Améni Makhlouf
email: makhouf.ameni@gmail.com

Bruno Marhic

Laurent Delahoche

Jean-Baptiste Masson

Hassani Messaoud

A new approach for "Smart Heating"

Keywords: Heating management system, belief function theory, mass distribution I

This paper presents a heating management algorithm that models and handles uncertainties in buildings, in order to design and produce a temperature trend that will be inserted in the Smart an Predictive Heating System (SPHS). The aim of this system is to reduce energy consumption in the building whilst maintaining a comfortable ambiance for the occupant. In this paper we propose two different mass distribution designs, we compare them and we present and discuss different experimental results in order to show the reliability of our proposed solution.

Introduction

Works of research aim to develop methods to reduce energy consumption and decrease its cost in the building. In fact, different elements have a direct influence on the heating management systems; amongst them the occupancy, the weather forecast and the thermal comfort. Works of research study these aspects separately for public buildings and residential buildings.

The first aspect that energy management models should consider is the occupancy as it strongly contributes to reducing the building's energy consumption. Some works of research study use the occupancy profile, for example, [START_REF] Yang | The coupled effects of personalized occupancy profile based HVAC schedules and room reassignment on building energy use[END_REF][START_REF] Azar | Evaluating the impact of extreme energy use behavior on occupancy interventions in commercial buildings[END_REF] demonstrate that a personalized occupancy profile on the HVAC start/stop schedule could save up to 9% energy compared to the conventional schedules. In addition, the occupant's activity or user's behavior is as important as the occupancy because it gives indications for the occupancy schedule. Therefore, this research [START_REF] Aerts | A method for the identification and modelling of realistic domestic occupancy sequences for building energy demand simulations and peer comparison[END_REF] concentrates on studying the occupant's behavior to define occupancy patterns in order to reduce energy consumption in residential buildings. The second aspect is the influence of the weather forecast on buildings, which was the topic for numerous papers. For example, in [START_REF] Pappas | Numerical investigation on thermal performance and correlations of double skin façade with buoyancy-driven airflow[END_REF] they developed a model to analyze the thermal performance of a double skin façade with buoyancy-driven airflow. The third aspect is the thermal comfort which is related to the two aspects quoted previously and it cannot be determined if the occupancy state is not clear because we usually try to establish a comfort ambiance when the occupant is at home or before he arrives (preheating period).

Different studies integrate different methods to maintain a reasonable thermal comfort state in the building. For example, a new control strategy for commercial buildings is introduced in [START_REF] Xue | A fast chiller power demand response control strategy for buildings connected to smart grid[END_REF], which aims to maintain internal thermal comfort by regulating the chilled water flow distribution.

A smart building is a building that incorporates smart technology, which refers to automated systems, sensors, building managements systems and data gathering devices. To collect information and to process it, we need to use a data fusion algorithm. In fact, different studies on heat management in buildings rely on the fusion of different information provided by the multiple sensors planted in the smart building. For example in [START_REF] Wanga | Multi-agent control system with information fusion based comfort model for smart buildings[END_REF] they propose an indoor energy and comfort management model based on information fusion using ordered weighted averaging (OWA) aggregation that was associated to a multi-agent building control system with particle swarm optimization (PSO) in order to achieve a high level of comfort with minimum power consumption.

The Dempster-Shafer method has proved its efficiency in different fields despite the risk of generating a conflict mass in the case of numerous and heterogeneous sources of information. In a previous work [START_REF] Makhlouf | Smart and Predictive Heating System: Belief model for indoor regulation[END_REF], we proposed an approach based on the Dempster-Shafer theory and we obtained encouraging results; however, since we aggregate heterogeneous and numerous sources we obtain an important conflict mass.

In this paper, we aim to reduce the conflict mass but we didn't use a conflict management algorithm and we didn't reduce the number of sources of information. We tried to contextualize the different mass distributions for certain sources and by doing so we tried to obtain the suitable decision with an acceptable conflict mass. In fact in the current work we will unify the different frames of discernment to reduce the conflict mass even more.

In fact, in different works researchers use the vacuous extension to unify the frames of discernment as in [START_REF] Mercier | Decision fusion for postal address recognition using belief functions[END_REF] where they use it to obtain the suitable address in the process of address recognition. Our main contribution is to generate the temperature trend to control the SPHS without generating an important conflict mass and the contribution is to demonstrate the flexibility of our algorithm as we test it on realistic scenarios as presented in the simulation section. This paper is organized as follows: Section 2 briefly introduces the belief theory and the TBM model. In section 3 our approach is explained in detail. Several simulation case studies are presented and discussed in section 4. Finally in section 5 we conclude the paper.

II. Preliminary notion

A. Belief function theory

The Dempster-Shafer theory, known as the evidence theory, is a powerful mathematical tool to model and fuse uncertain and inaccurate data. It was introduced by Dempster in 1967 and improved by Shafer in 1976 [START_REF] Shafer | A mathematical theory of evidence[END_REF]. The assets of this theory are its flexibility to model the information and its ability to represent the ignorance with a clearer and more efficient method than the probabilistic functions [START_REF] Ph | The combination of evidence in the transferable belief model[END_REF].

We define the Frame of Discernment (FoD) Ω as a set of N hypotheses that represent the exhaustive and exclusive solutions to the problem.

j i and , Ø; H with } H , … , H , {H i N 2 1 ≠ ∈ ∀ = ∩ = Ω N j i H j (1)
Therefore, we can define the power set 2 Ω = {A/ A⊆Ω}. This set presents the singletons hypothesis and all disjunctions of hypothesis 2 Ω = {Ø, H 1 ,…,H n , H 1 ∪H 2 , ……, Ω}. Thus we present the element that characterises the theory of evidence i.e. the mass function or the basic belief assignment (BBA) of each element of 2 Ω by the following relation.

 Ω ⊆ Ω = → → A A m with A m A m 1 ) ( ) ( ] 1 , 0 [ 2 :
(

The main combination rule of two mass functions is the orthogonal combination known as the Dempster rule of combination. For two sources S1 and S2 having respectively m1 and m2 as bba, the Dempster rule is defined by:

 = ∩ - = ⊕ A C B C m B m k A m m ) ( ) ( 1 1 ) ( 2 1 2 1 (3)
Where K presents the conflictual mass between the combined evidence function and defined by:

 = ∩ = Ø 2 1 ) ( ) ( C B C m B m k (4)

B. The Transferable Belief Model (TBM)

The Transferable Belief Model (TBM) is a model for quantified belief based on the use of belief functions. This formalism can model and manage doubt independently of the hypotheses. This is a major advantage of this theory compared to probabilistic one [START_REF] Ph | The transferable belief model[END_REF]. The TBM is based on a two-level model: the first level is the credal level and the second level is the pignistic level. The TBM conjunctive rule consists in combining beliefs linked to each expert with a conjunctive combination. We associate the mass m1 to the source 1 of information (i.e. expert 1) and the m2 to the source 2, the combination is as follows:

(5)

In addition, the following relation presents the pignistic probability, which is defined for each single hypothesis of Ω:

 ∈ Ω ⊆ - = A Y A m A A m Y BetP , Ø)) ( 1 ( ) ( ) ( (6)
For the different simulations and combinations we will use the Transferable Belief Model (TBM); consequently the decision will be taken according to the maximum of the pignistic criterion.

C. Discounting

To define the reliability of a final decision about a singleton hypothesis, it is possible to weigh the influence of a sensor in the final fusion process without completely removing it. The discounting proposed by Shafer [START_REF] Shafer | A mathematical theory of evidence[END_REF], associates a reliability index α∈[0, 1], and the new mass functions are presented as follows:

( ) (1 ) ( ) ( ) ( )(1 ) m A m A m m α α α = -   Ω = + Ω -  (7)

D. The vaccuous extension

The combination of two sources of information requires that combined mass functions share the same FoD, but in our case study, the experts state information on different FoD. However, it is possible to aggregate information that does not share the same FoD by translating it to the frame product [START_REF] Mercier | Decision fusion for postal address recognition using belief functions[END_REF]. This principle is known as the vacuous extension in the belief functions theory.

Let Θ and Ω represent two FoD. A mapping

Ω Θ →2 2 :
ρ is a refinement of Θ if it verifies the following properties [START_REF] Mercier | Decision fusion for postal address recognition using belief functions[END_REF]:

1. The set { } ( ) { } Ω ⊆ Θ ∈ 2 ,θ θ ρ is a partition of Ω.

For all

Θ ⊆ A : { } ( )  A A ∈ = θ θ ρ ρ ) ( (8)
Then the vacuous extension of m θ to Ω is represented as follows: a bba m θ on Θ may be transformed without any loss of information into a bba m Ω on a refinement Ω of Θ by transferring each mass

m θ (A) for A⊆Θ to )) ( ( ) ( : ) ( A m A m A B ρ ρ θ Ω = = III.

Method description

Our method has for objective to aggregate different and uncertain information provided by the sources of our three experts (Occupancy, Thermal comfort and Weather forecast). The fusion model we propose is subdivided into two parts; the first one where information is collected and treated and, the second one where we aggregate information to make a decision. The algorithm will produce a temperature trend, which will be inserted in the Smart and Predictive Heating System (SPHS).

A. Block B1: Occupancy

The Block B1 is the occupancy fusion part; it has three independent information sources or experts as in Fig. 1: the in/out sensor, and the weekly schedule of occupant sensors known as expert occupancy 1, and 2 respectively. The fusion of the two experts gives a decision on the occupancy state of the room.

•

Source occupancy 1: the presence sensor (Ps)

• Source occupancy 2: the daily Schedule(Sc) fixed by the occupant.

The occupancy expert has for FoD Ω1 = {Sun, So}; meaning Ω1 = {Soon unoccupied, Soon occupied}.

