Ignition dynamics of a hydrogen-fueled annular combustor

Nicolas Vaysse, Daniel Durox, Ronan Vicquelin, Sébastien Candel, Antoine Renaud

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Nicolas Vaysse, Daniel Durox, Ronan Vicquelin, Sébastien Candel, Antoine Renaud. Ignition dynamics of a hydrogen-fueled annular combustor. Proceedings of the Combustion Institute, 2025, 41 (1), pp.105893. 10.1016/j.proci.2025.105893. hal-05340842

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Distributed under a Creative Commons Attribution 4.0 International License
Ignition dynamics of a hydrogen-fueled annular combustor

Nicolas Vaysse<sup>a,*</sup>, Daniel Durox<sup>a</sup>, Ronan Vicquelin<sup>a</sup>,
Sébastien Candel<sup>a</sup>, Antoine Renaud<sup>a</sup>

<sup>a</sup>Laboratoire EM2C, CNRS, CentraleSupélec, Université Paris-Saclay, 8-10 rue Joliot Curie, Gif-sur-Yvette 91192, France

Abstract

Hydrogen is currently considered as a possible fuel substitute for gas turbines and aeroengines in the context of decarbonizing transportation and energy industries. However, its combustion raises scientific challenges due to its broad flammability domain and propensity to combustion instabilities. To ensure safe operation of hydrogen fueled systems, it is mandatory to study hydrogen combustion in industrially-relevant annular configurations that are typically found in applications. The present investigation is carried out in the MICCA facility equipped with 16 hydrogen injection units. In each injector, hydrogen is sent in cross-flow in a swirled air flow. The aim of this investigation is to study the light-round ignition dynamics of the hydrogen-fueled annular combustor. The ignition sequence is observed with a high-speed camera equipped with an OH* filter. The light-round delays are determined for a range of injection velocities and for equivalence ratios between 0.29 to 0.72. The relatively short light-round delays (from 18 ms to 35 ms), are considerably lower than those found for hydrocarbon flames. It is also found that at low equivalence ratios, the light-round proceeds but does not ignite all the flames. The light-round delay is shown to decrease when the equivalence ratio is increased, and also when the inlet velocity is augmented at constant equivalence ratio. An attempt is made to link the average flame displacement velocity to the turbulent burning velocity taking into account the thermal expansion. It is found that this can be achieved with a model combining two expressions for the turbulent burning velocity, corresponding to high and low values of the laminar flame speed. The model captures the influence of injection velocity and equivalence ratio on the flame displacement velocity during light round. It is thus possible to derive a correlation for the reduced light-round delay that suitably retrieves experimental data.

Keywords: Hydrogen flames; Annular combustor; Swirling flames; Ignition dynamics; Ignition time
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# 1. Introduction

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Hydrogen is considered as one of the fuels of the future for gas turbines and aircraft engines, but the hydrocarbon to hydrogen transition raises many issues. It is known that hydrogen/air flames laminar burning velocities are much higher than those of most hydrocarbon fuels, that their adiabatic burning temperature are larger and that the large species diffusion of hydrogen leads to Lewis numbers that notably differ from unity giving rise to thermo-diffusive instabilities. It is also known that hydrogen/air mixtures require much lower ignition energies and that their flammability limits are quite broad. These features have a notable impact on the ignition of practical devices fed with hydrogen as a fuel. Recent studies on the ignition of single-injector hydrogen combustors [1] or domestic boilers [2, 3] already underline the propensity of hydrogen flames to flashback at ignition, a process that is characterized by large amplitude pressure excursions. It is also found that after ignition hydrogen flames are more easily anchored in highly turbulent flows than pure methane flames, a feature explained in [4] by the high resistance to strain rate when the hydrogen content is augmented.

A review of the literature indicates that ignition of more complex systems like multiple injector configurations of the kind found in annular combustors is not well documented in the case where the system is fed with pure hydrogen. This process designated as “light-round” is now well covered in the case of hydrocarbon fuels. The work of Boileau et al. [5] probably describes the first large eddy simulation of this process in the case of a helicopter chamber comprising 24 burners. For the chosen operating point, the flame progresses regularly from burner to burner. A large amount of experimental work has been carried out later on in annular facilities developed at EM2C, in Cambridge and at NTNU. New insights on the light-round process were obtained by [6] using a facility designated as MICCA equipped with transparent side-walls and 16 swirled injectors supplying premixed propane and air. It was shown in particular that the flame displacement velocity increased with the laminar burning velocity and with the flow rate. It was found that fresh gases were flushed away by the flame progressing in the annulus, and that the wall temperature notably influenced the velocity of the front. Light-round experiments were also carried out in Cambridge using an annular chamber fed by non-premixed swirled injectors, each equipped with a central bluff-body [7]. Further experiments, low-order modelling and simulations carried out with swirled premixed flames established by injectors comprising bluff-bodies [8, 9] considered the effects of interburner spacing, spark plug location, equivalence ratio and the dependence of the front velocity on the laminar burning. Experiments at EM2C were also accompanied by large eddy simulations, leading to some remarkable comparisons between data and simulations [10, 11]. Work on light-round of premixed gases was

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also carried out in the TurboCombo facility inspired by the MICCA design, by injecting the mixture before or after sparking (FFSL or SFFL modes) [12]. It was found that the latter mode increased the asymmetry between flame branches and augmented the light-round delay. Oblique injectors were investigated to study the impact of circumferential flow velocity [13]. It was shown more recently [14] that the flame displacement velocity depended on the swirl number of the burners.

