# Light-round ignition dynamics of a hydrogen-fueled annular combustor: Parametric effects and reduced-order modeling

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

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Nicolas Vaysse, Daniel Durox, Ronan Vicquelin, Sébastien Candel, Antoine Renaud. Light-round ignition dynamics of a hydrogen-fueled annular combustor: Parametric effects and reduced-order modeling. Combustion and Flame, 2026, 285, pp.114725. 10.1016/j.combustflame.2025.114725. hal-05460651

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Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
Light-round ignition dynamics of a hydrogen-fueled annular
combustor: parametric effects and reduced-order modeling

Nicolas Vaysse¹, Daniel Durox¹, Ronan Vicquelin¹, Sébastien Candel¹, and Antoine Renaud¹

¹Laboratoire EM2C, CNRS, CentraleSupélec, Université Paris-Saclay, 3, rue Joliot Curie, 91192
Gif-sur-Yvette cedex, France

**Abstract**

One issue in the operation of annular combustors is to ensure a reliable light-round ignition that will establish flames on all injector units without excessive pressure excursion and in a relatively short period of time. This issue is here examined in the case where the annular system is fed with pure hydrogen by combing experimentation and reduced order modeling. Systematic experiments are carried out in a model scale configuration equipped with multiple injectors, in which pure hydrogen is delivered in cross-flow in a swirling stream of air. In this large set of experiments, ignition initiated by a single spark plug gives rise to a couple of flames traveling in clockwise and counterclockwise directions which at a later stage, propagate head-on and merge. It is found that the duration of this process is much shorter when the combustor is fed with pure H2 than when it is operated with gaseous propane-air mixtures or liquid sprays of heptane or dodecane. Systematic observations of the final stage before flame merging indicates that a layer of fresh reactants is formed between the two flame branches which slows down the flame propagation. This flame deceleration is here documented in the case of hydrogen flames. A reduced order model, that accounts for this final stage, is shown to suitably capture effects of global equivalence ratio and injection velocity on the light-round time delay. Experiments also provide indications on effects of injector swirl number and preheating of the chamber walls. In contrast with previous experiments with hydrocarbon flames, it is found that preheating has only a marginal effect on the light-round time. An examination of pressure records during ignition is fi-

nally carried out to quantify the amplitude of the ignition-
induced pressure excursion. A novel scaling law is de-
rived to estimate the corresponding pressure peaks and
this model is shown to be consistent with experimental
data. It is also found that under certain conditions, the ig-
nition is followed by a cyclic regime corresponding to a
thermoacoustic oscillation that is shown to be coupled by
the first azimuthal mode of the chamber.

Novelty and significance statement

The novelty of this research lies in the experimental inves-
tigation of light-round ignition in an annular combustor
fed with pure hydrogen, a case not well documented in the
literature. The broad set of experiments reported in this
article provides a comprehensive view of the influence of
global equivalence ratio, injection velocity, swirl number
and wall preheating on the light-round characteristic time
in the case of pure H₂ injection and probably constitutes
the only data set that fills an identified gap of knowledge.
The flames slowdown in their head-on merging is also
analyzed for the first time in the hydrogen case. A re-
duced-order model of the light-round ignition accounting
for equivalence ratio and injection velocity from previous
work of the same team is here extended to account for this
slowdown phenomenon and shown to provide improved
estimates of the flame velocity and light-round time delay.
The pressure peak induced by the process is analyzed, a
novel scaling law is derived to estimate this quantity and
is shown to be consistent with experimental data.
# Nomenclature

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$P_{th}$ Combustor thermal power [kW]

$\phi$ Global equivalence ratio [-]

$S$ Swirl number [-]

$\tau_{LR}$ Light-round ignition time [ms]

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$S_a$ Flame front absolute displacement velocity [m/s]

$S_T$ Turbulent burning velocity [m/s]

$S_L$ Laminar burning velocity [m/s]

$p'_{max}$ Pressure excursion at ignition [Pa]

4

## Geometrical parameters

$l_c$ Combustor length [mm]

$d_{ext}$ External diameter [mm]

$d_{int}$ Internal diameter [mm]

5

$\mathcal{P}$ Combustor perimeter [mm]

$\delta$ Half size of the flame slow-down layer [mm]

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## Superscripts and subscripts

b bulk value

7

· Measured average quantity

~ Modeled quantity

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# 1 Introduction

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A substantial amount of research has been expanded in recent years to analyze dynamical phenomena like thermoacoustic instabilities and light-round ignition. Much of this work has concerned ignition in annular combustion chambers, a geometry that is commonly found in gas turbines dedicated to energy production and in aircraft and helicopter engines. The light-round ignition, investigated in the present article, has a critical impact on their operability. However, much of the effort has concerned up to now hydrocarbon fueled systems. Since hydrogen is now considered as a possible fuel to achieve the decarbonization of industrial gas turbines and aeroengines, it has become important to examine the light-round dynamics when the system operates with this fuel. The present investigation is intended to bring new information on this process, examine more specifically the flame structures induced by spark ignition in the annular geometry, determine the time delay that leads to flame merging and the establishment of flames in the system, consider effects of operating parameters, examine the pressure excursions that accompany the

traveling front as it initiates the various flames and examine a manifestation of thermoacoustic instability arising immediately after ignition.

At this stage it is natural to examine the technical literature dealing with hydrogen flames ignition. Since the existing literature on ignition in annular combustors fed with pure hydrogen is quite limited, it is worth examining works dealing with ignition of single-injector burners fueled with hydrogen. Studies on ignition dynamics of single-injector hydrogen combustors [1] or domestic boilers [2, 3] have emphasized the propensity of H₂ flames to flashback at ignition and to be accompanied by large amplitude pressure excursions. Yahou and coworkers [4] indicate that during forced ignition, the high resistance to strain rate of flames formed by hydrogen or hydrogen-enriched methane allow them to cross highly-strained regions and to stabilize more easily than pure methane flames in highly turbulent flows.

Hydrogen ignition is also important in the context of fire safety with in particular auto-ignition issues of hydrogen leaking from high-pressure vessels that may cause severe damage. In this context, auto-ignition of hydrogen leaking from high-pressure vessels has also been studied both experimentally and numerically (see for example [5, 6], [7]).

