Gbocho Gilles

Quy Dong To
email: quy-dong.to@univ-eiffel.fr

Vincent Monchiet
email: vincent.monchiet@univ-eiffel.fr

Céline Léonard
email: celine.leonard@univ-eiffel.fr

Keywords: Evaporation condensation coefficient, accommodation coefficient, molecular dynamics, boundary conditions, vapor liquid interphase

Flows and heat transfers in micro-nano conducts are subject to significant interphase phenomena linked to molecular interaction in the vicinity of the wall. In the literature, both experiments and simulations revealed evidence of an enhancement of flow-rate, originated from slip velocity at the solid boundary, due to collisions between gas atoms and the solid wall. Accommodation coefficient and condensation/evaporation coefficients are used to express these velocity boundary conditions. In this work, we have developed a kinetic boundary condition model by a statistical learning study from the incident and reflected velocities of the gas molecules (methane) on the solid wall (quartz), collected from molecular dynamics simulations, using a Lennard Jones potential for methane molecules and a Buckingham potential for quartz. We first obtained the density profiles of the methane gas/liquid at the quartz surface as well as the residence time and the penetration depth of CH 4 in the quartz substrate. The value of the saturated vapor density obtained is in excellent agreement with those of the literature. Finally, we have determined the accommodation and condensation/evaporation coefficients.

Introduction

The objective of the present work is to use Molecular Dynamics (MD) simulations to determine more accurately the scattering behavior of vapor at a solid or liquid interphase by including both mass and other accommodation coefficients for momentum and energy. This scattering model serves as a boundary for kinetic and continuum transport equations. To this end, the velocity, displacement and resident time of atoms are tracked and collected as data, which are then analyzed with standard learning methods. Specifically, the accommodation coefficients are determined via correlation analysis [START_REF] Liao | Helium and argon interactions with gold surfaces[END_REF].

Material and method

The models are composed of quartz (SiO 2 ) substrate and methane (CH 4 ) periodic in x, y directions. The geometric parameters of SiO 2 crystal are as follows: a = b = 4.9137 Å, c = 5.4047 Å, α = β = 90 0 , γ = 120 0 [START_REF] Dolino | La transition αβ du quartz[END_REF]. The solid rectangular substrate has dimensions 8a × 9 √ 3b/2 × 4c and 864 Si atoms and 1728 O atoms. (see Fig. 1). The dimensions of the simulation box along x, y are equal to the corresponding dimensions of the silica substrate while the dimension along z is larger and varied so that we can fill with methane molecules. The Burckingham (BKS) force field [START_REF] Beest | Force Field for Silicas[END_REF] is used to describe the interaction between the Si and O quartz atoms

V BKS ij = C q i q j r ij + A ij exp (-b ij r ij ) - c ij r 6 ij (1)
and the Lennard-Jones (LJ) potential is used to describe the van der Waals interaction between CH 4 molecules, via TraPPE force field [4]

V LJ ij = ϵ ij σ ij r ij 12 - σ ij r ij 6 ( 2
)
and between a CH 4 molecule and Si and O of solid quartz via Lorentz-Berthelot mixing rule from CLAYFF force field [START_REF] Cygan | Molecular models of hydroxide, oxyhydroxide and c[END_REF]. The good performance of the united atom model has been shown in literature.

In Eq.(1, 2), r ij is the distance between two atoms i and j of charges q i and q j . The constants A ij , b ij , c ij are the parameters of BKS potential and ϵ ij and σ ij the parameters of LJ potential and C the energy conversion constant for the Coulombic term. The silica substrate is composed of one fixed lower layer and two upper layers maintained at temperature T w by NVT thermostat. The other boundary of the simulation box is an elastic reflected wall. A suitable number of CH 4 molecules, N , is placed between the solid surface and the reflected wall so that after equilibration process at T w , CH 4 is accumulated into a liquid film on the silica surface and diluted in the remaining space. The choice of temperature T w is also important to guarantee the two phases coexist and the gas phase is sufficiently dilute. In all simulations, T w = 110K, which is slightly above the triple point T tp = 90K. In reduced LJ unit, we have T * = k B T w /ϵ CH 4 = 0.7432, where k B is the Boltzmann's constant. The open source MD code LAMMPS [START_REF] Thompson | LAMMPS -a flexible simulation tool for particle-based materials modeling at the atomic, meso and continuum scales[END_REF] is used for all the simulations. Additional tools are developed to track the atom motions. The latter is placed at distance δ = 20 Å from the liquid-vapor interface. Specifically, when atoms cross the control plane, we are interested in the following quantities: the incoming velocity c in and the outgoing velocity c out , the penetration depth d and the resident time τ between the incoming and outgoing events. Due to the small gas density, it requires 4 × 10 6 time steps of 0.0005 ps to reach equilibrium state and another 10 8 steps for outputting the data. Finally, we analyze the distribution of the data and construct the statistical based models for the liquid-vapor interface.

Simulation results

n(z) = a -b tanh(2(z -c)/d) ⇒ n v sat = lim z→∞ n(z) = a -b (3)
In the case of a large volume of liquid and gas, a = 1 2 (n v sat + n liq sat ) and b = 1 2 (n liq sat -n v sat ), c the location of the interface and d the interface thickness [START_REF] Hansen | Theory of simple liquids[END_REF]. In most simulations, the saturated vapor density is n v sat ≃ 0.07 × 10 -3 Å-3 which corresponds to n v * sat = n v sat σ 3 CH 4 = 0.0036 at T * = 0.7432. The value of n v * sat obtained is in excellent agreement with LJ fluid simulations also worth 0.0036 by [START_REF] Errington | Direct calculation of liquid-vapor phase equilibria from transition matrix Monte Carlo simulation[END_REF] 1 . The accommodation coefficient α and the condensation coefficient α c (calculated as the fraction of condensing molecules N c to all incident molecules N in ), from correlation analysis, associated to a quantity Q can be defined as follow:

α k = 1 -ρ (Q in k ,Q out k ) , α c = N c N in , (N c = N in d>dc ), k = x, y, z (4)
where

ρ (Q in k ,Q out k ) is the correlation coefficient between Q in k and Q out k .
Assuming that the liquid surface is isotropic in the plane xOy, to improve the statistical signal, let us collect the two tangential velocity components c in In Fig. 4, we find that the condensation and the tangential accommodation coefficients are not sensible to the choice of those parameters. The condensation coefficient lies in the range 0.87 -0.89 and the accommodation coefficient 0.55 -0.62. As d c = δ = 20 Å has the physical meaning: atoms penetrating the liquid-vapor interface that we define previously, we shall adopt the criteria from now on. From Fig. 4, we find that the condensation coefficient decreases with increasing film thickness. Only when the film reach certain thickness, the coefficient start to stabilize and become constant. It is suggested the liquid layering has some impact on this coefficient as a large number of atoms are accumulated.

Figure 1 :

 1 Figure 1: Left: of MD system. Color code: blue for methane molecules (CH 4 ), red for oxygen atom (O) and yellow for silicon atom (Si). Right: illustration of penetration depth d and resident time τ .

Figure 2 :

 2 Figure 2: Density of the fluid across the system. The leftmost part of the profile corresponds to the silica wall and has zero density. The rightmost part corresponds to the small but non vanishing gas density.

x and c in y into one group c in xy and c out x and c out y into c out 5 )Figure 3 :

 53 Figure 3: Left: Distribution of resident time. Right: distribution of penetration depth.

Figure 4 :

 4 Figure 4: of the tangential accommodation coefficient α and condensation coefficient α c .

23

  Proceedings of the 4 th European Conference on Non-equilibrium Gas Flows -NEGF23 29-31 March, 2023, Eindhoven, the Netherlands

Proceedings of the 4 th European Conference on Non-equilibrium Gas Flows -NEGF23 29-31 March, 2023, Eindhoven, the Netherlands


Herv É Magnes
email: herve.magnes@imft.fr

Sylvain Marragou

Andrea Aniello

Laurent Selle

Thierry Poinsot

Thierry Schuller

IMPACT OF PREHEATING ON FLAME STABILIZATION AND NOX EMISSIONS FROM A DUAL SWIRL HYDROGEN INJECTOR

Flame stabilization, flame structure and pollutant emissions are investigated experimentally on a swirled injection system operating with globally lean air/hydrogen mixtures at atmospheric conditions and moderate Reynolds numbers. This injector consists of two coaxial ducts with separate injection of hydrogen into a central channel and of air into an annular channel. Both streams are swirled. The resulting flames exhibit two stabilization modes. In one case, the flame takes an M-shape and is anchored to the hydrogen injector lips. In the second case, the flame is aerodynamically stabilized above the injector and takes a Vshape. Regions of existence of each stabilization mode are determined according to the operating conditions. For low air flow rates, the flame can be either anchored or lifted above the hydrogen injector lips depending on the path followed to reach the operating condition. At high air flow rates, the flame is always lifted regardless of the trajectory followed. The impact of air inlet temperature on these stabilization regimes is then evaluated from T = 300 K up to 770 K. Flame re-attachment is shown to be controlled by edge flame propagation and the impact of preheating is well reproduced by the model. Unburnt hydrogen and NO x emissions are finally evaluated. Unburnt hydrogen is only observed for global equivalence ratios below 0.4 and at ambient inlet temperature. NO x emissions decrease when the global equivalence ratio is reduced. Furthermore, at fixed global equivalence ratio, NO x emissions decrease as the thermal power increases, regardless of air preheating and the flame stabilization regime. At high power, NO x emissions reach an asymptotic value that is independent of the thermal power. The impact of flame shape, air preheating and combustion chamber wall heat losses on NO x production is also evaluated. NO x emissions are shown to scale with the adiabatic flame temperature T ad at the global equivalence ratio and the residence time inside the combustor.

