temperature dependent material and gas properties, source rates for temperature field due to reversible and irreversible heat release processes.

Due to the 1D domain, the mathematical form of these equations is a system of nonlinear, coupled first order ordinary differential equations for 14 physical quantities (the “potentials” molar concentration for H2, H2O, O2, N2, temperature, electric potential, pressure and the respective flow quantities).

The strong non-linearity asks for efficient and robust methods numerical methods for its discretisation.

Fuel Cell Research Symposium, Modeling and exp. Validation, 18./19. March 2004

Implementation 1

The 2D domains are implemented as NM SESES models for anode and cathode, respectively with help of the finite element method.

The independent degrees of freedom are the gas species, the (averaged) temperature field, the pressure distribution and the velocity field for each compartment.

The 1D electrochemical interaction model turns out to be a source rate for the chemical species from the point of view of the 2D part models, i.e., it is cast into an effective, homogeneous chemical reaction.

Electrochemical reaction couples fields of the anode to the cathode domain→ interaction is non-local for FE model our model set up.

The non-locality of the interaction is, unfortunately, not a standard type of interaction in FEM (not physical for 3D or true 2D situations).

NM SESES offers user friendly and efficient interfaces for user-defined interactionsnon-locality is handled by domain decomposition methods in order to obtain an efficient, fast algorithm.

Fuel Cell Research Symposium, Modeling and exp. Validation, 18./19. March 2004

Implementation 2

Implementation of the 1D interaction

• Shooting Method for non-linear ODE system

• Realization as C-program

Setting up mapping transformation

Formulation of interactions in terms of functions of the form

Defining iteration algorithms

• Using domain decomposition techniques to decompose the degrees of freedom

• Adopting convergence acceleration methods (e.g. SOR)

Map tr(x,y)

)tr,OH(At,O,OH,Hfr 2222H2

Fuel Cell Research Symposium, Modeling and exp. Validation, 18./19. March 2004

Preliminary Results 1

Simple Test Model (Co or Counter flow)

H2O molar fraction current density H2O transfer rate

Fuel Cell Research Symposium, Modeling and exp. Validation, 18./19. March 2004

Preliminary Results 2

0 1 2 3 4 5 6 7 8

x 10-4

0

0.5

1

1.5

2

2.5

3

3.5Water content (lambda) / -

lambda (H2O)

0 1 2 3 4 5 6 7 8

x 10-4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1mass fractions / -

mH2mH2OmO2mN2

Inspection of internal states

0 1 2 3 4 5 6 7 8

x 10-4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1mass fractions / -

mH2mH2OmO2mN2

0 1 2 3 4 5 6 7 8

x 10-4

0

2

4

6

8

10

12

14Water content (lambda) / -

lambda (H2O)

λ value in Membrane

Mass fractions in GDL

Fuel Cell Research Symposium, Modeling and exp. Validation, 18./19. March 2004

Preliminary Results 3

Test Cell Model

Velocity

Cathode Anode

Pressure

Fuel Cell Research Symposium, Modeling and exp. Validation, 18./19. March 2004

Preliminary Results 4

Species molar fractions H2O

sheet resistance of Membrane

O2

H2

Fuel Cell Research Symposium, Modeling and exp. Validation, 18./19. March 2004

2½D Modeling is an interesting approach to bridge the gap between complex geometries / interactions and the need for PEM cell / stack models

NM SESES is easily equipped with user defined interactions that model electrochemistry, water transport, etc. in PEM membranes

Efficient numerical iteration schemes allow for fast solutions of these numerical models.

Full modeling for cells of technical relevance is in reach

There is a lot of work to do: extension of the water transport in GDL and Membrane (e.g., two phase description)

Extensive validation of the models is a demanding work in itself, but mandatory for save application in technical developments

Further Steps: Extensions to dynamic models to support the control system development

Conclusions

Fuel Cell Research Symposium, Modeling and exp. Validation, 18./19. March 2004

Proposal

Many Different Modeling approaches are (and will be) discussed. Each variant with its specific pros and cons.

Models, which are in vertical relation to each other, can provide parameter input to the lower level models (e.g., similar to the VAM)

Models which are on the same level can serve as test bench to improve the quality, accuracy and efficiency

Benchmarking

Choosing a test cell of technical relevance including all important data regarding geometry, material properties, typical operation conditions, etc. (provided, e.g., by the PSI group)

Defining operation states with extensive experimental data (already present?).

Benchmarking the approaches: Model Accuracy, using detailed models to evaluate parameters for coarser models, etc.

Setting up an Internet site with the contributions (including a news group?)

Financing?