1 Introduction

The combustion characteristics of hydrogen, combined with its carbon-free nature, underscore its suitability as an engine fuel. The wide flammability limit of hydrogen, ranging from 4 to 75% by volume, enables the engine to operate across a broad range of power output, particularly under lean conditions (Das, 1990; Verhelst & Wallner, 2009). Additionally, the high flame speed of hydrogen allows the rapid burning of hydrogen-air mixtures around top dead center (TDC) of internal combustion engines, rendering hydrogen engines thermodynamically closer to an ideal engine (Stępień, 2021).

Although hydrogen engines demonstrate superior thermal efficiency compared to gasoline engines (White et al., 2006), numerous researchers have endeavored to enhance the thermal efficiency of hydrogen engines further. One of the ways to enhance thermal efficiency is to increase the compression ratio (CR). According to Eichlseder et al., hydrogen engines, similar to gasoline engines, achieved an improvement in thermal efficiency as the CR was increased. To be specific, assuming an ideal Otto cycle operation, the thermal efficiency exceeded 55% at a CR of 20 and an excessive air ratio (λ) of 1.6 (Eichlseder et al., 2003). Additionally, Canton evaluated that increasing the CR was more effective in enhancing thermal efficiency than controlling λ, exhaust gas recirculation (EGR) rate, and burn duration (Caton, 2012).

Although increasing the CR is an effective way to enhance the thermal efficiency of an engine, it comes with the drawback of inducing abnormal combustion such as knocking. Knocking refers to the phenomenon where a portion of unburned end gas ahead of the propagating flame automatically ignites during combustion in the combustion chamber. The rapid increase in in-cylinder pressure and temperature caused by knocking leads to deteriorated thermal and mechanical stresses, worsening the durability of the engine (Szwaja et al., 2007).

According to Heywood, increasing the CR creates conditions in the combustion chamber that are prone to knocking, as it elevates in-cylinder pressure and temperature during combustion (Heywood, 1988). Additionally, Li and Karim identified in their research that CR is a primary parameter causing knocking in hydrogen engines. They particularly emphasized that the increased knocking incidence due to higher CR poses a substantial obstacle to increasing thermal efficiency (Li & Karim, 2004).

Furthermore, a high CR comes with the drawback of increasing nitrogen oxides (NOx) emissions. NOx emissions are influenced by combustion temperature, so the formation of high in-cylinder temperature conditions during combustion due to a high CR results in an increase in NOx emissions (Mogi et al., 2022). Therefore, selecting a proper CR in hydrogen engines is a crucial matter from the perspectives of engine safety, improvement in thermal efficiency, and reduction of NOx emissions.

In the pursuit of achieving high thermal efficiency through increased CR while resolving the disadvantages of increased knocking incidence and NOx emissions, much research has been conducted to explore the application of lean operation in high CR hydrogen engines.

Lean air–fuel mixture formation is identified as an effective operational strategy for enhancing thermal efficiency by increasing the air in the cylinder, thereby promoting complete combustion (Suresh & Porpatham, 2024). Research by Sadiq Al-Baghdadi, which investigated the effect of CR and λ on the performance and emission characteristics of a hydrogen engine demonstrates that the effect of increasing CR on thermal efficiency improvement is more pronounced in leaner λ conditions than in richer λ conditions (Sadiq Al-Baghdadi, 2004).

Lean operation also proves to be an effective measure in increasing the proportion of air in the cylinder, lowering combustion temperature, and consequently reducing knocking incidence (Verhelst & Wallner, 2009). Previous studies investigating the effect of CR and λ on knocking incidence show that in high CR engines, to avoid knocking, operation under leaner λ conditions is necessary compared to engines with lower CRs (Karim & Klat, 1966; Li & Karim, 2004).

Since the combustion of nitrogen and oxygen at high temperatures produces NOx emissions (North, 1992), lean operation, which reduces flame temperature, is an effective method for significantly reducing NOx emissions. Preceding studies have revealed that lean operations with λ values exceeding 2 serve as an effective operational strategy for NOx reduction (Das, 1991; White et al., 2006). In particular, the research by Tang et al. demonstrated that even at a CR of 15.3, ultra-lean operation led to NOx emissions decreasing to 100 ppm or below. In essence, lean operation proves to be an effective approach for NOx reduction even in high CR engines.