The survey of the literature also indicates that light-round in annular systems has received considerable attention in the recent period but that the case of hydrogen is not well documented. Much of the effort on light-round has focused on lab-scale experiments and on numerical modeling. A pioneering investigation carried out by [8] reports a simulation in the complex geometry of a helicopter combustor but these calculations could not be validated with respect to detailed experimental data. Such data were only generated a few years later in simpler laboratory-scale annular combustors. In [9], the annular system (designated as MICCA) was fed with premixed air and propane. This facility was used to examine flame configurations, time delays from ignition to flame merging and effects of injection velocity. Experimental results indicated that the front velocity was essentially related to the turbulent burning velocity and to the volumetric expansion accompanying the chemical conversion of fresh reactants into burnt gases. During the same period, the annular system of Cambridge and NTNU, that was initially used to study thermoacoustic instabilities coupled

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by azimuthal modes [10], provided additional insights on the light-round process in a non-premixed combustor with specific consideration of effects linked to the number of injectors and to their spacing [11]. Light-round experiments were carried out in a second stage with liquid sprays of heptane and dodecane [12, 13]. These studies with spray flames, indicated that a transient flashback was induced by the pressure wave produced by the volumetric expansion taking place when each injector was ignited. Effects of spark plug location and laminar burning velocity were examined by [14]. Another annular combustor, designated as TurboCombo and inspired by the MICCA design, was later built at Zhejiang University and used to study the influence of the ignition procedure on light-round dynamics [15]. It was found that injection of fuel after sparking increased the asymmetry between the flame branches and augmented the light-round time. Oblique injectors placed in the same rig were also used to study transverse convection effects of a mean circumferential flow [16]. The NTNU combustor was also used in more recent years to investigate the light-round of methane flames in gyrating mean flow [17]. Gaseous blends of methane and ammonia or hydrogen were also examined [18]. The latter work reports a case of pure-hydrogen light-round ignition, in a configuration comprising 6 or 12 injectors, for two operating points. It is found that hydrogen enrichment leads to a surprising reduction of the volumetric expansion effect which is explained as resulting from thermo-diffusive instabilities manifested during hydrogen combustion. This is represented by a scaling by the effective Lewis number. More recently, the effect of a global swirl and the influence of the injector swirl number on the light-round time and burner-to-burner propagation was investigated in a configuration similar to the Cambridge-NTNU annular combustor fueled with ammonia-methane blends [19].

In parallel to the previous experimental investigations, an effort has been made to develop numerical models of the process in the non-premixed case [20] and in the premixed annular configuration fueled by ethylene or by methane [14, 21]. Light-round simulations using LES were also developed leading to some remarkable renderings of the experimental data corresponding to the premixed gas experiments in terms of traveling flame structures and light-round delay times [22, 23]. Simulations of spray experiments were also carried out with a focus

on the leading point behavior [24, 25], turbulent combustion modeling [26] and the influence of wall temperature effects [27, 28]. Consistent with the experimental analysis, these detailed simulations highlight key factors such as the turbulent flame speed and the additional and significant acceleration due to the volumetric expansion of burnt gases. In non-premixed injection systems, the trajectory of the flame's leading edge is influenced by the inhomogeneous mixture of fresh gases, particularly in the regions between injectors.

The previous studies have brought considerable insight on the light-round process but this review also shows that little is available on this process when hydrogen is being used as a fuel. A recent study [29], produced by our team, reports some initial experiments and a reduced order model of the process providing an estimate of the light-round delay that compares favorably with experimental data. Expanding beyond prior findings, the present article presents a comprehensive experimental campaign combined with additional reduced-order modeling to capture the dynamics of flame head-on merging and the resulting pressure peaks. The objectives are here focused on: (1) the light-round sequence, (2) the light-round delay quantification, (3) the influence of operating conditions on this delay in terms of (a) equivalence ratio and injection velocity, (b) swirl number and (c) thermal boundary conditions, and (4) the impact of these parameters on the pressure excursions at ignition. This might appear as relatively diverse list of topics but is inherent to the process that is being investigated which depends on many parameters. The diversity is handled with two models that are proposed to gather data in a convenient form and to provide light-round time delay and pressure excursions estimates. This article begins with a brief description of the MICCA-H2 facility and of acoustic and optical instrumentation (Section 2). Images of light-round experiments are provided in Section 3 for a subset of operating conditions together with light-round data deduced from a large set of experiments. The influence of equivalence ratio and injection velocity on the light-round time is examined. A limited amount of data is also provided on the influence of the swirl number and of wall preheating on the light-round time. A reduced-order model derived in previous work is extended in Section 4 to represent effects linked to the mutual interaction of the two flame branches when they come close together and decelerate. The pressure and
light intensity signals observed during the ignition process are considered in Section 5 and used to identify the sequential initiation of the different flames and analyze the link between these two signals. This section also contains a quantification of the pressure excursion magnitude.

# 2 Experimental setup

## 2.1 The MICCA-H2 combustor

The MICCA-H2 annular combustor, shown schematically in Fig. 1, comprises a chamber formed by two cylindrical quartz walls of height $l_c = 200$ mm, with external diameter $d_{ext} = 400$ mm and internal diameter $d_{int} = 300$ mm. A thermocouple is placed on the outer quartz cylinder to measure the external wall temperature and ensure thermal stabilization. Its backplane is equipped with sixteen swirling injectors. The hydrogen fuel flow rate is measured through a Bronkhorst EL-FLOW controller with a full-scale capacity of 680 NL/min and relative accuracy of 0.2% at full scale, and the air flow rate through two Bronkhorst EL-FLOW flow controllers with full-scale capacities of 5000 NL/min and a relative accuracy of 0.5% at full scale.

