domain: sdv scco

text:
Chiara Valzolgher

Julie Gatel

Sabrina Bouzaid

Solene Grenouillet

Michela Todeschini

Gregoire Verdelet

Romeo Salemme

Valerie Gaveau

Eric Truy

Alessandro Farnè

Francesco Pavani

Reaching to Sounds Improves Spatial Hearing in Bilateral Cochlear Implant Users

Keywords: Active listening, Cochlear implant, Head movements, Reaching, Spatial hearing, Training, Virtual reality. (Ear & Hearing 2022, XX, 00-00)

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INTRODUCTION

Cochlear implants (CIs) have become standard intervention for neurosensory deafness [START_REF] Moore | Beyond cochlear implants: Awakening the deafened brain[END_REF][START_REF] Wilson | The remarkable cochlear implant and possibilities for the next large step forward[END_REF]. Bilateral CIs (BCIs) are increasingly common, thus allowing partial access to interaural auditory cues [START_REF] Aronoff | The use of interaural time and level difference cues by bilateral cochlear implant users[END_REF][START_REF] Gifford | Binaural cue sensitivity in cochlear implant recipients with acoustic hearing preservation[END_REF]. Benefits of CIs for speech understanding are now well-established in children [START_REF] Allen | Speech intelligibility in children after cochlear implantation[END_REF][START_REF] Calmels | Speech perception and speech intelligibility in children after cochlear implantation[END_REF], adults [START_REF] Wilson | Better speech recognition with cochlear implants[END_REF][START_REF] Stickney | Cochlear implant speech recognition with speech maskers[END_REF][START_REF] Wilson | The modern cochlear implant: A triumph of biomedical engineering and the first substantial restoration of human sense using a medical intervention[END_REF], and aging individuals [START_REF] Forli | Cochlear implant in the elderly: Results in terms of speech perception and quality of life[END_REF]). In addition, binaural hearing improves sound localization in the horizontal dimension for BCI users, compared to unilateral users (between group comparison) [START_REF] Smulders | Comparison of bilateral and unilateral cochlear implantation in adults a randomized clinical trial[END_REF], or to conditions in which one of the two CIs is switched off (within-group comparison) [START_REF] Litovsky | Spatial hearing and speech intelligibility in bilateral cochlear implant users[END_REF][START_REF] Asp | Bilateral versus unilateral cochlear implants in children: Speech recognition, sound localization, and parental reports[END_REF]).

Yet, spatial hearing skills of BCI users are substantially poorer compared to listeners with normal hearing, when locating stationary [START_REF] Kerber | Sound localization in noise by normalhearing listeners and cochlear implant users[END_REF][START_REF] Jones | Comparing sound localization deficits in bilateral cochlear-implant users and vocoder simulations with normal-hearing listeners[END_REF] as well as moving sound sources [START_REF] Moua | Auditory motion tracking ability of adults with normal hearing and with bilateral cochlear implants[END_REF]. A key factor causing such poor performance is the reduced availability of auditory cues. CIs limit input resolution in the temporal and frequency domains [START_REF] Moore | Beyond cochlear implants: Awakening the deafened brain[END_REF], alter sound levels through automatic gain control (AGC) (see, for instance, [START_REF] Dorman | Interaural level differences and sound source localization for bilateral cochlear implant patients[END_REF][START_REF] Archer-Boyd | Simulations of the effect of unlinked cochlear-implant automatic gain control and head movement on interaural level differences[END_REF], 2021), and change the auditory cues by the effect of microphone filtering strategies (both related to noise reduction and to emphasize higher frequencies) [START_REF] Seeber | Localization cues with bilateral cochlear implants[END_REF]. In addition, the two CI processors work in isolation from one another, leading to independent acoustic streams to the brain (for discussion, see [START_REF] Verhaert | Speech performance and sound localization abilities in Neurelec Digisonic® SP binaural cochlear implant users[END_REF][START_REF] Rosskothen-Kuhl | Microsecond interaural time difference discrimination restored by cochlear implants after neonatal deafness[END_REF]. Hence, BCI users can only access a degraded set of auditory cues to localize sound, among which the most salient ones are the interaural-level differences (ILDs) [START_REF] Van Hoesel | Exploring the benefits of bilateral cochlear implants[END_REF][START_REF] Grantham | Horizontal-plane localization of noise and speech signals by postlingually deafened adults fitted with bilateral cochlear implants[END_REF][START_REF] Seeber | Localization cues with bilateral cochlear implants[END_REF][START_REF] Grieco-Calub | Sound localization skills in children who use bilateral cochlear implants and in children with normal acoustic hearing[END_REF].

All these limitations pertain to peripheral auditory signals. Can we rely on more central auditory learning processes to better use the degraded signal? Relearning spatial hearing skills is possible in deafened ferrets with BCI after multisensory training with interleaved auditory and visual stimuli [START_REF] Isaiah | Multisensory training improves auditory spatial processing following bilateral cochlear implantation[END_REF]. Training-induced improvements were observed in the responsiveness of auditory cortical neurons and in their sensitivity to ILDs. Improvement emerged also in behavior: both in the sound localization responses and in sound-evoked headorienting movements made by early-deafened ferrets with BCI [START_REF] Isaiah | Multisensory training improves auditory spatial processing following bilateral cochlear implantation[END_REF]. Studies with normal-hearing participants exposed to altered auditory cues also suggest that relearning spatial hearing is possible. Training protocols leveraging multisensory perception and active interactions with sounds proved effective in promoting adaptation to altered auditory cues and improved spatial hearing skills [START_REF] Strelnikov | Effect of audiovisual training on monaural spatial hearing in horizontal plane[END_REF][START_REF] Carlile | The plastic ear and perceptual relearning in auditory spatial perception[END_REF][START_REF] Mendonça | A review on auditory space adaptations to altered head-related cues[END_REF][START_REF] Keating | Complementary adaptive processes contribute to the developmental plasticity of spatial hearing[END_REF][START_REF] Rabini | Interactions between egocentric and allocentric spatial coding of sounds revealed by a multisensory learning paradigm[END_REF][START_REF] Valzolgher | Reaching to sounds in virtual reality: A multisensory-motor approach to promote adaptation to altered auditory cues[END_REF]. Finally, preliminary results in unilateral cochlear implant users [START_REF] Luntz | Sound localization in patients with unilateral cochlear implants[END_REF]) and BCI users [START_REF] Tyler | Initial development of a spatially separated speech-in-noise and localization training program[END_REF] suggest that feedback-based training could also improve sound localization in this population. Yet, these pioneering works involved a limited number of participants and-critically-they did not explore if training effects could generalize beyond the trained task, which constitutes a hallmark of learning processes.

The aim of the present study was to assess whether spatial hearing can be trained in BCI users and whether training effects can generalize to untrained spatial auditory tasks. Building upon our previous work in normal-hearing adults listening with one ear plugged [START_REF] Valzolgher | Reaching to sounds in virtual reality: A multisensory-motor approach to promote adaptation to altered auditory cues[END_REF][START_REF] Valzolgher | Adapting to altered auditory cues: Generalization from manual reaching to head pointing[END_REF], we trained BCI users with a multisensory-motor task that combined reaching to near-by sounds, audiovisual feedback about sound position, and free-head movements. Reaching to sound could enhance spatial coding of sound position by incorporating the coordination of different effectors (eyes, head, hand) into a common reference frame [START_REF] Cohen | A common reference frame for movement plans in the posterior parietal cortex[END_REF][START_REF] Boyer | From ear to hand: The role of the auditory-motor loop in pointing to an auditory source[END_REF]. In addition, it could help directing attention toward the position occupied by the sound source and make the task more engaging, which is a fundamental feature in learning [START_REF] Dehaene | How We Learn: The New Science of Education and the Brain[END_REF]. Finally, in monaurally plugged normal-hearing individuals, reaching to sounds encourage additional head movements in response to sounds, which appear to serve the purpose to explore the auditory scene more widely and to expose the unplugged ear to the sound sources [START_REF] Valzolgher | Reaching to sounds in virtual reality: A multisensory-motor approach to promote adaptation to altered auditory cues[END_REF].

To assess training specificity, we used a crossover experimental design (Fig. 1A; see Video File in Supplemental Digital Content 1, http://links.lww.com/EANDH/B44) in which we compared the experimental spatial training with a control nonspatial training that used the same stimuli and multisensory feedback, but different task demands (i.e., discrimination of amplitude modulations in the sound). Thus, all participants performed both the experimental training and the control one. Crossover paradigms are particularly suited for clinical applications [START_REF] Senn | Cross-Over Trials in Clinical Research[END_REF], because they permit the involvement of the totality of participants in the experimental training without the need of testing a control group (which could not benefit from training). Furthermore, taking advantage of this design, we minimized any potential intergroup differences. Specifically, we assessed if the improvement induced by the experimental training (spatial training) extends (i.e., generalizes) to a headpointing sound localization task, which entails different sound positions and requires localizing sounds using a different effector (the head instead of the hand). In addition, to probe generalization effects also when implicit sound localization is required, we tested participants in an audiovisual attention-orienting task, in which they were asked to judge the elevation of a visual stimuli while listening for a sudden sound.

