Combustion Process Analysis of Secondary Jet-Guided Combustion in Hydrogen Direct-Injection Engines

Abstract

This study investigates the effects of secondary jet-guided combustion on the combustion and emissions of a hydrogen direct-injection engine through numerical simulations. The results show that secondary jet-guided combustion, which involves injecting and igniting the hydrogen jet at the end of the compression stroke, significantly shortens the delay period, improves combustion stability, and brings the combustion center closer to the top dead center (TDC), achieving a maximum indicative thermal efficiency (ITE) of 46.55% (λ = 2.4). However, this strategy results in higher NOx emissions due to high-temperature combustion. In contrast, single and double injections lead to worsened combustion and reduced thermal efficiency under lean-burn conditions, but with relatively lower NOx emissions. This study demonstrates that secondary jet-guided combustion can effectively enhance hydrogen engine performance by optimizing mixture stratification and flame propagation, providing theoretical support for clean and efficient combustion.

1. Introduction

Since being recognized as a clean fuel in the 1970s, hydrogen has been extensively studied for use in internal combustion engines [1,2]. Compared to conventional liquid fuels like gasoline or diesel, hydrogen offers several advantages, including improved cold-start capability, lower emissions of pollutants, and reduced lubricant contamination [3,4]. Hydrogen possesses a range of desirable properties that enhance combustion characteristics and engine performance, such as a higher flame speed, a higher lower heating value, a higher octane number, and a wider flammability range. Its high diffusivity promotes the rapid formation of a homogeneous mixture, while its fast flame propagation enables combustion that more closely approximates the ideal constant-volume combustion, thereby improving thermal efficiency [5]. However, this high flame speed also presents challenges. Under high mixture concentrations, hydrogen engines are prone to an excessively high rate of pressure rise during the initial combustion phase [6]. This elevated pressure rise rate can lead to increased combustion noise, higher engine vibration, and reduced operational reliability. Furthermore, the associated pressure fluctuations may induce abnormal combustion phenomena such as pre-ignition and backfire. Additionally, due to concentrated heat release and rapid flame propagation, in-cylinder temperatures rise sharply, leading to significantly elevated NOx emissions.

Direct-injection pure-hydrogen engines offer significant advantages by mitigating pumping losses through direct fuel injection, thereby enhancing thermal efficiency while avoiding the backfire issues associated with intake port injection. However, the shortened mixing time often leads to inadequate mixture homogeneity, which can promote abnormal combustion phenomena such as pre-ignition and knocking.

Optimizing the injection strategy is crucial for improving mixture preparation quality in direct-injection hydrogen engines, enabling stratified combustion and consequently enhancing engine performance. Hu [7] investigated mixture formation and combustion processes under varying injection pressures and found that low-pressure injection with a large nozzle aperture resulted in higher thermal efficiency and improved power output under appropriate injection timing. In contrast, Huang [8] observed that delayed injection timing worsened mixture homogeneity, reducing flame propagation speed. Compared to single injection strategies, multiple injections per cycle allow better formation of stratified mixture, thereby improving combustion and emission characteristics. Li [9] enhanced flame propagation speed in a gasoline/hydrogen dual-fuel engine by optimizing the proportion and timing of secondary injection, thereby improving combustion efficiency while simultaneously reducing NOx emissions. Similarly, Lee [10] demonstrated in a constant-volume combustion chamber that multiple injections promote more favorable hydrogen–air mixture near the spark plug compared to single injection. Cheng [11] investigated the optimization of engine performance using a double injection strategy in an ammonia/diesel dual-fuel engine. The study found that the split injection strategy effectively optimized the mixture formation within the combustion chamber, promoting faster and more complete combustion. This resulted in a more uniform combustion temperature distribution and simultaneously maintained all pollutant emissions at relatively low levels. Similarly, Fan Zhang [12], in a comparative study of single, double, and triple injection strategies on an ammonia/diesel dual-fuel engine, demonstrated that transitioning from single to double and triple injections increased ITE of the engine while reducing the peak pressure rise rate, leading to smoother and more efficient combustion. Furthermore, in a study on a diesel engine, Lu et al. [13] found that compared to single injection, double injection could increase mixing time. The optimized multiple injection strategy incorporated a short pilot injection before the main injection. This shortened the duration of in-cylinder turbulent motion and enhanced the mixing rate of the main injection with air, resulting in more thorough premixing and more complete combustion.

