Monja Knoll
email: monja.knoll@port.ac.uk.

Lisa Scharrer
email: lisa.scharrer@uni-muenster.de

Alan Costall
email: alan.costall@port.ac.uk

Running head: Evaluation of simulated sentence production "Look at the shark": Evaluation of student-and actress-produced standardised sentences of infant-and foreigner-directed speech 1

Standardised sentence production is routinely used in speech research to avoid content variability typical of natural speech production. However, the validity of such standardised material is not well understood. Here, we evaluated the use of standardised sentences by comparing them to two existing, non-standardised datasets of simulated free and natural speech (the latter produced by mothers in real interactions). Standardised sentences and simulated free speech were produced by students and actresses without an interaction partner. Each dataset comprised recordings of infant-(IDS), foreigner-(FDS) and adult-directed (ADS) speech, which were analysed for mean F 0 , vowel duration and hyperarticulation. Whilst students' mean F 0 pattern in standardised speech was closer to the natural speech than their previous 'simulated free speech', no difference in vowel hyperarticulation and duration patterns was found for students' standardised sentences between the three speech styles. Actresses' F 0 , vowel duration and hyperarticulation patterns in standardised speech were similar to the natural speech, and a part improvement on their 'simulated free speech'. These results suggest that successful reproduction of some acoustic measures (e.g., F 0 ) can be achieved with standardised content regardless of the type of speaker, whereas the production of other acoustic measures (e.g., hyperarticulation) are context-and speaker-dependent.

Introduction

The acoustic characteristics of a person's voice can provide a rich source of information about, for instance, their personality and emotional state [START_REF] Starkweather | Vocal behavior as an information channel of speaker status[END_REF]. However, investigations into these acoustic properties may require the separation of the verbal (semantic) from the non-verbal (acoustic) features of speech to alleviate the problem of semantic interference with acoustic and perceptual measurements. Not surprisingly, the achievement of this separation has been a frequent concern in speech research. A variety of different methodologies has been used depending on the relevant aspect of speech under study (e.g., linguistic or emotional), the type of data collection (e.g., natural conversational speech or standardised sentence production in the laboratory) and type of analysis (e.g., perceptual ratings or acoustic analysis). For instance, in emotional and personality research, a common approach has been to remove the semantic content, or to render the speech samples unintelligible by means of low-pass filtering (e.g., [START_REF] Cohen | Vocal cues to the identification of language[END_REF][START_REF] Milmoe | The doctor's voice: postdictor of successful referral of alcoholic patients[END_REF][START_REF] Rogers | Content filtering human speech: A simple electronic system[END_REF]Soskin and Kaufman, 1961;[START_REF] Starkweather | The communication-value of content-free speech[END_REF], content-splicing (e.g., [START_REF] Scherer | Randomized splicing: a note on a simple technique for masking speech content[END_REF][START_REF] Scherer | Minimal cues in the vocal communication of affect: judging emotions from content-masked speech[END_REF], speech reversal (e.g., [START_REF] Knower | Analysis of some experimental variations of simulated vocal expressions of the emotions[END_REF], the use of foreign speech samples (e.g., [START_REF] Kramer | Elimination of verbal cues in judgments of emotion from voice[END_REF] and 'reiterant'2 speech (e.g., [START_REF] Friend | A comparison of content-masking procedures for obtaining judgments of discrete affective states[END_REF].

The present study aimed to evaluate another widely used method of avoiding semantic interference, where the semantic content of speech is standardised by using identical sentences and utterances across different speakers and speech types (e.g., [START_REF] Anolli | Irony as a game of implicitness: acoustic profiles of ironic communication[END_REF][START_REF] Anolli | From "blame by praise" to "praise by blame". Analysis of vocal patterns in ironic communication[END_REF][START_REF] Bradlow | Speaking clearly for children with learning disabilities: sentence perception in noise[END_REF][START_REF] Cheang | The sound of sarcasm[END_REF][START_REF] Ladd | Evidence for the independent function of intonation contour type, voice quality, and F 0 range in signalling speaker affect[END_REF][START_REF] Rockwell | Lower, slower, louder: vocal cues of sarcasm[END_REF][START_REF] Scherer | Multimodal expression of emotion: Affect programs or componential appraisal patterns?[END_REF][START_REF] Tischer | Ein Verfahren zur Messung der vokalen Kommunikation von Gefuehlen[END_REF]. It should be noted that the current study is concerned with linguistic rather than emotional factors, although standardised sentences can be used to investigate either.

Standardised content

The reason that standardised sentences have been routinely used in speech research is that they facilitate perceptual and acoustic comparison across different speakers and conditions without the complication of variable content. By necessity, the use of standardised sentences precludes the collection of natural speech samples. Typically, speakers have been instructed to talk to a specific (imagined) listener (e.g., hearing impaired person or foreigner: [START_REF] Bradlow | Speaking clearly for children with learning disabilities: sentence perception in noise[END_REF][START_REF] Picheny | Speaking clearly for the hard of hearing I: intelligibility differences between clear and conversational speech[END_REF][START_REF] Smiljani | Production and perception of clear speech in Croatian and English[END_REF] whilst reciting the sentences, or they have been instructed to utter (read) the material in a specific emotional (e.g., happy, sad or ironic) 'tone of voice' (e.g., [START_REF] Anolli | Irony as a game of implicitness: acoustic profiles of ironic communication[END_REF][START_REF] Anolli | From "blame by praise" to "praise by blame". Analysis of vocal patterns in ironic communication[END_REF][START_REF] Banse | Acoustic profiles in vocal emotion expression[END_REF][START_REF] Bänziger | The role of intonation in emotional expressions[END_REF][START_REF] Breitenstein | The contribution of speech rate and pitch variation to the perception of vocal emotions in a German and an American sample[END_REF][START_REF] Cheang | The sound of sarcasm[END_REF][START_REF] Ross | Contribution of the lower audible frequencies to the recognition of emotions[END_REF][START_REF] Scherer | Vocal cues in emotion encoding and decoding[END_REF].

In some cases this standardised content has consisted of nonsense sentences (i.e., 'Hat sundig pron you venzy'; e.g., [START_REF] Banse | Acoustic profiles in vocal emotion expression[END_REF][START_REF] Bänziger | The role of intonation in emotional expressions[END_REF][START_REF] Scherer | Vocal cues in emotion encoding and decoding[END_REF]. Some studies have also provided the speakers with specific scenarios in which the target utterances were embedded in order to encourage a more 'ecologically valid'3 voice production, and to elicit the required effect, such as emotion or irony (e.g., [START_REF] Cheang | The sound of sarcasm[END_REF][START_REF] Rockwell | Lower, slower, louder: vocal cues of sarcasm[END_REF][START_REF] Tischer | Ein Verfahren zur Messung der vokalen Kommunikation von Gefuehlen[END_REF][START_REF] Trainor | Is infant-directed speech prosody a result of the vocal expression of emotion?[END_REF].

In most cases the speaker has been asked to address an imaginary speech partner, although some studies have used an interaction partner in the form of the researcher or another participant (e.g., [START_REF] Trainor | Is infant-directed speech prosody a result of the vocal expression of emotion?[END_REF][START_REF] Wallbott | Cues and channels in emotion recognition[END_REF]. Studies of this kind have utilised a variety of different speaker 'types', which include the use of professional actors (e.g., [START_REF] Banse | Acoustic profiles in vocal emotion expression[END_REF][START_REF] Breitenstein | The contribution of speech rate and pitch variation to the perception of vocal emotions in a German and an American sample[END_REF][START_REF] Laukka | A dimensional approach to vocal expression of emotion[END_REF][START_REF] Scherer | Multimodal expression of emotion: Affect programs or componential appraisal patterns?[END_REF][START_REF] Wallbott | Cues and channels in emotion recognition[END_REF], lay actors (e.g., [START_REF] Anolli | Irony as a game of implicitness: acoustic profiles of ironic communication[END_REF][START_REF] Anolli | From "blame by praise" to "praise by blame". Analysis of vocal patterns in ironic communication[END_REF][START_REF] Viscovich | Acoustical analysis of posed prosodic expressions: Effects of emotion and sex[END_REF], students or non-professional speakers (e.g., [START_REF] Bradlow | Intelligibility of normal speech I: global and fine-grained acoustic-phonetic talker characteristics[END_REF][START_REF] Cheang | The sound of sarcasm[END_REF][START_REF] Papousek | Tone and intonation in Mandarin babytalk to presyllabic infants: comparison with registers of adult conversation and foreign language instruction[END_REF][START_REF] Schaeffler | Comparing vocal parameters in spontaneous and posed child-directed speech[END_REF][START_REF] Trainor | Is infant-directed speech prosody a result of the vocal expression of emotion?[END_REF] and experienced speech professionals (e.g., [START_REF] Ferguson | Vowel intelligibility in clear and conversational speech for normal-hearing and hearing-impaired listeners[END_REF][START_REF] Kalikow | Development of a test of speech intelligibility in noise using sentence materials with controlled word predictability[END_REF][START_REF] Picheny | Speaking clearly for the hard of hearing I: intelligibility differences between clear and conversational speech[END_REF].

