Highly efficient operation of an innovative SOFC powered all-electric ship system using quick approach for ammonia to hydrogen

Abstract

The solid oxide fuel cell (SOFC) power system fueled by NH₃ is considered one of the most promising solutions for achieving ship decarbonization and carbon neutrality. This paper addresses the technical challenges faced by NH₃ fuel SOFC ship power system, including slow hydrogen (H₂) production, low efficiency, and limited space. It introduces an innovative a NH₃-integrated reactor for rapid H₂ production, establishes a safe and efficient all-electric SOFC all-electric propulsion system adaptable to various sailing conditions. The system is validated using a 2 kW prototype experimental rig. Results show that the SOFC system, designed for a target ship, has a rated power of 96 kW and an electrical efficiency of 60.13%, meeting the requirements for rated cruising conditions. Under identical catalytic scenarios, the designed reactor, with highly efficient heat transfer, measuring 1.1 m in length, can achieve complete NH₃ decomposition within 2.94 s, representing a 35% reduction in cracking time and a 42% decrease in required cabin space. During high-load voyage conditions, adjusting the circulation ratio (CR) and ammonia-oxygen ratio (A/O) improves system efficiency across a wide operational range. Among these adjustments, altering the A/O ratio proves to be the most efficient strategy. Under this configuration, the system achieves an efficiency of 55.02% at low load and 61.73% at high load, allowing operation across a power range of 20% to 110%. Experimental results indicate that the error for NH₃ cracking H₂ is less than 3% within the range of 570–700 °C, which is relevant to typical ship operation scenarios. At 656 °C, the NH₃ cracking H₂ rate reaches 100%. Under these conditions, the SOFC produces 2.045 kW of power with an efficiency of approximately 58.66%. The noise level detected is 58.6 dB, while the concentrations of CO₂, NO, and SO₂ in the flue gas approach zero. These findings support the transition of the shipping industry to green, clean systems, contributing significantly to future reductions in ocean carbon emissions.

Graphical abstract

Keywords

integrated ammonia cracker / hydrogen production / solid oxide fuel cell / all-electric propulsion system / shipping decarbonization

1 Introduction

Addressing global climate change has spurred significant interest among the world’s leading maritime nations in developing advanced, safe, and efficient green marine power systems [1,2]. Solid oxide fuel cells (SOFCs), known for their high efficiency and fuel adaptability, offer promising potential for maritime applications. Their application on ships could extend operational range, reduce emissions, and minimize thermal and acoustic signatures, making SOFCs one of the most promising technologies for next-generation marine power systems [3–6].

To mitigate carbon emissions, the International Maritime Organization has ratified an agreement with the expectation that by 2060, more than 60% of newly constructed ships will be utilizing ammonia (NH₃) or hydrogen (H₂) [7,8]. NH₃ is an inexpensive, non-flammable that is easily storable and transportable. It benefits from an established infrastructure for production, storage, and transportation, and can be easily liquefied at ambient temperature and pressure, offering greater convenience over gaseous fuels like methane.

When utilized in SOFCs, at high temperatures, ammonia directly decomposes into hydrogen and nitrogen, eliminating the issues associated with carbon-H₂ fuel reforming and carbon deposition and avoiding the complexity of fuel reforming. Additionally, ammonia can be produced using renewable energy, making it a more environmentally friendly option. Therefore, the development of an NH₃-fueled SOFC power system presents an effective strategy for advancing green and low-carbon ships [9–11].

When NH₃ is used as a fuel in cell fuels, it must first be cracked into H₂ and N₂ before participating in the electrochemical reaction to produce electricity. However, due to the high activation energy required for the breaking the N-H bonds and desorbing N₂, the reaction kinetics of NH₃ decomposition to produce H₂ is extremely slow. Only when the temperature exceeds 400 °C does NH₃ decomposition to produce H₂ begin to occur significantly, resulting in a substantial energy requirement for the decomposition process. Therefore, efficiently and economically producing H₂ from NH₃ has attracted great attention from researchers [12,13].

Tsai and Weinberg [14] measured the steady-state reaction rate for NH₃ decomposition on the Ru surface within a temperature range of 500–1250 K and at a pressure of 0.133×10⁻³ Pa They observed that, at relatively higher temperatures or lower pressures, the competition between breaking the N-H bond in molecular chemisorbed N₂ and the adsorption of molecular NH₃ governs the decomposition reaction rate. Takahashi and Fujitani [15] investigated NH₃ decomposition on nickel and ruthenium catalysts using a reaction kinetics mechanism model. The findings revealed that the activation energy for NH₃ dehydrogenation was highest on the nickel catalyst, whereas the activation energy for N₂ desorption was highest on the ruthenium catalyst.

Lucentini et al. [16] prepared catalysts with varying amounts of Ni and Ru using a co-impregnation method and determined that the activation energy of the catalyst ranged from 107 to 124 kJ/mol. They identified the adsorption of NH₃ on the catalyst surface as the rate-determining step. Additionally, factors such as catalyst particle size, reaction temperature, space velocity, and reactant composition were found to exert significant influence on the reaction. Yang et al. [17] utilized a Ni-TiO₂-Al₂O₃ composite as a catalyst to investigate the impact of NH₃ volumetric space velocity and inlet temperature on the NH₃ decomposition rate, and developed a predictive model for the NH₃ decomposition process.

Li et al. [18] established the two-dimensional steady-state chemical thermochemical equation for NH₃ decomposition, demonstrating that the reaction was influenced by factors such as gas flow rate, operating temperature, reactor tube length-to-diameter ratio, and other variables. Plana et al. [19] conducted a series of experiments using a whole-cell catalyst to investigate the influence of reaction products on catalyst activity. Their study showed that H₂ has an inhibitory effect on NH₃ decomposition, while N₂ has no such inhibitory effect. They attributed this inhibition by H₂ to the competition between H₂ and NH₃ for the same active site. Okura et al. [20] investigated the impact of NH₃, N₂, and H₂ partial pressures on catalyst activity using reaction kinetics. They observed that N₂ had no discernible effect on the reaction rate, while H₂ hindered the NH₃ decomposition.

Unlike on land, the space within a ship’s power plant is limited, presenting a challenge for installing an NH₃-SOFC power system in such confined quarters. As an integral component, the compact NH₃ cracker plays a pivotal role in facilitating the complete breakdown of NH₃, as it ensures the complete breakdown of NH₃ and a stable fuel cell power output. Abashar [21] proposed a model for a multi-stage fixed-bed membrane reactor (MSFBMR), a multi-stage reactor featuring interstage heating and sweep gas for NH₃ decomposition. The findings indicated that the 4-bed MSFBMR achieved complete conversion of NH₃.