B. Block B2: Thermal comfort

The thermal comfort is defined in [START_REF] Cantin | Complexity of thermal comfort in buildings[END_REF] as "a state of satisfaction of the body against the thermal environment". However, the concept of comfort varies from one person to another and different statistic studies were elaborated on representative samples of people to establish the different aspects of the thermal comfort criteria. Thus, in ISO 7730-2005 « Ergonomics of the thermal environment --Analytical determination and interpretation of thermal comfort using calculation of the PMV (Predicted Mean Vote) and PPD (Predicted Percentage of Dissatisfied) indices and local thermal comfort criteria » we can distinguish the intervals of different environmental characteristics that define the state of comfort or discomfort of a person in a specific ambience. We use different sensors to gather the information for each source. For instance the room temperature is measured by a thermometer and the relative velocity and humidity is given by the controlled mechanical ventilation (CMV) installed in the room. While the clothing expert is defined according to the seasons and the information for the activity is provided by different sensors. The FoD for the B2 is Ω2= {TC, Comf, TH}, meaning {Too-Cold, Comfortable, Too-Hot}. In our study, we will consider the following characteristics as the inputs (i.e. experts) of the block B2:

•

The temperature of comfort (Tc) in Celsius The first mass distribution represents the three hypothesis, their intersection between them and the mass of ignorance (m(Ω)). However in the second distribution we eliminate the assignement on the comfort and replace it with a mass of ignorance, because we know for certain when it is hot or cold but the concept of comfort is relative from one person to another. So the difference between the two mass distributions is in the the second one the masses are less comitted, but that doesn't affect the reliability, on the contrary it provides better results. We will present a simulation for different scenarios in section IV for the two distributions and we wil compare their results.

C. Block B3: Weather forecast

We will use the data, provided by the latest version of the weather model AROME [START_REF] Seity | The AROME-France convective scale operational model[END_REF] for the fusion of block B3. The nebulosity influences the temperature in the building and outdoors during the day and the night. Thus, our « expert temperature » will depend on the variation of the nebulosity. We specify an interval for each temperature value and we attribute a function to define the masses in that interval. Since AROME gives new prediction values every 3 hours, the fusion for block B3 will be repeated every 3 hours to update our information. The sources for this block B3 are: the external temperature (T), the wind (W), the nebulosity (N) and the precipitation (P). The thermal comfort expert has for FoD Ω2 = {TH, C, TC}; meaning Ω2 = {Too Hot, Comfortable, Too Cold}.

We integrate the result of the weather forecast aggregation as a source of information associated to the thermal comfort expert and not as an independent expert for two reasons. The first one is to minimize the conflict mass in the final result and the second one is to simplify the calculation process.

D. The frame of discernement for the fusion algorithm

Each expert gives its opinion on a different FoD, so we have two different FoDs, Ω1 = {Sun, So} and Ω2 = {TH, C, TC}. We use the vacuous extension to create an efficient fusion model we need to combine these two FoDs in order to obtain one FoD that gives us the necessary information; Thus the frame product, which we will use to make our decision rule for the different scenarios, will be Ω1×Ω2 = {(Bi, TH), (Bi, C), (Bi, TC), (Bo, TH), (Bo, C), (Bo, TC)}.

IV. Simulation results

We will present different real-life scenarios to prove the efficiency and reliability of the proposed approach to fuse heterogeneous, erroneous and uncertain data. The final decision provides a contextual temperature trend, which is a kind of predictive temperature reference, in order to manage the SPHS.

For each scenario, we will give the simulation results with the first and the second mass distribution for each scenario and we will make the decision concerning the heating system.

A. First scenario

The first scenario presents the case of a regular working day morning. The occupant is getting ready to go to work at 8:30 am and meanwhile he opens a window to freshen the room. For the first mass distribution the results indicate that the internal comfort is established and that the occupant is leaving soon (BetP(Sun, C) = 0.7721), however the conflict mass (m(∅)=0.5599) is very important and can influence the final decision since the reliability of the system can be questioned. The final decision to make is to decrease the heating because the occupant is leaving, but we can notice that this slight modification (the window is open for fifteen minutes), disturbs the fusion system for the first mass distribution. It seems that the results for the second mass distribution are conform to the results of the first mass distribution (BetP(Sun, C) = 0.7471), nevertheless we can notice that the pignistic probability on "Too Cold" increases (BetP(Sun, TC) = 0.1691 > 0.1455 (Table.II)), which is totally justified because the window is open and the temperature decreases quickly. Also we can notice that the conflict mass decreases with the second mass distribution (m(∅) = 0.0986 << m(∅) =0.5599 (Table II) This shows that the second mass distribution is more realistic and reliable than the first one and can adapt to minor and sudden variations in the room, which is very important for the real-time heating management system.

b. Result with the second mass distribution

B. Second scenario

In this second scenario we will present the influence of a major unexpected event, when the occupant comes home earlier than expected (according to the planning he was supposed to return home between 6:30 -7:00 pm) We are in the "Eco-Mode" (16° C), so the pignistic probabilities indicate that the ambiance in the room is uncomfortable; it is the "Too Cold" sensation (BetP(Sun, TC) = BetP(So, TC) = 0.3507) but we cannot decide on the state of occupancy, because in this case the occupant came home earlier than expected. Therefore, we do not consider the schedule as a source of information and the priority will be given to the presence sensor to decide on the occupancy. Since (E = 1) it confirms that the room is occupied and that the temperature trend will be to "Increase" the temperature immediately, to achieve a comfortable ambiance in a short time. The results with the second mass distribution indicates that the heating must "Increase" even if we lose more energy to achieve a comfortable ambiance for the occupant as we did find with the first mass distribution, which is conform to the decision rule. However, we can notice that, with the second mass distribution, the value of the pignistic probabilities are more important (BetP(Sun, TC) = 0.4559 > BetP(Sun, TC) = 0.3507 (Table .V)) and the conflict mass is much lower with this mass distribution (m(∅) = 0.0132 << m(∅) =0.5328 (Table .V)). We can conclude that once again the second mass distribution proved its efficiency, we obtain the suitable decision without an important conflict mass.

b. Result with the second mass distribution

V. Conclusion

We can conclude that the method presented this paper based on the belief function theory is reliable. Indeed, it proved its efficiency through the different real-life scenarios, We obtained a coherent decision for each scenario; the necessary 'tempera ture trend' was inserted in the 'Smart and Predictive Heating System', even in the case of an unexpected event. In addition, we succeed to minimize the conflict mass generated when the data was aggregated without using a conflict management algorithm but whilst solving the origin of the problem which was the mass distribution and the heterogeneity of the frame of discernment. In further works we will integrate a management conflict algorithm and a contextual discounting in order to minimize the conflict mass even more.

Fig. 1 .

 1 Fig. 1. Fusion method diagram

•

  The relative humidity (Rh) in percentage • The relative air velocity (Rv) in m/s • The clothing (Clo) in Clo index from clothing (ISO 7730-2005) • The activity (Ac) in met index from human metabolic activity (ISO 7730-2005) During the process of designing the fusion model we elaborate different mass distributions to improve the final decision and obtain reliable results. So in this section we will present in figure 2 and 3 the mass distribution as an example of the relative Air velocity.

Fig. 2 .

 2 Fig. 2. First Mass distribution for the expert Relative air velocity (MdRv1)

Fig. 3 .

 3 Fig. 3. Second Mass distribution for the expert Relative air velocity (MdRv2)

TABLE I

 I

			a. Result with the first mass distribution
	.	DATA FOR THE FIRST SCENARIO
	B1: Occupancy B2: Thermal comfort B3: Weather forecast
	Day : Wednesday	Tc =22 °C	T = -5°C
	Time : 07:45-	Rh =45 %	W=20 km/h
	08:15 am	Rv= 0.2 ms -1	N =45 %
	Presence sensor:	Clo =0.7clo	P = 4.5 mm
	E=1	Ac =1.2 met
	Ac=1.2 met

TABLE IV .

 IV DATA FOR THE SECOND SCENARIO

B1: Occupancy B2: Thermal comfort B3: Weather forecast

	Day : Wednesday	Tc =16 °C	T = 5°C
	Time : 05:00-	Rh =55 %	W=15 km/h
	05:30 am	Rv= 0.24 ms -1	N =40 %
	Presence sensor:	Clo =1clo	P =1.5 mm
	E=1	Ac =1 met
	Ac=1 met
	a. Result with the first mass distribution


Matthias Geier

Thibaut Carpentier

Markus Noisternig

Olivier Warusfel

Software tools for object-based audio production using the Audio Definition Model (ITU-R Recommendation BS.2076)

We present a publicly available set of tools for the integration of the Audio Definition Model (ADM) in production workflows. ADM is an open metadata model for the description of channel-, scene-, and object-based media within a Broadcast Wave Format (BWF) container. The software tools were developed within the European research project ORPHEUS (https://orpheus-audio.eu/) that aims at developing new end-to-end object-based media chains for broadcast. These tools allow for recording uncompressed multichannel audio files with embedded XML metadata according to the ADM specifications, and monitoring and rendering existing BWF-ADM files over headphones or arbitrary loudspeaker setups. The bundle also includes a plugin (available in all major plugin formats) for interoperability with digital audio workstations, which provides support for time-varying metadata via automation tracks.

Introduction

The tools presented here were originally developed for experimenting with incorporating reverb into an objectbased production workflow, within the scope of the ORPHEUS project [START_REF] Silzle | The EU project ORPHEUS: Object-based broadcasting -for next generation audio experiences[END_REF]. However, they can also be used in a more general context to create, load and play back audio files containing ADM metadata. In its current state, only a subset of the ADM specification [START_REF]Audio Definition Model[END_REF] is supported, but many common use cases are already covered. The current limitations, as well as the ADM format itself, are described below.

The ORPHEUS Project

The European research project ORPHEUS [START_REF] Silzle | The EU project ORPHEUS: Object-based broadcasting -for next generation audio experiences[END_REF] is dedicated to improving the production, distribution and reproduction of audio content. It is developing, implementing and validating a new end-to-end object-based media chain for audio content.

Object-based media is a novel approach for creating and deploying interactive, personalised, scalable and immersive content, by representing it as a set of individual assets together with metadata describing their relationships and associations. This allows media objects to be assembled in ground-breaking ways to create new user experiences.

ORPHEUS started in December 2015 and has a duration of 30 months. It receives funding from the European Commission under the Horizon 2020 programme.

The Audio Definition Model

Recommendation ITU-R BS.2076 [START_REF]Audio Definition Model[END_REF] -the Audio Definition Model (ADM) -is a metadata model for describing the technical format and content of audio files and streams. It primarily uses XML as its format language, and has been designed for incorporation into RIFF-based audio files like BWF [START_REF] Ebu | Tech 3285: BWF -A format for audio data files in broadcasting[END_REF] and BW64 [START_REF]Long-form file format for the international exchange of audio programme materials with metadata[END_REF] files. XML data is stored in a chunk of type <axml>, while the association of audio tracks with the identifiers used in the XML description is laid out in a chunk of type <chna>.

