Julien Meyer
email: julien.meyer@univ-lyon2.fr

Whistled speech: convergences with sung speech ACOUSTIC FEATURES AND PERCEPTIVE CUES OF SONGS AND DIALOGUES IN WHISTLED SPEECH: CONVERGENCES WITH SUNG SPEECH

Whistled speech is a little studied local use of language shaped by several cultures of the world either for distant dialogues or for rendering traditional songs. This practice consists of an emulation of the voice thanks to a simple modulated pitch. It is therefore the result of a transformation of the vocal signal that implies simplifications in the frequency domain. The whistlers adapt their productions to the way each language combines the qualities of height perceived simultaneously by the human ear in the complex frequency spectrum of the spoken or sung voice (pitch, timbre). As a consequence, this practice underlines key acoustic cues for the intelligibility of the concerned languages. The present study provides an analysis of the acoustic and phonetic features selected by whistled speech in several traditions either in purely oral whistles (Spanish, Turkish, Mazatec) or in whistles produced with an instrument like a leaf (Akha, Hmong). It underlines the convergences with the strategies of the singing voice to reach the audience or to render the phonetic information carried by the vowel (tone, identity) and some aesthetic effects like ornamentation.

INTRODUCTION

The pronunciation of spoken or sung words has been naturally adapted into whistles in several cultures. This complementary form of speech is used to overcome ambient noise and fight reverberation when the speaker is far from his interlocutor or from his audience. Its first functional use is to guarantee a good intelligibility of sentences in conditions for which spoken dialogues would be inefficient. Moreover, it is popular in some cultures for its aesthetical qualities and is therefore used to emulate songs. Such a traditional oral behaviour has been recently documented as still surviving in at least 14 languages all over the world: in Africa (Ewe, Ari), in Asia (Akha, Hmong), in America (Chinantec, Gaviao, Mazatec, Mixtec, Siberian Yupik, Surui), in Europe (Greek, Spanish, Turkish), in Oceania (Abu-Wam) [START_REF] Meyer | Description typologique et intelligibilité des langues sifflées: approche linguistique et bioacoustique[END_REF].

To emulate in whistles a sentence of his language, the whistler encodes the words in a modulated narrow band of frequency [START_REF] Busnel | Whistled languages[END_REF]. The main acoustic transformation is therefore in the frequency domain: from the multidimensional frequency spectrum of the voice to the mono-dimensional one of whistles. At the perceptive level, the linguistic information is synthesized in a single whistled pitch. On the contrary, the signal of the voice carries two perceptive qualities of height that are combined differently in each language to encode the words. These two qualities are the ones that have been observed in several perceptive tests in musical acoustics: (i) the perceptive sensation resulting from the F0, called pitch; and (ii) the perceptive sensation resulting from the complex aspect of the frequency spectrum, called timbre in music [START_REF] Risset | Sur certains aspects fonctionnels de l'audition[END_REF]. For example, pitch plays a primordial role in the intelligibility of several tone languages and the timbre space strongly characterizes the quality and the identity of a vowel through the formants. In response to these aspects, the whistled practices have adapted to the phonological rules of organisation of sounds of the transposed languages, selecting salient cues to optimise the intelligibility of the receiver.

The present paper underlines the convergence of some aspects of whistled speech with the singing voice while providing an overview of this phenomenon. A particular attention is drawn to the practice of popular singing and to the diversity of the concerned languages. Most of the whistled data analyzed here was documented since 2003 during fieldwork projects associating local researchers.

ACOUSTIC ADAPTATATION TO CONSTRAINTS Production

In whistling and singing, mastering the technique of production requires a phase of learning. An efficient emission relies on a homogenous, powerful, relaxed and precise control of both the air flow and the physiological constraints imposed by such types of articulations of words. In comparison to speaking, both increase the tension of the muscles of the vocal tract. These tensions reinforce the concentrations of energy in the signal because, apart from aesthetical and intelligibility exigencies that whistled and sung speech share in some cases, both have the common aim to carry the oral sound in the distance. As a sound source, the singing voice uses the vocal chords and a vocal tract often modified by a low larynx and large pharynx. The resulting signal bears a complex frequency spectrum characteristic of the human voice and largely described in the literature. For whistling, the lips are tight and the sound is produced by the turbulence of the air forced either into the smallest hole of the vocal tract or against an edge (depending of the technique). The reduced mouth cavity acts as a resonator to tune the sounds (figure 1). In some cultures a leaf can be used to whistle a message with a linguistic attitude, in these cases, the properties of vibration this instrument also play an important role (figure2).

Strategies to reach the audience

The acoustic strategies of whistling and singing share a common behavior in a significant band of frequency. The singing voice of a trained singer shows a concentration of energy between 2 and 4 kHz, especially for classical operatic singers of western music. It is formed by the proximity of two or three of the formants 3, 4, 5 or by the amplification of one of the formants already situated in this frequency domain. It has been called the Singing Formant and is sufficiently compact to favour a perceptive integration of the concerned frequencies [Bartholomew 34, Sundberg 1972[START_REF] Sundberg | Level and center frequency of the Singer´s Formant[END_REF]. In parallel, all whistled forms of languages use functional frequencies of whistling between 1 kHz and 4 kHz. In both cases, two reasons justify the choice of these bands of frequencies: firstly they place the signal above most of the concurrent frequencies of the performers´ environment; secondly they cover a domain that corresponds to the best performances of hearing in terms of selectivity and audibility. As a consequence the signal to noise ratio (SNR) at the reception is sufficiently high for a good perception. For example, in the case of singing, [START_REF] Pierce | The Science of Musical Sound[END_REF]cited by Woisard-Bassols, 2001] showed that the perception of the singer's voice above a chorus or an orchestra relies essentially on the singing formant. He measured that the SNR at its peak (2500 Hz) for a tenor voice was around 30 dB. Similarly, in the case of whistled speech, the signal remains largely above the natural background noise at relatively long distance. For example: an equivalent SNR of 30 dB -SNR measured in the frequency band of whistles-is obtained at around 200 m of the whistler for a sentence produced at 90-100 dB in a quiet environment (around 40 dB of noise). Apart from this common attitude, singing and whistling also show proper characteristics due to their sound source: sung speech shows amplifications around formant 1, whereas the whistled signal is shaped as a natural telecommunication system. Indeed, the bandwidth of its fundamental frequency emerging from the noise is less than 500 Hz, and its dynamic in amplitude is reduced compared to spoken speech [START_REF] Meyer | Whistled speech and whistled languages[END_REF]. Contrary to what occurs in the singing voice, the harmonics do not group in formants and do not play a fundamental role in speech recognition.

PHONETIC STRATEGIES: CONVERGENCES

Lengthening of vocalic duration

When compared to the spoken form of speech, the vocalic duration in the whistled form of speech is increased. Differences occur in function of the distance of the interlocutor. I measured that, for a dialog made at 150 m of distance, the vowels lasted meanly 26 % more in whistled Turkish than in spoken Turkish and 28 % more in whistled Akha than in spoken Akha of North Thailand. Some differences may appear in function of the individuals, as shown by [START_REF] Moles | Etude sociolinguistique de la langue sifflée de Kuskoy[END_REF] in whistled Turkish as the speakers keep their characteristics of elocution during the whistled articulation. At very long distances of practice (several km) or for the sung mode of whistled speech, the lengthening of the vowels can reach meanly 50 %; with some vowels much more emphasized than others. Contrary to what occurs in singing, such exaggerated durations do not reduce the intelligibility but still ease it. Indeed, the vowels with a very long duration are most of the time situated at the end of a speech group; this way, they help to sequence rhythmically a sentence in coherent units of meaning.

The sung form of speech is also characterized by an increase in vowel duration in most of the singing styles. It is the result of the combination of many parameters influencing the production in singing voice. First, artistic choices justify this strategy, for example to control the homogeneity of the timbre quality, especially in the bel canto technique [START_REF] Woisard-Bassols | Phonetique et articulation[END_REF]. Moreover, a slower tempo is often inherent to music and results in a slower rate of speech. Then, the articulatory movements last longer because of their greater range of variation [Scotto Di Carlo, 2005b]. Finally, this phonetic attitude partly relies on the fact that it is efficient to ease the perception of the voice quality and therefore favour a comfortable listening. In a similar way to what occurs in shouted and whistled speech, vowel lengthening is also an adaptation to the difficult conditions of communication. Within certain limits this phenomenon increases intelligibility; yet, when the duration of the vowels is beyond a tolerance threshold, the performances of recognition are affected and decrease [Scotto di carlo, 2005a].