Recent work at NTNU [15, 16] focused on the light-round ignition dynamics of CH₄ flames using spinning combustion [15], and of CH₄-NH₃ and CH₄-H₂ gaseous blends, as well as two experimental points with pure hydrogen [16]. The latter work showed an improvement of the flame displacement velocity with the hydrogen enrichment at constant laminar burning velocity, which was explained by the development of thermo-diffusive instabilities due to hydrogen enrichment, an effect captured by a scaling by the effective Lewis number.

Investigations at EM2C have concerned more recently the ignition of swirl spray injectors delivering liquid fuel (heptane and dodecane) through “hollow-cone” atomizer nozzles [17]. It was shown that ignition is faster under premixed conditions, and that the total light-round time increased with the least volatile fuel. It was also confirmed that the light-round delay was reduced when the laminar burning velocity was augmented. LES reported in [18] made it possible to examine the flushing of fuel droplets upstream of the flame front observed in [19], a motion caused by the flushing of the fresh stream of air. This was shown to give rise to heterogeneities in the local fuel concentration due to the differential motion of the droplets with respect to the fresh gases. Simulations by [20] aimed at analyzing the transient flashback observed at each burner during the spray ignition [19]. High-speed imaging indicated that the flame penetrated in the injector before moving out to its final position at a distance from the outlet, an effect due to the pressure excursion that arises when each burner is ignited. Further simulations confirmed that wall temperature had a significant impact on the light-round duration [21] and allowed to examine the leading point behavior [18, 22]. Light-round dynamics of liquid kerosene spray flames was investigated on a swirled staged annular combustor [23].

This review of the literature indicates that data on light-round of annular combustors fed with pure hydrogen is not available, except for a single experimental point reported by the group of Dawson at NTNU [16]. The aim of the present investigation is to fill this gap. This is accomplished by operating the MICCA system equipped with swirl injectors and fed with pure hydrogen, delivered in cross flow in each injection unit. This article gives a brief account of a broad set of experiments. The experimental configuration is described in Section 2. The timing between the spark activation and the fuel delivery
1. is also analyzed in that section. Typical results
2. discussed in Section 3 give access to the flame
3. structures during the process and to the time delay
4. that separates the time of flame merging from the
5. initiation of the process. A theoretical estimate of
6. the flame displacement velocity is derived in Section
7. 4 and shown to allow a reasonable match with
8. experimental data. This model is used in a second
9. stage to obtain estimates of the light round delay that
10. are also shown to correspond to the experimental data.

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## 2. Experimental setup

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### 2.1. The MICCA-H2 annular combustor

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The experimental configuration MICCA comprises an air plenum, 16 swirling injectors, and a combustion chamber formed by two cylindrical tubes allowing full optical access. Hydrogen is delivered through 6 radial holes in a swirling stream of air. The swirler chosen for this study, called 707, establishes a clockwise rotating flow characterized by a swirl number $S = 0.60$ and a pressure drop coefficient on the air stream $\sigma = \Delta p / [(1/2)\rho U_{b,air}^2] = 3.25$, where $U_{b,air}$ is the axial bulk velocity at the injector outlet. This injector, denoted as CFI-X1, is described in [24] and a schematic can be found on the right-hand side of Fig. 1. The external diameter of the combustion chamber is 400 mm and its internal diameter is 300 mm. The two cylindrical walls are $l_c = 200$ mm-long. The spacing between two adjacent injectors is equal to 69 mm. Air and hydrogen are delivered at ambient temperature through two Bronkhorst EL-FLOW meters with full-scale capacities of 5000 NL/min for air and 680 NL/min for hydrogen and with a relative accuracy of 0.5%. These controllers are placed 1.4 m upstream of the injector outlet, and hydrogen is conveyed through a network of 4-mm to 10-mm diameter tubes.

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<figure><img src="image_2.png" /><figcaption>Fig. 1: Left: Schematic top view of the MICCA-H2 experimental setup. Right: Schematic view of the CFI-X1 cross-flow injector.</figcaption></figure>

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### 2.2. Diagnostics

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The light-round process is visualized using high-speed imaging bandpass filtered at 310 nm in or-

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der to keep OH⁺ chemiluminescence emission. Images are recorded using an intensified high-speed CMOS camera APX-i2 comprising 1024×1024 pixels with an 8-bit resolution. The frame rate and exposure are respectively set at 1000 Hz and 900 µs. During each experiment, the injected mass flow rate of hydrogen is recorded using a LabVIEW software at a sampling rate of 16,384 Hz. The trigger signal of the fast camera is also acquired, precisely defining the timing corresponding to each frame and its instant with respect to the hydrogen mass flow rate record.

### 2.3. Protocol

The light-round ignition runs are performed in a FFSL (Fuel First, Spark Later) mode. Fuel injection begins before spark ignition, so that the reactive mixture fills the chamber prior to spark plug activation. The single spark igniter, comprising a tungsten electrode with its end located 2 mm above the backplane at a radial distance of 12 mm from the axis of injector 9, remains at that location in all experiments. Pulses producing a mean energy of 25 mJ are formed in the outer recirculation zone (ORZ) of this injector every 10 ms. The runs comprise 5 steps: (a) air is injected with a stabilized mass flow rate, (b) acquisition of high-speed images and mass flow rate of H₂ is started, (c) the H₂ mass flow meter is turned on with a target value, (d) the H₂ mass flow rate reaches a stable value after a time $T \approx 6$ s, the spark igniter is activated at $t_{sp}$, (e) after light round, the H₂ mass flow rate is turned off and data acquisition is terminated.

