<figure><img src="image_1.png" /></figure>

Full Length Article

# Experimental investigation of NOₓ impact on ignition delay times for lean H₂/air mixtures using a rapid compression machine under internal combustion engine conditions

N. Villenave<sup>a, *</sup>, G. Dayma<sup>b, c</sup>, P. Brequigny<sup>a</sup>, F. Foucher<sup>a</sup>

ARTICLE INFO

Keywords:

Hydrogen

Nitric oxides

Ignition delay times

Rapid compression machine

Internal combustion engines

Kinetic mechanisms

A B S T R A C T

This study investigates the effects of nitric oxides addition on ignition delay times of lean hydrogen/air mixtures ($\varphi = 0.4$), in the 890 K – 1000 K temperature range and for medium-to-high compression pressures ($p_C = 30, 40, 50$, and 60 bar). Results show that ignition delay times decrease with the addition of nitric oxide and nitrogen dioxide, regardless of the compression pressure. These datasets provide new insights to assess the validity of kinetic mechanisms under such conditions and predict autoignition phenomena. As such, a comparison with recent kinetic mechanisms is conducted. A sensitivity analysis on OH radical is performed and highlights the role of the $HO_2/H_2O_2$ and NO/NO₂ recycling sequences in OH production, yielding an increase in the mixture reactivity. Finally, this work highlighted the importance weight of (R17) in reactivity enhancement and gave a perspective to optimize NOₓ sub-mechanisms for hydrogen ignition under internal combustion engine conditions.

1. Introduction

Global warming is a crucial issue in the upcoming years, and the acceleration of the energy transition can no longer be postponed. The European "Net Zero Emission" scenario consists in the entire replacement of fossil fuels by renewable energy and free-carbon devices to limit the increase up to 1.5 °C by 2050 [1,2]. The transport sector is the second most polluting sector with emissions of around 7000 Mt of CO₂ in 2020 [3]. The key to decarbonizing this industry is replacing hydrocarbons such as diesel and gasoline with promising green e-fuels such as hydrogen ($H_2$). Hydrogen internal combustion engines ($H_2$ICEs) are a way to drastically reduce greenhouse gas emissions, especially if $H_2$ is produced through water electrolysis and/or photochemical water-splitting instead of methane steam-reforming [4]. Moreover, $H_2$ICEs are attractive because they allow an increase in thermal efficiency in comparison to hydrocarbon-fueled ICEs [5]. As a matter of fact, in comparison to hydrocarbon fuels, $H_2$ combustion properties, presented in Table 1, are promising, and its use as a fuel offers many advantages [6]. For example, the laminar flame speed of $H_2$ (~2.4 m/s) is almost five times higher than that of gasoline ($C_8H_{18}$) (~0.4 m/s) at the stoichiometry ($\varphi = 1$), ambient temperature and standard pressure. This

difference partly explains the higher efficiency of $H_2$ICEs, attributed to its faster combustion speed and wide range of flammability. However, such flame properties also brings disadvantages, especially for internal combustion engines where almost all abnormal combustion phenomenon are attributed to both properties.

It is important to emphasize that the concept of $H_2$ICE is hardly a new development. Das et al. [7] presented an overview of the development of $H_2$ICEs since 1930. This study highlights various undesirable combustion phenomena due to the physico-chemical properties of $H_2$ such as backfire, pre-ignition, and knocking. For the sake of clarity, backfire is a phenomenon induced by the interaction between the inlet $H_2$/air mixture with a source of high thermal energy to start combustion while the intake valves are still open. Pre-ignition occurs when the $H_2$/air mixture ignites before the spark timing while knocks are close to the pre-ignition problems caused by hot spots created far from the valve in the combustion chamber. Furthermore, the $H_2$ flame temperature is high (~2400 K at $\varphi = 1$), prone to high pollutant emissions especially nitric oxides (NO, $NO_2$) through the thermal-NO formation path, in addition to prompt-NO and $N_2O$ routes [8]. For all these reasons, recent studies, presented in [9], agreed on the use of ultra-lean ($\varphi < 0.4$) $H_2$/air combustion combined with exhaust gas recirculation devices, in $H_2$ spark-

<footnote><sup>a</sup> Univ. Orléans, INSA-CVL, PRISME, EA 4229, F45072 Orléans, France</footnote>

<footnote><sup>b</sup> CNRS ICARE, Avenue de la Recherche Scientifique, 45071 Orléans Cedex 2, France</footnote>

<footnote><sup>c</sup> Université d'Orléans, Orléans Cedex 2, France</footnote>

<footnote>* Corresponding author at: Univ. Orléans, INSA-CVL, PRISME, EA 4229, F45072 Orléans, France.</footnote>

<footnote>E-mail address: nicolas.villenave@univ-orleans.fr (N. Villenave).</footnote>
<caption>**Table 1**</caption>

Hydrogen/air, iso-octane/air, methanol/air, and methane/air properties at T = 298 K and p = 1 bar.