Based on work by [START_REF] Valzolgher | Reaching to sounds in virtual reality: A multisensory-motor approach to promote adaptation to altered auditory cues[END_REF][START_REF] Valzolgher | Adapting to altered auditory cues: Generalization from manual reaching to head pointing[END_REF], we predicted observing an improvement in sound localization across trials during the spatial training. In addition, we expected greater generalization effects after the spatial compared to the nonspatial training (as recently documented by [START_REF] Valzolgher | Adapting to altered auditory cues: Generalization from manual reaching to head pointing[END_REF], using a similar approach in normal-hearing adults listening with one ear plugged). Finally, because our apparatus allowed for unrestrained but measurable head movements, in line with [START_REF] Isaiah | Multisensory training improves auditory spatial processing following bilateral cochlear implantation[END_REF] we also studied changes in sound-related head-orienting movements. We predicted finding changes in sound-related head-orienting movements during [START_REF] Valzolgher | Adapting to altered auditory cues: Generalization from manual reaching to head pointing[END_REF]) and after training [START_REF] Isaiah | Multisensory training improves auditory spatial processing following bilateral cochlear implantation[END_REF], consistent with the expected error reductions.

MATERIALS AND METHODS

Study Design

All participants (BCI users) took part in two experimental sessions, with at least 15 days of washout interval. Each session comprised two testing phases and one training (Fig. 1A); they were identical in all respects except for the training task. Participants performed both training types, which were counterbalanced across participants in a within-subject crossover design. In one session, they engaged in the experimental spatial training task; in the other, they performed the control nonspatial training task. Testing phases included two auditory tasks: a head-pointing localization task (conducted in virtual reality (VR)) and an audiovisual attention-orienting task (conducted outside VR, see below). The head-pointing localization task differed with respect to training both in terms of targets spatial position and response effector (the head instead of the hand). The rationale was to minimize any potential effect of sensorimotor adaptation. The audiovisual attention-orienting task was instead an implicit sound localization task, in which sounds served as lateralized attention-orienting cues for the discrimination of visual targets (i.e., an audiovisual analog to the classic attention cueing paradigm) (see below for detailed descriptions of each tasks).

Participants

Twenty BCI participants (age: M = 45.6, SD = 13.1, 7 males, 15 right-handed) took part in the study (see the Materials for power calculation in Supplemental Digital Content 2, http:// links.lww.com/EANDH/B43).

They were recruited at the otorynolaringology department of the civil Hospital Edouard Herriot in Lyon (France), and tested in a dedicated room inside the Hospital Edouard Herriot premises. Participants signed an informed consent before starting the experiment, which was conducted according to the criteria of the Declaration of Helsinki (1964Helsinki ( , amended in 2013) ) and it was approved by the Ethical Committee (Ile de France X, N° ID RCB 2019-A02293-54), and recorded in clinicaltrials.gov (NCT04183348). All had normal or corrected-to-normal vision and reported no movement or vestibular deficit, nor neurological or psychiatric history. Age, sex and clinical data for individual BCI participants are provided in Table 1. During the experiment, participants used their daily sound processor settings (see Table 1 in Supplemental Digital Content 2, http:// links.lww.com/EANDH/B43 for details about CI model, processor strategy and microphone settings), to preserve the acoustic experience that each participant developed with the CIs.

Procedures

Testing Phases

Head-Pointing Sound Localization Task

This task was carried out entirely in VR, always using real sounds delivered in free field from predetermined positions computed on each trial based on the initial head position [START_REF] Coudert | Spatial Hearing Difficulties in Reaching Space in Bilateral Cochlear Implant Children Improve With Head Movements[END_REF]Valzolgher et al. 2020a,c). Our VR approach brings real sounds into visual VR and coordinates everything using Unity (see the Materials in Supplemental Digital Content 2, http://links.lww.com/EANDH/B43 for details about the apparatus and also [START_REF] Gaveau | SPHERE: A novel approach to 3D and active sound localization[END_REF]. Participants were immersed in a virtual room that matched the size of the real one but was devoid of any objects. Participants were instructed to localize sound sources and informed that sound could be presented anywhere in the surrounding space. At the beginning of each trial, participants were asked to direct their gaze in front of them, by aligning their head with a central fixation cross. When the correct posture was reached, the fixation cross turned from white to blue. In the meanwhile, the experimenter placed the speaker in one of the possible eight predetermined positions, using visual indications provided on a dedicated monitor (see [START_REF] Verdelet | Assessing spatial and temporal reliability of the vive System as a tool for naturalistic behavioural research[END_REF][START_REF] Gaveau | SPHERE: A novel approach to 3D and active sound localization[END_REF] for a validation of this method and Valzolgher et al. 2020a,c for examples). The predetermined positions (shown in the top part of Fig. 1B) result from the combination of 4 different azimuths in front space (-67.5°, -22.5°, 22.5°, or 67.5°; with respect to the participant's body midline), a single distance (55 cm from the center of the head) and 2 different elevations (5° above and 15° below ear level). Target elevation was changed only with the purpose of introducing variability in the auditory stimulation, and the asymmetrical arrangement elevation positions resulted from the fact that the software for placing the speakers at predetermined positions was based on the position of the VIVE tracker located above the speaker, rather than the position of the actual speaker. Crucially, the target sound was delivered only when the participant was in the correct start posture, and when the loudspeaker was positioned within a sphere with diameter of 5 cm centered on the predetermined location. This ensured that each stimulation position was fully replicable at the beginning of each trial. The target sound consisted of 3 sec of white noise, amplitude-modulated at 2.5 Hz, and delivered at about 65 dB SPL as measured from the participant's head. Participants were instructed to indicate sound position using their heads as a pointer. Note that head and trunk movements remained unconstrained during and after sound emission, allowing spontaneous active listening behavior. Note that participants were informed about their head projection due to a marker (white cross) and that they were only allowed to validate their response after the sound ended, by pressing a button on their handheld controller. To emphasize this instruction, the head projection marker (the cross) was white throughout the stimulation phase and turned red only when response validation was allowed. Since the speaker was invisible in VR, participants did not have visual cues about its position. Each head-pointing sound localization task comprised 40 trials (five repetitions, for each of the eight sound positions) delivered in random order. Five practice trials were also introduced but discarded from the analyses. The task lasted approximately 15 min. See the Materials for details about the apparatus and general setting in Supplemental Digital Content 2, http://links.lww.com/EANDH/B43.

Audiovisual Attention-Orienting Task

This task was carried out entirely outside VR. Participants sat at a table placed inside the same room in which the VR experiments are carried out. Unlike the VR tasks, in this audiovisual attention-orienting task participants rested their heads on a chinrest facing the screen where visual stimuli were displayed; hence, head movements were not allowed. Participants were instructed to indicate the elevation of a visual disk (i.e., appearing on the screen either above or below their eye level) as quickly and accurately as possible. Crucially, in each trial a task-irrelevant sound was presented simultaneously from one of the loudspeakers flanking the screen, either on the same side as the visual disk (spatially congruent trials), or from the opposite side (spatially incongruent trials). Each trial started with a white fixation cross appearing in the center of the screen and remaining visible until response. After a random delay (450-600 ms), an auditory stimulus (white noise, duration 100 ms) was emitted from one of the two loudspeakers, at approximately 60 dB SPL as measured from head position. After 100 ms from sound delivery, the visual target was presented. This consisted of a white disk (20 pixels radius, 0.5° of visual angle), appearing on a black background for 140 ms in the upper or lower hemifield with respect to the horizontal meridian passing through visual fixation (1.15° above or below the meridian), either in the left or right hemifield (10° from fixation). In half of the trials, the visual target and the sound appeared on the same hemispace (congruent trials), whereas on the remaining half, the visual target and the sound appeared on opposite hemispaces (incongruent trials).

Participants were asked to keep their gaze towards central fixation throughout the task and to indicate as quickly and accurately as possible the elevation of the visual target. Up/down responses were given using the up/down arrows keys on an external keyboard, using the index/middle fingers of the right hand (Fig. 1B). Participants had a timeout of 2000 ms to give their answer and received feedback on accuracy (percentage of correct responses) and mean response time (in ms) only at the end of each block. Importantly, they were also explicitly informed that sounds were always entirely task-irrelevant. The audiovisual attention-orienting task comprised 128 trials (16 repetitions, for each of the four disk positions and each sound side, divided in two blocks of 64 trials each) delivered in random order. Eight practice trials were also introduced but discarded from the analyses. The task lasted approximately 10 min. See the Materials for details about the apparatus and general setting in Supplemental Digital Content 2, http://links.lww.com/EANDH/B43.

Training Tasks

The training phases were carried out entirely in VR and took place in the same virtual room used for the other tasks detailed above. During both training tasks, the participant saw 13 virtual loudspeakers inside the Head-mounted display. The loudspeakers were arranged in a semicircle centered on the head (radius 50 cm), at -5° below ear level (due to the uncorrected offset between the tracker and the center of the speaker), and spanned between ±72° (with 12° of separation between each of them; see Fig. 1C and Video File in Supplemental Digital Content 1, http:// links.lww.com/EANDH/B44). The target stimulus consisted of a white noise, with two possible amplitude modulations (2 or 3 Hz). Targets sounds were delivered from each of the virtual speaker in random order (12 repetition for each of the 13 speakers, resulting in 156 trials overall, divided into three blocks of 52 trials each). In each trial, a single sound was presented from one of the speakers. Sounds were delivered when the experimenter brought the real speaker into correspondence with one of the virtual ones, following a computer-controlled procedure based on continuous position tracking. Crucially, the same stimuli were delivered in the two training tasks, thus making the auditory component of the trainings identical in this respect (i.e., sounds with two amplitude modulations were delivered from positions that changed on a trial-by-trial basis). In addition, both training tasks involved a similar motor response: a reaching movement. However, in the spatial training the reaching movement served to indicate the perceived sound position, whereas in the nonspatial training served to indicate the perceived amplitude modulation in the target sound. Participants always held the controller with their right hand. At the beginning of each trial, the controller was positioned on their sternum. See the Materials in Supplemental Digital Content 2, http://links.lww.com/EANDH/ B43 for details about the apparatus and general setting.