Each audio channel has one of the pre-defined types "Objects", "DirectSpeakers", "Binaural", "HOA" or "Matrix". Tracks of type "Objects" have an associated position, gain and several other parameters. All these parameters can potentially change over time. Linear interpolation between adjacent positions is available. The type "DirectSpeakers" can be used to include channelbased beds. Every channel represents one loudspeaker feed and it has the position of the loudspeaker associated with it. Pairs of channels of type "Binaural" simply hold the left and right channel of a binaural mix. The "HOA" type can be used to include different kinds of Ambisonics mixes. Channels of type "Matrix" contain gain and phase shift values that can be used to implement, for example, mid-side stereophony.

A single ADM file can contain multiple "audio programmes", which are different subsets of all available audio tracks and metadata, to be chosen by the consumer at rendering time. This can for example be used to provide parts of the material in multiple languages, while language-independent content like background music can be re-used in multiple "audio programmes".

The ADM Tools

The ADM tools are stand-alone programs, freely available for macOS and Windows. Currently, there are three tools available: a player with built-in renderer, a recorder which is using the same renderer for monitoring and a tool called "ADM ExtractXML" that can be used to get to the XML data stored inside a BWF/ADM file. The three tools are described in more detail in the following sections.

The ADM Player and the ADM Recorder can communicate with other programs via Open Sound Control (OSC) [START_REF] Wright | The Open Sound Control 1.0 specification[END_REF]. Note that OSC communication is not part of the ADM specification. The ADM Tools use an ad-hoc OSC syntax which facilitates the inter-app communication and can be easily used with other OSCaware software/devices. The "ToscA" plugin, described further below, can serve as an ancillary tool to connect a Digital Audio Workstation (DAW) to the ADM Recorder via OSC.

The ADM Tools can be downloaded from https://www. ircam.fr/project/detail/orpheus-1/ and the ToscA plugin for AU, VST, VST3 and AAX is available at http: //forumnet.ircam.fr/product/spat-en/tosca-en/.

ADM Player + Renderer

The ADM Player can load WAV/BWF/BW64 files and read ADM metadata and channel assignments from their respective chunks in the file. Upon loading a file, it performs a number of "sanity checks" on the ADM metadata. This can be very helpful to check whether a given ADM file is compliant. The ADM Player can play back the audio content of the file and produce synchronized control messages based on the ADM metadata obtained from the file. Using this audio data and the metadata, the built-in renderer can calculate appropriate signals for real-time reproduction using headphones or loudspeaker setups.

The main user interface is shown in figure 1. Summary information about the content of the currently open file (number of objects, number of tracks, duration, etc.) is displayed in the list on the right 1 . Controls for playback (start/stop/resume/loop/seek) are located on the left 2 . Below them, there are level meters for each audio track in the file 3 and below these there are level meters for the rendered output channels 4 . On the lower right, the rendering settings can be chosen 5 .

Both loudspeaker-based and headphone-based reproduction is possible. For rendering on loudspeakers, VBAP [START_REF] Pulkki | Virtual sound source positioning using Vector Base Amplitude Panning[END_REF] is used. The loudspeaker setup can be chosen from a predefined set of common loudspeaker setups or by manually specifying custom loudspeaker positions. Up to 64 loudspeakers are supported. For binaural rendering, Head-Related Transfer Functions (HRTFs) can be selected from a large set of available HRTF datasets. Further datasets can be loaded using the SOFA/AES69 format [START_REF] Majdak | Spatially Oriented Format for Acoustics: A data exchange format representing Head-Related Transfer Functions[END_REF]. In the top left corner of the user interface, OSC messages can be enabled which can for example be used to control an external renderer (while switching the built-in renderer to "bypass" mode) or further process the metadata generated by the ADM Player. The OSC messages can be sent to other applications running either on the same computer or on another computer on the network.

The "view scene" button opens a window showing the current position of all audio "objects" in the ADM file, as shown in figure 2. The scene window also allows interactively moving objects with the mouse.

In its current state, the ADM Player/Renderer only supports a subset of the ADM specifications. Most notably, it doesn't support multiple "audio programmes", nested ADM elements and non-PCM audio data.

ADM ExtractXML

Given a sound file with ADM metadata, this tool can be used to create a separate XML file containing only the ADM metadata (i.e. the contents of the <axml> chunk). The XML file will be stored in the same directory as the original ADM file. The contents of the <chna> chunk are also stored in a separate file. Like the ADM Player, this tool runs several "sanity checks" on the metadata to make sure it complies with the ADM specification [START_REF]Audio Definition Model[END_REF].

At the same time as extracting the <axml> chunk, the tool also creates structural representations of the XML elements in the DOT graph description language [START_REF] Emden | An open graph visualization system and its applications to software engineering[END_REF]. If the Graphviz 1 software is installed, PNG images with those graphs are automatically created. See figure 3 for an example graph.

ADM Recorder + Monitoring

The ADM Recorder can record up to 64 audio channels into a BWF/BW64 file. For each of these channels, it can also record automation data which is stored as ADM metadata in the same file. This automation data can be received via OSC messages.

The ADM Recorder has a built-in renderer that can be used for monitoring. The monitoring settings 1 in the bottom right of the window are the same as for the ADM Player/Renderer described above. The "configure" button 2 can be used to open a window for editing ADM metadata as shown in figure 5. On the top of this window, the programme and content name can be specified 1 . Below that, a list of "audio packs" 2 can be set up. Each pack can contain one or more "channels". For the "DirectSpeakers" type, one of a set of pre-defined channel-based setups (e.g. stereo, 5.1, 22.2) can be selected which populates the channels appropriately. A "Binaural" pack automatically contains two channels, one for the left and one for the right ear. Each channel has a unique channel number that can be used together with the routing matrix on the left side 3 to assign input audio channels to the desired ADM tracks.

Once the packs and channels are set up as desired, the "arm" button 4 can be used to enable recording. This will open a scene display window similar to figure 2 which allows configuration of the initial positions of all audio objects. The scene window also allows moving objects with the mouse during recording, which will record the object trajectories in the resulting ADM file. However, in practice it will be more convenient to connect the ADM Recorder to a Digital Audio Workstation (see the section about the "ToscA" plugin below) which can record automation data for multiple objects (possibly one after another). The DAW can then play back all automation tracks at once, which in turn can be recorded by the ADM Recorder. A track with an LTC time code signal can be used to synchronize start and stop times between the DAW and the ADM Recorder. Instead of using a DAW, the automation data can of course be produced by any software, as long as the generated OSC messages are compatible with the ADM Recorder.

In the top left of the main window (figure 4), host and port settings 3 can be configured for receiving and sending OSC messages that can transport ADM metadata between applications and between computers. Messages which are received via this interface are stored as XML metadata in the recorded ADM file. This interface can also be used to establish a connection with the ToscA plugin.

The ADM Recorder only supports a subset of the ADM specifications. It doesn't support multiple "audio programmes" nor audio channels with different lengths.

All audio content will have the same duration.

DAW Automation with ToscA

ToscA [START_REF] Carpentier | ToscA: An OSC communication plugin for object-oriented spatialization authoring[END_REF] is a plugin for Digital Audio Workstations (DAWs) that allows the recording of automation tracks for arbitrary parameters that can be sent and received as OSC messages via a network interface. Primarily developed for the remote control of spatial audio processors, this tool also turns out to be very handy for "linking" the ADM tools with a DAW. It can be used together with the ADM Recorder to record movements and changing gain values as automation tracks in a DAW.

An instance of the ToscA plugin has to be inserted into every track that is supposed to contain automation data, see figure 6. Each ToscA instance can then be configured with a channel ID that is used to associate tracks in the DAW with channels defined in the ADM Recorder. The ADM Recorder will in turn store the recorded automation data in the ADM file.

The audio outputs of the DAW tracks can be provided to the ADM Recorder either via hardware connections or via virtual sound drivers. Refer to [START_REF] Carpentier | ToscA: An OSC communication plugin for object-oriented spatialization authoring[END_REF] for additional details.

Future Work

As mentioned above, not all features of the ADM specification are implemented yet. Further tools are planned that will allow to select audio tracks and edit metadata of ADM files as well as to merge the contents of multiple files into one. This way, ADM files could be created that hold multiple "audio programmes", for example to enable selection between multiple language versions.

Preliminary support for HOA is provided, however this may evolve in future versions as future versions of the ADM specification are expected to contain significant changes in this area.

Figure 1 :

 1 Figure 1: Main user interface of the ADM Player/Renderer

Figure 2 :

 2 Figure 2: Scene display of the ADM Renderer. A very similar screen is used in the ADM Recorder. Left pane: view from above; right pane: view from behind. The displayed ADM file is machine aer bwf.wav from http://www.bbc.co.uk/rd/publications/saqas.

Figure 3 :

 3 Figure 3: Diagram of the XML metadata structure of an ADM file, generated with the tool ADM ExtractXML. The IDs shown in the boxes are used internally to create connections between ADM elements.

1 2 3Figure 4 :

 24 Figure 4: Main window of the ADM Recorder

Figure 4

 4 Figure4shows the main window of the ADM Recorder. The monitoring settings 1 in the bottom right of the window are the same as for the ADM Player/Renderer described above. The "configure" button 2 can be used to open a window for editing ADM metadata as shown in figure5. On the top of this window, the programme and content name can be specified1 . Below that, a list of "audio packs" 2 can be set up. Each pack can contain one or more "channels". For the "DirectSpeakers" type, one of a set of pre-defined channel-based setups (e.g. stereo, 5.1, 22.2) can be selected which populates the channels appropriately. A "Binaural" pack automatically contains two channels, one for the left and one for the right ear. Each channel has a unique channel number that can be used together with the routing matrix on the left side3

Figure 5 :

 5 Figure 5: Metadata editor and routing matrix. The resulting ADM structure for this example can be seen in figure 3.

Figure 6 :

 6 Figure 6: Using the ToscA plugin to connect a Digital Audio Workstation (DAW) to the ADM Recorder

Acknowledgements

This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement N o 687645.


Pallav Kant
email: p.kant@utwente.nl

Cesar Pairetti

Youssef Saade

Stéphane Popinet

Stéphane Zaleski
email: stephane.zaleski@sorbonne-universite.fr

Detlef Lohse
email: d.lohse@utwente.nli

Bags mediated film atomization in a cough machine

We combine experiments and numerical computations to examine underlying fluid mechanical processes associated with bioaerosol generation during violent respiratory manoeuvres, such as coughing or sneezing. Analogous experiments performed in a cough machine -consisting of a strong shearing airflow over a thin liquid film, allow us to illustrate the changes in film topology as it disintegrates into small droplets. We identify that aerosol generation during the shearing of the liquid film is mediated by the formation of inflated bag-like structures. The breakup of these bags is triggered by the appearance of retracting holes that puncture the bag surface. Consequently, the cascade from inflated bags to droplets is primarily controlled by the dynamics and stability of liquid rims bounding these retracting holes. We also reveal the key role of fluid viscosity in the overall fragmentation process. It is shown that more viscous films when sheared produce smaller droplets.