Influence of the language phonology

The case of whistled speech As explained in introduction, among the several languages of the world that have been compared according to their whistled behaviour, different types have been highlighted [START_REF] Meyer | Description typologique et intelligibilité des langues sifflées: approche linguistique et bioacoustique[END_REF]]. In most of the tone languages (like Mazatec, Chinantec, Akha, Hmong) whistling selects primarily pitch cues carried by tone registers and tone contours. In most of the non tonal languages (like Greek, Turkish, Spanish) it selects primarily timbre elements carried by segmental cues of the voice; and in an intermediary category of languages it selects cues from both pitch and timbre by jumping in real time for one to the other (tonal Surui, non tonal Siberian Yupik and Chepang). In fact, for each language the whistlers give priority in frequency to a dominant trait that is carried in the spoken voice either by the formant distribution (most of the non tonal languages; figure 3, left side) or by the fundamental frequency (most of the tonal languages; figure 3 right side). But in the case of an incipient tone language like Chepang or a language using a lot stress like Siberian Yupik, the contribution of both is balanced, which explains their intermediate strategy in whistles. The reduction of the frequency space in whistles classifies therefore the languages in typological categories. These categories depend on the respective roles played by the Fo and the formant distribution in the intelligibility of the spoken form. For example, in a tone language, variation in pitch or its physical correlate, fundamental frequency (F0), is used to contrast word meaning. Sometimes its contribution to intelligibility is greater than vowel identity, like in Chinese (17% for tones vs. 12 % for vowels [Fu and al 1997]) whereas in other languages like the two-tone Surui of Amazon, it is not enough to encode a large vocabulary of words. On the contrary, in several non tonal languages, the information encoded in the Fo -like stress-plays a secondary role for intelligibility whereas the aspects encoded in the formants are primordial (vowel identity and consonant transitions). The typology of whistled form of speech available in [START_REF] Meyer | Description typologique et intelligibilité des langues sifflées: approche linguistique et bioacoustique[END_REF] underlines that the specificities of each language are mirrored in whistled speech.

Comparison with sung speech

In a similar way to what occurs in whistled speech, the contributions for encoding the word meaning of both the Fo and the formant distribution may influence the composition and the interpretation of songs. Yet, due to the complex frequency spectrum of the singing voice, testing this aspect is less simple. Furthermore, other parameters enter in consideration: sung speech is not only focused on intelligibility as it takes into account artistic priorities that might interfere with the phonetics and the identification of words. For example, in operatic singing a soprano voice is much less intelligible than a bass [Scotto di Carlo 2005b]. Moreover, within a language there may be a wide range of variation between different styles of songs, some of them been borrowed from other cultures.

For the singing voice in non tonal languages, the research has been logically focused on understanding the aspects of the formant distribution influencing intelligibility [START_REF] Gottfried | Intelligibility of vowels sung by a countertenor[END_REF]Scotto di Carlo 2005b]. One of the main results is that the higher is the pitch, the more difficult is the identification of the phonemes. Moreover, the difficulty to identify the vowels in sung speech has been also attributed to the fact that the formants 2 and 3 are less phoneme-dependent than in spoken speech. These results underline that the intelligibility is advantaged when the frequency spectrum shows compact formants with a phoneme-dependent distribution. Such a conclusion is consistent with the fact that the human perception is sensible to formant proximity, especially for identifying the vowels [START_REF] Chistovitch | The center of gravity effect in vowel spectra and critical distance between the formants: psychoacoustical study of the perception of vowel like stimuli[END_REF][START_REF] Schwartz | A strong evidence for the existence of a large scale integrated spectral representation in vowel perception[END_REF]. For whistled speech it is an important aspect as such proximities would explain the frequency distribution of whistled vowels in non tonal languages [START_REF] Meyer | Description typologique et intelligibilité des langues sifflées: approche linguistique et bioacoustique[END_REF], with /i/ among the highest frequencies, /o/ among the lowest and /e/ and /a/ in between (figure 4). It would explain also the good performances of non whistlers of such languages to identify whistled vowels, /i/ being perceived as an acute timbre in spoken speech, and /o/ as a low one [START_REF] Meyer | Identification of whistled vowels by nonwhistlers[END_REF]. In the case of tone languages, the Fo parameter of singing voice is easy to test. For example, [START_REF] Wong | How can the lyrics of a song in a tone language be understood?[END_REF] investigated songs of Cantonese to further understand how songwriters reconcile the possible linguistic role of F 0 variation in expressing a lyric with the musical role of F 0 variation in specifying melodic intervals. According to their preliminary enquiry three options appear: "The first is to ignore lexical tones and word meaning and to use pitch exclusively to mark the melody. […] The second option is just the reverse: to preserve the normal pitch variations of lexical tones while ignoring the melody, sacrificing musicality for intelligibility.[…] The third option is intermediate between the first two. […] This preserves musicality at the cost of reduced lyric intelligibility." [Wong and Diehl 2002, p. 203]. These three attitudes have been observed in several studies: (i) the first option preserves musicality at the cost of reduced lyric intelligibility. It concerns mostly fixed melodies imposed to lyrics. [START_REF] Chao | Tone, intonations, singsong, chanting, recitative, tonal composition, and atonal composition in Chinese[END_REF] reported having observed it in Chinese contemporary songs. Similarly, [START_REF] Saurman | The agreement of Thai speech tones and melodic pitches[END_REF] measured the direction of pitch change over consecutive syllables in tones and song pitches: they matched in only 32 % of the cases for the Thai national anthem and 42 % for a foreign hymn translated into Thai. In Mexico, Casimiro [2007, pers. com.] reported the same phenomenon for the Mexican national anthem sung in Mazatec language at school. (ii) In the case of the second option, songs are very speech-like. It is the case of singsong themes in Chinese described by [START_REF] Chao | Tone, intonations, singsong, chanting, recitative, tonal composition, and atonal composition in Chinese[END_REF]. Moreover, according to the description of [START_REF] Van-Khe | Musique du Viet-Nam[END_REF] this option generally concerns a large body of traditional popular songs in Vietnam and of several cultures of South East Asia: "In the popular traditions of South-East Asia the improvisation is mostly poetic. The melody of the songs must follow the linguistic intonation of their text otherwise it would change the poetic signification" [ [START_REF] Van-Khe | Musique du Viet-Nam[END_REF]. [START_REF] Saurman | The agreement of Thai speech tones and melodic pitches[END_REF] confirmed this assertion for traditional Thai songs. I measured that it is also the case for popular songs in Akha language of North Thailand. Classical styles of singing are also concerned by this option. For example, [START_REF] Yung | Creative process in Cantonese opera I: the role of linguistic tones[END_REF] found a melody-tone relationship in Cantonese opera, that was somewhat similar to what [START_REF] Chao | Tone, intonations, singsong, chanting, recitative, tonal composition, and atonal composition in Chinese[END_REF] reported in singsongs. (iii) In the case of the third option: "songwriters may attempt to preserve at least partially the pitch contrasts of lexical tones while not unduly restricting the melodic role of F0 changes." [Wong and Diehl, 2002, p. 203]. Wong and Diehl proved that this strategy was at play in several contemporary songs in Cantonese. They not only examined the strategies used by composers and singers to reconcile linguistic and musical roles of F0, they also proved that corresponding strategies are used by listeners to extract the lexical meaning of the lyric: listeners apply an ordinal mapping rule in assigning tone categories.

SUNG MODE OF WHISTLED SPEECH: A FIRST APPROACH

The sung mode of whistled speech is the practice that consists of emulating the sung voice while producing a whistled sentence. It is not an aspect extensively developed in all the cultures concerned by whistled speech. It seems much more common in tone languages. It must be due to the fact that such languages often reconcile melody and meaning in singing them through a same physical parameter (Fo, see preceding paragraph). Usually, repertoires of old popular songs are concerned by this practice. Yet it is sometimes adapted to contemporary songs.

As an example, I present the Akha sung speech whistled with a leaf. Akha is a three tone language of south-east Asia for which whistled speech transposes primarily the Fo. It has a very rich oral repertoire of songs. Some of them, such as love songs, are more often used with whistling because the sung leaf is popular for courtship. As the aim is to transmit a poetic message, the melody of the songs follows the pitch of their lyrics. The acoustic propagation of this type of signal enables the message to reach easily the lover inside his/her wooden house (physical justification). The whistlers also say that whistling is more melodic (aesthetical justification). Indeed, several acoustical features are consistent with this second justification. First, whistling with an instrument like a leaf gives more sound energy to the harmonics (figure 5). Then the singers use classical techniques of ornamentation: they combine vowel lengthened durations with a vibrato. Finally, the singers impose at their sung sentence a modified rhythm: for example the rhythm is often iambic (stress is marked by a lengthened duration). The tone perception is not perturbed by the oscillations produced by the vibrato as these do not transcend the median frequency of the interval separating two tones (the tones of a same sentence do not overlap even in vibrato, figure 5).

CONCLUSIONS

Whistled and sung speech share several acoustic, phonetic and articulatory properties underlined in this paper. Such a comparative approach has also detailed how the phonology of a language influences both sung and whistled adaptations of speech. As the research on the singing voice has a long history, several phonetic results in this domain contribute to better understand the strategies of transformation of the spoken voice into whistles. For example, they provide an alternative point of view on the perception of the formant distribution, which is primordial to whistle a non tonal language. Finally, in some cultures sung and whistled speech merger in a one phenomenon that was called the sung mode of whistled speech. All these aspects have been illustrated thanks to unprecedented data collected in the field during the last four years.

Figure 1 :

 1 Figure 1: Open vocal tract. While singing (left) and while whistling (right)

Figure 3 :

 3 Figure 3: Left, a Turkish word spoken and whistled (/getirmek/). The /t/ in indicated. Right, a word spoken and whistled -pitch transposition-in Mazatec (4 tone language).