<table><thead><tr><th></th><th>Hydrogen</th><th>Gasoline</th><th>Methanol</th><th>Methane</th></tr></thead><tbody><tr><td>Formula</td><td>H<sub>2</sub></td><td>C<sub>8</sub>H<sub>18</sub></td><td>CH<sub>3</sub>OH</td><td>CH<sub>4</sub></td></tr><tr><td>Density (kg/m<sup>3</sup>)</td><td>0.08</td><td>692</td><td>0.791</td><td>0.716</td></tr><tr><td>Flammability range (φ)</td><td>0.2 – 7</td><td>0.7 – 4</td><td>0.5 – 4.0</td><td>0.5 – 1.7</td></tr><tr><td>Low Heating Value (MJ/kg)</td><td>120</td><td>44.3</td><td>23</td><td>55.5</td></tr><tr><td>Auto-ignition Temperature (K)</td><td>860</td><td>680</td><td>632</td><td>506</td></tr><tr><td>Adiabatic Temperature (K)</td><td>2380</td><td>2275</td><td>2150</td><td>2226</td></tr><tr><td>Laminar Flame Speed (m/s)</td><td>2.4</td><td>0.4</td><td>0.43</td><td>0.48</td></tr></tbody></table>

ignition engines (H₂SIEs), to avoid undesirable combustion phenomena such as the so-called “super-knocking”, while mitigating NO and NO₂ emissions.

Exhaust gas recirculation (EGR) is a promising strategy due to its high-dilution and low-temperature characteristics, promoting species distribution and temperature homogeneity, and thus mitigating NOₓ production inside the combustion chamber. The effect of water injection via EGR on NOₓ emission and combustion parameters of a H₂SIE has been studied and shows an important reduction in NO levels, an increase in the ignition delay, and combustion duration, but no change in cyclic variations under lean conditions [10]. Although water injection has shown great capacity to improve thermal efficiency and NOₓ emissions in SIE, some challenges remain: water injection control, water supply systems, water wall wetting, and water injection impact on engine aging [11]. Exhaust gas recirculation (EGR) can be used in both Compression Ignition Engines (CIEs) and SIEs to mitigate NOₓ emissions. Indeed, using EGR will reduce the combustion temperature inhibiting NOₓ formation. Dhyani et al. [12] performed an experimental study on the EGR effect in a constant-speed multi-cylinder SIE fuelled with H₂, under stoichiometric conditions, to control combustion anomalies as backfire or knocking and reduce NOₓ emissions. The EGR rate varied from 0 % to 28 % by volume at a 15 kW load. EGR reduces backfire phenomena and their propagation by a dilution effect and a reduction in flame speed. NOₓ emissions decrease when EGR increases. At a high EGR rate, issues with the stability of the combustion process were observed. However, for 25 % EGR, results show a diminution of 57 % for NOₓ emissions. The same results were obtained by Nande et al. [13]. EGR was considered as a method for the reduction of knocking and NOₓ emissions for stoichiometric operations. Experiments were carried out on a single-cylinder CFR engine at 900 rpm under part-load operation with 410 kPa Net Indicated Mean Effective Pressure, φ = 1, three different compression ratios (8:1, 10:1, and 12:1), and for various spark timings. Results show that low levels of EGR imply longer combustion duration, and reduction of knock intensities. NOₓ emissions decrease from 2500, 3250, and 4250 ppm (respectively to the compression ratio) for 0 % EGR to almost 0 at 35 % EGR regardless of the compression ratio. Hence, the use of EGR in H₂SIEs is a good way to find a trade-off between lean engine condition performance and low NOₓ emissions. Nevertheless, it has been shown that the species in EGR may impact the combustion in different ways [14,15], especially if a long-route or a short-route EGR loop (after or before the catalyst respectively) is used, NO and NO₂ are present in the air-EGR mixture at the intake.

A key to understand the impact of NOₓ on hydrogen combustion is the study of H₂/Air/NOₓ autoignition characteristics under ICE conditions. The use of a rapid compression machine (RCM) facility enables to

reach high-pressure and low-temperature conditions in the “weakly explosive” zone, as illustrated in Fig. 1, which are very close to relevant engine conditions. Several studies have been conducted on the impact of NOₓ on hydrocarbons ignition delays using a RCM and mimicking ICE conditions (650 K < T < 1000 K, 15 bar < p < 100 bar) [16–22]. These work highlights the non-linear impact of NOₓ addition on mixtures reactivity and draws attention on the accuracy of the chemical models.

According to the best of the author’s knowledge, few recent studies report the impact of NOₓ on H₂/O₂/diluent ignition delay times, particularly under H₂SIEs conditions. This topic was first investigated by Slack and Grillo [23] measuring the impact of NO and NO₂ on induction times for stoichiometric H₂/air mixtures at p = 0.27 – 3.0 atm, T = 800 – 1500 K, using a shock tube. A wide range of mixture compositions were studied: X<sub>NO</sub> = 0, 0.5, 1, 2.25, 4.5; X<sub>NO2</sub> = 0.75, 1.50, 3.56; X<sub>NO</sub>/X<sub>NO2</sub> = 1.1/0.85. General observation shows that NOₓ reduces significantly induction times. Later, the impact of NO₂ on H₂/O₂/Ar mixtures was studied by Mathieu et al. [24] also using shock tubes in a comprehensive modeling study. The study was performed for different NO₂ mole fractions (100, 400, and 1600 ppm), different φ for 100 ppm of NO₂ (0.3, 0.5, 1), and different pressure conditions (1.5, 13, and 30 atm). It shows an important dependence of ignition delays on the pressure and the NO₂ concentration in contrast to equivalence ratio variation. Regarding relevant H₂SIEs conditions (p = 30 atm), the addition of NO₂ enhances H₂/air mixture reactivity and reduces IDT, especially for the “lower” temperature conditions (~1050 K).