Eight Brüel & Kjær microphones, are plugged on waveguides connected to the chamber backplane in order to protect these sensors from the chamber's hot temperature environment. Each waveguide is fitted with a 25 m long pipe to avoid reflections from the termination. The waveguide ports are located on the mean circumference, at equal distance from two adjacent injectors. The light-round process is visualized using an intensified high-speed CMOS camera APX-i2 comprising 1024×1024 pixels with an 8-bit resolution. This UV camera lens is equipped with a 10 nm bandpass filter centered at 310 nm in order to record OH* chemiluminescence. The frame rate and exposure are respectively set at 2000 Hz and 450 µs. Eight photomultipliers (PMs) are placed in a semi-circle around the chamber, each facing one flame from a group of eight. The PMs are also equipped with a 10 nm bandpass filter centered at 310 nm and with a spatial filter to eliminate the light emitted by adjacent flames. To allow a full view of the flame dynamics in the system the core of the annulus is empty so that light emission from the flame that is diametrically op-

posed to that facing each PM may also reach this sensor. The corresponding light signal is much lower than that originating from the flame that is close to the PM. This signal, coming from further away, can be identified and does not complicate the interpretation. The microphones and PMs signals are recorded at a sampling frequency of 16,384 Hz.

In ignition experiments, the light emitted by excited radicals like OH* constitutes a measure of the combustion intensity. When flames operate in the premixed mode, many studies indicate that the relative intensity fluctuations approximately represent the relative fluctuations of the heat release rate i.e. that $\dot{Q}'/\dot{Q}_0 \simeq I'_{OH*}/\bar{I}_{OH*}$. This is well confirmed by experiments on premixed hydrocarbon flames. This relationship is less well established for technically premixed hydrogen flames. This relation is examined in more detail in a recent study by [30] where it is shown that the link between $\dot{Q}_0$ and $\bar{I}_{OH*}$ is less direct. It is noted that $\dot{Q}'$ and $I'_{OH*}$ have nearly the same phase, a feature indicating that $\dot{Q}'(t)$ and $I'_{OH*}(t)$ are nearly synchronized so that the intensity signal may serve to mark the timing of the light-round process. For the magnitude, there are no simple alternatives and one may tentatively assume that the relative light intensity fluctuations deduced from the photomultiplier signals may be treated as representative of the relative heat release rate fluctuations. This is admittedly an approximation that introduces some uncertainty in the estimation of the heat release rate. The problem is compounded by the fact that a fraction of the light may be emitted inside the injection unit. The uncertainty is more limited in what concerns the timing of the successive ignitions in the system.

## 2.2 Injection units

The injector, denoted as CFI-X1, comprises a 5.3 mm slender cone that is slightly longer than the one used in previous experiments [31, 32]. Six radial channels having a diameter of 1.5 mm are drilled in its base and convey gaseous hydrogen into the surrounding stream of swirling air. The injection plane is located at a distance $h_t = 11.1$ mm with respect to the injection unit outlet. The air passes through a radial swirler and flows in the axial direction. Downstream the cross-flow injection zone, the gaseous mixture enters a converging nozzle exiting in the combustion chamber through a hole with diam-
<figure><img src="image_2.png" /><figcaption>Figure 1: Schematic top view of the MICCA-H2 experimental setup. The letters PM represent the photomultiplier locations for the OH* measurements, P correspond to the eight chamber microphones and B to the burners.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 2: Left: Schematic view of the CFI-X1 cross-flow injector. Right: MICCA-H2 during stable operation.</figcaption></figure>

### 3 Light round process: qualitative description, time delay and parametric dependencies

The domain explored in this study covers a range of thermal powers, between 27 kW and 72 kW. The system operates in lean conditions at global equivalence ratios from 0.28 to 0.76. This results in bulk velocities $U_b$ spanning from 21 m/s to 54 m/s. These operating conditions are gathered in Table 1.

<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><tr><td>27-61</td><td>0.28-0.76</td><td>31.3</td><td>3.4-6.02</td><td>0.40-0.77</td></tr></tbody></table>

The ignition procedure consists in stabilizing the fuel flow rate first, and then triggering the spark igniter. This procedure is denoted as FFSL (fuel first, spark later) in [15, 16] in opposition to SFFL mode (spark first, fuel later), where the fuel flow rate may not be well established in the chamber when ignition occurs. In this work, acquisition of the signals is initiated, then the hydrogen mass flow controller is turned on and the flow rate of hydrogen reaches the desired operating condition. The resi-

deter $d_e = 8$ mm. A schematic presented on the left-hand side in Fig. 2 shows the injection cone, the radial swirler and the converging nozzle.

Two different swirlers are used in this study. The first designated as 707, comprises 6 non-radial channels characterized by their diameter $d_{sc} = 4$ mm, and the distance between the axis of the channels and the central axis of the swirler $R_0 = 4.6$ mm. When this swirler is placed in the injection unit, it generates a rotating flow featuring a measured 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. The second swirler, denoted 726, has the same layout but the distance of the channels to the central axis is $R_0 = 5.5$ mm and the channel diameter $d_{sc} = 3.5$ mm. This second swirler induces a larger swirl number $S = 0.74$ and a greater pressure drop coefficient $\sigma = 5.47$. A typical view of the MICCA combustor equipped with CFI-X1 injectors operating with pure hydrogen is shown in Fig. 2 (right).
dence time of the fresh gases in the chamber ranging from 0.25 s to 0.65 s, the spark plug is triggered two seconds after stabilization of the hydrogen flow rate to ensure a homogeneous distribution of hydrogen mass fraction in the chamber based on the flow meter command signal and considering the chamber as a well-stirred reactor [29]. Finally, the light-round ignition is recorded by the high-speed camera.

## 3.1 Description of the light-round process

In the typical light-round illustrated in Fig. 3, where the combustor is operated at a thermal power $P_{th} = 46$ kW and a global equivalence ratio $\phi = 0.57$, one distinguishes four periods. At first ($t = 0$ ms), a flame kernel is ignited next to the spark discharge and this kernel expands. In a second stage, a flame is formed and starts travelling sideways and upwards, in an arch-like fashion (it is visible on the third frame, at $t = 6$ ms). In a third stage, the flame reaches the chamber outlet and splits into two branches that propagate in opposite directions (between $t = 6$ ms and $t = 20$ ms, that correspond to frames 3 to 7 in Fig. 3). In the fourth stage, prior to merging, the two branches are slowed down by the layer of fresh gases in between (frame at $t = 21$ ms). Finally, the two branches merge (at $t = 24$ ms in the case of Fig. 3), and the reactive front is convected upwards. During the whole process, hydrogen flames stabilize one after the other behind the traveling fronts. This applies for all tested operating conditions. One interesting observation is that the flame branches are nearly perpendicular to the backplane when traveling all around the combustor. This contrasts with observations and simulations made with hydrocarbon flames [9, 12, 25], characterized by inclined flame branches, and leading points that are clearly identified and found to travel at a close distance from the chamber backplane.

