# Analysis of the origin of NOx emissions in non premixed dual swirl hydrogen flames

M. Vilespy, A. Aniello, D. Laera, T. Poinsot, T. Schuller, L. Selle

► To cite this version:

M. Vilespy, A. Aniello, D. Laera, T. Poinsot, T. Schuller, et al. Analysis of the origin of NOx emissions in non premixed dual swirl hydrogen flames. Combustion and Flame, 2025, 273, pp.113925. 10.1016/j.combustflame.2024.113925. hal-04922333

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# Analysis of the origin of NOₓ emissions in non premixed dual swirl hydrogen flames

M. Vilespyª, A. Anielloª, D. Laeraª,b, T. Poinsotª, T. Schullerª,c, L. Selleª

ªInstitut de Mécanique des Fluides de Toulouse, IMFT, Université de Toulouse, CNRS, Toulouse, France

ᵇDepartment of Mechanics, Mathematics and Management - Polytechnic of Bari, Bari, Italy

ᶜInstitut Universitaire de France (IUF)

## Abstract

The mechanisms of NOₓ formation in labscale swirled hydrogen-air flames are investigated with Large Eddy Simulations (LES). Two operating conditions, A (3 kW) and L (9 kW), are considered. Flame A (3 kW) is M-shaped with a first front attached to the hydrogen injector rim and a second flame front burning hydrogen and vitiated recirculating air. Flame L (9 kW), instead, is lifted and stabilized as a V-flame at the bottom of the central recirculation zone. Flame L also features a diffusion reaction layer in the central recirculation zone with partially premixed wings that develop along the inner shear layer above the injector. It is shown that the central diffusion front is common to both operating points and plays an essential role in the global NOₓ emissions of the burner for both operating conditions. A comparison between flamelets extracted from 3D simulations and results obtained with one-dimensional strained flames shows that strain plays an essential role in the production rate of NOₓ for all zones. In this regards, differences in NOₓ emissions between the attached (A) and the lifted (L) flames are analyzed. In both flames, nitrous oxides are mainly produced in the central diffusion front. The high temperature in this front favor NO formation through the thermal NO pathway, which is strongly dominant over the other pathways. Nevertheless, the central diffusion front of the lifted flame (L) is submitted to a higher strain rate than the attached flame (A), which leads to lower temperature and consequently to a smaller NO production. Interestingly, it is demonstrated that these differences can be predicted using one-dimensional strained diffusion flames. These simulations emphasize the key role of strain rate to control NO emissions from hydrogen non-premixed flames, and show that NO emissions are not necessarily increased by the diffusion hydrogen flames attached to the injector lips.

**Keywords:** Hydrogen swirling flames, Large Eddy Simulations, NOₓ, Strained flames, Diffusion flames

## Novelty and significance statement

NOₓ emissions are a key factor in designing future hydrogen gas turbines. While it is commonly assumed that diffusion-dominated flames produce high NOₓ levels, this paper shows that hydrogen swirled burners can achieve low NOₓ emissions even in a diffusion regime. Strained laminar diffusion hydrogen flames are known to limit NOₓ production, and this study extends that understanding to turbulent swirled flames. The main source of NO is not the typical diffusion ‘H₂/air’ flame (Flame I) near the injector, but rather a secondary ‘H₂/lean burnt gas’ diffusion layer (Flame II), stabilized downstream in the central recirculation zone. Simulations indicate that Flame I experiences high strain rates, while Flame II is nearly unstrained. This suggests that low NOₓ levels can be achieved by controlling the flow and local strain rates so that burning in a diffusion mode might not be a showstopper for future H₂ engines.

## Author contributions

**Martin Vilespy:** Conceptualization, Investigation, Writing-Original Draft.
**Andrea Aniello:** Conceptualization, Investigation, Writing-Review Editing.
**Davide Laera:** Conceptualization, Writing-Review Editing.
**Thierry Poinsot:** Conceptualization, Writing-Review Editing.

**Thierry Schuller:** Conceptualization, Writing-Review Editing, Supervision.
**Laurent Selle:** Conceptualization, Writing-Review Editing, Supervision.

## 1. Introduction

The need to decarbonize the current energy mix and reduce carbon dioxide emissions for transport makes hydrogen a promising alternative to fossile fuels in several sectors, including aeronautical and power-generation gas turbines [1, 2]. Despite the fact that H₂ is a carbon-free molecule, its combustion may favor the production of nitrogen oxides, i.e. NO, N₂O and NO₂, each one demonstrated to be harmful for human health. Moreover, N₂O is a direct greenhouse gas (GHG) and represented 6 % of GHG emissions from human activities in Europe in 2021 [3]. Additionnaly, NO and NO₂ have an indirect greenhouse effect, by increasing the ozone concentration for instance [4]. The limitation of nitrogen oxides is therefore essential for future gas turbines fueled with hydrogen.

