Modeling Optimizes Fuel Cells to Extract Peak Energy from our Fuels
By Paul G Schreier
Automotive and other vehicular applications place their own special requirements on fuel cells as a source of energy. In designing a cell, many things comes into play: cell potential, the pressure of the gas in the anode and the cathode, relative humidity (indicating how much water is in the fuel and the oxidant), and even the dimensions of key elements, among them the membrane and the gas channels.
Not just one best design
COMSOL Multiphysics has become an important tool for Galip Guvelioglu, who under the guidance of Professor Harvey Stenger is focusing on the optimization of Polymer electrolyte membrane fuel cell (PEMFC) designs in his PhD research at Lehigh University (Bethlehem, PA). As he explains, the design and operating conditions that give optimal performance depend on the application area. Stationary, portable, and transportation applications all have different requirements, operate in different environments, and the available fuel and oxidant conditions vary greatly. A PEMFC used in a stationary application could operate from fully humidified fuel and benefit from a compressor to increase air pressure, which increases the cell's power output. In contrast, a fuel cell in portable applications such as laptop PC or cell phone would most likely operate with air at atmospheric conditions. Furthermore, the amount of water available for fuel and air humidification in a portable fuel cell might be limited.
Other requirements vary by application, as well. The startup time and transient response requirements for a fuel cell used in transportation applications don't have the same importance as in a cell that is for stationary applications. Fuel cell weight is much more critical in mobile appliances, and it limits the choice of materials for manufacturing. What all this means to Guvelioglu is that "COMSOL Multiphysics makes it fast and easy to try all sorts of combinations of geometries, materials, and operating conditions to come up with an optimum design for the application."
Figure 1: Two key elements of a polymer electrolyte membrane (PEM) fuel cell are the catalyst layers, which separate the hydrogen into protons ans electrons, and the proton-exchange membrane, which allows protons to pass from the anode to the cathode where they are combined with oxygen and electrons to produce water.
A peek inside
To see in more detail how some of these requirements impact design approaches, look at the internal operation of a PEM fuel cell in Figure 1. The PEM cell gets its name from the type of electrolyte it uses, a polymer-based ion exchange membrane, which is an excellent proton conductor. The membrane is sandwiched between two platinum-based active catalyst layers. Those layers, in turn, are backed by porous gas-distribution electrodes, usually made of carbon cloth. This entire assembly is called the membrane electrode assembly (MEA), and its typical thickness is roughly 0.5 - 0.8 mm. Finally, the MEA is sandwiched between two plates whose etched channels serve not only as a manifold for the transfer of feed and exhaust products in and out of the cell but also as the current collector. In operation, the fuel cell continuously feeds gaseous hydrogen to the anode (negative electrode) compartment and also continuously feeds an oxidant, such as oxygen from the air, to the cathode (positive electrode) compartment. Electrochemical reactions at the electrodes produce an electric current (Figure 1).
A fuel cell, although having components and characteristics similar to those of a typical battery, differs in several respects. A battery is an energystorage device, with the maximum available energy determined by the amount of chemical reactant stored within the battery itself. The fuel cell, on the other hand, is an energy-conversion device that theoretically can produce electrical energy for as long as fuel and oxidant are supplied to the electrodes.
The waste products of fuel-cell reactions are water and heat. Because a fuel cell directly converts chemical energy to electrical energy, the maximum theoretical efficiency is not bound by the Carnot cycle. PEMFCs typically achieve fuel efficiencies as high as 50% and are attractive in automobile applications for several reasons. First is high power density-today they easily achieve 1 A/cm2. A single fuel cell produces roughly 0.6 V at high power output, so to get a potential difference that is usable, engineers stack multiple cells in series, similar to batteries. Constant improvements in engineering and materials have increased power density such that a fuel-cell stack smaller than an internal combustion engine can power a mid-size passenger vehicle.
To make this technology viable in the commercial marketplace, though, researchers must still address several challenges. The cells are sensitive to impurities in fuel and air. Engineers must also drastically reduce prices. The major costs of PEM fuel cells are those associated with materials used in production, where the platinum electrode contributes 50% of the total followed by the costs of the bipolar plate.
Thus today's researchers are looking for ways to reduce the amount of platinum needed and also to efficiently use available platinum by improving the cell-channel design and experimenting with alternative materials. They're also trying to increase full-cell reliability and durability while improving performance, manufacturability and operational flexibility.
Many advantages of COMSOL Multiphysics
Galip Guvelioglu, PhD student, Lehigh University.
Towards these goals, Guvelioglu is looking specifically for the best size and shape of the gas channels as well as choosing the proper components for cell construction. He´s also examining water and thermal-management issues to improve reliability.
