Welcome to the 3rd and final part of our special series of technical posts about computer simulations in engineering! If you want to have a complete overview of the project, check out the first part about CFD modeling and the second about FEA analysis. In the first part, we detailed the multiphysics modeling and CFD simulation of a fuel cell using Simcenter STAR-CCM+, while in the second part we did the modeling and structural analysis of a proton exchange membrane fuel cell (PEMFC) using Simcenter 3D.
Case Study
In the continuation of our series on fuel cell validation, we come to the third part, where we explore the simulation of fuel cells at the system level, that is, how they would operate integrated with other equipment and enable the analysis of their performance under different conditions. Unlike previous analyses focused on more detailed simulations, here we represent the behavior of the cell through a set of 1D equations simulated in Simcenter Amesim software. This approach allows the integration of the cell model into a vehicle system.
System simulation is a crucial step in understanding how a fuel cell behaves when incorporated into a larger system, such as an electric or hybrid vehicle. In this phase, the equations that govern the behavior of the fuel cell are solved together with the equations that describe the rest of the vehicle system. This approach provides a more holistic view of fuel cell performance in real-world operating scenarios.
Furthermore, the systems approach simplifies fuel cell behavior without compromising the accuracy of the results. In this approach, key parameters such as energy production, fuel consumption and efficiency are represented by differential equations that capture the essentials of the cell's operation.
Modeling
Integrating a fuel cell stack into a vehicle system represents a significant challenge. Indeed, a fuel cell system encompasses a variety of components, such as the stack itself, as well as the auxiliary Balance of Plant (BOP) equipment, which includes the cooling circuit, the air and hydrogen supply systems, the humidifier, among other devices necessary for the proper operation of the cell. In addition, multi-physical phenomena are involved, including electricity, heat transfer, fluid flow, mechanical (inertial) resistances and electrochemistry.
In this model, only the electrical aspect of the system was considered, which is the main focus of this study. This allows us to answer questions such as:
Will the proposed fuel cell system offer a significant efficiency improvement compared to other conventional or hybrid vehicle configurations?
What is the driving range of the fuel cell vehicle for a given duty cycle?
Systemic modeling includes sets of differential equations that characterize the dynamic and steady-state behavior of fuel cell elements. These equations adopt different approaches to describe cell behavior and can be divided into quasi-static and dynamic models, depending on the phenomena involved.
The results obtained in the Simcenter STAR-CCM+ software for the behavior of a single cell were extrapolated to a stack of cells. This stack was modeled as a stack of 200 cells connected in series, operating at a total voltage of 100 V. Each individual cell uses the polarization curve derived from the previous simulations.
Polarization curve of a fuel cell obtained in the Star-CCM+ software and imported into Amesim
A relevant study in this context is the experimental scalability study carried out by Bonnet et al. [2008], which explores the extent to which a single cell or a reduced set of cells can faithfully represent a larger system. This study is especially useful for determining which experimental data from individual cells are still applicable at full scale, including operating data under conditions that are potentially adverse to the cell's durability. The main conclusions of the study indicate that:
The polarization curves are nearly identical at different scales, suggesting that the scale effect is minimal under ideal conditions.
Under varying air and hydrogen flow conditions, experiments with single cells and stacks show similar behaviors.
The degradation effects with operating time follow similar trends at the different scales analyzed.
The study on the impact of air humidification is not conclusive: at low relative humidity, the behavior of the cells is similar, but above 60% RH, significant differences appear.
Integration with the Vehicle System
Once the fuel cell has been modeled, the next step is to integrate it into the vehicle system model. Here, the interactions of the fuel cell with other vehicle components, such as the drivetrain, batteries, and control systems, are considered. The simulation allows predicting how the fuel cell will respond to different driving profiles, including variations in power demand, temperature, and other environmental conditions.
Schematic representation of the vehicle system integrated with the fuel cell.
The simulation was performed with a lightweight vehicle weighing 1928 kg operating at a fixed torque conversion ratio of 1:8.786. The fuel cell was sized to deliver 88 kW, supplemented by a 1.5 kWh battery. Detailed system information and the corresponding model can be seen in the figure below.
Vehicle system model and system information in Simcenter Amesim
The driving cycle used in this simulation was the Japanese Cycle 08 (JC08) normalized cycle. The test represents driving in congested urban traffic, including periods of idling and frequent alternations of acceleration and deceleration. It is used for emissions measurement and fuel economy determination. The parameters selected for the JC08 cycle include:
Duration: 1204 s
Total distance: 8,171 km
Average speed: 24.4 km/h (34.8 km/h excluding idling)
Top speed: 81.6 km/h
Load ratio: 29.7%
The velocity curve along the JC08 cycle
Results: Performance Analysis under Operating Conditions
Integrating the fuel cell model into the vehicle system enables performance analysis under a variety of operating conditions. For example, system efficiency can be assessed during sudden acceleration, regenerative braking, and steady-state operation. These scenarios provide valuable data for model validation and system design refinement.
Plot of simulated speed versus driving cycle
It can be observed that the simulated speed follows the driving cycle, indicating that the traction system is sized appropriately. Furthermore, in this same cycle, we can observe consumption and acceleration characteristics, as well as extrapolate the average consumption to define the vehicle's autonomy. This autonomy calculation only considers the use of the fuel cell, without taking into account the potential use of the battery for vehicle propulsion when the fuel tank is empty.
Representation of the main characteristics of the system during the JC08 cycle
This analysis also includes the transient behavior of the system in terms of consumption and battery charge status.
Fuel consumption during the driving cycle
Evolution of the battery charge state during the driving cycle
The following graph shows the power control of the power bus. For lower power demands, power is supplied by the battery. When power demand is higher, the fuel cell supplies the power. During regenerative braking, power is directed to the battery for charging.
Power distribution between fuel cell and battery
Conclusion
System simulation is a powerful tool that complements the detailed analyses performed in the previous steps. By integrating the fuel cell into a vehicle system, we can obtain a more complete and accurate view of its behavior under real-world conditions. This approach enables the development of efficient and reliable propulsion systems.
This analysis reinforces the importance of validating fuel cell performance not only at the component level, but also in its final application.
Want to learn more and in more detail? Schedule a meeting or contact CAEXPERTS through our communication channels to discuss how we can collaborate in the optimization and validation of your project, integrating innovative solutions that increase performance in real conditions. Our team is ready to offer the necessary support to transform your simulations into concrete results. Also, follow our LinkedIn page @CAEXPERTS for more insights and news!
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Reference
Bonnet, C., Didierjean, S., Guillet, N., Besse, S., Colinart, T., & Carré, P. (2008). Design of an 80kW PEM Fuel Cell System: Scale Up Effect Investigation. Journal of Power Sources, 182(2), 441–448. DOI: https://doi.org/10.1016/j.jpowsour.2007.12.100.
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