Jeanne Hecquard

Justine Saint-Aubert

Ferran Argelaguet

Claudio Pacchierotti

Anatole Lécuyer

Marc Macé

Fostering empathy in social Virtual Reality through physiologically based affective haptic feedback

Keywords: Virtual Reality, Affective Haptics, Empathy, User Experience

We study the promotion of positive social interactions in VR by fostering empathy with other users present in the virtual scene. For this purpose, we propose using affective haptic feedback to reinforce the connection with another user through the direct perception of their physiological state. We developed a virtual meeting scenario where a human user attends a presentation with several virtual agents. Throughout the meeting, the presenting virtual agent faces various difficulties that alter her stress level. The human user directly feels her stress via two physiologically based affective haptic interfaces: a compression belt and a vibrator, simulating the breathing and the heart rate of the presenter, respectively. We conducted a user study that compared the use of such a "sympathetic" haptic rendering vs an "indifferent" one that does not communicate the presenter's stress status, remaining constant and relaxed at all times. Results are rather contrasted and user-dependent, but they show that sympathetic haptic feedback is globally preferred and can enhance empathy and perceived connection to the presenter. The results promote the use of affective haptics in social VR applications, in which fostering positive relationships plays an important role.

I. INTRODUCTION

T HE democratization of immersive Virtual Reality (VR) technologies has led to a significant increase in their application in many everyday activities, including gaming, teaching, training, remote working, as well as to interact with friends, family, and colleagues. As a result, virtual social events and platforms multiplied. However, such virtual social environments are affected by the same issues as other online discussion platforms, including cyberbullying and sexual harassment. The causes of cyberbullying are complex, rooted in ignorance but also in reduced empathy, which is strengthened by the anonymity and lack of accountability provided by online platforms [START_REF] Marin-Lopez | Empathy online and moral disengagement through technology as longitudinal predictors of cyberbullying victimization and perpetration[END_REF]. Therefore, preventing harassment and cyberbullying has become crucial to create safe virtual environments (VE) for all users.

In this respect, this paper proposes the use of haptic interfaces for conveying emotions during VR immersive experiences, as a way to address hateful behaviours by fostering empathy between users represented by virtual avatars. Haptic feedback has already been proven central for delivering emotions and increasing the sense of presence in a broad

The research leading to these results has been partially funded from the European Union Horizon 2020 research and innovation program under grant agreement No. 101017884 -GuestXR project. range of VR scenarios [START_REF] Pacchierotti | Wearable Haptic Systems for the Fingertip and the Hand: Taxonomy, Review, and Perspectives[END_REF]- [START_REF] Ju | Haptic empathy: Conveying emotional meaning through vibrotactile feedback[END_REF]. For instance, Ju et al. [START_REF] Ju | Haptic empathy: Conveying emotional meaning through vibrotactile feedback[END_REF] successfully used vibrotactile feedback to express different subjective feelings such as joy, sadness, or anger. We analyze the impact of affective haptics in immersive VR with respect to the feeling of empathy, but also to embodiment, presence, and anxiety. We conducted a VR user study where 38 participants attended a meeting involving a presentation made by a virtual agent. A wearable haptic system, composed of a vibrotactile actuator and a compression belt, was used to provide the participants with a dynamic physiologically based feedback of the emotional status and stress level of the presenter throughout the presentation. We expect such dynamic affective haptic feedback to increase the emotional connection with the presenter and, in turn, the level of empathy towards her.

II. RELATED WORKS

A. Fostering empathy in VR

Positive technology is defined as "the use of technology for improving the quality of our personal experience through its structuring, augmentation and/or replacement" [START_REF] Kitson | Immersive interactive technologies for positive change: A scoping review and design considerations[END_REF]. In this respect, Kim et al. [START_REF] Kim | The effect of immersion on emotional responses to film viewing in a virtual environment[END_REF] showed that, while victims often experience harsher attacks in immersive VE, (cyber)bullies are also more receptive to positive emotions in these settings. For these reasons, it is important to foster empathy in VR as a way to make users more aware of others' feelings and emotions, as also done in [START_REF] Hasler | Virtual race transformation reverses racial in-group bias[END_REF]- [START_REF] Seinfeld | Offenders become the victim in virtual reality: impact of changing perspective in domestic violence[END_REF] by embodying certain perpetrators in the body of their victims (also known as the Proteus effect [START_REF] Yee | The proteus effect: The effect of transformed self-representation on behavior[END_REF]). Hasler et al. [START_REF] Hasler | Virtual race transformation reverses racial in-group bias[END_REF] showed that this technique of embodiment in VR powerfully enhances mimicry behaviours, which are associated with interpersonal sensitivity and empathy; Peck et al. [START_REF] Peck | Putting yourself in the skin of a black avatar reduces implicit racial bias[END_REF] proved that a short period of embodiment of Caucasian people in black virtual bodies can make their racial bias against black people diminish; Schoeller et al. [START_REF] Schoeller | Combining virtual reality and biofeedback to foster empathic abilities in humans[END_REF] combined immersive VR and biofeedback to put users into the shoes of a distressed individual so as to train their sense of compassion. Herrera et al. [START_REF] Herrera | Building longterm empathy: A large-scale comparison of traditional and virtual reality perspective-taking[END_REF] presented the "Becoming Homeless" experience, where users could live in VR the experience of being evicted and then becoming homeless, proving a significant increase in empathy toward homeless people in the participants.

B. Measuring empathy in VR

Empathy is usually measured using self-reporting questionnaires, as well as observing the participants and collecting behavioural and physical measurements. In this respect, one of the most commonly used empathy measure is the Interpersonal Reactivity Index (IRI), which is composed of 28 questions targeting four areas [START_REF] Davis | A multidimensional approach to individual differences in empathy[END_REF]:

• Perspective Taking, assessing the tendency to spontaneously adopt the psychological point of view of others;

• Fantasy, assessing the tendency to transpose into the feelings and actions of fictitious characters in fiction;

• Empathic Concern, assessing feelings of sympathy and concern for unfortunate others;

• Personal Distress, assessing feelings of personal anxiety and unease in tense interpersonal settings. Herrera et al. [START_REF] Herrera | Building longterm empathy: A large-scale comparison of traditional and virtual reality perspective-taking[END_REF] also used self-report questionnaires to measure user levels of distress and empathy toward another avatar. Nonetheless, self-report questionnaire are often difficult to analyze and interpret, as they have been often proven less honest and effective than "objective" (e.g., behavioural and physical) measures [START_REF] Butters | Meta-analysis of empathy training programs for client populations[END_REF]. Examples of objective metrics can be the user's heart rate, gaze, electrodermal activity, or even some relevant post-experimental actions [START_REF] Herrera | Building longterm empathy: A large-scale comparison of traditional and virtual reality perspective-taking[END_REF], [START_REF] Neumann | Measures of Empathy[END_REF]- [START_REF] Eisenberg | The relation of empathy to prosocial and related behaviors[END_REF].

C. Affective haptics

Since haptic devices focus on the sense of touch, they are often combined with VR in order to magnify the users' sense of presence [START_REF] Bouzbib | Survey of Virtual Reality Interactions via Haptic Solutions[END_REF], [START_REF] Slater | A note on presence terminology[END_REF]. Affective haptics aims at influencing or communicating the emotional state of human users through the sense of touch [START_REF] Eid | Affective haptics: Current research and future directions[END_REF], [START_REF] Tsetserukou | Affective haptics in emotional communication[END_REF]. Most affective haptic systems have been designed to simulate the delivery of hugs or caresses during remote or virtual interactions [START_REF] Salminen | Emotional and behavioral responses to haptic stimulation[END_REF]- [START_REF] Huisman | Simulating affective touch: Using a vibrotactile array to generate pleasant stroking sensations[END_REF]. A representative example is the HaptiHug [START_REF] Tsetserukou | Haptihug: A novel haptic display for communication of hug over a distance[END_REF], [START_REF] Tsetserukou | World's first wearable humanoid robot that augments our emotions[END_REF], a wearable haptic belt wrapped around the user's torso, able to tighten/loosen to simulate a hug. A human subject study involving 300 participants showed the capability of this device to help convey emotions of happiness and relaxation. Ju et al. [START_REF] Ju | Haptic empathy: Conveying emotional meaning through vibrotactile feedback[END_REF] worked on emotion recognition via vibrotactile feedback and highlighted some possible universalities in affective vibrotactile stimuli which could support transferring emotions via haptic feedback. Other examples of affective haptic systems have been designed to deliver hearth rate feedback, which has been proven to affect the human's emotional state [START_REF] Arafsha | Emojacket: Consumer centric wearable affective jacket to enhance emotional immersion[END_REF].

III. METHODS

A. Apparatus

We used a wearable haptic system able to dynamically convey physiologically based feedback of hearth beat and breathing. The physiological feedback were rendered according to Moullec et al.'s physiological model [START_REF] Moullec | Multi-sensory display of self-avatar's physiological state: virtual breathing and heart beating can increase sensation of effort in VR[END_REF], that calculate cardiac and respiratory activity depending on the avatar's physiological characteristics as well as its walking speed and the slope of the road. We use the same physiological characteristics for our physiological model to convey distinct stages of stress and anxiety.