Kim et al. [22] developed a compact NH₃ decomposition system by enclosing the reformer around the combustion chamber. The findings indicate that the fuel equivalence ratio of the NH₃-H₂-air mixture and the air intake velocity influenced NH₃ decomposition performance. The NH₃ conversion rate, overall efficiency of the reformer, and NO_xemission concentration were 97.0%, 10.4%, and 158 ppm, respectively.

Di Carlo et al. [23] constructed a porous tube catalytic membrane reactor. Their 3D CFD simulation results showed an 18% increase in NH₃ conversion rate at 550 °C when utilizing a catalytic membrane reactor. Furthermore, beyond 550 °C, NH₃ could be progressively converted into N₂. Zhang et al. [24] investigated Pd membranes with exceptional transparency and selectivity, which were integrated into reactors for NH₃ decomposition, significantly improving the NH₃ conversion rate by removing H₂. Under experimental conditions, the NH₃ conversion rate reached 99.96%, and the service life was extended to 500 h.

The research is valuable for building a foundational understanding and serves as a reference for developing dynamic models, reaction mechanisms, and compact reaction systems for H₂ production via NH₃ decomposition.

A well-structured schematic is crucial for the safe and efficient operation of an NH₃-SOFC power system. Currently, there are two primary types of design approaches for NH₃-fueled SOFC power systems. In one design, NH₃ can undergo decomposition in a dedicated reactor, and the resulting gas mixture, which includes H₂ and N₂, is directed to the SOFC. In an alternative approach, NH₃ is directly supplied to the SOFC stack. This latter design is particularly intriguing as the internal NH₃ decomposition reaction absorbs the generated heat, reducing the necessity for additional cooling of the SOFC power unit.

Barelli et al. [25] developed a system to generate electricity by utilizing NH₃ as a fuel. This involves pre-cracking the NH₃ in a reactor before it enters the SOFC, and they also established thermodynamic models to assess its performance. Veldhuizen et al. [26] designed a configuration for an NH₃-SOFC system, which involves directly injecting NH₃ into the SOFC, where it undergoes decomposition on the anode, followed by parameter optimization studies.

Duong et al. [27] developed an innovative integrated system, combining an NH₃ fuel SOFC-GT-steam Rankine cycle with a waste heat boiler, where preheated NH₃ is directly injected into the SOFC. Wang et al. [28] proposed an SOFC-GT hybrid system featuring an anode and an exhaust gas re-circulation loop in the catalytic combustor, and investigated the impact of these two re-circulation interactions on the power system.

The Future Technology Research Institute in Republic of Korea, led by Kyunghwa Kim [29], developed an NH₃ fuel propulsion system for a 2500 TEU feeder container ship utilizing four distinct power sources: diesel engine, generator, PEMFC, and SOFC. The findings indicated that the NH₃-SOFC power system emerged as the most environmentally sustainable option among those evaluated, though it incurred a higher life-cycle cost.

Di Micco et al. [30] researched the design, modeling, and feasibility assessment of two NH₃-based ship propulsion systems. Their findings revealed that the installation of NH₃-based propulsion technology would lead to increased mass and volume compared to traditional diesel systems. It was estimated that fuel cell-based power systems could result in a cargo reduction of 3.3%– 4.8%. Wu et al. [31] evaluated the feasibility of integrating NH₃ decomposition with SOFC technology for container ships. Minutillo et al. [32] studied the technical and economic feasibility of a new H₂ refueling station based on the H₂ production route from NH₃ and SOFC technology, noting that NH₃ is directly supplied to the SOFC, which produces both electricity and H₂ by combining a high-efficiency energy system with H₂ storage.

In summary, ensuring the efficient and stable operation of SOFC power system for an NH₃-fueled all-electric ship requires addressing several key challenges. These include not only the technical difficulty of rapid NH₃ decomposition into high-concentration H₂ during ship operations, but also the effective recovery and utilization of heat in the SOFC power system. Moreover, the limited space within ship cabins. adds a significant constraint.

For the heat-absorbing NH₃ decomposition reaction, it is crucial to achieve efficient decomposition in a high temperature and catalyst-assisted environment. However, in the case of adopting the direct decomposition mode of NH₃, the catalyst on the SOFC anode may undergo nitridation and deactivation, resulting in performance degradation. On the other hand, the pre-decomposition method, requires more space and leads to increased heat dissipation between components.

Additionally, ships frequently operate outside their design parameters due to factors such as start-up and shutdown procedures, variations in passenger traffic on specific dates, and the impact of wind and waves causing rolling and pitching. These conditions can impact the performance of NH₃-fuel SOFC power systems. Therefore, in addition to addressing the technical challenges mentioned above, it is essential to consider the variability in operating conditions to prevent issues like thermal cracking and other potential faults. To the author’s knowledge, studies addressing these specific challenges remain largely unexplored.

Therefore, to address the technical challenges such as slow NH₃ for H₂ production, low efficiency under varying ship operating conditions, and limited hull space, this paper innovatively proposes a ribbed catalytic-combustion integrated ammonia cracker (IAC) for rapid H₂ production, using a target ship type as a case study. This approach aims to construct a safe and efficient SOFC all-electric propulsion system for the ship, achieving high efficiency across a wide range of operating conditions, with validation based on a 2 kW prototype experimental platform.

Additionally, considering the safety constraints of ship’s NH₃-SOFC working environment, this paper examines the coupling effects from a thermodynamic perspective. By analyzing the impacts of gas flow direction, anode exhaust gas circulation ratio (CR), and ammonia-oxygen ratio (A/O), the suitable operating range is identified. These research findings provide valuable technical insights for the design of green ship propulsion systems, supporting the promotion of sustainable development in the future.

2 Topology and modeling of an NH₃ fueled SOFC for all-electric ship propulsion system

2.1 Selection of target ship type

Sightseeing ships play a pivotal role in promoting tourism in coastal cities. These ships are usually compact in size and require long endurance and a lengthy service life, especially given the stricter requirements for emissions and noise levels [33,34]. The NH₃-fueled SOFC power configuration offers a viable solution, meeting the operational requirements of these ships while ensuring high performance and efficiency. This paper focuses on a sightseeing ship designed for inland rivers in coastal cities, with specifications including a length of 25.46 m, a width of 5.36 m, a maximum passenger capacity of 100 people, and a rated cruising speed of 14 km/h [35]. Detailed parameters are provided in Electronic Supplementary Material (ESM).

2.2 Topological diagram

To optimize the use of the limited internal space and improve the system efficiency, the topological structure of the NH₃-fueled, SOFC powered all-electric propulsion system designed in this paper is shown in Fig.1. This design, tailored to the target ship type and its navigation characteristics, mainly consists of a liquid NH₃ storage tank, a ribbed catalytic-combustion integrated NH₃ cracker, an ejector, SOFC, a three-way valve, an air compressor, a heat exchanger, and power inverter, among others.