Figure 4 :

 4 Figure 4: Frequency distribution of whistled Spanish vowels

Figure 5 :

 5 Figure 5: Extract of an Akha song whistled with the leaf, with ornamentations.


Julien Meyer
email: julien.meyer@univ-lyon2.fr

Fanny Meunier
email: fanny.meunier@univ-lyon2.fr

Laure Dentel
email: laure.dentel@theworldwhistles.org

Identification of Natural Whistled Vowels by Non-Whistlers

Keywords: speech perception, vowel identification, whistled speech, whistled languages, speech model

come   L'archive ouverte pluridisciplinaire

Introduction

Whistled speech of languages represents a little studied style of speech shaped for distant dialogues [START_REF] Busnel | Whistled languages[END_REF]. It consists of an emulation of the spoken voice based on modulated whistles and thus called 'whistled language'. In the typology of whistled languages, Spanish whistled strategy emulates primarily segmental acoustic cues of vowels and consonants [START_REF] Meyer | Description typologique et intelligibilité des langues sifflées : approche linguistique et bioacoustique[END_REF]. In order to deepen the understanding of the perception of such natural whistled vowels and their links to the vowels of the spoken speech, two variants of a same experiment were developed. We observed the whistled vowel categorisation performances for subjects who knew nothing about whistled languages. The performances of a native whistler of Spanish whistled language (Silbo) are also provided for reference. Participants had to recognize the four vowels /i, e, a, o/ in a simple and intuitive task. They did not receive any feedback on their performances or any information concerning the distribution of the whistled vowels before the end of the test. The first experiment tested the vowels presented on their own, without any context (Experiment A) while the second experiment tested the vowels presented in the context of a sentence (Experiment B).

Method

Participants

The tested subjects were 40 students of 19 to 29 years old who were French native speakers. 20 persons have performed Experiment A (vowels on their own), and the 20 others Experiment B (sentence context). The students' normal hearing thresholds were tested by audiogram. The participants had never listened to whistled speech before or to an explanation of the distribution of the vowels in non tonal whistled speech.

Stimuli

The tested four vowels from the Spanish whistled language of La Gomera (called Silbo) are: /i/, /e/, /a/, /o/. These vowels also exist in French with similar or close pronunciations [START_REF] Calliope | La parole et son traitement automatique[END_REF]. Another reason for this choice of four whistled vowels was that they have the same kind of frequency distribution in Greek and Turkish [START_REF] Meyer | Description typologique et intelligibilité des langues sifflées : approche linguistique et bioacoustique[END_REF][START_REF] Meyer | Whistled Turkish: statistical analysis of vowel distribution and consonant modulations[END_REF]. Given the structure of French, one can reasonably expect that whistled vowels of French would bear the same scale. The experimental material consisted of 84 vowels, all extracted from the recording of 20 long semispontaneous sentences whistled relatively slowly in a single session by the same whistler in controlled conditions (same whistling technique during the entire session, constant distance from the recorder and from the interlocutor and background noise between 40 and 50 dBA). These 84 vowels (21 /i/, 21 /e/, 21 /a/ and 21 /o/) were chosen by taking into account statistical criteria based on the analysis of whistled vowels in Silbo [START_REF] Meyer | Description typologique et intelligibilité des langues sifflées : approche linguistique et bioacoustique[END_REF]. First, the mean frequency of a whistled vowel is much easier and precise to measure than spoken formants as each occurrence of a whistled vowel is a rather stable and simple pitch. Next, each vowel is whistled in a specific interval of frequency values corresponding to the articulatory variability of the concerned vowel type. Silbo vocalic system is the result of a whistled emulation of the Spanish dialect spoken in the Canary Islands in which /o/ and /u/ are often assimilated [START_REF] Classe | The whistled language of La Gomera[END_REF]. The spoken vowels (i, e, a, o, u) are therefore whistled in five frequency intervals, two of which largely overlap. Four intervals are statistically different: /i/, /e/, /a/ and /o, u/ in a decreasing order of mean frequencies. Moreover, we excluded final vowels of sentences from the vowels presented in our experiments as they are often marked by an energy decrease. Finally, the selected vowels were chosen inside a confidence interval of 5% around the mean value of the frequencies of each vocalic interval. In this sense, the vowel frequency bands of the experiments do not overlap The sounds played in the Experiment A concerned only the vowel nucleus without the consonant modulations, whereas the stimuli of the corpus of Experiment B kept the part of whistled sentence preceding the vowel during two to three seconds. This second experiment aimed at testing the effect of the acoustical context on the subject and to get rid of some bias that might appear because of presenting nearly pure tones one after another. As a consequence, this second corpus consisted of 84 whistled sentences ending by a vowel. For both variants, among the 84 sounds, 20 (5 /i/, 5 /e/, 5 /a/, 5 /o/) were dedicated to a training phase and 64 (16 /i/, 16 /e/, 16 /a/, 16 /o/) to the test itself.

Design and procedure

For each experiment, participants listened to whistled vowel and right afterward selected the vowel type that he/she estimated was the closest to the one heard by clicking on one of the four buttons corresponding to the French letters « a », « é », « i », « o ». The task was therefore a four alternative forced-choice (4-AFC). The interface, programmed in Flash-Actionscript, controlled the presentation of the sounds: first the 20 sounds of the training phase in an ordered list containing all the possible successive combinations of vowels; then, the successive 64 sounds of the test in a nonrecurrent random algorithm. The subjects where tested in a quiet room with high quality Sennheiser headphones.

Results

A specific program was developed to summarize the answers in confusion matrices (tables 1, 2, 3, 4) and to present them graphically by reintegrating some information regarding for example the frequency distribution of played vowels (figure 2 and 3).

Reference performances of a whistler

In table 1 we present the performances of whistled vowel identification of a native whistler of La Gomera (Experiment A on isolated vowel, which represents the most difficult task). These performances confirm with a high level of correct answers (87,5 %), that a native whistler practicing nearly daily the Spanish whistled speech identifies accurately the 4 four whistled vowels [X 2 (9)=136.97, p<.0001] [START_REF] Meyer | Whistled Turkish: statistical analysis of vowel distribution and consonant modulations[END_REF]. The variability of pronunciation of the vowels in spontaneous speech and the distribution of the played vowels (figure 1) explain the few confusion errors. 0.00 /a/ 6.25 75.00 18.75 0.00 /e/ 0.00 6.25 87.5 6.25 /i/ 0.00 0.00 0.00 100.00

Identification of isolated vowels (Experiment A)

The mean level of success corresponding to correct answers was of 55%. Considering the protocol and the task these results are largely above chance (25 %) [X 2 (9)=900.39, p<.0001)]. But the mean rates of correct answers varied largely in function of the vowels. Moreover, most of the confusions can be qualified of logical in the sense that a vowel was generally confused with its frequency neighbouring vowels (83% of the cases of confusion: bold letters in table 2). In order to determine the influence of the individual frequency of each played vowel on the pattern of answers of the subjects, the results of the answers have also been presented in function of the frequency distribution of the whistled vowels presented during the experiment (figure 2). In this figure, appear also the estimated curves of the answers of the subject, averaged by polynomial interpolations of the second order.

Individual variability

Two participants have very high performances with 73,5 % of correct answers. Then a group of six persons has more than 40 correct answers for 64 sounds (62,5%). Four other persons follow them with more than 58% of correct answers. This means that half of the participants have good performances to the test. The ten other participants all have performances above 37% but below 54% of correct answers. Generally speaking, the less efficient participants still had a confusion matrix with logical confusions. Their relatively low performances were often due to a systematic confusion between two whistled vowels neighbour at the level of the frequencies. The variability of the performances depended on the concerned vowel: (i) for /i/ most of the participants had very good success results as 16 of them obtained a score over 75% and two even 100% of correct answers. The less efficient participant reached a rate of 56% of correct answers. (ii) For /o/, six persons identified more than 62,5% of the vowels. All the others often thought the /o/ is an /a/. (iii) The /a/ was the least well-identified letter, often mis-categorised as an /e/ or sometimes as an /o/. (iv) The /e/ was confused equally with its whistled neighbours /a/ and /i/. The lower performances for /a/ and /e/ can be partly explained by the fact that they both have two perceptive neighbours in terms of pitch, a situation which multiplies the possibilities of confusion in comparison to the more isolated vowels /i/ and /o/. In spite of this situation, the most efficient participants categorized them successfully as different vowels throught the pitch they perceived. Finally, the more frequent confusions were the following: the /o/ was often thought of as an /a/ and the /a/ and the /e / were reciprocally often mistaken one another, partly because of the proximity of their intervals of whistling.

Musicians vs. non-musicians

Among the subjects of this experiment, six were musicians. The results of this group were significantly different from the non-musicians [F (1,18)=6.71, p<.02]. One can therefore say that the musicians had more success to the task of the test than the non-musicians (64% of correct answers versus 51%).

Discussion

All the analysie detailed above support the fact that the French subjects were able to categorise the whistled vowels « a », « é », « i », « o », however they were not as accurate as a whistler from la Gomera Island [p<.001]. Nonetheless, the tendencies of the curves of correct answers show that the French-speaking subjects in general have good performances to the task. These results occur despite presenting isolated vowels without any sound context except the one of the preceding listened vowel. Indeed, some participant performances revealed some effect of one vowel on the following answer. For example, if for a whistled /e/ an answer /a/ was given and if the following played vowel was an /a/ the participants had the tendency to mistake it with /o/. Consequently, one can observe a cascading effect of logical confusions that stops when there is a significant frequency jump. This confirms that non-whistlers subjects perceptively floor their vowel prototypes in a distribution that depends on the frequency. In these conditions, it is not surprising to note that the musicians have better performances because they are more used to associating an isolated pitch to a sound reference culturally marked. Despite randomisation of item presentation this cascading effect is difficult to control with only four types of vowels,. For this reasonm, we developed Experiment B.