INTRODUCTION

Hydrogen is a promising fuel to achieve the decarbonization of the energy sector and an attractive solution to reduce the environmental impact of both aeronautical and land-based gas turbines. Although widely used in rocket propulsion, hydrogen combustion in gas turbines applications remains controversial. H 2 exhibits higher molecular diffusivity, greater laminar burning velocity, larger flammability limits and lower activation energy than standard hydrocarbons [START_REF] Sánchez | Recent advances in understanding of flammability characteristics of hydrogen[END_REF]. These characteristics increase the risk of spontaneous ignition and flashback in premixed systems, raising important safety concerns [START_REF] Yahou | Impact of chamber back pressure on the ignition dynamics of hydrogen enriched premixed flames[END_REF].

For these reasons, current H 2 technologies are mainly based on separate injection of reactants [START_REF] Etnglobal | Hydrogen Gas Turbines: The Path Towards a Zero-Carbon Gas Turbine[END_REF]. Nevertheless, this approach promotes the formation of diffusion-controlled flames that, exhibiting higher flame temperatures, produce greater NO x emissions [START_REF] Skottene | A study of NOx formation in hydrogen flames[END_REF]. Hence, it is necessary to develop combustion systems that simultaneously limit this NO x production and comply with safety standards.

In this respect, several approaches have been proposed and a comprehensive review of the technologies currently developed was proposed by Du Toit et al. [START_REF] Du Toit | Reviewing H2 Combustion: A Case Study for Non-Fuel-Cell Power Systems and Safety in Passive Autocatalytic Recombiners[END_REF]. It emerges that Dry Low NO x (DLN) technologies are the most widely accepted because they guarantee higher efficiency and durability. One example of DLN strategy is based on Lean Direct Injectors (LDI), which are designed to provide a late injection of fuel into the combustion chamber to avoid flashback on one side, and favor mixing between reactants to mitigate NO x emissions on the other side. This is the strategy used in Micromix Injection Systems (MMI), which consists on dividing the main fuel and air streams into a multitude of small nozzles distributed all over the combustion chamber backplane, leading to a collection of small flames. Many versions of MMI can be found, which differ mainly by the fuel injection system adopted: micro swirl-based injection [START_REF] Dodo | Combustion characteristics of a multiple-injection combustor for dry low-NOx combustion of hydrogen-rich fuels under medium pressure[END_REF][START_REF] Hernandez | Micro-mixing fuel injectors for low emissions hydrogen combustion[END_REF] or jet in cross-flow injection [START_REF] Funke | 30 years of dry low nox micromix combustor research for hydrogen-rich fuels: An overview of past and present activities[END_REF][START_REF] York | Development and testing of a low NOx hydrogen combustion system for heavy-duty gas turbines[END_REF][START_REF] Marek | Low emission hydrogen combustors for gas turbines using lean direct injection[END_REF]. Even though MMI technologies enable to reduce NO x emissions [START_REF] Haj Ayed | Improvement study for the dry-low-NOx hydrogen micromix combustion technology[END_REF], they require substantial modifications of the combustion chamber architecture, raising many challenges in terms of design, manufacturing and implementation. Moreover, Funke et al. [START_REF] Funke | 30 years of dry low nox micromix combustor research for hydrogen-rich fuels: An overview of past and present activities[END_REF] showed that to achieve safe and reliable nominal engine operation, specific procedures must be followed limiting the operability range of the engine. For instance, the M1A Micromix prototype requires a variable control of the injection zone to ensure flame stability during the ignition sequence [START_REF] Funke | 30 years of dry low nox micromix combustor research for hydrogen-rich fuels: An overview of past and present activities[END_REF].

These limitations make conventional swirl burners an appealing solution to design non-premixed systems because of the established know-how, the flexible control and their easier implementation in current combustion chamber architectures. Moreover, swirl flows are a well-known versatile solution to stabilize aerodynamically flames [START_REF] Syred | Combustion in swirling flows: A review[END_REF], limit flame blow-off [START_REF] Choi | Flame structure and NOx emission characteristics in a single hydrogen combustor[END_REF] and reduce NO x emissions [START_REF] Claypole | The effect of swirl burner aerodynamics on nox formation[END_REF] thanks to the mixing enhancement between reactants. Recent experimental and numerical investigations conducted with swirl burners powered by H 2 are mostly dedicated to premixed [START_REF] Reichel | Flow field manipulation by axial air injection to achieve flashback resistance and its impact on mixing quality[END_REF][START_REF] Capurso | NOx pathways in lean partially premixed swirling H2-air turbulent flame[END_REF] or technically-premixed systems [START_REF] Chterev | Effect of hydrogen enrichment on the dynamics of a lean technically premixed elevated pressure flame[END_REF]. Cheng et al. [START_REF] Cheng | Laboratory investigations of a low-swirl injector with H2 and CH4 at gas turbine conditions[END_REF], for instance, adopted a conventional premixed low swirled burner fueled with H 2 demonstrating that, despite its good performances in terms of emissions, premixed systems remain subjected to flame anchoring and flashback issues.

To counter these negative aspects and keep advantage of swirl injectors, an alternative system is proposed in this study. The HYdrogen LOw NO x injector (HYLON) is developed at IMFT laboratory in collaboration with Safran Helicopter Engine [START_REF] Richard | Dispositif d'injection de dihydrogène et d'air[END_REF]. It consists of two swirled coaxial ducts to keep the reactants separated upstream the combustion chamber [START_REF] Marragou | Stabilization regimes and pollutant emissions from a dual fuel CH4/H2 and dual swirl low NOx burner[END_REF]. As demonstrated by Yuasa et al. [START_REF] Yuasa | Effects of swirl on the stability of jet diffusion flames[END_REF], co-swirling fuel and air streams promotes flame lifting.

Degeneve et al. [START_REF] Degeneve | Effects of Swirl on the Stabilization of Non-Premixed Oxygen-Enriched Flames above Coaxial Injectors[END_REF][START_REF] Degeneve | Impact of co-And counter-swirl on flow recirculation and liftoff of non-premixed oxy-flames above coaxial injectors[END_REF] adopted a similar double-swirled injector to stabilize oxy-methane flames, putting in evidence several flame stabilization regimes depending on the impulsion ratio between the fuel and air streams. The same burner was exploited by Leroy et al. [START_REF] Leroy | Stabilization of Low-Nox Hydrogen Flames On a Dual-Swirl Coaxial Injector[END_REF] to investigate NO x productions from H 2 -air flames. In the meantime, Marragou et al. [START_REF] Marragou | Stabilization regimes and pollutant emissions from a dual fuel CH4/H2 and dual swirl low NOx burner[END_REF] conducted a geometrical parametric study on a coaxial swirled injector for H 2enriched flames. It was shown that a small recess between the hydrogen injector lip and the chamber backplane enables to widen the burner operability range leading to lifted flames. In the last two studies [START_REF] Marragou | Stabilization regimes and pollutant emissions from a dual fuel CH4/H2 and dual swirl low NOx burner[END_REF][START_REF] Leroy | Stabilization of Low-Nox Hydrogen Flames On a Dual-Swirl Coaxial Injector[END_REF], the chosen injection strategies lead to controlled NO x emissions for a variety of operating conditions and two main stabilization modes were identified: flames anchored to the hydrogen nozzle and aerodynamically stabilized flames.

A recent numerical study from Aniello et al. [START_REF] Aniello | Experimental and numerical investigation of two flame stabilization regimes observed in a dual swirl h2-air coaxial injector[END_REF] considers the HYLON injector and scrutinizes the flame structure and the stabilization mechanisms for the aforementioned regimes. They showed that H 2 attached flames are entirely governed by diffusion, while lifted flames present a central diffusion branch accompanied by a lateral partially premixed flame wing. Hence, the flame stabilization mode, the air and hydrogen injections velocities, alter the NO x emissions. More recently, Marragou et al. [START_REF] Marragou | Experimental analysis and theoretical lift-off criterion for h2/air flames stabilized on a dual swirl injector[END_REF] identified the edge flame displacement of the diffusion branch as the controlling mechanism for flame re-anchoring that was also corroborated by numerical flow simulations [START_REF] Aniello | Experimental and numerical investigation of two flame stabilization regimes observed in a dual swirl h2-air coaxial injector[END_REF].

The present work investigates an evolution of the HYLON injector with a new optimized geometry enabling to (1) augment the injection velocities by reducing pressure losses and (2) further widen its operability with lifted flames. The test rig is not designed to sustain high pressure, but air can be preheated to get closer to engine-like operating conditions. The objectives are to expand the range of operating conditions tested in previous studies and evaluate the impact of air pre-heating temperature on flame structure, flame stabilization, and NO x emissions.

The experimental setup is described in the next section, followed by a parametric analysis of flame stabilization with a focus on the impact of air preheating. Finally NO x emissions are considered for ambient and preheated conditions before conclusions are drawn.