## 3.2 Effects of equivalence ratio and injection velocity

The light-round time $\tau_{LR}$ is defined in this study as the time between the flame initial kernel formation and the merging of the two flame branches. Its values are displayed in Fig. 4 for all operating conditions, without wall preheating and with injectors equipped with 707 swirlers.

These values are between two and three times lower than those obtained with hydrocarbon flames with the same chamber diameter and for equivalent operating conditions (power and equivalence ratio) [9, 12], a reduction in light-round time delay that is mainly due to the high burning velocities of hydrogen flames. For instance, the condition $\phi = 0.76$ and $U_b = 31$ m/s that results in $\tau_{LR} = 18$ ms with hydrogen would led to 54 ms with propane in [9]. Figure 4 shows that the light-round time is notably diminished when the global equivalence ratio is augmented, which is not surprising since the laminar burning velocity increases with the equivalence ratio when the fresh reactant mixture is lean. Injection bulk velocity $U_b$ is also found to have a strong impact on the light-round time since $\tau_{LR}$ decreases when $U_b$ is increased and the level of turbulence is augmented.

It is natural to calculate a mean displacement velocity by simply dividing the half perimeter by the light-round time delay:

$$ \bar{S}_a = \frac{P/2}{\tau_{LR}} \qquad (1) $$

This mean velocity is inversely proportional to the light-round time delay. It increases with $\phi$ and with $U_b$. It will be shown in section 4 that this mean displacement velocity can be linked to the turbulent burning velocity so that the light-round time delay can be estimated from that quantity.

## 3.3 Influence of injector swirl number and wall preheating

The swirlers 707 in the sixteen injectors can be replaced by swirlers 726, leading to an increase in swirl number from 0.60 to 0.74. The light-round time measured with this new configuration appear in the last column of Table 2.

The light-round times that were between 30 and 28.5 ms with swirler 707 are reduced to 27.2 ms with swirler 726, and this reduction is even stronger at higher equivalence ratios since the light-round time diminishes from 19.5 ms with swirler 707 to 16.5 ms with swirler 726 at $\phi = 0.64$. These results indicate that increasing the swirl number leads to a decrease in light-round time for the conditions explored. A similar result was recently obtained in a combustor fed with ammonia-methane blends
<figure><img src="image_4.png" /><figcaption>Figure 3: Typical flame images (false color) during light-round ignition at equivalence ratio $\phi = 0.57$ and injection velocity $U_b = 29.2$ m/s, corresponding to $\mathcal{P}_{th} = 46$ kW. The walls are not preheated and the swirl number of 0.60 corresponds to swirler 707.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Figure 4: Influence of the global equivalence ratio and injection velocity on the measured light-round time.</figcaption></figure>

[19] but with injection units comprising a central bluff-body. An increase in swirl number induces a larger tangential velocity component in the jet flame established by each injector and one may tentatively infer that this in turn increases the turbulence level in the flow augmenting the turbulent burning velocity.

Previous results were obtained under room temperature conditions corresponding to a cold start. Another interesting case consists in relighting a combustor after flame blow out, i.e. when the chamber walls are already at a steady-state hot temperature. The corresponding procedure consists in firing the combustor at the target operating condition during a few minutes, until the external wall temperature is stabilized, and then turning off the fuel during a few seconds before beginning the FFSL ignition procedure. Experiments carried out in order to study the effect of wall preheating yield the light-round delay times that are shown in Fig. 5.

Data gathered under these hot wall conditions indicate that at low swirl number, wall preheating has only a minor effect on the light-round time. This notably differs from experimental and numerical results obtained for heptane spray flames [12, 27] where preheating was found to divide the light-round time by a factor of two or more. In these studies, the ignition scenario was identical (FFSL mode) and the thermocouple was placed at the same location. The protocol was identical with a waiting time of the same duration to reach a thermal steady-state before re-igniting the combustor. In [12], a thermal power of 80 kW and equivalence ratio of 0.9

<figure><img src="image_6.png" /><figcaption>Figure 5: Influence of preheating on light-round time at constant injection velocity $U_b = 31.3$ m/s using swirler 707.</figcaption></figure>

<table><caption>Table 2: Light-round times for cold and preheated conditions, and both swirlers 707 (designated “S”) and 726 (designated “U”). The injection velocity is kept constant at $U_b = 31.3$ m/s. Values of the light-round time result from an average of two runs for each condition. The typical error is $\pm 0.75$ ms.</caption><thead><tr><th>P<sub>th</sub><br>(kW)</th><th>φ</th><th>Swirl<br>intensity</th><th>Swirl<br>number</th><th>T<sub>wall</sub><br>[°C]</th><th>T<sub>LR</sub><br>[ms]</th></tr></thead><tbody><tr><td>37</td><td>0.4</td><td>Low</td><td>0.60</td><td>24</td><td>29.2</td></tr><tr><td>37</td><td>0.4</td><td>High</td><td>0.74</td><td>24</td><td>27.2</td></tr><tr><td>37</td><td>0.4</td><td>Low</td><td>0.60</td><td>267</td><td>28.7</td></tr><tr><td>37</td><td>0.4</td><td>High</td><td>0.74</td><td>280</td><td>24.7</td></tr><tr><td>53</td><td>0.64</td><td>Low</td><td>0.60</td><td>24</td><td>19.5</td></tr><tr><td>53</td><td>0.64</td><td>High</td><td>0.74</td><td>24</td><td>16.5</td></tr></tbody></table>