In this system, when valve 1 is opened, liquid NH₃ is released from the storage tank and undergoes a heat exchange with the cabin environment, transforming into NH₃ gas. After being pressurized, the gas passes through heat exchanger 1 for preheating before entering the catalytic NH₃ cracking reactor, where it undergoes thermal decomposition to produce H₂ and N₂. The high-pressure fluid outlet at the exit of the NH₃ cracker is connected to the injector inlet at 3 nodes, while the low-pressure gas inlet of the injector receives SOFC exhaust gas from 7 nodes. The resulting mixed gas is then directed into the SOFC anode. Air enters the air filter at node13, passes through the compressor and heat exchanger, and then enters the cathode of the SOFC stack as high-temperature air. Exhaust gas from the anode at node 5 pass through the recirculation three-way valve and is mixed with exhaust gas from the cathode at node 6. This pre-mixed exhaust gas is then directed into the catalytic combustor at node 9, where it is fully oxidized and releases heat.

To showcase the adaptability of the IAC designed in this system, it can operate in both counter-stream and co-stream flow configurations. The dashed line, indicating the flow direction from node 14 to 10 represents the co-stream movement of NH₃ and high-temperature flue gas, while the solid line, showing the flow direction from node 9 to 14, represents the counter-stream movement of NH₃ and high-temperature flue gas.

The electricity generated by the fuel cell is converted through a current converter between the inverter and the distribution board, providing power for both propeller rotation and ship’s daily loads.

2.3 Mathematical modeling

2.3.1 SOFC modeling

In this study, a mathematical model of anode-supported flat plate SOFC is employed, integrating both electrochemical and thermodynamic models. The electrochemical model focuses on the fuel cell’s electrochemical reaction mechanism, including electrode reaction kinetics and electrolyte conductivity. The thermodynamic model accounts for the gaseous properties of the fuel cell constituents and their behavior at varying operating temperatures, covering gas diffusion, thermal conduction, and convection within the cell. This is essential for ensuring stable operation and optimal performance across different temperature ranges.

Furthermore, the mathematical model incorporates various polarization losses, such as electrochemical polarization, concentration polarization, and ohmic polarization. The internal structure, flow directions of various substances, and heat exchange processes are depicted in Fig.2. Previous research has extensively investigated SOFC, validating the detailed mathematical equations, modeling methods, and model accuracy [28,36,37]. The specific modeling formulas are provided in detail in ESM.

The model incorporates mass conservation, energy conservation, momentum conservation, and electrochemical reactions. It is assumed that any residual NH₃ remaining after passing through the NH₃ decomposition unit will further decompose under the high-temperature catalytic conditions on the SOFC anode, as shown in Eq. (S2) in Table S1(ESM).

After NH₃ decomposition process, the high-concentration H₂ synthesis gas participates in the electrochemical reaction of the SOFC, as detailed in Eqs. (S5) and (S6) in Table S1(ESM).

The electrochemical reaction in a fuel cell involves the transfer of electrons between chemical substances on the surface of the electrodes and those near the adjacent electrode. Therefore, during the modeling process, the materials of the selected fuel cell are carefully considered, including electron conductivity in both anode and cathode, ion conductivity in the electrolyte, and the diffusion coefficients for H₂, H₂O, O₂, and N₂ in both anode and cathode [36,37].

2.3.2 Ribbed catalytic combustion integrated NH₃ cracker

The proposed integrated reactor structure is illustrated in Fig.3. The high-temperature exhaust gas from the SOFC is directed into the combustor for catalytic oxidation, and the combustor is wrapped in the outer side of the NH₃ cracker, allowing direct transfer heat through the tube wall. This integrated reactor has obvious advantages, including high heat transfer efficiency, superior thermal conductivity efficiency, compact size, and lightweight design compared to previously developed reactors. Preliminary calculations show a weight reduction of 30% and a 42% reduction in volume, making it well-suited for the limited space in the target ship’s hull. The model takes into account energy conservation, mass conservation, heat exchange, and gas viscosity to ensure an accurate mathematical representation.

The catalyst used in the framework model for the catalytic NH₃ cracker in this work closely matches the experimental conditions of the Ni-Pt/Al₂O₃ catalyst studied by Chellappa et al. [38]. The rate equation for this catalyst has been shown to be robust between 520 and 690 °C and remains reasonable at temperatures above 660 °C. The combustion equation is presented in Eq. (S1) in Table S1 and the kinetics of the NH₃ cracking reaction are shown in Eq. (S3) in Table S1.

To model the variable molecular reaction, the equilibrium equation and pressure distribution are utilized in conjunction to determine the apparent velocity and temperature distribution within the NH₃ decomposition reactor. This is achieved by using ideal gas and energy conservation equations, as outlined in Eqs. (S2) and (S1) in Table S1.

(1){\displaystyle \frac{\mathrm{d}{T}_{\mathrm{t}}}{\mathrm{d}z}}={\displaystyle \frac{h_{\mathrm{t}}(T_{\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{l}}-T_{\mathrm{t}}){\displaystyle \frac{\text{π}{d}_r}{{\mathrm{A}}_{\mathrm{t}}}}-\mathrm{\Delta }H\left(\mathrm{N}{\mathrm{H}}_3\right)\left(T_{\mathrm{t}}\right)r\left(\mathrm{N}{\mathrm{H}}_3\right)(T_{\mathrm{t}},p_{\mathrm{t}}(\mathrm{N}{\mathrm{H}}_3\left)\right)(1-\epsilon ){\rho }_{\mathrm{c}\mathrm{a}\mathrm{t}}}{u_{\mathrm{t}}{C}_{p,m,g,\mathrm{t}}\mathrm{\Sigma }{c}_{\mathrm{t},j}}},

where A, r, C, and u respectively represent cross-sectional area, reaction kinetics coefficient, heat capacity, and gas flow rate; subscripts t, cat represent the inner-tube of the integrated reactor, and catalyst respectively; and \epsilon is the bed porosity of reactor. The Pt catalyst is utilized in the outer-surrounding catalytic combustor. Equation (2) illustrates the one-step reaction kinetics of H₂ catalytic oxidation on this catalyst [39].

(2)r\left({\mathrm{H}}_2\right)( T_{\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{l}},c_{\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{l}}({\mathrm{H}}_2\left)\right)=14\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{14900}{\mathrm{R}{T}_{\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{l}}}\right)c_{\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{l}}({\mathrm{H}}_2).

By adding ribs, the contact area between the catalytic combustor and the NH₃ cracker tube wall is increased, enhancing the heat exchange between the two. The ribs also provide more attachment points for the catalytic combustion. Additionally, the ribs increase both the area of the protruding portion (A) and the flat wall area between them, with the total increase in area represented by Eq. (3).

