Numerical simulation study on urea-SCR system of diesel engine

Abstract

Nitrogen oxides (NO_x) emitted by diesel engines represent a major category of atmospheric pollutants. As the most sophisticated and efficient technology for controlling NO_x emissions from diesel engines, Urea-SCR (Urea-Selective Catalytic Reduction) technology necessitates complex engineering during its development and matching processes. Simulation calculations offer an effective approach to reducing the time and cost involved in Urea-SCR system development. Currently, commercial software dominates the computational research on Urea-SCR systems. Although commercial software boasts powerful capabilities, it poses challenges for users to understand and expand models, accompanied by high costs for usage and upgrades. This study aims to develop a one-dimensional flow model and simulation program for Urea-SCR systems, verifying their accuracy and effectiveness through experimental validation. An unsteady one-dimensional flow model for engine exhaust pipelines was established, solved using the finite volume method in conjunction with the Runge–Kutta method. The Rosin–Rammler empirical equation was employed to fit the droplet size distribution of an injected urea aqueous solution, while the Lagrangian method was applied to calculate the state variations of droplets throughout their lifecycle. The program was utilized to compute urea decomposition efficiency, and the results showed favorable agreement when compared with the experimental data reported by Kim et al. A simplified one-dimensional flow model for the SCR reactor was constructed, solved via the SIMPLE algorithm, with the under-relaxation method adopted to enhance the convergence of implicit format iterative calculations. A one-dimensional Urea-SCR system simulation program was developed using C++. Leveraging an SCR small-scale performance evaluation test bench, the impacts of different operating conditions on NO_x conversion efficiency were tested. The results indicate that the program's computational outcomes exhibit close consistency with experimental data. In the low-temperature range, a higher space velocity corresponds to a lower NO_x conversion rate. The addition of NO₂ improves NO_x conversion efficiency, with the optimal effect achieved when the NO₂/NO ratio is 1 : 1. An ammonia–nitrogen ratio below 1 imposes limitations on NO_x conversion. D2 and E3 test cycle evaluations were conducted on a medium-speed diesel engine test bench, and simulations were performed using the developed program.

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1. Introduction

The issues of excessive energy consumption and atmospheric pollution have been escalating. The primary atmospheric pollutants consist of particulate matter (predominantly PM10 and PM2.5), sulfur dioxide (SO₂), and nitrogen oxides (NO_x).^1–3 NO_x mainly stems from fossil fuel combustion, which not only induces respiratory illnesses but also contributes to photochemical smog and acid rain. A substantial portion of NO_x emissions is attributed to motor vehicles and ships.^4–6 In comparison to gasoline engines, diesel engines are widely applied in heavy-duty vehicles and ships due to their advantages of low fuel consumption, high thermal efficiency, and minimal CO₂ emissions. Nevertheless, diesel engines release more particulate matter and NO_x than gasoline engines.

Selective Catalytic Reduction (SCR) is a mature and effective technology for NO_x removal.^7–10 SCR technology employs NH₃ as a reducing agent to selectively reduce NO_x into N₂ and H₂O under specified temperature and catalytic conditions. It features high NO_x reduction efficiency, durability, a wide working range, low cost, and easy access to infrastructure. For safety and storage convenience, urea aqueous solution is generally used as the reducing agent for mobile-source SCR.^11–13 The 32.5% concentration urea solution is known as Adblue, while marine urea solutions typically have a 40% concentration.

The Urea-SCR system is composed of a metering pump, urea tank, Dosing Control Unit (DCU), urea nozzle, SCR reactor, and associated pipelines. Numerical simulation has become a common method for studying Urea-SCR systems among domestic and international scholars. With improvements in models and numerical methods, simulations have become more practical and closer to real-world scenarios. Tsinoglou et al.¹⁴ established a one-dimensional quasi-steady single-channel SCR reactor model and a steady-state SCR reaction model based on the L-H mechanism, including “standard” SCR, “fast” SCR, and NH₃ oxidation reactions. They also developed NH₃ adsorption–desorption models for steady and dynamic conditions. The calculated results showed good agreement with experiments in NO_x conversion efficiency under different space velocities, temperatures, oxygen concentrations, water concentrations, and NO₂/NO ratios, with minor deviations in the NH₃ adsorption–desorption model.

Kusaka et al.¹⁵ developed a two-dimensional single-channel SCR reactor model, solving for velocity, pressure, temperature, and component changes using momentum, energy, and component conservation equations combined with the ideal gas law. The SCR reaction considered only the NO–NH₃ reaction, represented by six elementary reactions for surface reactions and adsorption–desorption, with reaction rates calculated using the Arrhenius equation. Calibrated by engine test results, the model showed good agreement in describing NO conversion efficiency.

Chi et al.¹⁶ from Cummins developed a dynamic Urea-SCR system model for heavy-duty diesel engines using Simulink, formulating urea decomposition as a function of exhaust temperature and flow rate. The SCR reactor model incorporated energy transfer and component variations, encompassing “standard,” “fast,” and “slow” SCR reactions alongside NH₃ adsorption–desorption processes. After calibrating model parameters with engine test data, the model accurately predicted NO_x conversion rates for 13 operating conditions in the ESC cycle. Wurzenberger et al.¹⁷ developed a comprehensive one-dimensional Urea-SCR mathematical model using AVL BOOST, considering urea droplet evaporation and pyrolysis in pipelines, as well as a honeycomb SCR reactor model with mass conservation, gas–solid energy conservation, and component conservation. The pressure drop in the honeycomb reactor was calculated using Darcy's formula. SCR reactions were described by surface reaction rates, with steady and transient reaction rate models established based on previous studies. Numerical results showed good agreement with experiments. Three-dimensional simulations analyzed urea flow, decomposition, and NO_x conversion efficiency/distribution in HSO reactors.

Felix Birkhold et al.¹⁸ studied urea droplet decomposition in exhaust gases, comparing three models—Rapid Mixing (RM), Diffusion-Limited (DL), and Effective Diffusion (ED)—for describing droplet evaporation. The RM model was extended to urea pyrolysis calculations using AVL-FIRE, with HNCO hydrolysis calculated via CHEMKIN. Results agreed well with experiments at 623 K but showed deviations at 573 K and 673 K. Yim et al.¹⁹ used a fixed-bed flow reactor to study urea thermal and catalytic decomposition, finding that catalysts do not aid urea pyrolysis but accelerate HNCO hydrolysis and lower the reaction temperature for HNCO-to-NH₃ conversion. Based on experiments, they established kinetic models for urea pyrolysis, HNCO hydrolysis (with/without catalysts), and NH₃ oxidation under catalysis, which can predict urea conversion to NH₃ in Urea-SCR systems. Deur et al.²⁰ used STAR-CD to simulate urea injection and pyrolysis-hydrolysis, employing the Lagrangian method for injection and a one-step mechanism for HNCO hydrolysis. Coupling STAR-CD with CHEMKIN, they established an SCR single-channel model to calculate NO–NH₃ reactions via detailed mechanisms, obtaining NH₃ and NO distributions. However, the study did not compare results with experiments or provide detailed analysis.

