Computational Modeling Aspect of Fuel Cells: A Continuous Powerhouse

Overview

Fuel cells are called continuous powerhouses because it is a device that does not store energy but runs continuously to produce electricity as long as the fuel is provided. The byproduct of the fuel cell is water, hence the “clean energy” or “zero carbon emission” technology.

Components

A fuel cell is composed of two electrodes (one anode and one cathode), and an electrolyte. The anode is the negative charge collector and the cathode is the positive charge collector and is present on opposite sides of the electrolyte. The fuel H2 is fed through the anode and the oxygen is fed through the cathode. The electrolyte here is a polymer membrane that selectively allows only protons to pass through it. The catalyst deposited at the membrane spits the hydrogen into a proton and an electron. Electron takes the external circuit route to complete the circuit. The proton passes through the electrolyte and combines with Oxygen to produce water and heat (exothermic reaction). In usual practice, the polymer membrane is perfluorinated polymers with sulfonic acid groups commonly known as Nafion and the catalyst used is Platinum nanoparticles. This membrane exhibits high proton conductivity only when hydrated. On the cathode side, it helps in splitting the H2 in the proton and electron, and on the anode side, it helps in the reduction of oxygen and generating water afterward. The following is the table indicating the half-reactions and associated Gibbs free energy.

Table 1. Anode and cathode reactions for PEMFC

The scenario described before is for the Polymer Electrolyte Membrane Fuel Cell (PEMFC), which has the fuel as hydrogen and the proton exchange membrane selectively allows Hydrogen atoms to migrate through it. However, a variety of Fuel Cells are available based on the fuel provided, temperature ranges, and power generation capacity. Based on the fuel type the chemistry changes and so do the electrochemical reactions. Schematic

direct and indirect methanol fuel cells are shown in Figure 4 and Figure 5.

Polymer Electrolyte Membrane Fuel Cells (PEMFC)
Direct Methanol Fuel Cells (DMFC)
Alkaline Fuel Cells (AFC)
Phosphoric Acid Fuel Cells (PAFC)
Molten Carbonate Fuel Cells (MCFC)
Solid Oxide Fuel Cells (SOFC)
Reversible Fuel Cells (RFC)

The figure shown here (Figure 3) lists some of the types of fuel cells and their resulting electrochemical reactions.

Recent research practices in Fuel Cells

Although the major focus remains on Hydrogen fuel cells or PEMFC, recent interests also lean toward alcohol fuel cells. Methanol and ethanol fuel cell research is highly in focus nowadays and is gaining attention due to the storage challenge of Hydrogen. Methanol and ethanol have high energy density. Moreover, liquid fuel cells do not require hydration, or humidification in the membrane to function. Since the fuel storage cartridge is not large enough, these fuel cells are compact and have attractive applications in portable fuel cells. Research is following the pathway of miniaturizing the fuel cell systems and with appropriate stacking, even high output power can be obtained. However, the miniaturization and feasible usage of liquid fuel cells puts a limitation of “methanol crossover” i.e. the transport of methanol through the membrane from the anode to the cathode side, in turn, resulting in overpotential losses. This happens without the fuel fully undergoing the electrochemical reactions. Other challenges are associated with the flow of methanol, minimizing the pressure drop across the channel. This challenge amplifies when the channels are microchannels. Now the gravity forces are not prominent and capillary forces drive the flow. The cost of stacking put another toll on the smooth functioning and commercialization of these fuel cells.

Out of many applications of Fuel Cells, there are a few where efforts are made and products are commercialized.

Power backup
Electric Vehicles and Mobility
Maritime

Fuel Cell Market Growth

According to Fortune Business Insights, the global fuel cell market was valued at US$ 4.68 Billion in 2021, US$ 5.90 Billion in 2022, and is expected at US$36.41 Billion in 2029 at a CAGR of 29.7 from 2022 to 2029.