(3)A{s}^{\prime }=As+A.

The areas of ribs and protrusions is shown in Eq. (4).

(4)A=2N\times L\times H,

where N is the number of ribs increased, L is the length of ribs, and H is the height of ribs.

H₂ combustion occurs at atmospheric pressure, with the resistance of gas flow in the combustion combustor neglected. The velocity and temperature distributions of high-temperature gases in the combustion combustor along the axial length are calculated using the ideal gas equation and energy conservation equation, as shown in Eqs. (5) and (6).

(5)(\pm ) \frac{\mathrm{d}\left(u_s{c}_{s,i}\right)}{\mathrm{d}z}=u_{s,i}\frac{4d_r}{D_r^2-d_r^2}{k}_g\left[c_s\left({\mathrm{H}}_2\right)-c_{\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{l}}\left({\mathrm{H}}_2\right)\right],

(6)(\pm ) {\displaystyle \frac{\mathrm{d}{T}_s}{\mathrm{d}z}}={\displaystyle \frac{h_s\left(T_{\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{l}}-T_s\right){\displaystyle \frac{\text{π}{d}_r}{{\mathrm{A}}_{\mathrm{s}}}}}{u_s{C}_{p,m,g,s}\sum c_{s,i}}},

where k_g is mass transfer coefficient. Subscripts s represent the shell side of the reactor. d_r and D_r represent decomposer diameter and reactor, diameter, respectively. The combustor and NH₃ cracker exchange heat through the wall of the cracker, as depicted in Eq. (7), where the plus and minus signs before the equation denote the counter-stream and co-stream modes, respectively.

(7)\begin{array}{rl}& -r\left({\mathrm{H}}_2\right)\left(T_{\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{l}},c_{\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{l}}\left({\mathrm{H}}_2\right)\right)\mathrm{\Delta }{H}_{{\mathrm{H}}_2}\left(T_{\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{l}}\right)=\\ & h_s\left(T_{\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{l}}-T_s\right)+h_t\left(T_{\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{l}}-T_t\right).\end{array}

After calculations, the NH₃ cracking rate reaches 99% when the working temperature is 656 °C under normal pressure. In Simulink, MATLAB’s BVP solver is used to solve the multi-boundary ordinary differential equations governing both NH₃ decomposition and catalytic combustion. The specific heat capacity and viscosity of each gas component are calculated as the temperature changes. The formula for calculating the viscosity of each gas component is shown in Eq. (8).

(8){\mu }_i={\displaystyle \frac{C_{1i}\ast T^{C_{2i}}}{1+{\displaystyle \frac{C_{3i}}{T}}+{\displaystyle \frac{C_{4i}}{T^2}}}}.

The heat capacity of each gas component is calculated using Eq. (9).

(9)C_{P_i}=C_{5i} +C_{6i}\cdot {\left({\displaystyle \frac{{\displaystyle \frac{C_{7i}}{T}}}{\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{h}(C_{7i}/T)}}\right)}^2+C_{8i}\cdot {\left({\displaystyle \frac{{\displaystyle \frac{C_{9i}}{T}}}{\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{h}(C_{9i}/T)}}\right)}^2.

2.3.3 High and low-pressure ejector

To increase the anode fuel temperature and maximize the recovery of thermal energy from the SOFC exhaust gas for enhanced system efficiency, an injector is employed to achieve thorough mixing of high- and low-pressure fluids, as shown in Fig.4. After mixing, the gas flows into the diffuser, where the cross-sectional area expands, resulting in a gradual reduction of kinetic energy and subsequent pressure recovery. The detailed modeling method and validation are based on the team’s previous research [28,37], while this study focuses on presenting the key equations.

The momentum conversion equation of the inlet and outlet of the mixing section is shown in Eq. (10).

(10)\begin{array}{rl}& {\varphi }_2\left({\dot{m}}_P{w}_{P2}+{\dot{m}}_H{w}_{H2}\right)-\left({\dot{m}}_P+{\dot{m}}_H\right)w_3=\\ & \left(p_3-p_{P2}\right)f_{P2}+\left(P_3-P_{H2}\right)f_{H2},\end{array}

where m, w, p, and f respectively represent mass flow rate, velocity, pressure, and cross section area, {\varphi }_2 is friction loss coefficients in the mixing section; subscripts P, H, 2, and 3 represent the cracking gas, anode circulation exhaust gas, mixing section inlet, and outlet sections, respectively.

According to the continuity equation, mass conversion equation, and momentum conversion equation, the formula for calculating the entrainment rate u of the injector can be derived from Eq. (11).

(11)u\sqrt{\theta }= \frac{K_1{\lambda }_{P2}-K_3{\lambda }_{c3}}{K_4{\lambda }_{c3}-K_2{\lambda }_{H2}}.

Among them, the calculation formulas for K₁ to K₄ are shown in Eqs. (12) to (13) respectively.

(12)K_1= {\varphi }_1{\varphi }_2{\varphi }_3,

(13)K_2= {\varphi }_2{\varphi }_3{\varphi }_4,

(14)K_3=1 +{\varphi }_3 \frac{p_{\mathit{c}}}{p{}_{\mathit{P}}}\frac{{\mathrm{\Pi }}_{{}_{\mathit{c}3}}-{\displaystyle \frac{p_{\mathit{H}}}{p_{\mathit{c}}}}}{k{\mathrm{\Pi }}_{\ast }{\lambda }_{\mathit{c}3}{q}_{\mathit{P}2}},

(15)K_4=1 +{\varphi }_3 \frac{p_{\mathit{c}}}{p_{\mathit{H}}}\frac{{\mathrm{\Pi }}_{\mathit{c}3}-{\mathrm{\Pi }}_{\mathit{c}2}}{k{\mathrm{\Pi }}_{\ast }{\lambda }_{c3}{q}_{\mathit{H}2}},

where {\varphi }_1, {\varphi }_2, and {\varphi }_4 are the friction coefficients of the nozzle, suction section, and diffusion section respectively; λ is the velocity coefficient; Subscripts P, H, and c represent the primary, secondary, and mixed fluids, respectively, and subscripts 2 and 3 refer to the 2-2 and 3-3 cross sections, respectively.

The \theta calculation formula in Eq. (11) is shown in Eq. (16),

(16)\theta =\frac{T_{\mathit{H}}}{T{}_{\mathit{P}}}.

The flow areas of the primary and secondary fluids in Section 2.2 are shown in Eqs. (17) and (18), respectively.

(17)f_{P2} =\frac{{\stackrel{.}{m}}_P{a}_{P\ast }}{k_P{\mathrm{\Pi }}_{P\ast }{p}_P{q}_{P2}},

(18)f_{H2}=\frac{{\dot{m}}_H{a}_{H\ast }}{k_H{\mathrm{\Pi }}_{H\ast }{p}_H{q}_{H2}}.

