Detailed 3D multiphysics modeling of an ammonia-fueled solid oxide fuel cell Anode off-gas recirculation and Ni nitriding degradation

A deep understanding of underlying processes and possible challenges is required for the development of ammonia-fueled solid oxide fuel cell (SOFC) systems. In this context, a detailed 3D multiphysics model of an ammonia-fueled SOFC is developed in the current study. Anode off-gas recirculation and nickel nitriding as two of the main aspects of ammonia-fueled SOFCs are investigated in the current study. The developed model is validated with experimental data under various conditions including direct and pre-cracked ammonia cases for various flow rates at different temperatures (700–850 ◦ C ) as well as different recirculation rates. A good agreement is achieved between the model results and the measurement indicating that the physics are well captured. Furthermore, nickel nitriding as one of the main challenges in the direct ammonia-fueled SOFCs is addressed and qualitatively validated with experimental data. The model can explain the reduction of performance difference between direct ammonia-fueled SOFC compared to its pre-cracked counterpart by reducing the fuel flow rate (increasing fuel utilization) and increasing the operating temperature. The highest performance difference (5.87%) is observed at 700 ◦ C and fuel utilization of 14%, and the lowest difference (0.05%) belongs to 850 ◦ C and fuel utilization of 70% at 0.5A/cm 2 . Anode off-gas recirculation is found to yield significant savings in ammonia fuel around 21–27% while a slight power reduction (0.34–0.88%) is observed by increasing the recirculation rate from 70 to 90% compared to the case without recirculation. Excessive amount of nitrogen in the high recirculation rates does not show a significant effect on the performance. Nickel nitriding is reduced by increasing the temperature and fuel utilization.


Introduction
The continuous consumption of carbon-based fossil fuels has been identified as a major contributor to global warming, resulting in various environmental challenges such as melting glaciers and rising sea levels [1].Consequently, there is a pressing need for low-carbon energy technologies such as fuel cells due to their efficient power generation capabilities [2].The solid oxide fuel cell (SOFC) technology is promising for power generation due to their high electrical efficiency [3].One of the key advantages of SOFCs is their ability to operate at high temperatures, which facilitate fast electrochemical reaction rates, allowing for efficient internal conversion of fuel to electricity without the need for expensive and rare catalysts in pre-reformers [4].Another significant advantage of SOFCs is that they can directly use fuels such as hydrogen, methane, methanol, and ammonia without requiring complex reforming or purification processes [5].
Ammonia (NH 3 ) is a promising carbon-free fuel for SOFCs as it is less flammable, liquid from production, and thus more energy dense for transportation which makes it preferable compared to hydrogen in many cases [6].Nickel (Ni)-based anodes, such as Nickel/Yttria Stabilized Zirconia (Ni/YSZ), play a crucial role in enabling the direct utilization of ammonia in SOFCs.Ni acts as a catalyst, facilitating the cracking of ammonia into hydrogen and nitrogen inside the SOFC [7].This provides a large advantage over low-temperature fuel cells as they need a high temperature inefficient external cracking, and consequent cleaning of the produced hydrogen, which would require a large share of the produced power.Therefore, ammonia can be fed into SOFCs in two ways, either internally cracking inside the SOFC (direct) or externally cracking (pre-cracked also called indirect) [8].In direct ammonia-fueled SOFC systems, the internal endothermic cracking of ammonia offers a benefit in terms of the cells cooling requirement, which reduces the amount of external cooling needed from air blowers or other cooling mechanisms [9].
While the internal cracking of ammonia in direct ammonia-fueled SOFCs offers advantages, it also introduces some challenges and drawbacks.One of the major concerns is the formation of nickel (Ni)  Oxygen ohm Ohmic  Reference change creates some pits in the Ni surfaces in the fuel support and active layers.The repetitive nitriding-reduction cycles of Ni in direct ammonia-fueled SOFCs can lead to significant microstructural changes in the anode.This can lead to irreversible degradation which decreases the cell performance and possibly also the cell integrity as Ni is also a structural component [11].It is known that the Ni meshes used in the cell tests crumple after exposure and disassembly [12].A comprehensive stability analysis on a direct ammonia-fed SOFC with Ni/YSZ anode was conducted by Yang et al. [10].The results showed that Ni was partially nitrided by NH 3 , which led to a considerable morphology change.They also performed a temperature cycling test in the range of 600-700 • C. Ni nitriding led to delamination of the Ni/YSZ support layer that resulted in severe degradation of the cell performance [10].
Recently, Hendriksen et al. [13] observed morphological changes in the Ni/YSZ fuel support layer and Ni meshes due to Ni nitriding.However, to the authors' knowledge, there is no available numerical modeling study in the literature that is validated with experimental data to give further insights into the Ni nitriding formation possibility in NH 3 -fueled SOFC at the cell level.Anode off-gas recirculation (AOR) is a well-known method employed to enhance the performance of SOFCs.Fuel utilization can reach 70%-80% in the industrial SOFC stacks and higher values for fuel utilization can be risky for SOFC stack [14].Hence, approximately 20%-30% of the fuel remains unused in the SOFC.AOR entails recirculating the anode exhaust gas back to the fuel inlet, which limits the wasted energy by the unutilized fuel in the anode off-gas and improves the overall efficiency of the SOFC system.In carbonaceous fuels such as methane, methanol, etc., the implementation of AOR can introduce an increased risk of carbon deposition within SOFCs [15] which is not a problem in the case of utilizing hydrogen and ammonia as fuels in SOFCs.In a comprehensive study conducted by Rokni [16] on AOR in a SOFC system with various fuels, it was found that the efficiency of the system differed depending on the utilized fuel.Specifically, in the ammonia-fueled system, a lower efficiency was observed compared to a standalone SOFC system.This was attributed to the dilution of the fuel by steam when introducing AOR without condensation and separation of steam content.The presence of a high steam content in the AOR can negatively impact the performance of SOFCs.The excessive steam in the fuel can lead to a reduction in open circuit voltage (OCV) and power output.An effective method to mitigate this performance drop is to cool down the anode off-gas, facilitating the condensation of steam and subsequently removing the steam content [17][18][19][20][21]. Cooling the anode off-gas to condense water vapor may be perceived as an energy-wasting process.However, it should be noted that the anode off-gas has already been cooled to 150-250 • C before reaching the condenser, and this cooling is achieved by heating up the inlet fuel [17,21].Hence, the energy of anode off-gas is effectively utilized within the system.To the authors' knowledge, there is no available experimental and numerical study in the literature on the delusion effect of excessive amounts of nitrogen in AOR on the performance of the ammonia-fueled SOFCs.
Numerical models play a crucial role as complementary tools in understanding and analyzing the complex multiphysics phenomena occurring in direct ammonia-fueled SOFCs.In addition to considering the fundamental governing physics within SOFCs, it is essential to incorporate the ammonia cracking and the associated thermal sinks resulting from the endothermal cracking process.The cracking of ammonia is a significant aspect to consider in ammonia-fueled SOFCs, as it directly affects the fuel composition and reaction kinetics within the cell.There have been several numerical studies conducted on ammonia-fueled SOFCs.
A 2D model developed by Ni [22] focused on investigating the thermal cracking of ammonia in a planar SOFC at the cell level without validation with experimental data.The results of this study revealed that the thermal cracking of ammonia and the associated endothermal reaction contribute to localized variations in temperature within the cell, particularly near the inlet of the SOFC.In the study conducted by Kishimoto et al. [23], a 2D model was employed to compare the performance of direct and pre-cracked ammonia-fueled SOFCs without comparing the numerical results with experiments.The authors incorporated a correlation for the ammonia cracking rate, which was developed in their previous study [24], into the numerical model.The results of the study indicated that the direct ammonia-fueled operation exhibited performance comparable to that of the pre-cracked operation.However, a slight decrease in the performance of the direct ammoniafueled SOFCs was observed.The authors attributed this decrease in performance to the temperature reduction (around 20 • C) caused by the endothermic ammonia cracking reaction [23].
Oh et al. [25], conducted a comprehensive investigation of direct ammonia-fueled thin-film SOFC using a 2D multiphysics model and compared their results with experimental data.The results revealed that at lower operating temperatures (≤650 • C), direct ammonia-fueled thin-film SOFC experienced a considerable drop in performance.This drop in performance was attributed to two main factors: an insufficient supply of hydrogen from the reduced ammonia cracking reaction and poor mass transport.
To the authors' knowledge, a detailed 3D multiphysics modeling of direct and indirect NH 3 -fueled SOFCs including validation of numerical results with experimental data has not been carried out previously.Furthermore, a numerical and experimental investigation on the influence of excessive N 2 dilution in anode off-gas recirculation on the performance of SOFCs is missing in the literature.Also, there is no available numerical study supported with experimental data on the Ni nitriding potential in direct NH 3 -fueled SOFCs.Set against this background, the current study presents a detailed 3D multiphysics model of an NH 3fueled SOFC at the cell level and validates the model against a broad range of experiments.The current study also addresses the anode offgas recirculation and Ni nitriding as two of the main aspects in direct NH 3 -fueled SOFCs.
The paper is organized as follows.In the next section, the experimental tests are described briefly.Then, the numerical modeling including the geometry of the cell test house domain, and different layers are presented.It is followed by a description of the implemented numerical methods.In the results section, the developed model is first validated under sixteen operating conditions for high and low flow rates under direct and pre-cracked ammonia-fueled cases.The performance of cells as well as species distribution is then presented under high and low fuel flow rates.In addition to this, the developed model is validated under different anode off-gas recirculation rates, and the underlying phenomena are investigated.Finally, Ni nitriding as one of the main challenges in direct ammonia-fueled SOFCs is addressed.Conclusions from this study are outlined in the last section.