In light of these studies, it is crucial to study the impact of NOₓ on lean H₂/air ignition delays under SIE conditions. Noteworthy, to the best of the author’s knowledge, ignition delays of lean H₂/Air/NOₓ mixtures for low-to-intermediate temperature and medium-to-high pressure have never been investigated using a RCM. Therefore, the present work focuses on ignition delays measurement from lean H₂/Air/NOₓ mixtures on a RCM for a pressure range of 30 bar up to 60 bar, a temperature range of 890 K to 1000 K, and for NOₓ concentration variations from 50 ppm to 1250 ppm. Numerical simulations were performed to validate kinetic mechanisms and interpret the present results. Finally, sensitivity analyses were carried out for different NOₓ quantities and pressures to highlight the reactions involved in the mixture reactivity.

## 2. Experimental and numerical methodology

### 2.1. Experimental setup and ignition delay times measurement

The experimental facility used in this study is a rapid compression

<figure><img src="image_2.png" /><figcaption>**Fig. 1.** Explosion limits of H₂/O₂ mixtures at φ = 1.0.</figcaption></figure>
machine (RCM) designed at Orléans University. The RCM is illustrated in Fig. 2 and a detailed description of the RCM and its operating conditions can be found in [25]. The RCM is equipped with a single piston, pneumatically driven and hydraulically stopped at the end of the compression to reach the desired thermodynamic conditions at the top dead-center position. The piston used in this work has been designed with a crevice head to prevent vortex roll-up formation and ensure the homogeneity of the core gas [26]. This homogeneity allows the use of the adiabatic core hypothesis to calculate the conditions at the top dead center in the cylinder (see Section 2.2). The intake temperature ($T_0$) was measured with a K-thermocouple type with an uncertainty of ± 1 K. The intake pressure in the cylinder ($p_0$) and the pressure at the end of the compression ($p_C$) were measured with a pressure sensor KELLER PAA-33X/80794 (with an accuracy of 0.05 % FS over a range of 0 – 5 bar, corresponding to an uncertainty of 2.5 mbar) and with a piezoresistive transducer AVL QH32C (linearity of ± 0.2 % and accuracy of ± 1 %), respectively. The different H₂/Air/NOₓ mixtures studied here were prepared before the experiments in a stirred tank. The purity of the gases might influence the temperature-dependent specific heat ratio. As such, here is the uncertainty regarding the composition of each gas bottle (H₂: 99.993 %, O₂: 99.997 % and N₂: 99.986 %). The pressure sensor used on the reservoir is a KELLER PAA-21Y with an accuracy of 0.5 % FS over a range of 0 – 10 bar, corresponding to an uncertainty of 0.05 bar. This tank is filled with a mass flow controller BROOKS Cori-Flow M13V101 with an accuracy of ± 1 % on the flow rate.

The final temperature is deduced from the adiabatic core hypothesis as follows in Equation (1):

$$ \int_{T_0}^{T_C} \frac{\gamma}{\gamma - 1} \frac{dT}{T} = \int_{p_0}^{p_C} \frac{dp}{p} \qquad (1) $$

where $p_0$, $T_0$, $p_C$, $T_C$, and $\gamma$ are respectively the intake pressure, the intake temperature, the compression pressure, the compression temperature, and the temperature-dependent specific heat ratio. As shown in Fig. 3, IDT is determined from the experimental pressure trace and it is defined as the time between the TDC and the first-order time derivative of pressure.

Ignition delay times have been measured for both H₂/O₂/N₂ and H₂/O₂/N₂/NOₓ mixtures. These measurements were performed for lean conditions ($\phi$ = 0.4), low-to-intermediate temperature, and

<figure><img src="image_3.png" /><figcaption>Fig. 3. Experimental pressure profiles from the reactive and the non-reactive case. The reactive case was performed with H₂/O₂/N₂ mixture $\phi$ = 0.4, $T_C$ = 957 K, and $p_C$ = 30 bar. The non-reactive case was obtained by replacing O₂ with N₂ in the tank vessel to reach the same thermodynamic conditions as the reactive case.</figcaption></figure>

intermediate-to-high pressure as displayed in Table 2. At least three consecutive shots were recorded for each experimental condition to ensure repeatability and are plotted on the figures. Ignition delays statistical errors were determined using the Moffat methodology [27]. Additional uncertainty in ignition delay measurements also depends on the system acquisition frequency, which is equal to 10 kHz. Thus, the uncertainty on ignition delays is ± 0.1 ms, which is quite negligible. The uncertainties in compression temperatures were assessed following the approach detailed in the modeling study by Baigmohammadi et al. [28]. This assessment considered the purity of the gases, the pressure sensor of the tank vessel, the K-type thermocouple, the pressure sensor used for filling the combustion chamber, and also the piezoresistive pressure transducer used to measure the pressure evolution during the compression. To conclude, the temperature uncertainty at the end of compression is approximately ± 0.5 % (± 4 – 6 K). The focus was made on these operating points because it is of interest in the case of H₂-fuelled SI engines with and without EGR. Both reactive and non-reactive mixtures were studied. Pressure profiles from non-reactive cases were measured in order to represent heat losses in the simulations.

