Generative Design Puts Hydrogen Fuel Cell Development in High Gear

As an alternative to battery-electric vehicle drivetrains, Toyota is pursuing development of hydrogen–oxygen fuel cells to power cars, trucks, and even entire cities. Toyota Research Institute of North America (TRINA) has developed a simulation-driven methodology for accelerating the R&D process for fuel cell flow field plates.

By Alan Petrillo
April 2023

"Electrify everything." Among those seeking to reduce the world's reliance on fossil fuels, this phrase has become a rallying cry. We can see the electrification imperative in action all around us, as hybrid gas–electric vehicles (HEVs) and battery–electric vehicles (BEVs) are now familiar sights on the highway. But even as many automakers ramp up HEV and BEV production, one company is dedicated to developing electric cars that do not rely primarily on batteries for energy storage. Instead, these cars carry hydrogen, which provides electricity when combined with oxygen from the air inside a fuel cell.

The company pursuing this alternate route is Toyota. The commercialization of hydrogen-fueled vehicles faces many obstacles, but if anybody can put the world on fuel cell-powered wheels, it could be the world's largest automaker (Ref. 1). Toyota is directing great financial, physical, and human resources toward automotive fuel cell research, but it sees vehicle development as only the beginning of a long journey. The company's vision leads far beyond cars; it foresees the emergence of a global "hydrogen society". In this proposed society, fossil fuel-burning engines, heating systems, and generators would be replaced by fuel cells that extract electric current from hydrogen. Toyota's efforts to reach this destination are as far-sighted as its adoption of the Japanese city of Susono as a hydrogen-tech test bed, and as focused as its refinement of a generative design methodology for optimizing fuel cell performance.

Generative Design Enabled by Simulation

Toyota Research Institute of North America (TRINA) has developed a simulation-driven generative design method and applied it to the design of flow field microchannel plates, which direct the movement of fluid reactants in microreactors like hydrogen–oxygen fuel cells. While much of Toyota's fuel cell R&D is necessarily confidential, the TRINA team has published an article in Chemical Engineering Journal (Ref. 2) about their simulation-enabled "inverse design" process. Applying this process to flow field plates resulted in four distinctive microchannel designs, as shown in Figure 1.

Figure 1. Simulation results from the TRINA team's model, built using the COMSOL Multiphysics® software, showing the pressure distributions resulting from four different microchannel flow field designs.

Each of the four designs has particular merits; all of them outperform existing benchmark designs in terms of key metrics. Just as important, they exemplify the power of process. TRINA has shown how generative design enabled by simulation can accelerate innovation — even when a project's ultimate destination may be far into the future.

"We think that the inverse approach can revolutionize current design practice," says Yuqing Zhou, a research scientist at TRINA. "We are enabling the next step in a long journey, even though we cannot know exactly where that journey will lead."

Cleaner Powertrain Options

Considering this spirit of open-ended inquiry, perhaps it is understandable that Toyota is sustaining its decades-long pursuit of fuel cell research, even as most automakers have committed exclusively to battery power for electric vehicles. As Chairman Akio Toyoda put it in a November 2022 interview (Ref. 3): "Think of Toyota as a department store offering every available powertrain."

Figure 2. A schematic of the important components of a hydrogen fuel cell-powered vehicle. Image in the public domain, via the U.S. Department of Energy.

While a hydrogen–oxygen fuel cell may seem like an exotic way to supply power to a car (Figure 2), the technology itself is not new, and its operation is appealingly straightforward. Figure 3 presents the fundamentals of a generic fuel cell in action.

Figure 3. A schematic of a generic fuel cell design. One flow field plate distributes hydrogen gas toward the anode–electrolyte–cathode stack while the other plate distributes oxygen to the stack and channels away water. Note: While this illustration shows the oxygen-side fuel plate on top of the stack assembly and the hydrogen-side plate below, the actual orientation of a fuel cell can vary.

As hydrogen gas flows across the anode, it encounters a catalyst, which separates it into hydrogen ions and electrons. Whereas the hydrogen ions move through the electrolyte to reach the cathode, the electrons move through a conductor outside the fuel cell. It is this electric current that can be harnessed to perform useful work.

As oxygen gas from the air flows across the cathode, it encounters the hydrogen ions and returning electrons at the surface of the cathode. Here, the oxygen molecules split and combine with the hydrogen ions and electrons to form water.

A Reactant's Path Through a Flow Field Plate

For as long as hydrogen and oxygen keep flowing, a fuel cell will keep generating electric current. Managing the distribution of these essential gases is the job of the cell's flow field plates. Each plate includes both a microchannel structure and a porous sublayer. As hydrogen moves through the channels of the anode-side plate, it is also being forced through the sublayer toward the anode. Meanwhile, air is channeled through the flow field plate on the cathode side of the fuel cell. Air and water are exchanged through the cathode-side porous material layer, and the plate then channels excess air and water away from the cell stack. Figure 4 offers a simplified close-up of this essential process for the cathode side.