Spatial Training

Participants were instructed to reach the speaker emitting the sound using the handheld VR controller. The sound lasted until the participant reached and "touched" the correct speaker. If they reached the wrong speaker, the correct speaker started flashing while the sound continued to play. Specifically, a series of red concentric circles (1024 × 1024 px, 2 circles per second) expanded intermittently, irradiating from the correct sound source (see Video File in Supplemental Digital Content 1, http://links. lww.com/EANDH/B44). The rationale for using wide concentric circles was to capture the participants' attention even in case they were looking away from the correct sound source (e.g., toward the opposite hemispace). The visual feedback and the target sound stopped only when the subject reached the correct speaker position with the controller. This has two implications: first, a sense of agency was associated with the correct response (Valzolgher et al. 2020a,b,c); second, whenever the wrong speaker was originally selected, a combination of visual and auditory signals guided the participant to the correct sound source. To enhance the feeling that the virtual speaker was touched, the controller always produced a brief vibration when coming into "contact" with one of the virtual speakers. This did not serve as feedback for performance, because the vibration occurred irrespective of whether the response was correct or incorrect. To prevent participants from colliding with the real speaker (held by the experimenter), the virtual speakers were always presented with a 5-cm offset in depth. The task lasted approximately 45 min (considering the breaks).

Nonspatial Training

Participants were instructed to identify whether the target sound contained a fast (3 Hz) or slow (2 Hz) amplitude modulation. For fast amplitude-modulated sounds, participants directed the controller in front of them, aiming to touch an invisible virtual button above the central speaker. For slow amplitudemodulated sounds, participants reached toward an invisible virtual button below the same central speaker instead. The position and effects of these virtual buttons was demonstrated to participants during the practice trials. A vibration from the controller always indicated that one of two buttons was correctly reached. As in the Spatial Training feedback procedure, a visual feedback was delivered in the case of wrong responses. This was a series of red concentric semicircles that expanded intermittently from above or below the central speaker to indicate the correct response. Recall that target sounds were presented from different spatial positions also during the nonspatial training, but this spatial information was totally task-irrelevant (see Video File in Supplemental Digital Content 1, http://links.lww.com/EANDH/ B44). The task lasted approximately 20 min (including breaks).

Statistical Analysis

Linear mixed-effect (LME) modeling was used for all statistical analyses. Statistical analyses were run using R (version 1.0.143). For the LME model, we used the R-packages emmean, lme4, lmerTest in R Studio [START_REF] Bates | Fitting linear mixed-effects models using lme4[END_REF][START_REF] Fox | Using Car and Effects Functions in Other Functions 3[END_REF]. The R-package car was used to obtain deviance tables from the LME models. When appropriate, we calculated Cohen's d av as index of effect size [START_REF] Lakens | Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs[END_REF]. Data and R codes can be retrieved from osf.io/cqtmd.

The dependent variables considered in our analyses were sound localization azimuth error for the head-pointing sound localization task and for spatial training, and reaction time for the audiovisual attention-orienting task. Reaction time were instead analyzed for the audiovisual attention-orienting task. To study head movements, we extracted two dependent variables: number of head rotations and head-rotation extent [START_REF] Valzolgher | Reaching to sounds in virtual reality: A multisensory-motor approach to promote adaptation to altered auditory cues[END_REF].

RESULTS

Changes in Sound Localization and Head Movements During Spatial Training

Sound localization absolute error in azimuth at the beginning of the study was 24.1° ± 15.6° (head-pointing sound localization before training in the first session), matching previous studies in documenting a low auditory spatial resolution, for example, when compared to normal-hearing performance [START_REF] Kerber | Sound localization in noise by normalhearing listeners and cochlear implant users[END_REF][START_REF] Jones | Comparing sound localization deficits in bilateral cochlear-implant users and vocoder simulations with normal-hearing listeners[END_REF].

To examine if sound localization improved during the spatial training, we studied changes in absolute error in the horizontal dimension across successive trials using an LME model with trial number as fixed effect [START_REF] Valzolgher | Reaching to sounds in virtual reality: A multisensory-motor approach to promote adaptation to altered auditory cues[END_REF]). To account for the variability related to individual participants and session in which the Spatial training was completed (first or second), we also included the participant (intercept and slope) and session (intercept) as random effects in the model. As shown in Figure 2A, BCI users reduced their absolute error across trials (main effect of trial number, X 2 (1) = 15.84, p < 0.001). Performance in the nonspatial training was near ceiling (mean number of errors = 1.4%; see cumulative discrimination error across participants in Fig. 2B). During the nonspatial training, participants were also faster in completing the trial compared to the spatial training (nonspatial: mean ± SD = 1.68 ± 0.25 sec; spatial training: mean ± SD = 9.62 ± 6.99; t (19) = 5.15, p < 0.001 on paired t-test; Cohen's d av = 2.19).

During training the head was unrestrained and the target lasted until correct response, allowing active listening behavior (i.e., spontaneous head movements). To study head movements, we extracted two dependent variables: the number of head rotations and head-rotation extent [START_REF] Valzolgher | Reaching to sounds in virtual reality: A multisensory-motor approach to promote adaptation to altered auditory cues[END_REF]) (see Materials for details in Supplemental Digital Content 2, http://links.lww.com/EANDH/B43). As expected by design, head-rotation patterns differed in the two training protocols: more head rotations occurred in the spatial (5.72 ± 3.24) compared to the nonspatial training (1.15 ± 0.41, t (19) = 5.72, p < 0.001 on paired t-test); furthermore, the extent of head rotations was larger during the spatial (89.06° ± 41.86°) compared to the nonspatial training (4.00° ± 1.91°, t (19) = 9.20, p < 0.001 on paired t-test). Interestingly, head-behavior evolved during the course of the spatial training tasks. BCI users progressively adapted their spontaneous head movements as a function of sound eccentricity: the number of head rotations diminished for central sounds (twoway interaction, X 2 (1) = 5.35, p = 0.02), while head-rotation extent increased for more peripheral sounds (X 2 (1) = 4.78, p = 0.03; see Materials in Supplemental Digital Content 2, http://links.lww.com/EANDH/B43 and Fig. 3). To study the effect of spatial training on head-pointing sound localization, we entered absolute error in azimuth into an LME analysis phase (pre or post training), training (spatial or nonspatial) and azimuth as fixed effects. We also included participant (intercept and slope) and testing session (intercept) as random effects, to account for the variability across participants and the order of training type. We found a main effect of training (X 2 (1) = 4.89, p = 0.03). Crucially, the 2-way interaction between phase and training reached significance (X 2 (1) = 24.14, p < 0.001). The absolute error in azimuth decreased after the spatial (Pre: 25.2 ± 16.8; Post: 19.3 ± 11.1; t = 5.47, p < 0.001, Cohen's d av = 0.40, Fig. 3B,C), but not after the nonspatial training (Pre: 22.8 ± 14.7; Post: 24.5 ± 17.2, t = 1.48, p = 0.14, Cohen's d av = 0.11, Fig. 3D,E). Density plots of raw data (responses) in azimuth as a function of target position and training are shown in Figure S1 in Supplemental Digital Content 2, http://links.lww.com/EANDH/B43.* For completeness, we also report the analyses on absolute error in elevation (Table 1 in Supplemental Digital Content 2, http:// links.lww.com/EANDH/B43).

Effects of Spatial Training on Head-Pointing Sound Localization

To explore if participants who performed the spatial training in the first session (N = 10) maintained the improvement after the 2-weeks washout, we entered on their absolute errors in azimuth during the pretraining phase into an LME analysis with time (session 1 versus session 2) as fixed effects. Errors in the pre training phase were smaller on session 2 compared to session 1 (X 2 (1) = 4.64, p = 0.03). Albeit this effect was small (3°), it may provide initial evidence that the error reduction induced by the Spatial training may persist after the 2-week washout.

Following [START_REF] Isaiah | Multisensory training improves auditory spatial processing following bilateral cochlear implantation[END_REF] we also studied immediate headorienting movements (i.e., movements occurring around 0.90 sec after the beginning of the sound), which reflect the first spontaneous orienting response toward the sound. Saccade-like headorienting response were more accurate after the spatial training, as revealed by the significant interaction between training and phase on response density at target location (F (1,19) = 6.52, p = 0.02, n 2 = 0.11; see Materials and Figure S1 in Supplemental Digital Content 2, http://links.lww.com/EANDH/B43).

Finally, we examined if training benefits were modulated by clinical variables. We correlate the training effect (difference in absolute error before and after the spatial training) with the participant's age at the moment of deafness diagnosis, years spent with one CI only and years spent with two CIs. No significant correlation emerged (all ps > 0.35). *To examine to what extent changes in the amount of front-back confusions during the head-pointing task could impact on the observed training effects, we entered front-back confusions as variable in an LME with training and phase as fixed effects. We found a training by phase interaction (X 2 (1) = 8.61, p = 0.003). Before training, front-back confusions did not differ between spatial (12.2%) and nonspatial conditions (11.8%). After training, there were less front-back confusions in the spatial (4.6%) compared to the nonspatial condition (9.3%). Yet, this front-back confusion reduction did not fully explain our training related improvement. When we repeated the analysis of absolute azimuth error after removing all trials in which a frontback confusion was present, a training × phase interaction was still present (X 2 (1) = 14.64, p < 0.001).

Audiovisual Attention-Orienting Task

To examine the effects of our training protocols on the audiovisual attention-orienting task, we entered the response time (ms) into an LME analysis with testing phase (pre or post training), training type (spatial or nonspatial), and congruency between sound and visual target position (congruent or incongruent). Again, participant number and session (intercepts) were treated as random effects.