I. INTRODUCTION

Respiratory droplets (bioaerosols) expelled from oral and nasal cavities during different breathing manoeuvres, such as speaking, singing, coughing and sneezing, are primary vectors of respiratory infections [START_REF] Wells | Air-borne infection[END_REF][START_REF] Mittal | The flow physics of COVID-19[END_REF][START_REF] Xie | Exhaled droplets due to talking and coughing[END_REF][START_REF] Jones | Aerosol transmission of infectious disease[END_REF][START_REF] Fiegel | Airborne infectious disease and the suppression of pulmonary bioaerosols[END_REF][6][START_REF] Bourouiba | Turbulent gas clouds and respiratory pathogen emissions: potential implications for reducing transmission of COVID-19[END_REF][START_REF] Pöhlker | Respiratory aerosols and droplets in the transmission of infectious diseases[END_REF]. The size of these droplets, made of muco-salivary fluid lining respiratory tracts, typically ranges from hundreds of nanometers to a few millimetres [START_REF] Duguid | The size and the duration of air-carriage of respiratory droplets and droplet-nuclei[END_REF][START_REF] Loudon | Relation between the airborne diameters of respiratory droplets and the diameter of the stains left after recovery[END_REF][START_REF] Chao | Characterization of expiration air jets and droplet size distributions immediately at the mouth opening[END_REF][START_REF] Bagheri | Exhaled particles from nanometre to millimetre and their origin in the human respiratory tract[END_REF].

Crucially, the generation of bioaerosols is closely related to interfacial phenomena emerging at the free surface of the airway-lining-fluid [START_REF] Evrensel | Viscous airflow through a rigid tube with a compliant lining: a simple model for the air-mucus interaction in pulmonary airways[END_REF][START_REF] Kataoka | Generation and size distribution of droplet in annular two-phase flow[END_REF][START_REF] Moriarty | Flow-induced instabilities of a mucus-serous bilayer[END_REF][START_REF] Pairetti | On shear layer atomization within closed channels: Numerical simulations of a cough-replicating experiment[END_REF]. For example, the shearing action of the airflow within the lungs during coughing or sneezing destabilizes the thin layer of mucus accumulated along the airway passages. Consequently, the ensuing complex fluid mechanical processes, bearing several interfacial instabilities [START_REF] Mittal | The flow physics of COVID-19[END_REF], lead to the disintegration of the mucus layer into droplets with broad size statistics. In addition, a large number of sub-micron-sized droplets are also produced due to the capillary breakup of menisci pending the re-opening of collapsed terminal bronchioles during normal breathing [START_REF] Johnson | The mechanism of breath aerosol formation[END_REF][START_REF] Almstrand | Effect of airway opening on production of exhaled particles[END_REF][START_REF] Malashenko | Propagation and breakup of liquid menisci and aerosol generation in small airways[END_REF]. Notably, the rheological properties of the muco-salivary fluid play a crucial role in these atomization processes, thus, dictating size statistics of droplets exhaled [START_REF] Hamed | Surface rheological properties alter aerosol formation from mucus mimetic surfaces[END_REF][START_REF] Keshavarz | Ligament mediated fragmentation of viscoelastic liquids[END_REF]. Upon exhalation, the fate of these respiratory droplets largely depends on their size. While, large droplets of size greater than 100 µm behave ballistically due to their own weight, falling out of the exhaled turbulent "puff", smaller droplets often referred to as nuclei remain airborne for long periods. The lifetime of these airborne droplets then depends on a number of intrinsic factors such as intial size and composition, as well as extrinsic factors like ambient humidity, temperature and ventilation [START_REF] Morawska | Droplet fate in indoor environments, or can we prevent the spread of infection?[END_REF][START_REF] Holmgren | Relation between humidity and size of exhaled particles[END_REF][START_REF] Villermaux | Fine structure of the vapor field in evaporating dense sprays[END_REF][START_REF] Chong | Extended lifetime of respiratory droplets in a turbulent vapor puff and its implications on airborne disease transmission[END_REF]. Therefore, devising an effective infection control strategy, first and foremost, requires an intimate knowledge of the initial size distribution, velocity and ejection angles of bioaerosols generated during the different respiratory manoeuvres.

Here, in the context of droplets produced during coughing or sneezing, we study the fragmentation of thin films subject to interfacial stresses induced by a strong airflow. We employ the experimental configurations popularized by Clark et al. [START_REF] Clarke | Resistance to two-phase gas-liquid flow in airways[END_REF] and King et al. [START_REF] King | Clearance of mucus by simulated cough[END_REF] to study the flow resistance in airway passages due to the accumulation of mucus along the walls. Note that the scope of these earlier investigations was limited to non-atomization conditions in which modal stability analysis could explain observed interfacial disturbances.

More recently, Edwards et al. [START_REF] Edwards | Inhaling to mitigate exhaled bioaerosols[END_REF] employed a similar apparatus, along with in vivo measurements, to establish a direct link between the interfacial tension of the airway-lining fluid and the flux of exhaled bioaerosols. In contrast, here we use high-speed imaging and Phase-Doppler-Anemometry (PDA) to reveal the mechanics of fragmentation of the thin films and to characterize the resultant droplet size distributions, respectively. Additionally, we present a state-of-the-art numerical framework that can be used to study a similar class of fluid fragmentation problems. We perform analogous experiments and numerical computations of what we call a coughmachine to illustrate the topological changes of a thin film as it disintegrates into minute droplets. A schematic diagram of the experimental setup is shown in Fig. 1. The experimental configuration (cough-machine) consists of a 30 cm long, horizontal model-trachea made of transparent plexi-glass, with a 2 cm wide and 1 cm high rectangular cross-section. A thin, iii highly wetting glass coverslips of thickness 100 µm and length 12 cm cover the bottom of this rectangular channel at the upstream. The wetting nature of the coverslip allows us to create a uniform layer of an aqueous glycerol solution on top of it, imitating a coating of a muco-salivary fluid in the trachea, away from the oral cavity. The wettability of these removable coverslips was controlled by treatment with plasma after every few experiments.

II. METHODS

Experimental Setup

The desired film thickness H f is achieved by first layering the bottom of the cough machine with a fixed volume of glycerol solution, and then spreading it uniformly with a sharp edge scraper that runs over a rail. Experiments are carried out with different aqueous glycerol solutions of viscosity (µ l ) ranging between 1 mPa s and 132 mPa s. This range matches with the typical viscosity measurements reported for human mucus [START_REF] Lai | Micro-and macrorheology of mucus[END_REF]. Note that the typical cross-sectional shape of the tracheal lumen in an adult is ovoid [START_REF] Furlow | Surgical anatomy of the trachea[END_REF], however, here we chose a rectangular cross-section to achieve a uniform film of the model muco-salivarly fluid, which in the case of a round tube would tend to collect at the bottom. The upstream of the channel connects to a pressurized tank via a valve that is actuated to create an airflow mimicking a typical cough/sneeze, and the other end opens to atmosphere. A honeycomb structure is placed at the entrance of the channel to homogenize the inlet turbulence levels. During an experiment the valve opens for 400 ms. Within this duration the flow rate quickly ramps-up to its maximum and then drops down like a real cough [START_REF] King | Clearance of mucus by simulated cough[END_REF]. We must emphasize that the atomization of a thin film, as discussed in the following, takes place at much shorter timescales ∼ 1ms compared to the duration of operation of the valve (400 ms). Thus it is valid to consider approximately constant and uniform flow conditions during an atomization event.

Different free-stream velocities (U ∼ 10 -30 m/s) within the channel are achieved by varying the overhead pressure in the tank. Therefore, the corresponding shearing strength of the airflow ranges in between Γ ∼ µ l U /H f ∼ 10 -3900 Pa. Note that the mean free-stream velocity is determined from the flow-rate measured at the inlet of the channel via a flow meter (Bronkhosrt, EL-Flow Select). The atomization of thin-film inside the channel is recorded in top-view via a high-speed camera (SA12-NOVA, Photron ) at a maximum of 40,000 frames per second, and droplet size statistics are measured, using a Phase-Doppler-Anemometer (Dual PDA, Dantec Dynamics) at a distance of 10 cm from the exit of the channel as shown in Fig 1 . For details on the underlying principles of PDA technique, we refer the reader to Ref. [START_REF] Qiu | A reliable method for determining the measurement volume size and particle mass fluxes using phase-Doppler anemometry[END_REF].

Numerical scheme and Simulation setup

In the present investigations, both the muco-salivary fluid and the surrounding gas are treated as incompressible Newtonian fluids. In the context of uniform temperature conditions achieved during experiments, and high relative humidity within the expelled multiphasic puff from the channel, heat transfer and evaporative effects are ignored [START_REF] Villermaux | Fine structure of the vapor field in evaporating dense sprays[END_REF][START_REF] Chong | Extended lifetime of respiratory droplets in a turbulent vapor puff and its implications on airborne disease transmission[END_REF]. Accordingly, the flow in the gas medium and the liquid film is described by the Navier-Stokes equations as:

∇ ⋅ ⃗ u = 0, ∂ρ⃗ u ∂t + ∇ ⋅ (ρ ⃗ u ⃗ u) = -∇p + ∇ ⋅ (2 µ D) + σ κ ⃗ n s δ s , (1)
where ⃗ u (⃗ x, t) is the velocity field and p (⃗ x, t) is the pressure field. Tensor D is equal to

ρ = f ρ l + (1 -f ) ρ g µ = f µ l + (1 -f ) µ g , (2)
subscripts 'l' and 'g' correspond to the liquid and gas properties, respectively. The flow equations are discretised using the methodology described in Ref. [START_REF] Pairetti | On shear layer atomization within closed channels: Numerical simulations of a cough-replicating experiment[END_REF]. Notably, the advective fluxes in the discretized system are integrated explicitly based on a momentum-conserving v Bell-Collela-Glaz scheme [START_REF] Bell | A second-order projection method for the incompressible Navier-Stokes equations[END_REF] and the viscous term is computed in a semi-implicit manner.