## 2.2. Numerical methodology

Closed-homogeneous reactor simulations were performed using the simulation code CHEMKIN PRO [29] to test the capabilities of the recent

<caption>Table 2</caption>

RCM main characteristics for different experiments. The compression ratio (CR) corresponds to the volume ratio of the combustion chamber at the bottom dead centre configuration and at the top dead centre configuration respectively. $T_0$ and $p_0$ are the intake temperature and the intake pressure imposed respectively. $p_C$ is the compression pressure range measured and $T_C$ is the compression temperature obtained after the compression and calculated with the adiabatic core hypothesis.

<table><thead><tr><td>Parameters</td><td>Values</td></tr></thead><tbody><tr><td>CR [-]</td><td>13.2</td></tr><tr><td>Piston diameter [mm]</td><td>50</td></tr><tr><td>T<sub>0</sub> [K]</td><td>353 – 393</td></tr><tr><td>p<sub>0</sub> [bar]</td><td>0.890 – 1.965</td></tr><tr><td>T<sub>C</sub> [K]</td><td>890 – 970</td></tr><tr><td>p<sub>C</sub> [bar]</td><td>30/40/50/60</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>Fig. 2. Rapid compression machine (RCM) from Orléans University.</figcaption></figure>
kinetic mechanisms for H₂/O₂/N₂ and H₂/O₂/N₂/NOₓ mixtures at low- to intermediate temperature and medium-to-high pressure conditions. As such, effective adiabatic core volume was implemented using the non-reactive pressure trace to simulate accurately the isentropic compression and therefore account for heat losses before the ignition. Experimental results were compared with different kinetic mechanisms. An exhaustive list of kinetic mechanisms for hydrogen chemistry already exists [30], enabling IDTs prediction with varying degrees of accuracy, for lean H₂/air mixtures, under SIEs conditions. Three recent kinetic mechanisms, in alignment with the targeted conditions, were appraised and their range of validation are detailed in Table 3. In a previous study, Villenave et al. [31] proposed a kinetic mechanism for lean H₂/air mixtures, validated through a comparison with ignition delay measurements, conducted using a RCM at T<sub>C</sub> = 890 K – 1000 K, p<sub>C</sub> = 20 – 60 bar and φ = 0.2 – 0.5. This mechanism is based on the initial mechanism of Burke et al. [32] modified according to Klippenstein et al. [33] study with the addition of the self-reaction 2HO₂ = 2 OH + O₂. This kinetic mechanism has demonstrated excellent performance for hydrogen combustion. Simulations using this kinetic mechanism, to which an optimized NOₓ sub-mechanism from Glarborg et al. [34] was added, were performed. Furthermore, a comparison will be carried out with two optimized fuel/NOₓ kinetic mechanisms: the recently modified detailed kinetic mechanism NUIGMech1.2, proposed by Aljohani et al. [35], and the recent mechanism for H₂/CO/NOₓ chemistry proposed by Sun et al. [36]. A comparison will be also made with the GRI-Mech 3.0 mechanism [37], as it remains one of the most widely used kinetic mechanisms in the CFD community, although not designed to model hydrogen combustion. Additionally, it would be valuable to discuss the differences in the NOₓ sub-mechanism used by studied kinetic mechanisms. The kinetic mechanism from Aljohani et al. [35] incorporates the NOₓ sub-mechanism from Glarborg et al. [34]. Noteworthy, this model provides reasonable predictions of the formation and destruction of NO species while considering the significance of HONO/HNO₂ decomposition. The NOₓ sub-mechanism proposed by Sun et al. [36] is based on many constant rate reaction modifications using high-level quantum chemistry calculations and simulations to address the challenges in reproducing the kinetic decomposition of HONO and HNO₂ under high-pressure conditions. The NOₓ sub-chemistry is also presented in the GRI-Mech 3.0 [37] mechanism, but it is not optimized as it only considers the

<caption>**Table 3**</caption>

Kinetic mechanisms and experimental conditions for H₂/O₂/N₂/NOₓ and fuel/ O₂/N₂/NOₓ ignition delay times validation.

<table><thead><tr><th>Kinetic mechanisms</th><th>Experimental validation</th><th>Mixture</th><th>φ</th><th>p</th><th>T</th></tr></thead><tbody><tr><td rowspan="2">Villenave et al. [31]</td><td>Rapid</td><td>H₂/O₂/N₂</td><td>0.2 –</td><td>20 –</td><td>870 –</td></tr><tr><td>Compression Machine</td><td>X<sub>N2</sub>/X<sub>O2</sub> = 3.76</td><td>0.5</td><td>60 bar</td><td>1000 K</td></tr><tr><td rowspan="2">Aljohani et al. [35]</td><td>Rapid</td><td>Oxygenated</td><td>0.5 –</td><td>20 –</td><td>658 –</td></tr><tr><td>Compression Machine and Shock Tubes</td><td>Gasoline (Euro6 E10)/EGR/NOₓ/O₂/N₂<br>EGR: CO₂, H₂O, N₂<br>X<sub>NOx</sub> = 0, 874, 1501, 3174, 5568 ppm</td><td>1.0</td><td>30 bar</td><td>1598 K</td></tr><tr><td rowspan="2">Sun et al. [36]</td><td rowspan="2">Shock tubes</td><td>H₂/O₂/NO₂/Ar,</td><td>0.3 –</td><td>1.5 –</td><td>1038</td></tr><tr><td>X<sub>NO₂</sub> = 100, 400, 1600 ppm</td><td>1.01.0</td><td>30 atm</td><td>1744</td></tr><tr><td rowspan="2">GRI-Mech 3.0 [37]</td><td rowspan="2">Shock Tubes</td><td>H₂/Air/NO,</td><td></td><td>2.0 atm</td><td>770 –</td></tr><tr><td>X<sub>NO</sub> = 0.5 %</td><td></td><td></td><td>1190 K</td></tr><tr><td></td><td></td><td>CH₄/O₂/NO/Ar</td><td>1.0, 1.6</td><td>10 torr, 1.8 bar</td><td>2800 K</td></tr></tbody></table>

formation and the reburn chemistry of NO.