1) Heartbeat simulator: Conveying heart-rate feedback has been proven capable of conveying emotions [START_REF] Tsetserukou | World's first wearable humanoid robot that augments our emotions[END_REF], [START_REF] Moullec | Multi-sensory display of self-avatar's physiological state: virtual breathing and heart beating can increase sensation of effort in VR[END_REF]. We designed a heartbeat simulator able to simulate different hearrate in a compact and comfortable form factor [START_REF] Pacchierotti | Wearable Haptic Systems for the Fingertip and the Hand: Taxonomy, Review, and Perspectives[END_REF]. It is composed of a circular piezoelectric vibrating disc (R = 6 mm, 1 G acceleration) driven by Pulse Width Modulation through an Arduino board. An illustration of the vibrating feedback variation is visible in Figure 1c. The actuator is attached to the user's wrist via a soft Velcro band, enabling contact between the actuator and the skin as well as easy adaptation to different wrist sizes (Figure 1b). This device is capable of simulating heartbeats varying in speed and duration, e.g., to simulate a faster hearth rate, the period of the vibrations is reduced; to simulate stronger/more intensive beats, the duration of each vibration is increased. Both changes are used in the experiment to simulate heart rates comprised between 50-220 bpm (calmhigh stress [START_REF] Devy Widjaja | Cardiorespiratory dynamic response to mental stress: a multivariate time-frequency analysis[END_REF]) with a vibration/beat duration of 0.1-1 s.

2) Breathing simulator: The breathing simulator device was created by Moullec et al. [START_REF] Moullec | Multi-sensory display of self-avatar's physiological state: virtual breathing and heart beating can increase sensation of effort in VR[END_REF]. It is composed of a strapbased vest that users can wear and easily adjust to their own torso. An elastic belt is fastened around the user's waist, actuated by a servo motor to control the belt length so as to apply pressure and simulate breathing patterns. Figure 1a shows a user wearing the device. We control the speed and depth of the tightening and untightening action of the belt to simulate different breathing patterns, e.g., the stronger the belt tightens, the deeper the breaths are; the faster the belt tightens, the faster the breaths are. The range of the breath rates is between 6 and 60 breaths per minute with a wrapping/unwrapping speed between 0.4 and 4 m/s (calmhigh stress [START_REF] Devy Widjaja | Cardiorespiratory dynamic response to mental stress: a multivariate time-frequency analysis[END_REF]). At the beginning of the experiment, the belt is calibrated according to each user's body morphology.

3) VR environment: The experiment was designed using Unity3D. Participants were asked to wear a HTC Vive Pro VR headset to visualize the scene and hold two HTC Vive controllers to move around and interact with it. We used an internal avatar database for the users and the virtual agents, animated using an internal Unity3D add-on. Additional details about the content of the scene are reported below.

B. Experimental design

Participants were asked to attend a presentation in the context of a virtual professional meeting, where a female virtual presenter introduced the latest COVID-19 governmental guidelines. This study was carried out in early 2022, when this topic was very common. During the presentation, the virtual presenter experiences a series of issues, making her increasingly stressed as the presentation advances. Physiologically based (affective) haptic feedback is provided to the human participant to convey the emotional status of the virtual presenter, using the haptic interfaces described in Secs. III-A1 and III-A2. By analyzing the differences in terms of the participant's sense of presence, embodiment, anxiety, and empathy when using the proposed affective haptic rendering or not, we can analyze its role in fostering these feelings in the considered environment.

1) VR scenario: The scene is shown in Fig. 2. It is set in a virtual meeting room, composed of a large table, chairs, and a white screen, where the presentation is shown. Four male colleagues sit around the table while the female presenter stands next to a white screen. The avatar of the human participant also sits at the table, opposite to the other colleagues. Participants were able to select their best-matching avatar from 10 models (2 genders, 5 ethnicities). The verbal interactions in the scene, including the presentation, happened in our country's native language, which was the language spoken by the subjects involved in the experiment. For clarity, in this paper, we report the translated versions of these interactions. The presentation summarizes a new set of governmental guidelines designed to face the COVID-19 pandemic, such as social distancing.

Throughout the presentation, the presenter faces a series of stressors. Since the beginning and throughout the whole presentation, the four male colleagues do not appear to be interested, chatting, looking away, and working on their laptops instead of listening to her. Other stressor events [E] make the presenter increasingly stressed and anxious as the presentation proceeds, but the human participant can intervene [H] to help the presenter and reduce her stress level: • At t=250 s, two of the four male colleagues make rude remarks regarding the usefulness of the presentation and its excessive length ("Honestly, I don't really see the point of this meeting, you're wasting our time.", "Sigh, is this over yet?") [E]. The participant can ask questions and give positive feedback about the content of the talk [H]. The full presentation and the related human user's actions can be seen through the submitted supplementary materials. The presentation lasted 4 minutes and 27 s in total.

2) Physiologically based affective feedback: Haptic feedback is employed to communicate the presenter's stress level to the human participant. When the presenter's stress increases in response to one of the above mentioned stressors, the heartbeat simulator accelerates and grows stronger while the breathing simulator conveys quicker and shallower breaths. On the other hand, when the presenter's stress diminishes in response to the human participant's calming/reassuring actions, the heartbeat simulator slows down and gets weaker while the breathing simulator conveys slower and deeper breaths. This evolution is shown in Fig. 3.

3) Experimental protocol and conditions: The human subject is asked to seat comfortably on a revolving office chair and wear the VR and haptic systems described in Sec. III-A. Before starting the VR scenario described in Sec. III-B1, we immersed the user in the same virtual room, but without any virtual agent. We asked the user to familiarize with the environment by looking around the room while remaining seated. Users could see where the presentation will be held as well as be aware of the presence of a laser pointer on the table in front of them and bottles of water on a cabinet next to their chair. These items will be useful during the interaction with the presenter, as described in Sec. III-B1. After this familiarization step, we asked users to rotate towards their right, where they could look at their own avatar in a mirror attached to the wall. Moving their arms and head in the real world and seeing the same movements replicated by their virtual avatars strengthens their feeling of presence and embodiment [START_REF] Yee | The proteus effect: The effect of transformed self-representation on behavior[END_REF]. These familiarization and embodiment exercises lasted between 3 to 5 minutes.

As the user completes the above steps, the scene populates with the virtual agents (as in Fig. 2) and the presentation starts. Each user experienced the scene and its corresponding interactions twice, receiving (in a counterbalanced order) two types of feedback:

• Dynamic/Sympathetic: The haptic feedback changes with the level of stress of the presenter, as described in Sec. III-B2 and shown in Fig. 3 (blue solid line).

• Constant/Indifferent: The haptic feedback does not change with the stress of the presenter; it always conveys a sensation of relaxation, regardless what happens in the scene (heartbeat: 60 BPM with 0.1 s vibrations, breathing: 15/min with a wrapping/unwrapping speed of 4 s), as shown in Fig. 3 (red dashed line).

4) Subjects:

Thirty-eight subjects participated in the study (27 males, 11 females). None of the participants reported any deficiencies in their visual or haptic perception abilities. The experimenter explained the procedures and spent about two minutes adjusting the setup to be comfortable before the subject began the experiment. Participants signed an informed consent, including the declaration of having no conflict of interest. The study was approved by the authors' institutional ethical review board.

5) Evaluation criteria and metrics: Participants answered to three sets of questionnaires: pre-, mid-, and post-experience. The English translation of the questionnaires is available as supplementary material.

The objective of the pre-experience questionnaire was to analyze the user's background, experience, and potential to empathize with the presenter. To do so, we devised an adapted and translated version of the Interpersonal Reactivity Index Fig. 2. User experiencing the scenario in VR while wearing the haptic system. He is artificially connected to a virtual presenter by means of a physiologically based haptic feedback. He can "feel" the presenter's stress and relief through a virtual breathing and heartbeat rendering achieved using the compression belt wrapped around the torso and the vibrotactile feedback on the left wrist. (IRI) questionnaire, which is commonly used for measuring empathy (see Sec. II-B). Since users went through the same scenario twice, we provided a mid-experience questionnaire at the end of both rounds. Questions centered on user's feelings of empathy, anxiety, presence [START_REF] Skarbez | A survey of presence and related concepts[END_REF] and embodiment [START_REF] Gonzalez-Franco | Avatar embodiment. towards a standardized questionnaire[END_REF]. The questionnaires on empathy and anxiety were adapted from [START_REF] Herrera | Building longterm empathy: A large-scale comparison of traditional and virtual reality perspective-taking[END_REF] to evaluate users' sense of connection to the presenter and her situation. Questions on user anxiety included statements such as "What happened worried me" and "What happened made me uncomfortable". For empathy, users were asked to rank statements like "I felt sympathy for the presenter", "I was touched by the presenter", "I felt connected to the presenter".

The objective of the post-experience questionnaire was to evaluate the user's overall perception and feeling of the experience as well as the role of the haptic feedback. We directly asked users to compare their feelings of empathy, immersion, and anxiety between both conditions, as well as the differences they felt, and their preferences in terms of haptic feedback, notably regarding the belt. To not bias users towards the sympathetic and against the indifferent feedbacks, the questionnaires referred to them as "dynamic" and "constant".

Eventually, the user was given the possibility to write feedback about the experience as a whole in open questions.

In addition to the above-mentioned questionnaires, we also considered additional behavioral metrics. We recorded the users eye gaze so as to analyze the focus of their attention, and their reaction time in helping the presenter (e.g., the time elapsed between when the presenter asks for the water and when the user hands her the bottle, see Sec. III-B1).