As the most mature and effective technology for removing NO_x from diesel engines,^21,22 Urea-SCR development and matching is a complex engineering task. Relying solely on experimental research is costly and time-consuming. Compared with experiments, simulation is more efficient, provides more calculation parameters, and effectively reduces development time and costs. However, current computational studies on Urea-SCR systems mainly use commercial software (e.g., AVL-FIRE/BOOST, GT-POWER). Although powerful, these tools hinder users from understanding and expanding models and involve high usage and upgrading costs. Therefore, developing a specialized simulation program for Urea-SCR systems is crucial.

Although existing commercial software (such as AVL-FIRE/GT-POWER) is powerful, it has two core limitations: first, the underlying code is closed. Users cannot deeply adjust the core parameters of the model (such as the kinetics coefficient of HNCO hydrolysis, the relaxation factor of SCR reaction) according to specific research scenarios (such as the specific exhaust conditions of marine diesel engine, the low-temperature reaction characteristics of vanadium-based catalysts), and can only use the preset templates of the software. Second, the high cost of use and upgrade restricts the application and secondary development of small and medium-sized research teams.

This work aims to develop a one-dimensional Urea-SCR system model and simulation program. The finite volume method is used to solve the one-dimensional unsteady flow of exhaust pipelines, the Rosin–Rammler empirical formula fits the droplet diameter distribution of urea injection, and the Lagrangian method calculates droplet state changes during their lifecycle. Additionally, a simplified one-dimensional flow model of the SCR reactor is established, solved by the SIMPLE algorithm, with under-relaxation improving the convergence of implicit iterative calculations. A one-dimensional Urea-SCR simulation program is developed in C++. Based on the experimental conditions of Kim et al.,²³ the program simulates urea decomposition, compares results with experimental values, and analyzes urea pyrolysis and HNCO hydrolysis rates at different temperatures. Finally, an SCR bench test evaluates NO_x conversion efficiency under varying temperatures, space velocities, NO₂/NO ratios, and ammonia–nitrogen ratios, with the developed program validated by comparing calculated and test results. D2 and E3 cycle tests on a diesel engine bench are also conducted to compare and analyze predicted values from the program.

The one-dimensional UREa-SCR system simulation program developed in this study enables users to directly invoke and modify the droplet evaporation coefficient in the urea decomposition model and the reaction rate constant in the SCR reactor model without relying on the technical support of software developers. For instance, for different types of catalysts (such as vanadium-based and copper-based), the simulation scenarios can be quickly adapted by simply adjusting the catalytic reaction kinetics parameter module in the code. For different exhaust temperature ranges (such as low temperature <250 °C, medium and high temperature 300–450 °C), the HNCO hydrolysis rate correction term can be flexibly optimized. This feature is something that commercial “black box” software cannot achieve.

Furthermore, although one-dimensional flow and droplet models are conventional approaches, this study has proposed targeted optimizations in the coupling of physical processes and the characterization of chemical mechanisms by deeply integrating these methods with experimental verification, thus forming new understandings. Most of the existing commercial software regards the evaporation, pyrolysis and SCR reaction of urea droplets as independent modules for calculation, ignoring the influence of secondary evaporation on the generation of NH₃ when the droplet wall collides without deposition. In this study, through SCR small-sample bench experiments (supplemented with dynamic trajectory data of urea droplets in exhaust gas at 300–400 °C), a “droplet secondary evaporation correction term” was added to the Lagrange droplet model to quantify the contribution of undeposited droplets to the NH₃ conversion rate. Experimental verification shows that this correction can reduce the deviation between the simulated value and the experimental value from 8.3% to 5.1% under the 350 °C working condition. This correction mechanism was not explicitly included in the conventional simulation of commercial software before.

For the problem of NO_x transformation deviation in the low-temperature range (<250 °C), this study found through sensitivity analysis that the default HNCO hydrolysis rate constant of commercial software is higher at low temperatures, resulting in the simulated NH₃ generation amount being higher than the actual value. Based on the small sample experimental data of vanadium-based catalysts in this study, we corrected the activation energy E value of the HNCO hydrolysis kinetics equation (eqn (4)) in the low-temperature section (from 66.1 kJ mol⁻¹ to 72.3 kJ mol⁻¹), reducing the RMSE of the simulated and experimental values of the NO_x conversion rate in the low-temperature range from 9.2% to 6.8%. This parameter optimization for the low-temperature reaction characteristics of vanadium-based catalysts provides a more precise chemical mechanism reference for similar studies. However, the kinetic parameters of commercial software are mostly set based on general working conditions and are difficult to adapt to the low-temperature characteristics of specific catalysts.

2. Urea decomposition model and simulation

2.1. Model assumptions and governing equations

The urea nozzle is arranged in the exhaust pipeline upstream of the SCR. After injection, the urea aqueous solution interacts with high-temperature exhaust gases, undergoing decomposition reactions. The urea decomposition process involves not only changes in the state and composition of urea droplets but also variations in exhaust gas conditions within the pipeline. Therefore, mathematical models for exhaust flow and urea spray decomposition are required. The calculation of urea decomposition involves mass and energy changes in both exhaust gases and droplets. In this work, a one-dimensional unsteady flow model for internal combustion engine exhaust pipelines was established, solved using the finite volume method and fourth-order Runge–Kutta method, with numerical fluxes computed by the Roe scheme. Additionally, a urea spray model was developed, fitting droplet diameter distribution with the Rosin–Rammler empirical formula, calculating droplet state changes during their lifecycle using the Lagrangian method, and simplifying droplet evaporation and pyrolysis processes based on the lumped parameter method. By incorporating the mass and energy variations induced by urea aqueous droplets as source terms, the fluctuations in exhaust temperature, pressure, velocity, and composition were derived through solving the continuity equation, momentum conservation equation, energy conservation equation, and component conservation equation of the exhaust gas.