The chemistry of NOₓ has been intensely studied for decades, and four main pathways were identified for hydrogen enriched flames: the so-called thermal, prompt, N₂O and NNH pathways. The thermal NO route is associated to the Zeldovitch mechanism and consists of three reactions. In this regard, the
N₂ dissociation in NO + N is characterized by high activation energy [5], which produces the N radical and enables the two other reactions. This pathway is dominant at high temperature and has been the subject of numerous works [6, 7]. The prompt-NO pathway corresponding to the reaction between N₂ and CH was first highlighted by Fenimore [8] and studied experimentally and numerically in [9, 10, 11]. This mechanism is not relevant for pure hydrogen flames because of the absence of carbon atoms. Nitrous oxide N₂O is formed from N₂ through a third-body reaction characterized by low activation energy that is promoted at high pressure [12]. Finally, Bozzelli et al. [13] highlighted the contribution of NNH pathway in NO and NO₂ formation, which has been subject of several investigations [14, 15, 16].

In order to predict NO formation numerically, NOₓ chemistry in hydrocarbon flames has been extensively studied [17, 18] leading to the development of many detailed mechanisms such as Gri-Mech3.0 [19], CRECK [20], NUIG [21], Konnov 0.6 [22] and Glarborg et al. [18]. Experimental and numerical studies have been conducted to validate these mechanisms at atmospheric [23, 24] and high pressure [25, 26]. As the interest in hydrogen has grown over the last decade, many experimental studies were performed to understand NO formation mechanisms in diluted and pure-hydrogen flames at atmospheric pressure [24, 27]. They have shown that for hydrogen flames at low temperature, the NNH pathway becomes dominant over thermal NO. The contribution of the NNH pathway is however reduced as the pressure increases [28]. In this case, the conversion of N₂O to N₂ is strongly reduced, which increases the N₂O content. However, despite this higher N₂O concentration, the increase of NO production when increasing the pressure remains limited.

Together with pressure, the impact of stretch (strain and/or curvature) on NOₓ formation has been extensively studied. Drake et al. [29] were among the first to show experimentally the influence of strain on thermal NO for CO/H₂/N₂ laminar counterflow flames. In H₂/CO and pure hydrogen flames, strain reduces the temperature, while modifying the flame structure, increasing the radical O concentration [30, 31, 32]. These phenomena have competing effects: the increase in O radical concentration increases the maximum NO production rate, while the decreased temperature decreases the maximum NO production rate. At low strain rate, the effect of O radicals dominates and NO production rate increases, while the effect of the temperature fall off dominates at medium and high strain rates [31]. Similar trends were observed for counterflow diffusion flames [33] and counterflow premixed flames [34]. In hydrogen-air non-premixed jet flames, it was also shown that low temperature due to high turbulence intensity leads to lower NOₓ emissions, going with an increase in NO conversion to NO₂ [35]. Rørtveit et al. [33] compared the effect of the addition of a diluent (CO₂, N₂ and He) to that of increasing the strain rate on NO production in hydrogen-air flames. They showed that for a same maximum temperature, strain rate is more efficient than dilution to reduce NO formation, because it decreases the residence time within hot gas. More recently, Porcarelli et al. [34] studied strained premixed pure hydrogen

and methane flames, showing that increasing strain helps to reduce NOₓ production in both cases. As strain pushes the radicals towards the flame region, NO formation is decreased by this redistribution.

The impact of preferential diffusion on NOₓ formations has been studied by Direct Numerical Simulation (DNS) for hydrogen canonical flames bu Wen et al. [36, 37], in which a reduced chemistry model was derived from Glarborg et al. [18]. Large Eddy Simulation (LES) of complex premixed swirled flames have been performed for methane-air mixtures [38], using a reduced chemistry approach. Capurso et al. [39] performed LES of the hydrogen premix swirled TUB burner, and developed a reduced chemical scheme for LES simulations of hydrogen flames. Palulli et al. [40] studied NO formation in non-premixed diluted hydrogen-air flames, by combining 3D LES and 0D perfectly stirred reaction (PSR), using a chemical scheme based on Glarborg's mechanism [18] including the HNNO sub-mechanism. They observed that the NNH and the extended Zeldovitch pathways are dominant in the flame region, the Zeldovitch pathway contribution being reduced by dilution compared to dry hydrogen flames. Recently, Malé et al. [41] compared LES and NOₓ measurements of the LEAF combustor fueled with hydrogen, which features premixed and diffusion regimes. It was shown that in real burners, heat transfer has a significant impact on NOₓ prediction [38], and Conjugate Heat Transfer (CHT) needs to be taken into account [39]. LES of non-premixed complex methane-air flames with emphasis on NOₓ production have already been performed [42], but to the authors knowledge, there is a research gap for flames powered by pure swirled air and swirled hydrogen flows injected in separated channels.