This protocol is first followed at constant equivalence ratio $\phi = 0.57$ for an injection velocity range from $U_b = 21$ m/s to 45 m/s. The effect of equivalence ratio is evaluated at constant power $P_{th} = 46$ kW by sweeping values from $\phi = 0.29$ to 0.73, resulting in an injection velocity sweep from 24 m/s to 52 m/s. These conditions are summarized in Table 1. Two runs are acquired for each operating condition to examine the variability of the results and eliminate outliers.

<table><caption>Table 1: Operating conditions explored in this study. The volumetric expansion ratio $\rho_u/\rho_b$ and the effective Lewis number $Le_{eff}$ increase monotonically with the equivalence ratio $\phi$.</caption><thead><tr><th>P<sub>th</sub><br>[kW]</th><th>φ</th><th>U<sub>b</sub><br>[m/s]</th><th>ρ<sub>u</sub>/ρ<sub>b</sub></th><th>Le<sub>eff</sub></th></tr></thead><tbody><tr><td>34-70</td><td>0.57</td><td>21-45</td><td>5.15</td><td>0.59</td></tr><tr><td>46</td><td>0.29-0.73</td><td>24-52</td><td>3.5-5.92</td><td>0.41-0.74</td></tr></tbody></table>

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### 2.4. Modelling the chamber filling with reactive mixture

One issue in light-round experiments is to make sure that the hydrogen mass fraction prevailing in the chamber at ignition is close to the target setpoint value. One option would be to inject hydrogen for

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<figure><img src="image_3.png" /><figcaption>Fig. 2: Typical hydrogen flow rate function $f(t)$ such that $\dot{m}_{H_2}^i = \dot{m}_{H_2}^s f(t)$ (black line) and hydrogen mass fraction in the chamber $Y(t)$ (blue line).</figcaption></figure>

a long time to make sure that this value is reached but the drawback would be to have a large amount of hydrogen outside the chamber that might react upon ignition. One possibility is to use a model to estimate the mass fraction evolution inside the chamber. This will be used to control the ignition time with respect to the mass flow meter signal. The mass flow rate of air $\dot{m}_a$ is fixed at a constant value while the mass flow rate of hydrogen is initially augmented from zero to the setpoint value. This scheduling is controlled by the mass flow meter and may be represented as $\dot{m}_{H_2}^i = \dot{m}_{H_2}^s f(t)$, where $\dot{m}_{H_2}^s$ is the targeted value of the hydrogen mass flow rate.

The experimental record of $f(t)$ is shown in black in Fig. 2 for the case $P_{th} = 40$ kW and $\phi = 0.57$. The ignition time is represented by the red vertical line. The signal $f(t)$ is defined at the mass flow controller location, thus as a distance of 1.4 m upstream of the injectors, inducing a time delay between $f(t)$ and the effective mass flow injected in the chamber. For the typical flow rates used in this experiment, this delay varies between 30 ms and 63 ms which is fairly small compared to the time duration between the flow controller opening and the spark. This time delay will thus be neglected and one may then consider that the black signal in Fig. 2 defines the mass flow rate of hydrogen injected in the chamber. One observes that the injected hydrogen mass flow rate increases in two steps, that correspond to the electromechanical response of the flow meter. Its non-zero value at the beginning is due to an initial offset allowing to trigger the opening of the valve, which has no consequence on the setpoint value of the flow rate. The flow rate function $f(t)$ reaches unity after 5 s. One interesting feature of this curve is the small shift that occurs after ignition as a result of the ignition-induced counter-pressure: the mass flow rate must be increased to balance this pressure peak, but the response of the mass flow meter is slow. Thus, during the time it takes to apply this small shift, the pressure peak vanishes so the mass flow rate is decreased back, which takes roughly 2 s. The simplest model of the system is to assume that the chamber operates as a perfectly mixed system, and consider that the mass fraction of hydrogen is uniform and only depends on time $Y_{H_2} = Y(t)$. The total mass flow rate injected in the chamber is $\dot{m} = \dot{m}_a + \dot{m}_{H_2}$. It is worth

noting that $\dot{m}$ is approximately constant because the mass flow rate of hydrogen is small compared to the mass flow rate of air. The mass flow rate of hydrogen leaving the chamber is $\dot{m}_{H_2}^o = \dot{m}Y(t)$. With these definitions it is easy to write a mass balance for hydrogen:

$$ \frac{dM_{H_2}}{dt} = \dot{m}_{H_2}^i - \dot{m}Y(t) \quad (1) $$

One may now divide this equation by the mass of gas inside the chamber $M = \rho V$. Noting that $M_{H_2}/M = Y(t)$, one obtains:

$$ \frac{dY}{dt} = \frac{\dot{m}_{H_2}^i}{M} - \frac{\dot{m}}{M}Y(t) \quad (2) $$

It is worth noting that $M/\dot{m} = \tau$ where $\tau$ is the residence time in the chamber. It is convenient to write the first term on the right hand side in the following form:

$$ \frac{\dot{m}_{H_2}^i}{M} = \frac{\dot{m}_{H_2}^i}{\dot{m}} \frac{\dot{m}}{M} f(t) $$