EXPERIMENTAL SETUP

Figure 1(a) shows the test rig and the HYLON burner, which is an optimized version of the one investigated in [START_REF] Marragou | Stabilization regimes and pollutant emissions from a dual fuel CH4/H2 and dual swirl low NOx burner[END_REF][START_REF] Aniello | Experimental and numerical investigation of two flame stabilization regimes observed in a dual swirl h2-air coaxial injector[END_REF][START_REF] Marragou | Experimental analysis and theoretical lift-off criterion for h2/air flames stabilized on a dual swirl injector[END_REF]. The test bench is used to stabilize H 2 -air swirled flames with the objective to minimize the pressure losses through the injector and the range of operating conditions with lifted flames. The mass flow rates of air and hydrogen are regulated via two Brooks SLA 585x series mass flow controllers. Dry air is supplied at the bottom of the plenum and goes through a LEISTER 5000-DF heater, which is used in the study to control the air injection temperature inside the combustion chamber. The pre-heated air passes through a cylindrical plenum and through a convergent section. It then penetrates the annular channel of the injector with an external diameter d e = 18 mm. Hydrogen is injected at ambient conditions via a central lance of internal diameter d i = 6 mm, coincident with the central axis of the burner. A close up of the HYLON injector cross section is presented in Fig. 1(b). The annular nozzle is equipped with a radial to axial swirl vane shown in Fig. 1(c) that produces a swirl number S e = 0.9 estimated with geometrical considerations. The internal H 2 nozzle, instead, embeds an axial swirler shown in Fig. 1(d), which generates a swirl number S i = 0.6. Figure 1(b) also highlights an injector recess z i = 6 mm corresponding to the distance between the chamber backplane and the top of the hydrogen injection tube that favors mixing between reactants upstream the combustion chamber. The lip of the hydrogen nozzle features a 45 • chamfer that increases the H 2 tube external diameter from 10 mm to 12 mm. The flame is confined in a square combustion chamber, which is made of four quartz windows to provide full optical access to the reaction zone. The combustion chamber has a square cross section of d q = 78 mm width and L q = 150 mm length. It also A 50 mm-thick refractory ceramic fiber envelope can also be added around the combustion chamber to limit the wall heat losses. The temperature of the burnt gases T gb is measured by a double bead thermocouple coupled to the Reduced Radiation Error technique [START_REF] Brohez | A twothermocouples probe for radiation corrections of measured temperatures in compartment fires[END_REF]. Temperatures were measured at different locations at the combustion chamber outlet and show very similar results except near the walls. Only the temperature T gb in the center of the outlet section is presented.

Mean flame images are collected in the visible band with a Nikon D7500 with a lens Nikon AF-S VR Micro-Nikkor 105 mm f/2.8G IF-ED or with a Princeton PIMAX-4 intensified CCD camera equipped with a 105 mm f/4.5 Nikon Rayfact UV-105 lens. For the latter, a narrow band filter ASAHI XHQA310 centered at 310±10 nm is used to isolate the OH * signal peak emission, which is used as qualitative marker for the heat release rate [START_REF] Price | Optical studies of the generation of noise in turbulent flames[END_REF].

Emissions are measured with an ECOM J2KN Pro flue gas analyzer with a probe collector located at the outlet of the combustor chamber on the centerline as indicated in Fig. 1(a). Additional samples were also made at different radial locations, with and without the probe collector cooling, without showing substantial differences. The NO and NO 2 concentrations of the sampled dried flue gases are given with a confidence interval of ±5% with respect to the measured value. Data are here only reported as NO x without distinguishing between NO and NO 2 .

FLAME STABILIZATION

The different regimes obtained with this new version of the HYLON burner are reported in the stabilization map in Fig. 2 when air is injected at ambient temperature. Results are presented as a function of the mass flow rate of hydrogen ṁH 2 and mass flow rate of air ṁair . Iso-values of the global equivalence ratio are also reported as black lines from φ g = 0.1 to φ g = 1.0. The blue square markers in Fig. 2 represent the operating conditions that separate three zones corresponding to different stabilization regimes.

Zone 1 occupies the bottom left side of the map and is observed for low mass flow rates of air and hydrogen. This regime always results in anchored flames, such as the one shown in Fig. 3(a). This flame archetype was already observed in the previous version of the burner [START_REF] Marragou | Stabilization regimes and pollutant emissions from a dual fuel CH4/H2 and dual swirl low NOx burner[END_REF][START_REF] Aniello | Experimental and numerical investigation of two flame stabilization regimes observed in a dual swirl h2-air coaxial injector[END_REF]. Zone 2 is observed for higher fuel mass flow rates ṁH 2 than Zone 1 and for air mass flow rates ṁair higher than 1.3 g/s for this geometrical configuration of the HYLON injector. In this regime a dual stabilization mode is observed for the same operating conditions, with anchored or lifted flames depending either on the path followed to reach the operating point or on the ignition procedure adopted. For instance, Figs. 3(b-c) show anchored and lifted flames for the same reactants mass flow rates: ṁair = 3.46 g/s and ṁH 2 = 0.05 g/s. Flames belonging to Zone 1 and Zone 2 were already investigated in [START_REF] Marragou | Stabilization regimes and pollutant emissions from a dual fuel CH4/H2 and dual swirl low NOx burner[END_REF][START_REF] Aniello | Experimental and numerical investigation of two flame stabilization regimes observed in a dual swirl h2-air coaxial injector[END_REF] for gases injected at ambient conditions. It was shown that the transition from lifted to anchored flames, i.e. from Zone 2 to Zone 1, is controlled by the propagation of an edge flame [START_REF] Marragou | Experimental analysis and theoretical lift-off criterion for h2/air flames stabilized on a dual swirl injector[END_REF]. To identify the H 2 threshold velocity at which this transition takes place, the H 2 injection mass flow rate is gradually reduced until the sudden transition to an attached flame belonging to Zone 1.

Zone 3 is reached for air mass flow rates higher than roughly ṁair = 5.0 g/s, quasi-independently of the H 2 content. The threshold air velocity is determined by gradually increasing the air mass flow rate starting from an anchored flame in Zone II (e.g. Flame B). In this regime, the flame is unconditionally lifted regardless the path followed to reach the selected operating condition, except for very low hydrogen mass flow rates corresponding to the red color region at the bottom of the chart. An example of lifted flame in this regime is reported in Fig. 3(d). When the hydrogen mass flow rate is reduced, a reaction layer gradually approaches closer to the hydrogen nozzle rim an eventually ends up to re-attach to the burner rim. This transition is smooth and does not feature any hysteresis: when the hydrogen flow rate is re-increased the flame also progressively detaches from the hydrogen nozzle rim for the same conditions as those observed for flame anchoring to the nozzle. This smooth transition free of any hysteresis contrasts with the abrupt switch from lifted flames in Zone 2 to attached flames in Zone 1 as studied in [START_REF] Marragou | Experimental analysis and theoretical lift-off criterion for h2/air flames stabilized on a dual swirl injector[END_REF] when the hydrogen flow rate is reduced. The transition from Zone 1 to Zone 3, and conversely from Zone 3 to Zone 1, is intermittent with a flame randomly switching between the two stabilization modes.

Figures 3(a-d) show four mean flame images corresponding to the operating conditions described in Tab. 1 and highlighted by the colored disks in Fig. 2. The left-hand side of each image corresponds to the visible light recorded by a standard camera. The right-hand sides result from Abel deconvolution of the line of sight integrated OH * signal. They are used to infer the location of the different reaction layers in the axial plane of the burner.

Figures 3(a-b) correspond to attached flames A and B belonging to Zones 1 and 2 respectively. These flames feature the same global equivalence ratio φ g but different thermal powers P th . They both have an M-shape characterized by two main branches. The lateral one, denoted II and delimited by dotted lines in Figs. [START_REF] Etnglobal | Hydrogen Gas Turbines: The Path Towards a Zero-Carbon Gas Turbine[END_REF], penetrates inside the injector and stabilizes on the hydrogen injection tube lips. The flame root protruding in- [START_REF] Schefer | Visible emission of hydrogen flames[END_REF]. The normalized OH * signal is much weaker along the reaction front I than along the lateral branch II in Figs. 3(a-b). It was shown in [START_REF] Aniello | Experimental and numerical investigation of two flame stabilization regimes observed in a dual swirl h2-air coaxial injector[END_REF] that flames A and B are entirely controlled by diffusion processes. Figures 3(a-b) reveal however some differences. For instance, the OH * signal indicates that the apex of the central branch I of flame B is closer to the injector outlet than in flame A. This difference is due to the different intensity of the CRZ when the mass flow rates of reactants are increased. Moreover, while the distributions of the reaction rate are similar in the two cases, the thickness of the OH * footprint for the lateral branch II is narrower for flame B than for flame A. This observation corroborates the diffusion nature of this reaction layer. Flame B is subject to a higher strain rate due to higher air and hydrogen flow injection velocities leading to a reduction of the thickness of the reaction zone.

