Bruno Malet-Damour
email: bruno.malet-damour@univ-reunion.fr

Laurane Ruggeri

Dimitri Bigot

Jean-Pierre Habas

Re-use waste for building thermal insulation : case study of loose-fill plastic waste in cold and humid climate

Keywords: recycling, plastic waste, construction, thermal insulation, loose-fill

Plastic waste is a major environmental and scientific challenge of our century. The current paradigm of "waste management" must evolve towards "resource management" by identifying a highly sustainable material consuming sector. The general objective of this paper is to propose a simple, economical and efficient solution for the recovery of plastic waste for the building sector. We have experimentally evaluated the performance of a Loose-Fill Plastic Waste (LFPW) as a thermal insulation solution. For this purpose, a literature review was conducted to guide the design and conduct of an experimental study on test cells in the cold and humid climate of Reunion Island (France). Our literature review shows that this form of plastic waste recovery is a world first. The LFPW reduces surface temperatures by nearly 5.4 °C, with a maximum difference of nearly 16.5 °C. The thermal phase shift is also remarkable (between 70 and 150 minutes). This technical solution makes it possible to achieve performances comparable to conventional thermal insulation solutions while combining circularity and technological development. It is a realistic opportunity for emerging countries.

Introduction

Waste management seems to be a never-ending challenge as its quantity is steadily increasing. In 2010, the United Nations Program (UN-Habitat) considered waste as one of the biggest challenges of the 21 st century. By 2050, its global production is expected to increase by almost 70%. The most alarming situation is observed with plastic waste. The situation is even quite critical in emerging countries. Indeed, plastics' durability does not facilitate their degradation after use, which turns them into a real source of contamination. Global agreements have established the Sustainable Development Goals (SDGs) to overcome this problem. They were supported by the mandatory reduction of inequalities between states facing global challenges such as poverty, climate, or environmental degradation. The 12 th SDG, "Responsible Consumption and Production," describes solid waste recycling, especially plastics, as the first key environmental challenge. Today, plastic is present in many applications and often, in large quantities. Indeed, it has remarkable properties that make it a versatile material used throughout the world. However, this intensive use has led to a significant accumulation of plastic waste in the environment, impacting animal and human health because of their limited degradation [START_REF] Thompson | Plastics, the environment and human health: current consensus and future trends[END_REF]. While developed countries are already working to meet this challenge, emerging countries that are mainly affected by the energy and climate crises, need to make much greater efforts. In addition to the reduction of plastic use, one possible solution is to shift the current paradigm from "waste management" to "resource management." Waste management is a current environmental issue with great potential. Building construction is a sector that produces a very large amount of plastic waste. Thus, replacing part of the conventional materials with new materials made from recycled waste from buildings (or household origin…) seems to be an excellent compromise to reduce the environmental impact of this sector of activity.

As La Reunion is an island, waste management is a significant issue because space is necessarily more limited than on a continent. The burial of waste is therefore not a realistic and acceptable solution indefinitely. We are therefore interested in this local problem to develop a solution for recovering plastic waste at a reduced cost. Also, the island is subject to a humid tropical climate, which, in the heights, can combine problems of cold and very high relative humidity. The variation of temperature and humidity can cause the condensation of water contained in the air which impacts the efficiency of traditional insulators (glass wool, rock wool, cellulose) while generating fungal developments. However, due to the saturated coastal zone, the demographic evolution of the island shows that the high zone (altitude above 600 m) will be largely densified. New forms of insulating materials must be developed This article aims to propose a solution for the reuse of plastic waste without preliminary sorting and with limited technicality. The purpose of these different elements is to offer a highperformance technical solution at a lower cost. It consists in valuing this waste as thermal insulation in bulk. The only constraint would be to crush the waste to a size that guarantees a low density and thus a high thermal resistance. This method, associated with plastic parameters (durability, hydrophobicity, low thermal conductivity), is likely to offer an economical, thermohydric, and sanitary efficient answer.

In the first part, a brief review of state of the art is proposed to identify the modes of recovery of plastic waste, highlighting the originality and simplicity of our technical solution. In a second step, we study the thermal performances of the LFPW experimentally in a cold and humid tropical climate, representative of the high altitude area (1560 m). The analysis allows us to conclude about the interest of the technology in a cold and humid climate.