C. Hypotheses

We consider three hypotheses. H1 states that the dynamic/sympathetic haptic feedback, communicating to users the current emotions of the presenter, leads to users feeling more empathetic and connected towards the presenter. It would support other results in the literature where haptic feedback has been proven to help foster empathy and social abilities [START_REF] Tsetserukou | Haptihug: A novel haptic display for communication of hug over a distance[END_REF], [START_REF] Hoppe | A human touch: Social touch increases the perceived human-likeness of agents in virtual reality[END_REF], although in a different context and employing distinct haptic sensations. H2 states that the dynamic/sympathetic haptic feedback leads to users feeling higher anxiety and stress. H3 states that the dynamic/sympathetic haptic feedback leads to users feeling more immersed and present in the virtual environment and experience.

IV. RESULTS

We analyze the results with respect to the three main hypotheses presented in Sec. III-C, then we analyze the correlation between the different metrics.

A. Analysis of our hypotheses 1) Subjective questionnaires: Unless otherwise stated, all answers were rated on a 7-point Likert scale, and all questionnaire results were analyzed using Wilcoxon signed-rank or rank sum tests. For parametric data, we used paired t-tests.

Regarding empathy (H1), results from the mid-experience questionnaires revealed no significant differences between the feelings of empathy reported by users when comparing the sympathetic feedback vs. the indifferent one (W = 760.5, p = 0.69, r < 0.005). Overall, users reported relatively high feelings of empathy towards the presenter regardless of the condition (median (M D) = 5.6; interquartile range (IQR) = 1.25). This result therefore does not support H1, where we postulated that sympathetic haptic feedback would lead to a higher connection/empathy towards the presenter. However, when questioned about their preference regarding the two conditions, participants reported a significantly higher preference for the sympathetic feedback in terms of the empathy they felt (see Fig. 4, V = 1897, p < 0.001, moderate effect size), supporting H1. A Welch Two Sample t-test revealed no significant difference between empathy levels according to user gender (t(29.576) = 1.6448, p > 0.1). Similarly, ANOVA tests revealed no significant difference in empathy depending on user age (F (1, 74) = 0.28, p > 0.5) and technical experience (F (1, 74) = 2.07, p > 0.15).

Regarding anxiety (H2), the feelings of anxiety reported for the two feedback conditions were not significantly different (W = 758, p = 0.71, small effect size), which is not in accordance with H2. Users also mostly rated the belt as not harrowing, with a score significantly lower than "4 -No opinion" (V = 800, p < 0.05, small effect size). In contrast, the rising intensity of the belt's feedback was perceived by most users, with a score significantly higher than 4 (V = 2829, p < 0.001, large effect size). Users assimilated intensity with feeling "anxious" and "stressed": words in the semantic field of intensity ("intense", "strong") were used 25 times by users in the open questions. For anxiety, words such as or similar to "stress", "felt bad", "sad", "unease", "awkward", "uncomfortable", "anguish" were used 78 times for the whole experiment. Finally, five users commented that they felt "oppressed" during the experiment, with one participant comparing it to "being underwater": they reported having "the feeling of wanting to intervene, without quite knowing how", talking about stopping the colleagues from talking badly to the presenter. The feeling was usually reported to be more intense during the sympathetic haptic feedback: no feelings of stress or anxiety were relayed for the indifferent condition in the open questions, as opposed to the open questions on the sympathetic condition (11 words around "unease", 5 around "stress" and "anxiety", 6 around "intensity" of the feedback and the feelings). These results support H2.

Finally, regarding presence and embodiment (H3), no significantly differences were observed between the two feedback conditions (presence: W = 786, p > 0.5; embodiment: W = 780, p > 0.5). Overall, the scores for "presence" were moderately high (M D = 5; IQR = 1.1), and the scores for "embodiment" were close to the middle point (M D = 4.2; IQR = 1.4). However, the feeling of presence was shown to be significantly different between experiences with respect to the order they were presented to the users. Participants relayed a lessened sense of presence (W = 979, p < 0.01, moderate effect size, mean (M ) = 5.25 and 4.72; standard deviation (SD) = 0.94 and 0.80) during the second run of the experiment. The distributions were presented respectively for the first and second runs. Simultaneous Tests for General Linear Hypotheses from an ART ANOVA revealed that there is a significant difference in feelings of presence for users who went through the sympathetic haptic condition in first and those who went in second: there is an interaction effect between the order of the walk-throughs the participants experienced and the haptic feedback from each condition (F (1, 36) = 21.07, p < 0.001). For participants who started the experiment with the sympathetic condition, the difference between the presence they felt during that first walk-through and the second (with indifferent haptic feedback) was significant (t(36) = 4.32, p < 0.001). No other order effect was significant as revealed by ANOVA tests (F (3, 73) = 14.29, p > 0.88) for the empathy, the anxiety and the embodiment factors.

2) Objective behavioural measures: As mentioned earlier in Sec. III-B5, we also collected the users' reactivity in helping the presenter as well as their gaze. The user reactivity was calculated as the time elapsed between the moment the presenter asks for help and when the user helps her (see Sec. III-B1). Results did not highlight any significant difference between the two feedback conditions with respect to this metric. The range of reaction times were [0.19; 14.13] s (M D = 8.41; IQR = 2. [START_REF] Eisenberg | The relation of empathy to prosocial and related behaviors[END_REF]) and [0.12; 14.88] s (M D = 12.89; IQR = 5.31) for the laser and the bottle, respectively among all participants.

We measured the time percentage users spent watching key elements of the virtual environment. As a Shapiro test (W = 0.91, p < 0.001) showed the data to not be normally distributed, we carried out an Aligned Rank Transform (ART) ANOVA target vs % of time. The results showed that there were significant differences between the time spent looking at each target (F (5, 74) = 740, p < 0.001). Post-hoc pairwise comparisons (Tukey correction) revealed that the main target was the presenter (M D = 64.22; IQR = 18.91), followed by the colleagues and the slides, (M D = 10.86; IQR = 10.86), the mirror and the laser, (M D = 3.57; IQR = 3.39) and finally the bottles (M D = 0.63; IQR = 1.91) (all differences among these groups being significant (p < 0.001).

B. Correlations between empathy and other factors

1) Subjective questionnaires: Correlations between the answers to the mid-experience questionnaires are reported in Fig. 5. Additional correlations are reported on the same figure with respect to their answers on the pre-experience questionnaire regarding the IRI reviewed in Secs. II-B and III-B5.

The highest correlation is found between the empathy and the anxiety users felt during each condition with a correlation of 0.74 (t(74) = 9.57, p < 0.001) over the two factors. Additionally, while the difference between the empathy felt by participants for each feedback condition was not significant (see Sec. IV-A1), there are some correlations between the Fantasy coefficient of the Interpersonal Reactivity Index participants filled before the experience, and the empathy felt for each condition. As shown in Fig. 5, users who rated a higher Fantasy coefficient were more receptive to the sympathetic haptic feedback than the indifferent feedback. An Olkin's test, which compares two overlapping correlations based on dependent groups, revealed that the empathy felt by participants with the sympathetic feedback was significantly more correlated to the Fantasy coefficient than the empathy felt from the indifferent feedback (z = 2.6313, p < 0.005). Anxiety levels were also found to be more significantly correlated to the reported levels of empathy during the 'constant' (2) condition compared to the 'dynamic' (1) condition, according to an Olkin's test (z = 2.5870, p < 0.005).

2) Objective behavioural measures: Participant empathy and anxiety and the time they spent looking at the presenter was significantly correlated (0.26 for t(74) = 2.24, p < 0.05, and 0.40 for t(74) = 3.64, p < 0.001 respectively).

V. DISCUSSION

Reported feelings of empathy for each walk-through were overall relatively high (5.6 out of 7), as seen in Sec. IV-A1. This suggests a ceiling effect that did not allow for a significant difference between the two conditions, while the preference for sympathetic feedback was significant in reference to the empathy users felt. Likewise, although users did not seem to find the belt to be anxiety-inducing, they did find the scenario more intense/harrowing when receiving sympathetic haptic feedback, and commented more on their anxiety and distress after the sympathetic condition walk-through. Hence, while the results are contrasted, the first two hypotheses are supported by user feedback. The lack of large differences between participant feelings for each scenario could also be explained by user bias. As Carey et al. [START_REF] Carey | Toward measuring empathy in virtual reality[END_REF] highlighted, users often have trouble scaling their feelings during an experience, which can in turn make data harder to analyse. The last hypothesis (H3) on a stronger sense of presence was not supported by a majority of participants. The decrease in presence between the first run with sympathetic feedback and the second with constant feedback could be explained by the similarity between the two scenarios. Since the only difference between the two runs of the experience was the haptic feedback provided, users had time to get acclimated to the scene, which could have changed how they felt about their sense of place illusion and plausibility [START_REF] Skarbez | A survey of presence and related concepts[END_REF], [START_REF] Slater | Place illusion and plausibility can lead to realistic behaviour in immersive virtual environments[END_REF]. It is also possible that users felt a stronger difference in their sense of presence since the experience appeared less intense to them without the sympathetic haptic feedback. In the future, using multiple different scenarios and VE between the two conditions and more exhaustive tutorials might help mitigate this effect. Considering the contrasted results, it seems that participants might be divided into groups according to their reception of sympathetic haptic feedback. For example, participants who rated higher on the Fantasy coefficient of the Interpersonal Reactivity Index generally tended to be more susceptible to sympathetic haptic feedback, in intensity, presence, or even empathy. It might be interesting to study this distinction further, and find what type of haptic feedback works best for each type of person. This is especially important as these results were strengthened by the behavioural measures which correlated accordingly. Additionally, the strong correlation between the empathy and the anxiety felt by participants could be a useful tool in future experiments. There are several types of future works to consider from this paper. Firstly, the paper did include some limitations. The empathy measurements were simple, and the study had no 'haptic-less' control group. As a study on emotions, the number of participants (N=38) was small. We could also explore the characteristics that make users react differently to affective haptic feedback and study the effect of new haptic sensations with our current devices. Instead of using the compression belt to simulate breathing, it could be used as physiological pressure feedback, compressing the user's torso. Furthermore, we could focus on the link between visual emotion cues and affective haptic feedback to explore the possibilities of feedback plausibility.