Identification of vowels with preceding sentence context (Experiment B)

This second experiment aimed at testing the effect of the context on vowel perception. Particularly we hypothesized that by an approach nearest to the ecological conditions of listening of whistlers -who do not perceive the vowels isolated but integrated in a sound flux -one could observe a suppression of the cascading effect of confusions. The results show the same general tendencies as for Experiment A, with slightly better performances for the identification task: 60,2% [X 2 (9)=1201.63, p<.0001]. The whistled vowels /o/ and /i/ were even better identified than in the Experiment A (respectively 73,13% and 87,81%) whereas the vowels /a/ and /e/ were slightly less well identified (see table 3 for percentages and figure 3 for estimated curves of answers).

Confusions and inter-individual variations

Eight persons had a success score above 62,5%. 3 other even have more than 73%. The best subject, a saxophonist who has learned the musical pitches through a particular technique of localisation of the sounds by association to a part of his body reached an overall score of 75%. In contrast, the least efficient participant obtained a score of 46% of identification, which was more than in Experiment A. For the confusions, the better scores for /o/ showed that it is less thought as an /a/, whereas /a/ was still often confused with /e/. Finally, and this is new, /e/ was often thought of as an /i/ with strong differences between participants. It was often at the level of the identification of /a/ and /e/ that differences were found between subjects with high scores and subjects with lower scores.

No difference between musicians and nonmusicians

Again, there were six musicians among participants (despite the fact that the participants of the two experiments were distinct). An analysis of variance similar to the one performed for Experiment A showed that this time the results of the musicians were not significantly different from those of nonmusicians [F (1,18)=6.71, n.s.]. The context effect eased the choice of the non-musicians without affecting the performances of the musicians.

Limited effect of training

Because of the elimination of the confusions specific to Experiment A, due to successive presentation of isolated vowels, it is relevant in Experiment B to compare the performances of the test to the performances of the training phase in order to see if there is a learning effect. One can note that again answer distribution is far from chance [X 2 (9)=1113.47, p<.0001] and the tendencies described in the test were already at play in the training (table 4). These results were obtained in a first contact to whistled vowels with only 20 occurrences of vowels. As a consequence, it supports the fact that the subjects rely on categorizations that are already at play in their linguistic use.

Discussion

The results obtained for the two experiments of identification show that participants whose native language has the same types of vowels as the Spanish /i, e, a, and o/, succeed in categorizing the whistled emulations of these vowels without any cues on the phenomenon of whistled languages and even if they listened to such whistled sounds for the first time. The fact that this ability is already stable during the training phase shows that the tested subjects were already familiar with a perceptual representation of the vocalic space in a frequency scale. This suggests that such a representation must play an important role in the process of identification of the spoken French vowels /i, e, a, and o/. To explain these results, one must consider which parts of the frequency spectrum of the spoken voice carry perceptual cues explaining the frequency distribution of whistled vowels in non tonal languages. It appears to be a key of vowel identification, even for languages with larger vocalic inventories like Turkish [START_REF] Meyer | Whistled Turkish: statistical analysis of vowel distribution and consonant modulations[END_REF]. Some results obtained on the basis of production support that the second formant (F2) plays an important role: Brusis [START_REF] Brusis | Über die phonetische Structur der Pfeifsprache Silbo Gomero dargestellt an sonagraphischen Untersuchungen[END_REF] was the first to notice that F2 often shows frequency shapes similar to the transposed whistled signal. On this basis, Rialland [START_REF] Rialland | A New Perspective on Silbo Gomero[END_REF] proposed that only F2 is transposed in Silbo. But F2 may well be only one of the parameters of a more complex phenomenon. By using a protocol based on perception, our experiments draw the attention on this option. For example, a distribution of vowels in frequency scales is characteristic of other perceptual studies based either on the notion of perceptual integration between close formants [START_REF] Chistovitch | The center of gravity effect in vowel spectra and critical distance between the formants: psychoacoustical study of the perception of vowel like stimuli[END_REF], or on the notion of « effective upper formant » (F2') [START_REF] Carlson | Some studies concerning perception of isolated vowels[END_REF]. According to Stevens [START_REF] Stevens | Acoustic Phonetics[END_REF] these notions highlight strong effects at play in the classification of vowels. For example, Schwartz and Escudier [START_REF] Schwartz | A strong evidence for the existence of a large-scale integrated spectral representation in vowel perception[END_REF] showed that a greater formant convergence explains better performances of vowel identification and a better stability of vowels in shortterm memory. Concerning Spanish, the human ear is sensible to the convergence of F3 and F4 for /i/, F2 and F3 for /e/ and F2 and F1 for both /a/ and /o/. The fact that /a/ and /o/ share the same formant convergence would participate to the fact that /i/ is identified with better performances than /o/ (/i/ and /o/ being with only one neighbour in whistled frequency).

Conclusions

Our results confirm that the whistlers rely on a perceptual reality at play in spoken speech to transpose the vowels in whistled frequencies. For research on Silbo it confirms the observation of Classe [START_REF] Classe | The whistled language of La Gomera[END_REF] that at least 4 whistled vowels can be phonetically distinguished by whistlers of La Gomera and therefore invalidates another theory often denounced by local whistlers that stated that only two vowels are perceived in Silbo [START_REF] Trujillo | El Silbo Gomero: analisis linguistico[END_REF]. Finally our experiments prove that whistled speech is a good model to further investigate the processes of perceptual selection in the complex distribution of vowel formants.

Figure 1 :

 1 Figure 1: Frequency distribution of the played whistled vowels of the experiments.

Figure 2 :

 2 Figure 2: Intuitive perception of the isolated Spanish whistled vowels by 20 French subjects (distribution of the answers in function of the played frequencies).

Figure 3 :

 3 Figure 3: Distribution of the answers in function of the frequencies of the whistled vowels. Intuitive perception of the Spanish whistled vowels by 20 French subjects (vowels with preceding context).

Table 1 .

 1 Confusion matrix for the answers of a native whistler for isolated vowels ( in %)

		Answered vowels
	Played vowels	/o/ /o/ 87.5 12.50 0.00 /a/ /e/	/i/

Table 2 .

 2 Confusion matrix for the answers of 20 subjects for isolated vowels ( in %).

		Answered vowels
	Played vowels	/o/ /o/ 50.63 40.31 7.50 1.56 /a/ /e/ /i/
		/a/ 13.44 44.06 31.56 10.94
		/e/ 5.94 22.19 46.88 25.00
		/i/ 0.00 4.38 17.19 78.44

Table 3 .

 3 Confusion matrix for the answers of 20 subjects for isolated vowels ( in %).

			Answered vowels
	Played vowels	/o/ /o/ 73.13 23.13 2.81 0.94 /a/ /e/ /i/
		/a/ 10.94 39.06 39.38 10.63
		/e/ 5.00 19.38 40.94 34.69
		/i/	0.31 1.56 10.31 87.81

Table 4 .

 4 Confusion matrix for the answers of 20 subjects in training phase, listening to whistled vowels in context (%)

		Answered vowels
	Played vowels	/o/ /o/ 59.00 22.00 13.00 6.00 /a/ /e/ /i/
		/a/ 20.00 32.00 36.00 12.00
		/e/ 6.00 16.00 49.00 29.00
		/i/ 2.00 5.00 9.00 84.00

Acknowledgements

The authors would like to thank the whistlers and the participants for their collaboration. This research was supported by the CNRS and the Fyssen Foundation.


Damien David
email: damien.david@insa-lyon.fr

Frédéric Kuznik

Jean-Jacques Roux

Experimental Investigation of Natural Convection Near a Wall Containing Phase Change Material

Keywords: Natural Convection, Phase Change Material, Convection coefficient, PCM in Building Walls, Building Inertia

An experimental investigation is conducted to characterize the natural convection heat transfer along panels which contain phase change materials (PCM). A dedicated configuration has been defined for this study. In this configuration, the natural convection heat transfer is triggered by a temperature scan in the ambient air. The temperature scan is responsible for the energy storage and release in the PCM panels. The corresponding experimental set-up was built and several melting and solidification tests were performed, with different values of the ambient temperature scan speed. The tested PCM panel is the Energain®wallboard by DuPont. The system first reaches a stationary regime when the PCM is fully solid or liquid. During the stationary regime, the wall to air temperature difference and the convection heat flux are constant. The phase change causes an increase of these quantities. It is characterized by a first dynamic stage, a wall temperature slowdown / retrogression process, and a second dynamic stage. The two dynamic stages are well correlated to the PCM thermal characteristics. However, the temperature slowdown / retrogression phenomenon is unexpected. It consists in an extreme slowdown of the wall surface temperature evolution, which turns into a retrogression during the solidification experiments. The temperature slowdown / retrogression has never been observed before with PCM wallboards.