Plastic Waste for building construction

Several authors have addressed the issue of the environmental impact of incorporating recycled plastic into building materials. In 2011, a study compared the life cycle assessment of an insulation board made from recycled PET with one made from virgin PET [START_REF] Intini | Recycling in buildings: An LCA case study of a thermal insulation panel made of polyester fiber, recycled from post-consumer PET bottles[END_REF]. It concluded that using recycled PET reduced the product's carbon footprint by 50%. Another 2014 study showed that recycling PET means no more PET is produced, thus decreasing health, ecosystems, global warming, and resource impacts. The impact of using recycled PET has a negative score for all environmental criteria studied by [START_REF] Ingrao | Recycled-PET fibre based panels for building thermal insulation: environmental impact and improvement potential assessment for a greener production[END_REF]. Literature shows us that plastic waste has real potential as material and that we should ignore where it comes from (waste).

3

A bibliographical analysis was carried out to identify the modes of treatment of plastic waste for the construction sector. It allowed us to demonstrate that the solutions for recovery of these wastes in the building sector are essentially based on the solutions presented hereafter.

Integration in a cementing matrix in the form of an aggregate

Plastic waste in the form of aggregates is the most used in composite concrete and mortar because it is a simple technique [START_REF] Choi | Effects of waste PET bottles aggregate on the properties of concrete[END_REF][START_REF] Silva | Degradation of recycled PET fibers in Portland cement-based materials[END_REF][START_REF] Banthia | Influence of polypropylene fiber geometry on plastic shrinkage cracking in concrete[END_REF][START_REF] Bhogayata | Impact strength, permeability and chemical resistance of concrete reinforced with metalized plastic waste fibers[END_REF][START_REF] Rebeiz | Precast use of polymer concrete using unsaturated polyester resin based on recycled PET waste[END_REF][START_REF] Tawfik | Polymer Concrete from Marble Wastes and Recycled Poly(ethylene terephthalate)[END_REF][START_REF] Patnaik | Thermal and sound insulation materials from waste wool and recycled polyester fibers and their biodegradation studies[END_REF]. It requires crushing or shredding of the waste material. They are then incorporated in the same way as the natural aggregates already used in the preparation. The problem with this recovery is the deconstruction of the concrete-polymer element because the separation of the two materials is a consequent technical lock. Plastic waste is generally integrated into two sizes: coarse aggregate (CA) or fine aggregate (FA).

Since the density of plastic materials is lower than natural aggregates, composite concretes are considerably lighter [START_REF] Gu | Use of recycled plastics in concrete: A critical review[END_REF][START_REF] Saikia | Use of plastic waste as aggregate in cement mortar and concrete preparation: A review[END_REF]. The composite material's density decreases as the proportion of plastic used increases. This results in a reduction in the slump of the concrete [START_REF] Gu | Use of recycled plastics in concrete: A critical review[END_REF]. The interactions between the plastic aggregates and the cementing matrix are weak, so few bonds allow the different elements to combine well. The interfacial transition zone [START_REF] Gu | Use of recycled plastics in concrete: A critical review[END_REF] between the plastic aggregates and the cementing matrix is weaker than in the case of natural aggregates. The morphology and the smooth, hydrophobic surface of plastic aggregates do not help for good cohesion. The addition of a superplasticizer improves these interactions [START_REF] Needhidasan | Amalgamation of E-waste plastics in concrete with super plasticizer for better strength[END_REF]. The results of the literature differ regarding the tensile and flexural strength. However, the tendency is towards reducing strength in proportion to adding plastic aggregates [START_REF] Gu | Use of recycled plastics in concrete: A critical review[END_REF][START_REF] Treasa Shinu | An experimental study of replacing conventional coarse aggregate with E-waste plastic for M40 grade concrete using river sand[END_REF][START_REF] Saikia | Mechanical properties and abrasion behaviour of concrete containing shredded PET bottle waste as a partial substitution of natural aggregate[END_REF]. Plastic is a material with suitable elastic properties, it is resistant to cracking, and its flexibility gives composite concrete better ductility than conventional concrete [START_REF] Saxena | Impact resistance and energy absorption capacity of concrete containing plastic waste[END_REF]. Another study by [START_REF] Saikia | Mechanical properties and abrasion behaviour of concrete containing shredded PET bottle waste as a partial substitution of natural aggregate[END_REF] showed that the addition of CA in composite concrete has a beneficial effect on abrasion resistance. Most studies show that fine aggregates achieve better mechanical properties than coarse aggregates. Logically, the latter are the most common aggregates used in composite concrete.