The flow area of the mixed fluid in Section 3.3 can be expressed as

(19)f_{c3}=\frac{{\dot{m}}_c{a}_{c\ast }}{k_c{\mathrm{\Pi }}_{c\ast }{p}_c{q}_{c3}}.

2.3.4 Ship resistance and loading model

Ship resistance is primarily influenced by speed, hull shape, and environmental conditions, which can be mathematically characterized for a given vessel type. In this study, the overall ship resistance of ships was focus on, including frictional resistance and additional resistance due to wind and waves. Frictional resistance is mainly generated by the boundary layer of water flow around the ship, as shown in Eq. (20):

(20)R_{\mathrm{f}}= C_{\mathrm{f}}\frac{1}{2}\rho V_{\mathrm{s}}^{2}S ,

where C_{\mathrm{f}} is the friction coefficient, \rho is the density of water, V_{\mathrm{s}} is the ship speed, and S is the contact area between the water and the ship. The additional resistance caused by wind waves is shown in Eq. (21).

(21)\mathrm{\Delta }{R}_{\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}}=\frac{1}{2}{\rho }_{\mathrm{a}\mathrm{i}\mathrm{r}}{A}_{\mathrm{t}}{C}_{\mathrm{D}\mathrm{\_}\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}}\left[(V_{\mathrm{s}}+v_{\mathrm{w}}\cdot \mathrm{c}\mathrm{o}\mathrm{s}{\theta }_t{)}^2-(V_{\mathrm{s}}{)}^2\right],

where v_{\mathrm{w}} is the wind speed, C_{\mathrm{D}\mathrm{\_}\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}} is the wind resistance coefficient, A_{\mathrm{t}} is the front projection area of the ship, and {\theta }_t is the angle between the ship’s sailing direction and the wind speed direction.

The ship mainly depends on the power generated by the rotation of the propeller to overcome resistance and move through the water. The force created by propeller rotation to propel the ship forward is known as propeller thrust. Additionally, as the propeller rotates in water, it must overcome the resistance posed by the water to its motion. When the propeller operates at a certain speed, the thrust and torque coefficients are calculated as follows

(22)K_T= \frac{T}{\rho n^2{D}^4},

(23)K_Q= \frac{Q}{\rho n^2{D}^5},

where T and Q are thrust and torque respectively, K_T and K_Q represent thrust coefficient and torque coefficient respectively, \rho stands for fluid density, n is propeller speed, and D is the propeller diameter. The thrust and torque coefficients of the propeller can also be expressed as a function of advance ratio, as shown in Eq. (24).

(24)J=\frac{v_{\mathrm{P}}}{nD},

where v_p indicates the forward speed of the propeller. The performance characteristics of propellers in open water can serve as indicators of the relationship between propeller efficiency and advance ratio, which are typically determined by experimental results. The data utilized for the calculations in this study primarily stem from open water tests on propellers cited in Auf’m Keller [40].

The relationship between the actual thrust of the propeller and the resistance of the ship is shown in Eq. (25).

(25)R=T\left(1-t\right),

where t is the coefficient of thrust derating. The more detailed derivation of the relationship between the resistance and the required power of the target ship can be found in Carlton [37].

2.3.5 Mathematical models for other components

In this system, the other components such as heat exchangers, propeller drive motor, and mixers are modeled in detail based on their operating principles, as described in Refs. [28,37]. For the entire ship propulsion system, the efficiency can be calculated using Eq. (26).

(26)\eta =\frac{P_{\mathrm{S}\mathrm{O}\mathrm{F}\mathrm{C}}\times {\eta }_{\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{e}\mathrm{r}}-P_{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{o}\mathrm{r}}}{Q_{\mathrm{F}\mathrm{u}\mathrm{e}\mathrm{l}}}.

In the all-electric propulsion system currently being developed, the power generated by the SOFC system can be utilized to supply electrical systems on the ship. A DC/DC converter (efficiency = 97%) [41] and a DC/AC inverter (efficiency = 97%) are required to regulate the output voltage of the power system and convert it into AC power. Furthermore, an AC distribution panel and transformer are needed to distribute power to various shipboard facilities.

2.3.6 System modeling and iterative calculation procedure

The calculation flow for the strong coupled NH₃-fueled SOFC all-electric power system is outlined in Fig. S1. The state parameter constraints and the system characteristics between components are simulated through programming on the MATLAB/Simulink platform. The ship’s resistance is determined by considering design parameters, sailing conditions, and desired speed. By calculating the thrust reduction coefficient, the actual thrust and torque of the propeller, can be derived, allowing for the accurate determination of the power required for propulsion. The fuel flow is then adjusted based on the propeller load demand, and the air flow is adjusted according to the A/O ratio. Finally, the thermodynamic parameters and matching rules for different components in the SOFC powered ship propulsion system are obtained through an iterative calculation process.

2.4 Selection of operating parameters at design point

Based on the ship’s load requirements, the initial calculation for the SOFC stack in the propulsion system consists of 632 single cells, with a current density of 5000 A/m². According to the NH₃ reaction kinetics model and catalytic properties calculation in Section 1.3.2, the length of the reactor is designed to be 1.1 m. The detailed parameters under the design condition are provided in Tab.1.

2.5 Correlation between ship’s propulsion capacity and resistance

Based on the modeling work in Section 1.3.4, the relationship between ship resistance, required power, and cruising speed is shown in Fig.5. As expected, as the ship’s speed increases, both the resistance and energy required for propulsion increase significantly. When the ship is cruising at its rated speed, the power system must provide at least 94.8 kW to ensure the stable operation. At maximum cruising speed, the power system needs to provide 114.6 kW for ship propulsion, corresponding to a resistance of 5100 N experienced by the ship.

3 Performance analysis under design condition

The thermodynamic parameters and output performance of the power system under design conditions are initially calculated based on the co-stream mode of IAC, as presented in Table S3. The NH₃ decomposition rate reaches 100%, with the single fuel cell output voltage at 0.88 V. The efficiency of the fuel cell is 71.74%, while the exhaust heat utilization efficiency from the SOFC used in the IAC is 14.25%. Additionally, the waste heat recovery efficiency by the heat exchanger after the IAC is 57.93%. The total system output power reaches 96.01 kW, which meets the power demand for the maximum passenger capacity and rated cruising speed of the target sightseeing ship, as shown in Table S2. The designed propulsion system achieves an electrical efficiency of 60.13%, representing an 8.03% increase compared to the referenced system in Wang et al. [35], which has an efficiency of 52.1%. These results underscore the rationality and feasibility of the NH₃-fueled SOFC-powered system for the target ship, demonstrating its suitability for application.