Benefiting from the inherent physicochemical properties of hydrogen, such as its low ignition energy and high laminar flame speed, researchers have proposed a jet-guided combustion strategy inspired by the compression ignition principle of diesel engines. In this approach, hydrogen is injected near the end of the compression stroke and directly ignited to achieve stratified mixture formation and stabilized combustion. Mohammadi [14] investigated the jet combustion characteristics of both natural gas and hydrogen in a constant-volume combustion chamber. It was observed that when natural gas is ignited during injection, intense airflow motion can extinguish the initial flame kernel, leading to misfire. In contrast, hydrogen jets achieve reliable ignition during injection, and ignition occurring at the jet periphery further enhances combustion stability. Merotto et al. [15,16] applied the jet-guided combustion concept in a rapid compression machine and a conventional spark-ignition engine, achieving ultra-lean combustion with a global λ of 6.55.

On the other hand, some researchers have conducted preliminary investigations into the application of jet-guided combustion in engines as a measure to enhance ignition stability. Fawzi Mohd Ali et al. [17] studied secondary jet-guided combustion in compressed natural gas engines and observed a plume-like flame structure that promotes reliable flammability. Their study also revealed that the initial injection significantly influences flame development after ignition. The timing of this initial injection was identified as a critical factor for improving engine performance, with its optimal value being highly dependent on the equivalence ratio. In a study on ammonia-fueled engine, Guo [18] introduced a direct in-cylinder injection hydrogen jet to guide the ignition and combustion of the premixed ammonia/air mixture. It was found that when ignition occurred either at the start or during the injection phase of hydrogen, the continuous momentum of the hydrogen jet promoted forward flame propagation along the jet trajectory, resulting in significantly higher flame speeds compared to ignition triggered at the end of or after injection.

However, current research on jet-guided combustion, particularly studies that coordinate injection timing with ignition timing, has been conducted primarily in constant-volume combustion chambers and rapid compression machines, with limited application to actual engines. Furthermore, existing engine studies are often carried out under low-load conditions and at low speeds (600–1000 rpm). Under high-load conditions, where diffusion combustion becomes dominant, combustion duration tends to increase and the degree of constant-volume combustion decreases, ultimately reducing engine performance. As an ignition strategy, jet-guided combustion has been more widely applied in engines fueled by methane or ammonia. In contrast, hydrogen exhibits distinct properties: while it offers superior flammability, it has a lower volumetric energy density. Therefore, investigating the combustion and flame propagation characteristics of secondary jet-guided combustion in pure-hydrogen direct-injection spark-ignition engines is of significant importance for improving the thermal efficiency of hydrogen engines.

Accordingly, this paper examines the effects of secondary jet-guided combustion on thermal efficiency and NOx emissions in a hydrogen direct-injection engine. By comparing the flame propagation and combustion processes across single-injection, double injection, and secondary jet-guided combustion strategies, we aim to provide insights into optimizing hydrogen engine performance.

2. Numerical Model

2.1. Geometric Model

The engine model used in this research was an in-cylinder direct-injection hydrogen engine equipped with a spark plug, and the 3D simulation model included intake and exhaust ports, intake and exhaust tracts, intake and exhaust valves, piston, spark plug, cylinder head and cylinder liner as shown in Figure 1. The hydrogen injector was positioned on the intake side of the cylinder head, as illustrated in Figure 1b. It was oriented at a −72° jet angle relative to the cylinder axis. The injector featured a single nozzle with an orifice diameter of 1.5 mm.

The basic parameters of the model are shown in

Table 1. Main parameters of the engine.

Technical Specifications	Indicator
Cylinder	4
Dore (mm)	73.5
Stroke (mm)	90.44
Displacement (L)	1.5
Connecting rod length (mm)	141.51
Compression ratio	11.6

and the operational parameters are shown in

Table 2. Numerical simulation operating parameters.