VI. CONCLUSION

This paper studied the role of physiologically based haptic feedback in fostering feelings of connection and empathy during an immersive VR experience, comparing two different affective haptic feedback. The first one made the user feel the heartbeat and breathing patterns of a virtual agent experiencing a series of stressful interactions, transmitting/communicating her anxiety and stress to the user. The second feedback provided no such information, with the user experiencing constant heartbeat and breathing patterns regardless of what the virtual agent was experiencing and feeling. Results of a user study involving 38 participants showed that stress, relief, and anxiety could be communicated through affective haptic feedback, making, to a certain extent, participants feel closer to the agent haptically connected to them. These promising results show the viability of using haptic feedback to foster empathy in social VR scenarios. Taken together, they promote the use of empathetic haptics within VR applications in which inducing positive relationships plays an important role.

Fig. 1 .

 1 Fig. 1. Haptic setup for the experiment. (a) Compression belt, including the servomotor and the white belt wrapped around the waist. (b) Heartbeat simulator worn on the wrist, driven by an Arduino's PWM. (c) Variation of sound profile and PWM during a cardiac circle.

Fig. 3 .

 3 Fig.3. Evolution of the haptic feedback intensity and speed during the "sympathetic" haptic condition (dynamic) and the "indifferent" haptic condition (constant). The three peaks correlate to times the presenter's laser pointer runs out of battery (1), she experiences a dry throat (2), and she receives rude comments from her coworkers (3), as described in Sec. III-B1. The belt (left vertical axis) and vibration (right) feedback intensify accordingly. Each step is sharp to ensure a clear perception of the rising intensity.

Fig. 4 .

 4 Fig. 4. Haptic preferences in terms of empathy felt (1 = Indifferent feedback, 7 = Sympathetic feedback).

Fig. 5 .

 5 Fig. 5. Results. Correlations between participant feelings of empathy and other factors from the mid-experience questionnaires, and their results from the Interpersonal Reactivity Index. The two conditions corresponds to empathy felt during the sympathetic (dynamic) feedback (1), and during the indifferent (constant) feedback (2). *** denotes significant differences (p < 0.0001), and ** means p < 0.001.


domain: phys spi

text:
Julien Marty

-Benjamin Franc ¸ois 1 -Cédric Content

M L Menter-Langtry Results N U Nusselt

Roev Roe

INVESTIGATION OF ROTOR-STATOR INTERACTIONS AND LAMINAR-TURBULENT TRANSITION USING UNSTEADY SIMULATIONS AND THE MENTER-LANGTRY MODEL

Keywords: LAMINAR-TURBULENT TRANSITION, TURBINE, ROTOR-STATOR INTERACTION

A significant part of the flow at the turbine blade walls can be laminar which influences the heat transfer and separation. Thus, the assumption of fully turbulent flow is not well suited for turbine applications. The present study aims at validating the Menter-Langtry transition model for unsteady flows. The configuration supporting this study is the CT3 turbine stage (TATEF2 project), experimentally tested at the van Karman Institute. To carry out unsteady simulations without simulating the full annulus configuration, a sliding interface technique is used, this latter handling no-match connectivities and relative motion between rotor and stator, and based on a reduced blade count leading to a contraction or a dilatation of the rotor-stator interface (the blade geometry is not modified). Thus, the model validation is completed by a comparison of this method with a steady-state simulation applying the mixing plane approach, classically used in turbine design. Moreover, as the elsA software enables the use of structured and unstructured meshes in the same computational domain, this validation is performed on both mesh types and some numerical guidelines are given to a relevant comparison between structured and unstructured meshes. The comparison to experimental data highlights a good agreement and validates the model to predict the time-averaged performances. For this configuration, only the unsteady simulations with a transition model are able to capture both isentropic Mach and Nusselt numbers over rotor and stator walls. Other simulations (steady one with or without transition model, unsteady one with a full turbulent flow assumption) fail at matching measurements. The mesh type and numerical approach effects are also reported.

INTRODUCTION

In order to reduce weight of turbofan engines, manufacturers aim at increasing stage loading of compressors and turbines. This can be achieved by using trans-or supersonic stages. Consequently, the flow topology is more complex than within a subsonic one. As mentioned by [START_REF] Sandberg | Fluid dynamics of axial turbomachinery: Blade-and stage-level simulations and models[END_REF], sub-and supersonic stages, in opposition to isolated airfoils, are characterized by strong interactions between adjacent blades, allowing the significant deviation achieved in turbines, and between neighboring rows such as potential effects due to the small inter-row distance, incoming wakes influencing the flow inlet angle of downstream row. Moreover, the turbulence contained in wakes impacts the boundary layer evolution over blades of downstream rows. In supersonic configurations, the evolution of the pressure gradient is responsible for the generation of shock within the blade passage or at trailing edge. This leads to additional interactions: wake-shock, vortex-shock, causing higher losses. These features are commonly encountered in High-Pressure Turbine (HPT) where shocks are generated at the trailing edges of turbine vanes [START_REF] Sieverding | A review on turbine trailing edge flow[END_REF] and are responsible for huge fluctuations of stagnation pressure over the rotor, up to 40% [START_REF] Dénos | Investigation of the Unsteady Rotor Aerodynamics in a Transonic Turbine Stage[END_REF].

Thus, the life-cycle prediction of HPT depends on the prediction of the flow around blades, especially on the boundary layer development, in the framework of row interactions. Laminarity is important in HPT design for several reasons. Firstly, the heat transfer from the flow to the turbine blade depends strongly on the laminar-turbulent nature of the boundary layer. This quantity cannot be predicted accurately with an assumption of full-turbulent boundary layer. Secondly, turbine blades are high cambered and the flow is likely to separate. Boundary layer separation is also strongly dependent on the laminar-turbulent nature of the flow. Thirdly, in the inter-blade channels, the flow is accelerated and the flow may shift from a turbulent to a laminar state (relaminarization) with the associated impacts on the heat transfer and performance. For these reasons, the modeling of the laminar-turbulent transition in turbine design receives a growing attention. Consequently, many studies concentrated on HPT vane, such as the LS89 airfoil, experimentally tested at VKI [START_REF] Arts | Aero-Thermal Performance of a Two-Dimensional Highly Loaded Transonic Turbine Nozzle Guide Vane: A Test Case for Inviscid and Viscous Flow Computations[END_REF] at different oper-ating conditions and freestream turbulence intensities. By-pass transition [START_REF] Garai | Scale-Resolving Simulations of Bypass Transition in a High-Pressure Turbine Cascade Using a Spectral Element Discontinuous Galerkin Method[END_REF][START_REF] Cac ¸ão Ferreira | Investigation of Thermal Effect on Bypass Transition on a High-Pressure Turbine Guide Vane[END_REF], shock-induced transition [START_REF] Dupuy | Analysis of the effect of intermittency in a high-pressure turbine blade[END_REF] can occur in this configuration.

Under unsteady conditions, encountered in stage configuration due to rotor-stator interaction, the transition mechanism can be strongly modified. When the wake generated by the previous blade impinges the airfoil, thanks to the boundary layer receptivity, the transition can be by-passed and the transition onset moves upstream. After the wake passage, the boundary layer is not strictly laminar but perturbations are observed within the boundary layer. The shape factor H i , which is the ratio between displacement thickness and momentum thickness, decreases -and is below 2.59 -and the boundary layer is more able to overcome a strong adverse pressure gradient than a laminar one. Once the wakes are far from the airfoil and the perturbations are damped, the initial transition process can be newly observed up to the next wake passage. Similarly, shocks incoming from blades of the previous row impinge periodically blades, causing an unsteady shock-boundary layer interaction influencing the laminar-turbulent transition process.