Experimental
This section provides an explanation of the cell test house used in the experiments, describes the characteristics of the cell utilized in the experiments, and outlines the operating conditions employed in different tests.

Cell test house
Fig. 2a illustrates a schematic of the cell test house employed in the experimental tests conducted in the electrochemistry laboratory in DTU.Note that the dimensions depicted in the schematic are not to scale.The cell test house consists of two solid alumina (Al 2 O 3 ) blocks with several cut-outs that cover either side of the cell during the test.The cell test house is located inside a furnace with a controlled temperature.The cell test house serves as fuel and air inlet and outlet pipes and channels (see Fig. 2c-f).The fuel compartment is sealed using a 0.1 mm flat gold frame, whereas the air electrode compartment is left unsealed (see Fig. 2a).Gas flows to the cell are regulated using digital mass flow controllers manufactured by Brooks.The sample temperature is measured by a thermocouple in direct contact with the cell surface at the air side.

Cell properties
The cells used in the tests are state-of-the-art anode-supported cells with a total surface area of 53 × 53 mm and an active area of 40 × 40 mm.The cell consists of a thick Ni-YSZ porous support layer and a thin Ni-YSZ porous active electrode layer (see Fig. 2b).On top is a thin dense YSZ electrolyte and a porous composite LSCF-CGO air electrode.Air electrode and electrolyte are separated by a thin dense CGO barrier layer to avoid interaction of LSCF with YSZ.A contact layer composed of LSC is utilized to improve the current collection and the electric contact with the current collector.For a detailed description of the cell materials please refer to Ref. [26].Two layers of Ni meshes are used on the fuel side.The main difference between these two layers is the diameter of the Ni thread and the size of the meshes weave.The air electrode is contacted by a gold mesh.The schematic of these layers is presented Fig. 2b, and the geometrical specifications of the layers are presented in Table 1.