Comparative speech research

One area in which standardised sentences have recently been used is investigations into the linguistic and emotional functions of infant-directed speech (IDS; e.g., [START_REF] Papousek | Tone and intonation in Mandarin babytalk to presyllabic infants: comparison with registers of adult conversation and foreign language instruction[END_REF][START_REF] Schaeffler | Comparing vocal parameters in spontaneous and posed child-directed speech[END_REF][START_REF] Trainor | Is infant-directed speech prosody a result of the vocal expression of emotion?[END_REF]. Here, the acoustic and perceptual properties of IDS have been compared with speech directed to linguistic (e.g., foreigners: Biersack et al., 2005;[START_REF] Uther | Do you speak E-n-g-l-i-s-h? A comparison of foreigner-and infant-directed speech[END_REF] or emotional (e.g., partners, pets: [START_REF] Burnham | What's new pussycat? On talking to babies and animals[END_REF][START_REF] Trainor | Is infant-directed speech prosody a result of the vocal expression of emotion?[END_REF] comparison groups. Of course, the comparison of the semantically less diverse IDS with speech directed to adults is particularly challenging using non-standardised conversational material. Firstly, raters in perceptual studies may be able to identify the relevant speech recipient group (e.g., infants in IDS) from the semantic content alone, and their ratings may consequently be influenced by this. Secondly, in order to carry out specific acoustic analyses (e.g., formant analysis of vowel sounds), the semantic content in speech directed to different recipient groups needs to be similar. The use of standardised sentences solves both of these problems, and can also alleviate the need for an interaction partner, making data collection quicker and more convenient (e.g., it may be difficult to recruit a foreign confederate who is available for a prolonged period of time).

However, the comparability of such material with natural speech has not been assessed. Natural speech provides speakers with the opportunity to freely express themselves without the constraint of standardised semantic content, and the resulting speech is negotiated in social interactions with the listener (sensu [START_REF] Parkinson | Emotions are social[END_REF].

These aspects of 'real world' speech are eliminated in research based on standardised sentence production, as the semantic content is predefined and the resulting speech is based on imagined (simulated) interactions.

Comparison of natural and simulated interactions

Previously, we have already explored the effects of simulated interactions on the acoustic and perceptual properties of speech directed to different recipient groups [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF]. In that earlier study, we compared natural speech samples of an existing dataset [START_REF] Uther | Do you speak E-n-g-l-i-s-h? A comparison of foreigner-and infant-directed speech[END_REF] of infant-(IDS), foreigner-(FDS) and British adult-directed (ADS) speech with speech directed to an imaginary interaction partner by students and actresses [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF]. Student speakers were used as one comparison group because they constitute the most easily available participants in psychological research, and they have been previously used in simulated speech research (e.g., Biersack and Kempe, 2005;Biersack et al., 2005;[START_REF] Papousek | Tone and intonation in Mandarin babytalk to presyllabic infants: comparison with registers of adult conversation and foreign language instruction[END_REF]. Actresses were utilised as another comparison group because they should be more used to simulated role play, and recordings of actors' speech have already been extensively used in the area of vocal emotion (e.g., [START_REF] Banse | Acoustic profiles in vocal emotion expression[END_REF][START_REF] Kramer | Elimination of verbal cues in judgments of emotion from voice[END_REF][START_REF] Scherer | Vocal communication of emotion: A review of research paradigms[END_REF][START_REF] Scherer | Multimodal expression of emotion: Affect programs or componential appraisal patterns?[END_REF][START_REF] Scherer | Emotion inferences from vocal expression correlate across languages and cultures[END_REF][START_REF] Wallbott | Cues and channels in emotion recognition[END_REF][START_REF] Williams | Emotions and speech: some acoustical correlates[END_REF].

Although in that study we found that actress-produced speech approximated (i.e., shared a pattern of similarity) with natural speech with regard to hyperarticulation4 , and was consistent with the increased mean fundamental frequency (F 0 ) in natural IDS [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF], we were notably unsuccessful in reproducing these acoustic features in the student simulated interactions (see Table 1 for similarities and differences across the three speech styles; [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF]. Interestingly, neither the actresses nor the student speakers were able to reproduce the vowel duration patterns of the natural speech samples.

< insert Table 1 approximately here >

In contrast to previous studies, which have used standardised utterances (e.g., [START_REF] Papousek | Tone and intonation in Mandarin babytalk to presyllabic infants: comparison with registers of adult conversation and foreign language instruction[END_REF][START_REF] Schaeffler | Comparing vocal parameters in spontaneous and posed child-directed speech[END_REF][START_REF] Trainor | Is infant-directed speech prosody a result of the vocal expression of emotion?[END_REF], we had asked our participants to produce their own speech without a script and using their own scenarios (referred to as 'simulated free speech' to distinguish it from natural speech; see [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF]. However, we did provide them with the same materials (three toys) upon which to centre their scenarios to elicit the same target words, and with a description of the confederates used in the natural dataset [START_REF] Uther | Do you speak E-n-g-l-i-s-h? A comparison of foreigner-and infant-directed speech[END_REF]; but see Bradlow et al., 2007 for alternative method of eliciting controlled yet quasi-spontaneous speech -the Diapix Task). On the one hand, this approach should have resulted in speech that is closer to natural speech as the speakers were able to freely express themselves. On the other hand, the students might have been mainly concerned with producing a script relevant to IDS, FDS and ADS, which prevented them from concentrating on their primary task of reproducing acoustic speech modifications that are found in natural IDS and FDS. In our earlier study we suggested that it is possible that the additional task and freedom of inventing their own scenario 'dialogue' acted as a distraction to the student speakers through 'task overload' [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF]. The use of standardised sentence production might thus alleviate this problem of 'task overload' for the student speakers.

Although the actress speakers might have been accustomed to such 'multi-tasking' due to their acting experience and training, the use of sentences approximating actress scripts might also serve to improve the performance of the actresses for the same reasons (e.g., with regard to their vowel duration patterns, see Table 1).

Aim of the present study

This study aims to evaluate the use of standardised content in speech research by comparing speech modifications found in standardised sentences with those found in 'simulated free speech' [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF] and naturally produced speech [START_REF] Uther | Do you speak E-n-g-l-i-s-h? A comparison of foreigner-and infant-directed speech[END_REF] produced by three speaker groups across three different speech types (IDS, FDS and ADS). Both the standardised sentences used here and the 'simulated free speech' of [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF] were produced by students and actresses in imaginary interactions, whereas the natural speech samples were produced by mothers in real interactions [START_REF] Uther | Do you speak E-n-g-l-i-s-h? A comparison of foreigner-and infant-directed speech[END_REF]. To facilitate comparison between these three datasets, our analyses concentrate on a) mean F 0 , b) vowel hyperarticulation and c) mean vowel duration, because these acoustic properties had been investigated in both the natural speech dataset [START_REF] Uther | Do you speak E-n-g-l-i-s-h? A comparison of foreigner-and infant-directed speech[END_REF] and the 'simulated free speech' dataset [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF]. If the differences presented in our earlier study [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF]; see also Table 1) between the 'simulated free speech' and the natural dataset were due to 'task overload', we would expect student speakers to perform more similarly to the natural speech samples (e.g., similar hyperarticulation pattern: IDS = FDS > ADS; [START_REF] Uther | Do you speak E-n-g-l-i-s-h? A comparison of foreigner-and infant-directed speech[END_REF] in a standardised sentence condition than in their earlier 'simulated free speech' condition [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF]. We would also expect the actress speakers to produce acoustic modifications that are either consistent with their previous performance (see Table 1; [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF], or constitute an improvement in that they are even more similar to the natural speech samples through alleviation of the previously mentioned 'task overload'.

Method

Design

We applied a 2 x 3 mixed measures design, consisting of speaker type (actresses versus students; between subjects factor) and speech recipient groups (IDS, FDS and ADS; within subjects factor). The dependent variables were the different acoustic measurements (mean F 0 , mean vowel duration and mean vowel space). In addition to these acoustic measurements we also investigated whether the speech samples could be categorised into their intended respective speech recipient groups (IDS, FDS and ADS) for the actress and the student speakers by means of naïve raters. This was intended to provide an indication of how closely the samples resembled IDS, FDS or ADS perceptually, regardless of their quantitative acoustic measures.

Participants

Speakers

To facilitate comparison with the [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF] study, the same students and actresses took part in the present study. Student speakers consisted of 10 females with a mean age of 22.9 years (sd 8.84) recruited from the student population of the University of Portsmouth. None of the student speakers had previous acting experience. The actress group consisted of 10 professional actresses with a mean age of 28.4 years (sd 13.06) recruited from theatres and acting schools in London. All actresses had undergone professional acting training (including voice coaching) and had been acting for at least a year (mean 5.6 years; range 1 to 16 years) with most of their acting work carried out in the theatre. For each of the speakers we collected information regarding a) their previous exposure to each of the speech recipient groups (Likert-scale: 1 (not much exposure) to 5 (a lot of exposure)), b) which speech production condition they had found easier ('simulated free speech' or standardised sentences) and c) which speech recipient group they had found easiest to address (IDS, ADS or FDS). Speakers had no reported hearing or speech impairment and were British citizens with comparable southern English accents, who had been living in the south-east of England for most of their lives (> 16 years).

Raters

The raters consisted of four males and two females with a mean age of 39 years (sd 13.97), and were recruited from the student and staff population of the University of Portsmouth. None of the raters was hearing impaired. These raters were required to categorise the speech samples (sentences) into their respective speech recipient groups (IDS, FDS and ADS). Please note that the number of raters is comparable to those used in previous studies [START_REF] Trainor | Is infant-directed speech prosody a result of the vocal expression of emotion?[END_REF].

Procedure

Speech samples

The speakers were required to imagine talking to an infant, a British adult and a foreign adult in three separate interactions. For the infant interaction, they were instructed to imagine that they were talking to a close family member (e.g., niece, nephew or ideally their own child). However, we did not provide speakers with an example or idea of what IDS should sound like. For both the British and foreign adult interactions, the speakers were instructed to imagine talking to a female stranger in her early twenties. In the foreign interaction, the raters were also instructed to imagine that the person was a Chinese exchange student who had been living in the UK for less than two months, and that they might encounter some communication difficulties. The order of the interactions for each speaker was counterbalanced to avoid order effects.

