In this section, we consider the initial or basic design of the fuel-cell stack. The fuel-cell stack is part of the fuel-cell system, which itself is part of a larger system. Therefore, some of the important design specifications and constraints for the fuel-cell stack are derived from the high-level requirements of the larger system. For instance, we might be tasked to generate 400 kW of regulated AC power from natural gas using a SOFC, or to provide electrical power to a transit bus with a PEMFC running on compressed hydrogen, or to supply 100 W of electrical power for 36 hours continuously using a direct methanol fuel-cell system. A list of common high-level requirements is given in Table 10.1. For our purposes here, we will assume that we have already committed to a particular type of fuel cell and have identified the fuel and oxidant.

Table 10.1 Typical High-Level Requirements

Requirement	Units	Comments
Average net power	W	Conditioned electrical power minus ancillary power requirements
Nominal, maximum, and minimum voltages	V	Output voltage of the cell stack, not an individual cell.
System efficiency	–	As is done in practice, we’ll use the LHV, Equation 10.3.
Fuel source	–	Examples are compressed hydrogen, industrial natural gas, methanol
Oxidant source	–	Air in all but a few instances
Weight or mass	kg
Volume	m3
Heat sink	–	Available means to reject heat, typically the atmosphere is the sink
Lifetime	years	Important, but beyond the scope of this book

We now turn our attention to the design of the fuel-cell stack. As described in Chapter 9, the current versus potential or polarization curve establishes the basic performance of a single cell. Assuming that this performance is known and that the individual cell design is fixed, what is left for the fuel-cell designer to specify? It turns out that there are choices that can significantly impact the overall operation and efficiency. In this section, and those that follow, we will introduce a few basic concepts and trade-offs that are important to fuel-cell design. For example, consider the following:

1. At what point on the polarization curve should the fuel cell be designed to operate? A lower current density results in higher cell potential and greater efficiency. But the lower current density requires a larger cell area, increasing the mass, volume, and cost of the cell stack.
2. If the current density is established, is it preferred to have a few very large cells, or would a larger number of smaller cells be better? What shape should these cells take?
3. How will the required flow rates of air and fuel be distributed to these cells and within each cell?

We begin by developing an initial design for the fuel-cell stack. Table 10.2 lists variables that are critical to this design. Several important relationships exist between these variables that enable us to reduce the number that must be specified. The most important relationship is the polarization curve, written here as a function of the current density:

(10.10)

The second and third relationships are also connected to the polarization curve. The thermal voltage efficiency is directly proportional to the cell voltage (see Equation 10.6):

(10.11)

and the power generated per unit area is simply IV. Thus,

(10.12)

Table 10.2 Initial Design of a Fuel-Cell Stack Consisting of Eight Key Variables

Variable	Units	Comments
P	W	Power, gross average electrical power from the cell stack
ηV,t	–	Thermal voltage efficiency
Vs	V	Nominal voltage of the cell stack
Nc	–	Number of cells in the stack that are connected in series
Vcell	V	Potential of an individual cell
Ac	m2	Area of individual cell
A	m2	Total cell area, sometimes referred to as the separator area
i	A·m−2	Current density that corresponds to the nominal voltage

The total area and stack voltage are simply proportional to the number of cells in the stack, N_c:

(10.13)

(10.14)

where Equation 10.14 assumes that the cells are connected in series. With these five relationships (Equations 10.10–10.14), three of the eight variables must be specified to completely define a solution. Most commonly, the three specifications come from the system-level requirements and are the thermal voltage efficiency, the stack voltage, and the power.

The thermal voltage efficiency () needed for stack design can be estimated from the system thermal efficiency () with use of reasonable estimates for the fuel, mechanical, and power-conditioning efficiencies:

(10.15)

A similar estimation of the gross power of the stack can be made from the final power requirements for the system:

(10.16)

Use of these relationships is shown in the following illustration, where the number of cells and area are determined.

ILLUSTRATION 10.2

The fuel cell described in Illustration 10.1 requires a voltage for the stack of 190 V; determine the number of cells that must be connected in series and the area of each cell. Assume a power conditioning efficiency of 0.94 and a fuel efficiency of 0.76. The current–voltage performance of the cell is provided in the figure.

SOLUTION:

In the previous illustration, we assumed that the electrical losses were zero. When included, the gross electrical power generated by the stack must increase (Equation 10.16):

The thermal voltage efficiency () is needed for the stack design. We can estimate its value using () from Illustration 10.1, and the additional efficiencies given above. We still need the mechanical efficiency, which can be estimated from the information given in the previous illustration:

Next, we need to convert this thermal voltage efficiency to a cell potential. Applying Equation 10.11,

For the methane reaction at standard conditions, . Therefore, the cell voltage is 0.575 V. Using the graph, a cell potential of 0.575 V corresponds to a current density of 9500 A·m⁻². The number of cells in the stack is the number of cells in series needed to achieve the specified stack voltage.

Finally, we need the cell area. The gross power from the stack and the stack voltage can be used to determine the current required from the stack:

In the next three sections, we discuss how these cells are assembled and explain in more detail how the reactants are supplied. With this knowledge, we can see how volume and mass enter into the analysis.