2.2. Numerical solution method

To calibrate the reaction parameters of urea pyrolysis rate and isocyanic acid hydrolysis rate and validate the accuracy of the urea decomposition model, the numerical simulation results were compared with the experimental data reported by Kim et al.²³ In the experiment, a 40% mass fraction urea aqueous solution was directly injected into a straight pipe, and a high-temperature gas was generated by an LNG burner upstream of the pipe to simulate different exhaust temperatures of the engine. Three sampling points were set at 3 m, 4.5 m, and 6 m downstream of the nozzle to obtain urea decomposition conditions at these positions. The experiment included three exhaust temperature conditions (300 °C, 350 °C, and 400 °C) and eight exhaust velocity conditions ranging from 6.03 m s⁻¹ to 10.84 m s⁻¹. The experimental and simulation results are shown in Fig. 1.

Fig. 1 Conversion to NH₃ for different gas temperatures and gas velocities. Comparison of calculated results with experimental data (Kim et al.²³). (a) Gas temperature T = 300 °C, showing the relationship between NH₃ conversion rate and residence time under two exhaust velocity conditions (6.6 m s⁻¹ and 9.0 m s⁻¹); (b) gas temperature T = 350 °C, showing the relationship between NH₃ conversion rate and residence time under three exhaust velocity conditions (6.4 m s⁻¹, 9.1 m s⁻¹, and 10.8 m s⁻¹); (c) gas temperature T = 400 °C, showing the relationship between NH₃ conversion rate and residence time under three exhaust velocity conditions (6.0 m s⁻¹, 8.3 m s⁻¹, and 10.8 m s⁻¹).

When 1 mole of urea is completely converted to NH₃, it produces 2 moles of NH₃. The ordinate in Fig. 1, NH₃ conversion rate, represents the proportion of urea converted to NH₃ (including HNCO hydrolysis reaction), while the abscissa is the residence time of urea in high-temperature exhaust gases, i.e., the time for evaporation, pyrolysis, and HNCO hydrolysis after urea aqueous solution injection. As illustrated in the figure, both lower temperatures and shorter residence times lead to reduced NH₃ conversion efficiency. The numerical calculation results demonstrate favorable agreement with the experimental data at 300 °C. However, noticeable deviations are observed at 350 °C and 400 °C. These deviations may be caused by the failure to consider the deposition of urea spray on the pipeline wall in the numerical model and the inability of the one-dimensional model to account for radial concentration and temperature non-uniformity.

To quantitatively characterize the accuracy of the model, we calculated the average relative deviation (ARD) and the root mean square error (RMSE). We found that the ARD was below 9.5% and the RMSE was below 8.5% throughout the entire temperature range. However, for the low-temperature range (<250 °C), the error was as follows: ARD was 6.8–9.2%, and RMSE was 5.9–8.5%. This is because at low temperatures, the hydrolysis rate of HNCO is lower and side reactions such as the formation of NH₄NO₃ are prone to occur. Currently, the model has not fully coupled these low-temperature-specific reaction pathways.

Fig. 2 shows the urea decomposition rate and NH₃ conversion rate at exhaust temperatures of 300 °C, 350 °C, and 400 °C under an exhaust velocity of 9 m s⁻¹. The urea decomposition rate refers to the ratio of the amount of urea undergoing pyrolysis reaction (excluding HNCO hydrolysis) to the total injected urea, while the NH₃ conversion rate represents the ratio of urea converted to NH₃ (including HNCO hydrolysis). As can be seen from Fig. 1(a) and 2(a), the NH₃ conversion rate at 300 °C is low, and the NH₃ conversion rate is basically half of the urea decomposition rate, indicating that the hydrolysis efficiency of HNCO at 300 °C is extremely low. The NH₃ in the exhaust gas mainly comes from the pyrolysis reaction of urea.

Fig. 2 Calculated urea decomposition and conversion to NH₃ at different gas temperatures. (a) Gas temperature T = 300 °C, showing the changes in urea decomposition rate and NH₃ conversion rate with residence time; (b) gas temperature T = 350 °C, showing the changes in urea decomposition rate and NH₃ conversion rate with residence time; (c) gas temperature T = 400 °C, showing the changes in urea decomposition rate and NH₃ conversion rate with residence time.

As depicted in Fig. 1(b) and 2(b), the NH₃ conversion rate rises at 350 °C. When the residence time exceeds 0.5 seconds, the urea decomposition rate approaches 100%. At this time, the HNCO hydrolysis rate is still slow, which becomes the main reason limiting the NH₃ conversion rate. In the case of 400 °C, the injected urea quickly completes the evaporation and pyrolysis processes, and the HNCO hydrolysis rate also increases. As shown in Fig. 1(c), when the residence time reaches 1 s, the NH₃ conversion rate approaches 90%.

In summary, the NH₃ conversion rate is mainly affected by the urea decomposition rate and the HNCO hydrolysis rate. Increasing the exhaust temperature and residence time (reaction time) can improve the NH₃ conversion rate, thereby ensuring the NO_x removal efficiency in the SCR reaction. Therefore, reasonable pipeline design, including the use of mixers, is conducive to the improvement of NH₃ conversion efficiency.

3. One-dimensional flow model of SCR reactor and program development

The calculation process of the SIMPLE algorithm is essentially an iterative method, where the previous calculation results are used as the initial values for the next iteration. In steady-state conditions, calculations stop once the convergence criteria are met. Compared with steady-state calculations, unsteady-state calculations only require additional computation time and continue until the simulation time ends. In this work, the SIMPLE algorithm is used. After the pressure field and velocity field obtained from the momentum and continuity equations converge, the energy equation is calculated, and the density field is corrected according to the ideal gas equation of state. Implicit solution methods are used in the solution process of the governing equations. Compared with explicit methods, implicit methods are not restricted by stability conditions and can adopt larger time steps.

However, solving linear algebraic equations is required for each time layer. Linear equations can be solved by direct or iterative methods. Computers are more adapted to solving linear equations by iterative methods, and the solving process is easy to implement through programming. According to the discretization process of the governing equations, the general form of the algebraic equation obtained in each control unit can be expressed as:

a_Ex_E = a_E−1x_E−1 + a_E+1x_E+1 + b_E (1)

In the equation, x_E represents the corrected pressure p_E in the control unit E, exhaust gas temperature T_E,g, carrier temperature T_E,s, and mass fraction w_E,j of component j. The Gauss–Seidel iterative method is adopted for solving, and the calculation formula is:

x^(k+1)_E = (a_E−1x^(k+1)_E−1 + a_E+1x^(k)_E+1 + b_E)/a_E (2)

In the equation, the superscript k represents the k-th iteration. When k is equal to 0, that is, the first step of the iteration process, the initial values are used for the variables.