In order to better understand the flow physics within a HPT, several laboratories work on a turbine stage. [START_REF] Guenette | Fully Scaled Transonic Turbine Rotor Heat Transfer Measurements[END_REF] investigated heat transfer of a transonic turbine stage and proved similarity of flow at midspan, with 2-D cascade with passing bars. [START_REF] Gaetani | Investigation of the Flow Field in a High-Pressure Turbine Stage for Two Stator-Rotor Axial Gap -Part I: Three-Dimensional Time-Averaged Flow Field[END_REF] studied the rotor-stator interaction of a turbine stage through five-hole probe and a temperature gauge, highlighting the evolution of the flow across the stage, the modification of secondary flows. The work of [START_REF] Paniagua | Unsteady strong shock interactions in a transonic turbine: experimental and numerical analysis[END_REF] focused on unsteady interaction between vane shocks and rotor blades. The shock impingement is responsible for a small separation over the rotor blade, close to the leading edge, which periodically moves. The present work is based on the computations performed in [START_REF] Paniagua | Unsteady strong shock interactions in a transonic turbine: experimental and numerical analysis[END_REF] with elsA software. The transition model of [START_REF] Arnal | Théorie de l'instabilité laminaire et critères de transition en écoulement bi et tridimensionnel[END_REF] was applied on the stator blade, only. However, this model is dedicated to natural transition (freestream turbulence intensity lower than 1%) in which the transition onset is due to the instability of Tollmien-Schlichting waves. Conversely, HPT is characterized by high freestream turbulence, by by-pass or shock-induced transition. Thus, the present study aims at improving the flow prediction by using a more adapted transition model. On CFD side, other authors investigate the unsteady flow in turbine stage using transition model, as the Laminar Kinetic Energy model [START_REF] Pacciani | Urans analysis of wake-induced effects in high-lift low reynolds number cascade flows[END_REF], or not [START_REF] Tallman | Heat Transfer Measurements and Predictions for a Modern, High-Pressure, Transonic Turbine, Including Endwalls[END_REF][START_REF] Pinelli | Computational and Experimental Study of the Unsteady Convection of Entropy Waves Within a High-Pressure Turbine Stage[END_REF]. Nonetheless, the unsteady transition is mainly predicted using high-fidelity methods such as Large Eddy Simulation [START_REF] Papadogiannis | Effects of Subgrid Scale Modeling on the Deterministic and Stochastic Turbulent Energetic Distribution in Large-Eddy Simulations of a High-Pressure Turbine Stage[END_REF][START_REF] Leggett | High-Fidelity Simulation Study of the Unsteady Flow Effects on High-Pressure Turbine Blade Performance[END_REF].

As earlier mentioned, the present work is based on CFD computations performed by Paniagua et al. [2008] and focuses on the evaluation of the Menter-Langtry [START_REF] Menter | A Correlation-Based Transition Model Using Local Variables Part I -Model Formulation[END_REF][START_REF] Langtry | Correlation-Based Transition Modeling for Unstructured Parallelized Computational Fluid Dynamics Codes[END_REF] transition model on a turbine stage with unsteady simulations techniques and on both structured and unstructured grids. Firstly, the turbine stage is presented, followed by the turbulence and transition modelings used as well as the numerical setup. Then, the validation of the model is carried out step by step, from steady to unsteady simulations, from structured to unstructured meshes.

STAGE-CONFIGURATION CT3 Experimental facility

The present study focuses on the experimental turbine stage CT3 used in TATEF2 project [START_REF] Dénos | Investigation of the Unsteady Rotor Aerodynamics in a Transonic Turbine Stage[END_REF], De la Loma et al., 2008, Paniagua et al., 2008]. This turbine stage is representative of modern high-pressure turbine. The experimental setup includes measurements on the blade walls for the pressure and the heat flux (see Fig. 1). Different aerodynamic loadings (pressure ratios between outlet and inlet) have been tested during the experimental campaign.

The highest aerodynamic loading (P inlet /P outlet = 5.12) has been selected for the present study.

The key parameters of the operating point are recalled in Table 1. It should be noticed that only the "High" condition is considered in this investigation. The freestream turbulence intensity at the turbine inlet was measured by hot-wires and is equal to 5% at midspan, as mentioned in [START_REF] Yasa | Application of Hot-Wire Anemometry in a Blow-Down Turbine Facility[END_REF]. In 3D case, close to endwalls, this value increases up to 25% or even 45%, as the velocity magnitude is very low.

Numerical simulation setup

Figure 2 presents the mesh used for the 2.5D simulations, relative to the flow at midspan. This mesh is based on the work of [START_REF] Paniagua | Unsteady strong shock interactions in a transonic turbine: experimental and numerical analysis[END_REF]. Thus, there is no grid dependence study in the present work. It should be noticed that upper and lower boundaries of this 2.5D configuration are based on information coming from the 3D one. The spanwise height represents a little less than 1% of massflow. Only one single blade channel is shown here.100 points are used in the streamwise direction between the leading-edge and the trailing-edge for both blades. In the inter-blade channels, 150 points and 160 points are used in the azimuthal direction for the stator and the rotor respectively. On the CT3 configuration, steady and unsteady RANS simulations were performed. To reduce the CPU cost of the simulation, RANS simulations are performed on a computational domain comprising only one blade passage per row while URANS simulations are based on a computational domain reduced to two stator channels and three rotor channels, allowing the use of the technique developed by [START_REF] Fourmaux | Assessment of a low storage technique for a multi-stage turbomachinery Navier-Stokes computations[END_REF] for the unsteady simulation. This technique, also called Profile Transformation Approach (PTA), is close to the blade count reduction approach but the reduction is only applied at the rotor-stator interface (i.e. at the same location of the mixing plane). Thus, there is no rescale of geometry. With the present reduction, the azimuthal arc length is nearly the same between the two rows (16.74 • vs 16.88 • ). For the present application, the assumption is acceptable. It must be kept in mind that this unsteady technique modify the Blade Passing Frequency (BPF), especially if the rotor and stator blade numbers are prime. The evaluation is made in Table 3. Differences are below 1% and therefore acceptable for the intended flow physics to capture.

Computations were undertaken with the compressible Navier-Stokes solver elsA, software developed by ONERA and co-owned by Safran and ONERA [START_REF] Cambier | The Onera elsA CFD Software: Input from Research and Feedback from Industry[END_REF], using the Roe approximate Riemann solver [START_REF] Roe | Approximate Riemann solver, parameter vector and differences schemes[END_REF] with a second order MUSCL reconstruction smoothed by a Van Albada [START_REF] Van Albada | A Comparative Study of Computational Methods in Cosmic Gas Dynamics[END_REF] or a Venkatakrishnan limiter [START_REF] Venkatakrishnan | Convergence to steady state solutions of the euler equations on unstructured grids with limiters[END_REF], and a scalar LUSSOR implicit method [START_REF] Yoon | Three-dimensional incompressible navier-stokes solver using lower-upper symmetricgauss-seidel algorithm[END_REF].

The steady computations rely on a first order in time backward Euler scheme while the URANS simulations are performed with a second order time scheme [START_REF] Gear | Numerical Initial Value Problems in Ordinary Differential Equations[END_REF]. The number of sub-iterations is variable (a minimum of 5 is always performed), a convergence threshold at 0.01 is imposed at each timestep. Thus, this ensure a good accuracy of the transient flow [START_REF] Fourmaux | Assessment of a low storage technique for a multi-stage turbomachinery Navier-Stokes computations[END_REF] Figure 3: Mass flow time evolution prediction. As indicated in Table 3, 27, 511 timesteps are performed per complete revolution, namely around 430 for each rotor blade passage and 640 for each stator blade passage. For each simulation, three complete revolutions are performed, as shown in Figure 3, the first one being devoted to the transient part, and the last one to the time-average flow computation. The temporal evolution of mass flow at four stations (stator inlet, stator outlet, rotor inlet and rotor outlet) shows that the periodic convergence is reached after one revolution. Another revolution is computed in order to check the temporal periodicity accuracy, and finally the third revolution is used for the time-average computation and the post-processing. Periodic boundary conditions are used for the azimuthal boundary for both the steady and unsteady simulation. At the inlet, the subsonic boundary condition is used. Inlet stagnation pressure, temperature are imposed as well as an axial flow direction. The turbulence kinetic energy is deduced from the inlet turbulence rate. For the second turbulence variable ω, a laminar-turbulent viscosity ratio of 35 is assumed (based on previous experiences with the simulation of the LS89-MUR241 [START_REF] Benyahia | Mise en oeuvre et évaluation d'un modèle de transition à équations de transport pour la simulation d'écoulements en turbomachines[END_REF]). The first transition variable ργ is set to 1 while the second ρRe θ to 122. At the outlet, the simplified radial equilibrium is imposed and based on the pressure ratio earlier defined. At the blade walls, a no-slip isotherm boundary condition is used. The imposed wall temperature is T b = 288.5K. In this study, the wall is considered smooth i.e. without any roughness influencing the boundary layer development. There is no information on the wall surface condition in experiments. The ∆y + value is lower than 0.75, except close to the leading edge where the maximum value is 1.5. As only 2.5D configurations are considered in the present study, slip boundary conditions are used for the lower and upper radius borders, as these boundaries represent streamlines in 3D configurations.

Turbulence and transition models

In the present study, the laminar-turbulent transition is modeled through the Menter-Langtry model [START_REF] Menter | A Correlation-Based Transition Model Using Local Variables Part I -Model Formulation[END_REF][START_REF] Langtry | Correlation-Based Transition Modeling for Unstructured Parallelized Computational Fluid Dynamics Codes[END_REF], except that the correlations used are those of [START_REF] Content | Local correlation-based transition model[END_REF]. These correlations, called CH10, were built from two experimental datasets (a flat plate and a ogive cylinder with various inlet turbulence rates and pressure gradients). The Menter-Langtry model is composed of two transport equations: one for the intermittency γ and one for the transition Reynolds number Re θ . The intermittency variable γ denotes if the boundary layer is laminar (γ = 0), fully turbulent (γ = 1) or in a transient state (0 < γ < 1). Outside the boundary layer, this value must be equal to 1.

This transition model is coupled with k -ω Menter SST model [START_REF] Menter | Two-equation eddy-viscosity turbulence models for engineering applications[END_REF]. Accounting for the transition model requires to modify some terms in the turbulence model, especially production and destruction terms which are multiplied by the effective intermittency defined by γ eff = max (γ, γ sep ). More informations about this model implemented in elsA, are given in [START_REF] Bouchard | Validation of correlations-based transition modeling strategies applied to the spalart-allmaras turbulence model for the computation of separation-induced transition[END_REF], [START_REF] Dufau | Simulation of Passing Wakes Inducing Unsteady Boundary Layer Transition Around Low-Pressure Turbine Blade[END_REF].