As hydrogen exhibits higher flame speed and wider flammability limits than classical fuels [43, 44], the increase in the risk of flashback for premixed systems [45] makes burners featuring separate injections of air and fuel preferred. However, these burners tend to promote the stabilization of diffusion reaction layers, favoring high temperature flames [46]. To address this issue, various strategies involving late fuel injection and rapid mixing injectors are currently under development [47, 48, 46, 49, 50]. Among these strategies, swirled burners are intensively investigated [51, 48, 46, 49]. It was found that NOₓ emissions decrease with decreasing equivalence ratio [51], and scale with residence time and adiabatic flame temperature [46, 49]. Moreover, Chen et al. [51] showed that NO conversion to NO₂ is promoted at low equivalence ratio. In these conditions, adding secondary air downstream also favors NO conversion.

The HYdrogen LOw NOₓ (HYLON) burner investigated at the Institute of Fluid Mechanics of Toulouse (IMFT) relies on a double-swirled injector for air and hydrogen streams, with the objective to enhance mixing between the two reactants. Two flame stabilization modes have been studied experimentally [52] and numerically [53].

Regarding emissions, the HYLON burner has demonstrated low NOₓ levels in tests conducted under atmospheric conditions across various thermal power settings, including preheated conditions. Notably, a counter-intuitive reduction in NOₓ
levels with increasing thermal power was observed in these tests [48, 46]. When operated at low thermal power, similar low NOₓ levels have been measured in both anchored and lifted flames [46], showing that the main source of NOₓ production may be common to both stabilization modes. Magnes et al. [54] also showed that at low equivalence ratio and high injection velocities, combustion efficiency decreases because of strong fragmented reaction zones, which can be overcome with preheated air.

This work delves into the underlying mechanisms responsible for NO emissions for the swirled-stabilized non-premixed flames of the HYLON injector with LES. The two operating conditions considered in [53] featuring different flame stabilization modes, attached vs lifted, and burning regimes are considered.

The remainder of this paper is organised as follows. Section 2 recalls the burner geometry, the numerical setup and the LES model. Identification of NO production rates in the different flame branches is conducted in Sec. 3.2. The effect of strain rate is then analyzed, completed by a one dimensional comparison with strained flames in Sec. 3.3.

## 2. HYLON set-up

### 2.1. Burner geometry

A detailed description of the HYLON burner can be found in [53, 48]. It consists of a co-axial injector in which air and hydrogen are injected separately (Fig. 1a). The flow is swirled with radial and axial vanes for air and hydrogen, respectively. Hydrogen is injected through the central cylindrical nozzle (inner diameter $d_i$ = 6 mm) and is characterized by a geometrically-calculated swirl number $S_i$ = 0.60 [48]. The external annular duct features inner and outer diameter of $d_{ie}$ = 10 mm $d_e$ = 18 mm, respectively. It supplies air and is characterized by a swirl number $S_e$ = 0.65. The recess of the hydrogen injector with respect to the backplane of the chamber is denoted $z_i$.

Two flame stabilization modes, attached (A) and lifted (L), have been studied numerically [53]. The attached flame features an M-shape with two branches as shown in Fig. 2 (left): branch (I) is a vigorous reactive front attached to the injector lips, developed in the mixing layer between cold air and H₂ streams. LES show that this front is characterized by a high burning rate, confirmed by the experimental OH* chemiluminescence signal. The second branch (II), located downstream, is a weak diffusion front that consists of hydrogen burning with vitiated gas caught in the Central Recirculation Zone (CRZ). Unlike flame A, the lateral branch of flame L is not anchored to the injector lips but aerodynamically stabilized above the hydrogen injector as shown in Fig. 2 (right). A partially premixed front (denoted I) can be identified downstream [53]. This flame also features a central diffusion front, however, the location of branch (II) is different for flames A and L. Because of the stronger CRZ of operating point L, this central front is pushed upstream, and is stabilized in the wake of the injector [52, 46].

### 2.2. Numerical framework

Simulations are conducted with the compressible LES solver AVBP (www.cerfacs.fr/avbp7x/). The numerical framework used in this study is similar to the one validated in [53], therefore, it will be only briefly described here. The computational domain is shown in Fig. 1b. The inlet is placed at the top of the plenum so that both air and hydrogen swirlers are within the computational domain. The adequacy of the spatial discretization and the validation of the LES results against experiments were already demonstrated [53]. Inlet and outlet boundary conditions are imposed using the NSCBC formalism [55]. The SIGMA model is used for sub-grid scale modeling [56] and the DTFLES approach [57] for combustion modelling. Since the H₂-air flames investigated exhibit several combustion regimes, the local instantaneous Takeno index based on the fields of oxygen and fuel mass fractions is used to determine the local combustion regime. The flame is only thickened in the premixed zones and the DTFLES model is not activated in diffusion-controlled region. Because the focus of the present work is NOₓ emissions, the so-called San Diego scheme used in [53] is replaced by the skeletal mechanism developed by Capurso et al. [39], which includes 15 species and 47 reactions.