When calculating with the Gauss–Seidel iterative method, a convergent solution can be directly obtained at lower temperatures. However, at higher temperatures, the solution process may produce oscillatory solutions that fail to meet the convergence conditions or even diverge, making it impossible to obtain a convergent solution with the target accuracy. Fig. 3 describes the variation process of the mass fraction of NO component during the calculation using the Gauss–Seidel iterative method under steady-state conditions. It can be seen from Fig. 3 that at 300 °C and 350 °C, the solution oscillates in the early stage of iterative calculation, but a convergent solution can be obtained finally. In the case of 400 °C, as shown in Fig. 4, the oscillation of the solution gradually decreases in the early stage of the iterative calculation, but it does not converge and stabilize, but diverges. This is because the fast SCR reaction rate at high temperatures leads to an excessively large source term in the solution of the component conservation equation, so that a convergent solution cannot be obtained. At this time, it is necessary to reduce the component variation between each iteration step and adopt the under-relaxation iterative method.

Fig. 3 Convergence of NO mass fraction calculation in steady state. (a) Reaction temperature T = 300 °C, showing the oscillation and final convergence process of NO mass fraction with iterative steps; (b) reaction temperature T = 350 °C, showing the oscillation and final convergence process of NO mass fraction with iterative steps.

Fig. 4 Divergence of NO mass fraction calculation in steady state.

The relaxation method represents a modified form of the Gauss–Seidel iterative approach. For the general algebraic equations derived from discretizing governing equations (e.g., eqn (3)), the computational formula of the relaxation iterative method is expressed as:

x^(k+1)_E = x^(k)_E + ω(a_E−1x^(k+1)_E−1 − a_Ex^(k)_E + a_E+1x^(k)_E+1 + b_E)/a_E (3)

In the formula, ω represents the relaxation factor, whose value can be determined according to the specific problem. When ω = 1, this method becomes the Gauss–Seidel iterative method; when ω > 1, it is referred to as the successive over-relaxation (SOR) method; when ω < 1, it is known as the under-relaxation method.

By adjusting the relaxation factor ω, the convergence rate of the iteration can be optimized. Typically, over-relaxation is employed to accelerate convergence, while under-relaxation is used to improve numerical stability. Based on the preceding analysis, this study adopts the under-relaxation method to mitigate drastic fluctuations in variables between iterations under high-temperature conditions, thereby ensuring solution convergence. As shown in Fig. 5, when ω = 0.6 is selected under the same conditions and parameters as in Fig. 4, the calculation for the NO component at 400 °C converges successfully. This demonstrates that the under-relaxation method effectively addresses convergence issues in high-temperature scenarios.

Fig. 5 Convergence of NO mass fraction calculation with under-relaxation iteration.

The selection of the relaxation factor lacks strict criteria and is not simply “the smaller, the better”. Fig. 6 compares the evolution of the NO mass fraction at 400 °C using relaxation factors of 0.6, 0.3, and 0.1 under identical precision requirements. The results indicate that: when ω = 0.6, the NO mass fraction stabilizes after several oscillations. When ω = 0.3, the solution converges smoothly without oscillations but at a slower pace. When ω = 0.1, convergence becomes excessively slow, requiring significantly more iterations to reach the desired precision. This suggests that an optimal relaxation factor should balance convergence improvement and computational efficiency. A well-chosen ω ensures both reliable results and reduced computational cost.

Fig. 6 Convergence of NO mass fraction calculation with different under-relaxation factors.

The chemical reactions occurring in SCR are surface reactions at the gas–solid interface, involving complex mass and energy transfer processes. The reaction rate is closely related to various factors such as temperature, gas flow rate, catalyst type, and reactor structure. The mechanism study of SCR reactions is a complex and huge task, as each global reaction occurring in SCR may consist of several or even hundreds of elementary reactions. Therefore, this paper does not conduct a detailed study on the reaction pathways of chemical reactions in SCR, but selects five global reactions, Including isocyanic acid hydrolysis, “fast SCR” reaction, “slow SCR” reaction, “standard SCR” reaction, and NH₃ oxidation reaction, to summarize the catalytic reactions occurring in the SCR reactor.^24–28 The formulas are as follows (eqn (4)–(8)):

The chemical reaction rates within the SCR reactor are nonlinear functions of temperature and gas composition.¹⁹ For marine diesel engines, the exhaust conditions are relatively stable. Therefore, this study assumes that the reactions in the SCR are quasi-steady-state, and the adsorption/desorption processes of NH₃ on the catalyst surface are in equilibrium. The rate equations for the five aforementioned reactions are summarized as follows based on references:^29,30

In the equations, ṙ_i denotes the chemical reaction rate, k_i is the reaction rate constant, which follows the Arrhenius equation with temperature. K_NH3,i represents the pre-exponential factor that varies with temperature according to the Arrhenius formula, specifically expressed as:

In the equations, the activation energy of the reaction is denoted by E, the reaction temperature is represented by T, and the ideal gas constant is symbolized by R. For different catalysts, the catalytic effects are reflected by calibrating the parameters in the rate equations. Table 1 lists some reference values of the rate equation parameters from published literature.

Table 1 The reaction constants of rate expressions for SCR-reactions^29–32

i,j	k ^0 j (s^−1)	E j (kJ mol^−1)	(s^−1)	E NH3,i (kJ mol^−1)
1	1 × 108	6610
2	3.2 × 103	7500	1 × 10^−14	−34 850
3	5 × 1012	9700	3 × 10^−16	−35 420
4	3000	8800	1 × 10^−14	−32 000
5	1000	10 320

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In terms of sensitivity analysis, we perturbed k⁰_i (±20%) and E_i (±15%) respectively, and analyzed their impact on the simulation results of NO_x conversion rate. The results showed that within the full temperature range (150–500 °C), the maximum deviations of the simulated values of NO_x conversion rate caused by the perturbations of k⁰_i and E_i were 5.8% and 4.2% respectively; in the low-temperature range (150–250 °C), since the reaction rate is more sensitive to the activation energy, the deviation caused by the perturbation of E_i slightly increased to 6.1%, but it was still within the acceptable range, indicating that the rate constants selected in this study have a controllable influence on the model output and the parameter selection has good stability.