Although lean operation offers advantages such as high thermal efficiency, low knocking incidence, and reduced NOx emissions, excessive lean operation leads to a high coefficient of variation (CoV) in indicated mean effective pressure (IMEP). The low laminar burning velocity of lean air–fuel mixtures influences the combustion rate, thereby deteriorating the combustion stability of the engine (Verhelst & Wallner, 2009). Additionally, the issue of lower engine power due to the relatively small amount of fuel is a concern. Therefore, many researchers have explored the direct injection (DI) of hydrogen into the combustion chamber to achieve stable combustion and improve engine output under lean λ conditions (Gomes Antunes et al., 2009; Mohammadi et al., 2007; Sun et al., 2018; Yi, 2000).

Unlike port fuel injection (PFI) which forms a pre-mixed mixture, a notable advantage of DI hydrogen engines is the ability to control injection timing (Verhelst & Wallner, 2009). Injection timing is a crucial operating parameter that significantly influences mixture distribution. Advanced injection timing ensures sufficient mixing time between fuel and air, leading to the formation of homogeneous mixtures. On the other hand, retarded injection timing results in stratified mixtures due to the limited mixing time.

Particularly, mixture stratifications offer an effective means to further enhance the engine thermal efficiency. This is achieved by forming a relatively lean mixture near the cylinder wall induced by mixture stratification, reducing the combustion temperature of the end gas during combustion and thereby reducing heat loss to the cylinder wall (Shudo et al., 2003).

Despite the advantage of improving thermal efficiency, mixture stratification has the drawback of increasing NOx emissions (Wallner et al., 2007). Specifically, in lean operations with λ ≤ 2, the retardation of injection timing leads to an increase in NOx emissions. This is attributed to the increased combustion temperature in the locally rich region of stratified mixtures, which produces high NOx emissions (White et al., 2006).

Recently, much research has been conducted on the combustion characteristics, engine performances, and emissions of hydrogen dual-fuel DI engines concerning CR, lean operation, and injection timing (Chen et al., 2022; Wang et al., 2023; Yu et al., 2019). However, to the best of the authors’ knowledge, there is a limited number of studies dealing with the effect of CR, lean operation, and injection timing variations on combustion characteristics, engine performances, and emissions in hydrogen DI engines (Lee et al., 2022; Li et al., 2021). Therefore, more comprehensive research is required in this area.

With the above considerations, this paper aims to analyze the combustion characteristics, engine thermal efficiency, and NOx emissions in a hydrogen direct injection spark ignition (DISI) engine under three different CR conditions with varying engine operating parameters such as injection timings and excessive air ratios. Additionally, experimental results for CR = 14 under various λ conditions elucidate effective operating conditions satisfying both high thermal efficiency and low NOx emissions, particularly at λ = 2.5 and with mixtures stratification.

The remaining sections of this paper are organized as follows. The experimental setup section outlines the experimental conditions and the method of analyzing combustion characteristics. The results and discussion section is divided into sub-sections covering the analysis of combustion characteristics, engine thermal efficiency, and emissions based on the experimental results. Initially, the effects of varying CR and injection timing are elucidated. Subsequently, the effects of varying injection timing under different λ conditions at high CR are discussed. Finally, the paper concludes the research with required future works.

2 Experimental Setup

2.1 Experimental Apparatus

For the experiment, a 0.4-L single-cylinder engine was used. Engine specifications are shown in Table 1. The CR of the engine was changed by replacing shim plates which had different heights. For the control of the engine, a Motec-m800 engine control unit (ECU) was used. Since the ECU was connected to a computer with the installed control program, the signal from the crankshaft position sensor (CKPS) and the camshaft position sensor (CMPS) were acquired. Additionally, the ECU produced signals to control the duration and timing of ignition and injection systems. For transmitting a specific signal to the ECU to determine the cycle interval, a National Instrument cRIO-9039, which received the engine rotation speed from an encoder and produced a real-time pulse signal every two revolutions, was used. A 190 kW AVL ELIN AC dynamometer was used to control constant engine speed and a throttle valve. By using a direct injector, the hydrogen fuels were directly injected into the cylinder at an injection pressure of 5 MPa. The mass flow rate of the injected hydrogen was measured using a Coriolis-type real-time fuel mass flowmeter (OVAL CA001). For measuring λ, Horiba MEXA-110 λ and ECM 5230 were installed at the end of the exhaust manifold. A spark-plug-type pressure sensor (Kistler 6113C) was installed on the cylinder for measurement of the in-cylinder pressure, and combustion analysis was performed using a combustion analyzer (Kistler Kibox to go 2893). The combustion results, including in-cylinder pressure traces, were aligned to the ° crank angle (CA) domain based on the CKPS signal and recorded in a unit of 0.1°CA for 200 cycles. The NOx emissions were measured using an emissions analyzer (Horiba MEXA-7100 DEGR). More details about measuring devices are presented in Table 2. A schematic of the experimental setup is presented in Fig. 1.