RESULTS ON STRUCTURED GRIDS Flow analysis

Figure 4 depicts the iso-contours of relative velocity magnitude |W | (left), axial velocity V x (middle) and turbulent kinetic energy TKE (right) at three different instants: t = nT , nT + T 4 and nT + 3T 4 where T is the rotor period and, n the rotation number (2, in the present case). Those variables highlight the features of the flow around blades, such as acceleration or deceleration, separations, wakes, shock as well as interactions between them. Besides, the comparison between the three instants allow following the temporal evolution of identified features. It should be noted that the inlet Mach number is 0.15. Thus, flow is strongly accelerated in the stator passage due to the favorable pressure gradient and the convergent interblade channel. This becomes supersonic at the channel outlet, generating two oblique shock waves at the trailing edge. Downstream, the flow remains mainly supersonic. The first shock, (a) on figure 4(b), impacts the adjacent blade, creating a separation bubble responsible for the laminar-turbulent transition, as shown later thanks to the Nusselt number distribution over blade walls. The second shock (b) is oriented towards the rotor. With a steady-state simulation based on mixing plane approach, the interaction between this shock and the rotor is not accounted for. On the contrary, this stator-rotor interaction is responsible for the creation and disappearing of a small separation bubble -in which the laminar-turbulent transition occurs -over the rotor suction side, close to the leading edge, during a stator passage. According to the location of the rotor blade relative to the second shock (b), the flow at the leading edge differs significantly. When the shock impinges the rotor blade, (f) on figure 4(e), the boundary layer separates, causing the forming of a separation bubble in which transition occurs. On the contrary, when the shock is far from the blade, a separation bubble appears more downstream (g), close the axial position at 70 mm. For some specific instant, the separation bubble is not observed at the maximum thickness of the rotor blade (e). This can result from the interaction between the wake (c) and the second shock of the adjacent stator blade, which are responsible for a very small bubble at the leading edge, as shown by TKE contours. Because the relative velocity is very tangential downsteam the stator, the inlet relative Mach number in the rotor domain is subsonic. The flow accelerates before the entrance of the interblade channel because of the high camber of the suction side of the rotor, as shown by the magnitude of relative velocity. A supersonic area is visible on the suction side of the rotor, close to the leading-edge. The inter-blade passage between rotors forms a converging duct. The same phenomenon arises in the rotor: the flow becomes supersonic at the outlet of the channel, leading to the appearance of two shock waves at the rotor trailing edge, similarly to the stator. On pressure side, the shock is oriented towards the adjacent blade. This shock is strongly attenuated due to expansion. Nonetheless, the impact on suction side, close to three quarters of chord, is responsible for a low velocity region. This feature depends also on the state of the upstream boundary layer. For example, at t = nT + 3T 4 , the boundary layer over the middle rotor blade is not fully turbulent as the turbulent kinetic energy is quite small. Consequently, the shock-boundary layer interaction results in a thickening of the boundary layer. Thus, the flow complexity can be summarized by: (i) the laminar-turbulent transition is induced by a shock over stator suction side and by an unsteady separation bubble resulting from a shock -boundary layer interaction over the rotor suction side and (ii) a boundary layer separation occurs in the vicinity of the rotor trailing edge, over the suction side. The prediction of all these phenomena is strongly influenced by the flow modeling and the numerical setup. Figure 5 shows the distribution of static pressure and heat flux in terms of isentropic Mach and Nusselt numbers over the stator and the rotor blades, along with the curvilinear abscissa. Negative and positive values of abscissa are relative to the pressure ((a) on the figure) and the suction side (b), respectively. Numerical results are obtained by assuming the flow as fully turbulent (FT) or by modeling the laminar-turbulent transition (ML) and only the structured mesh is used in this subsection. The effect of transition model is quite small on the isentropic Mach number distribution. Both simulations show a peak over the suction side of the stator (c) which is the footprint of the impact of the shock wave generated by the trailing edge of adjacent stator blade. Numerical data agree well with experiments, except downstream of the shock (d). The separation bubble induced by the shock is not well predicted. Similarly, over the rotor blade, the main discrepancy with the experiments are obtained downstream of the shock generated at the rotor trailing edge (f), not by the stator trailing edge (e).

(a) |W | -t = nT (b) V x -t = nT (c) TKE -t = nT (d) |W | -t = nT + T 4 (e) V x -t = nT + T 4 (f) TKE -t = nT + T 4 (g) |W | -t = nT + 3T 4 (h) V x -t = nT + 3T 4 (i) TKE -t = nT + 3T 4

Steady computations

The transition modeling is of primary importance in order to well predict the Nusselt number. With a fully turbulent flow (S-SST-FT), heat fluxes are over-predicted, all along the stator blade, except over the suction side near the trailing edge as the laminar-turbulent transition has occurred due to the shock impact (g). Over the rotor blade, both simulations clearly fail to predict the Nusselt number distribution. The main hypothesis is the lack of rotor-stator interaction as the mixing plane acts as an azimuthal average and remove wake and interaction of the shock wave generated at stator trailing edge with the rotor boundary layer. In the following, only numerical results accounting for transition are considered. The isentropic Mach number and Nusselt number are plotted in Figure 6. On the stator blade, the unsteady effects are only observed over the suction side and close to the trailing edge. This is expected as the flow is chocked in the stator: the interaction with the rotor blade leads to small fluctuations which do not cross the throat of the stator inter-blade channel. The comparison between steady and time-averaged unsteady data shows that the static pressure plateau downstream the boundary layer -shock interaction is strongly influenced by rotor-stator interaction and a better prediction is obtained. Even if differences still remain on the rotor blade, the agreement with experimental data is improved thanks to the unsteady simulation. This means that the stator influences also the pressure distribution within separation over rotor blade wall. On the pressure side, the agreement is better with unsteady simulation.

Unsteady computations

(a) M is -stator (b) N u -stator (c) M is -rotor (d) Nu -rotor
Concerning the heat flux and the predicted Nusselt number, the distribution is quite similar over suction side between steady and unsteady simulations, except downstream of the shock where the steady computation is oddly in better agreement with experiments. Over the rotor wall, the predicted is significantly better when stator-rotor interactions are taken into account in the simulation. The Nusselt profile over the suction side is recovered with the unsteady simulation.

Thus, at least for this test case, stator-rotor interaction and transition modeling must be accounting for in order to well predict the Nusselt distribution over both stator and rotor walls.

RESULTS ON UNSTRUCTURED GRIDS

As the elsA software handles both structured and unstructured meshes, the transition model was also implemented for unstructured grids. The present investigation focuses on the validation of this implementation, not on the best practice in terms of creating an optimal unstructured mesh (prism layer or not, thickness of this layer, aspect ratio for tetrahedrons, ...). Thus, it was decided to use only hexahedrons in order to be fully comparable to structured mesh. However, the numerical setup cannot be strictly identical between these two mesh topologies. Before validating the transition model, the effect of numerical parameters must be investigated. In the present study, the choice was made to keep the Roe scheme. Thus, the focus concerns the MUSCL limiter. As discrepancies appear mainly on the Nusselt number, the following analysis relies only on this quantity. With the structured grid, the limiter linked to the Roe scheme, influences mainly the Nusselt distribution, over the suction side, close to the trailing edge, i.e. downstream of the shock. The limiter of Venkatakrishnan allows a better prediction of the heat flux rise. However, the agreement with experimental data is quite similar. On the rotor, there is no significant effect on the suction side while a better agreement is reached on the pressure side. In the present study, the unstructured mesh is a fully hexaedric one, comprising the same cell number. In other words, the mesh is identical and only the way to describe the mesh differs. The comparison of the Nusselt distribution over the suction side shows that the van Albada limiter behaves wrong downstream of the shock, leading to a mis-prediction of the heat flux rise due to the laminarturbulent transition. Moreover, some oscillations are observed on the pressure side. On the rotor, the discrepancies are much more smaller, leading to a similar agreement with experimental data. As shown by the work by [START_REF] Jawahar | A high-resolution procedure for euler and navier-stokes computations on unstructured grids[END_REF], the limiter of Venkatakrishnan is better than the one of van Albada, as this is a multidimensional limiter, which improves the robustness and accuracy by yielding oscillation-free solutions and recovering the second order of the numerical scheme. On the contrary, the van Albada limiter is not sufficiently effective in removing oscillations at discontinuities with unstructured meshes. In elsA software, this has been proved on several test cases during the PhD of [START_REF] Soismier | Stratégie de résolution hybride structurée / non structurée pour la simulation d'effets technologiques en turbomachines[END_REF]. In the following, only the Venkatakrishan limiter is used, for both structured and unstructured grids in order to validate the implementation of the transition model for unstructured mesh. The isentropic Mach number and the Nusselt number distributions over stator and rotor walls are plotted in Figure 8, for the two mesh types considered in this study. It should be noticed that the post-processing is identical for both structured and unstructured meshes. The isentropic Mach number curves are very close together as only a very small discrepancy is observed downstream of the shock impact. Concerning the Nusselt number, the agreement between numerical results is good over the stator wall as the main difference appears in the downstream part of the suction side and reveals that the production of turbulence is not strictly identical leading to a small mismatch in terms of heat flux. Over the rotor blade, the agreement is less satisfactory due to the difference in terms of upstream turbulence coming from the stator and of turbulence production. Nonetheless, the agreement with experiments is still good. Thus, the transition model of Menter-Langtry is validated for both grid types.