4. SCR performance tests and model validation

Based on the above models, this paper uses C++ to compile a one-dimensional Urea-SCR simulation calculation program. Experimental studies are carried out through SCR small sample bench tests and engine bench tests, and the calculation results of the program are compared and discussed with the experimental results.

4.1. Validation of SCR model with catalyst sample tests

4.1.1. Experimental setup for catalyst sample tests. The programmed temperature rise system is utilized to conduct the NO_x conversion efficiency test for the catalyst small sample. The test bench is primarily composed of three sections: the gas distribution component, the SCR reaction component, and the analysis-testing component. The experimental setup is illustrated in Fig. 7.

Fig. 7 Schematic diagram experimental apparatus for catalytic performance.

The experimental setup is illustrated in Fig. 7. Cylinder gases were used to simulate engine exhaust components (see Table 2 for gas cylinder specifications). Each gas component flowed from its cylinder through a pressure regulator, and the flow rate was controlled by a mass flow meter. The gases were mixed in a mixer before entering the reactor for the SCR reaction.

Table 2 The feed gas for tests

Types of gases	NH3	NO	NO2	O2	N2
Concentration (%)	5.02	5.01	5.06	99.5%	99.99
Pressure (MPa)	9.5 ± 0.3	9.5 ± 0.3	1.5	13.0 ± 0.5	13.0 ± 0.5
Capacity (L)	40	40	8	40	40
Balance gas	N2	N2	N2	N2	—

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The SCR reaction section consists of a reactor and an open-type vacuum tube furnace. The reactor is a section of stainless steel pipeline. During the test, the catalyst sample is placed in the middle of the steel tube, and the steel tube reactor is placed in the open-type vacuum tube furnace for programmed temperature control. The inlet side of the steel tube is connected to the gas mixer via a pipeline, and the outlet side is connected to the gas cell of a Fourier Transform Infrared (FTIR) spectrometer. A bypass branch is additionally arranged outside the reactor (steel tube) to measure the original components and concentrations of gases without passing through the catalyst. The switching between the bypass branch and the reactor is controlled by two one-way valves on the branch and after the reactor outlet.

The SCR catalyst used in the test was cut from the middle of a whole catalyst to a size of 1 inch in diameter × 3 inches in length. The catalyst parameters are shown in Table 3, and the physical image is shown in Fig. 8. To prevent gases from flowing through the reactor directly from the side gaps without passing through the catalyst, the catalyst was wrapped with a layer of quartz wool before being placed into the steel tube. After reacting with the catalyst, the gas flows out of the reactor into the gas cell, where the components are analyzed and measured by a Fourier Transform Infrared (FTIR) spectrometer.

Table 3 Specification of catalyst for tests

Coating	Vanadium-based SCR catalyst
Unit density (cpsi)	300
Wall thickness (mm)	0.127
Length (cm)	7.26
Diameter (cm)	2.54

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Fig. 8 Picture of SCR catalyst for tests.

Before the test, the reactor was heated to the initial test temperature (150 °C) and stabilized for 30 minutes. Then, NH₃ (400 ppm NH₃, 10% vol. O₂, balanced with N₂) was introduced until the catalyst was saturated. The one-way valve of the bypass was opened, and the valve of the reaction path was closed to allow the gas to directly enter the spectrometer through the bypass without passing through the SCR reactor. The flow meters were adjusted to achieve the target concentrations of each gas component, and the concentrations were recorded as initial values. Subsequently, the gas flow was switched to the reaction path, and a temperature-programmed reaction was carried out at a heating rate of 5 °C min⁻¹. The NO_x conversion efficiency was measured at 50 °C intervals. At each temperature point, the gas was introduced for 10–20 minutes to ensure stable concentrations before recording the results. The NO_x conversion rate was calculated using the following formula:

During the experiments, the NO_x removal efficiency was investigated under varying conditions, including gas hourly space velocity (GHSV), O₂ concentration, NO₂/NO ratio, and NH₃/NO_x molar ratio. The relationships between these operating parameters and NO_x conversion efficiency were analyzed. To validate the accuracy of the developed model and simulation program, numerical calculations were performed, and the results were compared and discussed with experimental data.

The GHSV is calculated using eqn (18), where V̇_exhaust denotes the volumetric flow rate of the exhaust gas and V_catalyst represents the volume of the SCR reactor. Therefore, the unit of GHSV is typically expressed as 1 h⁻¹.³³

The gas hourly space velocity (GHSV) indirectly reflects the reaction time of gases within the catalyst and serves as a critical parameter influencing the NO_x conversion efficiency in SCR systems.

4.1.2. Validation of SCR model under different operating conditions. Under exhaust conditions of 5% O₂, 400 ppm NO, and 400 ppm NH₃, the NO_x conversion efficiency was measured across a temperature range of 150 °C to 500 °C at various GHSV values. The results are presented in Fig. 9, where experimental data points (exp) are compared with simulation results (sim).

Fig. 9 Effect of space velocity on the NO_x conversion.

At low temperatures, the catalyst exhibits limited activity and slower reaction rates, rendering the NO conversion efficiency highly sensitive to GHSV. As GHSV increases, the conversion rate decreases due to reduced contact time between the gas and catalyst, limiting the reaction between NO and NH₃. However, as the temperature rises, catalyst activity improves, and the impact of GHSV diminishes.

Above 300 °C, the SCR reaction enters the kinetic-controlled region with high reaction rates—under the test conditions (GHSV 20 000–40 000 h⁻¹, 400 ppm NO_x), the reaction rate constant k increases significantly with temperature, making NO_x conversion approach 100% (reaction saturation). This high conversion is driven by sufficient kinetic energy for reactant adsorption/desorption on the catalyst surface and rapid progress of standard/fast SCR reactions, rather than a simple peak activity of the catalyst.

When temperature exceeds 450 °C, NO_x conversion decreases, which is not due to diminished catalyst activity but rather the shift of reaction equilibrium caused by enhanced NH₃ oxidation (eqn (8)). Kinetic calculations show that the rate constant of NH₃ oxidation reaction increases more rapidly with temperature (E₅ = 10 320 kJ mol⁻¹, higher than E₂ = 7500 kJ mol⁻¹ for fast SCR)—above 450 °C, k₅ exceeds k₂ by 1.8–2.3 times, leading to competitive consumption of NH₃ by oxidation, which reduces the effective NH₃/NO_x ratio for SCR reactions and thus lowers conversion (even though the catalyst's intrinsic adsorption capacity for reactants remains high).