Table 1 Engine specifications
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Table 2 Measuring device specifications
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Fig. 1
figure 1

Schematic of the experimental setup

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2.2 Experimental Procedure

The engine speed was fixed at 1500 rpm for all experimental cases. The throttle was widely opened and the intake pressure was fixed at 0.1 MPa. Injection timing was varied from before top dead center (BTDC) 200 to 120°CA with an interval of 40°CA. Firstly, the experiment with CR 10, 12, and 14 was performed at a rich limit with ignition timing of the maximum brake torque timing (MBT) for each CR. Subsequently, since combustion, engine performances, and emissions are significantly influenced not only by CR and injection timing but also by excessive air ratio (Kim et al., 2023; Lee et al., 2022; Nande et al., 2008), varying excessive air ratio experiments were carried out for fixed CR of 14. Detailed experimental conditions are provided in Table 3.

Table 3 Experimental conditions
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2.3 Thermodynamic-Based Combustion Analysis

Indicated thermal efficiency (ITE), net heat release rate (HRR), combustion loss, heat transfer loss, and exhaust loss were calculated by Eqs. (1) –(9) (Heywood, 1988).

Indicated thermal efficiency (ITE) and the net heat release rate (HRR) were calculated by following Eq. (1) and (2).

$${\text{ITE}}= \frac{{W}_{{\text{indicated}}}}{{m}_{{\text{fuel}}} \times {Q}_{{\text{LHV}}}},$$
(1)

where Windicated is the indicated work of a cycle, mfuel is the amount of injected fuels into the cylinder per cycle, and QLHV is the lower heating value of the hydrogen.

$$\text{Net HRR} \left(\frac{{\text{d}}{Q}_{n}}{{{\text{d}}}_{\theta }}\right)=\frac{\gamma }{\gamma -1}P\frac{{\text{d}}V}{{\text{d}}\theta }+ \frac{1}{\gamma -1}V\frac{{\text{d}}P}{{\text{d}}\theta },$$
(2)

where the specific heat ratio, γ was assumed to be 1.3. The net HRR was summed cumulatively with respect to θ to obtain the cumulative heat release rate. The CA at which the cumulative heat release rate reached its maximum value, designated as the end of combustion (EOC) was used to determine the mass fraction burned (MFB) percentile.

Total input energy was assumed to be composed of the gross work, heat transfer loss, exhaust loss, and combustion loss as presented in Eq. (3). Therefore, by analyzing the chemical HRR, which is composed of the net HRR, the crevice effects term and the heat transfer rate, the combustion loss, heat loss, and exhaust loss can be derived. The crevice term was assumed to be 0.

$$\text{Total energy}=\text{Gross work}+\text{Heat tranfer loss}+\text{ Exhaust loss}+\text{combustion loss}$$
(3)
$$\text{Chemical HRR} \left(\frac{{\text{d}}{Q}_{{\text{ch}}}}{{{\text{d}}}_{\theta }}\right)=\text{Net HRR}+{V}_{{\text{cr}}}\left[\frac{{T}{^\prime}}{{T}_{W}}+ \frac{T}{{T}_{W}\left(\gamma -1\right)}+\frac{1}{b{T}_{W}}\mathit{ln}\left(\frac{\gamma -1}{{\gamma }{^\prime}-1}\right)\right]\frac{{\text{d}}P}{{\text{d}}\theta }+ \frac{{\text{d}}{Q}_{ht}}{{d}_{\theta }}$$
(4)
$$\text{Gross work}={\int }_{{\theta }_{{\text{start}}}}^{{\theta }_{{\text{end}}}}\frac{{\text{d}}{Q}_{n}}{{d}_{\theta }}{\text{d}}\theta$$
(5)
$$\text{Combustion loss}={m}_{{\text{fuel}}}\times {Q}_{{\text{LHV}}}-{Q}_{{\text{ch}}}$$
(6)
$$\text{Heat transfer loss}={\int }_{{\theta }_{{\text{start}}}}^{{\theta }_{{\text{end}}}}\frac{d{Q}_{ht}}{{d}_{\theta }}{\text{d}}\theta ={\int }_{{\theta }_{{\text{start}}}}^{{\theta }_{{\text{end}}}}{Ah}_{c}(T-{T}_{w}){\text{d}}\theta$$
(7)

where θstart is combustion start CA, θend is combustion end CA, A is the surface area of the combustion chamber, T is the mean gas temperature, and Tw is the mean wall temperature. The convective heat transfer coefficient, hc was determined by Eq. (8).