Integration in a cement matrix in the form of fibers

The scientific papers related to this topic are showing satisfactory results. The addition of plastic fibers in cemented composite materials generally improves the mechanical properties in contrast to aggregates [START_REF] Choi | Effects of waste PET bottles aggregate on the properties of concrete[END_REF][START_REF] Tawfik | Polymer Concrete from Marble Wastes and Recycled Poly(ethylene terephthalate)[END_REF][START_REF] Dweik | Enhancing Concrete Strength and Thermal Insulation Using Thermoset Plastic Waste[END_REF][START_REF] Mohammadhosseini | The feasibility of improving impact resistance and strength properties of sustainable concrete composites by adding waste metalized plastic fibres[END_REF][START_REF] Mohammadinia | Strength evaluation of utilizing recycled plastic waste and recycled crushed glass in concrete footpaths[END_REF][START_REF] Taha | Properties of concrete contains mixed colour waste recycled glass as sand and cement replacement[END_REF][START_REF] Corinaldesi | Lightweight plasters containing plastic waste for sustainable and energy-efficient building[END_REF]. The reduced quantities of fibers that are necessary for the formulation make it a low-waste plastic solution. Indeed, the optimal rate is around 1%. Beyond that, the properties are weakened.

Integration as a binder

Another method of incorporating plastic waste into concrete is used to create a composite material, referred to in the literature as "polymer concrete" [START_REF] Ingrao | Recycled-PET fibre based panels for building thermal insulation: environmental impact and improvement potential assessment for a greener production[END_REF][START_REF] Treasa Shinu | An experimental study of replacing conventional coarse aggregate with E-waste plastic for M40 grade concrete using river sand[END_REF][START_REF] Siddique | Use of recycled plastic in concrete: A review[END_REF][START_REF] Awoyera | Plastic wastes to construction products: Status, limitations and future perspective[END_REF][START_REF] Pelisser | Effect of the addition of synthetic fibers to concrete thin slabs on plastic shrinkage cracking[END_REF]. The plastic waste is converted into a polymer resin. This resin is mixed with aggregates (gravel, sand, ash) and sometimes additives (such as initiator or catalyst). The process is then similar to conventional concrete (methods of vibration, hardening, and molding). The technique of manufacturing resin from plastic waste is described in the work of some authors [START_REF] Rebeiz | Precast use of polymer concrete using unsaturated polyester resin based on recycled PET waste[END_REF][START_REF] Tawfik | Polymer Concrete from Marble Wastes and Recycled Poly(ethylene terephthalate)[END_REF][START_REF] Rebeiz | Plastic waste management in construction: technological and institutional issues[END_REF]

Plastic brick or block with or without other materials

Some studies are interested in developing bricks or pavers using all or part of the plastic waste. In some cases, a mineral, vegetable, or polymeric filler is used for modifying the final product's properties. Note that waste is generally transformed (grinding, extrusion, 3D printing). In some cases, plastics, such as PET, can be directly reused from their initial form. This is a low-cost approach. Extrusion plays a significant role in recycling plastic waste into valuable products. The created paste can be combined with various plastics or even with different fillers. For example, the paper [START_REF] Bhat | Processing of Waste Plastics into Building Materials Using a Plastic Extruder and Compression Testing of Plastic[END_REF] describes the use of waste rubber powder as a filler. The developed composite brick shows mechanical results that are higher than those characteristics of usual clay bricks. The interest of this method also lies in the notable consumption of plastic waste (60-80% by weight) or in the good level of finishing or again reduced water absorption [START_REF] Hiremath | Utilization Of Waste Plastic In Manufacturing Of Plastic-Soil Bricks n[END_REF]. The use of plastic waste in bituminous mixtures improves its properties and also its resistance [START_REF] Singh | Use of Plastic Waste in[END_REF]. The most used waste plastics used are polyethylene, polystyrene, and polypropylene. The waste plastics are shredded, covered with aggregates, and mixed with hot bitumen.

Insulating panel

There is another form of recovery of plastic waste. The process consists in developing a rigid or semi-rigid insulating panel. In 2011, a study by [START_REF] Intini | Recycling in buildings: An LCA case study of a thermal insulation panel made of polyester fiber, recycled from post-consumer PET bottles[END_REF] compared the insulating panel made from recycled PET with other insulating materials commonly used in the building sector. From an environmental point of view, the PET board is equivalent to a rock wool board, which has a much lower impact than expanded PS or PU foam boards. The insulating performance of this plastic board made from waste is dependent on the final density of the material.