The surface tension force term is based on a discrete-balanced formulation to reduce spurious currents [START_REF] Popinet | Numerical models of surface tension[END_REF]. Importantly, we compute the interface curvature using second-order height functions defined by PLIC plane position based on the analytical formulation from Ref. [START_REF] Scardovelli | Direct numerical simulation of free-surface and interfacial flow[END_REF] The described flow solver is implemented in the open-source software program Basilisk [35].

In the simulations reported here, we apply Adaptive Mesh Refinement (AMR), in an octree mesh implementation using a wavelet-based criterion [START_REF] Van Hooft | Towards adaptive grids for atmospheric boundary-layer simulations[END_REF]. The finest simulation reported employs a maximum refinement level of thirteen (L13), resulting in a grid size of 18.3 µm.

For more details on the numerical scheme we refer the reader to Ref. [START_REF] Pairetti | On shear layer atomization within closed channels: Numerical simulations of a cough-replicating experiment[END_REF]. The sequence of snapshots in Fig. 1a highlights key events leading to the atomization of a water-glycerol film of thickness H f = 1mm when sheared by an impulsively started airflow, mimicking a cough or a sneeze. Since the corresponding Reynolds number Re = ρ l H f U /µ l and Weber number W e = ρ g U 2 H f /σ are sufficiently large, owing to a shear-induced Kelvin-Helmholtz instability, a localized wave-like interfacial disturbance develops close to the inlet immediately after the airflow initiates [START_REF] Scardovelli | Direct numerical simulation of free-surface and interfacial flow[END_REF][START_REF] Hoepffner | Self-similar wave produced by local perturbation of the Kelvin-Helmholtz shear-layer instability[END_REF]; here, ρ l , µ l and σ are the density, the dynamic vi viscosity, and the surface tension of the liquid, ρ g and U are the density and the mean flow velocity of the flowing gas. While this interfacial wave-like disturbance moves downstream at a constant velocity that scales as [START_REF] Hoepffner | Self-similar wave produced by local perturbation of the Kelvin-Helmholtz shear-layer instability[END_REF][START_REF] Dimotakis | Two-dimensional shear-layer entrainment[END_REF], the shear stress imposed by the airflow on the thin film modulates its morphology, stretching it into a thin liquid sheet with a thicker (cylindrical) rim at its free edge. At this stage, the liquid sheet disintegrates into small droplets with a wide size distribution primarily through the formation of multiple inflated structures (liquid bags) along the width of the film. Notably these hollow structures remain rooted at the crest of the downstream traveling interfacial wave, and are bordered by a thick liquid rim at the top. Since large accelerations are imparted from the gas flow to the liquid sheets during the expansion of the bags, their formation and growth are attributed to a Rayleigh-Taylor type mechanism. Correspondingly, the width of bags at the location of attachment with the interfacial wave is prescribed by the dominant wavelength associated with the Rayleigh-Taylor instability λ ∼ √ σ/ρ l a, where a ∼ H f /τ 2 is the initial acceleration of the inflating bag; τ = H f /U √ ρ l /ρ g is characteristic time scale associated with bursting of a bag [START_REF] Villermaux | Single-drop fragmentation determines size distribution of raindrops[END_REF]. For different glycerol solutions and experimental conditions (H f , U) investigated in experiments, the predicted instability wavelength is of the order of 2 mm, which is in agreement with observed sizes of bags in experiments.

III. RESULTS AND DISCUSSION

u wave ∼ U √ ρ g /( √ ρ g + √ ρ l ))
Corresponding 2D and 3D numerical simulations (Fig. 3) performed for the exact experimental configuration reveal an intricate interplay between aerodynamic stresses at the film interface and capillarity that drives the inflation of liquid bags. We find that once the amplitude of the initial interfacial perturbation increases significantly, the flow over its windward side develops a stagnation point where the pressure builds up, stretching it into a liquid sheet. Subsequently, local pressure gradients thins the liquid sheet heterogeneously, driving the inflation of several bags across the channel width. Upon the initial inflation, vortex shedding develops on the downwind side producing stagnation points that accelerate the local thinning of the sheets while the bags keep elongating.

Notably, both in our experiments and simulations, the bag-mediated fragmentation of a thin film occurs when the Weber number exceeds the threshold value W e c ∼ 8. Below this threshold value we do not observe any atomization of a thin film by the shearing airflow.

Interestingly, this threshold also corresponds to the limit beyond which a droplet exposed to high-speed airflow fragments into smaller droplets via a 'bag-breakup' mode [START_REF] Villermaux | Single-drop fragmentation determines size distribution of raindrops[END_REF][START_REF] Reyssat | Shape and instability of free-falling liquid globules[END_REF][START_REF] Marcotte | Density contrast matters for drop fragmentation thresholds at low Ohnesorge number[END_REF][START_REF] Jackiw | On aerodynamic droplet breakup[END_REF].

This suggests that the underlying physical mechanism driving the morphological change vii from the initial interfacial disturbance to a hollow inflated structure, as described above, is analogous to the case of impulsively accelerated droplet inflating into a bag morphology [START_REF] Villermaux | Single-drop fragmentation determines size distribution of raindrops[END_REF][START_REF] Reyssat | Shape and instability of free-falling liquid globules[END_REF][START_REF] Marcotte | Density contrast matters for drop fragmentation thresholds at low Ohnesorge number[END_REF][START_REF] Jackiw | On aerodynamic droplet breakup[END_REF][START_REF] Hsiang | Near-limit drop deformation and secondary breakup[END_REF][START_REF] Kulkarni | Bag breakup of low viscosity drops in the presence of a continuous air jet[END_REF][START_REF] Guildenbecher | Secondary atomization[END_REF]. In both scenarios, the aerodynamic drag on the bulk liquid first, deforms it into a thin sheet transverse to the airflow, which then inflates into a bag shape due to a stagnation- Accordingly, theoretical predictions of the critical Weber number show only minor variations for different film viscosities employed in experiments.

Using top-view recordings, we quantify the kinematics of the longitudinal and transversal expansion of liquid bags observed in current experiments. The data shown in Fig. 4a shows the longitudinal expansion of bags measured in experiments, for different film viscosities, as well as the corresponding behaviour recovered in numerical simulations. Remarkably, similar to the bag inflating from an impulsively accelerated droplet, we find that the temporal growth of the horizontal position of the tip of a bag in our experiments follows the power-law like behaviour R Tip ∼ t 2 [START_REF] Villermaux | Single-drop fragmentation determines size distribution of raindrops[END_REF]; R tip is the position of the tip of an inflating bag. This suggests that the the inflation of a bag is primarily dictated by inertial effects, while viscous effects play a dormant role. Moreover, in our numerical simulations we also recover the exponential thinning of the bag thickness h ∼ e -2t during the inflation process, also suggested for the single droplet case [START_REF] Villermaux | Single-drop fragmentation determines size distribution of raindrops[END_REF]. These comparisons confirm the strong similarity in physical mechanisms that dictate the bag-mediated fragmentation process in the two distinct scenarios.

However, the transverse expansion of the inflated morphologies observed in our experiments shows an interestingly different trend. Since the bags in current experiments always remain rooted at the crest of the downstream traveling interfacial wave, unlike the bags that are unhinderedly inflating all directions from a droplet, the transverse growth of bags is significantly altered. We find that the width of a bag at the location of attachment with the crest of the interfacial wave W B remains nearly constant throughout its lifetime. As highlighted in Fig. 4c, after an initial rapid growth at the root, that lasts less than 0.1 ms, the width of the bag does not change. In addition, we find that the maximum width of the bag is significantly affected by the viscosity of the thin-film. We observe that at a fixed Weber ix number, wider bags are favored for more viscous films; see Fig. 4d. Since the formation of the inflated morphologies is attributed to a Rayleigh-Taylor instability type mechanism, this observed trend in the width of the bag is in line with the expected increase in the dominant unstable wavelength with viscosity [START_REF] Plesset | Viscous effects in Rayleigh-Taylor instability[END_REF]. At the same time, we must also draw attention towards the apparent plateau in measured bag-widths at higher viscosities. We suspect this behaviour emerges from the physical constraint on the largest unstable wavelength that the stretched interfacial disturbance on the thin film can accommodate. A detailed investigation is further warranted to address this crucial aspect of the system, which is beyond the scope of the current investigations.

High-speed imaging of the fragmentation of a bag reveals that its fragmentation into small droplets is triggered by the appearance of 'weak-spots', particularly in the thinnest parts of the bag-sheet [START_REF] Villermaux | Fragmentation versus cohesion[END_REF][START_REF] Lohse | Double threshold behavior for breakup of liquid sheets[END_REF]. As shown in Fig. 5, these weak-spots are precursor to retracting holes that puncture the bag. These holes are bounded by thick liquid rims and retract at a constant velocity. The corresponding retraction thus is controlled by a Taylor-Culick process [START_REF] Villermaux | Single-drop fragmentation determines size distribution of raindrops[END_REF][START_REF] Savva | Viscous sheet retraction[END_REF][START_REF] Lhuissier | Bursting bubble aerosols[END_REF], and the retraction velocity is given by V TC = (2σ/ρ l h) 1/2 ; h is the thickness of the punctured liquid sheet. We use this relationship between the retraction velocity and the liquid sheet thickness to estimate the typical bag-thickness at the time of their bursting in our experiments. Our calculations indicate that bursting events occur when the bagthickness is close to 1 µm. Additionally, we find that viscous effects become important in the final moments of the bag inflation, thus controlling the minimum thickness of the bag and the resultant droplet size statistics. This crucial role of liquid viscosity on the droplet generation process is addressed in detail later in the discussion.

Note that the exact physical mechanism responsible for the nucleation of such weak spots is a subject of intense debate [START_REF] Villermaux | Fragmentation versus cohesion[END_REF][START_REF] Lohse | Double threshold behavior for breakup of liquid sheets[END_REF][START_REF] Villermaux | Fragmentation[END_REF]. Accordingly, several nucleation mechanisms relying on chemical/thermal inhomogeneities or the presence of foreign particles or micro-bubbles have been proposed. A few other investigations have also pointed out that extremely thin liquid sheets of thickness less than 1 nm are susceptible to thermal fluctuations or intermolecular interactions, which may also cause the nucleation of weak-spots [START_REF] Sharma | Instability of thin polymer films on coated substrates: rupture, dewetting, and drop formation[END_REF][START_REF] Casteletto | Stability of soap films: hysteresis and nucleation of black films[END_REF]. However, in the view of thicker bag sheets observed in our experiments and uniform experimental conditions, the above-mentioned mechanisms seemingly may not cause the nucleation of weak spots in our experiments. Instead, we speculate that the nucleation of weak-spots in our experiments may occur as a result of mechanical forcing, like the application of a pressure gradient, or pressure difference across a film [START_REF] Villermaux | Fragmentation versus cohesion[END_REF][START_REF] Vledouts | Explosive fragmentation of liquid shells[END_REF][START_REF] Klein | Drop fragmentation by laser-pulse impact[END_REF]. In such a case, the resulting acceleration may lead to film thickness modulations through a Rayleigh-Taylor mechanism, ultimately causing its puncture [START_REF] Bremond | Bursting thin liquid films[END_REF].