Influence of numerical setup

CONCLUSIONS

The present investigation is dedicated to the impact of rotor-stator interaction on laminarturbulent transition over turbine airfoils. The aim of this study is the validation of the Menter-Langtry transition model implemented in the elsA software to predict the unsteady flow and time-averaged performances of the CT3 stage configuration (TATEF2 project), on both structured and unstructured meshes. As a reminder this study aims at improving the flow modeling used by [START_REF] Paniagua | Unsteady strong shock interactions in a transonic turbine: experimental and numerical analysis[END_REF], to the Menter-Langtry model. However, this must be continued by applying this model on the 3D mesh for a more rigourous validation.

The analysis of the time-averaged performances underlined that transition modeling and unsteady modeling were both necessary to get consistent results with the measurements (isentropic Mach number and Nusselt number distributions on the blade) for the CT3 turbine. Numerical parameters can have a strong influence on CFD results, especially if their behavior differs from structured to unstructured grids. In the present study, with the Roe scheme, the main parameter is the limiter. On unstructured grid, the Venkatakrishnan limiter is used to recover consistent results with structured grids, allowing the validation of the Menter-Langtry transition model.

Further works are driven by three objectives: validation of the model on 3D configuration with unsteady effects, a better comprehension of physical mechanisms involved in transition trigger (role of shock, of wake...) thanks to high fidelity simulations (e.g. wall-resolved large eddy simulation).

Figure 1 :

 1 Figure 1: Experimental set-up -CT3 turbine

Figure 2 :

 2 Figure 2: Mesh for 2.5D configuration

Figure 4 :

 4 Figure 4: Contours of relative velocity magnitude |W | (left), axial velocity V x (middle) and turbulent kinetic energy TKE (right) at three different instants showing the flow complexity at midspan

  Figure 5: Distribution of isentropic Mach (left, M is ) and Nusselt (right, N u) numbers over stator (top) and rotor (bottom) blades predicted by steady computation on structured grids with fully turbulent assumption and transition modeling

Figure 6 :

 6 Figure 6: Distribution of isentropic Mach (left, M is ) and Nusselt (right, N u) numbers over stator (top) and rotor (bottom) blades predicted by steady and unsteady computations on structured grids with transition modeling

Figure 7 :

 7 Figure 7: Nusselt number distribution over stator (left) and rotor (right) blades predicted by unsteady simulations accounting for laminar-turbulent transition, on structured (top) and unstructured (bottom) meshes

Validation

Figure 8 :

 8 Figure 8: Distribution of isentropic Mach (left, M is ) and Nusselt (right, N u) numbers over stator (top) and rotor (bottom) blades predicted by unsteady computations on structured and unstructured grids with transition modeling and the Venkatakrishnan limiter

Table 1 :

 1

	Rotating speed	6474 rpm
	Reynolds number	1.1 * 10 6
	Outlet isentropic Mach number (plane 2)	1.249
	Outlet isentropic Mach number (plane 3)	1.18
	Blade wall temperature	288.5 K
	Inlet stagnation pressure	1.65 bar
	Inlet stagnation temperature	434 K
	Inlet turbulence rate	5 %

Operating conditions ("High" condition)

Table 2 .

 2

		Stator Rotor
	Blade number	43	64
	Axial chord [mm] 41.16 39.78
	Axial chord/span	0.812 0.738
	Hub-to-tip ratio	0.872 0.864
	Stagger angle [deg]	54	32

Table 2 :

 2 Geometrical features at mid-span

Table 3 :

 3 Timesteps and Blade Passing Frequencies (BPF) in the unsteady simulation based on the technique of

	Stator	Rotor

ACKNOWLEDGEMENTS

All simulations have been performed in the framework of the elsA agreement between SAFRAN and ONERA, which are co-owners of this software. This work was partially supported by the SONICE project, granted by the French Directorate General for Civil Aviation (DGAC).


Ambre Davat
email: ambre.davat@gipsa-lab.fr

Gang Feng

Véronique Aubergé

A Study on the Lombard Effect in Telepresence Robotics

In this study, we present a new experiment in order to study the Lombard effect in telepresence robotics. In this experiment, one person talks with a robot controled remotely by someone in a different room. The remote pilot (R) is immersed in both environments, while the local interlocutor (L) interacts directly with the robot. In this context, the position of the noise source, in the remote or in the local room, may modify the subjects' voice adaptations. In order to study in details this phenomenon, we propose four particular conditions: no added noise, noise in room R heard only by R, virtual noise in room L heard only by R, and noise in room L heard by both R and L. We measured the variations of maximum intensity in order to quantify the Lombard effect. Our results show that there is indeed a modification of voice intensity in all noisy conditions. However, the amplitude of this modification varies depending on the condition.

Introduction

When social entities are interacting, they automatically adapt their behavior to adverse conditions which could jeopardize their communication. In particular, vocal modifications due to noise are known as the Lombard effect. This phenomenon was first documented in humans [START_REF] Lombard | Le signe de l'élévation de la voix [The sign of voice raising[END_REF], then in other animal species, especially birds and mammals [START_REF] Zollinger | The evolution of the Lombard effect: 100 years of psychoacoustic research[END_REF]. Moreover, the Lombard effect has implications for the design of virtual agents and social robots. Indeed, it can impair speech recognition systems, which are generally based on speech corpus recorded in quiet conditions [START_REF] Hanson | Robust speaker-independent word recognition using static, dynamic and acceleration features: experiments with Lombard and noisy speech[END_REF][START_REF] Junqua | The Lombard reflex and its role on human listeners and automatic speech recognizers[END_REF]. Implementing the Lombard effect in dialog systems would also increase their adaptation to noisy environment in a biomimetic way.

The Lombard effect consists mainly in an increase of speech intensity. It is an automatic phenomenon, which can only partly be controlled by the speaker [START_REF] Pick | Inhibiting the Lombard effect[END_REF]. It varies with the type of noise and differs greatly from one individual to another. It also depends on the speaker's involvement. Indeed, there is some evidence showing that the Lombard effect is stronger during more interactive tasks: It increases during storytelling vs. labelling (Amazi Deborah K. & Garber Sharon R., 1982), communication with another vs. reading [START_REF] Junqua | The Lombard effect: a reflex to better communicate with others in noise[END_REF], or vs. self-talk [START_REF] Garnier | Influence of Sound Immersion and Communicative Interaction on the Lombard Effect[END_REF]. The sound immersion techniques used in such experiments are also important, as speech modifications may be stronger when noise is played through headphones than over loudspeakers [START_REF] Garnier | Influence of Sound Immersion and Communicative Interaction on the Lombard Effect[END_REF]. Furthermore, the intensity is well known as one of the prosodic parameters much implied for producing different socioaffective attitudes (authority, surprise etc.) in many languages [START_REF] Aubergé | Gestual-facial-vocal prosody as the main tool of the socio-affective "glue": interaction is a dynamic system[END_REF]. In face to face interaction, the intensity variations due to the Lombard effect are almost never confused with those having a socio-affective meaning. However, in the case of remote interaction, an ill-formed Lombard effect could be perceivably confused with social affect cues [START_REF] Aubergé | The socio-affective glue: how to manage with the empathic illusion of human for robot? Presented at VIHAR-2017 workshop[END_REF].

The paper will focus on a study concerning the Lombard effect in telepresence robotics. The specificity of this context is that all interlocutors are not present in the same room: one of them interacts remotely through a robot, which embodies its pilot in the "local" space. It is therefore an asymmetric system because the pilot needs to be acoustically immersed in both remote and local environment, while the interlocutors talk directly with the robot in the local environment. Because the Lombard effect happens automatically, it should affect the pilot's voice regardless of where the noise comes from. On the opposite, if the noise occurs in the remote space, the interlocutors cannot hear it as loud as the pilot, potentially not at all. However, they can hear the pilot's vocal adaptations, which could modify their behavior. In this paper, we propose an experiment in order to study these assumptions and present some results.

Materials & Methods

Methodology

In order to realize this study, we designed an experiment involving two subjects separated in two different rooms as shown on Figure 1. One of them played the role of the remote pilot (R), and the other one was the local interlocutor (L), interacting with the telepresence robot. Several configurations were tested in order to isolate the features of the Lombard effect in remote communication.

Test conditions

A: quiet in both rooms B: noise in the remote space C: "virtual noise" in the local space D: noise in the local space The condition A was used in order to have a reference with no added noise. In all other conditions, R heard a noise, but this noise was not always audible by L. In condition B, a noise was played in R's room. As R voice was recorded with a headworn microphone, this noise was largely attenuated for the other subject, thus there was no need for R to speak louder to improve speech intelligibility. On the contrary, even if L did not hear the noise in this condition, L could need to speak louder in order to be understood by R. In condition D, a noise was played in the local space, and both subjects could hear it. This case is close to the standard communication with noise, where interlocutors are sharing the same environment. Finally, in condition C, a pre-recorded noise was injected in the headphones of R, in order to make R believe that this sound was existing in the local space and was heard by L.