Flames B and C in Figs. 3(b-c) are now considered. They both can be found in Zone 2 and are obtained for the same injection conditions (see Tab. 1), but flame B is anchored to the hydrogen nozzle while flame C is lifted. The main difference between flames B and C is that the lateral branch II from flame C is detached from the hydrogen injector lips and stabilizes a few millimeters above the chamber backplane. Concomitantly, the central branch I in flame C is pushed closer to the injector outlet, as highlighted by the position of the dashed line in Fig. 3(c). Since the lateral branch II moves downstream and the central branch I stabilizes upstream, the two reaction layers get closer to each other with respect to the attached flames A and B, in which cases the reaction layers I and II are well separated. Furthermore, the normalized OH * intensity of the apex of the central reaction layer I from the lifted flame C in Fig. 3(c) lying on the symmetry axis of the burner takes now much higher values than the apex of the central branch I for the anchored flame B shown in Fig. 3(b). Simultaneously, the highest normalized OH * intensity reached along the reaction layer II shifts downstream with respect to flame B. While branches I and II from flame B are entirely dominated by diffusion reactions, the lifted branch II from flame C lies far from the hydrogen and air injector nozzles. Partial mixing takes place between the reactants before combustion and branch II is a partially premixed flame as confirmed in [START_REF] Aniello | Experimental and numerical investigation of two flame stabilization regimes observed in a dual swirl h2-air coaxial injector[END_REF]. This is the main reason why lifted flames produce less NO x than attached flames [START_REF] Marragou | Stabilization regimes and pollutant emissions from a dual fuel CH4/H2 and dual swirl low NOx burner[END_REF].

Flames C and D in Figs. 3(c-d) are finally compared. They share the same global equivalence ratio φ g but the thermal power P th is the double for flame D (see also Tab. 1). Doubling the reactant velocities, the flame length slightly increases from flame C to D and the location of the maximum reaction rate is pushed fur- ther downstream along the dotted line on the right in Fig. 3(d).

Interestingly, the left image in Fig. 3(d) also indicates that the flame branch I looses the reddish color from hot H 2 O * emission for the other operating conditions in Fig. 3(a-c). This suggests that the temperature along branch I is cooler for Flame D compared to previous operating conditions. Moreover, the lateral branch II and the central branch I cannot be distinguished anymore for flame D. The upstream displacement of the central flame branch I observed during the transition from flame B to C, is exacerbated in flame D, and the two branches I and II have merged. This again is corroborated by the simulations conducted in [START_REF] Aniello | Experimental and numerical investigation of two flame stabilization regimes observed in a dual swirl h2-air coaxial injector[END_REF] for different operating conditions. These experiments prove that at high flow rates, the central diffusion reaction layer I and the lateral partially premixed reaction layer II merge together leading to a unique lifted reaction layer with a diffusion structure at the flame apex lying on the burner symmetry axis and a mixture composition gradient along the wings of the flame brush.

Another interesting feature is that blow-off could not be reached for all the operating range which was tested, even at very lean injection conditions φ g < 0.1. This is due to the separate injection of air and hydrogen yielding always a stoichiometric zone close to the central injector outlet, even for very low hydrogen flow rates. However, injection of hydrogen at very lean conditions φ g ≤ 0.3 results in incomplete combustion with unburnt H 2 remaining in the exhaust gases, as indicated in Tab. 2. At φ g = 0.3, low levels of unburnt H 2 are only observed at low thermal power. Hence, although anchored flames are generally undesirable, they favor a better combustion efficiency. When φ g < 0.3, the H 2 concentration in the burnt gases remains high, regard-

H.MAGNES

IMPACT OF AIR PRE-HEATING

In a gas-turbine, air is compressed before entering the combustion chamber and its injection temperature can reach up to T air,in = 950 K. Hence, from technical perspective it is necessary to assess the impact of the thermodynamic inlet conditions on the stabilization chart shown in Fig. 2, which was obtained by injecting air at ambient temperature. The effect of the air preheating is analyzed in Fig. 4, while the impact of increasing pressure is left for further studies. The boundaries between Zone 1, Zone 2 and Zone 3 are only reported for air mass flow rates higher than ṁair = 3.2 g/s, which is the minimum required to avoid overheating of the air preheater.

Increasing the air inlet temperature T air,in shifts the boundary between Zones 1 and 2 towards higher H 2 mass flow rates ṁH 2 and the boundary between Zones 2 and 3 to lower air mass flow rates ṁair . Hence, Zones 1 and 3 expand by increasing the air inlet temperature, while Zone 2 shrinks at high H 2 mass flow rates. As a consequence, Zone 2 exhibiting a dual stabilization mode disappears by increasing the air inlet temperature and the transition between lifted and anchored flames becomes predominantly driven by the air mass flow rate.

The shift of the boundary between the Zones 2 and 3 with air preheating can be further analyzed. A higher air inlet temperature increases the reactivity of the combustible mixture and this effect is expected to delay the lift-off of the flame. Nevertheless, Fig. 4 shows the opposite trend. This may be caused by the air volumetric flow rate that increases linearly with the inlet temperature T air,in for these experiments conducted at atmospheric conditions. For a fixed air mass flow rate, the increase of the air injection velocity overwhelms the greater reactivity of the mixture, thereby promoting the lifted stabilization regime. It is important to note that in a real engine, temperature and pressure are closely related. In such cases, an increase in the air bulk velocity due to the rise of the air inlet temperature would be partially balanced by the increase in density due to the rise in pressure, and the velocity field would remain roughly unchanged. Thus, the sensitivity of flame stabilization regime to the air inlet temperature may vary when both temperature and pressure are changed.

The shift of the boundary between Zone 1 and Zone 2 due H.MAGNES 6 GTP-23-1517 to the increase of the air preheating is now considered. Figure 5 shows how the hydrogen injection velocity leading to flame reattachment, i.e. transition from Zone 2 to Zone 1, scales with the triple flame speed when air is preheated. Marragou et al. [START_REF] Marragou | Experimental analysis and theoretical lift-off criterion for h2/air flames stabilized on a dual swirl injector[END_REF] showed that lifted flame re-attachment is driven by the propagation of an edge flame, which is capable of reaching the hydrogen injector lip when the leading edge flame speed S d exceeds the local flow velocity along the most reactive mixture fraction line Z max [START_REF] Muñiz | Instantaneous flamestabilization velocities in lifted-jet diffusion flames[END_REF][START_REF] Joedicke | The stabilization mechanism and structure of turbulent hydrocarbon lifted flames[END_REF]. The edge flame velocity along this line is estimated with:

S d = S l,max ρ u ρ b 1/2 (1)
where S l,max corresponds to the maximum laminar burning velocity, and ρ u /ρ b is the volumetric expansion ratio of gases through the flame calculated for Z max with Cantera 1D simulations. In Fig. 5, the hydrogen transition velocity U H 2 ,T and the edge flame speed S d are both normalized by their respective values U 0 H 2 ,T and S 0 d obtained at ambient conditions. Only the operating conditions belonging to the boundaries between Zones 1 and 2 observed at different air preheating are considered. Figure 5 indicates that an increase in S d due to higher air preheating corresponds to a proportional increase in U H 2 ,T , which extends Zone I. This proportional relationship between the two parameters supports the flame re-anchoring mechanism identified in [START_REF] Marragou | Experimental analysis and theoretical lift-off criterion for h2/air flames stabilized on a dual swirl injector[END_REF]. In this analysis, H 2 which is injected at ambient temperature is assumed to be unaltered by air preheating.

The impact of T air,in on the shape taken by a flame belonging to Zone 3 is illustrated in Fig. 6. The normalized OH * distribution in the axial plane of the burner is presented for five flames characterized by an equivalence ratio φ g = 0.6, thermal power P th = 18 kW and different air inlet temperatures from T air,in = T amb to T air,in = 673 K. The air volumetric flow rate increases linearly with temperature, while the hydrogen flow rate is kept constant. Values for u b,air and u b,H 2 at different air inlet temperatures are given in Tab. 3.

The green markers correspond to the maximum OH * intensity for each operating condition. The position of the markers moves slightly closer to the injector outlet when the air inlet temperature T air,in increases, unveiling a small shortening of the flame due to air preheating. The reactivity of the mixture increases and the flame becomes more compact. This is in agreement with the intensity of the OH * signal that rises regularly with the increase of T air,in , suggesting larger burning rates. While increasing the air inlet temperature T air,in produces more compact flames, the stabilization mode in Zone 3 remains however unchanged. At least for the operating conditions considered, the flames remain lifted over a span of air inlet temperatures of technical interest.

NO x EMISSIONS

NO x are collected at the chamber outlet using the gas analyzer probe. Measurements are performed after the combustor has reached global thermal equilibrium determined by the inertia of the metallic walls. Thermocouples inserted at different locations in the metal are used to check that thermal equilibrium has been reached. It typically takes 20 minutes after ignition in the worst cases.

NO x concentrations in ppm (at 15% O 2 ) are reported in Fig. 7 as a function of the global equivalence ratio φ g and thermal power P th when the air inlet temperature is kept at ambient conditions T amb . Operating conditions with φ g < 0.3 are not considered in this study due to the significant amount of unburned H 2 present in the exhaust gases. The square markers denote lifted flames. Triangles correspond to anchored flames. At low thermal powers P th , flames are anchored at all global equivalence ratios. For thermal powers higher than P th = 12 kW, flames are always lifted due to the higher air and H 2 injection velocities that favor flame detachment. Nevertheless, there is a range of thermal powers for which flames undergo two possible sta- bilization modes, which also depends on the selected equivalence ratio. For φ g = 0.6, flames can be attached or lifted for 5 kW ≤ P th ≤ 10 kW.