To elicit the target words, we supplied the speakers with three toys (a shark, a sheep and a shoe). The speakers were required to incorporate these target words in four standardised sentences ("Look at the 'target word'" for each of the three target words in turn, and then combining all three target words in one sentence: "Look at the 'shark', the 'sheep' and the 'shoe'"). The order of production of the first three short sentences was counterbalanced for each of the speakers, but the long sentence was always produced at the end. The use of a small number of sentences per speaker is consistent with previous research incorporating standardised sentence production in IDS and ADS (e.g. [START_REF] Trainor | Is infant-directed speech prosody a result of the vocal expression of emotion?[END_REF], and was used to avoid deterioration of speech modifications due to satiation and speaker fatigue. Furthermore, the production of the sentences for each of the three interactions had been preceded by the corresponding 'simulated free speech' condition [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF] in which the speakers constructed and invented their own scenarios centred on the target words (e.g., the IDS sentence condition would have been preceded by the IDS 'simulated free speech' condition) and in which they would have already repeated the words several times. Ideally this procedure should have resulted in a more relaxed speech production for the standard sentences condition, and is comparable to inductor texts used in emotion and irony research (e.g., [START_REF] Anolli | Irony as a game of implicitness: acoustic profiles of ironic communication[END_REF][START_REF] Banse | Acoustic profiles in vocal emotion expression[END_REF].

Ratings

We selected the utterance "Look at the shark, the sheep and the shoe" as material for the rating part of the experiment, because the sentence contained all three target words, and the presentation of all 240 sentences might also have led to rater fatigue. The raters were required to listen to each of the 60 sentences (30 actress and 30 student sentences), and categorise them into the relevant speech recipient group (IDS, FDS and ADS). Speech samples were between one and four seconds long, and participants were only able to listen to each speech sample once. To avoid order effects, the speech samples were firstly randomised, and half of the participants were presented with the speech samples in the reversed order. Participants were given breaks at different intervals to avoid fatigue and semantic satiation [START_REF] Jakobovits | Repetition of auditory presented information[END_REF].

Acoustic analyses

The procedures used here were identical to those of [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF], and follow those of previous studies [START_REF] Burnham | What's new pussycat? On talking to babies and animals[END_REF][START_REF] Kuhl | Cross-language analysis of phonetic units in language addressed to infants[END_REF][START_REF] Uther | Do you speak E-n-g-l-i-s-h? A comparison of foreigner-and infant-directed speech[END_REF]. A total of 360 words were analysed (180 for each speaker group). Acoustic analyses were carried out using Praat 4.5.16, [START_REF] Boersma | Praat: doing phonetics by computer (Version 4.5.16[END_REF], and standard recommendations suggested by Praat for female voices were used. Based on previous research [START_REF] Burnham | What's new pussycat? On talking to babies and animals[END_REF][START_REF] Uther | Do you speak E-n-g-l-i-s-h? A comparison of foreigner-and infant-directed speech[END_REF] the analyses centred on the target words shark, sheep and shoe containing the corner vowels /a/, /i/ and /u/. These target words were also chosen to avoid problems of co-articulation due to different phonemes at the beginning of the words (i.e., each vowel was preceded by the phoneme /sh/). Vowel sounds were first extracted using Soundforge 6.0. The resulting sound samples were analysed for mean F 0 , mean vowel duration, and F1/F2 measures (taken at the midpoint of the vowel, see [START_REF] Kuhl | Cross-language analysis of phonetic units in language addressed to infants[END_REF]. Mean F1/F2 values were then used as x-y co-ordinates to plot bivariate vowel triangles for /a/, /i/ and /u/, from which vowel triangle area was calculated to detect 'hyperarticulation' of the vowels. Plotting and calculation of the vowel space was carried out in Autocad 2000.

Results

The data for the acoustic analyses (mean F 0 , F1/F2 vowel area expansion and mean vowel duration) were subjected to a series of mixed measures ANOVAs, whereas the data for the ratings were analysed with chi-square analysis. To provide a complete overview, the results of the acoustic analyses we present here also contain mean values for the 'simulated free speech' condition for the students and actresses (after [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF] and for the mothers' natural speech samples (after [START_REF] Uther | Do you speak E-n-g-l-i-s-h? A comparison of foreigner-and infant-directed speech[END_REF].

Previous exposure

As previously reported in [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF], there was no significant difference between actresses' and students' self-ratings on how much exposure each group had to infants and foreigners. Similarly, there was no difference between actress and student speakers' reports on which speech recipient group they found the easiest or most difficult to address. The majority of both speaker groups reported IDS as the easiest and FDS as the most difficult condition. However, student speakers reported both tasks (standardised sentences and 'simulated free speech') as more frustrating, difficult and uncomfortable than the actress speakers.

Interestingly, eight of the ten student speakers stated that they found the 'simulated free speech' condition more difficult than the sentence condition, whereas only four of the ten actress speakers found the 'simulated free speech' condition more difficult than the sentence condition.

Hyperarticulation (F1/F2 vowel area expansion)

Mean formant values for the three corner vowels and the resulting vowel triangles for each speech recipient group can be found in Figure 1 for both the students and the actresses. Overall, the natural speech is less hyperarticulated then either the actresses' or students' speech regardless of the intended recipient or the condition (i.e. standardised sentences or 'simulated free speech'; see Figure 2). However, we were interested in comparing the pattern of hyperarticulation across the recipient types rather than the absolute values. [START_REF] Uther | Do you speak E-n-g-l-i-s-h? A comparison of foreigner-and infant-directed speech[END_REF] had found that IDS and FDS were significantly more hyperarticulated than ADS, with no difference between IDS and FDS. We would expect the same pattern for the students and the actresses.

There was a significant main effect of speech recipient groups (F (2, 36) = 4.903, p = .013, = .214). IDS vowel space was significantly larger than ADS vowel space (F (1, 18) = 8.778, p = .001, = .328), but not larger than FDS vowel space. FDS exhibited greater vowel space than ADS (F (1, 18) = 10.479, p = .005, = .368). A significant main effect for speaker type was also found (F (1, 18) = 14.000, p = .001, =.437), with actresses achieving a significantly greater vowel space than students (Figures 1 and2). However, these main effects need to be interpreted in light of a significant interaction between the speakers and the speech recipient groups (F (2, 36) = 4.357, p = .02, = .195), which is due to an interaction between IDS and ADS (F (1, 18) = 7.597, p = .013, = .297), whereas the interaction between IDS and FDS only approached significance (F (1, 18) = 3.712, p = .07, = .171; Figure 2).

<insert Figure 1 about here> To investigate these interaction effects further, planned contrasts for each of the speaker conditions were carried out. For the actresses, IDS vowel space was significantly greater than ADS vowel space (F (1, 9) = 10.989, p = .009, = .550), with no difference between IDS and FDS. FDS was significantly greater than ADS vowel space (F (1, 9) = 8.468, p = .017, = .485). In contrast, there was no significant difference between the speech recipient groups for the student interactions (Figure 2, right panel). The data for the vowel space did not fully meet the assumption of homogeneity of variance between the students and the actresses. However, the results of the ANOVA were confirmed with a Friedman two-way analysis of ranks on the effect of speech recipient groups for students ( 2(2) = 3.800, ns) and for actresses ( 2(2) = 14.600, p < .001). Wilcoxon tests showed that actress-produced ADS vowel space was significantly smaller than IDS (z = -2.803, p = .001) and FDS (z = -2.293, p = .01), with no difference between IDS and FDS.

Overall, the vowel space results for the actresses are similar to the results of the natural speech samples [START_REF] Uther | Do you speak E-n-g-l-i-s-h? A comparison of foreigner-and infant-directed speech[END_REF] and the actresses' earlier 'simulated free speech' condition [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF]. In contrast, the results for the students are neither similar to their earlier 'simulated free speech' condition nor the natural speech samples (see also Figure 2).

<insert Figure 2

about here>

Vowel duration

There was no significant interaction between the speakers and the speech recipient groups for vowel duration. However, a significant main effect of speakers was observed (F (1, 18) = 4.920, p =.04, = .215), with actresses producing significantly longer vowels than students (Figure 3). There was also a significant main effect of speech recipient groups (F (2, 36) = 7.937, p = .001, = .360), with IDS exhibiting significantly longer mean vowel duration than FDS (F (1, 18) = 4.925, p = .04, = .215) and ADS (F (1, 18) =14.639, p = .001, = .449). No significant difference was found between ADS and FDS mean vowel duration.

To investigate whether these differences would remain constant in each of the speaker groups, planned contrasts were conducted between the speech recipient groups for each of the conditions. Consistent with their earlier performance in the 'simulated free speech' condition [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF], there was no significant difference for mean vowel duration between student-produced IDS, FDS and ADS, but is in contrast to the natural speech samples [START_REF] Uther | Do you speak E-n-g-l-i-s-h? A comparison of foreigner-and infant-directed speech[END_REF]; see Figure 3). However, a significant difference was found between mean vowel duration for actresses (F (2, 18) = 9.320, p = .002, = .509),

with IDS exhibiting longer vowel duration than FDS (F (1, 9) = 6.947, p = .027, = .436)

and ADS (F (1, 9) = 15.729, p = .003, = .636; Table 2), with no difference between the latter two. The results for the actresses were thus comparable to the natural speech samples [START_REF] Uther | Do you speak E-n-g-l-i-s-h? A comparison of foreigner-and infant-directed speech[END_REF], which constituted an improvement from their earlier 'simulated free speech' performance, where no difference in vowel duration between IDS, FDS and ADS was found [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF]; Figure 3).

