Modeling and simulation are key to developing FCEVs

Special Focus: Future of hydrogen energy

Modeling and simulation are key to developing FCEVs

A potential way to help reduce greenhouse gas emissions and slow climate change is replacing internal combustion engine vehicles with electric vehicles. Electric vehicles also offer the advantage of reducing pollutant emissions in densely populated areas, thereby improving air quality for citizens. Electric vehicles powered by wind electricity have very small greenhouse gas emissions during operation. However, substantial emissions levels arise during the manufacturing stage of these vehicles.

Fuel cell electric vehicles (FCEVs) offer several advantages compared to battery-powered electric vehicles (BPEVs). They can achieve a higher energy density (especially for heavy vehicles) and higher efficiency—if the comparison is made assuming that the electricity for charging the batteries is produced using H2—and they do not require capacity to deliver very high power from the electric grid when refueled, compared to the recharge of the battery-powered vehicles.

The main limitations of fuel cells for electric vehicles are the manufacturing cost, limited service life, and relatively low power density.1

The design limitations

The three limitations mentioned previously all boil down to the microscopic design of the active layer in the oxygen (O2)-reducing gas diffusion electrode: the cathode in the fuel cell. Other aspects are important, as well, but the design of the active layer is paramount.

The catalyst used in the active layer is platinum. The platinum loading of the active layer determines the lower limit for the manufacturing cost. The manufacturing cost of almost everything else in the fuel cell can be reduced, but it is difficult to reduce the cost of platinum. It is, therefore, necessary to develop active layers that require a very low catalyst loading without reduced performance.

Service life is limited by different degradation mechanisms, such as proton reduction, platinum dissolution, carbon corrosion, the formation of radicals that attack the membrane electrolyte in the active layer, adsorption of impurities on the catalyst sites, and accumulation of impurities in the pore electrolyte.2 Changes of hydrophobicity in the cathode’s active layer may cause flooding of the cathode.

The limitation in power density may be caused by the limited catalytic activity of the cathode: the O2 electrode. This activity can be increased by a higher catalyst loading. However, this also means a higher cost and a shorter service life since a higher power density requires a higher current density.

The active layer

To improve the design of the active layer for vehicle fuel cells, engineers and scientists must understand the fundamental transport phenomena, electrode kinetics, thermodynamics, electrolyte chemistry and catalytic surface activity involved in the charge transfer reactions in this layer at the microscopic level.

Let us look closer at the transport and reaction processes that may occur in the active layer in a fuel cell electrode. We can consider a proton exchange membrane fuel cell (PEMFC), which is the strongest fuel cell candidate for use in electric vehicles. The reactions at the anode and cathode are detailed here.

The electrons released at the anode are conducted by the electronic conducting electrode material to the outer circuit. In the outer circuit, the electrons are conducted over a load and then to the cathode. The protons (hydrogen ions) are transported in the electrolyte and the separator to the cathode. At the cathode, the protons react with O2 from the cathode gas, electrons are received from the external circuit, and water is formed.

FIG. 1 shows a schematic drawing of the processes at the anode’s active layer. Note that the active layer contains the anode material with the catalyst (blue), pore electrolyte (green) and gas-filled pores. The pore electrolyte consists of proton-conducting polymer that has been infused into the porous electrodes. H2 from external gas channels is transported in the gas-filled pores and dissolved in the pore electrolyte. It is then transported through a thin film of pore electrolyte to the active catalyst site (white dashed circle in FIG. 1) and oxidized to produce hydrogen ions (protons) at the active site. The electrons released in the oxidation are conducted through the anode material to the outer circuit.



FIG. 1. The processes that occur in the active layer in a PEMFC anode.



Once the hydrogen ions have migrated to the cathode, they may react with O2 at the active sites at the cathode (FIG. 2). O2 is transported through the gas-filled pores in the cathode and through a thin film of pore electrolyte before it reaches the active sites. At the active site, O2 and protons receive electrons, over the outer circuit and through conduction in the cathode electrode material, to produce water. The reaction at the active site depends on the local electrode potential in relation to equilibrium, the local O2 concentration and the local water activity. The formed water molecules can be transported out of the cathode as vapor or as liquid water. Precipitation of liquid water in the gas-filled pores may occur depending on the pore structure and on the local water vapor partial pressure.


FIG. 2. The transport and reaction processes that occur at the cathode.



The migration of hydrogen ions from the anode to the cathode also depends on the water content of the membrane. Each hydrogen ion drags a few water molecules over the membrane electrolyte from the anode to the cathode.

So, there are transport processes in the gas phases in both electrodes, transport in the pore electrolyte, transport of water and protons in the membrane, and kinetic expressions for the charge transport relations at the active sites. Processes may also be added that describe the deterioration of solid particles (e.g., through oxidation). The model equations describing these processes are coupled and depend on each other.