The temperature of the burner walls is known to have a strong impact on NOₓ levels [38, 39]. Conjugate heat transfer (CHT) between the gaseous and solid phases is thus considered by coupling the LES solver AVBP with AVTP [58, 59], which solves the heat equation inside the solid. In this numerical model, heat fluxes are obtained from the fluid domain and used as boundary conditions for the solid domain. The temperature field calculated at the solid wall is used as the boundary condition for the fluid solver. At least 10 points are prescribed in the wall thickness. The mesh used to discretize the solid and the fluid domain consist of 14M and 58M cells, respectively, to ensure at least 10 points in the wall thickness. The fluid and solid solvers have different characteristic time scales. Hence, several fluid iterations with the AVBP flow solver are performed between each AVTP iteration. In order to decrease the convergence time of the temperature in the solid domain and the computational cost associated, a desynchronized coupling strategy proposed by Duchaine et al. [59, 60] is used.

At the external face of the burner, a natural convection thermal boundary condition is imposed. The convective heat transfer coefficient $h_c$ is calculated following [61]. Under the conditions explored, $h_c$ = 5 W/m²K is imposed to the external side of the quartz windows and to the external side of the backplane in contact with ambient air to characterize the natural convection at the walls. The cooling system located below the backplane is considered by imposing a constant temperature $T_w$ = 300 K to its surface.

## 3. Results and discussion

### 3.1. Velocity and heat release rate fields validation

The numerical framework is similar to the one used in [53]. However, it differs in the chemical scheme and the use of
<figure><img src="image_2.png" /><figcaption>Figure 1: (a) The HYLON injector with axial internal and radial external swirlers. (b) Computational domain with fluid (colored) and solid domains (grey). (c) Fluid and Solid mesh size.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 2: HYLON main stabilization modes : anchored (left) and lifted (right), highlighting the main branches and the vitiated recirculating gases, from [46].</figcaption></figure>

CHT, which affect only the reactive case. Therefore, only reactive results are presented. Time-averaged solutions are obtained by averaging over a flow through time in both flames A and L. Velocity fields obtained with LES for flames A and L are plotted in Fig. 3 at two heights z = 5 mm and 15 mm above the backplane. LES results show good agreement with experimental data for both operating conditions. The central recirculation zone is well captured, as shown by the position of the velocity peaks. Figure 4 shows the experimental OH* Abel-deconvoluted chemiluminescence signal (left) and the LES OH* field (right) for both flames A and L. LES OH*

<figure><img src="image_4.png" /><figcaption>Figure 3: Mean and RMS velocity profiles comparison between LES (solid lines) and experimental data (black circles) for flames A (red line) and L (blue line) at two heights z = 5 mm (top) and z = 15 mm (bot) above the backplane.</figcaption></figure>

field is deduced following the work of Schiavone et al. [62], using the Kathrotia OH\* sub-mechanism [63]. Quasi-steady-state approximation is made on OH\* concentration, which is determined a posteriori. In both cases, the flame shape is well retrieved: flame A is attached to the hydrogen injector lips, while flame L is lifted. The height of the central front is in good agreement between experiments and LES: branch II from flame L being stabilized closer to the injector lips compared to branch II of flame A.

### 3.2. NO production in flame branches

Global NO emissions and outlet temperatures of flames A and L are compared in Tab. 1. The mean outlet molar fraction of NO,
<figure><img src="image_5.png" /><figcaption>Figure 4: Experimental vs LES (right) normalized OH* field (left) for (a) flame A and (b) flame L.</figcaption></figure>

averaged over the outlet cross section area, has been processed to be compared to experimental results (dry molar fraction in ppmv at 15% of O₂). The Emission Index of NO (EI<sub>NO</sub>) is the ratio between the total production rate of NO and the mass of H₂ supplied in the system and is expressed in g<sub>NO</sub>/kg<sub>H₂</sub>:

$$EI_{NO} = \frac{\int_{V} \dot{\omega}_{NO} dV}{\dot{m}_{H_{2}}} \qquad (1)$$

X<sub>NO</sub> and EINO of flame A are around 3 times higher than for flame L which is of the order of magnitude of the ratio of NO concentration measured experimentally in [64] for the same operating conditions. However, for both flames A and L, the outlet temperature and the molar fraction of NO is underestimated in the simulations compared to the experimental results.