<insert Figure 3 about here>

Fundamental frequency (F 0 )

There was no significant interaction for F 0 between the speakers and speech recipient groups, and no significant main effect for speakers. However, a significant main effect of speech recipient groups was observed (F (2, 36) = 21.302, p < .001, = .542), with IDS mean F 0 being significantly higher than ADS (F (1, 18) = 29.847, p = .001, = .624) and FDS (F (1, 18) = 21.459, p < .001, = .544). There was no difference between the adult groups (ADS and FDS; see Figure 4).

Planned contrasts for each of the speaker conditions showed that these differences between the speech groups were consistent for the actresses and students. Mean F 0 in IDS was significantly higher than in ADS (students: F (1, 9) = 7.406, p = .024, = .451; actresses: F (1, 9) = 17.252, p = .002, = .657) and FDS (students: F (1, 9) = 10.358, p = .011, = .515; actresses: F (1, 9) = 8.134, p = .019, = .451), while no difference between the adult conditions was found (see Figure 4). Overall, the pattern of F 0 results for the student speakers were consistent with those of the natural speech samples [START_REF] Uther | Do you speak E-n-g-l-i-s-h? A comparison of foreigner-and infant-directed speech[END_REF], and they also constituted an improvement compared to the students' previous 'simulated free speech' condition [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF]. The results for the actress speakers remained consistent with their previous performance in the 'simulated free speech' condition [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF], which were already close to the natural speech samples [START_REF] Uther | Do you speak E-n-g-l-i-s-h? A comparison of foreigner-and infant-directed speech[END_REF]; see also Figure 4).

<insert Figure 4 about here>

Ratings

The ratings data were analysed with standard frequency statistics (3 x 3 chi-square contingency table). Separate chi-square analyses for each of the raters (divided into actresses and students) were conducted. The raters' categorisations followed a similar pattern. In order to allow overall analyses and comparisons, and given that the patterns of association within the contingency tables were similar, the chi-square values for each of the individual raters were summated (see Johnson and Kotz, 1970a, p. 167). Chi-square results for the categorisation of the speech recipient groups separated into actress and student speech samples for each of the raters can be found in Table 2 5 . Rated speech recipient group variables were found to be associated with the true intended speech recipient group variables for actresses (cumulative 2 = 154.993, df = 24, p < 0.01) and for students (cumulative 2 = 66.68, df = 24, p < 0.01).

To compare whether the strength of the relationship between the variables differed significantly between the actresses and students, we calculated the F-value from the ratio of their respective chi-square/degrees of freedom values (see Johnson and Kotz, 1970b, p. 75 for relationship between the chi-square and F-distribution). Chi-square ratio comparison (F (24, 24) = 2.234, p < 0.01) between the two speaker groups showed that this association was significantly stronger for the actresses (mean contingency co-efficient .678) than for the students (mean contingency co-efficient .510; see Table 2).

<insert Table 2

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Overall, the majority of the rated speech samples were correctly identified for each of their respective speech recipient groups for both actress and student speech samples (see Table 3 for summary of raters' categorisations). Interestingly, actress-produced IDS and FDS speech samples achieved the highest correct identification rates, whereas their ADS speech samples were less well identified. In contrast, the majority of studentproduced ADS speech samples were correctly identified by the raters, with IDS and FDS samples achieving lower correct identification rates (Table 3). The overall recognition produced speech was much lower (57.77%).

<insert Table 3> Discussion

This study set out to evaluate the validity of standardised sentence production in comparative speech research. Our results suggest that successful reproduction of some of the acoustic characteristics of natural speech using simulated speech (e.g., speech elicited through descriptive scenarios and from speakers without interaction partner in the laboratory) may depend on the research paradigm ('simulated free speech' or standardised sentences) and also type of speaker (actresses or students).

Actresses

Consistent with our earlier findings in the 'simulated free speech' condition [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF], mean F 0 and vowel hyperarticulation measures produced by actresses in standardised sentences were similar to those found in natural interactions [START_REF] Uther | Do you speak E-n-g-l-i-s-h? A comparison of foreigner-and infant-directed speech[END_REF]. If anything, it could be argued that vowel hyperarticulation of the actresses in the sentence condition revealed a marginal improvement compared to their vowel hyperarticulation in the 'simulated free speech' condition, in that it bears a greater resemblance to hyperarticulation values of natural speech. FDS had been positioned

between IDS and ADS in the 'simulated free speech' condition 6 [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF] 6 In that study, parametric tests showed that FDS vowel space was not significantly different from IDS or ADS vowel space, although non-parametric tests followed the trend of the natural speech samples, and showed a significant difference between FDS and ADS vowel space with no difference between IDS and FDS vowel space.

21

whereas in the present study FDS vowel space was significantly more expanded than ADS vowel space, but not IDS vowel space. Interestingly, actresses were also able to improve their performance for vowel duration in the sentence condition, with IDS exhibiting longer vowel durations than the two adult conditions, which is a close approximation to the results of the natural speech samples.

We propose the following reason for these marginal improvements in the sentence compared to the 'simulated free speech' condition. In our earlier study [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF], we suggested that actresses should be used to role play and improvisations, explaining their ability to produce some of these modifications in the 'simulated free speech condition', particularly compared to the student speakers. Nonetheless, most of the actresses' work is likely to be based on scripts, and the extra task of improvising their own script may have interfered with their ability to produce a wider range of modifications in the 'simulated free speech' condition. Providing them with standardised sentences might thus have released them to concentrate fully on the production of the relevant speech modifications rather than the production of a script. These findings add further support to the notion that actresses are capable of producing simulated speech that is similar to speech in natural interactions (e.g., [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF]cf. Scherer 2003), and that their performance can even be improved by scripted speech.

Students

Interestingly, we were even able to approximate the mean F 0 findings previously found for natural speech [START_REF] Uther | Do you speak E-n-g-l-i-s-h? A comparison of foreigner-and infant-directed speech[END_REF] with standardised sentence production for our student speakers. This better approximation of mean F 0 is similar to previous research using simulated interactions (Biersack et al., 2005;[START_REF] Schaeffler | Comparing vocal parameters in spontaneous and posed child-directed speech[END_REF], but is also an improvement on the students' results for 'simulated free speech', which showed less similarity in F 0 to natural speech [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF]. As in the case of the actresses, although to a greater degree, it is possible that the additional requirement for the participants to invent their own script in our previous study [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF] might have interfered with the student speakers' ability to convincingly reproduce acoustic characteristics normally found in natural speech.

Another aspect that might also explain the improvement in performance for mean F 0 , is that the standardised sentences always followed each respective 'simulated free speech' condition. This was an intentional measure aimed to relax the participants and put them into the right mindset for each standardised sentence, similar to procedures used in basic emotional (cf. [START_REF] Scherer | Vocal communication of emotion: A review of research paradigms[END_REF] and irony research (e.g., [START_REF] Rockwell | Lower, slower, louder: vocal cues of sarcasm[END_REF]. It is thus possible that a slight training effect may have taken place for the increased F 0 . This would also be supported by the observation that the majority of student speakers found the sentence condition easier than the 'simulated free speech' condition. It is possible that this 'previous training' might have resulted in a more practiced and relaxed speech production, which consequently was perceived as less difficult by the speakers. However, this possibility remains to be confirmed.

Consistent with our findings for student 'simulated free speech' [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF], we were unable to replicate the occurrence of vowel hyperarticulation in both IDS and FDS in the standardised sentences condition. The occurrence of this hyperarticulation had been one of the main findings of Uther et al.'s (2007) natural speech study. It is surprising that the student hyperarticulation measures did not reflect the above discussed 'training effect', or benefit from the reduction of 'task load' to the same extent as the student F 0 measures or the actresses' hyperarticulation measures. The reason for this could be explained by the differing levels of conspicuousness of these two acoustic characteristics. Increased F 0 (pitch) is a more distinctive feature of IDS that is easily perceived by a naïve listener, and might thus be more likely to be approximated in 'simulated interactions', particularly where a 'training effect' is present. In contrast, hyperarticulation has been suggested to be an unconscious speech modification (e.g., [START_REF] Burnham | What's new pussycat? On talking to babies and animals[END_REF][START_REF] Lindblom | Explaining phonetic variation: A sketch of the H and H theory[END_REF], which might be less discernable to a listener, and therefore more difficult to replicate in 'simulated interactions'. To date, the occurrence of vowel hyperarticulation seems to have only been reported in studies where the speaker was either explicitly instructed to produce clear speech (e.g., [START_REF] Smiljani | Production and perception of clear speech in Croatian and English[END_REF], in human-computer interaction error feedback tasks (e.g., [START_REF] Oviatt | Modeling hyperarticulated speech during human-computer error resolution[END_REF], with actresses (e.g., [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF] or in comparative studies using real interaction partners who were perceived to be in need of some kind of linguistic modification (e.g., [START_REF] Burnham | What's new pussycat? On talking to babies and animals[END_REF][START_REF] Kuhl | Cross-language analysis of phonetic units in language addressed to infants[END_REF][START_REF] Uther | Do you speak E-n-g-l-i-s-h? A comparison of foreigner-and infant-directed speech[END_REF]. It is likely that relevant 'error' feedback from a physically present interaction partner clearly perceived as needing clarityenhancing linguistic modifications is crucial in eliciting this important feature in IDS (or any other relevant comparison speech recipient group), particularly if the speaker has no acting training or has not been specifically instructed to produce clear speech.