Overall, NO x emissions increase when the global equivalence ratio φ g increases from 0.3 to 0.6 due to the rise of the flame temperature that promotes the formation of NO x in the burnt gases through the thermal Zeldovich route. More interestingly, Fig. 7 also shows that NO x emissions reduce regularly by increasing the thermal power, regardless of the global equivalence ratio and irrespective of the flame stabilization regime. NO x concentrations tend towards a plateau for high thermal powers which appears to be only a function of global equivalence ratio. A thorough analysis of this behavior would require to scrutinize the structure of the reaction layers, which is out of the scope of this study. However, hypotheses can be made to interpret these results. For the thermal NO x route, emissions mainly depend on the adiabatic flame temperature. Thermal NO x are formed in zones where the temperature is greater than 1800 K [START_REF] Steele | Nox and n2o in lean-premixed jet-stirred flames[END_REF] and the residence time in these zones will determine the NO x concentrations. Hence, higher injection velocities leading to a lower residence time could explain the decrease of NO x emissions when the thermal power increases. Nevertheless, other reasons can also be identified. In case of separate injections of air and hydrogen, the flame temperature depends on the local combustion mode. For diffusion reaction layers, such as branch I of lifted flames and branches I and II for anchored flames, higher injection velocities lead to higher strain rates along these diffusion reaction layers, which become thinner and reduce their temper-H.MAGNES ature [START_REF] Lee | Flame structure and thermal no x formation in hydrogen diffusion flames with reduced kinetic mechanisms[END_REF]. This second mechanism also results in lower NO x concentrations. Finally, for the partially premixed rich branch II, the flame temperature is linked to the local equivalence ratio φ that mainly depends on the mixing efficiency between the air and hydrogen streams. Additional experiments not shown here indicate that mixing between the air and hydrogen streams exhausting from the HYLON burner mainly depends on the velocity ratio between the air and hydrogen streams. When the equivalence ratio is kept constant as in these experiments, this velocity ratio remains unchanged too. Consequently, the observed reduction of NO x emissions may probably not be attributed to a better mixing between the hydrogen and fuel streams. Finally, for the operating conditions leading either to anchored or lifted flames, NO x emissions are lower when the flame is lifted. At very low powers, the NO x levels become however comparable for lifted and anchored flames, like for instance at P th = 4 kW for φ g = 0.4 and φ g = 0.5.

The impact of air-preheating on NO x emissions is now investigated by keeping constant the global equivalence ratio to φ g = 0.4. Figure 8 plots the NO x concentrations in ppm against the input thermal power P th for air-inlet temperatures ranging from T amb = 293 K to T air,in = 673 K. A similar trend is observed as in Fig. 7 obtained for air injected at ambient conditions. Increasing the power, NO x concentrations decrease regularly towards a plateau, reaching a value below 5.0 ppm regardless of the air pre-heated temperature. NO x levels measured at T amb and T air,in = 373 K are close and only a further increase of the air inlet WHL ratio -66% -60% -53% -54% -49% temperature marks a detectable increase. Overall, NO x emissions only slightly increase when the air inlet temperature increases from T amb and T air,in = 673 K. This is consistent with the NO x dependence on the flame temperature [START_REF] Frassoldati | A wide range modeling study of NOx formation and nitrogen chemistry in hydrogen combustion[END_REF]. Moreover, increasing the air inlet temperature T air,in only alters the flame stabilization regime at low power. For example, increasing the air inlet temperature from T amb to 473 K at P th = 6 kW favors a transition from a lifted to an anchored flame. But, when P th ≥ 6 kW the flame stabilization regime becomes insensitive to the air injection temperature T air,in , confirming the results presented in Fig. 6. As a consequence, the gap in the NO x production is only the consequence of the air preheating and does not dependent on the way the flame is stabilized. Figure 9 shows how NO x emissions increase with the air preheat temperature T air,in at a fixed global equivalence ratio φ g = 0.4 and given thermal power P th = 9kW. Results are compared for two different insulations of the combustion chamber, leading to different heat losses from the exhaust gases leaving the combustor. The blue line corresponds to the results with four quartz windows. The red line corresponds to a chamber insulated with a refractory fiber ceramic shell. The global wall heat losses (WHL) for each condition are estimated in Tab. 4 by comparing the adiabatic flame temperature T ad with the temperature T gb at the chamber outlet. The adiabatic temperature T ad is calculated for a mixture featuring the global equivalence ratio. The results indicate an increasing dependence of NO x emissions on WHL when air is preheated. At ambient conditions, 66% reduction in WHL leads to only a 23% increase in NO x emissions, suggesting that most NO x are formed in zones where WHL have a weak impact, such as in flame fronts or in the CRZ, where the local temperature is high [START_REF] Aniello | Experimental and numerical investigation of two flame stabilization regimes observed in a dual swirl h2-air coaxial injector[END_REF]. The contribution from the outer recir- culation region and from the post-flame region, which are more sensitive to WHL, may explain the weak elevation of the difference in NO x emissions that increase with air preheating. For example, a 57% increase in NOx emissions is observed with a 49% reduction in WHL at T air,in = 723 K. Further experiments are needed to better evaluate the impact of WHL.

NO x emissions can here be scaled with the flame temperature T ad and the residence time τ r of the burnt gases inside the combustor, which are known to determine NO x emissions formed by the Zeldovich pathway [START_REF] Tuncer | Dynamics, NOx and flashback characteristics of confined premixed hydrogen-enriched methane flames[END_REF][START_REF] Oh | EINOx scaling in a non-premixed turbulent hydrogen jet with swirled coaxial air[END_REF][START_REF] Hwang | NOx Scaling of Syngas H2/CO Turbulent Non-Premixed Jet Flames[END_REF]. The adiabatic flame temperature T ad directly affects NO x formation in the flame front and can also impact post-flame regions depending on the residence time τ r . Oh et al. [START_REF] Oh | EINOx scaling in a non-premixed turbulent hydrogen jet with swirled coaxial air[END_REF] identified a relationship between NO x and τ 1/2.8 r for a fixed equivalence ratio. A similar relation is considered and tested in Fig. 10 using the entire set of data with the combustion chamber equipped with quartz windows. Different estimates of the residence time τ r can be used. Hwang et al. [START_REF] Hwang | NOx Scaling of Syngas H2/CO Turbulent Non-Premixed Jet Flames[END_REF] use the residence time of the hot gases in the flame volume [START_REF] Hwang | NOx Scaling of Syngas H2/CO Turbulent Non-Premixed Jet Flames[END_REF]. Leroy et al. [START_REF] Leroy | Stabilization of Low-Nox Hydrogen Flames On a Dual-Swirl Coaxial Injector[END_REF] used the residence time of the flow in the entire combustion chamber. The second approach is retained here by assuming that it is proportional to the effective residence time in high temperature regions:

τ r = L q S q ρ b /( ṁair + ṁH 2 ) (2)
where L q is the chamber length, S q is the square cross section area of the chamber and ρ b is the density of burned gases calculated by 1D Cantera simulations. Fig. 10 shows that NOx emis-sions scale with T ad τ 1/3 r , especially at high thermal power for lifted flames, which have lower local flame temperatures close to T ad . Departure from the scaling law are also observed for anchored flames in the upper right part in Fig. 10. This may be consequent to the reduction of the strain rate leading to an increase of the local flame temperature in diffusion reaction layers and higher NO x emissions, as observed in [START_REF] Hwang | NOx Scaling of Syngas H2/CO Turbulent Non-Premixed Jet Flames[END_REF].

Finally, Figs. 7 and8 show that NO x emissions remain globally low even at T air,in = 723 K, where NO x remain below 15 ppm. These emission levels should be compared to those measured for rupture low-NO x technologies like micromix systems [START_REF] Hernandez | Micro-mixing fuel injectors for low emissions hydrogen combustion[END_REF][START_REF] Marek | Low emission hydrogen combustors for gas turbines using lean direct injection[END_REF][START_REF] Haj Ayed | Improvement study for the dry-low-NOx hydrogen micromix combustion technology[END_REF] or premixed and technically premixed hydrogen injectors [START_REF] Reichel | Flow field manipulation by axial air injection to achieve flashback resistance and its impact on mixing quality[END_REF][START_REF] Brunetti | Experimental and numerical characterization of lean hydrogen combustion in a premix burner prototype[END_REF]. Operating the HYLON burner to ultra lean conditions with φ g ≤ 0.3 yields to a further abatement of NO x emissions.

CONCLUSION

The swirled HYLON injector operating with globally lean hydrogen/air mixtures has been tested with air injected at ambient temperature and with preheated air in a test rig at atmospheric pressure. Two flame archetypes have been observed. The first one is anchored to the hydrogen nozzle increasing the thermal load on this component. This burning mode is favored by the high reactivity of hydrogen. The second mode leads to aerodynamically stabilized flames with a low thermal stress on the burner.

It has been shown that the HYLON operability chart can be split in three zones. For low air and low hydrogen flow rates, the flame remains unconditionally anchored to the injector lips (Zone I). When the hydrogen injection velocity increases, the flame can be either anchored or lifted above the hydrogen injector lips depending on the path followed to reach the operating condition (Zone II). For high air flow rates, the flame is always lifted regardless of the path followed to reach the chosen operating condition (Zone III).

Flame transitions between these different zones have been determined together with the impact of the air inlet temperature up to 770 K. It was demonstrated that the size of Zone 1 is controlled by the increase of the edge flame velocity with the air preheat temperature. However, air preheating has minimal effect on Zone III, despite a reduction in flame size due to the increased reactivity of the preheated flames.