Operating conditions of experimental tests
Multiple experimental tests (24 test conditions) have been conducted in relation to NH 3 fueled SOFCs in the current study, which are used for validation of the developed model.First, the performance of the cell is examined under the direct ammonia (NH 3 ) and pre-cracked ammonia (H 2 + N 2 ) fueled conditions.In the pre-cracked condition, the cell is fed with H 2 and N 2 to simulate a completely cracked ammonia fuel.The tests are conducted under different operating temperatures at low and high fuel flow rates.The high flow rate cases correspond to a fuel utilization (FU) of 14% at the current density of 0.5 A/cm 2 , and the low high flow rate cases correspond to a FU of 70% at 0.5 A/cm 2 .The operating conditions for different cases are presented in Table 2.
The H 2 and N 2 flow rates in the pre-cracked cases are the equivalent values from cracking of ammonia: Subsequently, the impact of anode off-gas recirculation (AOR) on cell performance is examined experimentally.The operating conditions for different AOR rate tests are presented in Table 3.These cases correspond to a fuel utilization of 70% at 0.4 A/cm 2 .It is assumed that the water vapor content is eliminated through condensation prior to recirculation, resulting in an AOR stream primarily composed of hydrogen and nitrogen.This condensation process helps to avoid the accumulation of excessive steam in the system, which could negatively affect SOFC performance.The excessive steam (H 2 O) in the inlet stream can reduce the open circuit voltage and consequently reduce the output power of SOFC.The effect of H 2 O will be shown later in Section 3.3.In an operating system, some steam content may remain after the condensation.However, the main aim of the current experiments is the investigation of accumulated N 2 in AOR on the cell performance.Therefore, the experiments focus on this and assume that all steam content is removed to prevent possible errors in the tests originating from small amounts of H 2 O.
As mentioned in the introduction section the anode off-gas stream has already been cooled down to 150-250 • C before reaching the condenser.The energy from the cooling of AOR from around 800-850 • C to around 150-250 • C is not wasted and it is used for heating up the inlet fuel [17,21].There is still a possibility of using lowtemperature power production units such as organic Rankine cycles to produce energy from the stream with a temperature 150-250 • C before cooling down by the condenser.Hence, the energy of anode off-gas is effectively utilized within the system and it is not wasted.Therefore, removing the H 2 O content of anode off-gas by condensation can be considered as a practical method [17][18][19][20][21].

Numerical modeling
In this section, the geometrical domain of the cell test house model, modeling of the different layers of the cell, the partial differential equations to capture the underlying physics, and the numerical models used in the current study are described.This section is organized as follows: • Section 3.1: describes the modeling of the ammonia cracking rate in the different layers.• Section 3.2: presents the nickel nitriding potential calculation.
• Section 3.3: explains the cell polarization model for finding the properties of the cell.• Section 3.4: presents the cell test house model geometry, simulation domain, and multiphysics modeling.

Ammonia cracking rate modeling
Ammonia cracking rate plays an important role in the performance of the ammonia-fueled SOFCs, as it affects the distributions of hydrogen and temperature over the active area.Ammonia can undergo endothermic cracking on the Ni surfaces at high temperatures, which typically fall within the operating temperature range of SOFCs.Therefore, in the developed model for the cell test house, the ammonia cracking occurs in the fuel support layer and fuel electrode as well as nickel meshes.
For ammonia cracking in the Ni-YSZ support layer and active layer, the expression proposed by Kishimoto et al. [24] is used: where,  −   is the ammonia cracking rate in Ni-YSZ layers in [mol∕m 3 s],  − is the Ni-pore contact area density in [μm 2 /μm 3 ],  is the activation energy equal to 1.2 × 10 5 in [kJ∕mol],  NH 3 and  H 2 are the partial pressures of ammonia and hydrogen in [Pa], respectively.For  − the value of 0.58 measured by Trini et al. [27] is used in the current model.
For ammonia cracking on the Ni meshes, the following correlation developed by McCabe [28] for the ammonia cracking over nickel wires is utilized: here,    is the ammonia cracking rate over the nickel.The definitions of the parameters used in the above equation can be found in [28].
In the regions where ammonia cracking occurs, the associated heat sink () due to endothermal cracking is calculated by [29]: where,   is the cracking rate of ammonia, and  is the enthalpy change of the ammonia cracking which is the difference between the enthalpy of ammonia and the enthalpy of resulting hydrogen and nitrogen from cracking.

Nickel nitriding potential
Nickel (Ni) nitriding may have a harmful effect on direct the ammonia-fueled SOFCs as mentioned in the introduction section.Therefore, a better understanding of the Ni nitriding process helps us to protect the cells under direct ammonia-fed operating condition.
The Lehrer diagram [30] is a tool used to describe the phase stabilities in pure iron based on temperature.It provides valuable information about the formation of different nitride phases in iron and can be customized to determine the process control parameters for gas nitriding in steels [31].
Based on a customized Lehrer diagram for Ni [32] obtained from Thermo-Calc software, there are two stable phases exist in the Ni-rich part of the Ni-N system.The Face Centered Cubic (FCC), and the Ni 3 N phase, which is Hexagonal Close Packed (HCP) [33].Nitrogen can dissolve in pure Ni forming the FCC solid solution first, and then the Ni 3 N phase begins to form with the increase of nitrogen concentration in the binary system.The stability of the FCC solid solution is determined by temperature and nitrogen concentration.The variation of  , ( , ) which is the interface between these two phases is presented in Table 4.The stability of the FCC phase ( , ) decreases by raising the temperature, which means that the FCC phase is easier to transform   to the HCP phase at higher temperatures even with a low Nitrogen concentration.The Ni nitriding potential (  ), which is a parameter that specifies where Ni nitriding will probably occur, can be defined as follow [34]: where,  NH 3 and  H 2 are the mole fractions of ammonia and hydrogen, respectively.
To avoid Ni nitriding, the HCP phase should be avoided.Therefore, the safe region is the region, where   (Eq.( 5)) is lower than  , :

