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Allie Yuxin Lin
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Although fuel cells have recently gained prominence in today’s energy discourse, their conceptual origin dates back to the 19th century. In 1842, British scientist William Grove invented the first fuel cell, naming it a “gas battery.” For nearly a century, this curious invention would sit quietly in the scientific sidelines until the early 1930s, when English engineer Francis Bacon revisited Grove’s idea. Over the next two and a half decades, Bacon worked on an alkaline electrolyte fuel cell, which consumed pure oxygen and hydrogen. In 1959, his team revealed the “Bacon cell,” a six-kW prototype that was the first fuel cell powerful enough for practical use, setting a new benchmark for real-world energy applications and laying the foundation for modern fuel cell technology.
Fuel cells are electrochemical devices that convert the chemical energy of a fuel, such as hydrogen, and an oxidant, such as oxygen, directly into electrical energy. They are similar to batteries in that they produce electricity, but unlike batteries, they don’t need to be recharged, as long as a fuel source is provided. As such, fuel cells offer a clean energy alternative when used with renewable fuels, producing electricity with few emissions (i.e., water and heat).
However, these devices are notoriously difficult to model because they involve a complex interplay of physical, chemical, and electrical processes that occur simultaneously across multiple spatial and temporal scales. To function, fuel cells require electrochemical reactions, which are sensitive to variables like humidity, temperature, and pressure. Accurately capturing these reactions requires detailed modeling of mass transport, charge transfer, and heat management. Further, fuel cells often contain porous media, such as gas diffusion and catalyst layers, where multi-phase flow occurs.
With its autonomous meshing capabilities, CONVERGE can effectively capture the complexity of modern fuel cell geometries. Conjugate heat transfer (CHT) modeling in CONVERGE can be used to calculate the heat transfer throughout the fuel cell stack to locate regions of low or high temperature. Additionally, CONVERGE’s multi-phase modeling can simulate the flow of liquids and gases in the reactant supply channels and gas diffusion layers, which are represented as porous media. This can help fuel cell manufacturers predict local water content and simulate liquid water transport, which are important for evaluating the performance of the fuel cell. The fully coupled solution of electrochemistry, multi-phase fluid dynamics, and heat transfer in CONVERGE allows engineers to study the activation and mass transport losses in fuel cells, which can degrade cell performance.
At Convergent Science, we’re committed to pushing the boundaries of what our code can do, tackling new challenges and refining our tools with each new release. Our latest features overcome the challenges of fuel cell modeling, making our simulations sharper, faster, and more powerful than yesterday. Let’s dive into two case studies that showcase CONVERGE’s cutting-edge new features and how they’re driving innovation in fuel cell modeling.
Fuel cell performance can be heavily influenced by flow field design (i.e., the pattern of channels that direct gases across the cell’s surface). Different designs will affect how well reactants are distributed, how water and heat are managed, and ultimately, how efficiently the cell operates. Parallel flow fields use straight, side-by-side channels that offer low resistance and are easy to manufacture, but they can lead to uneven gas distribution and water buildup. Radial flow fields spread reactants from a central inlet, promoting uniform coverage. These designs are typically used in compact or round fuel cell geometries. One of the most popular and effective fuel cell designs is the serpentine flow field. In these fuel cells, the flow field for the gas channels is designed in a serpentine pattern, which ensures uniform gas distribution, enhances water management, and provides better heat transfer. These cells are especially useful in industries like automotive, aerospace, and portable energy, where reliable performance and compact design are critical. However, simulations of such devices are difficult due to the non-linear conjugate heat transfer, moving fluid flow, electric potential equations, and complex electrochemistry.
In this steady-state simulation, we used CONVERGE to simulate a serpentine fuel cell with hydrogen fuel to study the transport of reactants at different voltages. The geometry of a 50 cm2 cell with a five-path serpentine bipolar plate was derived from an experimental study.1 Both the mass flow rate of H2 at the anode inlet and O2 at the cathode inlet fluctuated with the applied voltage.
CONVERGE’s fully autonomous meshing easily handled the complex geometry of this case, and fixed embedding was applied around the catalytic and membrane layers for additional mesh refinement. The total cell count was 2.5 million, and the simulation was run with 24 cores.