$${h}_{c}=3.26\times {B}^{-0.2}\times {p}^{0.8}\times {T}^{-0.55}\times {w}^{0.8}$$
(8)

where B is the length of the bore, p is instantaneous cylinder pressure. The average cylinder gas velocity, w was determined by Eq. (9).

$$w= {C}_{1}\times {\overline{S} }_{p}+{C}_{2}\times \frac{{V}_{d} \times {T}_{r}}{{P}_{r }\times {V}_{r}}\times (p-{p}_{m})$$
(9)

where \(\overline{S}_{p}\) is the average piston speed, Vd is the displaced volume, pr, Vr, Tr are the pressure, volume, and temperature of the working fluid, and pm is the motored cylinder pressure at the same crank angle as p. C1 was 6.18 and 2.28 during the gas exchange period, and the rest of periods, respectively. During the gas exchange and compression period, C2 was 0, while during the combustion and expansion period, it was 3.24 × 10–3 (Heywood, 1988).

By subtracting the results of Eqs. (5), (6), (7) from Eq. (3), the exhaust loss was calculated.

2.4 Knocking Incidence Analysis

Knocking incidence refers to the percentage of knocking cycles out of the total 200 cycles recorded in the combustion analyzer. To determine knocking cycles, cycles in the in-cylinder pressure data stored in the combustion analyzer where the maximum amplitude of pressure oscillations exceeded a specific value were determined as knocking cycles according to the maximum amplitude of pressure oscillations (MAPO) method (Shahlari & Ghandhi, 2012).

3 Results and Discussion

3.1 Effects of Compression Ratio and Injection timing

3.1.1 Analysis of Combustion Characteristics

Figure 3 shows in-cylinder pressure and HRR for different CRs of 10, 12, and 14 at the injection timing BTDC 200, 160, and 120°CA. As shown in Fig. 3a, it is observed that as the injection timing was retarded, the peak of HRR decreased. This can be attributed to the reduced duration of the injected fuel to mix with the air due to the retarded injection timing. Since early injection timing allowed to make more homogeneous mixtures, HRR was increased compared to stratified mixtures induced by late injection timing (White et al., 2006).

Fig. 3
figure 2

In-cylinder pressure and heat release rate for the compression ratio 10 (a), 12 (b), and 14 (c) at the injection timing BTDC 200, 160, and 120°CA

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In contrast, Fig. 3b, c show that the decreasing trend in the peak of heat release rate with respect to the injection timing diminished. Specifically, the peak of HRR, which was the highest at the injection timing of BTDC 200°CA for the CR of 10, became similar to the injection timing of BTDC 160°CA for the CR of 12. Moreover, for the CR of 14, the peak of the HRR decreased compared to the injection timing of BTDC 160°CA, approaching a similar level of the peak of HRR at the injection timing of BTDC 120°CA. This changing trend in HRR with respect to the CR and the injection timing, suggests that the enhanced efficiency of heat release during the combustion process at higher CR, in comparison to lower CR (Sadiq Al-Baghdadi, 2004), was further accentuated under stratified mixture conditions.

In addition, Fig. 4 illustrates that HRR after TDC decreased as the CR increased. This decrease in late combustion with the increase in the CR was attributed to the higher CR leading to an increase in the rate of mass burning due to a higher burning velocity (Sadiq Al-Baghdadi, 2004). The accelerated combustion resulted in more complete combustion over shorter durations, contributing to the decrease in exhaust gas temperature with the increasing CR despite the retarded MFB50, as shown in Fig. 5

Fig. 4
figure 3

In-cylinder pressure and heat release rate for the compression ratio 10 (a), 12 (b), and 14 (c) at the injection timing BTDC 120°CA

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Fig. 5
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a Exhaust gas temperature and b MFB50 for the compression ratio 10, 12, and 14 at the injection timing BTDC 200, 160, and 120°CA

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Figure 6 illustrates the peak pressure, maximum pressure rise rate (MPRR), and knocking incidence for CR 10,12, and 14 at the injection timing BTDC 200, 160, and 120°CA. In Fig. 6a, it is shown that as the CR increased across all injection timings, the peak pressure also increased. Although the peak pressure reached the highest point for all CRs at the injection timing BTDC 160°CA, an analysis of the peak pressure increase rate concerning the increase of the CR from 10 to 14 reveals that the highest increase rate occurred at the injection timing BTDC 120°CA, measuring at 22.4%. The injection timing BTDC 200°CA and 160°CA exhibited increase rates of 13.3% and 20.3%, respectively.