Parameters	Value
Speed (rpm)	2000
Injection time (°CA ATDC)	−120
Injection pressure (MPa)	7
Ignition time (°CA ATDC)	−10
Intake valve opening/closing time (°CA ATDC)	−359.5/−177.5
Exhaust valve opening/closing time (°CA ATDC)	143.6/370.5

. The compression TDC is defined as 0 °CA and all the moments used in this paper are after top dead center (ATDC).

The combustion model employed in this study was the SAGE model [19], which simulates chemical kinetics by utilizing a detailed reaction mechanism as an input file and calculates the reaction rate for each elementary reaction. The hydrogen reaction mechanism adopted in this work comprises 11 species and 24 elementary reactions [20]. For turbulence modeling, the effects of turbulent vortices were taken into account to improve computational accuracy under high-turbulence conditions. Accordingly, the RNG k-ε model [21,22] was selected for conducting the numerical simulations. This combination may not be able to fully and accurately predict local extinction and flame surface wrinkling under high-intensity turbulence. However, by directly solving detailed chemical reaction mechanisms, it can spontaneously capture both the premixed and diffusion combustion modes coexisting in hydrogen jet-guided combustion without the need to predefine the flame structure.

2.2. Boundary Conditions and Simulation Conditions

In numerical simulations, the accuracy of the results is critically influenced by the boundary conditions and initial setup. In this study, the initial temperature and pressure were determined based on experimental data and computational results. The boundary and initial conditions were summarized in

Table 3. Initial and boundary conditions.

Parameters	Value
Temperature of combustion chamber top (K)	550
Temperature of piston crown (K)	550
Temperature of intake manifold (K)	320
Temperature of exhaust port (K)	550
Temperature of cylinder wall (K)	500
Intake air temperature (K)	310
Intake air pressure (Pa)	145,000
In-cylinder temperature (K)	500
In-cylinder pressure (Pa)	101,325

. The simulation covered a period from −373 °CA to 180 °CA ATDC.

At an engine speed of 2000 rpm, a secondary injection was implemented near the end of the compression stroke close to TDC, with the hydrogen injection pressure set to 7 MPa. By controlling both the injection timing and the ignition timing, ignition was triggered as the hydrogen jet reached the spark plug, thereby achieving secondary jet-guided combustion. To enable a detailed analysis of the impact of secondary jet-guided combustion on the combustion and emission characteristics of a direct-injection spark-ignition hydrogen engine, a comparative study was conducted under lean conditions (λ > 2) among the original engine (single injection), the double injection strategy, and the secondary jet-guided combustion strategy. In order to minimize the influence of variations in injection parameters, both the double injection and jet-guided combustion strategies employed the same injection timing as the baseline configuration, with a secondary injection mass fraction of 20%. The specific operating conditions were illustrated in Figure 2.

2.3. Grid Independence and Numerical Model Validation

Grid size significantly influences both computational efficiency and the accuracy of simulation results, making grid independence verification essential for the numerical model. In the CFD software CONVERGE v3.0, real-time mesh partitioning is achieved by configuring the base grid size, fixed grid refinement zones, and adaptive mesh refinement (AMR) technology. AMR is particularly effective in resolving regions with high local gradients in velocity and temperature, such as those occurring during hydrogen injection and combustion processes inside the cylinder. In this study, AMR was applied to perform three levels of refinement based on velocity and temperature gradients within the intake port and cylinder regions. Additionally, fixed refinement zones were established as detailed in

Table 4. Fixed refinement zones and refinement level.

Fixed Refinement Zones	Refinement Level
Cylinder	2
Intake valve	3
Exhaust valve	3
Hydrogen injector	3
Ignition source	6

.

Figure 3 presents the temperature and pressure curves from the numerical model under cold flow conditions for three base grid sizes: 8 mm, 4 mm, and 2 mm. As shown in the figure, the results for the 4 mm and 2 mm grid sizes were in close agreement, with minimal deviations in both temperature and pressure. In contrast, the 8 mm grid size yielded a significantly lower pressure peak and a discernible downward shift in the temperature curve. Considering both computational accuracy and resource efficiency, a base grid size of 4 mm was selected for all subsequent simulations in this study.