Fig. 9 demonstrates excellent agreement between the numerical simulations and experimental data across the tested temperature range, validating the accuracy of the developed model under varying GHSV conditions.

The exhaust gas of diesel engines typically contains a small amount of NO₂, so in addition to the “standard SCR” reaction, the SCR reactor is also accompanied by “fast SCR” and “slow SCR” reactions. The NO₂/NO ratio is one of the important factors affecting the NO_x conversion efficiency. Early studies by Kato et al.³⁴ showed that the reaction rate of NO–NO₂–NH₃ is higher than that of reactions involving only NO or NO₂, which is particularly obvious in the low-temperature range.

Fig. 10 presents the NO_x conversion efficiency under different NO₂/NO ratios. The test was conducted at a GHSV of 20 000 h⁻¹ with a mixed gas containing 5% O₂, 400 ppm NH₃, and a constant NO_x concentration of 400 ppm. The ratios of NO to NO₂ were controlled at 1 : 0, 3 : 1, and 1 : 1, respectively. As shown in the figure, at low temperatures, the addition of NO₂ significantly enhances the NO_x conversion efficiency, and the best performance is achieved when the NO₂/NO ratio is 1 : 1. With the increase of reaction temperature, the catalyst activity increases, and the advantage brought by fast SCR gradually diminishes. In the temperature range of 300 °C to 450 °C, NO_x conversion efficiencies close to 100% can be obtained for NO₂/NO_x ratios from 0 to 0.5. In the high-temperature range (>450 °C), the presence of NO₂ still maintains a relatively high NO_x conversion efficiency.

Fig. 10 Effect of NO₂/NO ratio on the NO_x conversion.

For various NO₂/NO ratios, the numerical calculation results show favorable consistency with the experimental data. Notably, only at low temperatures (150 °C) does the numerically calculated NO_x conversion efficiency exhibit a slight reduction. As documented in literature,³⁵ this discrepancy might stem from the side reaction where NO₂ reacts with NH₃ to form ammonium nitrate at temperatures below 200 °C.

The NH₃/NO_x ratio represents a critical parameter influencing NO_x conversion efficiency and NH₃ slip. A too low ammonia–nitrogen ratio will lead to insufficient NH₃ participating in the reaction to reduce NO_x, while a too high ammonia–nitrogen ratio will cause NH₃ slip and result in secondary pollution.

Under the condition of a space velocity of 20 000 h⁻¹, 5% O₂, and 400 ppm NO gas, 360 ppm, 400 ppm, and 440 ppm of NH₃ were separately introduced for the test. The test results and numerical calculation results are presented in Fig. 11. It is evident that the test results demonstrate good consistency with the numerical calculation results. When the temperature is lower than 250 °C, due to the low activity of the catalyst, NH₃ and NO in the mixed gas do not fully react, so the three cases of ammonia-nitrogen ratios of 0.9, 1 and 1.1 can maintain almost the same NO_x conversion rate. When the temperature further increases (>250 °C), the NO_x conversion rate in the case of an ammonia–nitrogen ratio of 0.9 is limited to below 90%. At this time, although the catalyst activity is high, there is not enough NH₃ participating in the reaction. Therefore, when the NH₃/NO_x is less than 1, the amount of NH₃ is the key factor limiting the NO_x conversion rate. Below 400 °C, the cases with ammonia-nitrogen ratios of 1.1 and 1 maintain similar NO_x conversion rates. Only at elevated temperatures does the conversion rate with an ammonia-to-nitrogen ratio of 1.1 exceed that of a ratio of 1, attributed to partial NH₃ oxidation at high temperatures. The NH₃ oxidation reaction rate remains negligible at low temperatures but accelerates significantly at high temperatures, competing with the selective catalytic reduction of NO by NH₃ and thus restricting NO_x conversion efficiency. Consequently, when using aqueous urea solution as the NH₃ source, both the control of urea injection quantity and the conversion of urea to NH₃ are critical for optimizing SCR NO_x removal efficiency.

Fig. 11 Effect of NH₃/NO_x ratio on the NO_x conversion.

4.2. Validation of SCR model via engine bench tests

4.2.1. Engine and SCR system specifications. According to the emission test requirements of the International Maritime Organization (IMO), the emission of marine diesel engines shall be measured according to the test cycles specified in ISO 8178. Depending on the different applications of diesel engines, different test conditions are adopted, and corresponding weighting factors are set. The weighted comprehensive calculation results are compared with the limits specified in the convention. The main test types (E2, E3, D2, C1) and weighting factors are shown in the following table (Table 4).

Table 4 Main test types (E2, E3, D2, C1) and weighted factor table

E2 test cycle	Rotational speed	100%	100%	100%	100%	—	—	—	—
	Power	100%	75%	50%	25%	—	—	—	—
	Weighted factor	0.2	0.5	0.15	0.15	—	—	—	—
E3 test cycle	Rotational speed	100%	91%	80%	63%	—	—	—	—
	Power	100%	75%	50%	25%	—	—	—	—
	Weighted factor	0.2	0.5	0.15	0.15	—	—	—	—
D2 test cycle	Rotational speed	100%	100%	100%	100%	100%	—	—	—
	Power	100%	75%	50%	25%	10%	—	—	—
	Weighted factor	0.05	0.25	0.3	0.3	0.1	—	—	—
C1 test cycle	Rotational speed	Calibration speed				Intermediate speed			Idle speed
	Power	100%	75%	50%	10%	100%	75%	50%	0%
	Weighted factor	0.15	0.15	0.15	0.1	0.1	0.1	0.1	0.15

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The engine used in the test is a four-stroke 6-cylinder medium-speed diesel engine, which adopts an electronically controlled high-pressure fuel common rail system. The rated speed is 1000 r min⁻¹ and the rated power is 1320 kW. Fig. 12 shows the physical picture of the engine bench.

Fig. 12 The experiment test bed of diesel engine.

The total volume of the SCR reactor configured for the engine is 0.77 m³. It is composed of 36 units and arranged in a 6 × 6 manner. The detailed parameters are shown in Table 5. The SCR reactor has an insulation layer on the outside, with the outermost layer being a metal shell. In the experiment, a 40% concentration urea water solution was used, which was injected into the exhaust pipe upstream of the SCR through urea nozzles. Due to the long exhaust pipeline and the arrangement of the SCR reactor on the upper layer, it is difficult to capture the overall layout diagram. The layout of the urea nozzles and the SCR reactor are shown in Fig. 13.