Previous exposure and ratings

Actresses and students did not report differing exposure to any of the speech recipient groups, suggesting that the differences in their performance were not due to their previous experience with any of the groups. Scherer (1986, p. 144) states that actresses might over-exaggerate obvious acoustic emotional cues, and miss other subtle ones.

Consistent with this view, we found that measures of actress vowel articulation and duration in the sentence condition were larger than those of the students and those found in the natural speech samples of [START_REF] Uther | Do you speak E-n-g-l-i-s-h? A comparison of foreigner-and infant-directed speech[END_REF]. This is also supported by the better rater identification of the different speech recipient groups for the actresses compared to the students. Most of the IDS and FDS speech samples for the actresses were correctly identified, whereas ADS achieved high confusion rates with IDS and FDS. It is possible that the actresses were exaggerating known stereotypical acoustic cues in those two speech types (e.g., high pitch in IDS, slow speech rate in FDS). In contrast, ADS as a speech type is less likely to have specific stereotypical acoustic cues, and this might have led to a poorer recognition rate for actress-produced ADS. It is also possible that the ADS speech samples were confused with IDS and FDS speech samples, because actress ADS speech samples comprised greater vowel articulation than all of the students speech samples. The recognition rates for student IDS and FDS were substantially lower than those of the actresses, but the recognition rate for ADS was relatively high for the student samples. This could be an artifact due to the majority of student speech samples being classified as ADS regardless of their actual speech recipient group, for instance, because of the smaller vowel articulation in the student speech samples compared to those of the actresses.

However, F 0 measures of the actresses were not significantly higher than those of the students and, if anything, their IDS F 0 measures were lower than those of the natural IDS speech samples [START_REF] Uther | Do you speak E-n-g-l-i-s-h? A comparison of foreigner-and infant-directed speech[END_REF]. As previously mentioned, vowel hyperarticulation in speech is probably less conspicuous than F 0 . Actresses' exaggeration of such a subtle acoustic cue (hyperarticulation) on the one hand, whilst not exaggerating a more obvious cue (F 0 ) on the other hand, would seem to contradict the assumption (cf. [START_REF] Scherer | Vocal communication of emotion: A review of research paradigms[END_REF] that actresses would fail to reproduce these more subtle cues.

Conclusions

Both student and actress speakers improved their reproduction of natural acoustic speech modifications using standardised sentences compared with their 'simulated free speech'.

These improvements are most likely to relate to a reduced 'task load', although a slight training effect in the sentence (compared to the 'simulated free speech') condition is also possible. Further research is required to investigate the relative importance of these factors. The difficulty in replicating hyperarticulation in simulated conditions with untrained, inexperienced or uninstructed speakers, even with a reduced 'task load', raises the question of what makes this modification such a unique characteristic in terms of its occurrence in linguistically relevant speech. We suspect that a reciprocal dynamic feedback between speaker and listener may be an important factor in the process of generating appropriate speech modifications, particularly if the speaker lacks acting training. A trade-off between the realism of the speech material and the need to limit speech content variability due to experimental control is probably inevitable. However, our results do suggest that if the experimental set-up requires such control and an interaction partner is absent, actresses should be used in preference to students.

Furthermore, scripted sentences should be used in preference to 'simulated free speech' scenarios, although the latter could be used as inductor dialogue.

variability typical of natural speech production. However, the validity of such standardised material is not well understood. Here, we evaluated the use of standardised sentences by comparing them to two existing, non-standardised datasets of simulated free and natural speech (the latter produced by mothers in real interactions). Standardised sentences and simulated free speech were produced by students and actresses without an interaction partner. Each dataset comprised recordings of infant-(IDS), foreigner-(FDS)

and adult-directed (ADS) speech, which were analysed for mean F 0 , vowel duration and hyperarticulation. Whilst students' mean F 0 pattern in standardised speech was closer to the natural speech than their previous 'simulated free speech', no difference in vowel hyperarticulation and duration patterns was found for students' standardised sentences between the three speech styles. Actresses' F 0 , vowel duration and hyperarticulation patterns in standardised speech were similar to the natural speech, and a part improvement on their 'simulated free speech'. These results suggest that successful reproduction of some acoustic measures (e.g., F 0 ) can be achieved with standardised content regardless of the type of speaker, whereas the production of other acoustic measures (e.g., hyperarticulation) are context-and speaker-dependent. No difference between the three speech recipient groups.

Simulated speech produced by actresses [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF] IDS greater than ADS. FDS positioned between IDS & ADS.

IDS greater than ADS & FDS. No difference between ADS & FDS.

No difference between the three speech recipient groups.

Unshaded cells represent aspects of simulated speech that are consistent with natural speech, light shaded areas indicate aspects that approximate natural speech, and darker shaded areas are inconsistent with natural speech.

  Fig1

Figure 1 .

 1 Figure 1. Mean vowel triangles as indexed by plotted F1/F2 mean values for the three

Figure 2 .

 2 Figure 2. IDS, FDS and ADS mean vowel area (calculated from F1/F2 vowel triangle

Figure 3 .

 3 Figure 3. IDS, FDS and ADS mean vowel duration for standardised sentence production

Figure 4 .

 4 Figure 4. IDS, FDS and ADS mean F 0 for standardised sentence production (right) and

Table 1

 1

		Vowel space	Mean F 0	Vowel duration
	Natural speech	IDS & FDS greater	IDS higher than	IDS longer than FDS
	samples	than ADS.	ADS & FDS. No	& ADS. No
	Uther et al. (2007)	No difference between IDS &	difference between ADS & FDS.	difference between ADS & FDS.
		FDS.
	Simulated speech	IDS smaller than	IDS greater than
	produced by	FDS & ADS. No	ADS. FDS
	students (Knoll et	difference between	positioned between
	al., 2009)	FDS & ADS.	IDS and ADS.

Table 2

 2

			Actresses			Students
		2	Contingency	Exact sig.	2	Contingency	Exact sig.
			co-efficient			co-efficient
	Rater 1	22.681	.656	.001	9.521	.491	.045
	Rater 2	27.982	.695	.001	15.5	.584	.002
	Rater 3	36.154	.739	.001	12.75	.546	.01
	Rater 4	29.167	.702	.001	6.5	.422	.171
	Rater 5	14.238	.567	.005	10.621	.511	.027
	Rater 6	30.539	.710	.001	10.621	.511	.027
	Total	154.993			66.68

Table 3

 3

				Rated
			IDS	FDS	ADS
	Actresses	IDS	93.34	3.33	3.33
		FDS	8.33	83.34	8.33
		ADS	23.33	28.33	48.34
	Students	IDS	48.34	28.33	23.33
		FDS	6.66	48.34	45.00
		ADS	6.66	18.34	75.00

Syllables in a word are exchanged with nonsense syllables to render the word unintelligible.

'Ecologically valid' as used here refers to voice production that might be close to natural speech production.

Hyperarticulation here refers to vowel space expansion due to shifts in formant 1 (F1) and formant 2 (F2) of the three corner vowels /a/, /i/ and /u/ (see[START_REF] Kuhl | Cross-language analysis of phonetic units in language addressed to infants[END_REF].

More than 20% of the cells had expected frequencies of less than five. To deal with this problem we calculated the exact significance for each of the raters' chi-square results.

Acknowledgements

We are grateful to two anonymous reviewers for helpful comments that greatly improved this manuscript. Our particular thanks go to David Bauckham and the 'The Bridge Theatre Training Company' for their invaluable help in recruiting the actresses used in this study. This research was supported by a research bursary from the Economic and Social Research Council (ESRC) to Monja Knoll.

Table captions:

Table 1 Comparison of findings of acoustic modifications in natural and simulated speech produced by actresses and students (after [START_REF] Knoll | Are actresses better simulators than female students? The effects of simulation on prosodic modifications of infant-and foreigner-directed speech[END_REF].

Table 2 Chi-square values, contingency co-efficient and exact significance for each of the raters' identification of IDS, FDS and ADS.

Table 3 Confusion matrix for type of speech recipient group (IDS, FDS and ADS) and rated speech recipient group for actresses and students (in percent). Shaded areas show percentages of correctly identified samples.


Zhi Shang
email: shangzhi@tsinghua.org.cn

Shuo Chen

Numerical Investigation of Diameter Effect on Heat Transfer of Supercritical Water Flows in Horizontal Round Tubes

Keywords: SCW, CFD, heat transfer, buoyancy, diameter, horizontal tube

The diameter effect on the heat transfer of supercritical water (SCW) flows in horizontal round tubes has been studied using computational fluid dynamics (CFD) technique. The numerical simulations are carried out by the STAR-CD solver combined with the user developed subroutines that control the numerical calculation procedures.

Through the tests it is found that the discretization scheme using CD, LUD or MARS will not affect the accuracy of the numerical simulations. Through the diameter effect studies, it is found that the heat transfer of supercritical water flows in the horizontal round tube is strongly affected by the buoyancy especially for the large diameter tube.

The large diameter (D=10mm) tube will have the high risk to have the strong heat transfer deterioration that can introduce 180 o C wall temperature difference between the top and bottom surfaces due to the buoyancy effects.

The magnitudes of the effects can be quantificationally expressed by a ratio of Grashof number over Reynolds number square. Under the high mass flux regime, the heat transfer deterioration will disappear for all the diameters from 5mm to 10mm. The different secondary flow patterns at different tube diameters are also studied.

Introduction

The applications about the flow and heat transfer of supercritical water, shorten as SCW, have taken a long time since 1930s. Supercritical water and fluid have many special characters that can be used in many special industrial areas. In the biomass gasification, the supercritical water is employed to generate hydrogen in [START_REF] Matsumura | Biomass gasification in near-and super-critical water: Status and prospects[END_REF].