NO x emissions have been measured for increasing thermal powers at different global equivalence ratios. Slight differences on NO x emissions are observed between the two stabilization modes but the emissions drop when the thermal power increases. The same trend is observed when air is preheated. For the lean operating conditions investigated, and regardless of the wall chamber heat losses, NO x concentrations remain low for all operating conditions tested. For instance, at φ g = 0.4, NO x emissions at 15% O 2 molar fraction remain in all cases below 15 ppm even H.MAGNES 10 GTP-23-1517 for air preheated up to T air,in = 770 K. Finally, it was shown that NO x emissions scale with the product of the adiabatic flame temperature T ad and chamber residence time τ r raised to the power 1/3. These experiments indicate that the HYLON injector has promising characteristics in terms of flame stabilization, low thermal stress and NO x emissions for aerojet engines. It enables to stabilize lifted flames over a wide range of operating conditions with flames that are barely affected by air preheating. However, additional investigations must be carried out to investigate its performance at higher pressures and higher Reynolds numbers to get closer to engine like conditions.

FIGURE 1 :

 1 FIGURE 1: Diagram of the HYLON bench containing a LEIS-TER 5000DF preheater (a), with a close up of the injector geometry (b) and pictures of the radial-axial air swirler (c) and axial H 2 swirler (d).

FIGURE 2 :

 2 FIGURE 2: Stabilization map identifying three zones that correspond to different flame stabilization regimes gathered for ambient air inlet temperature.

FIGURE 3 :

 3 FIGURE 3: Flame images corresponding to different stabilization regimes. Left: Direct visualization in the visible band. Right: Inverse Abel transformed OH * images. (a) Anchored flame in Zone 1. (b) Anchored flame in Zone 2. (c) Lifted flame in Zone 2. (d) Lifted flame in Zone 3. Operating conditions are given in Tab. 1.

FIGURE 4 :

 4 FIGURE 4: Flame stabilization maps obtained with the HYLON injector for different levels of air preheating: from ambient temperature to T air,in = 673 K. Red: Zone I. Green: Zone II. Blue: Zone III.

FIGURE 5 :

 5 FIGURE 5: Evolution of the H 2 bulk velocity U H 2 ,T corresponding to the transition between Zone 2 and Zone 1 with respect to the edge flame velocity S d calculated from CANTERA 1D simulations according to Eq. (1). Both variables are normalized by their values U 0 H 2 ,T and S 0 d at ambient temperature.

FIGURE 6 :

 6 FIGURE 6: Inverse Abel transformed OH * images collected for the same input thermal power P th = 18 kW and same global equivalence ratio φ g = 0.6 and increasing air preheating temperature T air,in from ambient to 673 K.

TABLE 3 :

 3 List of the operating conditions corresponding to the flame images shown in Fig. 6. Temperature [K] T amb 373 473 573 673 u b,air [m/s] 42.1 51.8 65.6 79.5 93.4 u b,H 2 [m/s] 65.4 65.4 65.4 65.4 65.4 S l [m/s] for φ g = 0

FIGURE 7 :

 7 FIGURE 7: NO x emissions as a function of the input thermal power P th for different global equivalence ratios φ g when air is injected at ambient temperature T air,in = T amb .

FIGURE 8 :

 8 FIGURE 8: NO x emissions as a function of the input thermal power P th for different air preheating levels at constant equivalence ratio φ g = 0.4.

FIGURE 9 :

 9 FIGURE 9: Effect of air preheating on NO x emissions for different heat losses through the combustion chamber at constant input thermal power P th = 9 kW and constant equivalence ratio φ g = 0.4.

FIGURE 10 :

 10 FIGURE 10: Distribution of NO x emissions with respect to the product between the adiabatic flame temperature T ad and the global residence time in the combustion chamber τ r raised to the power 1/3. The entire experimental dataset is reported.

TABLE 1 :

 1 List of operating conditions for the flames reported in Fig.3. The bulk flow velocities u b,air inside the air channel and u b,H2 inside the hydrogen channel are at ambient temperature. The central branch, instead, is delimited by dashed lines and noted I in Figs.[START_REF] Etnglobal | Hydrogen Gas Turbines: The Path Towards a Zero-Carbon Gas Turbine[END_REF]. Branch I develops in the shear layer between the hydrogen central jet exhausting from the burner and the hot gases inside the Central Recirculation Zone (CRZ). The weak reaction layer I in Figs.3(a-b) has a reddish color in the visible bandwidth corresponding to the chemiluminesence of hot H 2 O * radicals

	Flame	A	B and C	D
	ṁair [g/s]	1.15	3.46	6.92
	ṁH 2 [g/s]	0.02	0.05	0.10
	u b,air [m/s]	5.6	16.9	33.8
	u b,H 2 [m/s]	7.3	21.8	43.6
	φ g	0.5	0.5	0.5
	P th [kW]	2	6	12
	side the metallic burner is in these cases not visible. Reaction
	layer II is a diffusion reaction front between the air and hydrogen
	flows exhausting from the burner as shown in [25]. This reaction

layer appears as a blue wing in the visible range, while the normalized OH * signal distribution suggests that the reaction rate is more intense near the chamber backplane and reduces further

TABLE 2 :

 2 The ratio between the mass of the remaining H 2 in exhaust gases and the total mass of hydrogen injected (H 2 [%]) is presented as function of three globally lean equivalence ratios φ g and several input thermal powers P th . Data are presented for ambient air inlet temperature T air,in = T amb .

		P th [kW]	2	4	5	8	12	15
	φ 0.4 g =	H 2 [%] F. Shape	0.00 0.00 0.00 0.00 0.00 0.00 Anc. A/L A/L Lift Lift Lift
	φ 0.3 g =	H 2 [%] F. Shape	0.00 0.00 0.19 0.15 0.04 0.00 Anc. Anc. Lift Lift Lift Lift
	φ 0.2 g =	H 2 [%] F. Shape	0.11 2.49 3.20 3.54 4.96 Anc. Lift Lift Lift Lift	/ /

TABLE 4 :

 4 Evaluation of the global Wall Heat Losses (WHL) through the combustion chamber walls for different levels of air preheating at constant input thermal power P th = 9 kW and fixed equivalence ratio φ g = 0.4. Experiments with the standard combustion chamber (Ch.) and with the additional insulation layer around the chamber walls (Ch. + T.I.) are compared.

		T air,in [K]	T amb	373	473	573	673
		T ad [K]	1430 1484 1558 1633 1708
	Ch.	T gb [K]	1194 1216 1255 1293 1334
		WHL [kW]	1.8	2.0	2.3	2.7	3.0
	Ch.	T gb [K]	1349 1376 1417 1477 1517
	+ T.I. WHL [kW]	0.6	0.8	1.1	1.2	1.5

GTP-23-1517

ACKNOWLEDGMENT

This project has received funding from the European Research Council under the European Union's Horizon 2020 research and innovation program Grant Agreement 832248, SCIROCCO. The authors are grateful to the technical support from G. Albert, S. Lun Kwong Leon and L. Mouneix from IMFT.


Oscar Werner
email: oscarwerner@hotmail.fr

Lydia Ichay

Nabila Djouadi

Fernando Vetromile

Marie Vincenti

Sophie Guillaumont

Dominique P Germain

Marc Fila

Use of T1 mapping in cardiac MRI for the follow-up of Fabry disease in a pediatric population☆

Keywords: Fabry disease ERT Cardiac MRI T1 mapping FD, Fabry disease, GL-3, globotriaosylceramide, CKD, chronic kidney disease, ERT, Enzyme replacement therapy, CMR, cardiac magnetic resonance, HRQoL, Health related quality of life, TTE, Transthoracic echocardiography, LVEF, left ventricular ejection fraction, LGE, late gadolinium enhancement, LVH, left ventricular hypertrophy

Background:

Fabry disease (FD) is a rare X-linked lysosomal disorder caused by pathogenic variants in the alpha-galactosidase-A gene (GLA). Life threatening complications in adulthood include chronic kidney failure, strokes and the cardiac involvement which is the leading cause of mortality. Usually, it presents with hypertrophic cardiomyopathy, together with arrhythmia and conduction abnormalities. An early indicator is decreased T1 value on cardiac magnetic resonance (CMR). Enzyme replacement therapy (ERT) is effective on some extra-cardiac symptoms but its effect on cardiac lesions depends on the level of initial myocardial lesions. CMR is routinely used to monitor cardiac involvement in FD due to its capacity for tissular characterization. However, there is a lack of data on the pediatric population to understand how to integrate CMR into early therapeutic decisions.

Method:

Monocentric longitudinal study carried out at Montpellier University Hospital from 2016 to 2022. All pediatric patients with FD were evaluated over time with clinical, biological, and cardiac imaging (CMR, echocardiography).

Results:

Out of the six patients included, (3 males), five were treated with ERT during the study. Low T1 values were observed in 4 patients. The normalization of T1 values was observed after 4 years of ERT in 3 patients.

Conclusion:

Due to the lack of strong clinical and biological markers of FD in pediatric patients, initiation and follow-up of ERT efficacy remain challenging. CMR with T1-mapping, a noninvasive method, could play a role in the evaluation of early cardiac impairment in young patients at diagnosis and during follow-up with or without ERT.