To validate the reliability of the numerical model, a comparison was conducted between experimental and simulated cylinder pressure and heat release rate (HRR) at an engine speed of 2000 rpm and λ = 2.0. Figure 4 illustrates the comparison of cylinder pressure and HRR curves, while

Table 5. Comparison of engine simulation and experimental performance results.

	IMEP/Bar	CA10/°CA	CA50/°CA	CA90/°CA	Pmax/Bar	δPmax/°CA
Experiment	10.24	−1.98	5.70	13.74	9.30	10.50
Simulation	10.11	−2.14	5.41	13.49	9.18	10.71

presents the comparison of performance results between experiments and simulations. As shown in Figure 4, the simulated pressure and HRR curves showed good agreement with the experimental data, although the peak HRR was slightly overpredicted in the simulation. According to the comparative results of engine performance parameters presented in Table 5, all parameters except CA10 demonstrated relative errors within 5%, which fell within an acceptable range for engineering accuracy. Overall, it can be concluded that the numerical model adopted in this study is capable of accurately simulating the actual operational behavior of the engine.

3. Results and Discussion

3.1. Combustion Process Analysis

Figure 5 illustrates the in-cylinder average pressure, HRR, and average temperature curves under various operating conditions. The results demonstrated that the secondary jet-guided combustion strategy exhibited superior combustion characteristics across multiple indicators among the three modes. Most notably, the secondary jet-guided combustion mode achieved the highest average in-cylinder pressure and temperature among the three combustion strategies. The peak pressure occurred earlier and closer to TDC, indicating more efficient energy conversion. This advantage was particularly evident through the rapid hydrogen combustion following ignition, which triggered a sharp increase in HRR and enabled faster pressure rise toward an earlier peak. Furthermore, the secondary jet-guided combustion strategy demonstrated remarkable resilience to lean-burn conditions. As λ increased, both the original engine and double injection strategy suffered significant deterioration in performance, showing delayed and reduced peak pressures and temperatures, decreased peak HRR, and prolonged combustion duration. In contrast, the secondary jet-guided combustion maintained relatively stable performance with only slight reductions in average pressure, temperature, and the first HRR peak. These results collectively confirm that secondary jet-guided combustion provides superior stability in lean-burn operation.

The combustion process in an engine is generally categorized into three phases: the ignition delay period, the combustion duration period, and the afterburning period. In this study, the crank angles at which 10%, 50%, and 90% of the total cumulative heat release were achieved were defined as CA10, CA50, and CA90, respectively. The ignition delay period was calculated as the crankshaft interval from the spark timing to CA10. The combustion duration period is defined as the crankshaft interval from CA10 to CA90. The afterburning period represents the crankshaft interval from CA90 to the point at which the fuel is nearly completely combustion. CA50, also known as the combustion center, serves as a critical parameter for assessing the overall combustion process, as it typically indicates the phasing of combustion and the closeness to constant-volume combustion.

Figure 6 illustrates the ignition delay period, combustion duration period, and CA50 for the three strategies as functions of λ. As seen in Figure 6a, the secondary jet-guided combustion strategy exhibited the shortest ignition delay across all conditions, whereas the original engine showed the longest delay. This explained why HRR, pressure, and temperature rose earlier under the secondary jet-guided and dual-injection strategies compared to the original engine. With increasing λ, the ignition delay period extended noticeably for both the original engine and the double injection strategy, while it remained largely stable for the secondary jet-guided combustion approach. This indicated markedly enhanced ignition and early combustion stability with the secondary jet-guided mode. Figure 6b showed that the combustion duration increased under all three strategies as λ rose, but this extension was significantly less pronounced with secondary jet-guided combustion. Similarly, Figure 6c demonstrated that the CA50 values for secondary jet-guided combustion were consistently closer to TDC under various conditions. Although CA50 gradually shifted away from TDC with increasing λ, this deviation remained substantially smaller than that of the other two strategies, reflecting more concentrated heat release. As further illustrated in Figure 5, the first peak of the HRR curve in secondary jet-guided combustion remained almost unaffected by changes in λ, whereas the second HRR peak decreased in magnitude and broadened in duration as λ increased.