Supercritical carbon dioxide is used as the working fluid to produce power and heat by the instrument utilizing solar energy in [START_REF] Zhang | Theoretical analysis of a thermodynamic cycle for power and heat production using supercritical carbon dioxide[END_REF]. In nuclear industry, Atomic Energy of Canada Limited (AECL) has the long-term plan to develop the supercritical water reactor (SCWR) CANDU that is for generation IV nuclear reactor. This kind of nuclear reactor will have the higher thermal efficiency compared with the light water reactor of generation III and generation III+ in [START_REF] Torgerson | CANDU technology for generation III+ and IV reactor[END_REF]. Recently, the more advanced concept of the supercritical water fast reactor has already been put forward in [START_REF] Mori | Heterogeneous cores for improved safety performance a case study: the supercritical water fast reactor[END_REF][START_REF] Cao | Fuel, Core Design and Subchannel Analysis of a Superfast Reactor[END_REF].

SCW has the gas-like characteristic of low viscosity, and the liquid-like characteristic of high density. Near the pseudo-critical temperature, SCW has the dramatic variations of the physical properties in [START_REF] Bazargan | Effect of buoyancy on heat transfer in supercritical water flow in a horizontal round tube[END_REF]. Therefore, it is important for users to understand the behaviors of the heat transfer of SCW affected by these characteristics when SCW is employed. Now some empirical correlations are available for predicting the heat transfer of SCW of [START_REF] Pioro | Heat transfer to supercritical fluids flowing in channels -empirical correlations (survey)[END_REF][START_REF] Pioro | Experimental heat transfer in supercritical water flowing inside channels (survey)[END_REF] in the tube.

However, almost all the correlations are based on the one-dimensional theoretical analysis without considering the 3D effect. Actually, in the horizontal tube flow, the gravity and buoyancy will affect the flow and heat transfer.

Usually, these effects will introduce a full-3D flow in the horizontal tube in [START_REF] Shang | Numerical investigation of system pressure effect on heat transfer of supercritical water flows in a horizontal round tube[END_REF][START_REF] Zhang | Numerical analysis of supercritical water heat transfer in horizontal circular tube[END_REF]. Therefore, it is necessary to use a multi dimensional method to analyze the flows in horizontal tubes.

At present, some of CFD codes such as STAR-CD, FLUENT and CFX had been adopted for 3D numerical simulations of supercritical water flows and heat transfers in the vertical channels in [START_REF] Roelofs | CFD analyses of heat transfer to supercritical water flowing vertically upward in a tube[END_REF][START_REF] Cheng | Numerical analysis of heat transfer in supercritical water cooled flow channels[END_REF][START_REF] Yang | Numerical investigation of heat transfer in upward flows of supercritical water in circular tubes and tight fuel rod bundles[END_REF]. In this paper, STAR-CD code is employed to study the flow and heat transfer of SCW in the horizontal tubes. Through the studies, the effects of tube diameters on the flow and heat transfer are investigated.

Thermal physical properties of SCW

In this paper, the thermal-physical properties of SCW are taken from the latest releases of the International Association of Properties of Water and Steam (IAPWS). Although there is no liquid-vapor phase transition, the thermal-physical properties of SCW always vary following the temperature changes. The sharp changes of properties exist in the vicinity around the pseudo-critical temperature, shown in Fig. 1. Through the studies in [START_REF] Shang | Numerical investigation of system pressure effect on heat transfer of supercritical water flows in a horizontal round tube[END_REF][START_REF] Roelofs | CFD analyses of heat transfer to supercritical water flowing vertically upward in a tube[END_REF][START_REF] Cheng | Numerical analysis of heat transfer in supercritical water cooled flow channels[END_REF][START_REF] Yang | Numerical investigation of heat transfer in upward flows of supercritical water in circular tubes and tight fuel rod bundles[END_REF], it is found that the thermal-physical properties of SCW affect the heat transfer of SCW straightly.

Therefore the various thermal physical properties have to be considered during CFD simulations.

Fig. 1 Variations of thermal-physical properties of SCW at the pressure 24.4MPa

Methodology

Because of the special thermal-physical properties of SCW, the flow cannot be treated as a simple incompressible flow with the constant physical properties. Therefore the mass, momentum and energy conservation equations are employed as the following equations.

Governing equations

0 = ∂ ∂ + ∂ ∂ i i x u t ρ ρ (1) ( ) m ij k k i j j i j ref i i i j i i s x u x u x u x g x p x u u t u +         ∂ ∂ -         ∂ ∂ + ∂ ∂ ∂ ∂ + - + ∂ ∂ - = ∂ ∂ + ∂ ∂ δ µ µ ρ ρ ρ ρ 3 2 (2) h i i j i ij k k i j j i i i i i s x T x x u x u x u x u x p u t p x hu t h +         ∂ ∂ ∂ ∂ + ∂ ∂         ∂ ∂ -         ∂ ∂ + ∂ ∂ + ∂ ∂ + ∂ ∂ = ∂ ∂ + ∂ ∂ α δ µ µ ρ ρ 3 2 (3)
where the relationship connected between enthalpy and temperature is given as

ref pref p T c T c h - =
. For turbulent flow, the corresponding turbulence model is employed to describe the effects of the turbulent fluctuations.

Turbulence modelling

When the flow is turbulent, the source terms in equation ( 2) and ( 3) can be defined as the following formulas modeled as Reynolds stress and turbulent diffusion flux of enthalpy.

( )

' ' j i j m u u x s ρ ∂ ∂ - = (4) ( ) i i j i j i h x h u x u u u s ∂ ∂ - ∂ ∂ - = ' ' ' ' ρ ρ (5)
where

i h t i x h h u ∂ ∂ - = σ µ ρ ' '
and the Reynolds stress term, ' ' j i u u ρ , can be presented by the turbulence models.

The former researches indicated that the choice of the turbulence model is a key issue for SCW simulations.

After studying the two dimensional tube flows, in [START_REF] Roelofs | CFD analyses of heat transfer to supercritical water flowing vertically upward in a tube[END_REF] it was found that the turbulence models having the anisotropic characters would give more accurate predictions. The influence of the near wall mesh partitions was also studied in [START_REF] Roelofs | CFD analyses of heat transfer to supercritical water flowing vertically upward in a tube[END_REF]. It concluded that the y + value near wall should be less than 1 when RANS (Reynolds Average Navier-Stokes) turbulence models are employed for SCW. In [START_REF] Cheng | Numerical analysis of heat transfer in supercritical water cooled flow channels[END_REF] it studied the sub-channels of triangle and square rod bundles and found the non-uniform distribution of the wall temperature along the circumferential perimeter using the SSG (the Reynolds Stress model of Speziale, Sarkar and Gatski) turbulence model that has the anisotropic characters. In [START_REF] Yang | Numerical investigation of heat transfer in upward flows of supercritical water in circular tubes and tight fuel rod bundles[END_REF] it employed different turbulence models to compare the CFD results with experiments and had the conclusion that high Reynolds number k-ε turbulence model with the Hassid and Poreh near-wall treatment would give more accurate simulations than low Reynolds number k-ε turbulence model and k-ω turbulence model.

In [START_REF] Shang | Numerical investigation of system pressure effect on heat transfer of supercritical water flows in a horizontal round tube[END_REF] it studied the horizontal tubes compared with the experiments in [START_REF] Bazargan | Effect of buoyancy on heat transfer in supercritical water flow in a horizontal round tube[END_REF] and found the Speziale non-linear high Reynolds k-ε turbulence model with the Hassid and Poreh near-wall treatment under y + < 1.0 can give good predictions of the heat transfer of SCW using STAR-CD code. In this paper, the mesh partition method (stretched mesh near wall and general structure mesh inside main flow domain), y + value and the Speziale non-linear high Reynolds k-ε turbulence model with the Hassid and Poreh near-wall treatment are adopted same as in [START_REF] Shang | Numerical investigation of system pressure effect on heat transfer of supercritical water flows in a horizontal round tube[END_REF][START_REF] Shang | CFD investigation of vertical rod bundles of supercritical water-cooled nuclear reactor[END_REF][START_REF] Shang | Numerical investigation of supercritical water-cooled nuclear reactor in horizontal rod bundles[END_REF].

The Speziale non-linear high Reynolds k-ε turbulence model can be presented by the turbulence kinetic energy and the turbulence dissipation rate in [START_REF] Speziale | On nonlinear k-l and k-ε models of turbulence[END_REF] equations as the followings.