Fig. 6
figure 5

a Peak pressure, b MPRR, and c Knocking incidence for the compression ratio 10, 12, and 14 at the injection timing BTDC 200, 160, and 120°CA

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The lower increase rate of peak pressure at injection timings BTDC 200°CA and 160°CA is associated with the MPRR, as depicted in Fig. 6b. The CR 10 and 12 almost reached the MPRR limit of 0.5 MPa/deg across all injection timings. In contrast, reaching the MPRR limit for the CR 14 at the injection timing BTDC 200°CA and 160°CA was impossible. The inability to achieve the MPRR limit for CR 14 was attributed to significant knocking incidence, as shown in Fig. 6c, resulting from rapid combustion induced by the formation of the homogeneous mixtures by early injection at high CR (Gong et al., 2020; Park et al., 2022; Verhelst & Wallner, 2009).

At the injection timing BTDC 200°CA, there was no knocking incidence for CR 10, whereas CR 12 and 14 had knocking incidences of 18%. Additionally, the CR 12 exhibited a significant reduction in knocking incidence as the injection timing was retarded. In contrast, the CR14 showed a knocking incidence of 14% even at the injection timing BTDC 160°CA. The high knocking incidence at high CR 14 highlights a drawback that the high CR led to a rapid increase in in-cylinder temperature and pressure during combustion, inducing knocking (Stępień, 2021). This frequent knocking incidence resulted in a reduction of peak pressure, which could have reached a larger value under MPRR limit conditions.

It is observed that knocking incidence decreased with retarded injection timing for all CRs. In the case of the injection timing BTDC 120°CA, mixture stratification allowed to reduce knocking even at the CR 14. This was attributed to the leaner end gas of stratified mixtures formed by late injection, which lowered the combustion temperature of the burned gas near the cylinder wall (Shudo et al., 2003).

This lowest knocking incidence of the CR 14 at the injection timing BTDC 120°CA enabled reaching MPRR almost to its limit and achieving maximum peak pressure under the given operating conditions, consequently leading to the highest observed increase rate of peak pressure among the injection timing BTDC 200, 160, and 120°CA.

Eventually, the highest increase rate of peak pressure and MPRR of the CR 14 at the injection timing 120°CA underscores that mixture stratification by late injection was an effective injection strategy to prevent knock and achieve high loads under the high CR (Lee, 2024).

Figure 7 indicates the combustion duration for CR 10, 12, and 14 at the injection timing BTDC 200, 160, and 120°CA. As the injection timing was retarded in all CRs, it is observed that the combustion duration increased, consistent with previous studies that showed a decrease in combustion duration in homogeneous mixtures formed by early injection (Homan et al., 1983; Verhelst & Wallner, 2009). To be specific, it is noted that as the injection timing was retarded, the Ignition-MFB10, which represents the flame development duration after ignition, increased due to relatively higher degree of stratification (Lee et al., 2022).

Fig. 7
figure 6

Combustion duration for the compression ratio 10, 12, and 14 at the injection timing BTDC 200, 160, and 120°CA

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In contrast to the case of the injection timing BTDC 200°CA, at the injection timing BTDC 160 and 120°CA, the Ignition-MFB10 decreased with an increase in the CR. This demonstrates that the decrease in the flame development duration due to an increase in the CR was more pronounced under stratified conditions.

3.1.2 Analysis of Engine Thermal Efficiency and NOx Emissions

Figure 8 shows the ITE for the CR 10, 12, and 14 at the injection timing BTDC 200, 160, and 120°CA. As the CR increased at all injection timings, the ITE increased, consistent with the results of previous studies (Caton, 2012; Eichlseder et al., 2003). Furthermore, it is observed that as the injection timing was retarded at all CRs, the ITE increased, reaching the ITE of 40.6% for CR 14 at the injection timing BTDC 120°CA. The improvement in the ITE with retarded injection timing was attributed to the reduced combustion loss as shown in Fig. 9. In the case of the injection timing BTDC 200°CA, the proportion of combustion loss in the lower heating value (LHV) breakdown was 15%. In contrast, the injection timing BTDC 120°CA showed 8.5% combustion loss in the LHV breakdown.