## 2.3. NO-NO₂ interconversion

A separate tank is used to prepare the different mixtures and ensure their homogeneity. Initial NO is diluted in a bottle of N₂ and injected into the tank after the reactants. Many studies highlight the fast interconversion of NO into NO₂ in the presence of O₂ through the termolecular reaction 2NO + O₂ = 2 NO₂ [38,39]. Typically, modelling a perfectly homogeneous closed reactor enables quantifying this decomposition with optimized rate constants suggested in NOₓ sub-mechanisms, as underlined by Aljohani et al [35]. However, in order to quantify more accurately the final mixture composition, prior to its introduction into the combustion chamber, the NO interconversion was measured. Once the filling process is complete, a continuous flow of the prepared mixture is pumped through a precalibrated multi-compo laser infrared spectrometer LaserCEM®. The measurement uncertainty for NO and NO₂ is ± 5 ppm and to ensure reproducibility, the experiment was repeated three times. Notably, for an initial concentration of X<sub>NO,0</sub> = 50 ppm, the uncertainty at the end of the phase conversion is significant. However, for each repetitions, results did not vary by more than ± 1 ppm. As such, the NO mole fraction, X<sub>NO</sub>, and NO₂ mole fraction, X<sub>NO₂</sub>, evolutions were recorded, simultaneously for more than thirty minutes. Fig. 4 illustrates the interconversion of NO into NO₂ at p = 5 bar and T = 333 K, for the targeted initial NO mole fractions: (a) X<sub>NO,0</sub> = 50 ppm, (b) X<sub>NO,0</sub> = 250 ppm, and (c) X<sub>NO,0</sub> = 1250 ppm. First, regardless of X<sub>NO,0</sub>, X<sub>NO</sub>, and X<sub>NO₂</sub>, profiles display a logarithmic decay and growth, respectively, before reaching a plateau corresponding to the chemical equilibrium. Note that the time required to achieve this equilibrium seems to decrease when X<sub>NO,0</sub> increases. Three phases are observable: Phase I corresponds to the time interval during which the experimental rig does not allow for a precise determination of X<sub>NO</sub> and X<sub>NO₂</sub>. Indeed, the mixture is not yet complete, and the reaction between NO and O₂ has already started. Phase II constitutes the measurement range for the interconversion of NO into NO₂. Finally, phase III marks the end of measurements and the time after which the mixture is introduced into the combustion chamber, where it is assumed that the composition of NO and NO₂ remains constant. To validate the reliability of laser detection, the NO phase conversion was also calculated numerically using the studied kinetic mechanisms incorporating relevant NOₓ sub-chemistry. The present model demonstrates excellent agreement in NO interconversion for the case where X<sub>NO,0</sub> = 50 ppm. As X<sub>NO,0</sub> increases, the model seems to predict a faster NO phase conversion, particularly during the transition from region I to region II. Noteworthy, the plateau is well established after thirty minutes of residence time. The kinetic mechanism from Aljohani et al. [35] predicts a slightly faster interconversion compared to the current model, although both exhibit very similar trends. Their good agreement is primarily due to both mechanisms incorporating NOₓ sub-chemistry from Glarborg et al. [34]. The NO interconversion was also calculated using the model from Sun et al. [36], which employs a different NOₓ sub-mechanism. This model predicts a significantly faster NO interconversion compared to other models and experiments, regardless of X<sub>NO,0</sub>. This discrepancy is potentially due to the consideration of HNO₂ influence on the NO interconversion into NO₂, which is not considered in the NOₓ sub-chemistry from Glarborg et al. [34].

Hence, in the light of this study, the X<sub>NO</sub> and X<sub>NO₂</sub> measured at t = 2100 s (35 min) of analysis correspond to X<sub>NO</sub> and X<sub>NO₂</sub> introduced in the RCM. The compositions of the studied mixtures are summarized in Table 4.

## 3. Results and discussion

Despite the increasing focus on using EGR devices in H₂SIEs, a crucial lack exists in understanding the impact of EGR on lean H₂/air ignition. While the primary role of EGR is to cool down the flame through mostly
<figure><img src="image_5.png" /><figcaption>**Fig. 4.** Comparison of NO and NO₂ mole fractions evolution during the mixing in the RCM tank vessel at *p* = 5 bar, *T* = 333 K. The interconversion of NO into NO₂ was measured and estimated numerically [35,36] for different initial NO mole fractions: (a) *X*<sub>NO,0</sub> = 50 ppm, (b) *X*<sub>NO,0</sub> = 250 ppm, and (c) *X*<sub>NO,0</sub> = 1250 ppm. The residence time corresponds to the time before RCM experiments.</figcaption></figure>

<caption>**Table 4**</caption>

H₂/O₂/N₂ and H₂/O₂/N₂/NOₓ mixtures for the experiments introduced in a 4.18 L tank vessel at 333 K. Mixture #1: Pure H₂/air, mixture #2: X<sub>NO,0</sub> = 50 ppm, mixture #3: X<sub>NO,0</sub> = 250 ppm, mixture #4: X<sub>NO,0</sub> = 1250 ppm.