A detailed analysis of the flame propagation and combustion process, as illustrated in

Table 6. Comparison of flame front (T = 1800 K) development (λ = 2.2).

	Original Engine	Double Injection Strategy	Secondary Jet-Guided Combustion *
−5 °CA ATDC
0 °CA ATDC
5 °CA ATDC
10 °CA ATDC
15 °CA ATDC

* The secondary jet-guided combustion exhibited the fastest flame development.

, revealed that the secondary jet-guided combustion strategy achieved faster flame development, both during ignition and subsequent propagation, compared to the original engine and the double injection strategy. Although the double injection strategy exhibited relatively rapid flame propagation in the early stage (before 5 °CA ATDC), the flame speed decreased markedly as the flame approaches the cylinder wall. This behavior aligned well with the previously observed trends in combustion duration, further confirming the consistency between the flame dynamics and global combustion characteristics.

As illustrated in

Table 7. Comparison of spark plug cross-sectional equivalent ratio concentration distributions (λ = 2.2).

	Original Engine	Double Injection Strategy	Secondary Jet-Guided Combustion *
−10 °CA ATDC
−8 °CA ATDC
−5 °CA ATDC
0 °CA ATDC
5 °CA ATDC
10 °CA ATDC

* The secondary jet-guided combustion anchors the flame at the hydrogen jet leading edge, propagating along the premixed zone.

, the equivalence ratio distributions across the spark plug cross-section were compared for the three strategies at λ = 2.2, where the black contour denoted the flame front. The double injection strategy resulted in a richer mixture near the spark plug, promoting faster initial flame development. As the piston approached TDC, the hydrogen from the secondary injection was carried toward the central flame region with the piston motion. However, as the flame propagated toward the cylinder wall, its progress was impeded by regions of lean mixture, leading to a significantly shorter ignition delay period but a notably longer combustion duration compared to the original engine, as shown in Figure 6a,b.

In contrast, the mixture development in the secondary jet-guided combustion mode showed that during early flame growth, the flame anchored at the leading edge of the hydrogen jet and propagated along the premixed zone at the jet boundary toward the trailing edge. By −5 °CA ATDC, the flame nearly surrounded the entire jet region. Simultaneously, the flame front began to detach from the jet-associated premixed zone and propagated toward the cylinder wall, reaching it by 5 °CA ATDC. Thus, in terms of ignition delay, combustion duration, and CA50, the secondary jet-guided combustion strategy demonstrated superior performance over both the original engine and the double injection strategy.

3.2. Flame Propagation and Radical Analysis

As shown in Figure 7, which displays HRR curves, two distinct combustion modes were clearly evident during the secondary jet-guided combustion process. OH and H₂O₂ radicals act as key intermediates representing high-temperature and low-temperature reaction pathways, respectively, in hydrogen combustion. Analysis of these radical species offered deeper insight into the combustion mechanisms underlying jet-guided combustion. Under high-temperature conditions, hydrogen combustion is dominated by chain-branching reactions, as illustrated in reactions (1)–(3). OH radicals react with hydrogen molecules to form water and H radicals, thereby sustaining the chain reaction that supports continuous combustion. Under low-temperature conditions, the combustion process is primarily driven by reactions involving HO₂ and H₂O₂, as shown in reactions (4) and (5). These reactions proceed at a slower rate but still contribute effectively to the overall progression of combustion.

H + O₂ → O + OH

(1)

H₂ + O → OH + H

(2)

H₂ + OH → H₂O + H

(3)

HO₂ + H₂ → H₂O + H₂O₂

(4)

H₂O₂ → OH + OH

(5)

Table 8. Comparison of spark plug cross-sectional H₂O₂ radical concentration distribution (λ = 2.2).