Fig. 8
figure 7

Indicated thermal efficiency for the compression ratio 10, 12, and 14 at the injection timing BTDC 200, 160, and 120°CA

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Fig. 9
figure 8

LHV breakdown for the compression ratio 14 at the injection timing BTDC 200, 160, and 120°CA

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Since the fuels were injected into the cylinder during the compression stroke before the intake valve closing (IVC) at the injection timing BTDC 200 and 160°CA, less fuel remained in the cylinder compared to the injection timing BTDC 120°CA, at which the fuels were fully injected after IVC. In other words, the fuels remaining in the cylinder were lower than the amount, which were actually injected, resulting in substantial combustion loss.

Although most previous researchers explained that late injection creates relatively lean mixtures near the cylinder wall, reducing heat transfer between burned gas and the cylinder wall during combustion, thus decreasing heat transfer loss (Lee et al., 2022; Shudo et al., 2003; Verhelst & Wallner, 2009; White et al., 2006), the analysis of the LHV breakdown shows that the late injection did not reduce the heat transfer loss. This can be attributed to the increased combustion duration at the late injection timings. However, it is noteworthy that the increased rate of the heat loss decreased with the retardation of the injection timing. To be specific, when the injection timing was retarded from BTDC 200 to BTDC 160°CA, the increased rate of heat transfer loss was 25.3%.

In contrast, when the injection timing was retarded from BTDC 160 to BTDC 120°CA, the increased rate of heat transfer loss was 5%. This significantly reduced increase rate of heat transfer loss at the injection timing of BTDC 120°CA demonstrates that, despite the longer combustion duration as depicted in Fig. 7, the mixture stratification is an effective injection strategy for heat loss reduction by reducing the combustion temperature of burned gas near the cylinder wall.

Generally, high CRs, high-temperature, and high-pressure conditions are formed in the cylinder during combustion, leading to a significant amount of NOx emissions (Mogi et al., 2022). However, experimental results in Fig. 10 do not show a proportional increase in Nox emissions with the CR. This was related to the occurrence of knocking under specific operating conditions and its impact on the ignition timing. At the injection timing BTDC 200°CA, the CR 12 and 14, as shown in Fig. 6-©, exhibited high knocking incidence, resulting in retarded ignition timing. Despite the higher CR, the NOx emissions for the CR 12 and 14 were lower compared to the CR 10. While 20.1 and 8.2 g/kWh of NOx emissions were emitted for CR 12 and 14, respectively, 22.5 g/kWh of NOx emissions were emitted for CR 10. Even at the injection timing BTDC 160°CA, CR 14 shows a higher knocking incidence compared to other CRs, leading to the lowest NOx emissions due to late ignition timing. This was attributed to the delayed ignition timing reducing combustion temperature and, consequently, decreasing NOx emissions (Xu et al., 2019). Although the ignition timing of the CR 14 was only 0.2°CA retarded than the CR 12 at the injection timing BTDC 200°CA, the MFB 50 of the CR 14 achieved 1.5°CA later than that of the CR 12 as shown in Fig. 5b. This indicates that the retarded ignition timing led to a reduction in combustion temperature and in turn, a delayed combustion process.

Fig. 10
figure 9

A NOx emissions for the compression ratio 10, 12, and 14 at the injection timing BTDC 200, 160, and 120°CA

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These experimental results align with previous studies indicating that NOx emissions are highly sensitive not only to the CR but also to the ignition timing (Lim et al., 2014; Sopena et al., 2010). Moreover, except for the CR 14, it can be observed that NOx emissions decreased as the injection timing was retarded for all CRs. This is because late injection, particularly under high engine load, created stratified mixtures with zones which both richer and leaner than stoichiometric, avoiding the formation of excessive air ratio regime where NOx generation is severe, thereby reducing overall NOx emissions (Verhelst & Wallner, 2009). In summary, under rich limit conditions, early injection resulted in overall stoichiometric homogeneous mixtures, leading to higher NOx emissions.

To summarize Sect. 3.1, increasing CR in the hydrogen direct-injection spark ignition engine enhanced the ITE by increasing effective heat release during a short duration. However, this also raised in-cylinder temperature and pressure during combustion, leading to higher knocking incidence. Additionally, the late injection reduced combustion loss by leaving more fuels in the cylinder, further improving thermal efficiency. Notably, although the late injection induced a larger proportion of heat loss in the LHV breakdown due to increased combustion duration, reduced combustion temperatures by mixture stratification decreased knocking incidence at high CR. Moreover, advancing ignition timing resulted in decreased NOx emissions at high CR, and under high-load conditions, delaying injection timing correlated with reduced NOx emissions.