The mass $M$ is approximately constant because the changes in density $\rho$ are quite small as the mass of air is much larger than that of hydrogen. Since $\dot{m}_{H_2}^i = \dot{m}_{H_2}^s f(t)$ where $\dot{m}_{H_2}^s$ is the setpoint value of the hydrogen mass flow rate, it is also possible to write that $\dot{m}_{H_2}^s/\dot{m}$ is approximately constant and equal to the setpoint value of the hydrogen mass fraction $Y^s$. Moving the last term in equation (2) to the right hand side one obtains the following equation for the hydrogen mass fraction:

$$ \frac{dY}{dt} + \frac{1}{\tau}Y(t) = \frac{1}{\tau}Y^s f(t) \quad (3) $$

where the residence time $\tau$ is nearly constant during the whole process. In the considered operating conditions, the residence time deduced from total injected volumetric flow rate and the chamber volume is $\tau \approx 0.54$ s.

Since the time evolution of $f(t)$ is measured, it is possible to integrate this differential equation numerically. The resulting evolution of $Y_{H_2}(t)$ is plotted in blue in Fig. 2. Its shape is similar to that of the injected mass flow rate $\dot{m}_{H_2}$ but with a 0.6 s delay that is close to the calculated residence time $\tau$. Due to the small delay induced by the supply line between the controller and the injectors, the blue curve in Fig. 2 will be displaced to the right by a small amount (less than 0.1 s). The ignition time $t_{sp}$, represented by a red line in this graph, shows that when the ignition is triggered, the hydrogen mass fraction in the combustor $Y(t_{sp})$ is stabilized and very close to the target value $Y^s$. It is also possible to represent $f(t)$ by a piecewise linear function (comprising a linear growth followed by a plateau) and using Eq. (3) obtain an analytical expression for the spark time $t_{sp}$ ensuring that a steady state is reached for the hydrogen mass fraction $Y_{H_2}$ and facilitates the experimental design.

### 3. Results
## 3.1. Visualization of light-round dynamics

Fig. 3 presents the high-speed OH\* images for two ignitions at a fixed equivalence ratio $\phi = 0.57$ and injection velocities 25.4 m/s and 40.8 m/s. The time evolution of the volume-integrated OH\* light intensity is calculated from these images and plotted in Fig. 4. The ignition process comprises 4 periods: (1) a flame kernel is formed next to the discharge, (2) an arch-shaped flame expands and the integrated light intensity increases at a fast pace, (3) when the flame reaches the chamber outlet, two branches propagate in opposite directions and the integrated light intensity remains at a nearly constant level for a short period of time (Fig. 4), (4) the two branches are slowed down by the layer of fresh gases separating the two flame fronts. After merging the reactive front is connected upwards and the light intensity decreases until it reaches a steady state level corresponding to the 16 ignited flames. During this process, flames are established one after the other behind the flame front. In contrast with hydrocarbon flames [6, 17] the flame branches observed during the third period are nearly perpendicular to the backplane. This indicates that the reactive fronts progress in the various planes above the backplane at nearly the same absolute velocities so that the two fronts remain approximately parallel to the combustor axis and perpendicular to the backplane. This might be due to the reduced size of the hydrogen flames, which being less favorable to burner-to-burner ignition, promote initiation by flame propagation. The process is thus driven by turbulent flame displacement with the same burning velocity in every plane parallel to the backplane so that the front remains nearly perpendicular to that plane. The light-round delays, from the first flame kernel to the merging of the two branches, are respectively 26 ms and 19 ms, indicating that the average displacement velocity $\bar{S}_a$ increases with the injection velocity $U_b$.

## 3.2. Effects of injection velocity on light-round delay

The influence of the operating conditions on the light-round time is investigated in this section through two separated campaigns: at first, the equivalence ratio is kept constant at $\phi = 0.57$ in order to maintain a fixed laminar burning velocity between the points. The bulk injection velocity is varied from $U_b = 21$ m/s to $U_b = 45$ m/s and the light-round time is measured using the high-speed OH\* light emission images. Secondly, the hydrogen mass flow rate is kept constant at $\dot{m}_{H_2} = 258.4$ NL/min and the equivalence ratio is increased, thus at a fixed thermal power in the combustor $P_{th} = 46$ kW.

The light-round times obtained for various injection velocities are plotted on the left-hand side of Fig. 5 for $\phi = 0.57$.

One observes that although the laminar burning velocity is constant throughout this first study, the light-round time takes various values ranging from

28 ms to 18 ms. The latter value is quite low compared to the light-round times measured in [6] and [17] in the same combustor operating with hydrocarbon fuels, which is consistent with the fact that hydrogen combustion is characterized by much higher propagation speeds. At a constant equivalence ratio (Fig. 5, left), the light-round delay is notably decreased when the injection velocity is augmented. This is consistent with previous conclusions from the literature.