	Original Engine	Double Injection Strategy	Secondary Jet-Guided Combustion *
−10 °CA ATDC
−8 °CA ATDC
−5 °CA ATDC
0 °CA ATDC
5 °CA ATDC
10 °CA ATDC

* H₂O₂ distributes in the unburned zone ahead of the flame. Its band-like distribution in the secondary jet-guided combustion enhances flame propagation, whereas its detachment from the flame in the double injection strategy yields negligible enhancement.

and

Table 9. Comparison of spark plug cross-sectional OH radical concentration distribution (λ = 2.2).

	Original Engine	Double Injection Strategy	Secondary Jet-Guided Combustion *
−10 °CA ATDC
−8 °CA ATDC
−5 °CA ATDC
0 °CA ATDC
5 °CA ATDC
10 °CA ATDC

* In the secondary jet-guided combustion, sustained high OH concentration, distributed from the premixed zone at the jet leading edge to the flame interior and high-temperature regions, dominates both premixed and diffusion phases, resulting in multi-stage heat release.

presented the spatial distributions of H₂O₂ and OH radical concentrations on the spark plug cross-section during combustion at λ = 2.2 for the three strategies. As visible in Table 8, H₂O₂ radicals were primarily located in the outer low-temperature unburned zone ahead of the flame front, and their concentration increased gradually following ignition. A portion of the secondary jet flame remained embedded within the hydrogen jet, as shown in Table 7. In this region, higher concentrations of H₂O₂ radicals were observed on the outer side of the flame. After the flame had enveloped the jet region (by −5 °CA ATDC), the band-like distribution of H₂O₂ radicals thickened and diffused further into the unburned mixture. Meanwhile, the flame front gradually detached from the hydrogen jet. It is thus inferred that the intensified low-temperature reactions on the unburned side contributed to enhanced flame propagation. In the case of the double injection strategy, faster flame propagation near the piston crown caused the region of H₂O₂ radicals in the low-temperature unburned zone to become detached from the flame front at this cross-section. As a result, no significant enhancement in flame propagation was observed in this plane.

As shown in Table 9, in both the original engine and the double injection strategy, only minimal OH radical distributions were observed around the flame front prior to TDC. At this stage, the flame region was small and the in-cylinder temperature remained relatively low, causing OH radical formation to rely heavily on the decomposition of H₂O₂ radicals. In the original engine, after TDC, OH radicals gradually extended from the outer flame front toward the burned region inside the flame and continued to diffuse inward. This led to intense combustion within the burned zone, corresponding to the rapid increase in HRR shortly after TDC, as seen in Figure 5, which was sustained for a period before decreasing sharply. In the double injection strategy, a region of higher mixture concentration near the cylinder center after TDC gave rise to elevated OH radical levels, resulting in the first HRR peak around TDC. However, the subsequent decrease in local mixture concentration caused a decline in heat release. After 10 °CA ATDC, vigorous combustion resumed near the cylinder wall where the right flame front showed high OH radical concentration, leading to a second rise in HRR and a subsequent peak.

The distribution of OH radicals in the secondary jet-guided combustion mode differed markedly from that in the original engine and double injection strategies. Throughout the combustion process, the secondary jet-guided strategy maintained a region of high OH radical concentration. Initially, OH radicals accumulated predominantly in the premixed zone on the inner side of the flame front at the leading edge of the hydrogen jet. They propagated along with the flame from the jet’s leading edge toward its trailing edge through this premixed region. During this stage, intense premixed combustion occurred in the hydrogen jet periphery, causing HRR to rise rapidly to its first peak. This initial combustion phase is therefore dominated by premixed combustion, forming the so-called premixed peak. Around −5 °CA ATDC, as flame propagation continued, the flame front gradually detached from the outer premixed zone of the hydrogen jet. By this time, the jet was almost entirely enveloped by the flame, situated within the high-temperature burned region, while OH radicals persisted mainly along the outer periphery of the jet. At this stage, diffusion combustion becomes the dominant mode, sustaining a relatively high HRR.