Figure 5 shows the distribution of temperature, NO production rate and thickening for the two operating points A and L on an instantaneous solution. Isolines of temperatures and of NO source terms ω<sub>NO</sub> are superposed, as well as the isoline of normalized heat-release rate. As 1800 K is the reference activation temperature of thermal NO [65], isolines of T = 1800 K are plotted. Branch I of flame A features only limited zones of temperature above 1800 K (Fig. 5(a)). Branch I of flame L is characterized by temperature below 1800 K (Fig. 5(d)). For the attached flame A, branch II is hotter than

<table><caption>Table 1: Time and spatial average outlet temperature, molar fraction of NO @15% O₂ dry and EI<sub>NO</sub> from LES (vs experiments) for operating points A and L, as well as NO production rate and mean temperature calculated in both branches of flames A and L.</caption><thead><tr><th>Flame</th><th>T<sub>outlet</sub><br>[K]</th><th>NO<sub>outlet</sub><br>[ppmv]</th><th>EI<sub>NO</sub><br>[g/kg]</th><th>Branch</th><th>T<sub>branch</sub><br>[K]</th><th>∫<sub>V</sub> ω<sub>NO</sub> dV<br>[kg/s]</th></tr></thead><tbody><tr><td rowspan="3">A</td><td rowspan="3">1100<br>(1138)</td><td rowspan="3">6.0<br>(9.5)</td><td rowspan="3">7.3 10<sup>-1</sup></td><td>Total</td><td>1910</td><td>2.35 10<sup>-8</sup></td></tr><tr><td>I</td><td>1710</td><td>13%</td></tr><tr><td>II</td><td>1930</td><td>87%</td></tr><tr><td rowspan="3">L</td><td rowspan="3">1171<br>(1375)</td><td rowspan="3">2.1<br>(4.9)</td><td rowspan="3">2.2 10<sup>-1</sup></td><td>Total</td><td>1780</td><td>1.79 10<sup>-8</sup></td></tr><tr><td>I</td><td>1430</td><td>1%</td></tr><tr><td>II</td><td>1820</td><td>99%</td></tr></tbody></table>

branch I. For both flames A and L, high temperature zones match with the main NO production zones, and the highest NO production rates are found in the central part of the branches. The dominant reactions involved in the three main NO pathways (Thermal, N₂O and NNH) are described in Fig. 6. Their contribution accounts for 92% and 90% of the total NO production for flame A and L, respectively. The contribution of each branch of flames A and L is analyzed with the help of Fig. 7 and Table 1. Figure 7 shows the production rates of NO through the three main NO pathways (Thermal, N₂O and NNH) for flames A and L. Heat-release rate isolines of 10% HRR<sub>max</sub> are used to mark the location of branch I in both cases. Integral of NO production rate and time-averaged mean temperature of each flame branch are given in Table 1. Branch I of flame A accounts for 13% of the total NO production rate, with thermal NO remaining low because of the low temperature. Branch I of flame L is negligible in the total NO production. Branch II of flames A and L features high mean temperature leading to a thermal NO pathway that is strongly dominant with NO production rates an order of magnitude higher than those in the other branches. Comparing branch II for the flames A and L shows that the mean temperature is reduced from A to L. When lifting the flame from A to L, the mean temperature of branch II is substantially reduced by more than 100 K, leading to reduced thermal NO<sub>x</sub> emissions.

### 3.3. Effect of strain rate

The influence of strain on NO production for the two operating points A and L is analyzed. The strain rate is defined as [66]:

$$a = \nabla \cdot \mathbf{U} - \mathbf{n}\mathbf{n} : \nabla \mathbf{U} \qquad (2)$$

with **U** the local fluid velocity and **n** the normal vector to the flame front. The normal direction to the flame is calculated using the mixture fraction as the progress variable: **n** = ∇Z/|Z|, with Z the mixture fraction, using Bilger's definition [67] with air as oxidizer.

The local strain rate is calculated in LES for several instantaneous solutions over four convective characteristic times for the flame A branches I and II and for the flame L branch II. Results are plotted in Fig. 8 along the stoichiometric mixture fraction Z = Z<sub>st</sub>. Mean and standard deviation values of strain in each branch are given in Tab. 2.
<figure><img src="image_6.png" /><figcaption>Figure 5: Instantaneous field of temperature, NO production rate and thickening fields for flame A (a,b,c) and flame L (d,e,f). Isolines of $T = 1400$ (grey), $1800$ and $2000$ K (black), $\dot{\omega}_{NO} = 0.001$, $0.01 \text{ kg/m}^3\text{/s}$ (white) and $\text{HRR}_{norm} = 10\%$ isolines (red).</figcaption></figure>

As mentioned in Sec. 3.2, the highest NO production rates are found in the center part of branches II. Therefore, the strain rate values in the center region of branches II of flames A and L are given. Values are taken at 1/4 of the branches, around $r = 5$ mm and $r = 3$ mm, respectively, in Fig. 8. Considering flame A, the diffusion flame of branch I is on average more strained than the branch II stabilized in the CRZ, where higher temperature and higher NO production is observed (Fig. 5). Focusing on branch II, the center part (1/4 of their radius) are less strained than the rest of the branches in both flames A and L. This is consistent with the higher temperature and higher NO production observed in this region in Fig. 5. Moreover, as shown in Tab. 2, branch II of flame L is subjected to higher strain rates than branch II of flame A, which explains the lower temperature observed in Fig. 5(d) and the decrease in NO production via the thermal pathway (Fig. 7).