<table><thead><tr><th>#</th><th>φ</th><th>H<sub>2</sub> [% mol]</th><th>O<sub>2</sub> [% mol]</th><th>N<sub>2</sub> [% mol]</th><th>X<sub>NO</sub> [ppm]</th><th>X<sub>NO2</sub> [ppm]</th></tr></thead><tbody><tr><td>1</td><td>0.4</td><td>14.38</td><td>17.98</td><td>67.64</td><td>0</td><td>0</td></tr><tr><td>2</td><td>0.4</td><td>14.38</td><td>17.98</td><td>67.64</td><td>8</td><td>42</td></tr><tr><td>3</td><td>0.4</td><td>14.38</td><td>17.98</td><td>67.64</td><td>9</td><td>241</td></tr><tr><td>4</td><td>0.4</td><td>14.38</td><td>17.98</td><td>67.64</td><td>11</td><td>1239</td></tr></tbody></table>

N₂ dilution, other species such as NOₓ and even H₂O may have a substantial impact on the mixture reactivity. Fig. 5 illustrates the impact of NOₓ addition on H₂/air IDTs under lean conditions (φ = 0.4) and for moderate-to-high compression pressures *p*<sub>C</sub> = (a) 30, (b) 40, (c) 50, (d) 60 bar.

It may first be noted that ignition delay times show excellent repeatability, and none of these experimental data points seem to suffer from pre-ignition. As mentioned in Section 3, the fuel and oxidizer mixtures were fully premixed using a constantly stirred-fan tank. The short time interval between filling the combustion chamber and compression allows very short time for the mixture to develop inhomogeneities. Additionally, the accurate control of initial temperature, initial pressure, and crevice design enables repeatable experiments, minimizing variations in ignition delays. On the one hand, for a fixed mixture composition, ignition delay time decreases with the increase of the compression pressure, as already observed for pure hydrogen [31]. On the other hand, regardless of *p*<sub>C</sub>, ignition delay times depict a decrease with the increase of X<sub>NOx</sub>. At low pressure (*p*<sub>C</sub> = 30 bar) and *T*<sub>C</sub> = 920 K, a NOₓ addition of 50 ppm reduces the ignition delay by 18 %. However, for X<sub>NOx</sub> = 250 ppm and X<sub>NOx</sub> = 1250 ppm, ignition delays are drastically reduced by 50 % and 92 %, respectively. Conversely, at *T*<sub>C</sub> = 980 K, a NOₓ addition of 50 ppm and 250 ppm decreases the ignition delay by 11 % and 36 %, respectively, while for X<sub>NOx</sub> = 1250 ppm, IDTs are too short to be measured (<1 ms). As such, ignition delays appear to

be more sensitive to NOₓ addition at lower temperatures within the specified pressure range. These observations are applicable for both *p*<sub>C</sub> = 40 bar and *p*<sub>C</sub> = 50 bar. At a higher compression pressure (*p*<sub>C</sub> = 60 bar) and the lowest temperature condition (*T*<sub>C</sub> = 900 K), the introduction of 50 ppm of NOₓ results in a moderate 12 % reduction in the ignition delay. However, for X<sub>NOx</sub> = 250 ppm and X<sub>NOx</sub> = 1250 ppm, IDTs are drastically reduced by 46 % and 88 %, respectively. Interestingly, the promoting effect of NOₓ seems to decrease as *p*<sub>C</sub> increases; however, this experimental trend falls within the range of uncertainty of the measurements.

Overall, these new experimental results demonstrate that NOₓ addition enhances the reactivity of lean H₂/air mixtures. The fact that small amounts of NOₓ can significantly impact ignition delays is of primary importance for the design and optimization of H₂ICEs. Indeed, the lower the ignition delays, the more likely H₂SIE is prone to knocking (after spark ignition) and/or super-knocking (before spark ignition) [40]. Prevent knocking and super-knocking, through 0-D or 1-D numerical simulation, as an initial step for three-dimensional (3-D) H₂SIE simulations, is not an unexplored concept. Li and Karim [41] already proposed a two-zone numerical model able to predict knocking in hydrogen engines while Ye et al. [42] and Li et al. [43] proposed a 3-D numerical approach for H₂SIEs. As such, these numerical studies underline the crucial need for comprehensive and relevant kinetic mechanisms, able to predict the impact of NOₓ on H₂/air ignition delay times. In light of these studies, three H₂/air/NOₓ kinetic mechanisms (see Section 3) were appraised. For each reactive pressure profile, a non-reactive one is associated, and simulated ignition delays account for heat losses.