## 3.3. Effect of equivalence ratio on light-round delay

In lean conditions, increasing the equivalence ratio is expected to increase the laminar burning velocity and subsequently the turbulent burning velocity, leading to higher light-round propagation speed. This trend is indeed observed in the light-round experiments on the right-hand side of Fig. 5. It is shown that the light-round time decreases as the equivalence ratio is augmented. Since the thermal power is kept constant, the injection velocity decreases and cannot therefore explain the reduction in light-round time. This reduction is thus necessarily an effect of the shift in laminar burning velocity due to the equivalence ratio. Additionally, the thermal expansion factor $\rho_u/\rho_b$ rises when the equivalence ratio increases, which strengthens this effect. In the leanest condition, corresponding to $\phi = 0.29$, the flame front travels all around the combustor but it does not ignite all the flames: Fig. 6 shows the high-speed OH\* images corresponding to the two runs performed at this condition. In the first run, the light-round ignition time is the longest (35 ms) and 7 flames are ignited after 50 ms. In the second run, the light-round is slightly faster (33 ms) but only 5 flames are ignited at steady state. At these conditions, the laminar flame speed is very low: thus, in the injection zones, the high turbulent velocities lead to a low Damköhler number and the flame kernels are broken by the turbulence. Therefore, a large number of flames cannot stabilize above the burners. However, far from the injectors, the flow velocity is strongly reduced. There, the light-round propagation is thus enabled by the turbulence which enhances combustion. This is consistent with findings of [7] where the ignition limits of the annular combustor are shown to be narrower than the limits inside which flames are stabilized. Additionally, high-speed images in Fig. 6 show that the flame front travels further away from the backplane than at higher equivalence ratios, making it less capable of igniting an injector. In these ultra-lean conditions, the latter will have no possibility to ignite due to the absence of hot spots in its neighborhood. Another possible explanation is that as the operating point approaches the lean ignition limit of the annular combustor, flame sustainability becomes increasingly difficult, particularly in the leaner regions of the mixture. Previous numerical simulations of non-premixed injection in MICCA [18, 21] have shown that the region between injector units tends to be leaner. Therefore, the ob-
<figure><img src="image_4.png" /><figcaption>Fig. 3: Typical flame images during light-round ignition at equivalence ratio $\phi = 0.57$ for two different injection velocities, corresponding to $P_{th} = 40$ kW (top) and $P_{th} = 64$ kW (bottom).</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 4: Time evolution of the volume-integrated OH* intensity during light-round ignition at operating conditions $P_{th} = 40$ kW and $\phi = 0.57$.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 5: Light-round times, $\tau_{LR}$, between kernel ignition and merging of the two fronts, as a function of the injection bulk velocity $U_b$, and at constant equivalence ratio $\phi = 0.57$ (left), and as a function of the equivalence ratio, at a constant thermal power (right).</figcaption></figure>

1. served flame detachment from the back plane could result from reduced reactivity or even locally non-flammable mixtures in these areas.

## 4. Theoretical estimation of the flame displacement velocity

6. From a practical point of view, it is worth making an attempt to estimate the flame absolute displacement velocity during the light-round. It is important to remember that this velocity results from two components, the first $v_b$ corresponding to the burnt gas velocity behind the flame front, the second $w_n n$

representing the absolute velocity of the flame front in the normal direction so that $S_a = v_b + w_n n$. One may remember that when the velocity of the burnt gases vanishes as is the case for example in spherically expanding flames from an initial spark, the absolute velocity of the front in the normal direction is $w_n = (\rho_u/\rho_b)S_d$ where $S_d$ is the turbulent flame displacement velocity in the fresh gases. In the present experiments, the burnt gases are not at rest. There is a continuous injection of air and hydrogen and its velocity after conversion into products is augmented by the thermal expansion and also progressively by buoyancy, defining an axial velocity component. There is also an azimuthal component in the flow induced by the swirlers. These two velocity components form a velocity field $v_b = v_{bx}e_x + v_{b\theta}e_\theta$ [6]. In general $v_{b\theta}$ is small compared to $(\rho_u/\rho_b)S_d$ as can be deduced by noting that the two flame branches propagate in a nearly symmetric fashion and meet half way in a section that is opposite to the spark. One may then consider as a first approximation that the absolute flame displacement velocity near the chamber backplane is equal to the turbulent flame displacement velocity multiplied by the expansion factor:

$$S_a \approx (\rho_u/\rho_b)S_d \quad (4)$$

Assuming that flame stretch and curvature effects are negligible in this study, the displacement velocity in the fresh gases can be taken as $S_d = S_T$. One may now try to match measurements of $S_a$ and estimates of $(\rho_u/\rho_b)S_T$.

### 4.1. Modeling $S_T$ using turbulent velocity correlations

It is natural to use standard expressions derived in the literature for the turbulent burning velocity $S_T$. Such correlations [25–28] are known to have a limited degree of generality, but that of Zimont-Karpov [27], calibrated on hydrogen flames of equivalence ratios ranging from 0.18 to 5, is apparently the most appropriate and will be used in what follows, and
<figure><img src="image_7.png" /><figcaption>Fig. 6: Typical flame images during light-round at an equivalence ratio $\phi = 0.29$ close to the lean blow out limit. The two rows correspond to two runs of the same operating condition, characterized by light-round times of respectively 35 and 33 ms. In the last frame of the first raw, a seventh flame is being ignited (burner 1), and stabilized at 45 ms, in a frame not shown.</figcaption></figure>

designated as Z-K, to estimate the turbulent burning velocity. The scaling of the flame displacement velocity using the effective Lewis number $Le_{eff}$ as in [15] is suitable for blends of hydrogen and methane where $Le_{eff}$ covers a wide range of values (0.61 to 1.20). However, the present study only focuses on globally lean pure hydrogen conditions, where $Le_{eff}$ variations are small: $Le$ varies between 0.40 and 0.52, $Le_{eff}$ ranges from 0.41 to 0.74 (see Table 1). Hence, the major effect comes from the variation of equivalence ratio and injection velocity impacting the turbulent velocity $S_T$. The Z-K formula of $S_T$ fitted for hydrogen [27] does implicitly account for its specific non-unity Lewis number behavior and was validated for equivalence ratios ranging from 0.18 to 5. In the alternative correlation [25], accounting for the Lewis number, this parameter features a relatively small exponent (-0.3). This is why a scaling accounting for turbulent velocity variations has been preferred over the $Le_{eff}$ and $\bar{S}_L$ combination of [15] that was derived for multi-fuel systems but does not consider effects linked to the injection velocity. Accordingly, the burning velocity, that will be used to represent the turbulent flame displacement velocity, is given by:

$$S_T = S_L + C_z(v'S_L)^{1/2}(Re_l)^{1/4} \quad (5)$$

where $C_z$, $v'$ and $Re_l$ designate a model constant, a characteristic turbulence intensity level and the Reynolds number of the motion at the integral scale. The turbulent velocity $v'$ is computed assuming a constant turbulence intensity in the dataset, equal to $\chi = v'/U_b = 0.15$. The integral scale $l$ is estimated by matching the characteristic time at that scale and mechanical time defined by injection conditions so that $l/v' \simeq d_e/U_b$. Results of this first attempt at matching the measured absolute displacement velocity $\bar{S}_a$ are shown in Fig. 7. The values $\bar{S}_a$ are obtained by dividing the arc length traversed by each branch $\mathcal{P}/2$ by the measured light-round time $\tau_{LR}$, with $\mathcal{P} = 1.1$ m the perimeter of the MICCA chamber. A good match is obtained for cases cor-

<figure><img src="image_8.png" /><figcaption>Fig. 7: Comparison between absolute displacement velocity $\bar{S}_a$ and estimates of this velocity $(\rho_u/\rho_b)S_T$ based on the Z-K turbulent burning velocity correlation [27]. The points are colored by the laminar burning velocity $S_L$, the white color corresponding to $S_L = 0.5$ m/s, i.e. $\phi = 0.5$. The red line indicates that the estimated absolute displacement velocities are equal to the measured values.</figcaption></figure>

responding to laminar burning velocities $S_L$ greater than 0.5 m/s. Data corresponding to low values of the laminar burning velocity $S_L$ (low equivalence ratio) are not well described. This is so because the correlation (5) (and the other correlations as well), include a power-law dependence of $S_T$ with respect to $S_L$. Thus $S_T \to 0$ if $S_L \to 0$. According to (5) and to most of the other correlations $S_T$ becomes small when $S_L$ takes low values. This happens when the operating point is close to the lean limit, i.e. when the chemical time increases and the Damköhler number becomes small. One notes however that the absolute displacement velocity $\bar{S}_a$ keeps a finite value. One may then wonder if this cannot be treated by combining (5) with another expression to deal with cases featuring low $S_L$ values. For that, one needs a turbulent burning correlation that remains finite when $S_L$ is small and is essentially defined by the turbulence level. The simplest option is to use the initial expression proposed by Damköhler [29]:

$$S_T = S_L + kv' \quad (6)$$
<figure><img src="image_9.png" /><figcaption>Fig. 8: Measured light-round times $\tau_{LR}$ and estimates of this merging time $\tilde{\tau}_{LR}$. The light-round times are divided by $P/2U_b$ to obtain a dimensionless group. The square symbol is the pure hydrogen data point from [16]. The red line corresponds to an equality between estimates and data.</figcaption></figure>

Here $S_T \to kv'$ when $S_L \to 0$. One may now distinguish the operating conditions in terms of their laminar flame speed and treat a first group corresponding to high values of $S_L$ such that $S_L > S_{L,c}$ with the correlation (5), while a second group such that $S_L < S_{L,c}$ is represented with correlation (6). Since a low $S_L$ leads to a low Damköhler number, the two groups can be distinguished in terms of a critical Damköhler number $Da_c$. This modelling is admittedly empirical but it is nevertheless worth trying because: (1) it is based on the idea that regimes of turbulent combustion differ when $Da$ takes high or low values; and (2) it may yield an improved representation, of the light-round mean displacement velocity. The two expressions (5) and (6) need to be matched at the critical value $Da_c$ defining the two regimes:

$$S_L + C_z (v' S_L)^{1/2} (\mathrm{Re}_l)^{1/4} = S_L + kv' \quad (7)$$

Using standard expressions for the mechanical and chemical times $\tau_m = l/v'$ and $\tau_c = l_F/S_L = \nu/S_L^2$, Eq. (7) can be written as

$$C_z \left[ v' \left( \frac{\nu}{\tau_c} \right)^{1/2} \right]^{1/2} \left[ v'^2 \frac{\tau_m}{\nu} \right]^{1/4} = kv' \quad (8)$$

which yields $C_z v'(\tau_m/\tau_c)^{1/4} = kv'$. By recognizing the Damköhler number $Da = \tau_m/\tau_c$, one finds that $k = C_z(Da_c)^{1/4}$. The critical Damköhler number $Da_c$ is determined using Fig. 7 and corresponds to conditions where the data and the first model using the Z-K correlation for the turbulent burning velocity depart from each other. For $Da_c = 4$ and $C_z = 0.48$, one obtains $k = 0.68$. The correlations adopted in these two regimes perfectly match at that value. Since the relation between $C_z$ and $k$ does not depend on other parameters than $Da_c$, one may consider that the matching between the two correlations is consistent. When this relation is used together with Eqs. (5) and (6) all the data points come close to the

45° line. This is not shown due to space limitations but we will see below that this model of $S_a$ can be used to obtain estimates of the light round delay that suitably match experimental data. It is worth noting that the previous derivation relies on the assumption that air and hydrogen are fully premixed. However, this is not the case since injection takes place at a close distance from the outlet and the reactive streams are only partially premixed near the backplane so that they form heterogeneities that are not accounted for.