Crucially, our experiments reveal that the cascade from liquid sheet to droplets is predominantly controlled by the dynamics and stability of liquid rims formed upon the nucleation of holes. The retracting motion of such liquid rims is susceptible to longitudinal perturbations, resulting in the formation of elongated liquid-filament at the free edge which eventually break into small droplets [START_REF] Agbaglah | Longitudinal instability of a liquid rim[END_REF][START_REF] Krechetnikov | Stability of liquid sheet edges[END_REF][START_REF] Roisman | On the instability of a free viscous rim[END_REF]. This transition from a liquid-filament to droplet/s occurs either via end-pinching mode when a filament grows into a bulge that detaches as a sinxii FIG. 6. A schematic comparing the volume accompanying the inflated liquid sheet and the filament bordering thee inflated morphology.

gle droplet, or via ligament mode when the filament grows progressively to break up into multiple droplets [START_REF] Wang | Growth and breakup of ligaments in unsteady fragmentation[END_REF]. In the experiments, we observe both modes of droplet generation.

Notably, this physical process of droplet generation is controlled by a delicate interplay between Rayleigh-Plateau and Rayleigh-Taylor mechanisms [START_REF] Wang | Growth and breakup of ligaments in unsteady fragmentation[END_REF][START_REF] Wang | Universal rim thickness in unsteady sheet fragmentation[END_REF]. The size of droplets (less than 50 µm) produced via this mechanism is therefore determined by the size of the liquid rim that continuously evolves in time. Additionally, as shown in the last image of the sequence in Fig. 5, droplets of larger size (> 100 µm) are also produced from the breakup of the corrugated filament at the top-edge of the liquid bag via an aggregation-coalescence process [START_REF] Villermaux | Fragmentation[END_REF]. At this point, it is essential to point out that a significant portion of the total liquid volume that fragments into droplets is located in the inflated bag sheets

V sheet ∼ L B W B h,
and it is comparable to the total liquid volume carried by the liquid filament at edge of the bags (V filament ∼ r 2 filament W B ), as L B h ∼ r 2 filament Therefore, the poly-dispersity and skewness of the resultant droplet size distribution measured in our experiments is attributed to droplets originating from the bursting of inflated liquid sheets and the breakup of bordering corrugated filaments. We must point out that a similar conclusion was also reached in a recent experimental investigation concerning bag-mediated secondary atomization of a droplet [START_REF] Jackiw | Prediction of the droplet size distribution in aerodynamic droplet breakup[END_REF].

We find that the resultant droplet size statistics, measured at the exit of the coughmachine, are very-well captured by a log-normal distribution, see Fig. 7. This behaviour is confirmed for different film viscosities and shearing strengths. Note that our measurements include droplets as small as 1 µm that originate from the unsteady rim retraction dynamics. Crucially, our measurements of the volume size distribition (Fig. 7b) are inline with previously reported droplet statistics of bioaerosols exhaled during expiratory activities [63xiii 65]. Previous investigations report the presence of both unimodal and bimodal log-normal size distributions in bioaerosols exhaled by humans. Crucially, this variation is found to be dependent on the physiological characteristics of the test subjects. Therefore, a detailed investigation is warranted to quantify the influence of physiological characteristics on the physical (rheological) properties of the mucus-layer which in turn influences the droplet size statistics in exhaled bioaerosols. Further, we must also point that our results are in contrast with other droplet size distributions suggested for bag-mediated fluid fragmentation processes [START_REF] Villermaux | Single-drop fragmentation determines size distribution of raindrops[END_REF]. Notably, it has been proposed that in bag-mediated atomization scenarios, the aggregation and coalescence process of corrugations along the liquid filaments bordering inflated structures primarily selects the droplet size distribution. Whereas, here we argue that a significant volume of atomized liquid is associated with small drop fragments that originate from the bursting of inflated liquid sheets. In addition, we must also point out that due to the fact that the droplet size statistics are measured at a distance of 10 cm from the exit of the channel, the exact population of larger droplets formed due to the breakup of bordering filaments may not be well represented in our data, since large droplets are known to ballistically fall out of the expelled turbulent puff [START_REF] Wells | Air-borne infection[END_REF][START_REF] Chong | Extended lifetime of respiratory droplets in a turbulent vapor puff and its implications on airborne disease transmission[END_REF], thus providing a bias in the measured droplet size statistics.

Our experiments also reveal an important role of fluid viscosity in the breakup of liquid bags. We find that an increase in the film viscosity enhances the stability of inflated structures, resulting in the formation of deeper and wider liquid bags; Figs. 8a and4d. Crucially, the enhanced stability of these inflated structures also means that the bursting time (t burst ) of a bag is delayed. In Fig. 8b, we show the transition towards longer bursting times measured in experiments with an increase in film viscosity. Notably, this result is inline with a delay in characteristic breakup times measured for bag-mediated breakup of secondary atomization of viscous droplets [START_REF] Hsiang | Near-limit drop deformation and secondary breakup[END_REF]. Crucially, we find that the enhanced stability of the bag directly affects the mean size of droplet fragments produced as a result of the atomization process. As shown in Fig. 9, for higher film viscosity the mean size of droplet fragments reduces significantly, almost by a factor of two. Interestingly, this transition in mean droplet size occurs at the threshold given by the local Ohnesorge number Oh L = µ l /(ρ l σ h) 1/2 ∼ 1, indicating the existence of two distinct regimes where different physical processes control the eventual bursting of the inflated structure. We suspect that in the regime Oh L < 1, it is a balance between inertia and capillarity that determines the lifetime of an inflated structure, xiv whereas for Oh L > 1, viscous effects stabilize the accelerating bag. We also note that a similar stabilizing effect of fluid viscosity on the stability of thin films, in the context of surface bubbles, has been reported recently in Ref. [START_REF] Lorenceau | Lifetime of a single bubble on the surface of a water and ethanol bath[END_REF]. However, a detailed investigation is further needed to develop a comprehensive understanding of the stability of inflated structures in these two regimes discussed above, and is out of scope of the current work.

In summary, motivated by the generation of bioaerosols during violent breathing manoeuvres, we have analyzed physical processes associated with the atomization of a thin film subject to shearing airflow in a closed geometry. Our experiments and numerical simulations illustrate that the overall fragmentation process of a thin film is mediated by the formation of hollow bag-like structures. In contrast to previous investigations, we show that the cascade from an inflated bag to small droplets is controlled by the unstable motion of retracting liquid rims that border the holes puncturing the bag. Crucially, we find that small droplets generated from such retracting liquid rims collectively carry a large liquid volume than previously thought. Accordingly, an effective infection control strategy must emphasize on the reduced transport of such small droplets. Importantly, our measurements of the resultant droplet size distribution match well with the some of the previously reported xv 0.6 xvi droplet statistics for a real cough. However, the influence of a key feature of bioaerosol generation, i.e., viscoelasticity of the muco-salivary fluid, on droplet statistics is yet to be explored. We also reveal the stabilizing effect of fluid viscosity in the overall fragmentation process that eventually leads to the generation of smaller droplets. Finally, we envisage our investigation to motivate future research addressing the generation of bioaerosols, especially in the context of complex biological fluids.

FlowFIG. 1 .

 1 FIG. 1. Schematic diagram of the experimental setup. A transparent plexi-glass channel with rectangular cross-section (model-trachea) is connected with a pressurized tank via a valve. A thin layer of aqueous glycerol solutions covers the bottom of the channel. Upon actuation of the valve, the events leading to the fragmentation of thin-film are recorded by a high-speed camera in top view. Droplet statistics are measured at a distance of 10 cm away, along the center-line, from the exit of the channel.

1 2 [

 2 ∇⃗ u + (∇⃗ u) T ]. ρ and µ are the flow density and viscosity respectively. The last term on the right-hand side in Eq.(1) represents the surface tension force, where the coefficient σ is the interfacial tension between the aqueous glycerol solution and air. The force only acts at the free surface, hence the Dirac function δ s , and also depends on the interface shape, particularly on its curvature κ and normal ⃗ n s Simulations are performed for flow in a rectangular channel with bottom wall covered by a thin liquid film of thickness H f as described in the previous section. No-slip boundary condition is imposed on all dry boundaries of the channel. At the inlet cross-section, we apply uniform velocity, and outflow boundary conditions of Dirichlet on pressure and Neumann on velocity are imposed on the outlet cross-section. We solve the above equations by a simple finite volume discretization in the one-fluid numerical approach for two-phase flows, using a Piecewise Linear Interface Capturing (PLIC), Volume-Of-Fluid (VOF) method. The VOF function at a grid cell is defined as f = (1/V ) ∫ V c dV , representing the volume fraction of the liquid phase in a grid cell. Here, c indicates the presence of the liquid (c (⃗ x, t) = 1) or (c (⃗ x, t) = 0) gas phase. The fluid properties, density (ρ) and viscosity (µ), at the cell are defined by arithmetic averages:

FIG. 2 .

 2 FIG. 2. Sequence of experimental snapshots, at 0.25 ms intervals, highlight the key processes during the fragmentation of a thin-film of water-glycerol solution (film thickness H f = 1 mm and kinematic viscosity ν l = 5 cst) when sheared by an impulsively started airflow in a cough-machine. The mean velocity of the airflow is 15 m/s. The sequence shows the topological changes experienced by the film as multiple bags form along its width. The disintegration of these inflated structures generates droplets with broad size statistics. The first snapshot is captured 40 ms after the initiation of airflow in the channel.

FIG. 3 .