Nomenclature

Specific Symbols b∞

Ambient Temperature growth rate (set point) (K/s) b∞ Ambient Temperature growth rate (measured) (K/s) cp w

Wall heat capacity (J/kg K) cp wl

Wall heat capacity value when the PCM is in the liquid state (J/kg K) ew

Wall thickness (m) g

Earth gravity (m/ s 2 ) h

Heat transfer coefficient (W/m 2 K) k

Air thermal conductivity (W/m K) kw

Wall thermal conductivity (W/m K) q w

Convection Heat flux at the surface of the wall (W/m 2 ) q rad

Radiative Heat flux at the surface of the wall (W/m 2 ) q cond

Conduction Heat flux at the surface of the wall (W/m Wallboards containing Phase Change Materials (PCMs) can be used to increase the thermal inertia of building envelopes. The potential benefits of those wallboards have already been demonstrated through several full-scale experimental studies. (Kuznik et al. [START_REF] Kuznik | Energetic efficiency of room wall containing pcm wallboard: a full scale experiment[END_REF], Liu and Awbi [START_REF] Liu | Performance of phase change material boards under natural convection[END_REF], Castell and Farid [START_REF] Castell | Experimental validation of a methodology to assess PCM effectiveness in cooling building envelopes passively[END_REF], Lee et al. [START_REF] Kyoung | Assessing the integration of a thin phase change material (PCM) layer in a residential building wall for heat transfer reduction and management[END_REF] etc).

However, those panels have to be integrated into building simulation software to quantify precisely their effect on the indoor thermal comfort and the building energy consumption. Of course, such simulation is necessary to optimize PCM wallboard parameters: the phase change material, the position of the panel, the thickness of the panel...

The PCM wallboards aim to regulate the temperature within building rooms. Then, they should be located as close as possible to the interior side of the walls. In that case, the main heat transfer mode between the PCM layer and the room is natural convection. The modeling of the natural convection heat transfer between the wall and the room is decisive to get accurate predictions of PCM effect in the building.

Usually, building simulation software use an averaged heat transfer coefficient h to model the natural convection heat transfer along a wall. The determination of the value of h has a predominant impact on the simulation accuracy. Indeed, David et al. [START_REF] David | Numerical study of the influence of the convective heat transfer on the dynamical behavior of a phase change material wall[END_REF] confronted four correlations from the literature to simulate the amount of energy stored in a PCM layer 1 . They found up to 50% discrepancies in their results depending on the correlation! Some numerical studies use a constant value of h for PCM walls simulation: Bastani et al. [START_REF] Bastani | Designing building envelope with PCM wallboards: Design tool development[END_REF] set h = 8W/m 2 K, Kong et al. [START_REF] Kong | Numerical study on the thermal performance of building wall and roof incorporating phase change material panel for passive cooling application[END_REF] set h = 8, 7W/m 2 K, Matthieu-Potvin et al. [START_REF] Fran | Thermal shielding of multilayer walls with phase change materials under different transient boundary conditions[END_REF] set h = 10W/m 2 K, and Zhou et al. reported values ranging from 5, 7W/m 2 K to 12W/m 2 K. However, it is well known that, for natural convection, the averaged convection coefficient should depend at least on the temperature difference between the wall and the indoor environment. Moreover, those values of h was determined in a configuration without the presence of PCM in the walls.

More precise numerical studies used correlations to determine the value of the convection coefficient. David et al. [START_REF] David | Numerical study of the influence of the convective heat transfer on the dynamical behavior of a phase change material wall[END_REF] confronted four correlations from the literature. Evola and Marletta [START_REF] Evola | The Effectiveness of PCM Wallboards for the Energy Refurbishment of Lightweight Buildings[END_REF] and Soares et al. [START_REF] Soares | Multi-dimensional optimization of the incorporation of PCM-drywalls in lightweight steel-framed residential buildings in different climates[END_REF] used the built-in correlation from the building simulation platform EnergyPlus. Ibanez et al. [START_REF] Ibanez | An approach to the simulation of PCMs in building applications using TRNSYS[END_REF] and Kuznik et al. [START_REF] Fr?d?ric Kuznik | Development and validation of a new TRNSYS type for the simulation of external building walls containing PCM[END_REF] used the built-in correlation from the building simulation platform TRNSYS. Again, all those correlations were developed in a case of no PCM within the wall. An interesting experimental feature of the convection heat transfer coefficient seems to exist in large-scale tests. Kuznik et al. [START_REF] Kuznik | Energetic efficiency of room wall containing pcm wallboard: a full scale experiment[END_REF] and Liu and Awbi [START_REF] Liu | Performance of phase change material boards under natural convection[END_REF] performed experiments in full-scale test rooms with PCM wallboards. Both authors observed a heat transfer intensification along the PCM walls during the phase change. They estimated the convection heat transfer coefficient, and they obtained values far above the values predicted by the correlations from the literature. More recently, Sun et al. [START_REF] Sun | Experimental observations on the heat transfer enhancement caused by natural convection during melting of solide-liquid phase change materials[END_REF] observed a similar phenomenon along the faces of a cube filled with PCM.

This phenomenon needs to be deeply investigated to understand the rising convective heat transfer coefficient, and to model accurately the heat exchanges in buildings. Then, in this paper, we propose to present experimental investigations of natural convection along PCM walls.

Most of the studies about natural convection over a flat plate are based on configurations not suitable for the study of the natural convection heat transfer over a PCM wallboard. Indeed, imposing a static temperature difference between the plate and the environment, or a constant heat flux near the plate does not reflect the heat transfer mechanisms occurring along building walls containing PCM. The first step of the study is the definition of an original configuration, which enables to reproduce these mechanisms. This original configuration is described in the first section of the paper.

The two following sections concern the experimental device, in which the studied configuration is reproduced. A description of the experimental apparatus is given is Sec.3. The experimental protocol is explained in Sec.4. The remaining sections are dedicated to the analysis of the experimental results.

Studied configuration

Description

The studied configuration is represented in Fig. 1. It is a semi-infinite vertical flat wall with adiabatic conditions on the back side. The temperature of the whole system is homogeneous at the beginning of each test. The heat transfer is triggered by a temperature scan in the ambient air:

T ∞ (t) = T ∞,0 + b ∞ × t (1)
The geometry of the present configuration is similar to the geometry of the configuration used by Neeper [START_REF] Neeper | Thermal dynamics of wallboard with latent heat storage[END_REF], Zhou et al. [START_REF] Zhou | Parametric analysis of influencing factors in Phase Change Material Wallboard (PCMW)[END_REF] or Bastani et al. [START_REF] Bastani | Designing building envelope with PCM wallboards: Design tool development[END_REF] to study PCM wallboards effects. It reproduces one of the heat transfer phenomena occurring in real buildings. The fluctuation of the air temperature within the room is due to the internal heat gains (heating or cooling systems, occupancy, sun...) and the heat transfers through the other walls. This temperature fluctuation causes a heat storage / release in the PCM wall. The heat transfer mechanism between the air and the PCM wall is natural convection.

To be consistent with the temperature evolution observed in real buildings, the value of the temperature scan speed b ∞ should lies between -2 /h and +2 /h. 2.2. Expected behavior Fig. 2 shows the expected behavior of the studied configuration during a solidification process (b ∞ < 0) and through the time evolution of two quantities: the average heat flux q w over the wall, and the average temperature difference ∆T w = T w -T ∞ . T w is the wall surface temperature and T ∞ the ambient air temperature.

At the beginning of the test, the temperature is homogeneous and equal to T ∞,0 . Then the ambient temperature decreases. The wallboard releases energy. The quantities ∆T w and q w increase before a stabilization at the first stationary regime.

During the first stationary regime, the PCM remains in the liquid state. The temperature in the plate decreases with the same rate b ∞ than the ambient temperature: the temperature difference ∆T w is constant. If the plate is sufficiently thin, the heat transfer within the plate along the vertical direction can be neglected. The surface heat flux q w (y, t) is homogeneous and constant. It is equal to the reference heat flux q ref which depends on the wall thickness e w , the wall density ρ w , and the wall heat capacity when the PCM is liquid c p wl :

q ref = -e w × ρ w × c p wl × b ∞ (2)
The regime of interest for this study is the perturbation due to the phase change, which is represented schematically on Fig. 2. The phase change in the panel causes a distortion of the heat flux and temperature profiles, which results in a modification of the heat transfer coefficient value.

A second stationary regime is reached when the phase change perturbation vanishes. During the second stationary regime, the PCM remains fully solid. The behavior of the system should be similar to the first stationary regime.

Experimental set-up

Design of the experimental device

The experimental device was built from an insulated cube. The inner dimensions of the cube are 2.4 m × 2.4 m×2.4 m. The cube is divided into two halves. During the experiments, the two half cubes are assembled to form a closed air circuit.

One half cube contains the air preparation unit (Fig. 3). It is devoted to the distribution of ambient air, with a low velocity and a controlled temperature. It contains an air handling unit, an air mixing volume, and two extractions located at the top and the bottom of the cube. The air handling unit holds a blower, a heating unit (1 kW ) and a refrigerating unit (5 kW ). The homogeneity of the supplied air velocity is ensured by a micro-perforated membrane. The velocity of the air passing through the membrane is about 50 mm/s. A central shield redirects the air supply and extractions to the edges of the chamber. Air Handling Chamber The second half cube contains the test chamber where the studied configuration is reproduced (Fig. 4). The test chamber is fully symmetric, to reproduce the adiabatic conditions on the back side of the test walls. A sandwich made of two test walls separated by a 6mm thick insulation layer is held at the center of the chamber. Each test wall is 1.6m high, 0.6m wide and 5mm thick.

The volume in front of each test wall is divided into a test volume and a mixing volume. Those volumes are separated by a macro perforated membrane. The macro perforated membranes are safety blankets with regularly spaced 30mm holes, resulting in an opening ratio of 0.5. The air is supplied in the mixing volume, then it goes through the macro-perforated membrane to the test volume. It is drifted by the natural convection force to the openings at the top or the bottom of the macro-perforated membrane, then it is extracted through the extraction extensions.