One of his main tools is COMSOL Multiphysics, which he selected for several reasons. His options were to use a commercial CFD (computational fluid dynamics) package for modeling, or create a PDE solver from scratch to get the required modeling flexibility for studying all the applications. Most CFD packages require workarounds or simplifications of the model to get their application modes to suit his requirements. Another reason to use COMSOL is that it gives him the ability to define custom PDEs. "Writing my own PDE solver to model PEM fuel cells would be like inventing the wheel and then the car, just to go to the supermarket. COMSOL has invested hundreds of programmer-years for me, and by using COMSOL Multiphysics I get the best of both worlds-the benefits of their development work along with extreme flexibility in entering my own PDEs."
Another key advantage is the fact that COMSOL Multiphysics integrates so closely with MATLAB and Simulink from The MathWorks. A complete fuel-cell system involves compressors, pumps, humidifiers, heat exchangers, converters, and DC motors. Having an efficient fuel cell doesn�t necessarily mean the overall system is efficient, so engineers must take a systems approach during design and optimization. Towards this goal, Guvelioglu wants his fuel-cell models to tie into the Department of Energy´s Advanced Vehicle Simulator (ADVISOR). This Simulink-based program evaluates the performance of components such as motors, batteries, catalytic converters, climate-control systems, and alternative fuels as well as other modifications that might affect fuel economy, performance, or emissions. In this case, he takes his COMSOL Multiphysics model and converts it into a MATLAB M-file that he can call as a regular MATLAB function.
Entering custom PDEs directly from the keyboard
As noted earlier, Guvelioglu needs to work with specialized PDEs. A fuel cell is a complex multiphysics device that, besides well-known physics, involves specialized mass-transport equations that describe water-transport phenomena in the membrane. These equations are important because proton flow in the membrane affects the water transport there along with common convection and diffusion. His application thus invokes Darcy's law for flow in the porous electrodes, the Maxwell-Stefan equation for multicomponent diffusion and convection, electronic charge balance in the electrodes and membrane, and Butler-Volmer type kinetics for local current densities at the catalyst layers.
Further, in the specialized water mass-flux equation the first term governs migration. This term isn't typically included in a normal transport process, but with COMSOL's flexible user interface he was able to handle it by setting up the equations directly in the graphical user interface without writing a custom code, compiling it and linking it to the package.
Figure 2: These plots show PEM fuel-cell membrane water content and net water flux vectors at three different current densities for a fuel-cell operating at 80°C with fully humidified hydrogen and air at 3 and 5 atm pressures, respectively.
This analysis, coupled with thermal management, is a very critical aspect of the simulations because the membrane's ionic conductivity increases with water concentration in the membrane-and thus fuel-cell efficiency. The plots in Figure 2 summarize the membrane's water content and net water flux for three operating potentials (current densities). At low current densities (left) the net water flux is from cathode to anode due to higher pressure of the cathode side, thus yielding higher water content closer to anode. As the current density increases (middle), the migrative flux exceeds the diffusive and convective fluxes, thus the net flux of water changes direction. When the current density increases even more, the difference between migrative flux and diffusion and convection gets higher, resulting in decreased membrane water content at the anode side as visible in the plot on the right. Lower water content increases the membrane resistance, and the temperature rises due to resistive heating, potentially causing permanent damage to the membrane. At the same time, the increased net water flux from anode to cathode shows that the back diffusion and convection of the water from cathode to anode are not sufficient to keep the membrane hydrated, thus extra water must be added by humidifying the entering fuel and oxidant. Adding too much water, however, could flood the electrodes, creating transport limitations and reducing the power output and even interrupting it. Thus, Guvelioglu uses his COMSOL Multiphysics model to carefully balance the water content for efficient and reliable fuel-cell operation.
Easy model optimization
In designing a cell, everything comes into play: cell potential, the pressure of the gas in the anode and cathode, relative humidity (indicating how much water is in the fuel and the oxidant), and even the dimensions of various elements, key among them being the membrane and the gas channels.
Guvelioglu does much of his optimization and sensitivity work utilizing COMSOL Multiphysics with MATLAB because the command-line access provides enormous freedom for him to study the model´s geometric parameters such as channel and bipolar plate shoulder sizes as well as operating conditions. He can study them with a single MATLAB M-File by using For loops, a feature not available in other CFD packages. As he explains, "In COMSOL Multiphysics I can edit just one line of code to change the channel size. COMSOL also gives me the convenience of having one package and user interface for creating the geometry, meshing, and post-processing. I was able to use the tool for my research just hours after I completed a few tutorials. COMSOL Multiphysics gave me the opportunity to focus on the fuel-cell problem instead of devoting time to learning a specific tool."
This same flexibility and ease of use translate into other areas of research for Guvelioglu. "We've used COMSOL Multiphysics not just for fuel cells but for other problems in plasma generators and electrolysers. The time savings are enormous. Now I can model completely different problems in far less time than with other CFD packages. When I tell my colleagues, 'I can do that model in less than an hour,' they´re extremely impressed. The secret is COMSOL."