We found a main effect of congruency (X

DISCUSSION

In the present study, we examined if the ability of bilateral CI users to localize sounds in the horizontal plane improves as a result of training. Specifically, we implemented a spatial training based on reaching-to-sound, audiovisual feedback, and free-head movements. During this training, we found that sound localization in BCI users improved rapidly across trials. After training, sound localization ameliorated also in an auditory spatial task performed using a different motor response with respect to the trained task (head-pointing instead of hand-reaching) and different sound-source positions. This generalization was significantly more pronounced compared to the one observed in a nonspatial control training task.

Our findings add to the clinical population of CI users training effects observed in animal models [START_REF] Isaiah | Multisensory training improves auditory spatial processing following bilateral cochlear implantation[END_REF] and in normal-hearing human listeners [START_REF] Strelnikov | Effect of audiovisual training on monaural spatial hearing in horizontal plane[END_REF][START_REF] Rabini | Interactions between egocentric and allocentric spatial coding of sounds revealed by a multisensory learning paradigm[END_REF][START_REF] Steadman | Short-term effects of sound localization training in virtual reality[END_REF][START_REF] Valzolgher | Updating spatial hearing abilities through multisensory and motor cues[END_REF]. Most notably, they go beyond early reports on training effects in CI users [START_REF] Luntz | Sound localization in patients with unilateral cochlear implants[END_REF] in two ways. First, they originate from a crossover experimental design, which allowed testing each participant in both training types, thus excluding potential confounding group differences when assessing training efficacy. Second, they show generalization of training effects to a different auditory spatial task. We additionally provided initial evidence that sound localization benefits partially persisted after the 2-week washout in participants who trained in the spatial task during the first session. This effect was, however, numerically small (3° on average); thus, it remains to be ascertained how long this improvement can really persist over time, and paraphs how much this transfer to daily life.

Finally, our study also probed training generalization effects in a task that required implicit sound localization, that is, the audiovisual attention-orienting task. We found that lateralized auditory cues were effective in orienting BCIs' visual attention. This finding is novel and adds to previous work in unilateral CI users, in which this audiovisual attention-orienting ability was absent [START_REF] Pavani | Spatial and non-spatial multisensory cueing in unilateral cochlear implant users[END_REF]). Yet, no change in this task was observed after the spatial training. In fact, we observed a reduction of the attention-orienting effect after the nonspatial training. While this finding was unexpected and it will not be discussed further, it may suggest that repeated processing of nonspatial (rather than spatial) sound attributes could impact the ability to exploit sound position when orienting visual attention, at least in this clinical population.

While the spatial training produced a clear within-subject improvement, the BCI users in our study were fitted with different CI processors. This implies that the auditory cues available to each participant likely differed based on the various device brand and settings. Most notably, AGC types (i.e., which modulates the acoustic signal in amplitude, to compensate the reduced dynamic range of stimulated hearing provided by the implant), vary as a function of the manufacturer. AGC may distort ILDs across frequencies (which are fundamental for sound localization in CI users; see [START_REF] Dorman | Interaural level differences and sound source localization for bilateral cochlear implant patients[END_REF]) in a more or less aggressive way as a function of the processor (and manufacturer) type and of the settings made by the hearing care professional. In the present experiment, the lack of synchronization of AGCs between bilateral CI processors [START_REF] Pastore | Effects of bilateral automatic gain control synchronization in cochlear implants with and without head movements: Sound source localization in the frontal hemifield[END_REF][START_REF] Dwyer | Synchronized automatic gain control in bilateral cochlear implant recipients yields significant benefit in static and dynamic listening conditions[END_REF], the different duration of sound stimuli as a function of response time [START_REF] Boyle | Comparison of dual-time-constant and fast-acting automatic gain control (AGC) systems in cochlear implants[END_REF], and the possible AGC distortions as a function of head movements (Archer-Boyd & Carlyon 2019; see also Archer-Boyd & Carlyon 2021) could have substantially distorted the available ILDs. Yet, irrespective of the modulations introduced by the CI processor our spatial training was robust enough to allow generalization of training effects from the training task (in which sound duration continued until response, 9.6 sec on average), to a test task (in which the sound lasted only 3 sec).

Our instructions allowed free-head movement during sound, and our VR apparatus permitted continuous measuring of head movements. Several findings arose from this approach. First, during the spatial training, we observed that the number of head rotations diminished for central sounds compared to peripheral, across trial repetitions. BCI users appear to have learned to distinguish if sound came from the center or the periphery and thus, when sound sources were central, they did not need to move their heads, corroborating the improvement revealed by reduction of absolute errors across trials. Second, during the test task, we observed a training related improvement also in terms of the first head movement-orienting response. These immediate and spontaneous orienting movements of the head can reflect early encoding of sounds positions [START_REF] Muir | Newborn infants orient to sounds[END_REF] and can be considered an implicit index of participants' ability to identify sound direction (also described as saccade-like head-response by [START_REF] Isaiah | Multisensory training improves auditory spatial processing following bilateral cochlear implantation[END_REF]. Immediate head-orienting responses were more accurate in the spatial compared to the nonspatial training. This finding supports the training benefit documented using absolute errors as a dependent variable. Finally, a third observation concerns the potential role of head movements as effective behaviors strategies when relearning sound localization abilities [START_REF] Valzolgher | Reaching to sounds in virtual reality: A multisensory-motor approach to promote adaptation to altered auditory cues[END_REF]). We showed that head movements in BCI users changed across trial repetition during the spatial training. Although this was not correlated to changes in performance (see Materials in Supplemental Digital Content 2, http://links.lww.com/EANDH/B43), this preliminary observation suggests that BCI participants may also adapt their headrotation behavior when relearning their spatial hearing skills, by making it more purposeful across trials. This finding adds to the literature showing that, compared to static listening conditions, moving the head while listening to sounds improves sound localization not only in normal-hearing participants [START_REF] Pollack | Effect of head movement on the localization of sounds in the equatorial plane[END_REF]Perrett & Noble 1997a,b;[START_REF] Wightman | Resolution of front-back ambiguity in spatial hearing by listener and source movement[END_REF][START_REF] Vliegen | Dynamic sound localization during rapid eye-head gaze shifts[END_REF][START_REF] Brimijoin | The role of head movements and signal spectrum in an auditory front/back illusion[END_REF][START_REF] Honda | Effects of head movement and proprioceptive feedback in training of sound localization[END_REF][START_REF] Mcanally | Sound localization with head movement: Implications for 3-d audio displays[END_REF], but also in BCI users [START_REF] Coudert | Spatial Hearing Difficulties in Reaching Space in Bilateral Cochlear Implant Children Improve With Head Movements[END_REF][START_REF] Mueller | Sound localization with bilateral cochlear implants in noise: How much do head movements contribute to localization?[END_REF][START_REF] Pastore | Head movements allow listeners bilaterally implanted with cochlear implants to resolve front-back confusions[END_REF]. Future studies on spatial hearing relearning should examine further the spontaneous self-regulatory behaviors that participants implement during active listening, by adopting unconstrained head or even trunk movements and longlasting sounds, as here.

Limitations

Two methodological issues should be considered. First, our training protocols are likely not equally complex. Although neither task was speeded, while BCI users were relatively fast in responding to amplitude modulations in the target sound (1.7 sec on average), in the sound localization training they listened to each sound for a longer period before responding (9.6 sec). This raises the possibility that the greater efficacy of the spatial training could also reflect, to some extent, longer exposure to the sound. Second, head-pointing to sounds entails a motor response (i.e., head-turning) that is typically coupled with manual reaching movements. This may imply a partial overlap between the motor responses we adopted for the training and testing tasks. Future studies could examine the effects of a training performed with frontal and near sounds (as here), on test stimuli coming in back and/or far space. Changes in the acoustic features of training and test stimuli could also be implemented (syllables or words, as in [START_REF] Zheng | Development of sound localization strategies in children with bilateral cochlear implants[END_REF], instead of broad band sounds as used here).

CONCLUSION

Using a novel spatial training approach based on reachingto-sounds, audiovisual feedback, and free-head movements during listening, we showed that training auditory skills in BCI users is possible. This improvement can be accounted for in terms of central cognitive processes and/or self-regulation strategies since the auditory input from the CI remained largely unchanged. Furthermore, it stresses the positive contribution that multisensory and motor processes can play in adapting to CI. While our approach to training proved successful, it clearly originated from an experimental more than a translational perspective. To assess the implications of our finding for clinical settings and real life, it would be important to expand our approach by testing the efficacy of the principles subtending our Spatial training by extending its duration and by testing further its generalization to a wider range of spatial locations and stimuli. Ultimately, the main aim remains to enhance spatial hearing in real life for CI users. Our findings can be seen as a first step towards expanding training approaches from speech perception alone to spatial hearing, after implantation. In this respect, they contribute to enrich the domain of actions that clinicians and patients themselves can undertake to improve their experience with the CIs.

Fig. 1 .

 1 Fig. 1. Experimental procedure and setting. A, Schematic description of the overall crossover design. Each session (session 1 and session 2) comprised by two testing phases, with a training task in between. B, Testing phases. Top: schematic representation of the participant wearing the Head-mounted display (HMD) and holding the virtual reality (VR) controller during the head-pointing sound localization task. The eight spheres in front of the participant indicate predetermined speaker positions (not visible in the HMD). The hand holding the speaker represented near the red point was the experimenter's hand who move the speaker and bring it to the target position following instruction provided on a monitor. Bottom: schematic representation of the setting for the audiovisual attention-orienting task (conducted entirely outside VR). C, Training phase. Schematic representation of the participant wearing the HMD and holding the VR controller. The cylindrical speakers were visible only in VR (see inset) and indicated the possible sound positions during both training types. Inset: close-up of the scene as visible inside the HMD from participant's perspective. During the task participant saw a virtual scenario comprising a room, the speakers and the VR controller they were holding in their hand. See Video File in Supplemental Digital Content 1, http://links.lww.com/EANDH/B44 for animated description of the two training types.