Polarization modeling for finding the properties of cell
Different types of cells may have different properties as the thickness of layers, materials, porosity, fabrication, and other characteristics may be different.Therefore, polarization modeling is conducted here to find out the representing parameters of the utilized cell in the current study under a wide range of operating conditions.The governing equations used for the polarization model are represented in Table 5.The cell voltage (  ) is defined as the open-circuit voltage minus the sum of overpotentials in Eq. (7).A detailed explanation of the equations in Table 5 is presented in previous studies [35].
The governing equations presented in Table 5 have 13 free parameters, which can be adjusted by validation of the model polarization curves with the experimental ones. ohm and  ,ohm are initially calculated using electrochemical impedance spectroscopy data to reduce the number of unknowns to 11 parameters.The remaining 11 parameters are calculated to obtain the best validation with the available experimental data.
In total 24 series of experimental data are used for obtaining the parameters in Table 6.The comparison of the experimental (exp.)IV curves and the IV curves obtained from the cell model (sim.) are depicted in Fig. 1.There is a reasonable agreement between the experimental data and developed cell polarization model results.It is important to mention that this modeling is being conducted to identify the parameters representing various cell properties.As it can be seen these experimental tests only conducted H 2 and H 2 O to obtain the cell electrochemical properties.In the results and discussion section (Section 4), the obtained parameters for the cell are utilized in the 3D model of the ammonia-fueled SOFC considering different layers of cell and contact Ni and gold meshes.
To obtain the parameters reported in Table 6 using optimization, a simplified so-called 0.5D model is used as described in Ref. [35].This is deemed reasonable as the experiments had low fuel/feedstock utilization and consequently, the low variation of the species alongside the active layer is close to linear for most of the cases.The 0.5D model thus simply considers a linear variation of the species inside the cell between the inlet and outlet.This assumption is incorporated into the equations describing OCV (Eq.( 8)) and activation (Eqs.( 9), ( 10), ( 11)) and concentration (Eqs.(12), and ( 13)) overpotentials as well as the cell voltage calculation in Eq. ( 7).The species composition is known at the inlet but not at the outlet.This can however be determined through species conservation based on their inlet conditions and reactions as represented in Eqs. ( 20)- (23).Further explanations of the equations in Table 5 are presented in previous studies [35].For the fitting, the genetic algorithm is used to find the optimum values of the parameters that minimize the errors between the cell voltages from the 0.5D model and the experimental data: here,   is the objective function,   and   are numbers of operating conditions and load current densities, respectively, and abbreviations exp and sim denote the experimental and simulation data, respectively.As can be seen from Fig. 1, the quality of the fit is high for most of the cases.The deviation could originate from the simplification of the 0.5D model used for fitting.It is noteworthy that by comparing the cases with the same conditions and different H 2 O mole fractions in Fig. 1, it can be seen Open-circuit voltage (OCV) [36] Butler-Volmer (BV) [37] Anode exchange current density [37]  0, =   ( Cathode exchange current density [37]  0, =   ( Anode concentration overpotential [38]  , =  2 ( Cathode concentration overpotential [38]  , =  4 (( Ohmic overpotential [37] Dusty-gas model (DGM) fluxes [39]  1 Binary diffusion coefficient Knudsen diffusion coefficient   8)) and consequently cell performance reduces considerably.Therefore, it is important to avoid excessive amounts of H 2 O content in the anode off-gas recirculation.

Cell test house modeling with ammonia fuel
In the present study, 3D multiphysics simulations are performed using COMSOL Multiphysics 6.1.To replicate the same conditions as in the experimental tests as good as possible a detailed 3D model of the cell tests is developed.All of the parameters and models explained in Sections 3.1-3.3are transferred and coupled in the detailed 3D model to have a better understanding of ongoing processes in ammonia-fueled SOFCs.
The 3D computational domain is presented in Fig. 2c-f.To save computational power, only half of the cell test house (Fig. 2c) is modeled in this study with a symmetry boundary condition in the middle in the x direction.It should be mentioned that the whole cell test house was also modeled and the results were close to the results of the half of the cell test house and a maximum deviation of 0.5% was observed.The computational domain consists of fuel and air pipes and channels, the cell, the gold and Ni meshes, and the solid cover with all of the geometrical details.Air is provided centrally while fuel flow is from one side of the cell to the other side.
The governing transport equations of mass, momentum, species, charges, and heat are used in the developed model.The governing equations for the cell test house modeling are given in Table 7. Mixtureaveraged diffusion coefficients [40] are calculated for different species to model the diffusive fluxes in different layers.Ammonia cracking occurs in Ni mesh layers and fuel support and active layers (layers 6-9 in Fig. 2b).Anodic reactions occur on Ni-YSZ active layer which contain Ni catalyst (layer 6 in Fig. 2b), which is the fuel electrode and chatodic reactions take place on the LSC layer (layer 2 in Fig. 2b) which is the air electrode.For the inlets of air and fuel, the fully developed flow boundary condition is considered.The flow rates recorded in the experiments are in [NL/h] which are adjusted in the model based on the test furnace temperature.For the outlets of the air and fuel side, pressure boundary conditions are used.These outlet boundary conditions are far away from the domain and they did not influence the results.
A constant wall temperature boundary condition is considered for the outer walls of solid alumina cover.The wall temperature is assumed to be the same as the furnace temperature.It should be mentioned that convective heat transfer boundary conditions on the solid walls

Table 7
Governing equations for the cell test house model.

Description
Governing equation Eqs. were also tested, but it was not used in the final model as only a small deviation in local temperatures (1-2 • C) was observed from the constant wall temperature boundary condition.Due to the lack of information about the local ambient temperature inside the furnace, the constant wall temperature boundary condition is finally utilized in all of the simulations.A computational mesh consisting of 1.8 million finite elements is employed in the developed model and the number of degrees of freedom (DOF) is 4.0 millions.The computational mesh is shown in Fig. 3 for different regions of the cell test house.As mentioned before, to save  1. computational power, only half of the cell test house is modeled, which is shown in Fig. 3a.A coarser mesh is used for the solid alumina cover.For most of the regions, a free triangular mesh is used, while for the cell layers and gold and Ni meshes a mapped mesh is used to have higher control over the size and distribution of the element (please see Fig. 3c).A Fully Coupled solver is used, in which all the modeling variables are solved simultaneously.Mesh convergence analysis is carried out to ensure the mesh in-dependency of the numerical results.

Results and discussion
In this section, the results of the the developed detailed model of the ammonia-fueled SOFC are presented.The results section is organized as follows: • Section 4.1: compares the polarization curves and temperature of the developed 3D model and the experiments at the high and low flow rate for direct and pre-cracked ammonia-fueled cases.• Section 4.2: compares the performance of the cell for direct and pre-cracked ammonia-fueled cases.• Section 4.3: investigates the influence of anode off-gas recirculation on the cell performance by comparing the results with experimental data.• Section 4.4: investigates the Ni nitriding potential under the high and low flow rates as well as different anode off-gas recirculation rates.

