Modeling And Optimization Study of PEMFC Fueled With Ammonia Reforming Gas

: The storage of high-purity hydrogen has been a technical challenge limiting the large-scale application of fuel cells. Ammonia is an ideal hydrogen storage carrier with a storage mass density of up to 17 wt% and can be easily liquefied for storage and transportation, but ammonia requires complex separation equipment to re-generate high-purity hydrogen, which greatly reduces its advantages in hydrogen storage. Therefore, the development of direct ammonia reforming gas fuel cells, which can avoid complicated pure hydrogen separation equipment, has a very meaningful impact and can greatly expand the application of fuel cells. In this paper, we study the modeling simulation of ammonia reforming gas-fueled proton exchange membrane fuel cell (PEMFC) based on the preliminary experiments, and the concentration-dependent Butler-Volmer electrochemical model is used to simulate the ammonia reforming gas-fueled PEMFC. Firstly, the concentration-dependent Butler-Volmer electrochemical model was improved by adding a correction factor for the concentration difference polarization based on the characteristics of the experimental data to obtain a correction factor of 1.65 based on the experimental data; secondly, the effect of the anode channel length on the fuel cell performance was investigated. The results show that: firstly, the improved concentration-dependent Butler-Volmer electrochemical model can better match the experimental results; secondly, the anode channel length has less effect on the maximum power density and hydrogen concentration in the exhaust gas, and the current density gradient increases with decreasing anode channel length, but the fuel flow resistance decreases. The results of the study can provide a reference for the simulation study of PEMFC using ammonia reforming gas as fuel.


Introduction
Proton exchange membrane fuel cells (PEMFC) have gained initial commercial applications in recent years [1]. Currently, PEMFCs are still fueled by high-purity hydrogen, which is expensive to produce and has a low storage volume energy density, so the large-scale application of PEMFC is still limited [2,3]. In contrast, ammonia as a chemical storage carrier for hydrogen has the advantages of high hydrogen storage density and easy storage, but it yields a nitrogen-hydrogen mixture(crude hydrogen) during reforming. The conventional method of hydrogen production from ammonia is to obtain high purity hydrogen by separation of crude hydrogen by pressure swing adsorption, composite metal palladium membrane separation and other methods [4][5][6]. However, for small portable PEMFC on-site hydrogen production units, the above methods still suffer from the problem of oversized units. Therefore, the development of PEMFC using ammonia reforming gas directly is very meaningful and can greatly expand the application of PEMFC.
Hunter et al. established an ammonia-reforming gas-PEMFC demonstration platform to demonstrate the feasibility of PEMFC using ammonia reforming gas directly [7]. Meanwhile, there have been numerous studies for the efficient decomposition of ammonia [8,9], but there are few studies on the effect of high nitrogen concentration on PEMFC. Previous studies have shown that nitrogen affects the diffusion and transport of hydrogen in the flow channel, but when pure hydrogen is used as fuel, its final accumulation is not high as it is regularly discharged regularly with anode purging. Therefore, for a PEMFC using pure hydrogen as fuel, the main purpose of flow channel geometry optimization is to optimize water management, thermal management and material distribution inside the cell [10][11][12]. However, for ammonia reforming gas, experiments have shown that due to the high initial concentration of nitrogen, the anode purging strategy cannot guarantee the proper operation of the fuel cell, so only the fuel flow control strategy can be used. Moreover, the nitrogen is increasingly concentrated in the fuel cell along the flow direction, and the rate of concentration increase is mainly determined by the flow rate of the gas in the flow channel and the consumption rate of hydrogen, so the influence of the geometry of the fuel cell anode flow channel of the fuel cell must be further studied and analyzed.
In this paper, a two-dimensional PEMFC model was established, and the concentration-dependent electrochemical mathematical model was reasonably modified based on the experimental data. Next, the effects of the flow length on the maximum power density, exhaust hydrogen concentration, current density and resistance loss of the fuel cell were studied.