The solution of the model equations reveals the losses in the different reaction and transport processes. For example, if water precipitates in the gas-filled pores at the cathode, the transport of O2 gas through the gas-filled pores is slowed dramatically. If the model predicts a deterioration of the particles (e.g., by oxidation that causes them to detach from the pore electrolyte or the rest of the electrode material), then the electrons cannot be transported to and from the active sites, causing losses in performance.

Time scales

The contribution of the different processes to the losses in the cell are difficult to estimate experimentally. Here, combining models with experiments is a great help. The key to understanding the losses in the cell is that the different processes occur at different time scales.

The transport processes in the pore electrolyte and in the gas-filled pores, the conduction of ions, the conduction of electrons and the charge transfer reactions all occur at different time scales. Diffusion in the pore electrolyte is several orders of magnitude slower than diffusion in the gas-filled pores. Ionic and electronic conduction are extremely fast processes. Charge transfer reactions can be slow (cathode) or relatively fast (H2), but are relatively fast compared to the diffusion in the pore electrolyte. Transient techniques, such as current interrupt and impedance spectroscopy, can be modeled and then compared to and validated using experiments. The contribution of the different losses can also be followed over time for different operating conditions during the aging of a cell.

The principle of impedance spectroscopy is quite simple. An average voltage (V0) is applied with a small sinusoidal perturbation over time. As a consequence, a corresponding sinusoidal current is obtained as a response to the voltage perturbations (FIG. 3).


FIG. 3. A perturbation in electrical potential over the cell results in a current response.


The current response may have a shift in time (δt) compared to the voltage. A shift can be caused by processes that delay the response of the current to the sinusoidal perturbation in voltage. For example, at low frequencies, slow processes such as diffusion may be responsible for such a shift, while fast processes may be able to perfectly “follow” the voltage perturbations. At high frequencies, slow processes will only “see” the average voltage; they will not be able to respond to the voltage perturbations.

Instead, fast processes, such as the reaction kinetics, will be responsible for the shift in the response at high frequencies. Additionally, the amplitude of the response (δI) may also vary at different frequencies.

By sweeping over different frequencies, the method is able to separate processes with different time constants. The time shift and the current response’s amplitude to the voltage perturbation are reflected in the complex impedance, where a shift in time is reflected in the imaginary part of the impedance. The absolute value of the impedance reflects the proportionality of the response.

For a fuel cell, the impedance response gives insight into several fuel cell properties and processes. At high frequencies, short-time-scale processes, such as capacitance, electrochemical reactions and local resistances, affect the impedance. On the other hand, at low frequencies, phenomena such as the diffusion in the pore electrolyte contribute to the impedance. Frequency sweeps can be carried out at different polarizations of the fuel cell to investigate phenomena at different loads. The combination of modeling impedance spectroscopy and parameter estimation with experimental data can then provide accurate descriptions of transport and reaction properties in fuel cells during operation at different loads. Over time, the models and experiments may reveal the source of deterioration of a cell. This implies that the proper actions in design and material selection can be taken to increase performance and slow deterioration.

FIG. 4 shows a so-called Nyquist plot of the results from a high-fidelity model of a fuel cell unit cell. This is a small experimental cell where the conditions can be accurately controlled. The model shows the effect of the reaction kinetics at the active sites of the cathode. As the catalyst deteriorates, the cathodic semicircle grows (so the impedance grows). However, there is no change at very high frequencies since the kinetics are unable to react to very fast perturbation. The ohmic losses in the cells are constant. In this way, it is possible to separate other losses, too, such as ohmic or transport losses.


FIG. 4. Results from an impedance spectroscopy simulation of a fuel cell unit cell. The activity of the cathode catalyst is varied in four different frequency sweeps.


Modeling and simulations offer an effective, almost unique way of studying the processes. As mentioned above, it is difficult to measure the phenomena that occur in the active layer during operation. Instead, these phenomena can be modeled in detail, and their impact at the macroscopic level can also be modeled in so-called multiscale models.2 Experiments can be designed to verify the implications of the microdesign.

One example is the connection of physics-based models for impedance spectroscopy with measurements, as shown in FIG. 4. This allows for scientists and engineers to separate processes in different time scales, such as diffusion (slow) and current conduction (fast). Studying what limits the response to perturbations at different time scales may reveal which process limits the performance at the microscale.3,4,5

Once the processes are understood, more direct methods may be used. An example is the innovation of using ordered porous structures in the active layer to lower tortuosity. Ordered structures may increase the transport of reactants, improve access to the catalyst surface, and yield a uniform current density distribution in the active layer.1,6 The results may be improvements in performance without requiring a higher platinum load or causing the accumulation of water or harmful byproducts that may deteriorate the performance of the active layer over time.

Modeling and simulations are not only useful for exploring new ideas. Once a good design has been innovated, mathematical models can be used to further optimize design and operational parameters. This development is evolutionary and can be made almost automatic by gathering data from operation.