Minimization of the inlet flow perturbations

A natural convection heat transfer along the test walls requires a quiescent ambient medium. However, the air handling system causes a residual vertical velocity v and a residual horizontal velocity w along the wall. The inner geometry of the test chamber,presented above, is the result of series of computational fluid dynamic simulations aiming at reducing the residual velocity. The present section provides some details about these simulations and about the criterion used to validate the geometry.

A three dimensions steady-state laminar model was used with the commercial software StarCCM+. The entire volume of the test chamber was simulated. The mesh size was adjusted until we obtained a stabilization of the predicted velocities (over 2 million cells for each tested design). We applied an homogeneous heat flux q w = 5W/m 2 on the test walls, and a homogeneous velocity 50mm/s on the micro-perforated membrane. The thermal response of the cube shell was modeled with mixed boundary conditions, in order to take into account the heat losses through the insulated panels. The ambient velocities v and w were selected on a vertical plane located 2cm from one test wall. The limit ambient velocities degrading the natural convection heat transfer is expressed in terms of Richardson number. The Richardson number Ri H based on the plate height H and the vertical velocity v is defined as:

Ri H = gβ∆T w H v 2 (3)
Bejan [START_REF] Bejan | Convection Heat Transfer[END_REF] stated that natural convection occurs if Ri H > 10. Similarly, let Ri W be the Richardson number based on the ambient horizontal velocity w and the width of the plate W . Siebers [START_REF] Siebers | Experimental mixed convection from a large, vertical plate in a horizontal flow[END_REF] stated that the effect of the horizontal ambient velocity is negligible when Ri W > 10.

Our validation criterion was Ri H > 400 and Ri W > 400. It corresponds to u < 20mm/s and w < 20mm/s in the ambient medium. The geometry of the test chamber was adjusted until the simulated ambient velocities fulfilled this condition all over the selected plane.

Minimization of the radiative heat transfer

We selected low emissivity materials in order to lower radiative heat transfers along the tested plates. The macro perforated membranes are made from safety blankets (gold side ε = 0.039, silver side ε = 0.037). The other surfaces are covered with aluminum sheets (ε = 0.039). The most emissive surface in the test chamber is the micro perforated membrane (ε = 0.612). The PCM test wall did not need any special treatment for radiation, since the product is already covered with aluminum foil (ε = 0.05).

Metrology

The metrology was designed to measure the quantities required to compute 1) the heat transfer coefficient h(y, t) and 2) the performance indicators of the system.

Temperature sensors

Seventy-two 0.2mm diameter K-type thermocouples are implemented in the experimental setup. The locations of the thermocouples are indicated in Figures 3 and4.

The vertical profile of the test wall surface temperature T w (y, t) is measured on both test walls. Each profile is obtained with 11 equally spaced thermocouples plus 2 thermocouples located 50mm far from the top and bottom edges.

The ambient air temperature T ∞ (y, t) is measured using 10 thermocouples held on a vertical rack, located 200mm far from the left-hand-side test wall. The remaining thermocouples are spread all over the experimental setup to feed the radiation inverse model and to compute the performance indicators.

The temperature measurement period is 120s. Each temperature value is the averaged over twenty raw temperature measurements recorded at the frequency of 3Hz. The uncertainty on the mean temperature value is ±0.07 . The uncertainty on the difference between two mean values is ±0.09 . The overall uncertainty of temperature measurement is ±0.11 .

Calculation of the convective heat flux

To obtain the convective heat flux q w , both conduction heat flux leaving the wall q cond and radiative heat flux q rad are estimated. Then, convective heat flux is deduced from q w = q cond -q rad .

The conduction heat flux q cond is computed using an inverse conduction method. The measured surface temperatures T w (y, t) are time-filtered with a Gaussian filter, and spatially interpolated with a spline interpolation scheme. These data feed a 2D transient conduction model which computes the temperature field over a cross section of the plate. Then, the conduction heat flux distribution is estimated at the surface of the wall. The conduction model is based on the finite volume discretization: the cross section of the wall is divided into 10 × 160 rectangular cells. The phase change is taken into account by using the apparent heat capacity method c p w (T ). As the problem is non-linear, an iterative method is used. The iterative method is presented in details in David et al. [START_REF] David | Numerical study of the influence of the convective heat transfer on the dynamical behavior of a phase change material wall[END_REF].

The distribution of the radiative heat flux q rad (y, t) is computed with a radiative model fed by surface temperature measurements. Using the symmetry of the test chamber, the geometry of the radiation model is limited to a half of the test chamber (Fig. 5). The radiation model computes the radiation heat flux between 66 surfaces distributed among four rectangular cavities. The macro perforated membrane is treated as a semi-transparent surface shared between the cavities 1 and 2. The other shared surfaces are supposed to be fully transparent. A radiation balance is computed within each cavity using the radiosity method.

The uncertainty on the radiative and conduction heat flux was determined through a Monte-Carlo procedure. The procedure took into account the uncertainty on the temperature measurements and the uncertainty on the material characteristics. The resulting uncertainty on the convective heat flux is about 8%.

Experimental Protocol

Tested PCM wallboard

We performed the experiments with the PCM wallboard Energain®by DuPont. The wallboard contains 5mm of composite material (60% of a paraffin mixture and 40% copolymers), covered on both sides by 120µm thick aluminum foils (Fig. 6). The thermal characteristics of the panel are gathered in Tab.2, where c p cm is the apparent heat capacity of the composite material. It was measured using a differential scanning calorimeter and with a scanning rate of +3 /h.

The conduction model simulates the multi-layer panel as a unique layer of 5mm equivalent material, the heat capacity and the density being adjusted to take into account the foils. The resulting equivalent heat capacity c p w (T ) is presented in Fig. 7, for a melting and a solidification process. During the melting, the maximum heat capacity occurs at T f = 22.2 . During the solidification, it occurs at T s = 17.8 . Each experiment is preceded by a 6 hours pre-conditioning at the initial temperature to ensure a homogeneous temperature in the system.

Performance indicators

The quality of the experimental device and tests are evaluated through 4 performance indicators. These indicators are computed from the temperature measurements. Tab. The absolute value of the measured ambient temperature scan speed b∞ is slightly lower than the set point. This discrepancy does not degrade the quality of the measurements.

The ambient vertical thermal stratification Γ ∞ lies between 0.2 /m and 0.5 /m. These values are comparable to the smallest stratification values observed in similar setups from the literature: 0.2 /m for Pivovano et al. [START_REF] Pirovano | Convection naturelle en r?gime turbulent la long d'une plaque plane verticale[END_REF], 0.5 /m for Tsuji and Nagano [START_REF] Tsuji | Characteristics of a turbulent natural convection boundary layer along a vertical flat plate[END_REF], 1.8 /m for Cheesewright [START_REF] Cheeswright | Turbulent natural convection from a vertical flat plate[END_REF].

The default of symmetry is quantified from the temperature profiles T w1 (y) and T w2 (y) measured at the surface of both test walls. ∆T s is the maximum value of the difference between both profiles: ∆T s = max y |T w1 (y) -T w2 (y)|. It represents nearly 8% of the wall to air temperature difference when the temperature scan is low. It reduces to 3% when the temperature scan is faster. The parasitic heat flux which results from this default of symmetry is negligible due to the layer of insulation material separating the two wallboards.

The radiative heat flux q rad does not excess 7.5% of the conduction heat flux. It is generally higher near the leading edge of the plate, which might cause a slight distortion of the convection heat flux profile.

The discrepancies between the experimental setup and the ideal studied configuration are integrated into a new definition of the reference heat flux q ref . This new definition takes into account the measured values of the temperature scan speed b∞ , and the average radiative heat flux over the plate q ray : q ref = e w × ρ w × c p wl × b∞ -q ray (4)

Test D10 D15 D20 I10 I15 I20 Set point b ∞ [ /h] -1 -1.5 -

conclusion

The experimental apparatus was designed to measure the evolution of the natural convection heat transfer characteristics along a PCM panel. Those characteristics are the wall to air temperature profile ∆T w (y) = T w (y)-T ∞ (y) and the convection heat flux profile q w (y). The heat transfer coefficient h(y) = q w (y)/∆T w (y) is deduced from those two quantities.

The measurement results are presented in the three following sections. In section 5, the stationary regime is we fully characterized. In sections 6 and 7, the phase change regime is examined.

Temperature and heat flux profiles during the stationary regime

The first stationary regime occurs when the wall temperature difference profiles and the heat flux profiles stabilize. The stationary regime was observed during all the experiments, just before the phase change in the walls. In this section, the characteristics of the heat transfer along the wall during this particular regime are analyzed.

Analysis of the temperature and heat flux profiles

The temperature difference and heat flux profiles given in Fig. 8 were obtained by averaging the measured data over a 40min time period, during the first stationary regime of experiments D10, D15, and D20.

The heat flux q w is nearly homogeneous along the plates for all the experiments. The slight distortions observed for experiments D15 and D20 are due to a non-homogeneous distribution of the radiative heat flux. The agreement between the mean heat flux value and the reference heat flux q ref (Eq.4) is excellent.

The temperature difference profiles ∆T w (y) highlight two heat transfer regimes along the plate. At the bottom of the plate, ∆T w grows with the vertical coordinate y. This is the bottom zone regime (BZ). After a transition located around y = 0.5m, ∆T w stabilizes. This is the top zone regime (TZ).