The relative difference in ignition delay time (ε) is presented in Equation (2) and is calculated to determine the agreement between the experimental and the simulated ignition delays (τ<sup>exp</sup> and τ<sup>sim</sup>, respectively).

$$ \epsilon = \frac{(\tau^{\text{sim}} - \tau^{\text{exp}})}{\tau^{\text{exp}}}.100 \qquad (2) $$

All mean relative deviations (ε) were calculated and are presented in
<figure><img src="image_6.png" /><figcaption>**Fig. 5.** Ignition delays times of H₂/O₂/N₂/NOₓ mixtures at φ = 0.4, pC = 30 (a), 40 (b), 50 (c), 60 (d) bar and for different NOₓ mole fractions: XNOₓ = 0 ppm, 50 ppm, 250 ppm and 1250 ppm. Comparison with the present model, Aljohani et al. model [35], Sun et al. model [36], and the GRI-Mech 3.0 model [37].</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Fig. 6.** Sensitive reactions on OH radical for H₂/air/NOₓ mixtures for XNOₓ = 0 ppm, 50 ppm, 250 ppm, 1250 ppm at pC = 50 bar, and Tc = 908 K.</figcaption></figure>
the **Supplementary Materials.** Globally, the calculated ignition delay times obtained from the model developed in this work show the best agreement with our experimental results. Indeed, the present model exhibits the best-bounded absolute relative difference, ranging from $ε = 0.6\%$ at $p_C = 30$ bar and $T_C = 920$ K for a pure H₂/air mixture up to $ε = 47.8\%$ at $p_C = 60$ bar and $T_C = 960$ K. Noteworthy, this model tends to underpredict ignition delays as $X_{NOx}$ increases, especially at higher pressures, averaging a $ε = 40\%$ relative deviation. The Aljohani et al. mechanism demonstrates similar good performance under all the targeted conditions, being slightly too reactive for the highest temperatures, but exhibiting a better agreement for the lowest temperatures. The mechanism proposed by Sun et al. exhibits more discrepancies, being too reactive when $X_{NOx}$ increases, with a relative difference ranging from $ε = -20\%$ at $p_C = 30$ bar and $T_C = 920$ K to $ε = -73.3\%$ at $p_C = 60$ bar and $T_C = 960$ K. Finally, the GRI-Mech 3.0 model fails to accurately predict ignition delays for pure H₂/air mixtures, with a minimum absolute relative difference of 50 %. Additionally, it appears that this mechanism does not capture H₂/O₂/NOₓ chemistry as well. It consistently overpredicts ignition delay times for all the studied conditions and seems insensitive to NOₓ addition, while it is still widely used. Consequently, the current model constitutes a promising candidate for predicting ignition delay times in lean H₂/air/NOₓ mixtures under internal combustion engine conditions.

A sensitivity analysis on OH radical regarding $X_{NOx}$ addition is illustrated in Fig. 6. This analysis was performed using the present model, at 5 % of H₂ consumption, $T_C = 908$ K, $p_C = 50$ bar, and for $X_{NOx} = 0, 50, 250, 1250$ ppm. An identical sensitivity analysis on OH radical was conducted for the kinetic mechanism from Aljohani et al. [35], which shows very good performance, particularly under conditions with the highest NOₓ concentrations. This sensitivity analysis is available in the **Supplementary Materials.** Only the ten most sensitive reactions are presented and note that the most sensitive reactions are always the same except for the case with pure H₂. Concerning pure H₂/air mixtures, there is a well-known competition between the two most promoting reactions (R19) H₂O₂ (+M) = 2 OH (+M) ($s_{R19} = 9.8$), (R21) H₂O₂ + H = HO₂ + H₂ ($s_{R21} = 10.4$) and the most inhibiting reaction (R18) 2 HO₂ = H₂O₂ + O₂ ($s_{R18} = -5.53$). The sensitivity of these reactions decreases when $X_{NOx}$ increases while (R4) H₂ + OH = H₂O + H sensitivity remains globally constant, with $-0.8 < s_{R4} < -0.9$. When $X_{NOx}$ increases, the third-body chain terminating reaction (R11) becomes one of the most sensitive reactions, decreasing the reactivity of the mixture by consuming H radicals to produce more stable HO₂ radicals. However, as the experiments are conducted on the weakly explosive side, HO₂ reacts with H₂ through the chain continuation reaction (R21) HO₂ + H₂ = H + H₂O₂ ($s_{R21} = 0.4$ when $X_{NOx} = 1250$ ppm) to produce H atoms and hydrogen peroxide, H₂O₂. Under these conditions, H₂O₂ is not stable and it breaks into two OH via the third-body chain branching reaction (R19) H₂O₂ (+M) = 2 OH (+M) ($s_{R19} = 0.29$ when $X_{NOx} = 1250$ ppm), increasing the reactivity of the mixture. This highlights that a portion of OH radicals is produced through HO₂/H₂O₂ sequences, albeit the sensitivity decreases with increasing $X_{NOx}$. Alongside, the inhibiting reactions (R11) and (R4) competes with NO/NO₂ reactions (R120) NO₂ + H = NO + OH, (R122) NO₂ + HO₂ = HONO + O₂ and (R124) HONO (+M) = NO + OH (+M), as $X_{NOx}$ increases. Noteworthy, the sensitivity of these reactions is always positive, indicating reactivity enhancement. For $X_{NOx} = 50$ ppm and $X_{NOx} = 250$ ppm, the aforementioned reaction sensitivities are very low, explaining the slight impact of NOₓ on ignition delay times. However, for $X_{NOx} = 1250$ ppm, (R120) becomes the most sensitive reaction on the “promoting” side ($s_{R120} = 1.4$), illustrating the impact of NOₓ on the reactivity enhancement. As observed in Fig. 4, the mixture is mostly composed of NO₂, and during the induction time, it reacts directly with H to create NO and OH via (R120). In the meantime, NO interacts with HO₂ through (R118) NO + HO₂ = NO₂ + OH and regenerates NO₂. This is underlined by numerical simulations, presented in the **Supplementary Materials**, which give similar results when considering that NOₓ is composed only of NO or NO₂. There is another path for NO₂