Validation of numerical model under high and low flow rates
In this section, the results of the developed 3D Multiphysics model are compared with the experimental data (overview in Table 2).The comparison of the numerical model results and the experimental data for high flow rate cases (FU = 14% at 0.5 A/cm 2 ) is presented in Fig. 4a  and b.As can be seen, there is a good agreement between the numerical simulation results and experimental data that shows the developed numerical model under both direct and pre-cracked ammonia-fueled conditions for most of the cases captures the physics well.
There is a deviation between the numerical results and the experimental data at 700 • C for the direct ammonia-fueled case.It should be mentioned that the electrochemical reactions in the cell polarization model (see Section 3.3) only consider hydrogen as fuel.Therefore, this deviation is probably due to the influence of ammonia on the electrochemical reactions at lower temperatures, which is not considered in the current model.Considering this kind of effect in the electrochemical reactions thus needs comprehensive dedicated experimental tests and characterization model development which is out of the scope of this study.
The simulation results are compared with experimental data under low flow rate cases (FU = 70% at 0.5 A/cm 2 ) in Fig. 4c and d which shows a good agreement between the numerical and experimental results.As can be seen from Fig. 4d, the deviation between the model and experimental data is low under low temperature of 700 • C is lower than that in the high flow rate (Fig. 4b).This is because, at low flow rates (high FU), the residence time of ammonia on the catalyst layers is longer and consequently ammonia cracking rate is higher compared to the high flow rate cases.This will be elaborated further in the next sections.
The cell temperature is measured at the cathode side in the experimental tests that indicate around 8-10 • C temperature reduction compared to the test temperature (furnace temperature) under high flow rate due to endothermal cracking of NH 3 in the high flow rate cases.Fig. 4e and f show the cell temperature at the air side for operating temperatures of 750 and 850 • C. As can be seen, the numerical results correspond well with the measurements i.e. a temperature drop of 8-10 • C. It is noteworthy that the temperature reduction is higher and more localized for the 850 • C case than that of 750 • C.This is because of the higher cracking rate of ammonia at higher temperatures.
It is also noteworthy that in the current tests, the cell test house is located inside a furnace as shown in Fig. 2a.This leads to heat transfer between the cell test house and the surrounding ambient which is the furnace with a controlled temperature.Therefore, the cell temperature in the test is probably different from the cell temperature inside a stack that is isolated under the same operating conditions.

Performance of cell under low and high flow rates 4.2.1. Power of direct and pre-cracked ammonia-fueled SOFCs
In this section, the performance of direct and pre-cracked ammoniafueled SOFCs is compared in terms of output power under low and high flow rates and different temperatures.Using direct ammonia in the SOFC leads to a reduction in the cell voltage and produced power of the cell at a specific current density.Table 8 presents the performance reduction in direct NH 3 fueled SOFC compared to its pre-cracked counterpart.Power reduction (PR) can be defined as follows: where,  NH 3 and  N 2 H 2 are the produced power for the direct and precracked ammonia cases, respectively.Under some operating conditions, experimental data for voltage and power were not available, which are shown by (-) in Table 8.
As can be seen in Table 8, under the high flow rate cases (FU = 14% at 0.5 A/cm 2 ) the power reduction is higher than in the low flow rate cases (FU = 70% at 0.5 A/cm 2 ).This is due to the higher amount of ammonia in the high flow rate cases, which leads to a difference in hydrogen distribution and a higher temperature reduction and reduction of the cell voltage.It can be seen under the low flow rate operating condition at the current density of 0.5 A/cm 2 which corresponds to FU of 70%, the cell performance reduction is not considerable (less than 1.5%), especially at high operating temperatures.

Distribution of ammonia for direct ammonia-fueled SOFCs
The 3D spatial distribution of ammonia in the fuel side of the cell test house is presented in Fig. 5 under low and high flow rates at 700 and 850 • C for the direct NH 3 fueled cases.
The region shown by the blue arrow in the zoom view is removed from the contours in order to better visualize the variation of NH 3 within the cell.In the high flow rate case (FU = 14% at 0.5 A/cm 2 ) at

Table 8
Performance reduction (PR) in the direct NH 3 feed SOFC compared to its pre-cracked NH 3 counterpart at different current densities (J).

Flow rate
Temperature [ • C, ammonia fuel is not completely cracked, and the molar fraction of NH 3 at the outlet of the fuel side is around 0.15.This is due to the lower cracking rate of ammonia at lower temperatures (Eq.( 2)) and the lower residence time of ammonia on the catalyst layers due to the high flow rate.In the high flow rate case at 850 • C and in the low flow rate (FU = 70% at 0.5 A/cm 2 ) cases all of the ammonia is cracked before the outlet.It also can be seen from Fig. 5 that the distribution of ammonia is non-uniform at the inlet of the active area due to the high fuel flow rates through the fuel pipes.