led to a steady-state wall temperature of 900 K after 500 s, which is much higher than the typical values obtained in this study (600 K for 46 kW and $\phi = 0.52$ after thermal stabilization). This is due to three factors: first, the lower equivalence ratios investigated lead to lower adiabatic flame temperatures. Secondly, since the system is not adiabatic, the lower thermal powers involved reduce the heat transfer from the burnt gases to the walls. Finally, the lower wall temperature is also due to the small width of the hydrogen flames compared to the spray flames studied in [12], leading to an increased distance to the walls. It is thus possible that the smaller effect of preheating on the light-round time in the current
study compared to previous work could be attributed to the lower wall temperatures. In [12], the notable reduction of the light-round time delay was linked to the preheating of reactants as they flow through the system inducing an increase in the laminar burning velocity which more than compensates the decrease in volumetric expansion ratio $ρ_u/ρ_b$. This effect probably persists in hydrogen flames, as Table 2 shows a more pronounced reduction in light-round time when the swirl number is increased. Specifically, with swirler 726, the light-round time decreases from 27.2 ms (with cold walls) to 24.7 ms (with preheated walls). One possible explanation is that replacing swirler 707 with 726 increases turbulence, thereby enhancing heat transfer from the wall to the fresh gases. This would raise the reactants' temperature at ignition and increase the flame displacement velocity. It is also possible that increasing the swirl number leads to stronger recirculation near the wall, increasing the fresh reactant stream residence time and thus enhancing their preheating near the outer recirculation zone around each burner. The previous discussion is admittedly speculative and the previous explanations need to be confirmed by further experiments and more measurements of the thermal state of the combustor backplane and lateral boundaries.

One question that was not investigated is the influence of the ignitor position. In the present experiments, the spark plug is located near an injector outlet. Since hydrogen is flammable over a wide range of equivalence ratios, the initial kernel is easily generated whatever the ignitor position provided that it is close to the backplane. The light-round is then essentially independent of this kernel generation and only weakly depends on its initiation. If the initial kernel were created at a distance from the backplane, one may infer from other experiments that this would have notably influenced the process.

## 4 Theoretical estimation of the light-round displacement velocity

From a practical point of view, it is worth making an attempt to estimate the light-round mean displacement velocity $\bar{S}_a$ defined in the previous section by Eq. 1. Exper-

imental data indicates that $\bar{S}_a$ essentially depends on the equivalence ratio and on the injection velocity or equivalently on the turbulence intensity level. One is then immediately led to think that $\bar{S}_a$ might be linked to the turbulent burning velocity. This idea was explored in previous work of the same team on MICCA [9, 29], where a reduced-order model was developed which considers that the flame propagation is essentially governed by this turbulent burning velocity and by the volumetric expansion. The light-round absolute displacement velocity is then modeled as $S_a = (\rho_u/\rho_b)S_d$ as widely used in the literature [33]. In this expression the flame displacement velocity $S_d$ is deduced from standard correlations of the turbulent burning velocity $S_T$. It is noted however in [29] that a single correlation for $S_T$ could not account for the wide range of operating conditions covered in the present experiments and that two different expressions had to be considered. The first corresponds to equivalence ratios greater than 0.5 where the laminar burning velocity takes finite values i.e. such that $S_L \ge 0.5$ m/s. One considers that $S_d$ is approximately equal to $S_T$ which in turn is determined with a correlation for the turbulent burning velocity. Systematic trials indicated that the Zimont-Karpov correlation [34], calibrated on hydrogen flames for equivalence ratios between 0.18 and 5, provided the best match with experimental data in the first range of equivalence ratios (i.e. for $\phi \ge 0.5$). This correlation takes the form:

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

In the previous expression, $C_z$ is a constant and the “l” subscript is used to indicate that the Reynolds number characterizes turbulence at the integral scale. At low equivalence ratios, corresponding to laminar burning velocities $S_L < 0.5$ m/s, it was observed in [29] that the light-round propagation was mainly driven by the flow turbulence. Indeed, the laminar burning velocity and the density ratio $\rho_u/\rho_b$ both take low values in that range but the absolute flame displacement velocity remains finite. The points of operation that correspond to these conditions cannot be treated with a correlation like (2) in which the two terms contain various powers of the laminar burning velocity. For these points, one has to replace Eq. (2) by a correlation that de-emphasizes the role of the laminar burning velocity. The simplest option was to use an expression initially derived by Damköhler [35]:
<figure><img src="image_7.png" /><figcaption>Figure 6: Low-order modeling of the light-round displacement velocity using the 2-regime model from [29]. The coefficient of determination between the data and the model is R² = 0.67.</figcaption></figure>

$$S_T = S_L + kv' \quad (3)$$

The switch between the two correlations (2) and (3) yields a new estimate denoted by $\tilde{S}_T$ and is controlled by the value of the Damköhler number as explained in [29]. It was found that the switching value was $Da_c = 4$ and that continuity between the two expressions could be assured after some algebra by linking the two constants $C_z$ and $k$ by $k = C_z(Da_c)^{1/4}$. The consistency of this scheme is supported by the simplicity of this last relation. In applying the previous expressions, it was found more appropriate to use experimentally determined values of $S_L$ in the second range corresponding to low values of the equivalence ratio [36]. Indeed, classical numerical models tend to underestimate the value of $S_L$ at low equivalence ratios. The validation of this reduced-order modeling of the light-round displacement velocity is carried out in Fig. 6 in which the horizontal and vertical axes respectively correspond to calculated values of $(\rho_u/\rho_b)\tilde{S}_T$ and to experimental values of the average flame displacement velocity $\bar{S}_a$ from ignition to final merging.

Most of the points are close to the 45° straight line indicating that the model is accurate for a wide range of op-

erating conditions. However, the displacement velocity is overestimated by the model compared to the experiments when the system operates at high equivalence ratios. The average light-round displacement velocity saturates and takes a nearly constant value in this range (corresponding to the highest values of $S_L$ shown in dark red) while the displacement velocity estimates take increasing values. This can be seen in Fig. 6 where the corresponding points are shifted away from the 45° line. One possibility might be that the turbulent burning correlation does not behave in a suitable manner at high values of $S_L$. Another explanation that may be inferred from detailed observations of the flame motion is that the flames decelerate during the final stages of their head-on merging, when the two flame branches come close together. During the final phase of the process, the fresh gases that are typically flushed ahead of each flame front become trapped between them, creating a buffer zone. This phenomenon was also observed in detailed simulations [25, 28], where the accelerated azimuthal flow of fresh gases in front of each flame front diminishes near the merging plane. As a result, the two flame fronts decelerate before merging, and this effect is all the stronger, the faster the flames go. In the layer of fresh reactants between the two flames, the velocity distribution may be roughly approximated to that existing in a stagnation point configuration and the front velocity is progressively reduced.