Figure

  Figure 3A shows absolute localization errors in head-pointing sound localization across the two sessions of the experiment. The black line and circles indicate BCI users who performed the spatial training before the nonspatial training; the gray line and

Fig. 2 .

 2 Fig. 2. Participants' preformance during training. A, Reduction of absolute error in the horizontal dimension, as a function of trial in the spatial training. Linear regression (solid line), with 95% confidence intervals (dashed lines). B, Cumulative discrimination error across participants as a function of trials in the nonspatial training (i.e., number of participants who made a mistake in the trial).

  2 (1) = 30.45, p < 0.001) caused by faster visual discrimination responses when the auditory cue matched target side (congruent: M = 291.2 ms, SD = 79.2 ms) compared to when it occurred on the opposite side of space (incongruent trials: M = 307.3 ms, SD = 79.4 ms, Cohen's d av = 0.20). We also found a 3-way interaction between testing phase, training type, and sound position (X 2 (1) = 4.90, p = 0.03). After the nonspatial training, audiovisual attention-orienting effect decreased (Pre: M = 23.1 ms, SD = 17.8 ms; Post: M = 10.9 ms, SD = 20.5 ms; X 2 (1) = 4.25, p = 0.04, Cohen's d av = 0.64), while it persisted after the spatial one (Pre: M = 11.9 ms, SD = 17.5 ms; Post: M = 18.4 ms, SD = 19.6 ms; X 2 (1) = 1.15, p = 0.28, Cohen's d av = 0.35).

Fig. 3 .

 3 Fig. 3. Performance in head-pointing sound localization. A, Absolute localization across the four testing sessions of the experimental design, separately for participants who completed the Spatial training on session 1 (gray) or session 2 (black line). Error bars represent standard errors. B-D, Absolute errors (in degrees) as a function of phase before and after the spatial (red, B) and nonspatial (blue, D) training. C-E, Training effect (deg): the difference between pre and post training session (pre-post) in absolute error as function of training task (C, spatial in red and E, nonspatial in blue). Positive values in (C) and (E) represent improvements after the training.

TABLE 1 .

 1 Biographic and anamnestic and clinical characteristics of CI participants

					Age at	Age at first	Age at	Age at
				Etiology of	deaf diagnosis	hearing aid	implantation	implantation	Years with	Years with
	ID	Sex	Age, y	deafness	(y;m)	(y;m)	(right ear)	(left ear)	one CI	two CIs
	1	F	22	Unknown	0;5	0;7	2	15	13	7
	2	F	65	Unknown	45	49	54	53	1	11
	3	F	60	Genetic	10	10	40	51	11	9
	4	F	46	Meningitis	1	5	39	44	5	2
	5	F	47	Genetic	10	12	42	43	1	4
	6	M	55	Genetic/sudden	1	44	50	52	2	3
				deafness
	7	M	41	Ototoxicity	2	6	34	35	1	6
	8	F	47	Genetic	16	21	42	39	3	5
	9	M	32	Meningitis	2	2	3	28	25	4
	10	M	25	Unknown	3	3	18	21	3	4
	11	F	49	Unknown	13	30	39	39	0	10
	12	M	59	Head trauma	52	No	53	53	0	6
	13	F	47	Genetic	3	3	45	42	3	2
	14	F	54	Genetic	42	42	50	51	1	3
	15	M	24	Genetic	2;6	3	18	12	6	6
	16	M	65	Otosclerosis	35	55	59	60	1	5
	17	F	32	Otosclerosis of the	10	12	23	25	2	7
				cochlea
	18	F	38	Genetic	13	18	26	30	4	8
	19	F	51	Unknown	6	6	43	46	3	5
	20	F	52	Genetic	6	23	43	51	8	1

CI indicates cochlear implant; F, female; M, male.

ACKNOWLEDGMENTS

We are grateful to all the participants who accepted to participate in this study and to the three anonymous reviewers for comments on a previous version of the manuscript. We thank Jean-Louis Borach and Sonia Alouche for administrative support of this project and Eric Koun for technical support. We thank Giordana Torresani for her contributions to Figure 1. C.V., F.P., and A.F. were supported by a grant of the Agence Nationale de la Recherche (ANR-16-CE17-0016, VIRTUALHEARING3D, France). C.V. was also supported by a grant of the Università Italo-Francese/Université Franco-Italienne, the Zegna Founder's Scholarship and Associazione Amici di Claudio Demattè. F.P. and A.F. were also supported by a prize of the Foundation Medisite (France), by the Neurodis Foundation (France), by a grant from the Italian Ministry for Research and University (MUR, PRIN 20177894ZH to F.P.) and grants from IHU CaSaMe ANR-10-UBHU-0003 and ANR 2019CE37 Blind Touch (to A.F.). C.V., F.P., and A.F. conceptualized and design the experiment and managed funding acquisition and project administration. C.V., J.G., S.B., S.G., and M.T. performed the experiment. C.V. and F.P. analyzed data and wrote the paper. G.V. and R.S. worked on software. All authors discussed the results and implications and commented on the manuscript. F. P., A.F., and E.T. supervised the project and managed funding.

The authors have no conflicts of interest to declare.

Address for correspondence: Chiara Valzolgher, Palazzo Fedrigotti -Corso Bettini 31, 38068 Rovereto (TN), Italy. E-mail: chiara.valzolgher@unitn.it Received August 12, 2021; accepted May 31, 2022


Léo C C Mesquita

Aymeric Vié
email: aymeric.vie@centralesupelec.fr

Sébastien Ducruix

Flashback-induced flame shape transition in a two-stage LPP aeronautical combustor

Keywords: Lean Premixed Prevapourised, Large-Eddy Simulations, Flashback, Bifurcation, Staged combustion . . . (8/10)

Large-Eddy Simulations were performed to study the flashback-induced flame shape transition of a lean premixed M flame in a staged liquid-fuelled aeronautical lean-burner, as observed experimentally. The BIMER combustor is a Lean Premixed Prevapourised (LPP) burner composed of two stages, each with its own injector and swirler: the main outer stage, called multipoint, uses jet-in-crossflow injection to achieve the LPP regime, while the central stage, called pilot, uses a pressure swirl injector to create a hollow cone spray to stabilise the flame. During LPP operation, this M flame presents a strong acoustic activity, promoting a periodic flashback of its leading edge. When, aiming to stabilise the flame, the pilot injection is increased and the multipoint injection decreased, the oscillating leading edge (due to the longitudinal acoustic perturbations) attaches to the pilot spray, changing the flame into a Tulip shape. Two phenomena were identified as being the most relevant causes of this flame shape transition. First, the leading edge position and the thermoacoustic instability amplitude are directly linked to the combustion chamber final temperature. The higher the temperature in the chamber, the more upstream the leading edge stabilises and the higher the acoustic oscillation amplitude, increasing the risk of a successful flashback. Second, the injection regime with high pilot injection allows the leading edge to attach to the pilot spray, as the flame only reattaches when the pilot spray is sufficiently high. The higher the pilot fuel flow, the higher the amount of fuel sprayed in the critical region where the flame might attach for a transition to the Tulip shape. Therefore, as the change in injection regime is the main mechanism lean staged burners use to reduce emissions while increasing operability, this works shows that an M flame is unsuitable to such burners with similar aerodynamic topology and properties.

Introduction

Lean Premixed Prevaporized (LPP) burners aim at a more efficient and cleaner combustion by targeting a lean and homogeneous mixture, reducing temperature and nitrogen oxides. However, LPP regimes are prone to unstable behaviours [START_REF] Ducruix | Combustion dynamics and instabilities: Elementary coupling and driving mechanisms[END_REF][START_REF] Lieuwen | Unsteady Combustor Physics[END_REF], as lean extinction, flashback or thermoacoustic instabilities. Staged injection, which can control the flame behaviour by splitting the fuel supply in several swirler and injector stages, is currently being investigated as a viable strategy to stabilise the combustion in LPP regime [START_REF] Huang | Dynamics and stability of leanpremixed swirl-stabilized combustion[END_REF]. The two-stage BIMER combustor has been designed at the EM2C laboratory aiming to further study and develop this type of burner. It is composed of a central pilot stage, which uses a pressure-swirl injector to sustain a spray diffusion-like pilot flame, and an outer swirl stage, which uses multi-point injection to generate the LPP mixture and flame inside the chamber [START_REF] Renaud | Flame shape transition in a swirl stabilised liquid fueled burner[END_REF].