Loose-fill material for thermal insulation

Insulation materials can be manufactured in different forms: loose fill, roll, rigid or padded board, or again foam. The choice of the appropriate form and, at the same time, of the type of insulation material mainly depends on the type of application as well as the wished physical properties [START_REF] Abdou | Comparison of Thermal Conductivity Measurements of Building Insulation Materials under Various Operating Temperatures[END_REF]. Loose-fill insulation achieves a higher thermal resistance due to its low density with entrapped air resulting in a low thermal conductivity [START_REF] Besant | Thermal Resistance of Loose-Fill Fiberglass Insulation in Spaces Heated From Below[END_REF]. This technical solution has the advantage of being simple to implement practically since it is generally done by blowing/insufflation in vertical and horizontal walls.

Most of the related studies concern cellulose [START_REF] Zhao | A mini-review on building insulation materials from perspective of plastic pollution: Current issues and natural fibres as a possible solution[END_REF][START_REF] Nicolajsen | Thermal transmittance of a cellulose loose-fill insulation material[END_REF][START_REF] Hurtado | A review on the properties of cellulose fibre insulation[END_REF][START_REF] Arenas | Sound insulation material[END_REF][START_REF] Vėjelis | Performance of loose-fill cellulose insulation[END_REF], wood chips [START_REF] Steen-Hansen | Smouldering combustion in loose-fill wood fibre thermal insulation: an experimental study[END_REF], glass fiber [START_REF] Wilkes | Thermal performance of one loose-fill fiberglass attic insulation[END_REF], raw hemp fiber [START_REF] Kosiński | Thermal Properties of Raw Hemp Fiber as a Loose-Fill Insulation Material[END_REF], perlite [START_REF] Sa | Measurements of thermal properties of insulation materials by using transient plane source technique[END_REF] or hemp shives [START_REF] Vėjelis | Loose fill material from hemp shives and binding material for thermal insulation and structural use[END_REF]. For example, for cellulose fiber, the thermal conductivity can be around 0.04 W/(m.K) with a consistency similar to that of absorbent cotton [START_REF] Hurtado | A review on the properties of cellulose fibre insulation[END_REF]. This value is close to that of hemp fibers in bulk, for which a study has shown a variation of 0.040 to 0.049 W/(m-K) for a density of about 85 kg/m 3 [START_REF] Kosiński | Thermal Properties of Raw Hemp Fiber as a Loose-Fill Insulation Material[END_REF]. Perlite, a mineral filler, achieves a thermal conductivity close to 0.054 W/(m.K) for a density of 94 kg/m 3 [START_REF] Intini | Recycling in buildings: An LCA case study of a thermal insulation panel made of polyester fiber, recycled from post-consumer PET bottles[END_REF]. Studies indicate that in environments where the relative humidity exceeds 90%, fungi growth is potentially favored [START_REF] Hurtado | A review on the properties of cellulose fibre insulation[END_REF]. This is likely to have significant consequences on the durability and thermal properties of the insulation [START_REF] Sandberg | Determination of the effects of moisture on the thermal transmissivity of cellulose fiber loose-fill insulation[END_REF], not to mention the health risks. Moreover, it is widely recognized that wet lignocellulosic materials can allow fungi growth, but this unwished phenomenon can be corrected by adding additives [START_REF] Hurtado | A review on the properties of cellulose fibre insulation[END_REF]. The choice of the material to be disposed of in bulk must therefore be made according to the environmental conditions and the risks of fungal developments.

As we have seen, most studies devoted to the possible use of plastic waste in building investigated the development of composite concrete and rigid or flexible thermal insulation panel. These recovery routes require processing steps with possible additional environmental impacts or energy consumption. However, all these works agree that the addition of plastic in any form improves the thermal performance of the final product. This improvement of thermal properties in cemented composite materials is mainly because plastic has a lower conductivity than the components usually found in conventional concrete and mortar [START_REF] Awoyera | Plastic wastes to construction products: Status, limitations and future perspective[END_REF]. This advantage is observed with the "loose-fill" technique but has the additional advantage to require a reduced processing cost. Mixing different plastics is also not prohibited, which facilitates its reuse since it does not require any form of sorting. Also, the limits of use and constraints of the plastic waste are an added value here: great durability; low interaction with other materials (low surface energy); hydrophobicity limiting the fungi development.