The fuel cell unit cell and stack

Each microscopic part of a fuel cell is affected by the configuration of each cell and of the entire fuel cell stack. This implies that the microscopic details cannot be studied in isolation. They have to couple to the macroscopic factors that may impact a cell. The simulation shown in FIG. 4 treats an H2 channel and an oxygen channel in a fuel cell unit cell, with the electrodes and the membrane in between, as shown in FIG. 5.


FIG. 5. A unit cell model may consider a part of the membrane-electrode assembly, as well as the metallic plates that serve as the current collectors and feeders.



Each unit may be part of a stack connected to an external circuit, as shown in FIG. 6. The units may be equipped with straight parallel channels (FIG. 6) or serpentine channels (FIG. 7). Modern fuel cells, like in the Toyota Mirai,7 may also have a more complex structure for the O2 (air) gas feed. Here, a louver-like structure allows for water to flow down with gravity, away from the cathode, while oxygen can flow upward.


FIG. 6. Left: Stack with crossflow configuration, i.e., the O2 and H2 channels run in a 90° angle relative to each other. Right: One cell in the stack. FIGS. 1, 2, 5 and 6 illustrate the transition from the microscale to the stack scale.



FIG. 7. Relative humidity in a section of a serpentine channel PEMFC, in contrast to the straight channel configuration in FIG. 6. The section is small enough to include all of the relevant transport and reaction processes in the fuel cell in a high-fidelity model. Simulation in COMSOL Multiphysics.



In this way, the transport of liquid water in the O2 electrode is enhanced, which also enhances the transport of O2 to the active layer. Liquid water in the porous electrode hinders the transport of O2 and may also cause flooding. In addition, the use of a thinner membrane allows for back diffusion of water from the cathode to the anode, which also eliminates the need for humidifying the anode gas and lowers the risk of flooding. Toyota, with this design, has considerably enhanced the performance and simplified the design of its fuel cell.7 FIG. 8 shows a schematic drawing of what this louver structure may look like.



FIG. 8. A louver-like structure allows for water to flow down and O2 (air) to flow up. In this way, the transport of liquid water away from the cathode is enhanced and does not obstruct the transport of O2 in the electrode.7


High-fidelity models can be coupled and incorporated in models of a fuel cell unit cell, a stack and an entire system, including the electric drivetrain of the vehicle (the load in FIG. 6). This requires using fitted lumped models and reduced models that are automatically updated using detailed models when a new range of operation is encountered. In this way, modeling and simulations can also be used to determine the state and remaining service life of a fuel cell system.3


The development of fuel cells and the design of the active layer will continue to lead to lower platinum loads, longer service life and increased power density. To a great extent, this will be due to the understanding, innovation and optimization tools offered by modeling and simulations. These tools will also allow for an optimal combination of fuel cells, batteries and supercapacitors to deliver energy and power density at a low cost and with maximum service life. Modeling and simulations will continue to be important in the work of reducing greenhouse gas emissions and other pollutants from cars, buses and trucks.H2T



  1 Bethoux, O., “H2 fuel cell road vehicles and their infrastructure: An option towards an environmentally friendly energy transition,” Energies 2020, online:

  2 Strahl, S., A. Husar and A. Franco, “Electrode structure effects on the performance of open-cathode proton exchange membrane fuel cells:
A multiscale modeling approach,” International Journal of Hydrogen Energy, 2014.

  3 Sorrentino, A., K. Sundmacher and T. Vidakovic-Koch, “Polymer electrolyte fuel cell degradation mechanisms and their diagnosis by frequency response analysis methods: A review,” Energies 2020, online:

  4 Wiezell, K., P. Gode and G. Lindbergh, “Steady-state and EIS investigations of hydrogen electrodes and membranes in polymer electrolyte fuel cells,”
Journal of the Electrochemical Society, 2006.

  5 Wiezell, K., “Modeling and experimental investigation of the dynamics in polymer electrolyte fuel cells,” KTH Royal Institute of Technology, licensed thesis, Stockholm, Sweden, 2009.

  6 Sandström, R., “Innovations in nanomaterials for proton exchange membrane fuel cells,” doctoral thesis, Department of Physics, Umeå 2019.

  7 Yoshida, T. and K. Kojima, “Toyota MIRAI fuel cell vehicle and progress toward a future hydrogen society,” The Electrochemical Society Interface,
Vol. 24, No. 2, 2015.


Ed Fontes is the Chief Technology Officer at COMSOL. He has been with COMSOL since 1999, and previously served as the Lead Developer for the CFD, heat transfer and chemical engineering products. Dr. Fontes received his PhD in chemical engineering from the Royal Institute of Technology, Stockholm.


Henrik Ekström is the Technology Manager for electrochemistry at COMSOL. Prior to joining COMSOL in 2010, Dr. Ekström worked at various fuel cell startup firms in Sweden. He received his PhD in chemical engineering from the Royal Institute of Technology, Stockholm.