Introduction

Fabry disease (FD, OMIM 301500) is a rare X-linked lysosomal disorder caused by pathogenic variants in the alpha-galactosidase A gene (GLA) and is characterized by an accumulation of globotriaosylceramide (GL-3) and other glycolipids in lysosomes and body fluids [START_REF] Ortiz | Fabry disease revisited: management and treatment recommendations for adult patients[END_REF]. This multisystem disease involves principally the kidney, the central nervous system, and the heart leading to chronic kidney disease (CKD), cerebrovascular events, and progressive hypertrophic cardiomyopathy with arrhythmias and conduction defects [START_REF] Ortiz | Fabry disease revisited: management and treatment recommendations for adult patients[END_REF]. The prognosis lies in the severity of the cardiac involvement which has become the leading cause of mortality (40%) [START_REF] Pieroni | Cardiac involvement in Fabry disease[END_REF]. Usually, FD presents in the third decade of life with hypertrophic cardiomyopathy (up to 88% of men with classical FD), valvular disease, or conduction abnormalities that can be complicated by heart failure and arrhythmia. In rarer cases, some aortic dilatation may be seen (in about 30% of male patients with FD). Organ types of cardiac cells (myocytes, endothelial cells, and valvular fibroblast) [START_REF] Pieroni | Cardiac involvement in Fabry disease[END_REF]. This storage is also present in the other organs and begins early in life. Some authors suggest that this process begins even before birth [START_REF] Vedder | Manifestations of Fabry disease in placental tissue[END_REF][START_REF] Augusto | The myocardial phenotype of Fabry disease pre-hypertrophy and pre-detectable storage[END_REF].

Enzyme replacement therapy (ERT) has shown a positive effect to prevent the decline of the glomerular filtration rate especially when started early in life [START_REF] Van Der Veen | Early start of enzyme replacement therapy in pediatric male patients with classical Fabry disease is associated with attenuated disease progression[END_REF][START_REF] Stamerra | Effects of agalsidase-β administration on vascular function and blood pressure in familial Anderson-Fabry disease[END_REF][START_REF] Spada | The effect of enzyme replacement therapy on clinical outcomes in paediatric patients with Fabry disease a systematic literature review by a European panel of experts[END_REF]. ERT may also reduce GL-3 accumulation in cardiac cells and a reduction of left ventricular mass and cardiac wall thickness has been observed [START_REF] Spada | The effect of enzyme replacement therapy on clinical outcomes in paediatric patients with Fabry disease a systematic literature review by a European panel of experts[END_REF]. ERT is effective in the early phase of storage but seems to have limited efficacy in the late stage of the disease especially when the process of inflammation and fibrosis is initiated [START_REF] Augusto | The myocardial phenotype of Fabry disease pre-hypertrophy and pre-detectable storage[END_REF][START_REF] Spada | The effect of enzyme replacement therapy on clinical outcomes in paediatric patients with Fabry disease a systematic literature review by a European panel of experts[END_REF]. Considering that, an early ERT initiation can prevent organ damage and delay both morbidity and mortality in patients with FD, this is in favor of a shift from treatment to prevention of organ damage with the aim to maintain organ function. Guidelines for the introduction of ERT have been recently updated in France and ERT should be considered in male patients with FD from 7 to 8 years old and in symptomatic pediatric female patients with skewed and unfavorable X-linked inactivation [START_REF] Germain | Consensus recommendations for diagnosis, management and treatment of Fabry disease in paediatric patients[END_REF]. The risk of adverse events occurrence such as hypersensitivity to ERT, the psychological impact of a long-life treatment in pediatric patients, and the cost of the treatment have to be taken into account before treating asymptomatic patients [START_REF] Germain | Consensus recommendations for diagnosis, management and treatment of Fabry disease in paediatric patients[END_REF].

To date, only a few noninvasive biomarkers (plasma GL-3 and microalbuminuria) are available in pediatric patients with FD to monitor the organ's impairment and the efficacy of the ERT. Most biological (GFR, proteinuria) and radiological features (echocardiography and cerebral MRI) remain in the normal range in pediatric patients with FD. A study carried out on pediatric patients with iterative renal biopsies showed a clear reduction in GL-3 deposits in the podocytes after 1 to 5 years of ERT. However, it is an invasive technique that cannot be performed routinely. The validation of non-invasive techniques allowing the monitoring of the efficacy of ERT is a research avenue, particularly in pediatric patients.

Outside of EKG and echocardiography which are usually normal in our young patients, cardiac magnetic resonance (CMR) has been proposed as a key exam in the evaluation and the understanding of FD. In the adult population, presenting with unexplained cardiomyopathy, CMR gives strong and specific arguments for FD: low T1 values, elevated T2 values, late gadolinium enhancement, and normal extracellular volumes [START_REF] Pieroni | Cardiac involvement in Fabry disease[END_REF][START_REF] Augusto | The myocardial phenotype of Fabry disease pre-hypertrophy and pre-detectable storage[END_REF]. Mapping sequences can detect the early stage of sphingolipid storage presenting as isolated decreased T1-values [START_REF] Augusto | The myocardial phenotype of Fabry disease pre-hypertrophy and pre-detectable storage[END_REF][START_REF] Messroghli | Clinical recommendations for cardiovascular magnetic resonance mapping of T1, T2, T2* and extracellular volume: a consensus statement by the Society for Cardiovascular Magnetic Resonance (SCMR) endorsed by the European Association for Cardiovascular Imaging (EACVI)[END_REF][START_REF] Deborde | Differentiation between Fabry disease and hypertrophic cardiomyopathy with cardiac T1 mapping[END_REF][START_REF] Hag`ege | Fabry disease in cardiology practice: literature review and expert point of view[END_REF] and could potentially be used to guide the ERT prescription in this prehypertrophic phase of the cardiac involvement of FD.

To date, there is a lack of data in the pediatric population to understand how to integrate CMR and especially mapping sequences in early therapeutic decisions. This cross-sectional study aims to describe the evolution of a pediatric cohort of FD and to specify the place of CMR in the follow-up.

Patients and methods

This work was a monocentric longitudinal study carried out in Montpellier University Hospital from October 2016 to January 2022 on pediatric patients with a genetically proven diagnosis of FD. The following parameters were assessed for each patient at FD diagnosis, at ERT initiation (if treated), and at the last follow-up:

-Clinical and general characteristics: sex, age, weight, height, body mass index (BMI), arterial pressure, specific FD symptoms (cutaneous, neurologic, digestive, and ophthalmologic).

-Kidney function was assessed using analysis: Schwartz 2012 formula, albuminuria/urinary creatinine ratio, proteinuria/urinary creatinine ratio and GL-3 level.

-The health-related Quality of life (HRQoL) with the PedsQL score: this instrument is a generic pediatric HRQoL instrument, designed for children aged from 2 to 18 years, developed from a large cohort of healthy children as well as children with acute or chronic health conditions The PedsQL questionnaire has four multidimensional scales: physical functioning, emotional functioning, social functioning, and school functioning. The three summary scores are the total scale score (23 items), the physical health summary score (8 items), and the psychosocial health summary score (15 items). Items are reversed scored and linearly transformed to a 0-100 scale, with higher scores indicating a better HRQoL.

-Cardiologic assessment: CMR examinations were performed on a 1.5 T Aera® unit (Siemens Healthineers) with a cardiac 32 channel cardiac coil for signal reception and electrocardiographic (EKG) gating. Cardiac function assessment was performed using cine-MRI sequences obtained with retrospectively EKG-gated balanced steady-state-free precession (SSFP) sequences in the long axis and short axis providing full coverage of the LV. Native T1 mapping was performed using short-axis planes in all patients. Modified Look-Locker inversion recovery (MOLLI®) technique was used to evaluate T1 values. We conducted measurements in the septal, lateral, and inferior segments at both the base (S1-S6) and medioventricular portions (S7-S12) of the myocardium. Subsequently, we calculated the T1 mapping values for both the basal and medioventricular regions. The mean value, derived as the average between the basal and medioventricular measurements, is then juxtaposed with the mean T1 value for a healthy reference. The apical short axis slice (S12-S16) was not used because of the quality of the signal as this level where the myocardium is very thin.

The normal values of T1 and T2 have initially been determined on a healthy pediatric population aged from 8 to 18 years old part of an ongoing clinical trial (QUALIMYORYTHM NCT04712136). As recommended, we provided the normal values accompanied by the mean and standard deviation, along with sex-specific cutoffs [START_REF] Messroghli | Clinical recommendations for cardiovascular magnetic resonance mapping of T1, T2, T2* and extracellular volume: a consensus statement by the Society for Cardiovascular Magnetic Resonance (SCMR) endorsed by the European Association for Cardiovascular Imaging (EACVI)[END_REF]. The T1 values were considered "low" under 1SD from the normal.

Delayed contrast-enhanced images were captured 10 min post-gadolinium injection, maintaining identical positions to the cine images. Evaluation of each LV segment was conducted to assess the presence of LGE in accordance with recommended guidelines.

-Ethics:

The study was conducted in compliance with the Good Clinical Practices protocol and declaration of Helsinki principles and was approved by the local Ethics Committee of the University Hospital of Arnaud de Villeneuve -Montpellier, France (IRB-MTP_2022_12_202201284). Oral informed consent was obtained from each patient.

Results

Six patients (3 males and 3 females) with genetically confirmed FD, were included in this study. The diagnosis of Fabry disease was made at a median age of 11,5 years (min 4 years, max 16 years). The mean follow-up was 5 years. ERT was started in 5 patients with a mean time on ERT of 30 months (min 6 monthsmax 4 years) at the last follow-up. Cinical data for each patient were summarized in Table 1.