This is supported by a detailed examination of Fig. 7 which shows a sequence of light-round propagation before the merging of the two branches, for an equivalence ratio of 0.64. The radial lines drawn in blue on the chamber backplane link each injector center to the chamber center and materialize the sixteen sectors of the annular chamber. One observes starting from the fourth image of Fig. 7 that the branch on the right is slowed down to a notable extent whereas the left front travels at a speed that decreases more slowly. The deceleration begins when the two flame branches are separated by two sectors.

The arc-length locations of the flame front can be tracked by making use of the pattern of radial lines drawn on the chamber backplane and the flame positions may be plotted as a function of time. It is also possible to use the photomultiplier signals to detect these positions, and the two methods give consistent results. Figure 8 shows the results extracted from the high-speed images for two equivalence ratios, 0.52 and 0.64 and a constant injection
<figure><img src="image_8.png" /><figcaption>Figure 7: High-speed images of the end of the light-round ignition at equivalence ratio $\phi = 0.64$ and injection velocity $U_b = 31.3$ m/s, corresponding to $\mathcal{P}_{th} = 54$ kW. Swirler 707.</figcaption></figure>

velocity $U_b = 31.3$ m/s. The mid line between the left and right branches indicates if there is a discernable reduction in the average travelling time of the two flame fronts.

One observes that although the right front is slightly slowed down for $\phi = 0.52$, the mean flame front travels at a constant speed, whereas a bending of the mid line is observed for $\phi = 0.64$.

A model is thus developed to account for the mean flame front slow-down at equivalence ratios $\phi \ge 0.64$ (Fig. 9). This model consists in splitting the light-round process into two parts: a phase 1 that corresponds to the free propagation of the two flame branches, and a phase 2 where the fronts slow down before merging. The total arc length that is traversed by each branch of the front is denoted as $x_0 = \mathcal{P}/2$ where $\mathcal{P} = 1.1$ m is the perimeter of the MICCA chamber. The distance at which the front starts to slow down is $\delta = (1/8)x_0$, corresponding to one sector on each side, while $x_f$ denotes the instantaneous position of the flame branch. In phase 1, corresponding to $x_f < x_0 - \delta$, the light-round displacement velocity is equal to $(\rho_u/\rho_b)S_d$, as in the initial model. During phase 2 ($x_0 - \delta < x_f < x_0$), the influence of the fresh gases layer is captured by assuming that the absolute velocity gradually decreases from $(\rho_u/\rho_b)S_d$ to $S_d$, since the ac-

celerating effect of volumetric expansion vanishes during merging.

It is convenient to define $\Theta = \rho_u/\rho_b - 1$ that measures the volumetric expansion effect on the displacement velocity, a quantity that monotonically increases with the equivalence ratio and goes to zero at merging. Differences in mid-line bending between the two cases in Fig. 8 indicate that the slow-down phenomenon appears from $\phi = 0.64$ ($\Theta = 4.49$), so a critical expansion ratio $\Theta_c = 4.4$ can be identified, defining the threshold above which the model of phase 2 will be applied.

For $x_f < x_0 - \delta$, the position of the front can be expressed as:

$$ \frac{dx_f}{dt} = S_d(1 + \Theta) \qquad (4) $$

and for $x_0 - \delta < x_f < x_0$ in the case where $\Theta > \Theta_c$:

$$ \frac{dx_f}{dt} = S_d + \frac{x_0 - x_f}{\delta} S_d \Theta \qquad (5) $$

It is then easy to integrate the two velocity expressions and obtain the time durations corresponding to the two
<figure><img src="image_9.png" /><figcaption>Figure 8: Positions of the flame front for $\phi = 0.52$ (top) and $\phi = 0.64$ (bottom). The coordinate $x$ corresponds to the curvilinear abscissa along the mean perimeter of the chamber.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Figure 9: Reduced-order model of the unfolded light-round displacement velocity derived to accounting for the flame front being slowed down by the layer of fresh gases, for cases where the expansion factor is $\Theta > 4.4$. Yellow bars correspond to the two flame branches, and white arrows represent their displacement. The dark blue zone represents the zone of mutual interaction between the two branches.</figcaption></figure>

phases

$$ \tau_1 = \frac{x_0 - \delta}{S_d(1 + \Theta)} \qquad (6) $$

$$ \tau_2 = \frac{\delta}{S_d \Theta} \log_e (1 + \Theta) \qquad (7) $$

The light-round time is then the sum of these two durations:

$$ \widetilde{\tau_{LR}} = \frac{x_0 - \delta}{S_d(1 + \Theta)} + \frac{\delta}{S_d \Theta} \log_e (1 + \Theta) \qquad (8) $$

and the resulting estimate of the light-round displacement velocity is finally $\bar{S}_a = (P/2)/\widetilde{\tau_{LR}}$.

It is possible to validate the previous model accounting for the mutual interaction between the flame branches by plotting in Fig. 10 the estimated average displacement velocity $(P/2)/\widetilde{\tau_{LR}}$ along the horizontal axis versus the observed value of this quantity $\bar{S}_a$ along the vertical axis. The corresponding points are close to the 45° line and this is in particular the case for the points which were away from that line in the model that did not account for the final deceleration of the flame branches. This can be seen by comparing Figs. 6 and 10 (top).
It is also useful to consider the estimated dimensionless light-round delay

$$ \frac{\tau_{LR}U_b}{x_0} = \frac{x_0 - \delta}{x_0} \frac{U_b}{S_d(1+\Theta)} + \frac{\delta}{x_0} \frac{U_b}{S_d\Theta} \log_e(1+\Theta) \quad (9) $$

This quantity is plotted in the bottom of Fig. 10 along the horizontal axis while the vertical axis corresponds to the experimental value. Here again the points are close to the 45° line indicating that the previous expression provides values of the light-round delay that suitably estimate this quantity. It would be tempting to apply this reduced-order model to hydrocarbon flames, but this comparison would be limited to cold walls experiments, since a different influence of wall preheating has been observed between hydrogen and hydrocarbons. Thus, the model developed for hydrogen flames would not be sufficient to capture the dependency of the light-round delay on the thermal state of the combustor in the case of hydrocarbon flames.