Procedure

The experiment was introduced to the subjects as a test of the visual interface of a telepresence robot. The subject L was sitting in front of the robot and asked a list of simple questions to the subject R, who was the pilot of the robot. These questions were designed in order to be very simple, and trigger a finite set of answers. Examples of these questions (translated in English) are: "Which is the color of the grass?", "How many legs does a horse have?", "How much are 2 x 2?". Every 10 questions, there was a special instruction, requesting R to handle the robot via the interface. We pretended that we were measuring the answering time, in order to quantify the accessibility of the pilot interface. The subjects were informed that the test has to be done without a break. Indeed, during our first test, the subject L stopped speaking when the noise D was playing. The three different noises were regularly triggered by an experimenter.

To prevent bias in the experimental results, we wanted to nudge the subjects into thinking that noise occurrences had no link with the experiment. The noise sources were therefore hidden and diffused occasionally. We used pre-recorded realistic noises of a coffee machine and a drill. A ladder and a tool box were placed in the corridor at the entrance of the platform to suggest that there were building works in progress. Before the debriefing, most of the subjects believed that the noises were incidental, and none of them guessed that the aim of the experiment was to measure their vocal adaptation to noise. This confirms that our scenario was credible. Fulfilling the list of 140 questions took approximately 15 minutes long.

Technical specifications

Robot

The telepresence robot used was RobAIR Social Touch. It was co-constructed with the fablab of the LIG (Laboratoire d'Informatique de Grenoble). It uses a ROS architecture, and the teleconferencing interface is based on WebRTC. Contrary to most of telepresence robots [START_REF] Kristoffersson | A Review of Mobile Robotic Telepresence[END_REF], it does not look like a screen on wheels, but is closer to a slightly anthropomorphic robot carrying a tablet computer. On either side of the "head" of the robot, one omnidirectional microphone Behringer B5 is placed. Signals recorded by both microphones are digitalized by an audio interface UR22MKII (Steinberg), and sent to R's headphones in order to reproduce a pseudo binaural hearing. R's voice is emitted by a loudspeaker JBL GO+ which is placed under the tablet computer.

Echo cancelation

A local wireless router was used, the network latency was therefore negligible. However, visual and vocal signals cannot be transmitted instantaneously by WebRTC applications. As [START_REF] Počta | A Black Box Analysis of WebRTC Mouth-to-Ear Delays[END_REF], we obtained a mouth-to-ear delay of around 150 ms, which is pretty good according to telecommunication standards (ITU, 2003). This delay means, though, that there is an echo effect: the pilot R can hear her/his voice emitted by the loudspeakers of the robot and recorded by its microphones. This echo effect can greatly affect the quality of communication, so we used an algorithm of echo-cancelation. It consists simply in reducing the volume of R's headphones when s/he is talking, and waiting 150 ms before returning to the usual volume.

Noise sources

We used two loudspeakers JBL GO+ as sound sources. One was placed next to a coffee machine in the corridor adjacent to R's room. It diffused an amplified audio recording of the coffee machine startup (condition B). The other loudspeaker was placed in a room adjacent to L's room and diffused drill noises (condition D), which were pre-recorded with the microphones of the robot (condition C). Both sound sources were calibrated at 55 dB(A) with a sound level meter (Lutron SL-4001) placed at the location of the subjects. Moreover, the local space was particularly reverberant, with a reverberation time of about 0.8 s.

Recordings and calibration

The voices of both subjects were captured by two wireless headworn microphones Sennheiser HSP4 and digitalized with an audio interface UR22MKII (Steinberg). R's signal was sent to L through the loudspeakers of the robot. However, L's signal was only used for measurement purpose. What R heard of the local space was recorded by the microphones of the robot. In addition, the signal of the internal microphone of the computer, as well as the monitor signal of the stream heard by R were also recorded, in order to be able to track noise occurrences.

The headphones worn by R were an AKG K242. They were calibrated with an artificial ear (Brüel & Kjaer), in order to make the sounds perceived by R as loud as those in L's room. The sound attenuation through these headphones is negligible. The loudspeaker of the robot was also calibrated with a sound level meter (Lutron SL-4001), to ensure that the loudness of R's voice was faithfully transmitted.

Analysis of the results

14 groups of 2 subjects participated in this experiment. Most of them were native French speakers (25/28), two were fluent in French and one has a basic level, but sufficient to read the questions. Noise sequences were annotated and we extracted each keyword answered by subjects R (ex: "green"), and each pattern of questions read by subjects L (ex: "What is the color of…?"). We studied only the keywords / questions which were repeated at least 50 times among all the tests.

Recordings were filtered with a A-weighting digital filter (Zhivomirov, 2019) and voice intensity was computed by segments of 20 ms. Global results for maximum intensity can be seen on Figure 2. However, these results hide a great variability between subjects and between key-words / questions which could bias the analysis. Indeed, the number of each keyword in each condition varies from on experiment to another, because the answers of subjects R are not constrained. Therefore, in order to properly quantify the differences between each condition, we implemented a linear mixed effect model with R, following the tutorial of [START_REF] Winter | Linear models and linear mixed effects models in R with linguistic applications[END_REF]. This method allows to build a very simple model from the data, and at the same time, it provides measures of statistical significance. Written in R formula, this model is:

𝑚𝑎𝑥 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 ~ 𝑛𝑜𝑖𝑠𝑒 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛 + (1|𝑘𝑒𝑦𝑤𝑜𝑟𝑑) + (1|𝑠𝑢𝑏𝑗𝑒𝑐𝑡)

Figure 2. Maximum intensity in each noise condition

Summary of the models are shown in Table 1. They are coherent with the previous visualization, which means that we can base our observations on both figures. First, we note that the subjects R increased their maximum intensity in the 3 noisy conditions, while the subjects L spoke louder only in condition D, that is, when they could hear the noise. This shows that the Lombard Effect can be observed during telepresence robotics. However, it seems that for everyday noise with a moderate intensity level and when the subjects are focused on a question/answer task, this effect is very small, in the range of 1 to 3 dB. By way of comparison, [START_REF] Alison | Speech Breathing and the Lombard Effect[END_REF] found an increase up to 10 dB SPL with a Cocktail party noise at 55 dB SPL for reading and monologue tasks. Another interesting result is that the increase of intensity for subjects R depends on the noise condition. It is higher in condition B vs C and D, namely when the noise was played in the same room as the pilot, and not in the headphones, which is the opposite of the results expected from [START_REF] Garnier | Influence of Sound Immersion and Communicative Interaction on the Lombard Effect[END_REF]. However, the noises used in condition B were very different from the ones used in C/D. Indeed, they presented some intensity spikes up to 61 dB(A). Moreover, a posteriori recordings with the robot in R's room also showed that the intensity of the noises B was about 3 dB louder during stationary phase than the noises C/D. Besides, it is worth noticing that while the subjects R were talking, the volume of their headphones was reduced from 50% to 10%, in order to perform echo cancelation, which means that the intensity of noises C/D was greatly reduced at the time they spoke, which was not the case in condition B.

Subjects

The most interesting result concerns the difference between condition C and D. The subjects R heard the same noises in both conditions, but their increase of intensity was greater in condition D, when the subjects L could also hear the noise and adapt to it. This may highlight an effect of entrainment: the subjects R increased their voice intensity not only because of the noise, but also because their interlocutors L were speaking louder. Such observations were also made by [START_REF] Székely | The Effect of Soft, Modal and Loud Voice Levels on Entrainment in Noisy Conditions[END_REF]. However, this effect was not observed for the subjects L, who did not increase their voice intensity in condition B and C. This may be explained by the nature of their task (reading) or because they were not able to hear the noise which made their interlocutors speak louder.

Discussion and conclusion

In order to study the Lombard effect in the context of telepresence robotics, we performed an experiment with pairs of subjects (R and L), focused on a question/answer task. Four noise conditions were tested: A -without noise, B -only R hears the noise, C -only R hears the noise over headphones, and D -R and L hear the noise. The noise occurrences were very short and perceived as accidental by the participants. However, whenever they were able to hear the noise, they had a tendency to speak a bit louder. An entrainment effect was also noted for the subjects R, who spoke louder when L could also hear the noise. These increases of voice intensity being very subtle, they could easily be mistaken as expressive variations indicating socio-affects. Further work will involve comparing the pitch and durations of vocal productions in the four different noise conditions.

Figure 1 .

 1 Figure 1. Experimental set-up.

Table 1 .

 1 Results of the linear mixed effect model (applied separately for R-data and L-data).

				R			Subjects L
	Condition	A	B	C	D	A	B	C	D
	Maximum intensity (dB)	64.61	+ 2.98	+ 1.19	+ 2.38	69.19	-0.06	-0.30	+ 2.24
	Standard error (dB)	1.11	0.36	0.37	0.36	1.86	0.21	0.21	0.20
	Number of extracts	1263	160	146	150	1125	118	129	143
	Statistical significance	𝜒 2 (1) = 98.47 ; 𝑝 < 2.2 𝑒 -16	𝜒 2 (1) = 132.59 ; 𝑝 < 2.2 𝑒 -16
	Statistical significance was obtained by comparison with the null-model: 𝑚𝑎𝑥 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 ~ 1 + (1|𝑘𝑒𝑦𝑤𝑜𝑟𝑑) + (1|𝑠𝑢𝑏𝑗𝑒𝑐𝑡)

Acknowledgements

We would like to thank Coriandre Villain (GIPSA-lab) for his technical assistance during the calibration. Thanks also to Emeline Le Goff and Zoé Giorgis (Univ. Grenoble Alpes) for their support during the development of the experimenter's interface and for annotating the data.