Figure 4. A simplified schematic of how fluid moves through the cathode-side flow field plate assembly of a fuel cell. A microchannel structure (shown in dark gray) defines a path through which reactant fluid (in this case, air) moves from an inlet to an outlet. As the fluid flows, some of it is diverted away from the flow field, through a porous material layer toward the cathode surface.

In their journal article on this project, the TRINA team explains that "uniformity of fluid residence time or fluid flow distribution, and the relationship to optimal heat transfer, is directly related to the design of the flow structure, which is of primary importance for proper control of chemical reactions."

Accordingly, the two main objectives for fuel cell flow field plate design are to maximize fluid flow across the plate's microchannel flow field and through the porous material layer, in order to supply sufficient reactant to the electrode. The first objective can be understood as a goal of reducing resistance to reactant flow, while the second seeks to enhance reactant conversion and reaction uniformity across the entire area of the electrode surface.

Inverse Design: A Simpler Process for Creating Complex Formal Solutions

The physical arrangement of microchannels helps determine how well a flow field plate meets its performance objectives. Historically, microchannel designs have followed a few familiar patterns, such as the serpentine type shown at left in Figure 5. More complex forms could improve performance, but increasing a design's complexity adds to the time needed to define, fabricate, test, and adjust that design.

Figure 5. Existing designs for flow field microchannels have followed simple patterns, such as the serpentine type shown at left. More intricate channel designs (right) could distribute fluid through the porous material layer more effectively, but adding physical complexity can also make design and manufacturing more complex.

Zhou and his colleagues recognized that before trying to optimize their designs, they first had to optimize their design process. To generate a more complex (and higher-performing) formal solution to their problem, the TRINA team created their simulation-driven inverse design methodology. Their methodology does not define forms in advance of testing, but rather sets key parameters and then directs algorithms to generate forms that fulfill those parameters. Versions of this approach have been variously described as generative design, topology optimization, and inverse design.

"We were seeking an efficient way of approximating what a more complex simulation would show. We have sacrificed some modeling complexity, which actually enables us to explore more elaborate designs in less time," Zhou says.

To illustrate his point, Zhou points to complex microchannel designs like the one shown at right in Figure 5. "Some people use topology optimization for problems like this, and they come up with designs that maybe have 10 channels. This is because they are asking their algorithm to determine the exact placement of every physical element of the channels in advance, which requires a lot of computing power and time to achieve a complex design like we see here," he explains.

From Desired Results to Novel Forms, Faster

So how could the TRINA team use its methodology to efficiently generate better microchannel designs? First, they simulated idealized flow trajectories through the effective anisotropic porous material, as shown at left in Figure 6; then they extracted values that described the idealized fluid behavior. Next, they input those values into another simulation, which generated the microchannel forms that would cause that behavior, as shown at right in Figure 6. Essentially, they defined the effect they wanted their designs to produce before designing anything. This sequence describes the inversion behind inverse design.

As described in the TRINA team's research paper:

"By abandoning the explicit modeling of channels during the optimization stage, which requires a large number of function evaluations, the physics inside an anisotropic porous media is captured using relatively coarse mesh discretization of the design domain."
Figure 6. An illustration of desired flow trajectories through the porous material (left), and at right, a simulation image of microchannel forms that will cause fluid to follow the desired trajectories.

"Our COMSOL model of the porous material has only two material values and a very coarse mesh," Zhou explains. "We implement a sensitivity-based optimization process based on Navier–Stokes and advection–reaction–diffusion equations. We assume steady-state, incompressible, and laminar fluid flow through the porous media, and that the desired chemical reactions will occur proportionally to the reactant concentration. We run these simulations to arrive at an optimal distribution of fluid flow orientation through the pores. This process gives us valuable results with a huge reduction in computational complexity."

Zhou describes this part of the overall design process as homogenization. Having now established a pattern of ideal trajectories of fluid through the plate's pores, the next step is dehomogenization. This step involves the equation-driven definition of microchannel forms that will force fluid to follow these optimal paths.

Generated Designs That Maximize Flow, Reaction, or Both

The dehomogenization step is needed, Zhou says, because "we cannot fabricate an ideal porous material with each pore individually designed. We need to install walls and channels to direct fluid through the pores in ways that approximate the ideal. To generate this design, we use COMSOL Multiphysics® to solve a customized partial differential equation (PDE) for pattern generation. The software also gives us plotting functions we can use to visualize the results."

Two of the formal options created by TRINA's dehomogenization equations are shown in Figure 7 and Figure 8. As noted earlier, the guiding performance objectives are: 1) to reduce resistance to reactant flow and 2) to enhance reactant supply and reaction uniformity across the entire plate. These objectives are represented by governing variables in the model's PDE. By assigning different weighting factors to these two objectives, Zhou and his team can induce the model to generate different design options. They can then evaluate the relative merits of each option and make adjustments to produce further iterations.