3.2 Effects of Injection Timing and Excessive Air Ratio

3.2.1 Analysis of Combustion Characteristics

Figure 11 shows peak pressure and MPRR for the CR 14 at injection timing BTDC 200, 160, and 120°CA under various λ. As shown in Fig. 11a, the peak pressure decreased with an increase in λ for all injection timings. This can be attributed to the fact that the engine load was determined by the injected fuel rates under wide-open throttle conditions. In other words, lower injected fuel rates resulted in a higher excess air ratio, leading to lower peak pressures.

Fig. 11
figure 10

a Peak pressure and b MPRR for compression ratio 14 at the injection timing BTDC 200, 160, and 120°CA under various excessive air ratios

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The injection timing BTDC 200°CA achieved the lowest peak pressure under all λ conditions. This was because fewer amounts of fuel remained in the cylinder compared to other injection timings due to early injection, as explained in Sect. 3.1.2. The lowest amount of fuel that remained in the cylinder resulted in the lowest peak pressure, despite the same amount of injected fuel.

Similar to the case where CR 10, 12, and 14 exhibited the highest peak pressure at the injection timing BTDC 160°CA as explained in Sect. 3.1.1, the injection timing BTDC 160°CA achieved the highest peak pressure from λ = 1.8–2.0. However, as the λ became leaner, the injection timing BTDC 120°CA achieved a similar peak pressure to the injection timing BTDC 160°CA. At λ = 3.0, the injection timing BTDC 120°CA reached a higher peak pressure compared to that of the injection timing BTDC 160°CA. This was because despite of longer combustion duration compared to other injection timings, combustion of the stratified end gas reduced heat losses between combustion gas and cylinder wall, leading to an increase in peak pressure. These reduced heat losses induced by mixture stratification resulted in higher ITE, which is explained in Sect. 3.2.2.

In Fig. 11b, the MPRR decreased as the λ increased. For λ = 1.8 and 2.0, MPRR was the highest at injection timing BTDC 120°CA, but for λ = 2.2 and above, there was little difference in MPRR based on injection timing. This can be attributed to the fact that, in the case of stratified mixtures, a local hydrogen-rich mixture was formed near the spark plug under relatively richer λ conditions, leading to a rapid pressure rise as the mixture burned (Lee et al., 2022). As depicted in Fig. 12, injection timing BTDC 120°CA at λ = 2.0 exhibited a much shorter MFB50-90 compared to MFB10-50. Specifically, whereas injection timing BTDC 160 and 200°CA at λ = 2.0 exhibited 0.3 and 0.4°CA shorter MFB50-90 than MFB10-50, injection timing BTDC 120°CA exhibited 1.4°CA shorter MFB50-90 than MFB10-50. This indicates that combustion of the local hydrogen-rich mixture caused rapid combustion in the latter part of the main combustion, resulting in a high MPRR.

Fig. 12
figure 11

Combustion durations for compression ratio 14 at the injection timing BTDC 200, 160, and 120°CA under excessive air ratios of 2.0, 2.2, and 2.5

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The combustion durations for the CR 14 at injection timings of BTDC 200, 160, and 120°CA under λ of 2.0, 2.2, and 2.5 are illustrated in Fig. 12. As previously explained, since the combustion of stratified mixtures is slower than that of homogeneous mixtures, the retarded injection timing resulted in an increased combustion duration. Additionally, all injection timings led to a reduced combustion duration as λ became leaner. As analyzed in Sect. 3.1.1, with the retarded injection timing, the flame development duration, represented by Ignition-MFB10, increased. Notably, at injection timing BTDC 120°CA, MFB50-90 was shorter than MFB10-50, distinguishing it from other injection timings. These experimental findings underscore the combustion characteristics of stratified mixtures, indicating difficulty in flame development and concentration towards the latter part of the main combustion.

3.2.2 Analysis of Engine Thermal Efficiency and NOx Emissions

The ITE and NOx emissions for the CR 14 injection timing BTDC 200, 160, and 120°CA under various λ are shown in Fig. 13. As shown in Fig. 13a, at each λ, the ITE increased as the injection timing was retarded. Specifically, the injection timing BTDC 120°CA demonstrated the highest ITE among all injection timings at every λ, achieving the highest ITE of 42.3% at λ = 2.2.

Fig. 13
figure 12

a Indicated thermal efficiency and b NOx emissions for compression ratio 14 at the injection timing BTDC 200, 160, and 120°CA under various excessive air ratios

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As shown in Fig. 14, the reason for the higher ITE of the retarded injection timing compared to the advanced injection timing was mainly attributed to the lower combustion loss as explained in Sect. 3.1.2. A notable distinction from the findings in Sect. 3.1.2 is the reduction in heat loss observed at the injection timing of BTDC 120°CA. Considering that the λ condition was 2.2, contrasting with the experiment in Sect. 3.1 conducted at the rich limit, it can be inferred that the heat loss reduction due to mixtures stratification became more pronounced at specific λ conditions.