Major Fuel Cell Manufacturers

Recent News on Fuel Cells

German auto supplier Bosch will invest almost 2.5 billion euros ($2.8 billion) in hydrogen fuel cell technology from 2021 to 2026 and expects to generate roughly 5 billion in sales from it by 2030, the company said on Thursday.
Fuel cell technology, powered by hydrogen, is emerging as a significant component of the e-mobility landscape.
In September 2015, Aditya Birla Group bought more than 200 fuel cells from Ballard Industries to power its telecom towers.
In September 2015, Intelligent Energy announced a deal of € 1.2 billion for the supply of fuel cells to power 27,400 towers in India.
French rail vehicle manufacturer Alstom in collaboration with Germany and Canada demonstrated a fuel cell-based zero carbon emission train named Coradia iLint.
In March 2018 TATA announced India’s first fuel cell powered bus.
The number of fuel cell vehicles like Toyota Myriad, Honda FCX clarity, Mercedes Benz F-Cell, and Hyundai ix35 FCEV.
The world’s first megawatt-scale carbonate fuel-cell power plant, built by Toyota and Fuel Cell Energy to be in operation by 2020 could generate 2.36 Megawatt of electricity and 1.2 tonnes of hydrogen daily at the port of Long Beach, California.
The 2020 Olympics are going to be held in Tokyo, Japan. The Japanese government. aims to install 35 hydrogen gas stations in the city to have 6000 fuel cell-based cars on the roads and increase the quantities of fuel cell-based buses in Tokyo.
Several aircraft like HY4 and Lockheed CL-400 Sultan are based on fuel cell technology which emits zero carbon emission.
In August 2022, Proton Motor enabled train and engineering manufacturers, Integrators, and SMEs to realize green emission-free fuel cell electric drives through its new hydrogen fuel cell system, HyRail.
In June 2022, Doosan fuel cell company signed an MoU with Korea Southern Power along with Samsung C&T and the Korea Institute of Energy Research. The MoU is about the development of fuel cell coupled CCU technologies and an ammonia fuel cell demonstration project.
In January 2022, Fuel Cell Energy announced the commencement of commercial operation of a 7.4 MW source fuel cell project in New York.
In August 2021, SFC Energy and Nel ASA Hydrogen collaborated on developing the First integrated electrolyzer and hydrogen fuel cell system to launch to the market to replace diesel generators.
In July 2021, Bloom Energy declared a 4.2 MW combined heat and power project in collaboration with the S K Eco plant. This project will mark South Korea's first utility-scale Solid Oxide fuel cell combined heat and power initiative.

Underline physics

If we classify the physics that goes on in a regular fuel cell, the following are the broad categories we have:

Electrochemistry: Electrochemistry is the first and foremost principle used by fuel cells. The potential difference is the driving force for the conversion of chemical energy from fuels into electricity. Electrochemistry is responsible for the redox reactions in half cells in the presence of the electrolyte. As soon as the gases reach the catalyst layer, mostly platinum nanomaterial, the interaction carbon supported platinum with hydrogen enables the splitting of hydrogen into protons on the anode side, and on the cathode side, platinum interaction with oxygen initiates the reduction reaction in the presence of the protons. The protons in this reaction originate from the anode reaction and thus generate electricity and water as the by-product.

Flow dynamics: The flow of the reactants including fuel and the oxidizer such as hydrogen, methanol, and oxygen from the source is driven by the pressure gradient in the channel. The optimal flow is modeled using computational fluid dynamics. Minimizing the pressure drop across the flow channel is the prime requirement. Due to this reason, innovative designs of the flow plate are the major area of research.

Porosity: The gas diffusion layer is one component that is responsible for the flow of gases from the flow plate to the catalyst layer. The gas diffusion layer allows the flow of gases or liquids through porous media and GDL porosity plays an important role in mass transfer and subsequent surface reactions and selective adsorption of the gases. Therefore the implementation of the porosity model i.e. Darcy-Forchheimer mechanism can deduce the porosity-driven flow. Porosity is also implemented in the case of the electrolyte since the electrolyte here is the membrane that only allows the transport of proton through it.

The major functions of GDL are:

(i) It provides a gas-diffused pathway to transport the gases to the catalyst

(ii) It prevents the flooding of H2O in the fuel cell by removing water that is generated as a by-product of the redox reactions.

(iii) GDL is also a significant component that provides enough mechanical strength to membrane electrode assembly

(iv) Absorbs some water and retains it at the surface for effective proton conductivity

Heat transfer: Understanding the flow of heat in the fuel cell is important to eliminate the hot spots in the unit. During the operation, a poor thermal management system can lead to an extensive rise in the temperature that hampers the process efficiency of the fuel cell. Operating temperatures and the heating effects in different types of fuel cells such as solid oxide fuel cells (SOFC) and polymer electrolyte membrane fuel cells (PEMFC) are different. SOFC operates at 600-1000 ºC whereas PEMFC operates at low temperatures (LT-PEMFC) at 60-80 ºC and high-temperature HT- PEMFC operates at 160 ºC. The presence of water in these fuel cells limits the operating temperature below 100 ºC. Excessive heat in these systems is controlled by water looping or circulation.