      ∂ ∂         + ∂ ∂ + + ∂ ∂         + ∂ ∂ - -         ∂ ∂ - ∂ ∂ = ∂ ∂ + ∂ ∂ i k t i NL t i i i i t i h i j i ij t i i x k x P x u k x u x g x u S x ku t k σ µ µ µ ρ µ ρε ρ ρσ µ ρ ρ 3 2 (6)       ∂ ∂         + ∂ ∂ + + ∂ ∂ + ∂ ∂ - -         ∂ ∂         + ∂ ∂ - ∂ ∂ = ∂ ∂ + ∂ ∂ i t i NL t i i i h i t i i i i t j i ij t i i x x P k C x u C x g k C k C x u k x u x u S k C x u t ε σ µ µ ε µ ρε ρ ρσ ε µ ε ρ ρ µ µ ε ρε ρε ε ε ε ε ε ε 1 4 3 2 2 1 3 2 (7) where i j j i ij x u x u S ∂ ∂ + ∂ ∂ = ,         ∂ ∂         + ∂ ∂ - ∂ ∂ - ∂ ∂ - = i i i i j i ij j i j i NL x u k x u x u S x u u u P µ ρ µ ρ 3 2 ' ' and ε ρ µ µ 2 k C t =
. Table 1 gives the corresponding constant coefficients for the Speziale non-linear high Reynolds k-ε turbulence model. Table 1 Coefficients of the Speziale non-linear high Reynolds k-ε turbulence model

C µ σ k σ ε σ h C ε1 C ε2 C ε3 C ε4 0.09 1.0 1.219 0.9 1.44 1.92 1.44 -0.33
Normally, the high Reynolds k-ε turbulence models employ wall functions to avoid directly describing the fluid flow near wall where y + < 10.0 in [START_REF]STAR-CD Methodology[END_REF]. For dealing with this issue, STAR-CD uses some one-equation turbulence models to perform the simulations for the regions of y + < 10.0. Through the sensitive studies of the one-equation turbulence models for the heat transfer of SCW, in [START_REF] Shang | Numerical investigation of system pressure effect on heat transfer of supercritical water flows in a horizontal round tube[END_REF] it indicated that the Hassid and Poreh in [START_REF] Hassid | A turbulent energy dissipation model foe flows with drag reduction[END_REF] model would be the best to describe the flow and heat transfer of SCW within the near wall regions. This one-equation mode calculates the turbulence kinetic energy k from the transport equation like equation ( 6) and the turbulence dissipation rate ε is gotten from an algebraic function as the following. , where y is the normal distance from the wall.

Numerical method

Through the tests, it is found that the steady and unsteady simulations for the horizontal tubes can reach the same results finally. However the unsteady calculation will spend longer time than the steady computation. Therefore, in this paper, all the simulations are based on the steady calculation. It means all the temporal terms in the equations (1, 2, 3, 6 and 7) can be treated as 0, i.e., 0

= ∂ ∂ t φ .
The finite volume scheme is employed to do the spatial discretization. Generally, the differential manner of the convective and diffusive fluxes will affect the numerical accuracy and stability. As usual CFD applications, the central differential scheme for the diffusive fluxes is employed. It is difficult for the convective fluxes to keep a high differencing accuracy meanwhile preserving the numerical stability especially for the sharp changes of the physical properties like SCW around the pseudo-critical temperature in Fig. 1. The following convective differencing schemes, shown in Table 2, will be tested in this paper. In Table 2, CD means the central differencing, LUD means linear upwind differencing and MARS is abbreviatory for Monotone Advection and Reconstruction Scheme. QUICK is of the quadratic upstream interpolation of convective kinematics. In the practical numerical application, QUICK scheme uses two points upstream and one point downstream to get the interpolated value. If the grid is skewed, it has the potential risk to have the numerical dispersion in [START_REF]STAR-CD Methodology[END_REF].

The other three schemes have the same accurate order. LUD is derived from a scheme originally proposed for structure meshes. Same as QUICK scheme it can produce solutions that are outside the physical bounds on φ in [START_REF]STAR-CD Methodology[END_REF]. CD simply interpolates linearly on the nearest neighbor grids without considering the flow direction. This scheme produces less numerical diffusion, but can be dispersive potentially in [START_REF]STAR-CD Methodology[END_REF]. MARS does not rely on any problem dependent parameters to work properly and it can automatically deal with all flow problems. Of all schemes available in STAR-CD, MARS possesses the least sensitivity of solution accuracy to the mesh structure and skewness in [START_REF]STAR-CD Methodology[END_REF].

After deciding the differencing scheme, the last issue for the numerical method is the solution algorithm. Here SIMPLE algorithm in [START_REF] Patankar | A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows[END_REF] is chosen for the steady flow situation and PISO algorithm in [START_REF] Issa | Solution of the implicitly discretised fluid flow equatins by operator-splitting[END_REF] is used for the transient (unsteady) flow regime. During the simulation, the default settings in the code are adopted. The CG (conjugate gradient) method in [START_REF] William | Fundamentals of aerodynamics[END_REF] is used to solve the final linear algebraic equations.

Physical problem and computational conditions

Fig. 2 shows the schematic geometry. The computational test parameters are used same as the experiments in [START_REF] Bazargan | Effect of buoyancy on heat transfer in supercritical water flow in a horizontal round tube[END_REF].

Fig. 2 Schematic geometry of flow system

In the geometry sketch, L is the tube length and D is the tube diameter. The supercritical water with the system pressure 24.4MPa enters into the tube from the right-hand-side, flows out from the left-hand-side and is heated by the tube wall same as the experiment. The flow direction is normal to the gravity.

In the former studies, in [START_REF] Shang | Numerical investigation of system pressure effect on heat transfer of supercritical water flows in a horizontal round tube[END_REF] it used different meshes to test the horizontal tube and found the suitable mesh partitions. In this paper, mesh partitions near wall are same as in [START_REF] Shang | Numerical investigation of system pressure effect on heat transfer of supercritical water flows in a horizontal round tube[END_REF] keeping y + < 1.0. In the practice, the specific mesh partitions are found by the mesh sensitive studies for every individual diameter.

The boundary conditions for the round tube are straightforward. The inlet keeps the uniform mass flux and the wall boundary with a uniform heat flux. The default outlet settings of STAR-CD code are adopted at the outlet.

Discretization scheme tests

The mass flux of 340kg/m 2 s and the wall heat flux of 300kW/m 2 are used as the flow parameters for the discretization scheme influence studies. They are same as the experiment in [START_REF] Bazargan | Effect of buoyancy on heat transfer in supercritical water flow in a horizontal round tube[END_REF]. In the experiment, the round tube is L=3m long with the inner diameter D=6.3mm. Fig. 3 shows the numerical results of the 4 cases in Table 2 compared with the experiment data.

(a) At bottom surface (b) At top surface Fig. 3 Comparisons of discretization scheme influence on heat transfer coefficients From Fig. 3, it can be seen that QUICK scheme (case 4) departures from experiments more than the others especially when the bulk temperature, which is the average fluid temperature at the corresponding cross section vertical to the tube axes, is greater than 400 o C at the bottom surface. At the top surface, all of the schemes get the similar accurate results. The errors of CD and LUD schemes are within ±1% using MARS scheme as the reference.

However, QUICK scheme has the maximum error exceeds 5%. It can be seen that differencing discretization schemes are not sensitive to the numerical simulations for the flow and heat transfer of SCW, just among CD, LUD and MARS schemes. The MARS scheme will be employed in this paper for the late case studies.

Results and Discussions

After the discretization scheme tests, the formal studies of the diameter effects on the heat transfer are carried out. Table 3 shows the corresponding cases. The mesh sensitivity studies are carried out for all the cases to get the mesh independent results as in [START_REF] Shang | Numerical investigation of system pressure effect on heat transfer of supercritical water flows in a horizontal round tube[END_REF][START_REF] Shang | CFD investigation of vertical rod bundles of supercritical water-cooled nuclear reactor[END_REF][START_REF] Shang | Numerical investigation of supercritical water-cooled nuclear reactor in horizontal rod bundles[END_REF].

Low mass flux regime

The low mass flux regime (340 kg/m 2 s) of case 5-10 in Table 3 is firstly studied. without the evident temperature increase. This phenomenon is quite like the boiling heat transfer that the heat is absorbed by the liquid to generate the vapor rather than to increase the temperature in [START_REF] Bennett | Forced convective boiling in vertical tubes for saturated pure components and binary mixtures[END_REF]. Therefore the tube wall temperature does not increase evidently. When the bulk enthalpy greater than 2250kJ/kg, the specific heat ( where will be up to the stronger one. Due to the stronger buoyancy in large diameter tube, seen in Fig. 6, when the fluid reaches the upper domain the gravity, comparing with buoyancy, is not strong enough to drive the fluid down.

However, because of the blockage of the top wall, the fluid cannot be driven flowing up anymore. Finally the fluid is stopped at the upper domain of the tube to generate a stagnant flow. The stagnation flow cannot provide the convection heat transfer to take away the accumulated heat. Therefore it will lead the temperature ascending. For an extreme, it can make the wall temperature to increase abruptly, shown in Fig. 4(b).

Usually the Gr/Re 2 ratio is employed to quantify the buoyancy effect in [START_REF] Bazargan | Effect of buoyancy on heat transfer in supercritical water flow in a horizontal round tube[END_REF]. Once it has the order of unity or higher, the buoyancy effect cannot be neglected. In physics, the ratio represents the competition between the buoyancy and inertia forces. The greater the ratio value the stronger the buoyancy effect. The definition of the Gr number uses the following formula that considers the temperature gradient variations inside the flow field. The buoyancy not only affects the heat transfer but also affects the secondary flow patterns as well. Fig. 7 shows the velocity vectors of the secondary convective flow of the cross section at the pseudo-critical temperature where the bulk temperature equals to the pseudo-critical temperature (382.7 o C). These two velocity vectors are different. From Fig. 7, it can be seen that at large diameter (D=10mm) the circumfluence locates at the lower part of the tube and the centers of the circumfluence are near the wall. A wide stagnation domain can be observed for the large diameter of D=10mm near the top region. 10) is chosen as the theoretical prediction formula in [START_REF] Dittus | Heat transfer in automobile radiators of the tubular type[END_REF]

High mass flux regime

As the former studies for the horizontal tubes, the high mass flux situation is also studied in this paper using cases 11-16 in Table 3. In [START_REF] Bazargan | Effect of buoyancy on heat transfer in supercritical water flow in a horizontal round tube[END_REF] it declared that at the conditions of mass flux of 964kg/m 2 s and heat flux of 307kW/m 2 the buoyancy effect can be negligible. In [START_REF] Shang | Numerical investigation of system pressure effect on heat transfer of supercritical water flows in a horizontal round tube[END_REF] it studied this flow condition at different system pressures and also found the heat transfer characters of the high mass flux were different from the low mass flux. Therefore it is necessary to do the studies of the diameter effects for the horizontal tubes of SCW at high mass flux. Here the conditions of mass flux of 964kg/m 2 s and heat flux of 307kW/m 2 are kept same as the high mass flux regime in [START_REF] Bazargan | Effect of buoyancy on heat transfer in supercritical water flow in a horizontal round tube[END_REF][START_REF] Shang | Numerical investigation of system pressure effect on heat transfer of supercritical water flows in a horizontal round tube[END_REF]. In [START_REF] Bazargan | Effect of buoyancy on heat transfer in supercritical water flow in a horizontal round tube[END_REF][START_REF] Shang | Numerical investigation of system pressure effect on heat transfer of supercritical water flows in a horizontal round tube[END_REF] it found the high mass flux would induce weak buoyancy effects. Here the quantificational analysis of the Gr/Re 2 ratio shown in Fig. 11 will help to understand the weak buoyancy effect of the high mass flux. Fig. 11 shows the Gr/Re 2 ratio comparisons for different tubes at the bulk enthalpy of 2143.59kJ/kg (382.7 o C). It can be seen that all the Gr/Re 2 ratios are much less than 1. This means the high mass flux can eliminate the buoyancy effects.