Hydrogen distribution for direct and pre-cracked ammonia-fueled SOFCs
To gain more insights into the ammonia cracking and the aforementioned non-uniform distribution, the hydrogen mole fraction distribution is shown in Fig. 6.The center of the active area is the origin of the coordinate system in Fig. 6.Therefore, in Fig. 6c, x = −20.0mm and x = 20.0 mm specify the start and end of the active area in the fuel flow direction, respectively.In Fig. 6a and b, d shows the distance from the start of the active area (x = −20.0mm).For example, d = 2.5 mm and d = 38 mm specify two locations in the fuel flow direction with 2.5 mm and 38 mm distance from the start of the active area (see Fig. 6d).The mole fractions of H 2 are obtained alongside the lines in the y direction at six different distances from the start of the active area of the cell (shown by a dashed line in Fig. 5) at the middle of the fuel support layer (layer 7 in Fig. 2b).
As it can be seen from Fig. 6a and b, even at the smaller distance from the start of the active area (d = 0.0 mm), there is a considerable amount of hydrogen due to ammonia cracking.In Fig. 6c, the high molar fraction of hydrogen at the start of active area (x = −20.0mm) is more visible in the low flow rate cases which is around 0.4 and 0.6 at 700 and 850 • C, respectively.There are a few reasons for this high hydrogen molar fraction at the start of the active area.When ammonia enters the fuel inlet header, part of it cracks in the fuel support layer (shown by a red arrow in Fig. 5) before entering the active area.Also, part of the ammonia cracks inside the Ni meshes before reaching the fuel support layer.Furthermore, some part of the hydrogen from ammonia cracking diffuses into the fuel inlet header.All of these together lead to a high mole fraction of H 2 at the start of the active area.
In the low flow rate cases, the residence time of ammonia on the catalyst layers is higher than that in the high flow rate cases.Furthermore, the ratio of convective flow to diffusive flow of hydrogen is lower in low flow rates, leading to higher H 2 mole fractions at the start of the active area compared to the high flow rate cases.It is worth mentioning that due to the above-mentioned phenomena, the cell test may not completely represent the condition in the SOFC stack, and probably the undesirable effects of direct ammonia utilization be higher in the stack.It means that the degradation rate of cells in the direct ammonia-fueled stacks may be higher than in the single-cell tests.direct ammonia-fueled SOFCs.This distance is shorter for the low flow rate cases which is around 2.5 mm.In the high flow rate cases, the H 2 mole fractions continuously increase by increasing the distance from the start of the active area which is due to low fuel utilization in the high flow rate cases (FU = 14% at 0.5 A/cm 2 ).On the other hand, the H 2 mole fractions in the low flow rate cases are high at the locations close to the start of the active area and decrease along the cell due to high fuel utilization (FU = 70% at 0.5 A/cm 2 ).
To have an understanding of the reason for the performance difference between the direct and pre-cracked ammonia cases (Table 8), the hydrogen mole fraction is presented in the x direction (alongside the fuel flow direction) for low and high flow rate cases in Fig. 6c.The hydrogen distributions are presented at 700 and 850 • C which are the lower and upper bounds of the simulations.
As can be seen, there is a large difference between the hydrogen mole fraction for the high flow rate case at 700 • C, especially at the start of the active area.This is due to the lower rate of ammonia cracking at low temperatures.Even at the end of the active area, the hydrogen mole fraction in the direct ammonia-fueled case (H-700-NH 3 ) is around 0.14 lower than its pre-cracked counterpart (H-700-N 2 H 2 ) because part of ammonia leaving the active area before cracking under this condition.The H 2 distribution for high flow under the direct and pre-cracked ammonia condition at 850 • C is much closer than that of 700 • C especially at the second half of the cell (x > 0.0 mm).This leads to a lower performance difference at higher operating temperatures according to Table 8.Under the low flow rate condition, the distribution of H 2 mole fractions is very similar for the direct and precracked NH 3 cells, especially at 850 • C (Fig. 6c).This leads to a very low performance penalty by direct ammonia utilization in the SOFC compared to the pre-cracked condition.
It is worth mentioning that temperature reduction is higher in the high flow rate cases (8-10 • C) compared to the low flow rate cases (2-4 • C) due to higher amount of cracked NH 3 in the high flow rate.Therefore, some part of the performance reduction in direct ammonia cases compared to pre-cracked cases is attributed to this temperature reduction.It should be noted that the performance reductions reported in this section (Table 8) are specific to the cell tests conducted with a surrounding furnace with a controlled temperature.The conditions and performance reductions in an operational ammonia-fueled SOFC stack with insulated walls are different.In a stack with insulated walls, the temperature reductions due to endothermic cracking of ammonia and the corresponding effect on the performance will be higher under similar fuel utilization factors (FU = 14% and 70% at 0.5 A/cm 2 ).The temperature reductions could influence the stack quite differently depending on the flow conditions and inlet temperature.This is addressed in Ref. [29] and further in future work.

Anode off-gas recirculation
The developed detailed 3D model is used to investigate the influence of anode off-gas recirculation (AOR) on the cell performance under different recirculation rates.The main objectives are to examine the validity of utilized models for simulation of AOR and to investigate the influence of dilution in high recirculation rates on the performance of ammonia-fueled SOFCs.3. The percentage of cracked ammonia in a 2D model similar to the 2D model in [24] under different flow rates of hydrogen and nitrogen is represented in (d).

Table 9
Fuel saving and performance reduction compared to the base case without recirculation (DA-R0) for different anode off-gas recirculation rates.

Case ID
Fuel

Validation for different anode off-gas recirculation rates
The comparison of numerical model results for I-V curves and experimental data (Table 3) is presented in Fig. 7a for different AOR rates.There is a good agreement between the simulation results and the experimental data.It can clearly be seen in the zoom of the I-V curves in Fig. 7a, that both experimental data and numerical results show a slight reduction of cell voltage and consequently cell output power by increasing the recirculation rate.

Effect of anode off-gas recirculation on the cell performance
To assess the impact of AOR on the cell performance, the fuel saving and power reduction in different AOR rates are compared to the base case without recirculation (DA-R0) in Table 9. Fuel saving represents the amount of reduced inlet ammonia fuel flow rate (for ammonia flow rates refer to Table 3) compared to DA-R0 case and power reduction shows the reduction of cell produced power under different AOR rates compared to DA-R0 case.As can be seen, a considerable amount of ammonia fuel (21-27%) can be saved by AOR, while the performance reduction by increasing the AOR rate is negligible (less than 1%).This makes the AOR a practical method for efficiency improvement in direct ammonia-fueled SOFCs by reduction of the utilized fuel.It should be mentioned that in an operational ammonia-fueled SOFC system, it may be hard to remove all of the water content from the AOR.The small amount of water will make the fuel gas less potent (Eq.( 8)) and reduce the power slightly.