Mathematical modeling
Since the anode and cathode channel of the PEMFC used in the experiment are perpendicular to each other, the air and fuel flow directions are cross-flowing, and the air composition on the cathode side corresponding to different anode channel will change along the air flow direction. Therefore, the modeling location in this paper is chosen to be in the mid-profile of the first anode channel at the air inlet [13]. To simplify the model, the air composition at the outer surface of the cathode diffusion layer is assumed to be the same as at the air inlet [14].The model contains six domains: anode channel, anode gas diffusion layer(an_GDL), anode catalyst layer(an_CL), proton exchange membrane(PEM), cathode catalyst layer(ca_CL), and cathode gas diffusion layer(ca_GDL) as shown in Figure 1. In order to further simplify the model, the following assumptions are adopted in this paper [15][16][17][18][19]: (1) Each gas is regarded as an ideal gas.
(2) The generated water can quickly flow out with air in a gaseous form, and there is no liquid water in the cathode.
(3) The temperature distribution in PEMFC is uniform and constant. (4) The penetration of water and nitrogen from the cathode side to the anode side is ignored.

Fig.1 two-dimensional section of the modeling area 2.1. Electrochemical model
The cell voltage V is described as follows: Where E0 is the theoretical reversible voltage which can be calculated from the Nernst equation [ Anode local current density ia (Concentration-dependent Butler-Vo lmer equation) Cathode local current density ic (Butler-Volmer equation) F is the Faraday's constant (SI unit: C mol -1 ), ci,ref is the material reference concentration (SI unit: mol m -3 ), i0,a and i0,c is the standard exchange current density (SI unit: A m -2 ),R is the gas constant, T is the temperature (SI unit: K), αa,a, αa,c,αc,a,αc,c is the transfer coefficient.
Anode over-potential ηa, cathode over-potential ηc and total over-potential ηact are given by the following equation: Where Eeq,i (SI unit: V) represents the equilibrium voltage, φs is the electronic potential (IS unit: V), and φl is the ionic potential (IS unit: V).

2.2.Momentum conservation equation
Navier-Stokes equation and Brinkman equation are adopted to describe the flow in the free zone (anode channel) and porous zone, respectively. [20] The combination of Navier-Stokes equations and continuity equations can be expressed as: Where ρ is the mixture density of the gas phase(SI unit: kg m -3 ), I is Unit Matrix，P is the pressure(SI unit: Pa), μ represents the gas viscosity(SI unit: Pa s),u is the velocity.
The combination of Brinkman equation and continuity equation can be expressed as: Where k is permeability(IS unit: m 2 ), ε is porosity.

Mass conservation equation
The model takes into account two species in the anode(H2 and N2) and three species at the cathode(O2, H2O and N2), and uses Maxwell-Stefan multicomponent diffusion, governed by the following equations [20] Where wi is mass fraction of species i, Ri is chemical reaction rate of species i(IS unit: kg m -3 s -1 ), ji is the diffusion mass flow density of species i, which is defined as follows: Here xk is mole fraction, Mi is Molecular mass, Di m is the equivalent diffusion coefficient of species i in multicomponent，Dik is binary diffusion coefficient, which can be calculated by Fuller's empirical formula [21]:  (17) Where vi is the molar diffusion volume of gas (IS unit: cm 3 mol -1 ).
The binary diffusion coefficient obtained by Equation (20) needs to be modified in the porous region: Here τ is the tortuosity factor.

2.4.Initial and boundary conditions of the fuel cell model
The potential difference between the cathode and anode current collectors The molar fraction of nitrogen at the anode inlet of the fuel cell is 0.25 and the molar fraction of hydrogen is 0.75. 1.18×10 -11 [22] Permeability inside an_CL and ca_CL domains, κcl(m 2 ) 2.36×10 -12 [22] Porosity inside an_GDL and ca_GDL domains, εdgl 0.4 [22] Porosity inside an_CL and ca_CL domains, εcl 0  Table 1 shows the parameters used in the model. Figure 2a shows the simulation results after optimization based on the experimental data. It can be seen that in the low voltage region (corresponding to high current and low hydrogen concentration), the simulation results are significantly higher than the experimental values, which indicates that the mathematical model does not respond better to the actual electrochemical process in this interval. In the low voltage region, the hydrogen concentration decreases significantly, and the effect of nitrogen on hydrogen should be significantly higher. Since it is very difficult to correct the binary diffusion coefficient of the gas in the mass transfer model. Therefore, equation 3 is modified in this paper by setting the correction factor γ for the concentration polarization. the corrected local current density of the anode is as follows.