As the flame continued to propagate toward the cylinder wall, the high concentration of H₂O₂ radicals ahead of the flame front supported subsequent oxidation, while high levels of OH radicals reappeared inside the flame front. At this point, both premixed and diffusion combustion occurred simultaneously at high intensity, leading to a second HRR peak. However, due to the lean mixture near the cylinder wall and the fact that diffusion-controlled combustion is limited by fuel-air mixing rates, the magnitude of this HRR peak is lower than that of the initial premixed peak, referred to as the diffusion peak.

Figure 8 illustrates the variation in H₂O₂ and OH radical concentrations under secondary jet-guided combustion at λ = 2.2, 2.4, and 2.6. As shown in Figure 8a, after ignition, the concentration of H₂O₂ radicals displayed two distinct rising phases with different slopes, followed by a rapid decline after reaching its peak. Variations in λ did not significantly alter the behavior of H₂O₂ radicals, only causing a slight reduction and delay in the peak value and its timing. However, as λ increases, the overall mixture concentration decreases, resulting in a higher equilibrium concentration of H₂O₂ radicals.

In Figure 8b, the concentration of OH radicals rose rapidly to a peak after ignition and then decreased sharply. With increasing λ, the peak value showed a notable decreasing trend, reflecting a reduction in reaction intensity. This decline in OH radical concentration correlates with the gradual decrease in the diffusion peak of HRR for secondary jet-guided combustion as λ increases, as previously shown in Figure 7.

A further analysis was conducted on the flame front structure, equivalence ratio distribution, and H₂O₂/OH radical concentrations across the spark plug cross-section at λ = 2.6 under secondary jet-guided combustion. As shown in

Table 10. Flame front, equivalent ratio and radical distribution of secondary jet-guided combustion (λ = 2.6).

	−5 °CA ATDC	0 °CA ATDC	5 °CA ATDC *
Flame front
Equivalent ratio
H2O2
OH

* At high λ, the flame is difficult to detach from the hydrogen jet, preferentially propagating along the piston crown. This results in retarded flame development at the spark plug cross-section and reduced diffusion combustion intensity.

, the results revealed the mechanism through which increasing λ influenced the combustion behavior. It could clearly be observed that higher λ values led to a reduction in mixture concentration throughout the cylinder except within the hydrogen jet region. This made it difficult for the flame front at the spark plug cross-section to propagate toward the cylinder wall. Instead, the flame remained attached to the periphery of the hydrogen jet, trapping a significant number of OH radicals on the inner side of the flame surrounding the jet. When the hydrogen jet impinged on the piston surface, the flame propagated preferentially along the piston crown. As a result, flame development near the piston advanced more rapidly than in the region around the spark plug. This caused the high-concentration zone of H₂O₂ radicals in the spark plug cross-section to detach from the flame front. Furthermore, a small number of OH radicals were observed ahead of the flame front by the time of TDC.

By 5 °CA ATDC, the flame near the piston crown propagated to the vicinity of the cylinder wall, resulting in a high-temperature reaction zone and a localized high concentration of OH radicals near the cylinder wall within the spark plug cross-section. This analysis indicates that as λ increases, it becomes increasingly difficult for the flame front to detach from the hydrogen jet. This reduces the intensity of premixed combustion during the diffusion-dominated phase. Since the diffusion rate is considerably slower than the chemical reaction rate, OH radicals accumulate gradually, leading to a delayed peak as shown in Figure 8b. Consequently, the diffusion peak of the heat release rate decreases progressively with increasing λ and remains substantially lower than the premixed peak.

3.3. Unburned Hydrogen and ITE

Figure 9 illustrates the variation in unburned hydrogen and ITE under the three strategies at λ = 2.2, 2.4, and 2.6. As shown in Figure 9a, unburned hydrogen emissions were nearly identical and close to zero across all strategies at λ = 2.2. However, as λ increased, unburned hydrogen emissions gradually rose, and combustion deterioration occurred to varying degrees in all operating modes. As analyzed in Table 10, the increase in λ primarily reduces the intensity of premixed combustion during the diffusion combustion dominated phase. Thanks to its robust combustion characteristics, the secondary jet-guided combustion strategy maintained stable combustion even under high λ conditions, resulting in the smallest increase in unburned hydrogen emissions with rising λ. As observed in Figure 6, the original engine experienced smaller changes in combustion duration compared to the double injection strategy, along with an overall shorter duration. This led to both a smaller increase in unburned hydrogen and lower unburned hydrogen levels than those of the double injection strategy.