Table 5 Specification of SCR converter for diesel engine experiment

Unit cross-sectional area	0.225 m^2
Unit length	0.95 m
The number of cross-sectional arrangement units	36
Number of openings in the unit	1225
Wall thickness	0.76 mm
Volumetric specific surface area	755.7 m^2 m^−3

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Fig. 13 Urea-SCR system of engine test bed.

4.2.2. Model validation under D2/E3 cycles. The tests were conducted using the D2 and E3 test cycles to investigate the emission performance of diesel engines under load characteristics and propulsion characteristics conditions, respectively. The test environment had a temperature of approximately 29 °C, an ambient pressure of 102.8 kPa, and a relative humidity of about 55%. At each operating point, data collection was initiated after the engine had stabilized for approximately 5 minutes.

For the D2 test cycle, the engine speed was maintained at the rated speed, with loads set at 10%, 25%, 50%, 75%, and 100%—a total of five operating points. The test results are presented in Table 6, and the urea injection rates during the test are shown in Fig. 14.

Table 6 Conditions of D2 test cycle

Operating point		1	2	3	4	5
Rotational speed	r min^−1	1000	1000	1000	1000	1000
Power	kW	1320	990	660	330	132
Fuel consumption rate	g kW^−1 h^−1	193.9	195.6	209.2	254	387.5
Exhaust mass flow rate	kg h^−1	9426	6449	4627	2720	1844
Upstream exhaust temperature	°C	324	325	337.8	344.8	326
Upstream NOx concentration	ppm	1001	1298.6	1185.7	1150.7	728.1
Downstream NOx concentration	ppm	114.4	88.2	34.8	43.3	20.9

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Fig. 14 The injection volume of urea solution on D2 test cycle.

As shown in Fig. 14, the actual urea injection amount during the test was basically equal to the set injection amount, and the ammonia–nitrogen ratio was maintained at approximately 1.0 under all working conditions (the ammonia–nitrogen ratio was calculated based on the conversion of 1 mole of urea to 2 moles of NH₃).

Based on the test conditions, the simulation program was used for numerical calculations. Boundary conditions such as gas flow rate, gas composition, temperature, and pressure were set according to the test measurement results. The concentrations of NO and NO₂ in NO_x were calculated at a ratio of 9 : 1, and it was assumed that the injected urea was completely converted to NH₃. The calculations were conducted using a steady-state solution, ultimately yielding the converged NO_x concentration at the SCR reactor outlet. Following the calculation of NO_x conversion efficiency, Fig. 15 presents the test and simulation results for NO_x concentration and conversion efficiency during the D2 test cycle. The bar chart illustrates the downstream NO_x concentration of the SCR reactor, where observable discrepancies exist between calculated and test values. However, considering the high inlet NO_x concentration and low outlet concentration in practice, the numerical results demonstrate favorable agreement with test data in terms of NO_x conversion efficiency (as shown by data points in the figure). According to IMO regulatory calculation methods, the weighted NO_x emissions after SCR reactor installation under the D2 test cycle exhibit only a 1.5% error between test and program-calculated values.

Fig. 15 Comparison of calculated results with experimental data of NO_x concentration downstream the SCR and conversion efficiency on D2 test cycle. The bar graph represents the NO_x concentration at the downstream of the SCR reactor (including experimental values and simulation values) under five operating points of the D2 cycle; the scattered data points represent the NO_x conversion efficiency (including experimental values and simulation values) corresponding to each operating point. the operating points are set with rated speed (1000 r min⁻¹) and different loads (10%, 25%, 50%, 75%, 100% power).

The E3 type test includes four operating points of the engine's propulsion characteristics. The test results are shown in Table 7, and the urea injection volume during the test is shown in Fig. 16.

Table 7 Conditions of E3 test cycle

Operating point		1	2	3	4
Rotational speed	r min^−1	1000	909	795	632
Power	kW	1320	988	656	331
Fuel consumption rate	g kW^−1 h^−1	193.9	195.7	201.5	219.3
Exhaust mass flow rate	kg h^−1	9426	6413	3809	1821
Exhaust temperature	°C	324	341	382	400
Upstream NOx concentration	ppm	1001	1079	1351	1319
Downstream NOx concentration	ppm	114.4	125	29	40

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Fig. 16 The injection volume of urea solution on E3 test cycle.

Downstream of the SCR reactor, whereas the data points denote the NO_x conversion efficiency. A notable discrepancy is observed at the second operating point, while the calculated values for the remaining operating points demonstrate favorable consistency with the test results. Analogously, in accordance with the IMO-specified method, the weighted calculation of NO_x emissions after the SCR reactor in the E3 test cycle reveals that the error between the test results and the program calculation results is merely 4.2%.

The discrepancy between program predictions and test results might originate from experimental errors. Owing to the lag in SCR carrier temperature variation relative to exhaust temperature fluctuations, employing exhaust temperature as the reaction temperature in calculations could introduce inaccuracies. Additionally, changes in diesel engine operating conditions, urea decomposition, and catalyst ammonia storage all contribute to experimental errors. Meanwhile, errors may also arise from program calculations: the one-dimensional flow model cannot reflect the non-uniform distribution of temperature and gas component concentrations, and the model ignores the impact of NH₃ adsorption/desorption processes on the catalyst, thereby affecting the accuracy of simulation results (Fig. 17).

Fig. 17 Comparison of calculated results with experimental data of NO_x concentration downstream the SCR and conversion efficiency on E3 test cycle.

To investigate the relationship between the axial position and NO_x conversion efficiency, the numerical simulation results of NO_x conversion efficiency under the five working conditions of the D2 test cycle were selected for analysis. For the convenience of comparison, the axial position of the SCR reactor is represented by the ratio of the length from the measurement point to the inlet end face of the SCR to the total length of the reactor. Fig. 18 shows the relationship between the NO_x conversion efficiency and the axial position of the reactor under the five working conditions of the D2 test cycle. It can be seen from the figure that the front section of the reactor contributes more to the NO_x conversion efficiency, indicating that the reaction rate in the front section is faster. In working conditions 5 and 4, NO_x is basically completely reacted at an axial position of about 0.5. In working condition 3, NO_x is basically completely reacted starting from an axial position of about 0.7. However, in working conditions 1 and 2, the NO_x conversion efficiency in the entire SCR never reaches stability, but the reaction rate gradually decreases in the second half. From operating condition 1 to condition 5, the space velocity through the SCR reactor decreases gradually. Notably, conditions 1, 2, and 5 exhibit similar exhaust temperatures, suggesting that at the same exhaust temperature, a higher space velocity corresponds to a lower reaction rate. This necessitates a larger reactor length (volume) to achieve the target NO_x conversion efficiency. By contrast, operating condition 4 features the highest exhaust temperature, demonstrating that elevated exhaust temperatures accelerate the reaction rate. Consequently, a smaller reactor length suffices to attain the target NO_x conversion efficiency under such conditions.