## 4.2. Estimation of the light round delay

Using the previous expressions it is possible to derive estimates $\tilde{\tau}_{LR}$ for the light round delay. It is convenient to use a reduced variable $\tilde{\tau}_{LR}U_b/(P/2)$. One obtains Fig. 8 where the abscissa and ordinate respectively correspond to the dimensionless estimate and to data. The points in the diagram are close to the 45° line. This diagram also includes an experimental data point obtained by [16], with our estimate of the reduced light-round delay which is also close to the 45° line indicating that the model has perhaps a greater degree of generality than initially expected.

## 5. Conclusion

This article describes one of the first investigations of light-round ignition of hydrogen-fueled annular combustors. A model is developed to ensure that the target hydrogen mass fraction is reached before the spark is initiated. High-speed imaging of OH* emission indicates that the process is faster than those observed with hydrocarbon fuels but comprises the same phases: (a) kernel creation in the spark vicinity, (b) propagation in an arch-like fashion, (c) flame splitting into branches that are nearly perpendicular to the backplane and travel in opposite directions, (d) merging of the two branches with flushing of burnt gases outwards. Near the lean blow out limit, the light-round occurs without establishing all the flames. Apart from these ultra-lean conditions, the two flame fronts ignite all the injectors one after another, in the same order as their positions along the chamber. The light-round delay decreases when the injection velocity or global equivalence ratio are augmented. A model is derived for the absolute flame displacement velocity using a combination of turbulent burning velocity expressions that separately deal with cases corresponding to high and low laminar burning velocities. This model provides estimates of the light-round delay which suitably agree with experimental data.

## Novelty and Significance Statement

The novelty of this research essentially lies in the experimental investigation of light-round ignition in an annular combustor fed with pure hydrogen. Only one operating point has been tested with pure hydrogen before (on the NTNU annular combustor). The process is investigated for a broad set of operating conditions, which has never been done previously.
The systematic experiments reported in the present article are thus the only study that provides a comprehensive view of the influence of global equivalence ratio and injection velocity on the light-round ignition time in the case of pure hydrogen injection. A particular phenomenon is also uncovered where the flame branches propagate on the two sides of the annular system, merge but only partially establish flames, a situation that was not reported previously. A novel model is derived to represent the light-round displacement velocity and obtain estimates of a dimensionless light round merging time that closely matches experimental data and could be used in engineering design.

## 12 Author Contributions

N.V. performed the experiments, processed the data, analyzed the data and wrote the paper. D.D. supervised the research, designed the experiments, analyzed the data and edited the paper. R.V. supervised the research, interpreted data and edited the paper. S.C. derived analytical models, interpreted data, wrote parts of the manuscript and edited the paper. A.R. supervised the research, analyzed the data, edited the paper and obtained the funding.

## 22 Declaration of competing interest

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

## 26 Acknowledgments

This work was partially supported by the FlyHy project ANR-21-CE05-0008. For open access purposes, a CC-BY license has been applied by the authors to this document and will be applied to any subsequent version up to the author's manuscript accepted for publication resulting from this submission.

## 33 References

[1] T. Yahou, J. R. Dawson, T. Schuller, Impact of chamber back pressure on the ignition dynamics of hydrogen enriched premixed flames, Symp. (Int.) Combust. (2022) 9.

[2] A. Aniello, T. Poinsot, L. Selle, T. Schuller, Hydrogen substitution of natural-gas in premixed burners and implications for blow-off and flashback limits, Int. J. Hydrogen Energy 47 (77) (2022) 33067-33081.

[3] H. Pers, A. Aniello, F. Morisseau, T. Schuller, Autoignition-induced flashback in hydrogen-enriched laminar premixed burners, Int. J. Hydrogen Energy (2022) 10235-10249.

[4] T. Yahou, J. R. Dawson, T. Poinsot, L. Selle, T. Schuller, Flame front dynamics during ignition of lean premixed H2/Air and CH4/Air flames, Combust. Flame 269 (2024) 113708.

[5] M. Boileau, G. Staffelbach, B. Cuenot, T. Poinsot, C. Bérat, LES of an ignition sequence in a gas turbine engine, Combust. Flame 154 (1) (2008) 2-22.

[6] J.-F. Bourgouin, D. Durox, T. Schuller, J. Beaunier, S. Candel, Ignition dynamics of an annular combustor equipped with multiple swirling injectors, Combust. Flame 160 (8) (2013) 1398-1413.

[7] E. Machover, E. Mastorakos, Spark ignition of annular non-premixed combustors, Exp. Therm. Fluid Sci. 73 (2016) 64-70.

[8] R. Ciardiello, P. M. de Oliveira, A. W. Skiba, E. Mastorakos, P. M. Allison, Effect of spark location and laminar flame speed on the ignition transient of a premixed annular combustor, Combust. Flame 221 (2020) 296-310.

[9] R. Ciardiello, L. C. Mesquita, E. Mastorakos, Low-order modelling of the light-round ignition transient in a premixed annular combustor, Combust. Theor. Model. 26 (3) (2022) 399-421.