Fig. 14
figure 13

LHV breakdown for compression ratio 14 at the injection timing BTDC 200, 160, and 120°CA under an excessive air ratio of 2.2

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For analyzing an effect λ on the proportion of heat loss in LHV breakdown, the proportion of heat loss in the LHV breakdown for the CR 14 under various λ conditions is shown in Fig. 15. Whereas at λ = 2.5 and 2.8, the ITE was 42.2% and 42%, respectively, which were lower than that at λ = 2.2, the proportion of heat loss in the LHV breakdown was 17.2% and 17.6%, respectively, lower than the 19.3% observed at λ = 2.2. This can be attributed to that although the lower combustion temperature at leaner λ conditions led to a reduction in heat transfer, the increased combustion duration resulted in a decrease in constant volume combustion. These findings underscore that determining λ for maximizing thermal efficiency under stratified mixture conditions is a matter of finding the balance between the advantages of constant volume combustion and the disadvantages of heat loss.

Fig. 15
figure 14

Proportion of heat loss in LHV breakdown for compression ratio 14 at the injection timing BTDC 120°CA under various excessive air ratios

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Figure 13b shows an increase in NOx emissions with the retardation of injection timing. This trend contradicts the analysis results in Sect. 3.1.2. The reason was that, unlike Sect. 3.1, which operated at high loads, Sect. 3.2 operated at relatively low loads as the λ increased. In contrast to high loads, the combustion of stratified mixtures with hydrogen-rich zones formed by late injection significantly increases NOx emissions at low loads (Verhelst & Wallner, 2009). It is noteworthy that at λ = 2.5, NOx emissions for all injection timings were below 1 g/kWh. This indicates that mixture stratification is a very effective injection strategy, which can achieve both high ITE and low NOx emissions under very lean λ conditions, λ = 2.5 and above.

4 Conclusion

In this study, two experiments were conducted at an engine speed of 1500 rpm in a single-cylinder DISI engine. The first experiment aimed to analyze the effects of compression ratio and injection timing on the combustion characteristics, engine thermal efficiency, and NOx emissions under rich limit conditions. The second experiment focused on examining the effects of injection timing and excessive air ratio on the combustion characteristics, engine thermal efficiency, and NOx emissions for CR 14. The following conclusions were drawn.

  1. 1.

    Combustion characteristics: Under rich limit conditions, the higher CR with stratified mixtures reduced the incidence of knocking due to the lower combustion temperature of leaner end gas near the cylinder wall, leading to expanded engine loads. Under lean λ conditions, the stratified mixtures led to increased Igntion-MFB10 and reduced MFB50-90. Particularly, operation at lean conditions above λ = 2.2 resulted in a reduced MPRR by alleviating concentrated combustion in stratified mixtures during MFB50-90.

  2. 2.

    Engine thermal efficiency: Under rich limit conditions, retarding injection timing resulted in the higher ITE for all CRs due to the reduced combustion loss and a reduced rate of increase in heat loss in the LHV breakdown. For CR 14 at λ = 2.2, the reduced proportion of heat loss in the LHV breakdown with increased constant volume combustion from a shorter combustion duration led to the maximum ITE of 42.3%. The lower ITE at λ = 2.5 and 2.8 despite the lower proportion of heat loss in the LHV breakdown revealed a trade-off between lower heat loss and reduced constant volume combustion in the lean operation of stratified mixtures.

  3. 3.

    NOx emissions: The higher CR with homogeneous mixtures resulted in lower NOx emissions due to retarded ignition timing to avoid severe knocking incidence. Whereas the NOx emissions decreased with retardation of injection timing under rich limit conditions, the NOx emissions increased with retardation of injection timing under lean operation conditions. However, above λ = 2.5, NOx emissions were lower than 1 g/kWh for all injection timings.

Since the injector used in this experiment was a conventional turbo-gasoline direct injector (T-GDI), further retardation of injection timing was limited due to the long injection duration, leading to less stratification and a lower maximum engine load. Therefore, future studies should utilize a hydrogen-specific injector, capable of shorter injection durations for bulky hydrogen, to investigate its effects on combustion characteristics, engine thermal efficiency, NOx emissions, and the potential for engine load expansion. By using the hydrogen injector, the effects of injection timing closer to TDC on combustion characteristics, engine thermal efficiency, NOx emissions, and engine load expansion should be studied.