Experimental and numerical studies have shown that three flame archetypes can be stabilised in this burner: a V flame, an M flame and a Tulip flame [START_REF] Renaud | Flame shape transition in a swirl stabilised liquid fueled burner[END_REF][START_REF] Mesquita | LES of the Ignition of a Two-Phase Staged Swirling Burner: Influence of Ignition Location and Operating Conditions on the Flame Shape[END_REF]. Three flame shape bifurcations can be triggered by a change in the the distribution of fuel between the two stages [START_REF] Renaud | Flame shape transition in a swirl stabilised liquid fueled burner[END_REF][START_REF] Renaud | Bistable behaviour and thermo-acoustic instability triggering in a gas turbine model combustor[END_REF][START_REF] Mesquita | Numerical analysis of flame shape bifurcation in a two-stage swirled liquid burner using large eddy simulation[END_REF]. Between these flames, the M one is a premixed lifted flame, thus showing optimal properties in terms of a clean combustion. However, in [START_REF] Renaud | Flame shape transition in a swirl stabilised liquid fueled burner[END_REF] the authors have observed a flashback of the lifted flame while increasing fuel from the pilot injector, which is the designed manoeuvre of staged burners to reduce flame dynamics and instabilities [START_REF] Huang | Dynamics and stability of leanpremixed swirl-stabilized combustion[END_REF]. The M flame then reattaches to the pilot spray and transitions to a Tulip shape, a diffusion-like and potentially highly-polluting flame. This transition is clearly undesirable, as it changes a clean premixed flame into a source of pollutant emissions, nullifying the use of an LPP system. Furthermore, it happens when the pilot stage is activated with the objective of stabilising the system, thus also nullifying this action of the staged injection technology. Moreover, even if there are other studies in the literature about flashback in staged burners [START_REF] Hermeth | Bistable swirled flames and influence on flame transfer functions[END_REF][START_REF] Lapeyre | Acoustically Induced Flashback in a Staged Swirl-Stabilized Combustor[END_REF], they only focus on gaseous premixed systems, which neglect important phenomena such as liquid injection regime. Therefore, the purpose of this work is to investigate further this M to Tulip flame shape transition on the BIMER combustor and to shed light on the mechanisms leading to the flashback and the flame reattachment to the pilot spray in this LPP burner.

This paper is organized as follows. First, the BIMER rig is described, and the operating conditions are presented. Then, the numerical setup is characterized. Finally, the numerical simulations of the transition results are presented, compared with experiments and analysed. As mentioned, the BIMER combustor was designed to study the operation of a swirling lean-burn two-stage injector. The rig is composed by a cylindrical plenum and a rectangular combustion chamber (500 × 150 × 150mm 3 ). Three of the combustion chamber walls are water-cooled (entrance, top and bottom) and the two lateral ones are silica windows for optical access. The injector is composed of two swirling stages (Fig. 1): at the centre is the pilot stage, where 15 % of the total air mass flow rate goes through and that uses a pressurized nozzle to create a fuel spray with a hollow cone shape and a spray half angle of 30 • . This stage swirler has a geometric swirl number of 0.6. The outer and main stage, where 85 % of the air mass flows, is called the multi-point stage, as its injector uses 10 holes of 0.3 mm diameter placed at the swirler exits to create a jet in cross-flow injection and improve mixing. This stage swirler is characterized by a geometric swirl number of 1.

Description of the setup

Experimental setup and operating conditions

The burner is operated at atmospheric pressure, with preheated air at 433K, a total air mass flow rate of 43 g s -1 , a total fuel mass flow rate of 1.64 g s -1 , resulting in a global equivalence ratio of 0.6, and a thermal power of ≈ 73 kW. During this study, the aforementioned global parameters are constant. The staged burner technology relies on changing the fuel distribution between the stages to change the flame behaviour. This study explores such variation and the impact on the flame. The fuel distribution between stages characterised by the staging factor α, that equals the ratio between the pilot fuel mass flow rate over the total fuel mass flow rate in percent. Here, the staging factor is increased from 15% to 20%, matching the experiments of Renaud [START_REF] Renaud | Flame shape transition in a swirl stabilised liquid fueled burner[END_REF] (as well as all other parameters).

Numerical setup

The LES is performed using the AVBP code, codeveloped by CERFACS and IFPEN [START_REF] Wolf | Using LES to study reacting flows and instabilities in annular combustion chambers[END_REF]. The WALE model [START_REF] Nicoud | Subgrid-scale stress modelling based on the square of the velocity gradient tensor[END_REF] is used to model the LES sub-grid scales. A Two-step Taylor-Galerkin (TTGC) scheme (3 rd order in space and time) is used.The Navier-Stokes Characteristic Boundary Conditions (NSCBC) [START_REF] Poinsot | Boundary conditions for direct simulations of compressible viscous flows[END_REF] are used to impose the gaseous inlet and outlet boundary conditions. Walls are considered as adiabatic, as no experimental measurement of the wall temperatures was available, and non-slipping. The liquid phase is modelled using a lagrangian framework, where one numerical parcel represents one physical droplet.

The Abramzon-Sirignano model [START_REF] Abramzon | Droplet vaporization model for spray combustion calculations[END_REF] is used to model droplet evaporation. The interaction between droplets and the walls are modelled as a slip-only condition, where droplets slip on the wall to approximate a film-like behaviour. The injected droplet properties (i.e. velocity, diameter distribution) have been extracted from experimental studies of Renaud [START_REF] Renaud | Flame shape transition in a swirl stabilised liquid fueled burner[END_REF] and the injected PDFs correspond to the measurements. This injection setup has been compared to the experiments and validated in a dedicated study in [START_REF] Mesquita | Large eddy simulations of a two-phase staged swirling burner using an euler-lagrange approach: validation of the injection strategy[END_REF]. Due to the absence of measurements for different staging values, the diameter distribution is considered constant and the velocity is scaled according to the fuel mass flow rate. The BFER reduced scheme [START_REF] Franzelli | A two-step chemical scheme for kerosene-air premixed flames[END_REF] is used to model the chemistry, assuming a unity Lewis number, coupled to the Thickened Flame (TFLES) [START_REF] Poinsot | Theoretical and Numerical Combustion[END_REF] combustion model, where the Charlette's efficiency function [START_REF] Charlette | A power-law flame wrinkling model for LES of premixed turbulent combustion part II: dynamic formulation[END_REF] is used to calculate the flame wrinkling and the flame-turbulence interaction. An unstructured tetrahedra mesh of 132 million elements is used, which keeps the flame thickening factor between 3 and 7.

Initialisation procedure

In [START_REF] Renaud | Flame shape transition in a swirl stabilised liquid fueled burner[END_REF], this transition is triggered by a change in the staging factor. From the stable M flame at α = 15%, the staging factor is progressively increased and when reaching values around α = 20%, the M flame reattaches. Here, the same procedure as [START_REF] Renaud | Flame shape transition in a swirl stabilised liquid fueled burner[END_REF] is reproduced numerically to simulate the flame reattachment. First, the M flame at stable α = 15% is simulated and validated against numerical data from [START_REF] Renaud | Flame shape transition in a swirl stabilised liquid fueled burner[END_REF]. Afterwards, α is progressively increased at the rate of 1% per ms. The initial t = 0 ms is defined as the moment when the staging factor starts being changed.

Results

Reattachment of the flame

Figure 2 shows the key instants of the reattachment of the flame comparing the instantaneous CH* chemiluminescence images acquired in [START_REF] Renaud | Flame shape transition in a swirl stabilised liquid fueled burner[END_REF] with the XZ cut of heat release rate instantaneous snapshots extracted from the LES. The cut was preferred in comparison to an integrated image to improve the visualisation of the flame movement. At first, one can clearly observe the M-shaped flame (t = 3.5 ms). Both experimental and numerical results highlight the flame presence over the Outer Shear Layer (OSL), where droplets concentrate due to their interaction with the divergent walls, and on the centre line, characterised by the flame leading edge. Nonetheless, in the experiments, the branches of the flame that are stabilised over the OSL seem to be completely lifted, while this portion of the numerical flame is attached to the edges of the divergent. The second instant (t = 4.5 ms) shows the leading edge of the flame flashbacking at position x = 20mm, while the outer portions of the flame move downstream. Then, the leading edge moves further upstream, reaching the edges of the divergent (t = 5 ms) and consequently entering it (t = 5.5 ms), while the outer portions of the flame continue to move downstream. In the following snapshots, a new and independent portion of flame is ignited inside the divergent (t = 7 ms) by the flashback of the leading edge. It starts then to propagate downstream (t = 8 ms) while, apparently independently, the outer portions of the flame move downstream again. The next image (t = 8.5 ms) shows the instant when the newly ignited flame inside the divergent merges with the leading edge of the M flame and start uniting. This forms the final flame, which has a Tulip shape (t = 12 ms). This instant seems particularly well captured by the LES, as the inner branches of the flame around the Inner Shear Layer (ISL) and the Central Recirculation Zone (CRZ) highlight the stabilisation of this flame around the bubble of the Bubble Vortex Breakdown (BVB) topology. Also, the persistence of the outer branches of the flame stabilised over the OSL, similarly to the one observed for the M flame at t = 3.5 ms, supports the idea that the tulip flame is actually an M flame with its leading edge attached to the pilot spray. In opposition to the M flame, that is lean and premixed, the Tulip one is attached to the spray, burning in a diffusion-like regime. Thus, the Tulip flame produces very hot temperature inside the CRZ bubble, very likely being more pollutant than the M one [START_REF] Lefebvre | Gas Turbine Combustion (3rd Edition)[END_REF]. Furthermore, the Tulip flame is as acoustically active as the M one, showing no gain in stability either. Therefore, avoiding this transition is essential to allow the burner to operate in lean regimes, as it is intended for this type of technology.

This comparison between experimental and numerical results shows that the LES captures very well the main events of the transition and can be used as a powerful tool to give more insight on the mechanism controlling this transition. In the following sections the most relevant phenomena leading to this transition are analysed.

