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Bond Graph Modelling of a Solid Oxide Fuel Cell

  • P. VijayEmail author
  • A.K. Samantaray
  • A. Mukherjee
Chapter

Abstract

Fuel cells are environmentally friendly futuristic power sources. They involve multiple energy domains and hence bond graph method is suitable for their modelling. A true bond graph model of a solid oxide fuel cell is presented in this chapter. This model is based on the concepts of network thermodynamics , in which the couplings between the various energy domains are represented in a unified manner. The simulations indicate that the model captures all the essential dynamics of the fuel cell and therefore is useful for control theoretic analysis.

Keywords

Solid oxide fuel cell Bond graph Network thermodynamics Electrochemical reaction Fuel utilization 

Notation

Ac

Effective cell area (m2)

cp, cv

Specific heat capacity at constant pressure and volume (J kg−1 K−1)

E

Activation energy (J mol−1)

F

Faraday’s constant (C mol−1)

G

Gibbs free energy (J)

h

Specific enthalpy (J kg−1)

H

Enthalpy (J)

i

Current (A)

K

Valve coefficient (m s)

m

Mass (kg)

\(\dot {m}\)

Mass flow rate (kg s−1)

M

Molar mass (g)

n

Number of moles (mol)

ne

Number of electrons participating in the reaction

p

Pressure (N m−2)

R

Specific gas constant (J kg−1 K−1)

R

Universal gas constant (J mol−1 K−1)

s

Specific entropy (J kg−1 K−1)

S

Entropy (J K−1)

\(\dot {S}\)

Entropy flow rate (J K−1 s −1)

T

Temperature (K)

u

Specific internal energy (J kg−1)

U

Internal energy (J)

v

Specific volume (m3 kg−1)

V

Volume (m3)

\(\dot {V}\)

Volume flow rate (m3 s−1)

w

Mass fraction

x

Valve stem position (m)

ν

Stoichiometric coefficient

η

Over-voltage (V)

μ

Chemical potential (J kg−1)

ψ

Pre-exponential coefficient (A m−2)

ξ

Reaction advancement coordinate (mol)

\(\zeta_\mathrm{f} ,\zeta_\mathrm{o} \)

Fuel and oxygen utilisations

β

Charge transfer coefficient

λ

Convection heat trans. coefficient (J m−2 s−1 K−1)

Subscripts

ai

Anode side inlet

an

Anode

ao

Anode side outlet

act

Activation

AS

Air source

b

Bulk

ca

Cathode

ci

Cathode side inlet

co

Cathode side outlet

conc

Concentration

d

Downstream side

ENV

Environment

gen

Generated

H

Hydrogen gas

HS

Hydrogen source

I1

Interconnect on anode side

I2

Interconnect on cathode side

L

Limiting

M

Membrane electrode assembly

N

Nitrogen gas

ohm

Ohmic

O

Oxygen gas

PL

Polarisation losses

r

Reaction

TPB

Triple phase boundary

u

Upstream side

W

Water vapour

Superscripts

i

Inlet

o

Outlet

r

Reaction

ref

Reference state

0

Initial state

Notes

Acknowledgments

The first author would like to acknowledge Prof. Moses Tadé, Dean of Engineering, Curtin University of Technology, for kindly permitting him to write this chapter during his stay as a research associate at the University.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Chemical EngineeringCurtin University of TechnologyPerthAustralia
  2. 2.Department of Mechanical EngineeringIndian Institute of TechnologyKharagpurIndia

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