We used CONVERGE’s pseudo-transient steady solver, which reformulates the steady-state problem into an equivalent transient problem by adding an artificial time derivative to the governing equations. This allows the solution to evolve over “psuedo-time” until it reaches a steady state, which can be faster than a true transient or direct steady-state simulation.
For this direct current (DC) application, we employed the 3D electric potential solver, which predicts the electric potential, current field distributions, and associated Joule and electrochemical heat generation. When this is activated, CONVERGE solves for an electric potential solution within solid streams and porous media volumes with nonzero electrical conductivity. In doing so, CONVERGE accounts for ohmic heat dissipation (i.e., Joule heating).
CONVERGE accurately predicted the response of the fuel cell to applied voltages and reproduced three different polarization curves (activation polarization, ohmic polarization, and concentration polarization). These curves represent different types of voltage losses that can impact fuel cell performance.
Proton exchange membrane (PEM) fuel cells, which are also known as polymer exchange membrane fuel cells, work by splitting hydrogen into protons and electrons, which generates an electric current. PEM cell performance depends on tightly balanced electrochemical and transport processes, making these devices sensitive to variables such as temperature, pressure, porous media, species’ concentrations, and charge transfer coefficients.
Understanding what effect these operating conditions have on cell performance is key to improving fuel cell stability and efficiency. We carried out a sensitivity study on a simplified PEM fuel cell model to identify the most critical parameters and explore mitigation strategies.
CONVERGE assumes laminar flow and captures multi-phase flow with the evaporation and condensation models. Conjugate heat transfer modeling is applied on the cell membrane to capture conduction and convection.
At the cathode level, we applied the lumped electrochemistry model, which is currently implemented in CONVERGE as a user-defined function (UDF). The name “lumped” comes from the fact that the electrical resistance used to compute the current density is obtained with a “lumped” sum of the electrical resistance in all PEM layers (i.e., the membrane, the anode and cathode catalyst layers, the gas diffusion layers, the micro-porous layers, and the bipolar plates). This simplified 0D approach allows us to solve a simpler algebraic nonlinear equation for current density at each computational cell instead of a full 3D differential equation. After replacing a single equation with a series of smaller nonlinear algebraic equations, we can begin solving iteratively. In this way, our simulation still reaps the benefits of a full 3D model, but only incurs the cost of solving algebraic nonlinear equations, resulting in faster turnaround for fuel cell simulations.
The Nernst equation calculates the cell potential of an electrochemical cell and shows how changes in reactant and product concentrations alter the cell’s voltage. According to this equation, increasing pressure would increase the cell potential. In our model, we increased the pressure by 0.5 bar on both the anode and cathode sides of the PEM fuel cell, which immediately increased the power output from the device. By increasing the pressure of the system, we increased the availability of reactant species, which offsets the limited current density and results in higher voltage output.
The main chemical reaction in a PEM fuel cell occurs at the membrane, when hydrogen reacts with oxygen to generate an electric current and water. However, in practice, industrial fuel cells typically supply air to the cathode, which only contains about 17-20% oxygen. As a result, oxygen depletion at the reaction site can lead to activation and concentration overpotentials. In our model, we used CONVERGE to generate the polarization curves of the fuel cell under three O2 concentrations: air-like (17.5% O2), O2-intermediate (37.5% O2), and O2-rich (70% O2). We found that as the oxygen concentration increased, so did the power output.
Fuel cell technology, which has certainly come a long way since its inception in the mid-19th century, represents the promise of efficient, sustainable energy. However, realizing that promise on a global scale requires overcoming engineering challenges in design, optimization, and operation. CONVERGE’s suite of state-of-the-art computational tools provides engineers and researchers the ability to simulate complex fuel cell processes with accuracy and efficiency. Thank you to William Grove and Francis Bacon for pioneering this revolutionary technology and setting the foundation for progress. Now, our tools can help shape the next chapter of fuel cell development, contributing to a greener future.
[1] Iranzo, Alfredo, et al. “Numerical Model for the Performance Prediction of a PEM Fuel Cell. Model Results and Experimental Validation.” International Journal of Hydrogen Energy, 35(20), 2010, 11533–11550. https://doi.org/10.1016/j.ijhydene.2010.04.129