# 5 Heat release rate and pressure signals

Further insights on the light-round dynamics may be gained by examining the OH* emission signals detected by the photomultipliers. One may first examine a typical signal recorded by photomultiplier PM4 plotted on top of Fig. 11, together with the instantaneous flow rate of hydrogen delivered to the MICCA combustor.

The flow rate signal in brown shows that a steady-state is already reached well before ignition. A simple modeling of the hydrogen mass fraction evolution $Y_{H_2}$ in the chamber [29] indicates that this ensures that $Y_{H_2}$ has reached its target value.

In the upper Fig. 11, the OH* light intensity signal recorded by PM4 rapidly increases when the flame front passes by the corresponding injector and inititates combustion at that injector. This allows an additional measurement method of the flame front location as a function of time. At a later time one observes a second “bump” in the signal corresponding to the ignition of the flame facing the PM4 photomultiplier on the opposite side of the combustor. The shape of this bump is broader because it corresponds to a wider arc segment and the maximum is less pronounced because the OH* intensity is reduced

<figure><img src="image_11.png" /><figcaption>Figure 10: Low-order modeling of the light-round displacement velocity when accounting for the flame fronts being slowed down by their mutual interaction. The results are expressed in terms of displacement velocity (top) and in dimensionless light-round time (bottom). In the top graph, the coefficient of determination between the data and the model is $R^2 = 0.87$.</figcaption></figure>
<figure><img src="image_12.png" /></figure>

Figure 11: Top: OH\* emission signal recorded by PM4 during the ignition sequence $\phi = 0.57$ and injection velocity $U_b = 29.2$ m/s, corresponding to $P_{th} = 46$ kW. The brown signal corresponds to the measurement of the hydrogen mass flow rate. Bottom: signal recorded by PM5. The instants $t_i^{\text{near}}$ and $t_i^{\text{far}}$ correspond to the successive passings of the flame branches as explained with Fig. 12. The unit of the intensity is arbitrary and depends on the sensitivity of each photomultiplier.

<figure><img src="image_13.png" /></figure>

Figure 12: Schematic explaining the flame branch passing directly near PM4 and PM5 (at instants $t_i^{\text{near}}$), and the later passing of the opposed branch in their field of view (at instants $t_i^{\text{far}}$) just before merging. The red sectors correspond to the intersection between the flame branches and the PMs fields of view.

by the distance to the flame and the successive quartz interfaces. This is explained on the schematic in Fig. 12. The lower Fig. 11 represents the OH\* intensity recorded by PM5. It shows the same features as PM4, i.e. a sharp peak and a broad bump, but respectively after and before PM4. This is so because the right flame branch goes from PM4 to PM5 whereas the left flame branch crosses their respective fields of view in the opposite order. This timing is also explained in Fig. 12. The left flame front travels a quarter perimeter between the detection of the opposite flame front by PM5 and its own detection by the same photomultiplier. Thus, the time delay between the first peak and the bump detected by PM5 is expected to be half of the light-round time, i.e. 12 ms. This is indeed the measured value of $t_1^{\text{far}} - t_2^{\text{near}}$ in the bottom of Fig. 11.

The light intensity drops down to a plateau, corresponding to the OH\* light intensity level of the stable flame. However, starting from $t = 6535$ ms, the PM signal features nonlinear oscillations at a frequency of 828 Hz. This corresponds to the onset of a thermoacoustic instability coupled by the first azimuthal mode of the chamber. This instability is observed for this operating condition and a large number of other operating conditions examined in this study, but this is not the case for all of them.
<figure><img src="image_14.png" /><figcaption>Figure 13: Pressure signals P5 and P6 recorded at the backplane during the ignition sequence $\phi = 0.57$ and injection velocity $U_b = 29.2$ m/s, corresponding to $P_{th} = 46$ kW. The orange and blue time intervals respectively pertain to the light-round until flame merging and to the established flame regime which in this case becomes oscillatory and corresponds to a thermoacoustic instability. The inset corresponds to the first two peaks recorded by each microphone, after the ignition of the first flame.</figcaption></figure>

The signals recorded by the microphones are also instructive, because they enable to quantify the pressure peak produced by the light-round ignition. The raw signals recorded by P5 and P6 are displayed in Fig. 13. They show that a pressure peak of 600 Pa is obtained at ignition. The first two peaks in P5 and two peaks in P6 (inset of Fig. 13) correspond to the detection of the first pressure wave traveling in the clockwise and counterclockwise directions and respectively detected by P5 then P6, and P6 then P5. The time delay between peaks of microphones P5 and P6 corresponds quantitatively to the traveling time of the pressure wave propagating to sensors P5 and P6. Indeed, its measurement on the inset gives 0.36 ms, which is equal to the value obtained by dividing the arc length between the two microphones by a speed of sound of 380 m/s, pertaining to a mixture of hydrogen and air at $\phi = 0.57$ and room temperature. The following peaks correspond to the successive flames being ignited. One also notices that periodic oscillations appear in the two signals begining at time 6525 ms with a period of about 1.16 ms corresponding to a frequency of $\approx 860$ Hz. These oscillations are damped out at $t = 6530$ ms. When the two flame branches have merged and all flames are estab-

<figure><img src="image_15.png" /><figcaption>Figure 14: Amplitudes of the pressure peak at ignition, as a function of the light-round time $\tau_{LR}$. The colors correspond to the injection velocity $U_b$.</figcaption></figure>

lished, oscillations grow again starting from $t = 6535$ ms, leading to a limit cycle regime of thermoacoustic instability. The frequency of these oscillations is 828 Hz, corresponding to the 1A1L mode of the chamber. This mode is standing and its nodal line passes at a close distance from the igniter location (burner 9). Details on modal identification are provided in [37].

