Page 332 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

308 High Temperature Solid Oxide Fuel Cells: Fundamentals, Design and Applications

11.5 Cell- and Stack-Level Modelling
The coupled continuum-level electrochemical, flow, and thermal models are
usually discretised in a finite element mesh [23,24]. When the necessary
material properties, geometrical parameters, operating parameters, and
boundary conditions are supplied, cell- and stack-level performance can be
analysed. The combined models can determine the cell/stack voltage, the total
current output, temperature distribution, species concentration, etc.
An important outcome of the combined models at the cell level is the
cell efficiency, and at the stack level, the stack efficiency as well. The electrical
efficiency of a cell and of the stack is defined as
E,I = electrical power output/chemical energy input per unit time (23)

for the cell in question, and for the stack, respectively.
The electrical efficiency therefore depends to some extent on the definition of
the fuel energy input and on whether power for gas pumping and the like is
subtracted from the generated power. &,I may be expressed in terms of current,
voltage, etc., as follows:
eel = VI/(AHdn/dt) (244

This can be considered the product of three additional fundamental efficiencies,
namely the ideal or thermodynamic efficiency ( AG/AH}, the voltage efficiency
{V/Eo}, and the fuel utilisation (Uf}:
E,] = VI/(AHdn/dt) = {AG/AH}(V/Eo}(Uf} (24b)

The fuel utilisation, Uf, is the ratio of the delivered current to the stoichiometric
current equivalent to the fuel flow rate:

uf = I/(2Fdn/dt) (244

The ideal efficiency AG/AH may be considered a measure of the
thermodynamic reversibility of the reaction and depends only on the operating
temperature and fuel used. It is typically between 80 and 100%. The voltage
efficiency and fuel utilisation, as well as the electrical energy efficiency, are
useful measures for the success of the cell and stack design.
Another important figure of merit predicted by the combined model is the
power density of a cell, or of the stack as a whole. The power density of a cell is
usually defined on the basis of the cell or electrode area, that is

Pce.l = I(current).V(cell voItage)/A(area) (254

The power density of a stack is conveniently defined on the basis of stack volume:

Pstack = I(current) .V(staclr voltage)/V(stack volume) (297)