A correlation was built to characterize the natural convection heat transfer during the stationary regime. This correlation is a combination of two correlations: one for the bottom zone regime, and one for the top zone regime. Both correlations are expressed as functions of the Rayleigh number Ra y based on the reference heat flux:

Ra y = gβ q ref y 4 kαν (5)
They are combined with the formalism from Churchill and Usagi [START_REF] Churchill | Transient, laminar free convection from a uniformly heated vertical plate[END_REF]:

N u y = α BZ Ra 1/5 y n + α T Z Ra 1/4 y n 1/n (6)
The exponent 1/5 corresponds to a laminar convection flow, with a homogeneous heat flux on the plate, and without thermal stratification in the ambient medium. This is the regime expected at the bottom of the plate. The exponent 1/4 corresponds to a homogeneous temperature difference along the plate.

The coefficients α BZ , α T Z and n were computed through successive least square method. Their numerical values are given in Tab.4. They lead to an excellent agreement between the correlation and the measurement results for both heat transfer regimes (Fig. 9).

Reproducibility of the stationary regime

During the stationary regime, only sensible heat is stored in the PCM wall. This regime should occur whatever the material composing the wallboard. Additional tests were conducted with gypsum boards, in order to assess the reproducibility of the measurements.

Similarly to Energaintests, a bottom zone and a top zone regime were observed. Correlations were built by following the same procedure. The resulting coefficients α BZ , α T Z and n are given in Tab.4. They are in accordance with the coefficient obtained for Energainproduct (within 5%). The stationary regime was successfully reproduced in both cases, assessing the reproducibility of the measurements.

Comments

There are numerous literature references about natural convection over a vertical flat plate subjected to an homogeneous heat flux. Those references propose two ways of interpreting the transition between the bottom zone regime and the top zone regime: either it is due to a transition between a laminar flow regime and a turbulent flow regime, or it is due to the ambient thermal stratification.

At the bottom of the plate, a laminar flow regime is expected, without ambient thermal stratification effects. Sparrow and Gregg [START_REF] Sparrow | Laminar free convection from a vertical plate with uniform surface heat flux[END_REF] provide the corresponding correlation coefficient α BZ = 0.52, which is nearly 20% lower than the measured coefficient.

At the top of the plate, either a fully turbulent flow regime or a fully stratified medium is expected. Vliet and Liu [START_REF] Vliet | Turbulent natural convection on upward and downward facing inclined constant heat flux surfaces[END_REF] and Armfield et al. [START_REF] Armfield | Scaling investigation of the natural convection boundary layer on an evenly heated plate[END_REF] provide the respective correlation coefficients: α T Z = 0.17 and α T Z = [kΓ ∞ /(4q ref )] 1/4 ≈ 0.13. Again, these coefficient values are lower than the measured values. There are two potential explanations for the discrepancies between the measurement results and the literature coefficients. First, the studied configuration is not exactly the classical configuration of the vertical flat plate with a constant heat flux, since the heat transfer is generated by a decrease of the ambient temperature. Then, the top zone regime can be due to a combination of stratification and turbulent effects. However, this interaction is not studied in the literature so far.

An overview of the phase change perturbation

This section focuses on the representation of the measurement results given in Fig. 10. In this figure, the measured quantities are represented in terms of average relative quantities, as a function of the average wall temperature T w . Since the overall temperature of the system is decreasing during the experiments D10, D15 and D20, the curves must be read from the right side (high temperatures) to the left side (low temperatures).

There are several justifications for using this representation. First, this is the only representation which enables a global appreciation of the system behavior during the whole duration of the three experiments. The first stationary regime is identified with the number 1, and the phase change perturbation is decomposed into three stages 2a, 2b and 2c. The second stationary regime is not reached.

The fact that we use relative values emphasis the deviation of the natural convection characteristics due to the phase change inside the wall. Since the quantities are averaged over the wall surface, they correspond to the quantities used in building simulation codes. By analyzing the evolution of the average relative convection coefficient h rel , it is possible to determine a way to modulate the average convection coefficient h in building simulation codes in order to take into account the presence of PCM.

Definition of the average relative quantities

The relative wall surface heat capacity c p rel = c p w (T w )/c p wl is reminded on each graphic. The PCM is fully liquid between 35 and 25 : this temperature range corresponds to the first stationary regime.

∆T w , q w , and h = q w /∆T w are the averaged values over the wall surface of the wall temperature difference, the convective heat flux and the convective heat transfer coefficient. The average relative quantities express the deviation of those average quantities from the values they would have during the stationary regime. They highlight the effect of the phase change on convection heat transfer characteristics.

The relative average heat flux q rel the ratio between q w and the reference heat flux q ref from Equation 4. The relative convection heat transfer coefficient is h rel = h/h stat , where h stat is the mean value of h during the whole duration of the stationary regime. The value of h stat is 2.3W/m 2 K for experiment D10, 2.45W/m 2 K for experiment D15, and 2.65W/m 2 K for experiment D20. The average relative wall surface temperature difference is ∆T rel = ∆T w /(h stat .q ref ).

As expected, the values of ∆T rel , q rel and h rel are stable and equal to 1 during the stationary regime.

Beginning of the phase change regime: prior dynamic stage (2a)

At the beginning of the phase change regime, the PCM solidification slows down the decrease of the wall surface temperature. Since the ambient temperature still decreasing at the rate b ∞ , the relative temperature difference ∆T rel increases. Similarly, the surface heat flux q rel increases due to higher values of the material heat capacity. The deviations of q rel and ∆T rel are more pronounced when the evolution of the ambient temperature is slow.

The phase change process also results in an increase of the convective heat transfer coefficient: h rel > 1. Unlike the evolution of q rel and ∆T rel , the evolution of h rel appears to be nearly independent on the ambient temperature increase rate (see maximum values given in Tab.5).

However the evolution of the heat transfer coefficient is closely related to the evolution of the PCM heat capacity: at the beginning of the phase change process, c p rel rises quickly, leading to high values of h rel , then the evolution of c p rel slows down, and h rel reaches smaller values. It is possible to express the value of the relative convection coefficient as a function of the slope of the c p rel curve:

h rel (T w ) = 1 + 0.73 × ∂c p rel ∂T (T w + 1.2) 0.4 (7)
The temperature shift T w + 1.2 is justified by the time needed to diffuse the heat inside the plate. For a melting process, this temperature shift would be T w -1.2.

Temperature slowdown / retrogression (2b)

After the first stage of the phase change regime, the temperature differences ∆T rel exhibit a sudden increase. This evolution indicates that the wall surface temperature slows down, while the ambient temperature still decreasing.

This event is located with an average fixation temperature (T w ) p . This is the average wall temperature for which the quantity ∂T w /∂t is minimum. The values of the average fixation temperature are given in Tab.5. They are very close to the heat capacity maximum temperature: T s = 17.8 .

The temperature slowdown turns into a temperature retrogression for experiment D10. During this experiment, a slight but non-null increase of the average wall temperature is measured, while the ambient temperature still decreasing.

The slowdown / retrogression of the wall temperature is not an instantaneous process. The duration of this event ∆t p [h] is given in Tab.5. It lasts for at least 2 hours during each experiment.

Obviously, the heat flux model predicts a sudden drop of the heat flux, causing a similar drop of the convection coefficient. However, given the unexpected behavior of the wall temperature, it is not possible to have confident in the heat flux predictions. This is particularly true for experiment D10, where the temperature retrogression cannot be interpreted by an excessive increase of the wall heat capacity.

End of the phase change regime: second dynamic stage (2c)

The second dynamic stage happens when the wall temperature difference decreases, i.e. when the wall surface temperature decreases faster than the ambient air temperature. The rapid evolution of the wall temperature leads to higher heat flux values.

The value of the relative convection coefficient h rel at the beginning of the second dynamic stage is similar to its value at the end of the first dynamic stage. Then, the coefficient decreases gradually.

There are little discrepancies on the values of the convection coefficient h rel between the three tests. These discrepancies are mainly due to the temperature stabilization which is more pronounced for test D10. Despite these discrepancies, it is to have a relatively good estimation of the relative convection coefficient by expressing this coefficient in a similar way than for the first dynamic stage:

h rel (T w ) = 1 + 0.6 × ∂c p rel ∂T (T w ) 0.7 (8)

Comments

During experiments D10, D15 and D20, the three stages of the phase change process are well correlated with the PCM thermal characteristics: the first and second dynamic stages correspond to the increase and decrease of the apparent heat capacity, the temperature stabilization occurs when the wall heat capacity is maximum. There was no such correlation during the melting tests I10, I15, and I20. That is the reason why the results of the melting experiments were not presented in this section.

The temperature slowdown / retrogression phenomenon is an unexpected event existing for all the experiments. During this event, the heat flux predictions are not reliable. However, it is possible to analyze the way it materializes on the evolution of the wall surface temperature profiles. This is the purpose of the next section. 7. The wall temperature slowdown / retrogression Fig. 11 shows, for each test, a sequence of measured wall temperature profiles around the temperature slowdown / retrogression event. The profile evolution should be read from the right side to the left side for the tests D10, D15, and D20. They should be read from the left side to the right side for the tests I10, I15, and I20. For those tests, the y-axis was reversed to locate the leading edge of the plate at the bottom of the curve.

The temperature profiles at the beginning and at the end of each sequence are typical from the tworegime heat transfer observed during the stationary regime: there is a bottom zone regime (the temperature grows along the y coordinate) and a top zone regime (the surface temperature difference is homogeneous). The structural distribution of the heat transfer along the plate is not modified during the first and second dynamic stages of the phase change process.