Distribution of species for different anode off-gas recirculation rates
To understand the underlying reasons for the variation in cell power when increasing the AOR rate, Fig. 7b and c is plotted.The center of the active area is the origin of the coordinate system in Fig. 6.Therefore, in Fig. 6c, x = −20.0mm and x = 20.0 mm specify the start and end of the active area in the fuel flow direction, respectively.This figure shows the ammonia (NH 3 ) and hydrogen (H 2 ) mole fractions together with their normalized values by their inlet value.The inlet hydrogen mole fraction ( H 2 − ) is defined as the total amount of hydrogen in the inlet including the hydrogen content in NH 3 and H 2 flows.The normalized NH 3 and H 2 mole fractions are presented as increasing the AOR rate increases the H 2 flow rate (Table 3) and mole fraction considerably.Therefore, relying solely on the NH 3 and H 2 mole fractions may be misleading when assessing the performance of the SOFC system with increased AOR rates.
Fig. 7b shows that NH 3 mole fraction decreases by increasing the AOR rate which is expected according to Table 3.However, the normalized NH 3 mole fraction ( NH 3 / NH 3 − ) increases by AOR rate increment.This means that ammonia cracking delays by increasing the AOR rate.
In the experiments performed by Kishimoto et al. [24] it was observed that by increasing the inert gas (Ar gas is considered as an inert gas in their experiments) the cracking rate of ammonia reduces due to lower residence time on Ni catalyst layer.They also showed that increasing the hydrogen amount in the inlet gas considerably reduces the ammonia cracking rate [24].To numerically investigate this phenomenon, Fig. 7d represents the percentage of cracked ammonia under different flow rates of hydrogen and nitrogen in the developed 2D model similar to the 2D model in [24].The ammonia flow rate is assumed to be constant and fixed at a value of 50 ml/min for all cases in Fig. 7d.This figure demonstrates that increasing the flow rates of hydrogen and inert nitrogen leads to a decrease in ammonia cracking.
In the case of utilizing AOR, both of the aforementioned factors that reduce ammonia cracking are present.By increasing the AOR rate the amount of N 2 inert gas and H 2 increases (see Table 3) which reduces the ammonia cracking rate.This proves the observed trend for  NH 3 / NH 3 − in Fig. 7b, where uncracked ammonia exhibits greater penetration into the cell in the x direction.
According to Fig. 7c, the hydrogen mole fraction reduces considerably by increasing the AOR rate due to N 2 content increment.However, the normalized H 2 mole fraction ( H 2 / H 2 − ) which shows the ratio of local H 2 mole fraction to inlet H 2 mole fraction slightly decreases by increasing the AOR rate.It can also be seen from Fig. 7c that the location of maximum  H 2 / H 2 − moves farther from the inlet by increasing the AOR rate.This is because the NH 3 cracking as the main hydrogen holder delays by increasing the AOR rate which leads to a slight reduction in  H 2 / H 2 − .The small reduction in the output power by AOR rate increment (Table 9) is attributed to this variation in the H 2 distribution.
As mentioned in Section 2.1, experimental tests in this study are conducted inside the furnace with a controlled temperature.Therefore, there is a heat transfer to the cell, which affects the temperature distribution.Hence, the temperature effect on the cell performance is not considerable for the current AOR tests.From these tests, it can mainly be concluded that the inlet fuel dilution by nitrogen does not influence the performance of the cell significantly.The temperature variation inside a stack was addressed in a recent study [41].It was demonstrated that increasing the recirculation rate in a thermally insulated ammoniafueled SOFC stack resulted in a decrease in temperature reduction, attributed to the reduced endothermic ammonia cracking.This was mainly because of lower ammonia content in the higher AOR rates.

Nickel (Ni) nitriding
As stated in the introduction section, Ni nitriding is recognized as one of the main challenges in direct ammonia-fueled SOFCs.Therefore, the Ni nitriding potential is investigated here under various operating conditions.Fig. 8a and b display scanning electron microscopy (SEM) images of the outer region of the support layer at the fuel inlet and outlet for temperatures of 650 and 750 • C under high flow rate conditions.The provided images were obtained after conducting long-term testing for approximately 1000 h.It is important to note that both long-term testing and SEM analysis were only carried out for these two operating conditions.
In the low voltage, SEM pictures captured with an acceleration voltage of 1 kV is possible to observe the percolating Ni structure as the bright phase (light gray).In the test carried out with direct ammonia, the Ni network shows the formation of pores and cavities in the original structure, visible as the dark spots marked in Fig. 8a  and b.The observation is consistent with the Ni nitriding mechanism.In the tests conducted with pre-cracked ammonia (N 2 +H 2 ) these dark gray stains on light gray regions are not observed (not shown here).From Fig. 8a and b, it is evident that both inlet and outlet regions of the support layer are similarly affected by Ni nitriding at 650 • C. At 750 • C, the inlet is less affected by Ni nitriding compared to the inlet at 650 • C. Furthermore, a comparison of the inlet and outlet at 750 • C proves that the outlet is much less affected by Ni nitriding than the inlet.
Fig. 8c and d presents the ratio of Ni nitriding potential to the critical nitriding potential (K  /K , ) under high and low flow rates at 650, 750, and 850 • C. As mentioned in Section 3.2, there is a risk of Ni nitriding in the locations with a K  /K , value higher than 1.As can be seen in Fig. 8a, at 650 • C under the high flow rate, almost all of the cell is exposed to Ni nitriding.This trend can also be observed in the experimental SEM pictures (Fig. 8a and b) at 650 • C.This is due to the low cracking of ammonia under the high flow rate at low temperatures (650 and 700 • C) which leaves the uncracked ammonia even at the outlet of the cell.At 750 • C, the inlet is exposed to Ni nitriding, while the outlet is less affected by Ni nitriding similar to the presented experimental SEM pictures in Fig. 8a and b.The Ni nitriding potential is lower at 850 • C than that in 650 and 750 • C due to the high cracking rate of ammonia at high temperatures.
It is worth mentioning that Ni nitriding potential is higher in the Ni meshes than that in the Ni-YSZ layers, which is easily visible under the high flow rate case at 850 • C.This is probably due to a high flow rate of ammonia in the Ni meshes than that in the Ni-YSZ layers which leads to more penetration of uncracked ammonia into the cell and higher Ni nitriding potential in these layers.Furthermore, the residence time of ammonia on Ni mesh layers is lower which results in a lower cracking of ammonia on Ni meshes.Thus, in the experimental tests, a larger area of Ni meshes should be affected by Ni nitriding than Ni-YSZ layers.
The Ni nitriding potential under the low flow rate cases, which corresponds to fuel utilization of 70% at 0.5 A/cm 2 , is much lower than in their high flow rate (FU = 14% at 0.5 A/cm 2 ) counterparts.Fuel utilization of 70%-80% is more relevant for the operational condition of commercial SOFC stacks.Especially at 850 • C which is almost no Ni nitriding potential in the active area.This is due to the lower amount of ammonia and also the higher residence time of ammonia on the Ni catalyst which leads to a higher cracking rate of ammonia under the low flow rate operating condition.
There are some differences between the cell test and the condition in NH 3 -fueled SOFC stacks.1-The flow and therefore, ammonia cracking and resulting Ni nitriding may be different in the cell test and stack.2-In some SOFC stacks, there are also Ni meshes in the channel.However, the amount and distribution of Ni meshes may be different from the cell test which leads to different NH 3 cracking rates.3-In the SOFC stack there are steel interconnects that may be affected by nitriding, which is not the case in the cell tests.4-In some of the SOFC stacks, based on the cell and design, the extended part of the support layer (shown by the red arrow in Fig. 5a) is sealed.This should affect the ammonia cracking and availability of hydrogen in the active area, as well as the nitriding of different layers.All of these differences may change the degradation rate in the NH 3 -fueled SOFC stack compared to the cell test.However, the model developed in the present study is well-suited for stack modeling as well.