Heat in a fuel cell is generated by entropy changes in an electrochemical reaction. This entropic heat accounts for 30 % of the total heat generated in the system. Irreversibility of an electrochemical reaction due to the overpotential i.e. irreversible heat accounts for 60 % of the total heat. The remaining 10 % heating is due to the ionic and electrical resistances i.e. joule heating. If there is phase change involved in the process, it can cause the release of latent heat i.e. phase change heat.

For fuel cells of high capacity > 10 KW, air cooling seems to be ineffective due to its lower density, thermal conductivity, and specific heat capacity. Liquids such as water, glycol, acetone, and oils are common choices for liquid cooling where liquid recirculation loops or pumps are used to circulate the liquid and exchangers to absorb or transfer the heat.

There are ways for passive cooling as well: immersion cooling with liquid vapor phase change, heat pipes, and phase change material cooling.

Solid oxide fuel cells operate at 600-1000 ºC, therefore normal cooling strategies may not work at those temperatures. The temperature gradient in the positive electrode, electrolyte, and negative electrode (PEN structure) should not exceed 10 ºC/cm. High-temperature gradients in fuel cells can cause structural damage to the components and also can have adverse effects on the overall performance. Apart from forced air convection with optimal flow rate, flow channel designs, flow arrangements, integration of heat pipes and fuel composition can manage the thermal management and temperature gradient.

Mass transfer

In fuel cells, mass transport occurs in two domains; 1. the fuel and the oxidizer flow in the flow plate, 2. flow across the electrodes and the membrane. The underlying transport mechanism and the driving force of both flows are different due to the length scales. The first one follows the bulk fluid flow due to convection as the flow channel dimensions are in millimeter and centimeter scale. In the electrodes, the flow is in the micrometer and nanometer range, which occurs through the pores and is dominated by diffusion [Sundén, Bengt, and Mohammad Faghri, eds., Vol. 19. WIT press, 2005].

The convective forces in the flow plate develop by the flow rate that the user gives as input. Flow rates higher than a certain range can be problematic because the high-pressure imposition can create structural damage and other problems. On the other hand, the concentration gradients across the electrode develop due to the species consumption or production in the catalyst layer.

In a nutshell, mass transfer governs the requirement and removal of the reactants and products in a fuel cell. If the mass transfer is poor, it can lead to poor fuel cell performance due to insufficient reactant at the reaction front. The absence of the reactant in the electrode due to diffusive transport limitation causes the limiting current density. There are two losses occurring due to the reactant depletion (i) Nernst losses and (ii) reaction losses. On one hand, the cell voltage drops due to limited reactant availability and on the other hand, the kinetic reaction rate reduces. Concentration losses can be tackled well with careful consideration of the convective transport ie. choice of the flow channel and patterns.

Challenges

Fuel cells in current times have surpassed a lot of challenges, but still face a lot of challenges in terms of efficacy, and scale-up. However, apart from these challenges, there are technical challenges that limit the efficacy and long-term performance of fuel cells. Right thermal management and water management strategies are critical challenges that need to be eliminated.

Thermal management -Heat usually accounts for 50 % of the total energy produced by the fuel cell. Excessive heat generation during the operation can lead to reduced fuel cell performance. Also, the heat is generated in different sections of the fuel cell, resulting in non-uniform temperature distribution. As local heat flux greatly affects the performance and the durability of the fuel cells. The geometrical shapes and designs play of cooling channels i.e. bipolar plates play an important role in the thermal performance of the stack. In the literature, extensive studies have been carried out to optimize the design of the channels and to analyze and control the impact of the flow field on the cooling of the stack. The most applied configurations are mainly four: parallel-like, serpentine-like, 2D wavy-like with multi-pass, and 3D fine mesh flow. In the industry, there are parallel flow channels in Ballard stacks, wavy flow channels in Honda stacks, and similar 3D mesh coolant flow channels adapted by Toyota. The parallel flow channel is also known as a straight channel. It is distinguished by its fabrication simplicity but with a reduced cooling efficiency.