[10] M. Philip, M. Boileau, R. Vicquelin, T. Schmitt, D. Durox, J.-F. Bourgouin, S. Candel, Simulation of the ignition process in an annular multiple-injector combustor and comparison with experiments, J. Eng. Gas Turb. Power 137 (031501) (Sep. 2014).

[11] M. Philip, M. Boileau, R. Vicquelin, E. Riber, T. Schmitt, B. Cuenot, D. Durox, S. Candel, Large Eddy Simulations of the ignition sequence of an annular multiple-injector combustor, Proc. Combust. Inst. 35 (3) (2015) 3159-3166.

[12] Y. Xia, C. Linghu, Y. Zheng, C. Ye, C. Ma, H. Ge, G. Wang, Experimental investigation of the flame front propagation characteristic during light-round ignition in an annular combustor, Flow Turbul. Combust. 103 (1) (2019) 247-269.

[13] G. Wang, L. Zhong, Y. Yang, Y. Zheng, Y. Fang, Y. Xia, C. Ye, Experimental investigation of the ignition dynamics in an annular premixed combustor with oblique-injecting swirling burners, Fuel 287 (2021) 119494.

[14] C. Liu, H. Yang, X. Li, L. Yu, X. Lu, Experimental study on the impact of swirl configurations and ammonia-methane blends on the ignition dynamics of a premixed annular combustor, Fuel 389 (2025) 134583.

[15] Y. H. Kwah, P. W. Agostinelli, S. Richard, G. Exilard, S. Pascaud, L. Gicquel, J. R. Dawson, Effect of Strong Azimuthal Swirl on Ignition and Light-Around in an Annular Combustor, J. Eng. Gas Turb. Power 144 (11) (Sep. 2022).

[16] Y. H. Kwah, S. Wiseman, J. R. Dawson, The effect of methane-ammonia and methane-hydrogen blends on ignition and light-around in an annular combustor, in: Volume 3A: Combustion, Fuels, and Emissions, American Society of Mechanical Engineers. ASME Paper GT2023-101255, Boston, Massachusetts, USA, 2023.

[17] K. Prieur, D. Durox, J. Beaunier, T. Schuller, S. Candel, Ignition dynamics in an annular combustor for liquid spray and premixed gaseous injection, Proc. Combust. Inst. 36 (3) (2017) 3717-3724.

[18] T. Lancien, K. Prieur, D. Durox, S. Candel, R. Vicquelin, Large Eddy Simulation of light-round in an annular combustor with liquid spray injection and comparison with experiments, J. Eng. Gas Turb. Power 140 (021504) (Oct. 2017).

[19] K. Prieur, G. Vignat, D. Durox, T. Schuller, S. Candel, Flame and spray dynamics during the light-round process in an annular system equipped with multiple swirl spray injectors, J. Eng. Gas Turb. Power 141 (061007) (Jan. 2019).

[20] K. Töpperwien, F. Collin-Bastiani, E. Riber,
120 B. Cuenot, G. Vignat, K. Prieur, D. Durox, S. Candel, R. Vicquelin, Large-Eddy Simulation of flame dynamics during the ignition of a swirling injector unit and comparison with experiments, J. Eng. Gas Turb. Power 143 (021015) (Jan. 2021).

125 [21] K. Töpperwien, S. Puggelli, R. Vicquelin, Analysis of flame propagation mechanisms during light-round in an annular spray flame combustor: the impact of wall heat transfer and two-phase flow, Combust. Flame 241 (2022) 112105.

1

2

3

4

5

6

7

8

[22] T. Lancien, K. Prieur, D. Durox, S. Candel, R. Vicquelin, Leading point behavior during the ignition of an annular combustor with liquid n-heptane injectors, Proc. Combust. Inst. 37 (4) (2019) 5021–5029.

9

10

11

12

[23] W. Gao, J. Yang, F. Liu, Y. Mu, C. Liu, G. Xu, Experimental investigation on the flame propagation pattern of a staged partially premixed annular combustor, Combust. Flame 230 (2021) 111445.

13

14

15

16

[24] N. Vaysse, D. Durox, R. Vicquelin, S. Candel, A. Reinaud, Analysis of thermo-acoustic instabilities induced by hydrogen swirling flames, J. Eng. Gas Turb. Power 147 (1) (2025) 011011.

17

18

19

20

[25] D. Bradley, A. K. C. Lau, M. Lawes, F. T. Smith, Flame stretch rate as a determinant of turbulent burning velocity, Philos. Trans. A Math. Phys. Eng. Sci. 338 (1650) (1992) 359–387.

21

22

23

24

[26] A. Lipatnikov, J. Chomiak, Turbulent flame speed and thickness: phenomenology, evaluation, and application in multi-dimensional simulations, Prog. Energy Combust. Sci. 28 (1) (2002) 1–74.

25

26

27

[27] V. Karpov, A. Lipatnikov, V. Zimont, A test of an engineering model of premixed turbulent combustion, Symp. (Int.) Combust. 26 (1) (1996) 249–257.

28

29

30

31

[28] H. Kobayashi, K. Seyama, H. Hagiwara, Y. Ogami, Burning velocity correlation of methane/air turbulent premixed flames at high pressure and high temperature, Proc. Combust. Inst. 30 (1) (2005) 827–834.

32

33

34

[29] G. Damköhler, The Effect of Turbulence on the Flame Velocity in Gas Mixtures, NACA (NACA-TM-1112) (Jan. 1947).