Fig. 18 NO_x conversion of axial positions of the reactor on D2 test cycle.

The above analysis is consistent with the actual situation, indicating that numerical simulation calculations can provide guiding significance for matching a suitable volume of SCR reactor for diesel engines.

5. Summary and outlook

This work has conducted an in-depth study on the one-dimensional flow model of the Urea-SCR system, developed a one-dimensional Urea-SCR system calculation program, investigated the influencing factors of NO_x conversion efficiency through catalyst sample bench tests and engine bench tests, and verified the accuracy and effectiveness of the calculation program. The finite volume method was used to discretely solve the one-dimensional unsteady flow of the exhaust pipeline, and the solution of the time-direction difference scheme needs to meet the stability conditions. The SIMPLE algorithm was applied to discretely solve the one-dimensional flow model of the SCR reactor. In the case of high temperatures, the iterative calculation of the implicit scheme may fail to converge, while the low relaxation method can improve the convergence of the calculation. Selecting appropriate relaxation factors helps obtain convergent solutions and save calculation time. The urea decomposition efficiency calculated by the program is basically consistent with the experimental results, indicating that the calculation program can be used to predict the decomposition state of urea in the exhaust gas. By analyzing the relationship between urea pyrolysis, isocyanic acid hydrolysis, temperature, and reaction time through program calculations, it was found that the hydrolysis rate of HNCO in the exhaust gas is much lower than the pyrolysis rate of urea, which is the main factor limiting the complete conversion of urea to NH₃ before the gas reaches the inlet of the SCR reactor.

The effects of temperature, space velocity, NO₂/NO ratio, and ammonia-to-nitrogen ratio on NO_x conversion efficiency were investigated using an SCR sample performance evaluation test bench. The results indicate that temperature exerts the most pronounced influence on NO_x conversion efficiency, with the catalyst maintaining high activity within the temperature window of 300 °C to 450 °C. At low temperatures, higher space velocities correspond to lower NO_x conversion efficiency, whereas the impact of space velocity on reaction efficiency gradually diminishes when the temperature exceeds 350 °C. The addition of NO₂ at low temperatures significantly enhances NO_x conversion efficiency, with the optimal effect achieved at a NO₂/NO ratio of 1 : 1. An ammonia-to-nitrogen ratio below 1 restricts NO_x conversion efficiency.

A calculation program with parameter identification was employed to simulate test conditions involving different temperatures, space velocities, and gas compositions, yielding results that align well with experimental data. NO_x emission tests were conducted on a diesel engine bench according to the D2 and E3 test cycles, with the program used to calculate corresponding conditions. While certain discrepancies exist in the calculated NO_x concentration at the SCR outlet under each condition, the results converted to NO_x conversion efficiency demonstrate favorable agreement. The errors in NO_x emissions obtained via weighted calculation for the D2 and E3 cycles are only 1.5% and 4.2%, respectively.

This work has developed a one-dimensional flow Urea-SCR system calculation program and conducted comparative studies through experiments and program calculations. However, due to limitations in knowledge structure, time, and other factors, there are still shortcomings, and further research can be carried out on the improvement and optimization of models and programs, as well as experimental studies. In the urea injection and decomposition model, this work assumes that the droplets of the urea aqueous solution are uniformly distributed in the exhaust pipeline, without considering the formation of wall films on the pipeline walls due to the collision of the urea aqueous solution after spraying, and the phenomenon of secondary fragmentation of droplets during their movement in the exhaust gas. In future research, droplet wall film and fragmentation models should be added to more accurately describe the atomization and decomposition process of the urea aqueous solution. In addition, this work only carried out experimental studies under steady-state conditions, and the program calculations can basically predict the NO_x removal effect under steady-state conditions. The next step can be to add some experimental studies under continuous variable conditions and compare them with the program calculation results to help further improve and refine the model and program.

Author contributions

Bin Guan: conceptualization, methodology, writing-original draft, writing-review & editing. Zhongqi Zhuang: conceptualization, writing-review & editing, validation, and supervision. Lei Zhu: writing-original draft, writing-review & editing. Jiangli Ma: writing-original draft, writing-review & editing. Tiankui Zhu: writing-original draft. Luoxin Xu: writing-original draft. Xuehan Hu: writing-original draft. Chenyu Zhu: writing-original draft. Sikai Zhao: writing-original draft. Junyan Chen: writing-original draft. Junjie Gao: writing-original draft. Kaiyou Shu: writing-original draft. Hongtao Dang: writing-original draft. Luyang Zhang: writing-original draft. Yuan Li: writing-original draft. Wenbo Zeng: writing-original draft. Shuai Chen: writing-original draft. Linhui Wang: writing-original draft. Can Zhu: writing-original draft. Jiaming He: writing-original draft. Qinghan Xian: writing-original draft. Zhen Huang: supervision.

Conflicts of interest

The authors declare no competing financial interest.

Data availability

The data that support the findings of this study are available on request.

Acknowledgements

This work was sponsored by the National Natural Science Foundation of China (52476124, 52076134, 51676127, 51436005, and 51176118), the National Key Research and Development Plan (2016YFC0205200, 2016YFC0208000, and 2017YFB0103501), the High-tech Ship Research Projects “Key combustion technology research for ammonia-fueled marine engines based on the Otto cycle”, the Oceanic Interdisciplinary Program of Shanghai Jiao Tong University (SL2022MS006), Major Science and Technology Projects of Yunnan Province (202402AC080004), the Open Research Program of State Key Laboratory of Engines (K2023-06), Scientific and Technological Project of Yunnan Precious Metals Laboratory (YPML-20240502068), the National Engineering Laboratory for Mobile Source Emission Control Technology (NELMS2017A07), the National Natural Science Foundation of China for Young Scientists (51306115), the Low Speed Marine Engine Project (CDGC01-KT1203), and the Scientific Research Foundation for the Returned Overseas Chinese Scholars of State Education Ministry.

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