4 Variable characteristics of NH₃-SOFC powered ship propulsion system

Due to the complex operational conditions in the ocean-atmosphere environment, adjusting multiple parameters to enhance the ship’s ability to navigate efficiently and quickly through diverse environmental conditions presents a significant challenge for the crew. Therefore, this study fully considers the actual ship operation characteristics of the crew in navigation. From the perspective of easy operation and implementation, it investigates the interconnected influences of gas flow direction, CR, and A/O ratio on the NH₃-fueled SOFC-powered propulsion system. This is done while maintaining a constant fuel utilization rate, with the aim of achieving a broader adjustment range and higher efficiency of the ship under high-load conditions.

4.1 Analysis of gas flow direction changes in IAC

As shown in Fig.7, the gas flow in the IAC can operate in two directions: co-stream, and counter-stream. These different gas flow modes inevitably affect the heat exchange between the NH₃ cracker and the catalytic combustor, which in turn influences the NH₃ cracking rate. This change in cracking rate subsequently affects the electrochemical reaction in SOFC and alters the system output efficiency. Additionally, the direction of the high-temperature exhaust gas after catalytic combustion also affects the heat exchange between heat exchangers 1 and 2. The comparison results for the different gas flow modes are presented in Tab.2 and Fig.6.

From Tab.2, and by comparing the performance parameters at the design point in co-stream mode as discussed in Section 2, it can be seen that only changing the gas flow in the IAC, while keeping other parameters constant, results in a higher fuel requirement in counter-stream mode compared to co-stream mode for the same system output power of 96 kW. The system efficiency decreases from 60.13% to 57.05%, and NH₃ decomposition rate is reduced to 96.32%.

Fig.7(a) and Fig.7(b) show the NH₃ decomposition speed and NH₃ decomposition rate along the reactor’s axis in co-stream and counter-stream modes, respectively. In the co-stream mode, the decomposition speed reaches its maximum value at x = 0.143 m, and decreases to zero at x = L. The NH₃ decomposition rate reaches 100%. Through relative calculations based on NH₃ transfer velocity, the length and radius of the reactor, it is found that NH₃ is completely broken down only in 2.94 s, which is 35% faster than the current NH₃ decomposition methods for H₂ production [18].

In contrast, as shown in Fig.7(b), when the counter-stream mode is adopted, the NH₃ decomposition speed peaks at x = 0.253 m but does not decrease to zero at x = L, resulting in a NH₃ decomposition rate of 96.32%, indicating incomplete NH₃ decomposition. The co-stream mode proves to be more advantageous for NH₃ decomposition compared to the counter-stream mode, due to enhanced heat exchange between the combustion gas and NH₃.

Fig.7(c) and Fig.7(d) further show that in the co-stream mode, the syngas outlet temperature reaches 946 K, whereas in counter-stream mode, it is only 922 K. The main reason for this is that, in the co-stream mode, the highest temperature in the catalytic combustor and the lowest temperature in the NH₃ cracker are aligned on the same side in the IAC. At x = 0, where both gases meet, the heat demand for NH₃ decomposition is at its peak. The catalytic combustion effectively supplies the necessary heat, resulting in the maximum NH₃ decomposition rate at x = 0.143 m. In counter-stream mode, both ends of the catalytic combustor and NH₃ cracker are cooler than in co-stream mode. As NH₃ cracking requires significant heat to accelerate the reaction, the hydrogen in the catalytic combustor side is nearly, depleted and unable to provide sufficient heat for NH₃ cracking, leading to suboptimal decomposition.

These results show that the co-stream mode of the IAC is a viable option for designing an SOFC propulsion system fueled by NH₃ for the target ship under the conditions specified in Section 3. Given the space constraints, this study focuses on the coordinated regulation rules of A/O and CR in co-stream mode in Section 4.2.

4.2 Impact of A/O and CR on system performance

By analyzing the navigation trajectory of the target ship, it was found that the ship mostly operates in high-load conditions [35]. Therefore, from both the perspective of safety and economy, this study focuses on coordinating the range of A/O from 0.3 to 0.55, and the range of CR from 0 to 50%. This coordination is aimed at ensuring a flexible and safe operation of the propulsion system, tailored for the ship’s high-load conditions.

Fig.8 shows that the operating temperature of the SOFC increases with the increase of both A/O and CR. This is mainly due to that, as A/O increases, air flow rate increases, leading to a reduced heat removal from the SOFC and a subsequent rise in the operating temperature. Similarly, when the CR increases, the unreacted high-temperature gas is recirculated to the anode, raising the inlet fuel gas temperature. Additionally, the increased hydrogen flow leads to greater heat release, contributing to a higher overall operating temperature of the SOFC.

To prevent potential failure of fuel cell due to overheating, this study defines the “overtemperature operating zone” (highlighted by dark red lines on the A/O and CR axis plot), where the temperature exceeds 1123 K. This safety limit is determined by the selected fuel cell material and design. It is observed that when CR exceeds 30% and A/O exceeds 0.48, there is a risk of exceeding the operating temperature, which could lead to uneven thermal stress distribution and thermal cracking of the fuel cell. For example, when CR is 50% and A/O is 0.53, the fuel cell temperature reaches 1128 K, the highest observed. Therefore, it is essential to adjust valve 2 and the inlet air flow during ship operation to prevent excessively high CR and A/O ratios. Furthermore, when CR is below 15%, the SOFC operates within a low-temperature range, regardless of the A/O adjustment.

From Fig.9, it is seen that the SOFC output voltage increases as the A/O ratio increases within the safe operating region. However, as the CR increases. the voltage initially rises and then falls. Notably, when A/O remains unchanged and only CR is varied, the SOFC output voltage exhibits a peak in the CR range of 10% to 15%. For instance, when the A/O is maintained at 0.4, increasing CR from 0 to 15% causes the fuel cell voltage to increase from 0.88 to 0.96 V. Beyond 15%, the voltage decreases from 0.96 to 0.85 V. This behavior occurs because, as CR increases from 0 to 15%, the recirculation of high-temperature fuel cell exhaust gas increases the fuel cell inlet temperature and H₂ partial pressure, thereby increasing the fuel cell voltage. However, when CR exceeds 15%, the fuel cell working temperature rises only slightly (by only 7–8 °C), and the flue gas flow rate entering the combustion combustor decreases significantly, reducing the oxidation reaction rate and leading to a drop in the exit temperature of the combustion combustor, which consequently reduces the working temperature of the NH₃ cracker and heat exchanger 2. As a result, NH₃ cracking becomes incomplete and the H₂ partial pressure at the inlet of the fuel cell decreases, causing the voltage to drop.

At CR=10% and A/O=0.53, the fuel cell output voltage reaches its peak value of 1.00 V. When the operating point shifts to CR=15% and A/O=0.53, the system efficiency reaches its maximum value of 61.73%, with a voltage of 0.99 V.