These results suggest that increasing the strain rate of the flame alters NO formation by decreasing its temperature. The thermal NO pathway being dominant, the NO production is globally reduced.

To verify this hypothesis, a comparison between LES data and one-dimensional flames is now conducted. As mentioned in Sec. 2.1, branch I of flame A is a diffusion front developed in the mixing layer between air and hydrogen streams, both injected at temperature $T = 300$ K. Branch II of flames A and L is instead

<figure><img src="image_7.png" /><figcaption>Figure 6: Main pathways involved in NO and $N_2O-NNH$ productions.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 7: Production rates of NO through the three main pathways (Thermal, $N_2O$ and $NNH$) for the branches I and II of flames A and L.</figcaption></figure>

a diffusion front with hydrogen (injected at $T = 300$ K) burning with vitiated recirculating gases. Table 3 shows the time and spatial average composition of the main species ($Y_k > 10^{-5}$) and temperature of the CRZ for both flames A and L. The CRZ is delimited by a negative mean axial velocity in the center of the chamber. These values are compared with the burned gases of a one-dimensional H$_2$-Air premixed flame at equivalence ratio $\bar{\Phi} = 0.45$, corresponding to the global equivalence ratio of the operating conditions studied, considering fresh gases at injected at 300 K and atmospheric pressure. In flames A and L, the composition of these recirculating gases matches the burnt gases of the premixed flame, with an error of around 4% for the three major species O$_2$, H$_2$O and N$_2$. A larger difference is found for OH, but in all cases its concentration remains low. Non-adiabatic walls lead to heat losses in the LES: 1200 and 2000 W for quartz windows for flame A and L respectively. These losses reduce the temperature of the recirculated gases, and explains the difference between the temperature observed
<figure><img src="image_9.png" /><figcaption>Figure 8: Temperature field of an instantaneous solution for (a) flame A and (b) flame L. Isoline Z=$Z_{st}$ is colored by the strain rate $\bar{a}$ [$s^{-1}$].</figcaption></figure>

<table><caption>Table 2: Mean ($\bar{a}$) and standard deviation ($\sigma_a$) of strain rate for branch I, branch II and the center of branch II of flames A and L.</caption><thead><tr><th>Flame</th><th>Branch</th><th>a&#773; [$s^{-1}$]</th><th>σ<sub>a</sub> [$s^{-1}$]</th></tr></thead><tbody><tr><td rowspan="3">A</td><td>I</td><td>4560</td><td>150</td></tr><tr><td>II</td><td>1270</td><td>80</td></tr><tr><td>II center (r=5 mm)</td><td>112</td><td>79</td></tr><tr><td rowspan="2">L</td><td>II</td><td>4530</td><td>255</td></tr><tr><td>II center (r=3 mm)</td><td>820</td><td>510</td></tr></tbody></table>

in the 3D simulations and the adiabatic 1D flame.

Flames A and L can therefore be characterized by two different types of strained counterflow diffusion flames solved in Cantera [68]: branch I of flame A is characterized by H₂-air counterflow flames, while branch II of flames A and L are characterized by counterflow H₂ vs equilibrium products of a 1D premixed flame at global equivalence ratio $\Phi = 0.45$. This last one is called CFHO flame, which refers to a counterflow flame with Cold Fuel (H₂ injected at $T = 300$ K) and Hot Oxidizer (burnt gases from 1D flame at $\Phi = 0.45$ injected at $T = 1300$ K). The temperature of 1300 K matches the temperature of the CRZ observed in the LES.

<table><caption>Table 3: Time and spatial averaged mass fractions of the O₂, H₂O, N₂, OH and temperature extracted from the CRZ simulated by LES and from burnt gases of a premixed one-dimensional flame at $\phi = 0.45$ at ambient temperature and pressure.</caption><thead><tr><th>Flame</th><th>Y<sub>O₂</sub></th><th>Y<sub>H₂O</sub></th><th>Y<sub>N₂</sub></th><th>Y<sub>OH</sub></th><th>T&#773;<sub>CRZ</sub> [K]</th></tr></thead><tbody><tr><td>A</td><td>0.122</td><td>0.121</td><td>0.757</td><td>3.8 10<sup>-5</sup></td><td>1310</td></tr><tr><td>L</td><td>0.125</td><td>0.118</td><td>0.757</td><td>6.5 10<sup>-5</sup></td><td>1340</td></tr><tr><td>1D<sub>Φ=0.45</sub></td><td>0.127</td><td>0.116</td><td>0.757</td><td>1.99 10<sup>-4</sup></td><td>1530</td></tr></tbody></table>

To be able to compare with LES data. The same chemical scheme adopted in LES is used for the one-dimensional flame

simulations. In Cantera, the strain rate is evaluated at the flame front location $Z = Z_{st}$ by:

$$a = \left( \frac{1}{\rho} \frac{\partial \rho u}{\partial x} \right)_{st} \qquad (3)$$

where $Z_{st}$ denotes the stoichiometric mixture fraction.