Water management - Water management is required in fuel cells because water is generated as a by-product of electrochemical reactions. The electrolyte layer requires hydration to allow the exchange of protons through it. Also, if the channel width is relatively large, flow distribution becomes non-uniform, and thus the retention of water increases in the channels. In the case of parallel configuration pressure drop reduces due to multiple fuel inlets. Whereas in the case of serpentine or interdigitated due to the single fuel inlet and fuel path, the water is forced to exit the channel. Ballard fuel cell PEMFC stacks use the hybrid design utilizing the advantages of both, parallel and serpentine channels. Interdigitated designs also offer improved water management and better mass transport. These parameters are best explored using CFD modeling, which is discussed in upcoming sections.

Computational Modeling Aspects

Modeling provides an improved scientific understanding of the fundamental transport phenomena. Therefore taking the right assumptions before carrying out the modelling and simulation is of utmost importance. Also, compartmentalizing the problem and target parameters needs to be looked at carefully. Basis the physics and criteria of interest, one can explore the following modeling aspects.

(i) Thermal modeling- For heat transfer and thermal management-related problems such as air cooling, liquid cooling, and phase change material cooling. Heat transfer due to conduction, convection, radiation, and phase change can be modeled using the appropriate heat transfer solvers. Conjugate heat transfer considers all the heat transfer methods. Figure 13 shows a 2D representation of the membrane electrode assembly and respective thermal boundary conditions in the system.

(ii) Multiphase modeling - If the user is optimizing the fluid flow problems related to flow from bipolar plates, minimizing the pressure drops, minimizing the water retention, and modeling the flow through porous media (electrodes and the electrolyte membrane) one can use appropriate multiphase or single phase solvers. For all design and parameter optimizations, single-phase fluid flow analyses coupled with thermal modeling can be used.

(iii) Electrochemical modeling - Electrochemical modeling is used to model the governing equations in electrochemistry ie. Tafel equation correlating the electrochemical kinetics with the overpotential and the Butler-Volmer equation correlating the overpotential to the current density. It also accounts for the membrane conductivity with respect to water content and corresponding ohmic losses in the system. This modeling approach will also include electrochemical reactions with the right kinetics.

(iv) Coupled fluid flow and electrochemical modeling - A complete analysis of fuel cells can only be done using a coupled modeling approach where electrochemical modeling meets multiphase and thermal modeling.

Computational Modeling Approach:

A detailed methodology of fuel cell modeling is discussed in this research [Weber, Norbert, et al., OpenFOAM® Journal 3 (2023): 26-48].

Source term due to phase change:

The phase change source term is deduced from the difference between the partial pressure of vapor and the saturation pressure (p𝜘v−psat) and from the ideal gas law

𝛾 denotes the condensation or evaporation rate constant, 𝜘𝜈 the molar fraction of vapor, T temperature, and R the universal gas constant steady-state continuity equation: The flow equations are written such that they hold for both the channels and the porous electrodes.

Membrane model: The membrane model accounts for water transfer due to osmotic transport (from anode to cathode) and back-diffusion (from cathode to anode). The water transfer through the membrane is

where the first term describes electroosmotic transport and the second water diffusion through the membrane. Here, z denotes the number of electrons, ρdry the (dry) membrane density, Mm the equivalent weight of the membrane, z′ the normal coordinate, and λ the water content.

Electrochemical reactions: The current density is obtained

With U denoting the open circuit potential, R the area-specific resistance, and η the activation overpotentials

Overpotentials and losses: The area-specific resistance Where δ denotes the thickness of the membrane. The membrane conductivity

At a membrane water content of λ < 1, the conductivity is assumed to be constant. Activation overpotential: Tafel or Butler-Volmer equation

with α the charge transfer coefficient and the number of electrons exchanged. The exchange current density

With j0,ref denoting the reference exchange current density, Eact the activation energy and γ the order of the reaction, which accounts for the depletion of the reactant I (oxygen for cathode, or hydrogen for anode)

Heat transfer: Neglecting pressure work, species diffusion, and viscous dissipation, the energy equation is the effective thermal conductivity

ks denoting the thermal conductivity of the solid cell parts. The heat source term, accounts for ohmic heating in the electrolyte and the latent heat in the GDLs, with hcond denoting the heat of condensation.

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