Fig.10 shows the variation of fuel cell output power with changes in A/O and CR. The trend of output power closely mirrors that of the voltage. As shown, as A/O increases, the system output power continues to rise. When A/O remains unchanged and CR is varied, a peak output power is observed in the range of 10% to 15% of CR. Notably, under the conditions of CR=10% and A/O=0.53, the system output power reaches its maximum value of 110 kW.

Therefore, when the ship requires acceleration or experiences an instantaneous increase in load, the opening of valve 5 can be adjusted to 10%. It is crucial to ensure that the opening of valve 5 remains within the range of 2.5% to 40%, as this is essential for meeting the ship’s power output requirements.

Fig.11 shows the variation in SOFC powered propulsion system efficiency with the change of A/O and CR. In this study, the high-efficiency region, defined as the area where efficiency exceeds 60%, is marked with a solid line on the efficiency surface. This high-efficiency operating surface is mapped onto a plane consisting of the A/O and CR axes, represented by a series of gray lines.

By analyzing the power diagram in Fig.11 alongside the efficiency diagram in Fig.12, and considering the safety of system operation, it is clear that when the system operates in the A/O range of 0.4 to 0.53 and CR from 10% to 20%, the crew can adjust both operating parameters to achieve high-efficiency operation in high-load conditions. To optimize system operation for economy and efficiency, valve 5 should not be opened less than 2.5%. For fuel-saving modes, adjusting valve 5 to approximately 10% to 15% will help achieve the desired outcomes.

In summary, from the point of view of improving system efficiency, both adjusting CR and A/O can achieve the high efficiency output under high fuel utilization (FU) conditions. Adjusting the A/O provides better temperature stability for the SOFC, preventing large fluctuations and ensuring the fuel cell operates within the safe operating temperature range. Additionally, when the ship requires an acceleration boost or needs to avoid obstacles, thus demanding additional power for a shorter period, the optimal results can be achieved by adjusting the A/O, regardless of whether the CR is high or low.

Furthermore, by properly adjusting the A/O with other operating parameters, the propulsion system can operate efficiently across a wide range of conditions, as shown in Fig.12. The power efficiency at ultra-low load (0.2 relative power ratio) and ultra-high load (1.1 relative power ratio) operation points are 55.12% and 61.73%, respectively. This ensures that the ship can maintain high efficiency across a wide-load power range from 20% to 110%. Although the efficiency increases when the propulsion system power exceeds 110%, the risk of fuel cell over-temperature increases, which can lead to long-term operation issues, thus making such high-power operations unsustainable.

4.3 Analysis of space saving

According to the system structures mentioned in Refs. [12,21,22,30,31,42], it can be observed that the current SOFC power systems, or SOFC/GT hybrid system using NH₃ as fuel, typically incorporate separate devices for NH₃ cracking, catalytic combustion, and heat exchange. This configuration undoubtedly increases the overall volume and weight, complicating the spatial structure layout of the whole system.

To highlight the advantages of the proposed IAC in terms of compactness and reduced space requirements, Tab.3 presents a theoretical comparison of the total volume between the IAC and the three independent devices. The volume data for the ammonia cracker and combustor are calculated based on the design parameters in Tab.1. For the heat exchanger, the H050 high-temperature plate heat exchanger from Ningbo KAORI Technology Company in China is used, scaled proportionally to the required area and heat transfer.

From Tab.1, it is evident that when using the traditional design approach for the power system, the heat exchanger occupies a significantly larger space, resulting in a 75% increase in overall volume compared to the IAC proposed in this work. The IAC designed achieves efficient heat exchange between different gas flows using only the tube wall of the NH₃ cracker, eliminating the need for additional piping. This results in a theoretical saving of more than 42% in ship power cabin space.

5 Experimental verifications

5.1 Experimental platform

Based on the thermal operating state parameters of the SOFC powered all-electric propulsion system discussed above, a NH₃-fueled 2 kW SOFC experimental platform is established, including a fuel cell stack, an integrated NH₃ cracking/catalytic combustor device, a data acquisition system, an embedded controller, a liquid NH₃ storage and heating device, a gas analyzer, pipelines, and other related equipment, as shown in Fig.13.

In this experimental system, liquid NH₃ is first heated by a heat exchanger and then enters the NH₃ cracker. The pre-cracked gas passes into the SOFC anode, while a sample of the cracked gas is directed into a gas analyzer to measure NH₃ and H₂ concentrations. The high-temperature exhaust gas from the SOFC is fed into the combustor for catalytic oxidation. In this process, catalytic combustion provides the heat for NH₃ cracking to produce H₂. The high-temperature exhaust gas after catalytic combustion is used to heat ammonia and air, and is finally discharged from the experimental platform.

This system utilizes stainless steel pipes to ensure corrosion resistance under experimental conditions ranging from 23 to 850 °C. Additionally, heat treatment is required when welding the pipes, which must be fully welded before the heat treatment process can continue.

The cold-start response time of the ammonia fuel integrator is relatively long, and the exhaust temperature of the cracked gas does not reach the operating temperature for hydrogen production through catalytic cracking. During experiments under this mode, a large amount of unburned ammonia gas is generated during the startup phase. This ammonia gas absorbs heat from the furnace, preventing its introduction during electric heating. Once the temperature reaches the experimental requirements, ammonia is introduced.

Since gas consumption during the experiment is relatively small, the liquid fuel in the small storage tank is used in gaseous form after being depressurized through a relief valve. In actual industrial applications where large amounts are needed, an evaporation system must be configured, either by inputting new energy to evaporate the liquid fuel or by integrating it with other systems requiring cooling, with the latter being more beneficial for improving the overall energy efficiency of the system. The system mainly consists of stainless-steel pipes, a pressure relief valve, a flow meter, a flow display meter, and a check valve. Given that NH₃ is corrosive to metals such as copper, iron, and aluminum, all pipes, valves, and fittings are made of stainless steel.

The pressure regulation part of the supply system, as described in the literature needs improvement. Therefore, a secondary pressure relief valve is used at the ammonia fuel inlet side to further control the ammonia gas flow within the system, ensuring safe operation.

In this study, due to the need to process a large amount of ammonia gas and for cost-saving purposes, the use of Ru catalysts is not avoided. Ni, a relatively inexpensive metal, offers catalytic efficiency second only to Ru. Thus, Ni is selected as the catalyst for ammonia cracking hydrogen production. However, previous experiments found that Ni/Al₂O₃ had poor thermal stability and could not operate for extended periods under high-temperature conditions. Therefore, a more thermally and chemically stable nickel catalyst is selected, despite its higher production cost, as its efficiency over the long-term reduces overall costs use.