 3 FIG. 3. (a) An isometric view of that bag morphology resulting from the shearing of a thin film of thickness H f = 1mm within the cough machine. Side-walls of the rectangular channel (cough-machine) are not shown for the ease of visualization. The shearing velocity used in the 3D computations is 15 m/s. A vorticity map shown on the vertical cross-section (grey panel) highlights the flow structure around the inflated liquid bag. (b) Snapshots illustrating the inflation and atomization of a liquid bag observed in 3D simulations. (c) Side-view of bag-breakup mode observed in 2D simulations. All computations are performed using Basilisk.

  point flow on its windward face. Crucially, we find that the critical Weber number beyond which such bag-mediated atomization events are observed in current experiments remains viii unchanged for the range of fluid viscosities considered in experiments. Understanding the influence of viscous effects on critical Weber number for bag formation on sheared thin films demands a detailed investigation addressing the non-linear stretching and thinning of the interfacial wave formed initially due to Kelvin-Helmholtz instability, which is beyond the scope of the current investigation. However, we should point out that this weak dependence of the critical Weber number on film viscosity is well captured by the theoretical predictionW e c = 12 (1 + (2/3)Oh 2 )[START_REF] Kulkarni | Bag breakup of low viscosity drops in the presence of a continuous air jet[END_REF] suggested for bag inflation from a droplet, which accounts for viscous effects through Ohnesorge number Oh = µ l /(ρ l σH f ) 1/2 . Note that for the range of film viscosities used in experiments the maximum Ohnesorge number is of the order of 10 -1 .

xFIG. 4 .FIG. 5 .

 45 FIG. 4. (a) Kinematics of bag expansion measured for different film viscosities ν = 5 cst, 50 cst and 75 cst. Symbols are color coded according to the film viscosity. Data from 3D simulations (☀ = 15 m/s) and 2D numerical simulations (• = 30 m/s and ∎ = 15 m/s) are performed for film viscosity ν = 5 cst. Solid black line is theoretical prediction for bag-inflation kinematics, R Tip ∼ t 2 . (b) Theoretical exponential decay in bag thickness, h ∼ e -2t (solid black line), measured in numerical computations. Here, the bag-thickness is non-dimensionalised by its maximum value. (c) Sequence of experimental snapshots illustrating the fact that the width of the bag W B at the location of the attachment with the crest of the interfacial wave remains nearly constant while it inflates. The vertical lines on each snapshot corresponds to the instantaneous width of the bag. The horizontal scale-bar shown on the first snapshot corresponds to 1 mm. (d) Experimentally measured variation in bag width with film viscosity. The data corresponds to experiments performed with film thickness H f = 1 mm and U = 30 m/s.

FIG. 7 .

 7 FIG. 7. Droplet size distribution measured at 10 cm away from the the exit of the channel. (a) Size statistics measured for different film viscosity • = 5 cst, • = 25 cst and • = 105 cst. For these measurements the flow velocity and film thickness was fixed at U = 30 m/s and H f = 1 mm. Solid lines are a log-normal fit to the data. (b) Volume based size statistics measured for different film viscosities. Solid lines are corresponding log-normal fits to the data.

FIG. 8 .

 8 FIG. 8. (a) Histograms comparing the length of inflated morphologies measured at the time of bursting for different film viscosity (blue) 5 cst and (red) 75 cst. Stabilizing effect of viscosity prolongs the lifetime of inflated structures. Accordingly, we measure delay in burst time of liquid bags with increase in film viscosity (b).

FIG. 9 .

 9 FIG. 9. Experimentally measured variation in the mean droplet size ⟨d⟩ with local Ohnesorge number Oh l = µ/(ρ σ h) 1/2 . The length scale in Oh l is the typical bag-thickness h ∼ 1 µm. In Regime-I, Oh l < 1 a balance between inertia and capillary forces decides the eventual fate of a bag, causing it rupture early, whereas in Regime-II, Oh l > 1 viscous effects enhance the stability of the thin sheets, causing it to burst at later times, thus producing smaller droplets.

ACKNOWLEDGMENTS

The authors thank Gert-Wim Bruggert for the technical support in building the experimental setup, and Pim Wassdorp for the help in PDA measurements. We acknowledge the funding by Max Planck Center Twente, NWO and from the ERC Adv. Grant DDD 740479.


Najoua Mekaddem

Magali Fois

Ben Samia

Atef Ali

Laurent Mazioud

Ahmed Ibos

Hannachi

Ibos

Caractérisation

Caractérisation thermophysique de composites perlite expansée/ paraffine/ plâtre destinés au stockage d'énergie dans le bâtiment

Caractérisation thermophysique de composites perlite expansée/ paraffine/ plâtre destinés au stockage d'énergie dans le bâtiment

Najoua MEKADDEM 1* , Magali FOIS 2 , Samia BEN ALI 1 , Atef MAZIOUD 2 , Laurent IBOS 2 , Ahmed HANNACHI 1 1 Laboratoire de Génie des Procédés et Systèmes Industriels, Ecole Nationale d'Ingénieurs de Gabes Rue Omar Ibn Elkhattab -6029Gabes, Tunisie 2 UPE, Centre d'Etude et de Recherche en Thermique, Environnement et Systèmes, Université Paris-Est Créteil, 61, av. du Général de Gaulle -94010 Créteil Cedex * (auteur correspondant : mekaddem.najoua@gmail.com) Résumé L'intégration des matériaux à changement de phase (MCPs) dans les parois est une solution pour réduire les dépenses énergétiques dans le bâtiment. Ce travail a pour but de préparer et de caractériser un composite contenant un MCP. Le composite étudié est formé de la paraffine /perlite expansée inséré dans le plâtre. Une étude en calorimétrie différentielle à balayage (DSC) et des mesures des propriétés thermophysiques ont été faites. L'addition de 10% d'une poudre en aluminium améliore légèrement la conductivité thermique des échantillons.

Nomenclature

k conductivité thermique, W.m -1 .K -1 a diffusivité thermique, mm 2 .s -1 f fusion c cristallisation ss transition solide-solide
Cp capacité thermique, J.g -1 . °C-1 T température, °C ΔH enthalpie, J. g -1 l'insertion de MCP dans des structures conductrices et la dispersion de nanotubes de carbone ou de particules de nano-métal dans le MCP. Kim et al. [START_REF] Kim | High latent heat storage and high thermal conductive phase change materials using exfoliated graphite nanoplatelets[END_REF] ont étudié l'effet de l'addition des nano plaquettes de graphite exfoliées (xGnP) sur les propriétés thermiques du composite préparé sous une forme stable de MCP. Ils ont trouvé que la conductivité thermique de MCP augmente proportionnellement avec la fraction massique du graphite.

Dans le domaine du bâtiment, l'insertion du MCP dans des matériaux de construction tels que le plâtre ou le béton conduit à la fuite de ce MCP utilisé lorsqu'il passe à l'état liquide. Afin d'éviter la fuite de MCP liquide, des formes stables de composites à MCP ont été proposées en dispersant les MCPs dans une matrice poreuse qui est chimiquement inerte et sa structure reste stable à la température de changement de phase [START_REF] Zhong | Preparation and thermal properties of porous heterogeneous composite phase change materials based on molten salts/expanded graphite[END_REF]. Par exemple, Sari [START_REF] Sari | Fabrication and thermal characterization of kaolin-based composite phase change materials for latent heat storage in buildings[END_REF] a utilisé une sorte d'argile comme support pour le MCP et le graphite expansé comme un agent pour améliorer la conductivité thermique. L'addition de 5% de ce dernier en fraction massique à trois composites fabriqués a provoqué une augmentation de plus de 35% en conductivités thermiques. Jiao et al [START_REF] Jiao | Preparation and properties of lauric acid-stearic acid/expanded perlite composite as phase change materials for thermal energy storage[END_REF] ont étudié la caractérisation thermophysique des composites comportant un mélange d'acides laurique et stéarique inséré dans la perlite expansée. Ils trouvent une dispersion uniforme de MCP dans la structure poreuse de la perlite expansée avec une température de fusion environ 33°C et une chaleur latente de 131.3 J/g. Chung et al [START_REF] Chung | Preparation of energy efficient paraffinic PCMs/expanded vermiculite and perlite composites for energy saving in buildings[END_REF] ont également comparé les performances chimiques et thermiques de deux composites paraffine / perlite expansée et paraffine / vermiculite. Leurs résultats en DSC montrent que les deux composites ont des chaleurs latentes et des températures de changement de phase adéquates pour une application de stockage d'énergie à basse température. Ceci est en raison de la grande surface de la perlite expansée et de la vermiculite et la bonne dispersion de la paraffine dans les pores de deux supports.

Ce travail porte sur la préparation d'une forme stable de composite paraffine/perlite expansée pour le stockage d'énergie à basse température dans l'habitat. Ce composite a été inséré dans du plâtre. Les propriétés thermophysiques de composite seul et de composite/plâtre ont été mesurées par un dispositif développé au CERTES (DICO) et par analyse enthalpique différentielle (DSC).

Matériel et méthodes

Préparation de composites perlite expansée / paraffine / plâtre

La paraffine RT27 a été utilisée comme matériau à changement de phase. Ce MCP est vendu par 'Rubitherm Technologies GmbH' et sa température de fusion est comprise entre 25°C et 28°C. La fusion se trouve dans la plage de température de confort thermique à l'intérieur des bâtiments. Sa capacité de stockage de chaleurs latente et sensible entre 20 et 35°C est de 179 kJ.kg -1 et sa conductivité thermique est de 0,2 W.m -1 .K -1 , selon la fiche technique. La matrice support est la perlite expansée fournie par 'PERLA group'. C'est une roche volcanique minérale poreuse utilisée dans l'isolation thermique. Sa composition chimique élémentaire est présentée dans la figure 2b.

Le composite paraffine/perlite expansée est préparé par insertion directe de la paraffine liquide dans une quantité sèche de perlite expansée comme le montre la figure 1. Puis, le composite obtenu a été enrobé par une couche de résine pour éviter la fuite de la paraffine liquide. La quantité maximale de paraffine insérée dans le support est de 60% en masse. Afin d'améliorer la conductivité thermique de ce composite, une quantité de poudre d'aluminium à 10% en masse a été ajoutée. Le composite obtenu avec et sans aluminium a été mélangé au plâtre pour différentes fractions massiques variant entre 20 et 50%. Une analyse en Microscopie Electronique à Balayage (MEB) de la perlite expansée a été effectuée. Elle présente de grands pores et de fines parois (figure 2a), sa composition a été déterminée par spectrométrie de dispersion des rayons X (figure 2b).

Méthodes de mesure

Les valeurs des conductivités et diffusivités thermiques ont par ailleurs été mesurées avec un dispositif de mesure élaboré au laboratoire CERTES (DICO). Des mesures d'enthalpie et de Cp de la paraffineRT27 et des composites intégrés dans le plâtre ont été réalisées en DSC.