consumption through the chain reactions (R122) NO₂ + HO₂ = HONO + O₂ ($s_{R122} = 0.26$) and (R125) NO₂ + H₂ = HONO + H, both producing nitrous acid HONO, which could constitute a well for OH. Nevertheless, under the targeted pressure conditions (30 bar < *p* < 60 bar), the decomposition of nitrous acid is favored through reaction (R124) HONO (+M) = NO + OH (+M) ($s_{R124} = 0.15$), increasing also the reactivity. As such, the HO₂/H₂O₂ sequence is not the exclusive contributor to OH production; indeed, there is a recycling loop between NO and NO₂ contributing to a more important production of OH, promoting of the overall reactivity of the mixture and thus decreasing ignition delay times.

Discrepancies between experimental results and IDTs calculated with the present mechanism are observed with increasing NOₓ mole fractions, for a fixed $p_C$. It appears to be due to the recent and moderately sensitive reaction (R17) 2 HO₂ = 2 OH + O₂ suggested by Klippenstein et al. [33]. Indeed, it increases the reactivity of pure H₂/air mixture although the sensitivity of this reaction decreases slightly with the addition of NOₓ ($s_{R17} = 1.24, 0.7, 0.5, 0.3$ for $X_{NOx} = 0, 50, 250, 1250$ ppm, respectively), decreasing ignition delays. In addition, Fig. 7 displays a sensitivity analysis on the OH radical as a function of $p_C$, for a given composition ($X_{NOx} = 1250$ ppm). The competition between (R11), (R120), and (R4) is still observed and the sensitivity of (R120) decreases slightly when $p_C$ increases ($s_{R120} = 2.1, 1.2, 1, 0.9$ for $p_C = 30, 40, 50$ and 60 bar, respectively. Alongside, the reaction (R17) shows a merely constant sensitivity with increasing $p_C$ ($0.15 < s_{R17} < 0.2$). As a matter of fact, recently developed NOₓ sub-mechanisms, including the one from Glarborg et al. [34] used in this study, were generally validated without taking into account (R17). Hence, the promoting effect of the NO/NO₂ recycling loop is combined with the promoting effect of (R17), explaining the shorter predicted ignition delays for the highest $X_{NOx}$. Noteworthy, the impact of (R17) on the other kinetic mechanisms predictions was also investigated, showing similar results. The ignition delays calculated with the Aljohani et al. including (R17) are available in the **Supplementary Materials**. Therefore, in light of this experimental and modelling study, it appears that NOₓ sub-mechanisms need to be revisited considering (R17).

## 4. Conclusions

The main objective of this study was to measure ignition delay times for lean H₂/O₂/N₂/NOₓ mixtures under realistic hydrogen spark ignition engine conditions ($φ = 0.4, p_C = 30$ bar – 60 bar, and $T_C = 890$ K – 1000 K) and provide a reliable kinetic mechanism based on our previous work

<figure><img src="image_8.png" /><figcaption>**Fig. 7.** Sensitivity on OH radical for H₂/air/NOₓ mixtures for $X_{NOx} = 1250$ ppm, at $T_C = 920$ K, and $p_C = 30$ bar, 40 bar, 50 bar, 60 bar.</figcaption></figure>
[31]. Four different mixtures were investigated with NOₓ mole fractions of 0, 50 ppm, 250 ppm, and 1250 ppm. The interconversion of NO into NO₂ was simulated and experimentally quantified to account for the NOₓ composition introduced in the chamber. Results indicate that ignition delay times decrease with NOₓ addition, irrespective of the compression pressure. This highlights the importance of accurately predicting such combustion properties for modelling hydrogen internal combustion engines. Recent and optimized kinetic mechanisms were tested, notably our previously validated H₂/air kinetic mechanism [31] under similar conditions, completed with recent NOₓ sub-chemistry. The proposed model displays very good agreement with experimental results. However, discrepancies appear for the highest NOₓ concentrations. To understand the origins of these discrepancies and identify key reactions influencing the mixture reactivity enhancement, sensitivity analyses on the OH radical were performed. They reveal that the NO/NO₂ recycling loop combines with the HO₂/H₂O₂ pathway to increase the OH pool. In addition, the recent dismutation of HO₂ followed by the prompt dissociation of H₂O₂, namely 2 HO₂ = 2 OH + O₂, tends to promote the reactivity when the NOₓ and the pressure increase, yielding an overprediction of the global reactivity. For future work, it is therefore crucial to focus the efforts on revisiting NOₓ sub-mechanisms, taking into account this new reaction.

### CRediT authorship contribution statement

**N. Villenave:** Writing – original draft, Software, Methodology, Investigation, Formal analysis, Data curation. **G. Dayma:** Writing – review & editing, Supervision, Formal analysis. **P. Brequigny:** Writing – review & editing, Supervision. **F. Foucher:** Writing – review & editing, Supervision, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Data availability

Supplementary data related to this article can be found in Supplementary Materials.

### Acknowledgments

The support of the National Research Agency under grant number ANR-21-CE05-0004 (SPEEDYH ANR Project) is gratefully acknowledged. The authors are grateful for the support from Eng. B. Moreau and Dr. R. Oung from PRISME laboratory.

### Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.fuel.2024.132482.

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