A gas analyzer is used to measure the volume fraction of each gas component in the gas after NH₃ cracking process. The volume fraction of NH₃ ranges from 0 to 50% (± 1% accuracy), and the volume fraction of H₂ ranges from 0 to 80% (± 3% accuracy). The NH₃ flowmeter has a range of 0.5–5 m³/h with an accuracy of ± 2%. The catalyst is a nickel-based catalyst with NiO content ≥ 14% (kg/kg), prepared in a gray Raschig ring with dimensions of 19 mm × 19 mm × 9 mm (outer diameter × height × inner diameter).

In this experiment, the ammonia cracking reaction was conducted to simulate the thermal environment temperature range of the power system, which requires operation under high-temperature conditions between 400 and 740 °C. The ammonia cracking catalyst must have a long lifespan at high temperatures and an internal hollow structure to ensure full contact with the ammonia gas. Therefore, the HG2273Ni catalyst was selected, with its structural parameters and chemical composition shown in Tab.4.

5.2 Experimental data and model verification of NH₃ cracking for H₂ production

In the start-up stage, the decompression valve at the outlet of the liquid NH₃ storage tank is adjusted to control the NH₃ pressure entering the experimental platform to 70 kPa and the NH₃ flow rate to 2.5 m³/h. The gas in the integrated reactor is preheated by using electric heating, and the temperature of the NH₃ cracker gradually rises until it reaches 800 °C. Once the temperature of the reactor and the volume fraction of each gas of the cracked gas stabilize, the experiment begins and the data is recorded. Subsequently, the reactor temperature is decreased by 20 °C at a time. During this process, the operator constantly adjusts the pressure-reducing valve and monitors the NH₃ flowmeter to maintain stable gas flow and pressure.

The change of the volume fraction of each gas component with the working temperature are recorded, and Eqs. (27) and (28) are used to calculate the NH₃ decomposition rate.

(27)\mu =\frac{2{\phi }_{{\mathrm{H}}_2}}{(3{\phi }_{\mathrm{N}{\mathrm{H}}_3}+2{\phi }_{{\mathrm{H}}_2})},\begin{array}{cc}& {\phi }_{\mathrm{N}{\mathrm{H}}_3}⩽50\mathrm{\%},\end{array}

(28)\mu =\frac{2{\phi }_{{\mathrm{H}}_2}}{(3-2{\phi }_{{\mathrm{H}}_2})},\begin{array}{cc}& {\phi }_{\mathrm{N}{\mathrm{H}}_3}>50\mathrm{\%},\end{array}

where \mu is the NH₃ decomposition rate and \phi is each gas concentration. Tab.2 shows the H₂ volume fraction and NH₃ decomposition rate corresponding to each temperature state in the experiment.

As can be seen from Tab.4, the NH₃ decomposition rate reaches 100% at temperatures above 656 °C, at which the volume fraction of H₂ reaches 75% by volume. The NH₃ decomposition rate changes most dramatically between 496 and 656 °C, with the volume fraction of H₂ increasing by approximately 10% per 20 °C rise in temperature. Below 496 °C, the NH₃ decomposition rate remains below 6.59%, and the volume fraction of H₂ is less than 9.5% by volume, resulting in a similar result to that reported in Di Carlo et al. [23].

Based on Tab.4, it can be found that the trend of change between the experimental data and the model data is very similar, with small errors when the temperature is either below 496 °C or above 596 °C. However, when the temperature ranges from 512 to 542 °C, the error increases. After analyzing the data and the operation process, it was found that the NH₃ flow rate gradually increased from the set value of 2.5 to 2.70 m³/h due to the expansion of NH₃ gas upon being heated. To maintain stable gas flow, the flow rate was adjusted back to 2.5 m³/h using the pressure reducing valve, which resulted in slight fluctuations in the H₂ volume fraction measured by the gas analyzer.

At 400 °C, the experimental and simulated NH₃ decomposition rates are 0.81% and 0.09% respectively, with an absolute error of 0.71%. At 596 °C, the decomposition rates are 76.24% and 78.13%, with an absolute error of 1.89%. At 656 °C, both the experimental and simulated decomposition rates reach 100%. As shown in Fig.7, in the temperature range of 570–700 °C, where the NH₃ cracker operates efficiently, the error between the experiment and the model remains within 3%. This result not only validates the feasibility of the model but also reflects the experimental operating characteristics of the NH₃ cracker.

Based on the experimental strategy for automatic heating and automatic loading of the NH₃-SOFC power system, the performance of NH₃ SOFC power system was tested, and the I–V curve of the power system is obtained, as shown in the Fig.14.

It can be deduced and analyzed that when using NH₃ decomposition gas as fuel, the voltage of the fuel cell stack is higher, resulting in an output of 2050.38 W, as depicted in Fig.14. At this point, the flow rate of the NH₃ decomposition gas is 24.2SLPM. The system’s efficiency, calculated based on the low heating value of NH₃ decomposition gas, is 62.7%. Considering the power consumption of other experimental components, the overall efficiency is approximately 58.66%. On-site measurements indicate a noise level of 58.6 dB for the system, with CO₂, NO, and SO₂ in flue gas close to zero. These results provide valuable technical support for the future development of large single-unit ship propulsion systems and the demonstration of 100-kW class marine power systems composed of multi-module arrays.

6 Conclusions

This paper presents an innovative and compact NH₃ fuel SOFC all-electric propulsion system for ships, using a target ship type as a case study. It investigates the influence of CR and N/O operating parameters on system performance, enabling efficient and versatile operation for the ship’s propulsion system. Validation was conducted using a 2-kW prototype test rig, leading to the following conclusions.

The NH₃-SOFC powered propulsion system designed for the sightseeing ship delivers a rated power of 96 kW and an electrical efficiency of 60.13%, fully meeting the ship’s cruising requirements. In the same catalytic scenario, the 1.1-meter-long reactor, with highly efficient heat transfer, achieves complete NH₃ decomposition in 2.94 s, reducing cracking time by 35% and saving cabin space by 42%.

Under high-load navigation conditions, both adjusting CR and A/O adjustments improve system efficiency at high fuel utilization, with A/O adjustments proving to be the most effective. For A/O values ranging from 0.4 to 0.53 and CR values from 10% to 20%, operators can adjust these parameters flexibly, ensuring high-efficiency operation in demanding conditions. The power system must maintain efficiency between 55.02% at low load and 61.73% at high load, supporting optimal performance across a power range of 20% to 110%.

Experimental results from the 2 kW NH₃-SOFC tightest rig indicate that temperature-related deviations in 570 to 700 °C range remain below 3%. At 656 °C, both experimental and simulated H₂ production rates reach 100%. The SOFC output power reaches 2048 W with an efficiency of approximately 58.66%, a noise level at 58.6 dB, and minimal CO₂, NO, and SO₂ emissions. These results validate the model accuracy and the feasibility of adjusting parameters under changing navigation conditions.

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