Conclusions

The heat transfer characteristics of SCW can be affected by many influence factors, such as geometry sizes, flow conditions and driven forces. A good understanding to these influences is very important for the facilities (e.g. SCWR) which use SCW as the refrigerant. Following the previous works in [START_REF] Bazargan | Effect of buoyancy on heat transfer in supercritical water flow in a horizontal round tube[END_REF][START_REF] Shang | Numerical investigation of system pressure effect on heat transfer of supercritical water flows in a horizontal round tube[END_REF], this paper extends the research focus on the diameter effect on the heat transfer. Through the studies, it is found when the mass flux is low the diameter will strongly affect the heat transfer and wall temperature for the horizontal tubes due to the buoyancy effects. Except this, the following observations can be made:

(1) Through the tests, the convective differencing discretization schemes are not sensitive for the flow and heat transfer of SCW among CD, LUD and MARS. In practice, MARS scheme in STAR-CD is recommended.

(2) The diameter has the great influences on the heat transfer for the low mass flux regime. The small diameter is helpful to reduce the buoyancy effect and to enhance the heat transfer. The wall temperature difference increase following the increase of the tube diameter. The strong buoyancy can generate a large wall temperature difference.

( The number of tables: 3

Fig. 4

 4 shows the variations of the wall temperature against the bulk enthalpy at different diameters from 5mm to 10mm. All the curves of the wall temperature at the bottom surface almost collapse together in Fig.4(a). They have the same shapes and tendencies. When the bulk enthalpy is less than 1750kJ/kg (365.42 o C), the wall temperature ascends pseudo-linearly following the enthalpy increase. The wall temperature curves become flat between 1750kJ/kg (365.42 o C) and 2250kJ/kg (383.95 o C) because this enthalpy gap just covers over the pseudo-critical point (2143.59kJ/kg, 382.7 o C), in Fig.1. The big specific heat capacity (c p ) will allow SCW to absorb lots of heat

Fig. 4 Fig. 5

 45 Fig.4Comparisons of different diameter influence on wall temperature Fig.5shows the variations of the heat transfer coefficients. From Fig.5, it can be seen that the heat transfer coefficients decrease following the diameter increase. The values of heat transfer coefficients around the pseudo-critical temperature not only reduce the amplitude but also turn down to the valley following the increase of the diameter. This phenomenon is called as the heat transfer deterioration.

Fig. 6 Fig. 7

 67 Fig.6Gr/Re 2 ratio comparisons at low mass flux Fig.6shows the Gr/Re 2 ratio comparisons curves of different tubes at the cross section with the bulk enthalpy of 2111.74kJ/kg (382.4 o C). From Fig.6, it can be seen that near the bottom surface (r/R = -1) all the Gr/Re 2 ratios of the tubes are less than 1. It means the buoyancy effect on the heat transfer can be ignored. However, near the top surface (r/R = 1), the Gr/Re 2 ratios are larger than 1. It means there are strong buoyancy effects around the top surface.

Fig. 8

 8 Fig.8shows the comparisons between the CFD results and the classical theoretical predictions. Here the Dittus-Boelter formula for single phase fluids shown in equation (10) is chosen as the theoretical prediction

  .

  Nusselt number and Pr b is Prandtl number of the fluid at the bulk temperature.

Fig. 8

 8 Fig. 8 Comparisons between CFD and classical theoretical prediction From Fig. 8, it can be seen, the differences between Dittus-Boelter formula and CFD are smaller at the bottom surface. However, at the top surface, the predictions of Dittus-Boelter formula are quite different from CFD results. The reason is because Dittus-Boelter formula does not consider the buoyancy effects.

Fig. 9 Fig. 9

 99 Fig.9shows the variations of the heat transfer coefficients at different diameters. From the comparisons, it can be seen that the top surface and the bottom surface have the similar variations of the heat transfer coefficients. It is only the heat transfer coefficients at the bottom surface are more concentrated than the top surface especially when the bulk temperature is less then the pseudo-critical temperature. The small diameter has the higher heat transfer coefficients.

Fig. 11

 11 Fig. 11 Gr/Re 2 ratio comparisons at high mass flux 6.3 Circumference distributions of wall temperature According to the practical engineering design, the tube wall temperature distribution is one of the critical criteria for the safe operations in [6, 9, 12-13]. Therefore it is necessary to know the wall temperature distributions along the circumference. Fig. 12 shows wall temperature distributions along the circumference for different diameters at both regimes of low and high mass flux. The cross sections are at the bulk enthalpy of 2111.74kJ/kg (382.4 o C) for the low mass flux regime and the pseudo-critical bulk enthalpy of 2143.59kJ/kg (382.7 o C) for the high mass flux regime. The θ direction starts from the bottom surface, turns to the top surface following counter-clockwise from 0 o to 360 o .

)( 4 )

 4 The low mass flux has the risk to introduce the heat transfer deteriorations which hinder the heat transfer for the horizontal tubes. The effects are becoming stronger following the diameter increase. The heat transfer deteriorations not only affect the wall temperature, but also produce different secondary flow patterns at the cross sections for different diameters. The high mass flux can eliminate the heat transfer deteriorations caused by the buoyancy. At high mass flux regime, the Gr/Re 2 ratios are much less than 1 for all the diameters. Even the heat transfer coefficients can be predicted by the classical theoretical Dittus-Boelter formula.

Fig. 1 1 Fig. 2 Fig. 3 The number of figures: 3 Fig. 3 The number of figures: 3 Fig. 4 The number of figures: 4 Fig. 4 The number of figures: 4 Fig. 5 The number of figures: 5 Fig. 6 The number of figures: 6 (Fig. 7 The number of figures: 7 Fig. 7 The number of figures: 7 Fig. 8 The number of figures: 8 TheFig. 8 First author: Zhi Shang The number of figures: 8 Fig. 9 The number of figures: 9 Fig. 9 First author: Zhi Shang The number of figures: 9 The

 112333344445566777788889999 Fig. 1 Variations of thermal-physical properties of SCW at the pressure 24.4MPa

Fig. 10 First author: Zhi Shang The number of figures: 10 The

 1010 Fig. 10 Comparisons between CFD and Dittus-Boelter formula

Fig. 10

 10 Fig. 10 Comparisons between CFD and Dittus-Boelter formula

Table 2

 2 Convective differencing discretization schemes

	Cases	Discretization scheme	Accuracy of differencing scheme
	1	CD	second order
	2	LUD	second order
	3	MARS	second order
	4	QUICK	third order

Table 3

 3 Flow conditions of simulation cases

	Cases	System pressure	Mass flux	Heat flux	Diameters
	5 -10	24.4 MPa	340 kg/m 2 s	300 kW/m 2	5 -10 mm
	11 -16	24.4 MPa	964 kg/m 2 s	307 kW/m 2	5 -10 mm

Table 1

 1 Coefficients of the Speziale non-linear high Reynolds k-ε turbulence model

	C µ	σ k	σ ε	σ h	C ε1	C ε2	C ε3	C ε4
	0.09	1.0	1.219	0.9	1.44	1.92	1.44	-0.33

Title of paper: Numerical Investigation of Diameter Effect on Heat Transfer of Supercritical Water Flows in Horizontal Round Tubes First author: Zhi Shang The number of tables: 1Table 2

 2 Convective differencing discretization schemes

	Cases	Discretization scheme	Accuracy of differencing scheme
	1	CD	second order
	2	LUD	second order
	3	MARS	second order
	4	QUICK	third order
	Title

of paper: Numerical Investigation of Diameter Effect on Heat Transfer of Supercritical Water Flows in Horizontal Round Tubes First author: Zhi Shang The number of tables: 2

Table 3

 3 Flow conditions of simulation cases

	Cases	pressure	Mass flux	Heat flux	Diameters
	5 -10	24.4 MPa	340 kg/m 2 s	300 kW/m 2	5 -10 mm
	11 -16	24.4 MPa	964 kg/m 2 s	307 kW/m 2	5 -10 mm

Title of paper: Numerical Investigation of Diameter Effect on Heat Transfer of Supercritical Water Flows in Horizontal Round Tubes First author: Zhi Shang

Acknowledgements

The first author wishes to acknowledge the CD-adapco London Company for providing the software and the technique supports.