The trend in ITE, shown in Figure 9b, is largely inverse to that of unburned hydrogen. ITE gradually decreases as λ increases. The secondary jet-guided combustion strategy was the least affected by changes in λ, allowing it to maintain high ITE even under increasingly lean conditions. At λ = 2.4, it achieved the highest ITE (46.55%) among all operating points, and even at the extremely lean condition of λ = 2.6, the indicated thermal efficiency remained as high as 46.15%. In contrast, the double injection strategy exhibited the largest variation in ITE and consistently performed at the lowest efficiency level across all λ values.

3.4. NOx Emissions

Figure 10 presents the NOx emissions for the three strategies at λ = 2.2, 2.4, and 2.6. As shown, NOx emissions decrease with increasing λ for all strategies. At a given excess air ratio, the secondary jet-guided combustion strategy produced the highest NOx emissions, while the original engine yielded the lowest. At λ = 2.4 and λ = 2.6, combustion deterioration led to nearly zero NOx emissions for both the original engine and the double injection strategy.

In hydrogen engines, NOx formation is predominantly thermal NOx, which depends mainly on the presence of O and OH radicals under high-temperature conditions. The NOx formation rate increases significantly when temperatures exceed 1500 K. At a fixed λ, higher peak temperatures and longer exposure to high temperatures result in greater NOx production [23]. OH radicals contribute to NOx formation through reactions (6) and (7). Although reaction (7) is not the primary pathway for thermal NOx formation, it substantially promotes NOx generation at elevated temperatures.

N + OH → H + NO

(6)

OH + N₂ → NO + HN

(7)

As illustrated in

Table 11. Temperature distribution cloud map (λ = 2.2).

	Original Engine	Double Injection Strategy	Secondary Jet-Guided Combustion *
−5 °CA ATDC
5 °CA ATDC
15 °CA ATDC
25 °CA ATDC

* The secondary jet-guided combustion sustains regions of higher temperature over more crank angles and for a longer duration, which is the primary reason for its elevated NOx production.

, the secondary jet-guided combustion process reached higher peak temperatures and maintained high-temperature conditions for a longer duration compared to the other strategies. Table 9 and Table 10 further showed that OH radicals remained at high concentrations throughout the combustion process under this strategy and were largely confined to regions with temperatures above 1800 K. The promoted reaction (7) under these conditions enhances NOx formation, leading to consistently higher NOx emissions than those of the original engine and double injection strategies. As indicated in Figure 8b, an increase in λ reduces the concentration of OH radicals during combustion, which in turn contributes to the decline in NOx emissions across all strategies.

4. Conclusions

This study employs numerical simulations to compare and analyze the effects of single-injection, double-injection, and secondary jet-guided combustion strategies on the combustion and emission characteristics of a direct-injection hydrogen engine. The main conclusions are as follows:

(1)

The secondary jet-guided combustion strategy significantly enhances combustion performance. By injecting hydrogen near the end of the compression stroke and igniting it at the leading edge of the jet, this approach shortens the ignition delay, improves combustion stability, and shifts CA50 closer to TDC. These improvements lead to a substantial increase in ITE under lean conditions, reaching up to 46.55%, while maintaining high efficiency (46.15%) even under extremely lean operation (λ = 2.6).

(2)

The secondary jet-guided combustion strategy effectively integrates premixed and diffusion combustion modes through enhanced mixture stratification. This integration ensures reliable ignition and optimizes flame propagation, offering a viable pathway for the efficient and clean operation of hydrogen engines under lean-burn conditions.

(3)

NOx emissions are strongly influenced by the combustion mode. The secondary jet-guided combustion strategy leads to higher NOx emissions due to elevated temperatures and high concentrations of OH radicals. Nevertheless, the NOx emission level remains relatively low (<600 ppm). In contrast, both single- and double-injection strategies exhibit poorer combustion performance under lean conditions, resulting in lower NOx emissions and reduced ITE.