DSC

Une DSC Diamond de Perkin Elmer a été utilisée. Elle a été calibrée en température avec de l'indium, de l'étain et de l'eau. Un intracooler III permet d'atteindre une température de -90°C. Des échantillons ont été sertis dans des coupelles à solide en aluminium pour faire l'étude des changements de phase.

Propriétés thermophysiques (dispositif DICO)

Une méthode périodique a été utilisée pour l'estimation simultanée des conductivités et diffusivités thermiques des composites [START_REF] Chung | Preparation of energy efficient paraffinic PCMs/expanded vermiculite and perlite composites for energy saving in buildings[END_REF][START_REF] Boudenne | A simultaneous characterization of thermal conductivity and diffusivity of polymer materials by a periodic method[END_REF]. Le principe de la mesure est de placer un échantillon parallélépipédique entre deux plaques métalliques (de dimensions : 44mm×44mm×10mm). La plaque inférieure est modulée en température grâce à un module à effet Peltier. La sollicitation thermique imposée à la plaque inférieure est une somme de cinq sinusoïdes dont on choisit l'amplitude et la fréquence. Le transfert de chaleur dans l'épaisseur de l'échantillon conduit à une variation de température dans la plaque supérieure. Les paramètres thermiques (la conductivité et la diffusivité thermique) sont alors estimés par méthode inverse à partir de l'enregistrement des variations de température en entrée et en

Résultats et discussion

Etude en DSC

Les mesures en DSC ont été effectuées à 10°C/min entre -30 et 60°C, les spectres obtenus lors d'un chauffage et d'un refroidissement successifs d'une quantité de paraffine (9,70mg) sont présentés dans les figures 3 et 4. Deux pics sont observés, le premier pic, proche de 0°C, de moindre amplitude par rapport au second, correspond probablement à une transition de phase solide-solide comme on peut l'observer sur le n-heptadecane [START_REF] Sari | Preparation, characterization and thermal properties of PMMA/n-heptadecane microcapsules as novel solid-liquid microPCM for thermal energy storage[END_REF]. Le second pic correspond à la fusion de la paraffine, avec une température d'onset proche de 25°C. La chaleur latente de fusion de la paraffine est de 151 J/g. Lors du refroidissement la cristallisation et la transition solide-solide sont observées. La figure 5 illustre les spectres de chauffage et de refroidissement des différents composites intégrés dans le plâtre. La quantité d'énergie stockée est proportionnelle à la quantité de composite ajoutée. L'analyse de ces spectres est présentée dans les tableaux 1 et 2. Pour les échantillons contenant 40% en masse de composites la chaleur latente de fusion est de 18.2 J/g ce qui est bien inférieur aux 151 J/g de la paraffine seule. Les mesures de capacité thermique permettront de calculer la quantité de chaleur totale stockée. Sur la figure 6, les courbes obtenues pour une calibration en Cp à 10°C/min lors de l'étude en chauffage et en refroidissement d'un composite contenant 20% de paraffine / perlite expansée ont été tracées. Le décalage en température des courbes est dû à la surfusion de la paraffine. Un calcul de l'aire sous le pic de fusion entre 8 et 32°C donne une aire de 34,9 J /g qui est très proche de la valeur calculée par sommation de la chaleur sensible et la chaleur latente (34,53 J/g). De même pour l'échantillon contenant 50% de composite l'aire sous le pic est de 55,96 J /g et la valeur calculée est de 56,4 J/g. Les valeurs de la capacité thermique ne peuvent être prises qu'en dehors des pics. Ces résultats ont été donnés sur la figure 7. On remarque que pour tous les échantillons, le Cp mesuré quand la paraffine est à l'état solide (en dessous de -10°C) est bien inférieur au Cp mesuré quand la paraffine est à l'état liquide (au dessus de 33°C). Des valeurs de Cp plus importantes se trouvent dans la zone entre la transition solide-solide et la transition solideliquide. Cette croissance peut correspondre au début du pic de fusion. Les mesures de conductivité (k) et diffusivité (a) thermiques ont été réalisées pour tous les composites à une température de 12°C, à laquelle aucune transition n'est observée. L'objectif de l'ajout de l'aluminium était d'augmenter la conductivité thermique. Les résultats sont présentés sur les figures 8 et 9. Globalement la conductivité thermique augmente avec l'ajout de métal mais cette augmentation est relativement faible. Une chute de la conductivité thermique pour les composites sans Al à 50% indique une potentielle 'dégradation' du matériau composite qui n'est peut-être plus homogène. Une valeur maximale de 40% sans Al en masse de composite dans le plâtre est donc probable. Avec l'ajout de l'aluminium, pour une fraction de 40% de composite la conductivité thermique augmente de 19%.

Evolution de la capacité thermique

Propriétés thermophysiques

Conclusion

Un composite paraffine/perlite expansée inséré dans du plâtre a été préparé par imprégnation directe afin d'obtenir une forme stable contenant un MCP sans avoir de fuite. Les résultats de DSC ont montré que les températures de fusion et de cristallisation et les chaleurs latentes de composite conviennent aux applications de stockage d'énergie thermique à basse température. Il faut optimiser la quantité du métal ajouté au composite pour améliorer la conductivité thermique sans réduire sa capacité de stockage de chaleur.

Figure 1 :

 1 Figure 1 : Imprégnation directe

Figure 2 :

 2 Figure 2 : Observation en microscopie électronique à balayage (a) et composition chimique élémentaire (b) de la perlite expansée

Figures 3 et 4 :Figure 5 :

 45 Figures 3 et 4 : Etude en DSC de la RT27 lors d'une chauffe et d'un refroidissement à 10°C/min

Figure 6 :Figure 7 :

 67 Figure 6 : Courbes obtenues pour une calibration en Cp lors de l'étude en chauffe et en refroidissement d'un composite contenant 20% de paraffine / perlite expansée

Figure 8 et 9 :

 89 Figure 8 et 9 : Conductivité et diffusivité thermiques des composites perlite expansée/ paraffine/ plâtre en fonction de la fraction massique en composite perlite expansée/ paraffine avec et sans aluminium

  Analyse des changements de phase des composites insérés dans le plâtre en refroidissement

			Transition solide -solide		Fusion
		Masse	Aire	ΔHss	Tss	Aire	ΔHf	Tf
	%composite	(mg)	(mJ)	(J/g)	(°C)	(mJ)	(J/g)	(°C)
	20	9.23	8.29	0.90	2.03	75.01	8.13	26.00
	30	9.27	14.97	1.61	2.22	131.93	14.23	26.00
	40	9.75	21.50	2.20	2.13	176.90	18.14	25.91
	50	9.61	26.12	2.72	2.04	219.38	22.83	25.81
	Tableau 1 : Analyse des changements de phase des composites insérés dans le plâtre en chauffe
				Cristallisation		Transition solide -solide
		Masse	Aire	ΔHc	Tc	Aire	ΔHss	Tss
	%composite	(mg)	(mJ)	(J/g)	(°C)	(mJ)	(J/g)	(°C)
	20	9.23	64.2	6.95	25.36	7.29	0.79	-0.07
	30	9.27	118.6	12.8	25.52	11.10	1.20	0.33
	40	9.75	157.9	16.2	25.21	21.30	2.18	-0.02
	50	9.61	212.0	22.1	25.13	22.86	2.38	-0.24
	Tableau 2 :

Afin de réduire les besoins énergétiques et d'améliorer le confort thermique dans le bâtiment, la mise en oeuvre de nouveaux systèmes de stockage d'énergie parait nécessaire. Le stockage d'énergie se fait sous trois formes principales ; stockage par chaleur sensible, par chaleur latente et par voie thermochimique. Le stockage par chaleur latente est plus important, il a suscité actuellement un regain d'intérêt. Il est basé sur le stockage et la restitution d'énergie lorsqu'un matériau subit un changement de phase du solide au liquide ou vice versa[START_REF] Dutil | Modeling phase change materials behavior in building applications : Comments on material characterization and model validation[END_REF]. Le principe de ce stockage est d'intégrer les matériaux à changement de phase dans les structures de bâtiment; mur[START_REF] Virgone | Energetic efficiency of room wall containing PCM wallboard : A fullscale experimental investigation[END_REF][START_REF] Fiorito | Trombe walls for lightweight buildings in temperate and hot climates. Exploring the use of phase-change materials for performances improvement[END_REF], plancher[START_REF] Royon | Thermal energy storage and release of a new component with PCM for integration in floors for thermal management of buildings[END_REF], toiture[START_REF] Pasupathy | Experimental investigation and numerical simulation analysis on the thermal performance of a building roof incorporating phase change material ( PCM ) for thermal management[END_REF], brique[START_REF] Castell | Experimental study of using PCM in brick constructive solutions for passive cooling[END_REF], plâtre[START_REF] Karaipekli | Development and thermal performance of pumice/organic PCM/gypsum composite plasters for thermal energy storage in buildings[END_REF][START_REF] Kheradmand | Experimental and numerical studies of hybrid PCM embedded in plastering mortar for enhanced thermal behaviour of buildings[END_REF]. Les MCPs sont généralement classés en trois groupes: organiques, inorganiques et eutectiques. Les cires de paraffine sont des MCPs organiques constitués d'hydrocarbures saturés. Pour un nombre de carbone variant entre 12 et 33 le point de fusion augmente de -12°C à 71°C[START_REF] Sharma | Latent heat storage materials and systems: A review[END_REF]. Ces n-alcanes présentent différents points de fusion qui appartiennent à la zone de confort thermique ainsi qu'une large gamme de chaleurs latentes. Ceci les acquiert des caractéristiques appropriées pour des applications de régulation de la température dans l'habitat. Ces composés sont chimiquement stables, compatibles avec des matériaux d'encapsulation, à faible coût et non toxiques. Cependant, ces matériaux sont inflammables et ont une faible conductivité thermique allant de 0,1 à 0,3 W. m -1 . K -1[START_REF] Sharma | Developments in organic solid-liquid phase change materials and their applications in thermal energy storage[END_REF]. Par conséquent le taux de stockage et de déstockage de la chaleur subit une réduction légère pendant les cycles de fusion et de solidification. Pour surmonter cet inconvénient, quelques techniques ont été étudiées, comme

Remerciements

Ce projet est réalisé dans le cadre d'une thèse de doctorat MOBIDOC du programme PASRI financé par l'UE et administré par l'ANPR.