To compare LES results with the 1D flame simulations, two flamelets are isolated in flame A (Fig. 9(b)left): the first one is located at the intersection of the horizontal plane 3 mm above the injector lips with the stoichiometric isurface ($Z = Z_{st}$) in branch I of flame A (blue). The second one is located at the center of branch II (orange). For flame L, only the flamelet in the center of branch II is considered (Fig. 9(b)right). The normal vector to the flame front, calculated using the mixture fraction gradient $\mathbf{n} = \nabla Z/|Z|$, is used as the directing vector of the flamelet. For each flamelets, several instantaneous solutions are extracted over four convective characteristic times of branch II. This duration corresponds to the highest convective characteristic time scale (5.5 ms for flame A branch II against 0.33 ms for flame A branch I), defined as the inverse of the time averaged strain rate, given by Table 4.

<table><caption>Table 4: Time averaged strain rate, maximum temperature and maximum NO mass fraction of three flamelets extracted from flame A branches I and II and flame L branch II.</caption><thead><tr><th>Flamelet</th><th>a&#773;[$s^{-1}$]</th><th>T&#773;<sub>max</sub>[K]</th><th>Y&#773;<sub>NO max</sub></th></tr></thead><tbody><tr><td>Flame A BI</td><td>3000</td><td>1842</td><td>2.7 10<sup>-6</sup></td></tr><tr><td>Flame A BII</td><td>180</td><td>2385</td><td>1.67 10<sup>-4</sup></td></tr><tr><td>Flame L BI</td><td>450</td><td>2227</td><td>4.2 10<sup>-5</sup></td></tr></tbody></table>

Scatter plots of temperature and mass fractions of the main species involved in NO production against the normalized mixture fraction $Z/Z_{st}$ are shown in Fig. 9(a) for flame A branch I (blue circles), flame A branch II (orange squares) and flame L branch II (green crosses). For each branch, a one-dimensional laminar counterflow diffusion flame is superposed: a H₂-air flame at strain rate $a = 3000 \ s^{-1}$ for flame A branch I, a CFHO flame at strain rate $a = 180 \ s^{-1}$ for flame A branch II and a CFHO flame at strain rate $a = 450 \ s^{-1}$ for flame L branch II. The strain rate of the 1D flames is chosen to match the mean strain rate of the flamelets. Table 4 and Fig. 9(a) show that for the flamelets, the higher the strain rate, the lower the maximum temperature and the lower the maximum NO mass fraction. Flame A branch II peak of NO mass fraction is two order of magnitude above the one of flame A branch I.

Focusing on flame A branch I and the H₂-air 1D flame (blue circles vs black dashed line), the profiles of intermediate species mass fractions are in qualitative agreement. The temperature profile of the 1D flame is located on the highest value of temperature observed in the LES, which is attributed to small heat losses at the injector lips. Similarly to the temperature, O, OH and N radicals are slightly underestimated in the 3D simulation. As the temperature is low, the thermal pathway is not strongly activated and N radicals remain in low concentration. $Y_{NO}$ has the same order of magnitude for the 1D
<figure><img src="image_10.png" /><figcaption>Figure 9: (a): Instantaneous scatter-plot of temperature, $Y_{H_2}$, $Y_{NO}$, $Y_O$, $Y_{OH}$, $Y_N$ of flamelets extracted from flame A branches I and II and flame L branch II. In flame A branch I (blue circles): flamelets located at $z = 3$ mm above the injector lips. In branch II of flames A and L (orange scares and green crosses respectively): flamelets are extracted in the center of the branch. 1D counterflow flames are superposed: $H_2$-air flame with strain rate $a = 3000 \ s^{-1}$ (black dashed line), CFHO flame with strain rate $a = 180 \ s^{-1}$ (black solid line), CFHO flame with strain rate $a = 450 \ s^{-1}$ (black dotted line). (b) Location of the extracted flamelets: blue and orange lines in flame A (left) and green line in flame L (right).</figcaption></figure>

flame and the 3D LES. These observations show that high strain rates reduce the maximum temperature of the $H_2$-air flame (~ 1850 K), leading to low N concentration and consequently to low thermal NO and low mass fraction of NO ($Y_{NO} \sim 10^{-6}$). Branch II of flame A (orange squares) and branch II of flame L (green crosses) exhibit a similar structure than their associated CFHO flames (solid and dotted lines respectively) in the flame region. The temperatures of branches II of flame A and L are respectively around 2385 and 2227 K, which are much higher than the temperature of branch I from flame A. Moreover, the scatter plot in Fig. 9 shows that the maximum mass fraction of NO of flame A branch II is three times higher than the one of flame L branch II. These results are consistent with

the observations made in Sec. 3.2: the higher the temperature, the higher the N radical mass fraction produced through $N_2 + O \leftrightarrow NO + N$, and therefore the higher the NO mass fraction.