The amplitudes of the pressure peaks at ignition can be represented as a function of the light-round time, as in Fig. 14. A first striking feature is that the pressure excursions produced by the ignition of the first flame are characterized by high amplitudes, ranging from 250 Pa up to 1200 Pa. The pressure peak amplitudes appear to be linked to the light-round time $\tau_{LR}$. When the light-round time decreases, the pressure peak level is augmented. Faster light-round processes corresponding to higher absolute flame velocities lead to higher pressure excursions at ignition. Additionally, one observes that the pressure peak amplitude is more sensitive to the injection velocity than the light-round time. One can take this effect into account by deriving a scaling law for the pressure excursion $p'_{max}$. For this one may use an expression linking the acoustic pressure to the rate of change of the heat release rate [38]:

$$p'(\boldsymbol{r}, t) = \frac{\gamma - 1}{4\pi c^2} \frac{1}{|\boldsymbol{r} - \boldsymbol{r}_0|} \frac{d\dot{Q}'}{dt} \left( \boldsymbol{r}_0, t - \frac{|\boldsymbol{r} - \boldsymbol{r}_0|}{c} \right) \quad (10)$$

In this expression $p'(\boldsymbol{r}, t)$ represents the pressure fluctu-
ation at $r$ and $\gamma$, $\rho_0$, c and $\dot{Q}'$ respectively designate the specific heat ratio, density, speed of sound and heat release rate at the location $r_0$. The previous expression is valid in free space for a point source. It was already used by [13] to examine the transient operation of an injector when it is initiated. It is here exploited to obtain an estimate of the pressure pulse generated by the rate of change in heat release rate $d\dot{Q}'/dt$. This is admittedly crude but this expression only serves as a guide in the derivation of a scaling law for the pressure excursion using dimensional analysis. Considering that $|r-r_0| \simeq d_e$, $\dot{Q}' \simeq \rho_0 U_b d_e^2 c_p (T_b - T_u)$, that $c^2 \simeq \gamma r T_u$ and that the rate of change of $Q'$ is governed by a typical time $d_e/S_a$, one finds that the pressure disturbance induced by ignition of an injector may be estimated from:

$$ \frac{p'_{\max}}{\rho_0 U_b^2} = k \frac{1}{2\pi} \frac{S_a}{U_b} \Theta \quad (11) $$

with the same notations as previously, where $k$ is a constant. The comparison of this model with experimental data, shown in Fig. 15, indicates that this scaling law suitably correlates with data gathered over a broad range of conditions. This law is probably applicable in other situations but the constant $k$ which is here found equal to $\simeq 3/2$ is specific to the present configuration. It is also possible to replace $S_a$ by $(P/2)/\tau_{LR}$ in (11) and obtain

$$ p'_{\max} = \rho_0 k \frac{1}{2\pi} \frac{P/2}{\tau_{LR}} U_b \Theta \quad (12) $$

This expression indicates that the pressure peak at ignition is reduced as $\tau_{LR}$ is augmented as observed in Fig. 14, but it also shows that the dependency is more complex since the peak pressure is also proportional to $U_b\Theta$ explaining the data dispersion in that figure.

## 6 Conclusion

The light-round ignition investigated in this article using a laboratory scale annular combustor reveals features that are specific to pure hydrogen injection. This process characterized by high speed imaging gives access to the light-round delay (the time duration separating spark ignition and flame merging). The propagation of two flame branches from the initial kernel formed by the spark plug

<figure><img src="image_16.png" /><figcaption>Figure 15: Modeling of the reduced pressure peak amplitudes at ignition. The colors correspond to the injection velocity $U_b$. The red line corresponds to a linear relationship. The slope of this line determines the constant in Eq. 11. One finds $k \simeq 3/2$.</figcaption></figure>

to their merging resembles that observed previously for hydrocarbon flames. However, in contrast with the hydrocarbon spray case, it is found 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.

The set of experiments carried out for a broad range of global equivalence ratios and thermal powers indicates that the light-round delay time is reduced when the nominal thermal power or equivalence ratio are augmented. This process is much faster with hydrogen injection than that observed in the same facility when the combustor is fed with premixed propane and air or with sprays of liquid heptane or dodecane.

A reduced-order model is developed to predict the light-round time while accounting for the slowdown of the flame fronts prior to their merging. This model can be used to derive estimates of the light-round delay from algebraic expressions.

Further experiments have shown that increasing the swirl number induced by the injection units while maintaining the other conditions speeds up the process to some extent. In contrast with observations made with hydrocarbon flames when the lateral walls and chamber backplane are hot, preheating of the combustor only has a marginal effect on the light-round time corresponding to hydrogen
injection. However, one must note that in the latter case the steady-state wall temperatures are much lower, partly because of hydrogen flames being more compact than hydrocarbon flames. Additionally, the effect of wall preheating is more significant when the swirl number is increased. However, the number of points investigated on this topic remains limited, thus the provided explanations need to be confirmed with further measurements.

The initial pressure excursions observed during ignition are measured and a scaling law is deduced in dimensionless form that is consistent with experimental data.

It has been observed that on many operating conditions, the light-round ignition is immediately followed by a thermo-acoustic instability coupled by the first azimuthal-first longitudinal (1A1L) mode of the combustion chamber.

In general, this study shows that light-round ignition of hydrogen-fueled annular combustors needs to be carefully examined. It will be important to further document the link between the short light-round times and the high pressure excursions in the chamber and to examine conditions under which this process leads to the onset of thermoacoustic instabilities.

## CREDIT authorship contribution statement

N.V: Data Curation, Formal Analysis, Investigation, Methodology, Writing - original draft. D.D: Conceptualization, Investigation, Supervision, Validation, Writing - review & editing. R.V: Supervision, Validation, Writing - review & editing. S.C: Formal analysis, Methodology, Supervision, Validation, Writing - review & editing. A.R: Funding Acquisition, Project Administration, Supervision, Validation, Writing - review & editing.

## Declaration of competing interest

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

## Acknowledgements

This work was partially supported by the FlyHy project of the Agence Nationale de la Recherche (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.

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