Conclusion
In the present work, a detailed 3D multiphysics model of an ammonia (NH 3 )-fueled solid oxide fuel cell (SOFC) is developed at the cell level.All underlying physics such as transport equations, heat transfer, electrochemical reactions, and NH 3 cracking reaction coupled together to provide a detailed understanding of the ongoing processes.The model is shown to provide good agreement with experimental data under various conditions including direct (NH 3 ) and pre-cracked (H 2 +N 2 ) ammonia-fueled cases for high and low flow rates at different temperatures in the range of 700-850 • C. High and low flow rate cases correspond to low and high fuel utilization (FU) of (14% and 70% at 0.5 A/cm 2 ), respectively.The developed model is also validated under different anode off-gas recirculation (AOR) rates.Furthermore, Ni nitriding as one of the main challenges in the direct NH 3 -fueled SOFCs is addressed in this study.The main findings can be summarized as follows:

Fig. 1 .
Fig. 1.Comparisons of the polarization curves from the experimental data (exp.)and the cell model (sim.) with H 2 /H 2 O mixtures as fuel for 24 different operating conditions.

Fig. 2 .
Fig. 2. Schematic of (a) cell test house configuration, (b) right hand side of different layers including cell, gold mesh, and Ni meshes, (c) computational domain including solid cover, (d) computational domain without solid cover (air inlet in green and air outlet in blue), (e) air side pipe and channels, (f) fuel side pipe and channels.

Fig. 3 .
Fig. 3. Computational mesh (a) whole computational domain (blue arrows show the air flow direction), (b), air and fuel channels, cell and Ni and gold meshes, and (c) different layers including cell, gold mesh, and Ni meshes.For numbers of layers in (c) please refer to Table1.

Fig. 4 .
Fig. 4. Comparisons of the polarization curves from simulation and experimental data under (a) high flow, pre-cracked ammonia, (b) high flow, direct ammonia, (c) low flow, pre-cracked ammonia, and (d) low flow, direct ammonia cases.Distribution of temperature on the air side of the cell under high flow rate at (e) 750 and (f) 850 • C. The fuel flow direction in (e) and (f) is left to right.

Fig. 5 .
Fig. 5. Distribution of NH 3 mole fraction in the fuel side of the cell test house (a) high flow rate (FU = 14% at 0.5 A/cm 2 ) and (b) low flow rate (FU = 70% at 0.5 A/cm 2 ) cases.The dashed line shows the start of the cell's active area.The region shown with a blue arrow is the elongated part of the cell (please see Fig. 2b and Table 1) which is removed from the contours.The red arrow shows the support layer.The green arrow shows the Ni meshes.The black arrows show the fuel inlet header.
Fig. 6a and b also shows that it takes around 7.5-10.0mm until the H 2 distributions are uniform in the width of the cell.This nonuniformity shows the importance of 3D modeling of the cell tests in

Fig. 6 .
Fig. 6.H 2 mole fraction distribution on lines in y direction at six different locations for (a) high flow rate and (b) low flow rate cases.The location of the six lines in y direction (c).H 2 mole fraction distribution on a line in x direction for high flow rate (H) and low flow rate (L) cases is presented in (c).The location of lines in the y and x directions are represented in (d) and (e), respectively.The figures are presented on lines in the middle of the support layer in z direction at 0.5 A/cm 2 .

Fig. 7 .
Fig. 7. Validation of polarization curves under different recirculation rates (a).Distribution of (b) NH 3 mole fraction ( NH 3 ) with normalized NH 3 mole ( NH 3 / NH 3 − ) and (c) H 2 mole fraction ( H 2 ) with normalized H 2 mole fraction ( H 2 / H 2 − ) for different AOR rates at 0.4 A/cm 2 .Solid lines represent the mole fraction and dashed lines represent the normalized mole fraction.For the name of the cases refer to Table3.The percentage of cracked ammonia in a 2D model similar to the 2D model in[24] under different flow rates of hydrogen and nitrogen is represented in (d).

Fig. 8 .
Fig. 8. SEM micrographs of the fuel support layer of the cell obtained after 1000 h testing at (a) the fuel inlet and (b) the fuel outlet under high flow rate (Table 2).Green arrows show the Ni nitriding.Distribution of the ratio of K  /K , under (c) high flow rate and (d) low flow rate.For better visualization, the -axis scale is doubled.
nitride https://doi.org/10.1016/j.enconman.2024.118396Received 9 November 2023; Received in revised form 30 March 2024; Accepted 3 April 2024 [10]he fuel electrode, including the support layer and the active electrode[10].Ni nitride takes up a relatively higher volume as compared to Ni, leading to a local expansion.This is a problem because the nitride may be unstable, and after the decomposition of Ni nitride, the volume

Table 1
Different layers of the cell and contact meshes.For the number of layers refer to Fig.2b.

Table 2
The operating conditions under high and low flow rate tests for direct and pre-cracked ammonia-fueled cases.

Table 4
Variation of critical nitriding potential ( , ) by temperature.

Table 6
Values of parameters for cell model obtained from validation with experimental data.Constant of the prefactor used for the anode exchange current density [A/m 2 K]  0, 2.531 × 10 8 Constant of the prefactor used for the cathode exchange current density [A/m 2 K] that by increasing the H 2 O content, open-circuit voltage (Eq.(