Patient 1 was a female with a rare presentation of FD. She had a drastically decreased alphagalactosidase activity because of an unfavorable skewed X chromosome inactivation. She has an elevated level of GL-3 and symptoms that occurred before the age of 10. ERT was started in November 2018. The evolution of CMR T1, GL-3 level, and quality of life score are described in Fig. 1.

Patient 2, was the sister of Patient 1. She was not treated until 2021 because of the absence of symptoms of FD. T1 values at this time were at lower limit. The occurrence of acroparesthesia, significant albuminuria, and the diminution of T1 mapping values during the follow-up prompted to start ERT in 2021 (Fig. 1). Her GL-3 level was only slightly increased before the start of the ERT (5 nmol/L). Patients 3 and 4, both males with a phenotype of classic FD, exhibited an association of typical clinical symptoms and biological analysis related to FD (acroparaesthesia, abdominal pain, and headache), elevated GL-3, and low T1 mapping. The evolution of T1, GL-3 level, and Quality of Life score are described in Figs. 2. Patient 5, male, presented with a genetically proven late onset FD with a familial history of early severe cardiac and renal impairment. After a multidisciplinary discussion, according to the parents and the patient requests, ERT was started despite the absence of symptoms and no biological or imaging patterns. The evolution of T1, GL-3 level, and Quality of Life score are described in Figs. 2. Patient 6, is the sister of Patient 5. As usually in pediatric patient with late onset FD, she is not treated due to absent symptoms, no cardiac lesion, and a first CMR evaluation that was normal.

Importantly, outside of the T1 mapping results, the CMRs revealed no other abnormality of volume, myocardial thickness, late gadolinium enhancement, or T2 mapping time in any of the 6 patients (Table 2).

Discussion

This study is the first to describe the integration of CMR and mapping sequences in the follow-up of a pediatric population with FD. This prospective observational study aimed to describe the utility of multimodality imaging to help with the therapeutic decision and follow-up of this specific population. CMR is considered routine care in the FD adult population, as a method of diagnosis of early cardiac involvement as well as in the follow-up of patients [START_REF] Augusto | The myocardial phenotype of Fabry disease pre-hypertrophy and pre-detectable storage[END_REF][START_REF] Perry | The role of cardiac imaging in the diagnosis and management of Anderson-Fabry disease[END_REF][START_REF] Nordin | Myocardial storage, inflammation, and cardiac phenotype in Fabry disease after one year of enzyme replacement therapy[END_REF]. The pediatric population is more challenging because it is heterogenous ranging from symptomatic patients to less severe forms diagnosed through familial screening [START_REF] Germain | The benefits and challenges of family genetic testing in rare genetic diseases-lessons from Fabry disease[END_REF]. Since the storage process begins during the fetal period, it is interesting to carefully evaluate before ERT initiation the level of myocardial GL-3 accumulation that may be part of patients' prognosis. A CMR exam can be performed in children without sedation from 6 years old depending on his/her maturity. To improve the tolerance of a CMR, one should focus on qualitative T2, T1 weighted and mapping sequences as no left ventricle hypertrophy is expected to be found in the early stage of the disease. Lesions of fibrosis can occur earlier than the hypertrophy (up to 60% of adult patients with FDs) [START_REF] Germain | The benefits and challenges of family genetic testing in rare genetic diseases-lessons from Fabry disease[END_REF]. Performing a late gadolinium enhancement sequence can be useful with the aim of predicting cardiac events [START_REF] Weidemann | Early detection of organ involvement in Fabry disease by biomarker assessment in conjunction with LGE cardiac MRI: results from the SOPHIA study[END_REF]. T1 mapping sequences are crucial as they help in the diagnosis of idiopathic cardiomyopathy. A cut-off value has been fixed around 900 msec but in practice, every engine of every brand has its specific cut-off value depending on the field strength (1,5 or 3 Tesla) or the sequence characteristics. It has to be determined with a control population to be used in clinical practice [START_REF] Augusto | The myocardial phenotype of Fabry disease pre-hypertrophy and pre-detectable storage[END_REF][START_REF] Deborde | Differentiation between Fabry disease and hypertrophic cardiomyopathy with cardiac T1 mapping[END_REF].

In confirmed cases, CMR could be used to evaluate the evolution of the myocardial GL-3 accumulation. Nordin et al. described, this process as a progressive mechanism. Our work intends to illustrate it with the evolution of the T1 values especially in Patient n•2 (Figure n•2) with a significant reduction/decrease of the values before ERT initiation [START_REF] Nordin | Myocardial storage, inflammation, and cardiac phenotype in Fabry disease after one year of enzyme replacement therapy[END_REF]. The use of CMR seems to be particularly relevant in female patients because of the possible discordance between the symptoms and the level of plasma GL-3 that can stay in the low range. Moreover, since there is a lack of consensus on the timing of the introduction of ERT in pediatric patients. The use of a non-invasive method to document organ accumulation of glycosphingolipids may be helpful to the decision of ERT initiation [START_REF] Germain | Consensus recommendations for diagnosis, management and treatment of Fabry disease in paediatric patients[END_REF]. For Patient n•2, CMR data was integrated into the decision-making process as an argument for a cardiac impairment. In the absence of well-defined cut-off values in pediatric population, a dynamic approach of the T1 mapping values could be helpful in these patients. Furthers studies should focus on defining Z-scores of T1 normal values in FD pediatric patients. The ERT has shown benefits in FD adult and pediatric population, but its efficacy on constituted myocardial lesions is debated [START_REF] Spada | The effect of enzyme replacement therapy on clinical outcomes in paediatric patients with Fabry disease a systematic literature review by a European panel of experts[END_REF][START_REF] Nordin | Myocardial storage, inflammation, and cardiac phenotype in Fabry disease after one year of enzyme replacement therapy[END_REF][START_REF] Parini | Analysis of renal and cardiac outcomes in male participants in the Fabry outcome survey starting agalsidase alfa enzyme replacement therapy before and after 18 years of age[END_REF].

The ERT has its maximum efficacy in the early storage phase and the positive evolution of T1 values in Patients 1, 3, and 4 seems to be in line with these results. The presence of myocardium hypertrophy, inflammation (elevated T2 values), and/or constituted fibrotic scares (late gadolinium enhancement) seems to compromise the positive effect of ERT on cardiac lesions [START_REF] Nordin | Myocardial storage, inflammation, and cardiac phenotype in Fabry disease after one year of enzyme replacement therapy[END_REF]. This is in favor of extensive familial screening [START_REF] Germain | The benefits and challenges of family genetic testing in rare genetic diseases-lessons from Fabry disease[END_REF] and early therapeutic initiation with regular follow-up. The improvement of the cardiac prognosis may also depend on the dose and regimen of ERT that is used. [START_REF] Germain | Consensus recommendations for diagnosis, management and treatment of Fabry disease in paediatric patients[END_REF][START_REF] Germain | Analysis of left ventricular mass in untreated men and in men treated with agalsidase-β: data from the Fabry registry[END_REF][START_REF] Kampmann | Effectiveness of agalsidase alfa enzyme replacement in Fabry disease: cardiac outcomes after 10 years' treatment[END_REF]. The use of other imaging techniques could be also discussed. Trans thoracic echocardiography (TTE) is also in constant evolution and it seems that Speckle tracking imaging with the global longitudinal strain (GLS) could be an interesting parameter to explore [START_REF] Levy | Reference ranges of left ventricular strain measures by two-dimensional speckle-tracking echocardiography in children: a systematic review and meta-analysis[END_REF]. The GLS explores the potential for distortion of the myocardial muscle. Every aggression of the myocardium can lead to an early modification of the strain rate. The storage process of FD seems to have an early negative impact on myocardial function (even before the hypertrophic phase) with a correlation with lower T1 values in CMR [START_REF] Vijapurapu | Global longitudinal strain, myocardial storage and hypertrophy in Fabry disease[END_REF]. TTE could be used in pediatric populations in centers having difficulties of access to CMR, or when there are challenges with the acceptance of CMR by the child. Considering our results and the limited literature on pediatric population, there is a strong need for prospective research on the subject, especially on the long-term benefit of an early prescription of ERT considering the potential side effects. Integrating multimodal imaging such as CMR and TTE in the outcome's measures are interesting options in view of the lack of strong clinical indicators in this paucisymptomatic population.

Conclusion

Due to the lack of strong clinical and biological markers of FD in pediatric patients, initiation and follow-up of ERT efficacy remain challenging. CMR could play a role in the evaluation of early organ impairment in these patients. Our work on a small cohort of pediatric patients suggests some promising results in the use of cardiac T1 mapping as a noninvasive method to assess the cardiac impairment at diagnosis and during the follow-up with or without ERT.

  EKG: Heart rate, arrhythmia and conduction disorder. Transthoracic echocardiography (TTE): left ventricular end fraction (LVEF), Left ventricular wall thickness, left ventricular end-diastolic diameter. CMR: T1, T2 mapping values, LVEF, indexed left ventricular (LV) mass, indexed LV enddiastolic volume (iLVEDV), indexed LV end-systolic volume (iLVESV), late gadolinium enhancement (LGE). --CMR protocol:

Acknowledgement

Thanks to patients and families for accepting to participate to this study.

Fundings

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Data availability

Data will be made available on request.

Author statement

The authors declare that they did not use any AI or and AI-assisted technologies in the writing process of this article.

CRediT authorship contribution statement

Declaration of Competing Interest

D.P.G. is a consultant for Amicus, Sanofi-Genzyme and Shire. He has received speaker's honoraria from Amicus, Sanofi-Genzyme and Shire.