M flame leading edge position

As illustrated in Fig. 2, the leading edge of the M flame plays a central role on the triggering of this transition. Thus, understanding its stabilisation process is essential to the transition analysis. In the BIMER combustor, the M flame is stabilised by a Bubble Vortex Breakdown (BVB) [START_REF] Lucca-Negro | Vortex breakdown: a review[END_REF], which creates a CRZ with two parts. Upstream, an axisymmetric bubble is created by the high swirl, then, after a contraction behind the bubble, the CRZ shows radially diverging shape. In this flow topology, the CRZ bubble is a toroidal vortex (the time-averaged flow pseudo-streamlines in Fig. 3a show that in the average flow the CRZ is an asymmetric toroidal vortex) that is in depression compared to the swirling flow [START_REF] Mesquita | Numerical analysis of flame shape bifurcation in a two-stage swirled liquid burner using large eddy simulation[END_REF]. These two elements attract part of the cold fresh mixture inside the CRZ bubble [START_REF] Mesquita | Numerical analysis of flame shape bifurcation in a two-stage swirled liquid burner using large eddy simulation[END_REF], much reducing the temperature inside the bubble when compared to the rest of the CRZ, filled with hot combustion products (the flow path is shown by the pseudo-streamlines and green arrows in Fig. 3a ). While the outer parts of the M flame are stabilised over the OSL, the stabilisation of its leading edge inside the CRZ is determined precisely by the flow topology. The leading edge stabilises itself between the bubble and diverging CRZ, separating then CRZ in two zones, a Cold CRZ (CCRZ -blue regions in Fig. 3) before the flame and a Hot CRZ (HCRZ -yellow to pink regions in Fig. 3), behind the flame. Finally, it is the mix of burnt and fresh gases inside the CRZ and the consequent final temperature in this mixing zone that determines the axial position of the leading edge of the M flame.

To further explore this influence of the flow temperature on the M flame stabilisation, we study it in a second wall conditions with heat losses. This is done by considering the top and bottom walls of the chamber (intended to be water-cooled) at 100 • C, which is a rough estimation based on the experimental data of a cold wall condition. Figure 3 compares the M flame with adiabatic walls (Fig. 3a) and with heat losses (Fig. 3b). The main differences between the two cases are the higher equilibrium temperature inside the combustion chamber for the adiabatic case and, consequently, the position of the leading edge. As shown in Fig. 3, the higher the temperature, the more upstream the M flame leading edge is. This feature is so important in this case that moving the leading edge downstream by reducing the walls temperature prevents the transition from happening. This shows that the warmer walls, achieved in this case by the adiabatic conditions, are necessary to reproduce the experiments properly and to capture transition. In the adiabatic case, the temperatures inside the HCRZ and CCRZ are higher, placing the leading edge inside the CRZ bubble, at the centre of the CRZ toroidal vortex. This region presents the highest negative axial velocity inside the bubble, which will strongly favour the flashback of the edge.

Self-sustained oscillations and periodic flashbacks

Figure 4 shows the evolution in time of the integrated heat release rate inside the chamber and the pressure measured near the wall at half its length, along with the flame leading edge position and axial velocity, all measured from the LES. The pressure signal from the LES was also compared to the experiments showing that the LES captures very well the frequency of the quarter-wave mode f λ/4 ≈ 300 Hz as identified by [START_REF] Renaud | Flame shape transition in a swirl stabilised liquid fueled burner[END_REF]. Looking at Fig. 4, one can clearly see that this operating point is unstable and that strong self-sustained oscillations are taking place. This is caused by the thermoacoustic coupling between the flame and the longitudinal quarter-wave mode [START_REF] Renaud | Flame shape transition in a swirl stabilised liquid fueled burner[END_REF]. In this case, as we will see, the major triggering mechanism of the instability is the fluctuation in fuel equivalence ratio that reaches the flame. This known mechanism [START_REF] Ducruix | Combustion dynamics and instabilities: Elementary coupling and driving mechanisms[END_REF][START_REF] Lieuwen | Unsteady Combustor Physics[END_REF] happens here because most of the fuel comes from small droplets (SM D ≈ 15 µm) of the multipoint injection that, in their majority, evaporate and mix with the incoming air before burning, with only a small portion of droplets, with a small diameter, reaching the flame. The flow oscillations create fuel-rich pockets that modulate this mixing upstream of the flame (equivalence ratio oscillations). This causes heat release rate fluctuations in the flame that generate strong acoustic waves, further disturbing the flow, thus closing the feedback loop. In this situation, the acoustic waves strongly alters the axial velocity of the flow. The M flame leading edge then moves up-and downstream following the passage of the acoustic waves, as the flow axial velocity inside the CRZ becomes either more negative or positive when the amplitude of the axial acoustic velocity becomes higher than the local convective one and its direction is opposite. Analysing Fig. 4, one can see that the flashback instants -defined here as the instants when the flame leading edge gets inside the divergent (i.e. the leading edge has a negative axial position) -always occur following a pressure trough, moment that precedes the minimum axial velocity value inside the CRZ. This is a case of combustion instability triggered flashback [START_REF] Lieuwen | Unsteady Combustor Physics[END_REF][START_REF] Benim | Flashback Mechanisms in Lean Premixed Gas Turbine Combustion[END_REF], as the leading edge is pushed upstream as a consequence of the acoustic wave passage, as also observed in [START_REF] Lapeyre | Acoustically Induced Flashback in a Staged Swirl-Stabilized Combustor[END_REF]. Both the experimental and numerical results shown in Fig. 2 corroborate this conclusion, as the visible coordinated motion of the leading edge moving upstream, while the outer portions of the flame move downstream, is characteristic of this type of premixed flame being subject to acoustic modulations ( [START_REF] Lieuwen | Unsteady Combustor Physics[END_REF][START_REF] Candel | Dynamics of swirling flames[END_REF]). As shown in Fig. 4.a, the amplitude of oscillations is considerably higher for the adiabatic case, showing that a second effect of increasing the walls temperature is the increase in the amplitude of pressure oscillations. With higher pressure waves, the negative velocity inside the CRZ is made more negative by the passing waves, strongly increasing the chance of flashback (as described by [START_REF] Lieuwen | Unsteady Combustor Physics[END_REF]). Indeed, considering the wall heat losses during the simulations prevented the reattachment of the flame for two reasons: 1) the stable position of the leading edge was further downstream; 2) the oscillations were smaller both when compared to the adiabatic case. Additionally, the injection regime and the flow topology are the second necessary ingredient to trigger this flame transition. Both are addressed in the next section.

Spatio-temporal fuel segregation and flow topology

The change in axial velocity amplitude as a consequence of the propagation of the acoustic waves is not the sole phenomenon in this flame flashback. As already discussed, the M flame is stabilised over a BVB topology and its leading edge is stabilised just after the entry of fresh gases inside the CRZ bubble. Thus, the acoustic waves also affect the entire flow topology and, of particular interest in this analysis, the fuel flow and its spatial distribution in time. In comparison with flashback studies with gaseous fuel [START_REF] Hermeth | Bistable swirled flames and influence on flame transfer functions[END_REF][START_REF] Lapeyre | Acoustically Induced Flashback in a Staged Swirl-Stabilized Combustor[END_REF], this aspect constitutes the main novelty, as the liquid fuel injection and dynamics play a major role in reattaching the flame and changing its shape, as we will see.

During stable operation, the BVB flow topology naturally brings part of the fuel inside the CRZ, but this creates a mixture that is too lean to be ignited. The passage of the acoustic waves creates an oscil-lation of the fuel flow and this effect, summed with the BVB flow topology, creates a spatio-temporal fuel segregation. Figure 5 shows such a cycle, illustrating the spatio-temporal evolution of fuel and its interaction with the flow topology in two successive cycles that will first fail and then succeed in leading to a flame transition. As the axial velocity of the flow starts increasing, this also creates a wave of high fuel concentration, convected downstream by the flow, as shown by the green arrows in Fig. 5a. At this moment, the flame leading edge is also pushed downstream by the flow. As the pressure wave moves downstream, this increase in axial velocity also affects the bubble, increasing momentarily the flow rate of fresh gases entering the bubble. This is caused by the CRZ toroidal vortex (made visible by the average streamlines in Fig. 3), which pushes a wave of high fuel concentration inside the CRZ more intensely due to the passage of the pressure wave and axial velocity increase (Fig. 5b). Thus, a mixture richer than what is normally present inside the bubble is created by this effect. This increase in fuel mass fraction inside the bubble happens simultaneously as the leading edge of the flame is pushed upstream by the axial velocity inside the CRZ becoming more negative due to the passage of the pressure wave, as shown by the axial velocity contours in Figs. 5a, 5b and 5c. As the flame moves upstream, more fuel goes inside the bubble, feeding the flame from behind and sustaining it in this further upstream position for a while (Fig. 5c). This allows the flame leading edge to get closer to the pilot spray and the rich fuel mixture stocked just downstream of the pilot injector, but barely reaching it. Indeed, at this instant the staging factor (and thus the pilot fuel flow and its penetration inside the CRZ) was not high enough for the leading edge to anchor itself at the pilot spray, despite causing a local ignition of the mixture, that later extinguishes (Fig. 5d). The leading edge, then, moves back downstream as a new cycle starts and the passage of the following pressure wave reduces the amplitude of negative velocity inside the CRZ.

The following cycle starts in a similar way as the previous one. However, at the beginning of this cycle, the change in staging factor is half way through the prescribed change (Fig. 5d: α = 18.5%). This means that the pilot fuel flow rate is higher than for the last cycle and will progressively increase while the flame is moving as a consequence of the thermoacoustic instability. In the BVB flow topology, the majority of the pilot flow recirculates inside the bubble. The progressive increase in pilot fuel flow, thus, tends to increase the quantity of fuel that is convected inside the bubble by the self-sustained oscillations instability. At the same time, an increase in pilot fuel flow rate increases the penetration of spray and the rich evaporated fuel zone inside the CRZ bubble. Therefore, the increase in staging factor favours the flashback of the flame in these two aspects. Indeed, as the flame leading edge starts moving upstream, the change in staging factor is practically finished and the staging factor has reached the α = 20% value just before the flame leading edge enters the divergent (Fig. 5e). We also see in this instant the CRZ toroidal vortex both pushing fuel inside the CRZ and accelerating the flame upstream. This increase in pilot fuel flow extends further downstream the rich mixture zone allowing more of the flashbacking leading edge to reach this region. Thus, with the higher pilot fuel flow rate corresponding to staging factor α = 20%, the flame leading edge ignites the fuel mixture around the pilot spray and an independent flame stabilises anchored at the spray (Fig. 5f). As the M flame leading edge moves back downstream as a consequence of the instability cycle, the newly-ignited pilot flame propagates downstream.