<figure><img src="image_11.png" /><figcaption>Figure 10: Time average temperature field of (a) flame A and (b) flame L. Isolines of $HRR_{norm}=2\%$ (red). The temperature threshold > 1000 K with negative axial velocity located upstream of branch II is highlighted in white.</figcaption></figure>

Figure 10 shows the time-averaged temperature field of flame A (a) and flame L (b). The flame is located by the heat release rate isocontour (red). The combined threshold of temperature $T > 1000$ K and negative axial velocity $w < 0$ m/s is highlighted in white. For both flames A and L, a high temperature zone is visible in the central flame front, highlighted in Fig. 10(a) and (b) in white, affecting the upcoming hydrogen on branch II. This zone is a 3D consequence of the swirled flow, that cannot be reproduced in 1D flame simulations. For flame A, this 3D effect is noticeable in the N radical profiles, that is overestimated on the fuel side in the LES compared to the 1D flame simulations: the higher temperatures observed in LES lead to higher N concentrations. However, the maximum N mass fraction and the maximum temperature are well captured in the flame region, which shows that this 3D effect does not impact the N concentration in the flame. For flame L, the differences between LES and 1D flame simulations are much smaller. The temperature and N mass fraction profiles are in better agreement. Branch II is stabilized closer to the injector lips, leading to a cooler temperature zone near the injector lips. The reduced size of this high temperature zone reduces its effect on the upcoming hydrogen stream, and N formation is not favored.

Figure 11 shows the maximum temperature and maximum mass fraction of NO versus strain rate for $H_2$-air (black circles) and CFHO flames (black diamonds), as well as the time-averaged value and standard deviation of the maximum temperature and the maximum $Y_{NO}$ from the flamelets extracted from the
<figure><img src="image_12.png" /><figcaption>Figure 11: Maximum temperature (top) and maximum NO mass fraction $Y_{NO_{max}}$ (bottom) versus strain rate for H₂-Air (●-●) and CFHO (■-■) one dimensional diffusion flames, using the chemical scheme from Capurso et al. [39] with the Cantera solver. Mean and standard deviation of maximum temperature and maximum NO mass fraction of 3D flamelets of flame A branches I and II and flame L branch II (red).</figcaption></figure>

3D simulation (red) and shown in Table 4. The maximum temperature and maximum mass fraction of NO of hydrogen-air diffusion flames decrease when the strain rate increases, which is consistent with previous studies [30, 33]. The same trend is found for the CFHO flames. CFHO flames are slightly less sensitive to strain rate than H₂-air flames. Comparing flamelets obtained from the 3D simulation with 1D flame simulations show that the dependence of temperature and $Y_{NO}$ to strain rate is well captured. These results confirm the major role of strain in NO production of H₂-air and CFHO flames as observed for flames A and L.

## 4. Conclusion

This paper shows that NO in a swirled H₂-air flame is not necessarily formed where expected, i.e. in the diffusion flame at the base, and that strain is a major controlling factor for NO emissions. Large-Eddy Simulations have been performed with the chemical scheme developed by Capurso et al. [39] to assess the formation of NO for two flames stabilized on the HYLON IMFT burner. These flames correspond to flames A and L studied by Aniello et al. [53], which are respectively attached and lifted from the hydrogen injector rim. Results demonstrate that NO production does not take place near the injection zone (Branch I) but downstream, in the so-called

branch II. This reaction layer situated at the edge of the central recirculation zone of the flow is characterized by low strain rates and high temperatures, typically above 1800 K, which favor the thermal NO pathway. On the other hand, Branch I yields little NO because it is highly strained. Results of LES, confirmed by one-dimensional laminar counterflow diffusion flame simulations, show that the high strain rates values of Branch I reduce the flame temperature below 1800 K, hindering the thermal NO formation pathway. Comparing branch II of flames A and L shows that in flame A, the strain rate is lower and the temperature is higher than in flame L, leading to higher NO production. As branch II of flame L is stabilized closer to the hydrogen injector, the flow is accelerated and strain is increased. As a general design rule, pushing the CRZ towards the hydrogen injector seems to be a promising way to increase strain on the central branch, reducing the temperature of hydrogen diffusion controlled flame branches, and therefore limiting NO pollutant emissions.

## 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.

## Acknowledgments

This project has received funding from the ERC H2020 Grant Agreement 832248 (SCIROCCO). HPC resources from GENCI (allocation A0152B10627) is also highly acknowledged.

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