Figure 7. Four visualizations that describe different aspects of a flow-optimized microchannel design. In all figures, fluid flows from the inlet at the upper left to the outlet at the lower right. Upper left: the desired flow orientation vectors through the porous material. Upper right: orientation paths across the microchannel that can produce the desired vectors. Lower left: a dehomogenized microchannel design. Lower right: a simulation image of the sublayer showing the distribution of the reactant concentration.

Of the design shown in Figure 7, Zhou says, "We call this the 'flow design' because it leads to the smallest pressure drop across the entire flow field surface. The model generated paths that are relatively parallel and straight, without much side branching."

While this design effectively moves fluid across the plate, it does less well at distributing reactant evenly through the porous material layer. Simulation shows lower reactant concentration (shown in green and blue in the lower-right image in Figure 7) on the outlet side of the design, which can limit reaction uniformity and the resulting power output from the fuel cell.

What if the weighting factors in the governing equation were adjusted to prioritize reaction uniformity, rather than flow? The model would then generate a design like the one shown in Figure 8, which Zhou calls the "reaction design". High reactant concentrations (shown in red and orange in the lower-right image) now predominate, indicating that a larger share of the available reactant is being put to work. The intricate forms of the "reaction design" microchannels may seem familiar to students of biology.

Figure 8. Four visualizations that describe different aspects of a reaction-optimized microchannel design. This option features a mix of primary "arteries" and secondary "capillaries". The arteries sustain overall flow toward the outlet, while capillaries enable broader reactant distribution toward the electrode. In all figures, fluid flows from the inlet at the upper left to the outlet at the lower right.

"Most commercial microreactors would use a design somewhat similar to the 'flow design'," says Zhou. But naturally occurring systems that distribute fluid reactants — such as leaves, lungs, and blood vessels — more closely resemble the forms of Figure 8.

"Engineers might prefer to use straight channels with no side branching, but nature chooses the 'reaction design'," Zhou says. The TRINA team's research paper notes that while some have previously experimented with natural-looking, fractal, or hierarchical forms selected a priori for flow field channels, "this is the first time that such large-scale branching flow fields have been discovered using an inverse design approach without assuming prescribed layouts."

Rather Than Trying to Predict the Future, Create It

Along with the "flow versus reaction" comparison illustrated above, TRINA produced two further designs (not shown) that combined attributes of those in Figures 7 and 8. Tellingly, every one of TRINA's four iterations outperformed baseline conventional designs across key reaction-fluid performance metrics. An additional design that was fabricated and experimentally tested (Ref. 4) by the TRINA team is shown in Figure 9.

Figure 9. A machined metal prototype flow field plate based on one of TRINA's generated designs.

So, what is the ideal design for a flow field plate? There is no such thing, just as there is not a single ideal technology for replacing gasoline-powered automobiles. "From our point of view, we succeed by providing multiple good options for our engineers to consider," Zhou says.

TRINA is part of a large network of Toyota R&D teams that are striving to realize a potential hydrogen society. The company has continued to improve the range and performance of the hydrogen-fueled cars it calls Mirai, which is a Japanese word that means "the future", or literally, "not yet come". Perhaps, in a world not yet come, we will be living in smog-free cities equipped with hydrogen-distributing infrastructure and fuel cell-powered cars, trucks, trains, and buildings. Even though we cannot be sure of reaching this destination, we who live in today's petroleum society can still be inspired by Toyota's journey toward mirai.

Yuqing Zhou shares some advice that guides him and his colleagues: "Our chief scientist has said: 'We must stop trying to predict the future, and just work on trying to create it.'"

Figure 10. Four core contributors to the flow field design project. From left to right: Ercan M. Dede, Tsuyoshi Nomura, Yuqing Zhou, and Danny J. Lohan. Nomura is affiliated with Toyota Central R&D Labs in Japan, while the others work at Toyota Research Institute of North America.


  1. L. Printz, "Toyota Remains the World's Largest Automaker," The Detroit Bureau, 28 Jan. 2022;
  2. Y. Zhou et al., "Inverse Design of Microreactor Flow Fields through Anisotropic Porous Media Optimization and Dehomogenization," Chemical Engineering Journal, vol. 435, pt. 2, May 2022;
  3. "Akio Toyoda Fields Questions on Carbon Neutrality from U.S. Reporters," Toyota Times, 22 Nov. 2022;
  4. E. Dede et al., "Measurement of Low Reynolds Number Flow Emanating from a Turing Pattern Microchannel Array Using a Modified Bernoulli Equation Technique," Experimental Thermal and Fluid Science, vol. 139, November 2022;

Toyota Mirai is a registered trademark of Toyota Motor Corporation.