To understand better this flame ignition and anchoring step, Fig. 6 shows the evolution of the flame leading edge position, along with the position of iso-contours representing lean (Y f uel ϕ=0.5 ), global (Y f uel ϕ=0.6 ) and stoichiometric (Y f uel stoich ) fuel mass fraction. This graph further supports the previous discussion on how the combustion instability interaction with the flow topology provides the fuel necessary for the flame to flashback. Just after the flame reaches its downstream-most position (meaning that the fuel is about to enter the CRZ bubble, as shown in Fig. 5) the mixture at the leading edge location becomes richer. This fuel movement immediately precedes each flame flashback, feeding the flame and allowing it to move upstream. However, when analysing the axial oscillation of the stoichiometric fuel mass fraction (Fig. 6: top red line graph) one can see that it oscillates in phase with the leading edge. This means that, as the leading edge moves upstream, also does the stoichiometric and rich fuel mixture regions, preventing the leading edge from igniting this mixture. Indeed, in all the flashbacks before the start of the staging factor modification (i.e. before t = 0 ms) and particularly the one at t = -1 ms, the leading edge does not reach the stoichiometric mixture region. When increasing the staging factor, though, the flame leading edge is able to reach the stoichiometric region at t ≈ 3 ms, as shown in Fig. 6. Thus, during the first flashback presented in Fig. 5d the leading edge reaches the stoichiometric zone and, as shown by the spike in temperature in the same graph, it was able to ignite the mixture momentarily. Nevertheless, a flame could not be stabilised because the staging factor was still too low, meaning the mixture reached by the bulk of the flame was still too upstream and too lean. In the following flashback (shown in Fig. 5e), however, when the flame moves upstream the stoichiometric region is located more downstream than during the previous cycle, as the staging factor is already α = 20%. Again as the flame leading edge moves upstream, so does the stoichiometric mixture region, but as now the pilot fuel flow rate is higher, the stoichiometric region travels further downstream and the less back, upstream. This difference makes the flame leading edge meet the stoichiometric region in a more downstream posi- tion than before and, thus, reach it (and also richer mixtures zones) with more energy, successfully igniting the mixture and stabilising a new flame. This last observation shows that the increase in staging factor reduces the upstream motion of the stoichiometric zone, as the increase in magnitude of negative axial velocity that pushed the flame upstream also pushes the rich mixture upstream. Again, the bottom part of Fig. 6 confirms these results, showing that just before the increase in temperature caused by the consistent ignition and attachment of the pilot flame, the leading edge reaches the stoichiometric region and moves further upstream to richer mixture zones.

Conclusions

This work studied with high-fidelity LES the flashback and transition of a lean premixed M flame in a staged liquid-fuelled lean-burner, as observed experimentally in [START_REF] Renaud | Flame shape transition in a swirl stabilised liquid fueled burner[END_REF]. First, it is shown that the LPP α = 15% M flame presents a strong acoustic activity, which creates a periodic temporary flashback of its leading edge. However, when the staging factor is increased to α = 20%, increasing the pilot injection in a manoeuvre that should stabilise the burner dynamics, the flame leading edge not only flashbacks, but reattaches at the pilot spray, changing the flame into a Tulip shape. Two phenomena were identified as being the most relevant ones controlling this flame shape transition: the final temperature of the combustion chamber and the injection regime.

The temperature of the combustion chamber impacts the M flame in two ways. First, it controls the stable axial position of the leading edge. The M flame being completely aerodynamically stabilised by a Bubble Vortex Breakdown and the CRZ bubble being filled with fresh cold air, the leading edge of the M flame stabilises behind the bubble at the threshold of the hot burnt gases. Therefore, the higher the final equilibrium burnt gases temperature and, thus, the more upstream the leading edge is stabilised. This effect was seen here by changing the heat losses at the chamber walls, which modified the final temperature in the chamber and, thus the stable position of the M flame leading edge. Second, as this is a combustioninstability-induced flashback, the higher the combustion chamber temperature, the higher the acoustic oscillations, which creates periodic flashbacks of the leading edge and contributes to increase the distance travelled by it.

However, the reattachment of the flame, and thus the flame transition, only occurs when, additionally to a sufficiently high temperature inside the chamber, the pilot injection attains a certain level. Increasing the pilot injection fuel mass flow rate increases the distance where the spray-created fuel rich zone penetrates inside the divergent. This allows the periodic flashback of the leading edge to reach and ignite this fuel rich zone, re-creating the flame root and making the flame transition into a Tulip shape.

Finally, this work provided insights that can be generalised and some control parameters that can be manipulated for a safer operation of LPP M flames. First, as the flashback of the M flame leading edge is intrinsic to high acoustic activity, the suppression of any acoustic feedback is critical. However, even in the absence of self-sustained thermoacoustic oscillations in the chamber this transition could be triggered if the final temperature inside the chamber is high enough to put the leading edge of the M flame too close of the pilot spray. Thus, the final equilibrium temperature must be controlled (by regulating the global equivalence ratio, for example) to place the M flame leading edge sufficiently downstream of the injection systems. Lastly, one can prevent this flame shape transition by avoiding the leading edge to reach the pilot spray. This implies two possible design paths for this staged LPP burner: either this injector requires a different flow topology to operate with an M lifted flame, where the Central Recirculation Zone does not connect the flame to the pilot injector, or another flame shape should be used. As increasing the staging factor does not represent an increase in stability for the M lifted flame (which is the objective of staged injection [START_REF] Huang | Dynamics and stability of leanpremixed swirl-stabilized combustion[END_REF]), but rather the use of the pilot injection represents a major risk for the M flame operation, it seems that the M lifted flame is not adapted to staged burners, and another flame shape, possibly attached or stabilised over the ISL without a lifted leading edge, could respond better to the multiple injection regimes of staged burners and offer more benefits for this type of combustor.

Fig. 1 :

 1 Fig. 1: 2D view of the injector at the entrance of the combustion chamber. The central blue arrow indicates the pilot injector, while the two external red arrows, the radial position of multi-point injection holes. Flow from left to right.

Fig. 2 :

 2 Fig. 2: Comparison between the experimental instantaneous CH* chemiluminescence images (left) [4] and XZ plane instantaneous snapshots from the LES of heat release rate (right) at the same time instants during the first step of the M to Tulip flame shape transition.

Fig. 3 :

 3 XZ plane time averaged fields of temperature (top) and kerosene mass fraction (bottom), clipped to fit in the limits [0 ; 2 × Y stoich = 0.125] and stressing Y ϕ=0.6 = 0.0384, for the (a) adiabatic and (b) isotherm walls condition. The iso-contour of zero axial velocity is shown in white lines in all images, highlighting the recirculation zones.The iso-contour of Heat Release Rate HRR = 3 × 10 7 W/m 3 is shown in black on the top half and in blue in the bottom half of images. In both images the pseudo-streamlines are shown to highlight the flow path (highlighted by the green arrows) and the vortical structures, in particular the CRZ toroidal vortex.

Fig. 4 :

 4 Fig.4: Top: time evolution of the integrated heat release rate (blue) and pressure (adiabatic walls -red, isotherm walls -yellow) measured by a probe at the microphone position at (x, y, z) = [0.25, 0, 0.075] m. Bottom: time evolution of the flame leading edge axial position (blue) and velocity (red). Time instant t = 0 ms indicates when the staging factor starts being modified and the dashed vertical line indicates the moment when the flame anchors.

Fig. 5 :

 5 Fig. 5: Instantaneous XZ plane snapshots of two flashbacks. Top: 2D pseudo-streamlines coloured by kerosene mass fraction (clipped to fit in the limits [0 ; 2 × Y stoich = 0.125] and stressing Y ϕ=0.6 = 0.0384) with superimposed the product of absolute Heat Release Rate and the Takeno index |HRR| × T I = |HRR| • ∇Y Kero •∇Y O 2 / ∇Y Kero •∇Y O 2 (clipped to fit in the limits [-10 9 ; 10 9 ] W/m 3 ). Bottom: 2D pseudo-streamlines coloured by axial velocity (the CRZ is shown in blue) with heat release rate 10 8 W/m 3 iso-contour in black. Green arrows represent the fuel movement, while the purple ones represent the flame movement.

Fig. 6 :

 6 Fig.6: Top: time evolution of the axial position of the flame leading edge (blue), the iso-contour of Y f uel ϕ=0.5 = 0.0322 (bright yellow), the iso-contour of Y f uel ϕ=0.6 = 0.0384 (orange) and the iso-contour of Y f uel stoich = 0.0625 (red). Bottom: time evolution of the temperature (blue) and the fuel mass fraction (red) at the leading edge position.

Acknowledgments

We thank CERFACS for sharing the AVBP solver.

This work was granted access to the HPC resources of CINES under the allocation A0012B00164 made available by GENCI, and of the mesocentre computing center of Centrale-Supélec and Ecole Normale Supérieure Paris-Saclay supported by CNRS and Region Ile-de-France (http://mesocentre.centralesupelec.fr/). We finally thank CentraleSupélec and Université Paris-Saclay for Léo's Ph.D. grant.