3.1.Verification of simulation model
The correction factor γ = 1.65 obtained by the COMSOL software optimization tool using the experimental data. Figure 2b shows the results of the simulation results with the experimental values. It can be seen that the simulation results can match well with the experimental values. Especially near the peak power, the simulation model can predict the experimental results well. And the study in this paper focuses on the region near the peak power, so it can be considered that the model is applicable in this paper. Figure 3 shows the variation of maximum power of fuel cell with anode channel length for a given boundary conditions (output voltage of single cell is not less than 0.5V, fuel efficiency is not less than 45%). When the length of anode channel is more than 90mm, the maximum power density changes little with the length of anode channel. When the length of anode channel is less than 90mm, the maximum power density increases gradually with the decrease of channel length, and the slope of the curve increases gradually. However, the maximum power density when the length is 10 mm is only 2.2% higher than the maximum power density when the length is 180 mm. Therefore, the anode runner length has little effect on the maximum power density.

Figure3. Variation of maximum power density with anode channel length 3.3. influence of anode channel length on hydrogen molar concentration at anode outlet
The variation trend of hydrogen's molar concentration at anode channel outlet with the channel length is similar to that of power density, as shown in Figure 4. The high molar concentration of hydrogen at the outlet of the anode channel indicates that the proportion of hydrogen participating in the electrochemical reaction is reduced, and the energy of hydrogen participating in the electrochemical reaction is converted into more electric energy, thus reducing the heat release during the electrochemical reaction. This is beneficial to the thermal management of the fuel cell. Also the higher molar concentration of hydrogen makes the exhaust waste heat utilization of the fuel cell more valuable. However, the molar concentration of hydrogen at a length of 10 mm is only 4.5% higher than that at a length of 180 mm. Therefore, the anode runner length also has little effect on the exit hydrogen molar concentration.
Figure4. Variation of hydrogen molar concentration at anode outlet with anode channel length 3.4. influence of anode channel length on current density Figure 5 shows the variation of current density along the anode channel for different anode channel lengths. It can be seen from the figure that the current density at the entrance of the channel is the same, and there is a small increase in the current density at the exit as the anode channel length decreases, but the gradient of the current density increases sharply, which is a detrimental effect on the operation of the fuel cell, so the length of the anode channel length should not be too short.
Figure5. Variation of current density with anode channel length 3.5. influence of anode channel length on the fuel's flow resistance From Figure 6, it can be seen that the resistance loss of fuel flow is linearly proportional to the length of the anode channel, and the dashed line represents the average flow velocity of fuel in the channel, which is also linearly proportional to the length of the anode channel. However, comparing the slope of the two curves, the rising speed of pressure loss is less than that of velocity. At the same time, the fuel resistance loss of 180 mm length is 14 times of that of 10 mm length. Therefore, the length of anode channel has a great influence on the flow resistance loss of fuel.
Figure6. Variation of fuel flow velocity and flow resistance with anode channel length

Conclusion
In this paper, a two-dimensional simulation model of PEMFC fueled with ammonia reforming gas is established, and the concentration-dependent electrochemical reaction model is suitably modified according to the experimental results by adding a correction factor for the concentration difference polarization, and the correction factor γ=1.65 is obtained by an optimization algorithm. Next, the influence of anode channel length on the characteristics of fuel cell was further studied. The results show that the length of the anode channel has little effect on the maximum power density and the molar concentration of residual hydrogen at the outlet of the fuel cell, but has a greater impact on the current density and the flow resistance of the fuel. Increasing the length of the anode channel can make the current density more uniform, but will increase the flow resistance of the fuel. Therefore, a compromise should be considered in the geometric optimization of the fuel cell.