The time interval between each temperature profile is constant within each plot. The temperature slowdown / retrogression manifests itself through a high concentration of temperature profiles all along the plate. To characterize this phenomenon, two quantities are introduced: the fixation temperature T p (y) and the retrogression amplitude ∆T p (y). These two quantities are explicitly presented in Fig. 12. The fixation temperature is the temperature having the slowest evolution. The retrogression amplitude is the amplitude of the wall temperature fluctuation during the retrogression. These quantities are computed all along the y coordinate.

Conclusions

The results of the present study reveal the complexity of the interactions between a plate containing phase change materials and a natural convection boundary layer. We designed a configuration specially dedicated to the study of those interactions. The corresponding experimental setup was built. As expected, the thermal behavior of the whole system undergoes a stationary regime which is now well understood. Then, the phase change occurs within the plate: it strongly modifies the transfer characteristics at the surface of the plate.

The effect of the phase change can be split into three consecutive stages: the first dynamic stage, the wall surface temperature slowdown / retrogression, and the second dynamic stage.

During the first and the second dynamic stages, the deviation of the average convective heat transfer coefficient is well correlated to the PCM characteristics. It does not depend on the ambient temperature growth rate. This deviation is expressed as a relative heat flux h rel , and two correlations was built to predict the value h rel from the evolution of the PCM relative heat capacity. The first one (Eq.7) is valid before the heat capacity peak, the other one ( 8) is valid after the peak. Those correlations can be integrated in building simulation codes, in order to modulate the natural convection heat transfer coefficient for a wall containing PCM. Of course, this is a first approximation of the PCM effect as the correlations do not take into account the temperature slowdown / retrogression phenomenon.

The temperature slowdown / retrogression phenomenon consists in an extreme slow down of the wall surface temperature. The detailed analysis of the wall surface temperature profiles highlighted two different mechanisms: one for the solidification tests, and one for melting tests. For the solidification tests, the phenomenon is local. It could be explained by the presence of subcooling within the PCM. For the melting tests, the phenomenon is randomly triggered near the leading edge of the plate. Then, it is propagated along the plate.

The behavior of the system is not fully understood during the temperature slowdown / retrogression event. But if we want to go further in the interpretation of the experimental results, more accurate PCM models are required. These models should be able to predict subcooling in order to fully characterize the solidification test. They should be able to integrate the random behavior of the material near the leading edge effect during the melting tests. And finally, they will need to be coupled with a fluid dynamics model in order to to predict the transport mechanism occurring during those melting tests.

y

  2 ) q ref Reference Heat flux (W/m 2 ) q ref Reference Heat flux corrected with the measured radiative heat flux (W/m 2 ) Vertical coordinate (m) T f , Ts Melting, Solidification temperatures ( o C) Tp Fixation temperature ( o C) Tw Temperature at the surface of the wall ( o C) T∞ Temperature in the ambient medium ( o C) ∆Tw Temperature difference between the surface of the wall and the ambient medium Tw -T∞ (K) ∆Tp Retrogression amplitude (K) ε Emissivity Greek Letters α Thermal diffusivity of air (m 2 /s) β Thermal expansion coefficient (K -1 ) ν Kinematic viscosity (m 2 /s) Subscripts, Overbar rel Relative quantity q Surface average over the wall. Acronyms P CM Phase Change Material Dimensionless Numbers Ray Rayleigh Number based on the reference heat flux gβ q ref y 4 kαν

Figure 1 :

 1 Figure 1: Studied configuration

1 2 3 Figure 2 :

 132 Figure 2: Expected thermal behavior of the system during a solidification experiment. 1: Stationary regime liquid phase. 2: Perturbation due to the phase change. 3: Stationary regime solid phase

Figure 4 :

 4 Figure 4: Design of the experimental setup: test chamber. Surface temperature measurements are identified by red points. Air temperature measurements are identified by red circles. The temperature is measured on the surface of both test walls.

Figure 5 :

 5 Figure 5: Geometry of the radiation model (right). Correspondence with the inner geometry of the test chamber (left)

Figure 7 :

 7 Figure 7: Equivalent heat capacity of the EnergainPanel. The melting curve was obtained with a scanning rate of +3 /h. The solidification curve was obtained with a scanning rate of -3 /h.

Figure 8 :Table 4 :

 84 Figure 8: Temperature difference and heat flux profiles during the stationary regime α BZ α T Z n Energain 0.635 0.235 25 Gypsum Board 0.607 0.229 25Table 4: Coefficients of the correlations. Comparison with natural convection along a gypsum board

Figure 9 :

 9 Figure 9: Comparison between the correlation (black lines) and the measurement data (gray dashed lines), during the stationary regime, for experiments D10 D15 and D20.

Figure 10 :

 10 Figure 10: Surface average relative heat flux q rel , relative temperature difference at the plate ∆T rel , relative heat transfer coefficient h rel , as a function of the average wall surface temperature T w . Measurement results from experiments D10, D15, and D20

14

 14

Figure 11 :

 11 Figure 11: Localization of the fixation temperature Tp(y) on sequences of wall temperature profiles. The first curve of each sequence is the bold dashed curve, the last curve is the bold full curve. The fixation temperature is located on the thick gray curve

Figure 13 :

 13 Figure 13: Fixation temperature Tp and retrogression value ∆Tp profiles for experiments D10, D15 and D20

Figure 14 :

 14 Figure 14: Fixation temperature Tp and retrogression value ∆Tp profiles for experiments I10, I15 and I20

  Design of the experimental setup: air handling chamber. Surface temperature measurements are identified by red points. Air temperature measurements are identified by red circles. The air is supplied through the micro-perforated membrane. Is is extracted through the extraction openings

	3
		1 Micro-perforated membrane
		2 Air Extractions
		3 Shield
	1200	4 Shutters 5 Air Handling Unit 6 Insulated duct
		7 Shunt
		No Désignation
	Figure 3:

Table 2 :

 2 3 reports the average values of the performance indicators during the first stationary regime of each experiment. Thermal characteristics of the Energainpanels

		e	ρ	c p	k
		[mm]	[kg/m 3 ] [kJ/kgK]	[W/mK]
	Composite material 5	853	c p cm (T )	0.2
	Aluminum foils	2x0.12 2700	0.897	-
	Equivalent panel	5	853	c p cm +0.148 0.2

Table 3 :

 3 Average value of the four performance indicators during the first stationary regime

	2 1 1.5 2

Table 5 :

 5 Analysis of the mean quantities evolutions

Correlations developed for non-PCM walls.

Slowdown Retrogression

Figure 12: The fixation temperature effect: slowdown or retrogression. Definition of the fixation temperature Tp and retrogression amplitude ∆Tp in both cases 7.1. Decreasing temperature tests Fig. 13 contains the profiles of T p (y) and ∆T p (y) for experiments D10, D15, and D20. The solidification temperature T s is also presented. The fixation temperature T p lies within the interval T s ± 0.2 . Given the uncertainty on the temperature measurements, and the uncertainty on the determination of T s , it is possible to assume that the temperature slowdown / retrogression phenomenon occurs at the solidification temperature.

The retrogression amplitude is higher at the center of the top zone (y ≈ 1m). The maximum retrogression values ∆T p were obtained during experiment D10. During experiment D20, the retrogression occurs on a limited area of the wall.

Increasing ambient temperature

The temperature slowdown phenomenon also occurred during experiments I10, I15 and I20. Fig. 14 displays the profiles of T p (y) and ∆T p (y) for experiments I10, I15 and I20. The melting temperature T f is also indicated. Here, the retrogression amplitudes are much smaller. They lie in the interval of the temperature measurement error. We mostly observe a temperature slowdown phenomenon.

The shapes of the fixation temperature profiles T p (y) are very different during the increasing temperature experiments. Figure 12 shows that the temperature slowdown phenomenon is triggered at the leading edge of the plate y = 0 (i.e. at the top side of the plate). Then, this phenomenon propagates all along the plate (toward the bottom direction of the plate). However, during the time taken by the slowdown phenomenon to propagate, the temperature of the rest of the plate increases: that is the reason why the fixation temperature gets higher when y increases in Fig. 14.

An other aspect of the present results is surprising: it is the temperature at which the phenomenon is triggered. This temperature is 18 o C for experiment I10, 24.3 o C for experiment I10, and 20.5 o C for experiment I10. Those temperature are not coherent with the associates ambient temperature rates b ∞ . They are very different from the melting temperature T f = 17.8 o C.

Comments

The temperature slowdown and retrogression effect is clearly driven by different mechanisms during the decreasing and the increasing ambient temperature experiments.

For the decreasing tests, the temperature slowdown / retrogression occurs nearly at the solidification temperature T s all along the plate: this is a local phenomenon. This phenomenon may possibly find an interpretation in the sub-cooling effect. The sub-cooling effect would cause sudden heat releases which would reheat locally the plate near the surface, leading to a local increase of the plate surface temperature.

For the increasing tests, the retrogression is negligible. However, the temperature slowdown is not anymore a local phenomenon. It is triggered at the leading edge of the wall, then it is transported all along the wall. The transport of the temperature slowdown phenomenon might occur within the wall, or within the boundary layer, which would suggest a complex coupling between the PCM panel and the natural convection boundary layer. The triggering of the temperature slowdown occurs at a nearly random temperature.