Therefore, we looked to identify studies that have paid particular attention to the use of loosefill plastic waste and its characterization as a thermal insulator. The keywords used in this bibliographic section were: waste; plastic; flakes; thermal insulation; bulk; loose fill; insulation material. But, as a result, no studies could be found on the use of loose-fill plastic aggregates. Our paper can be considered as a pioneer in studying shredded and loose plastic waste for thermal insulation.

Materials and methods

The performance of this type of insulation were evaluated in a tropical context, in the winter, and at high altitudes (cold and humid climates). This climate allows us to demonstrate this technology's interest in limiting heat transfers or thermal losses from the roof.

Description of the test cells

The experimentation was carried out on small-scale measurement cells, named "ISOTEST", whose dimensions are shown in Figure 1.

To investigate the interest of the technical solution, two cells were studied: one reference cell (without LFPW) and the other one equipped with a horizontal wall-type false ceiling containing the loose-fill plastic waste (LFPW). The vertical walls were composed of expanded polyurethane encapsulated in two steel plates for an overall thickness of 4 cm. The roof was made of dark blue corrugated sheet. A horizontal wall acted as a false ceiling. In the case of the cell equipped with the insulation to be tested, the loose-fill plastic was placed on this ceiling. In other words, this configuration was similar to a sandwich panel composed of plasterboard in the lower part (1.3 cm), 8 cm of loose-fill plastic wastes (LFPW) and topped by a plywood panel in the upper part (4 mm), allowing guaranteeing the thickness homogeneity of the plastic layer (Figure 2). The contribution of this last plate to the global thermal behavior of this wall was neglected in our study.

Different sensors have been installed in an identical way on both cells. K-type thermocouples were manufactured and calibrated following a rigorous experimental protocol. The different sensors were positioned as shown in Figure 2. A thermocouple was positioned at the surface of the plasterboard ceiling (𝑇 !,#$%&%'(,)*+ for the reference cell and 𝑇 !,#$%&%'(,,+-. for the tested wall). Three thermocouples were placed at various thicknesses to measure the thermal gradient 𝑇 (,/ , 𝑇 (,0 and 𝑇 (,1 within the loose-fill plastic layer. All these thermocouples were connected to a multiplexer (AM25T from Campbell Scientific®), which allowed for deporting an acquisition unit's channels (CR3000). We also placed Testo® brand stand-alone thermohygrometers in each of the ISOTESTs, to measure the operative temperatures (𝑇 23,)*+ and 𝑇 23,,+-. ) as well as the relative moisture (𝐻𝑅 )*+ and 𝐻𝑅 ,+-. ) throughout the experiment. In parallel, weather conditions were measured from Meteo France stations. Thus, the air temperature 𝑇 4,256 , relative humidity 𝐻𝑅 256 , and global solar radiation 𝐺𝐿𝑂 256 were regularly measured along the experiment phase. All data were collected at a time step of one minute for ISOTEST cells, and hourly for meteorological data.

T s,ceiling T g,3 T g,2 T g,1 T op HR PLYWOOD (0.4) PLASTERBOARD (1.3) Z Tg,2 = 4 Z Tg,1 = 2 Z Tg,3 = 6 LFPW (8)

Plastic wastes used

The plastic waste used was made of a mixture of polypropylene (PP) and polyethylene (PE), two thermoplastics from the retail sector and the industrial sector (packaging, household appliances, etc). These plastics were ground and then analyzed using a sieve column to determine their particule size distribution. Indeed, this parameter is likely to influence the apparent density of the resulting insulating layer and its thermal performance.

Figure 3 : Size analysis of loose-fill plastic waste with aggregate size equivalence

The results of the granulometry analysis can be seen in Figure 3, which shows the weight percentage of aggregates that passed through each of the sieves. According to the ranking used in literature, 70% of the waste analyzed can be considered as Fine Aggregate (FA), and the remaining 30% as Coarse Aggregate (CA). If we compare with the aggregates usually used for concrete, such granulometry would be represented by coarse sand and normal sand. The LFPW wall was made using only plastic particles larger than 3-4 mm.

Study climate and analysis period

La Reunion Island is subject to a humid tropical climate, divided into about forty microclimates related to its very uneven relief resulting from its volcanic geology. The standardization of these climates made it possible to orient the climatic classification described in the thermal regulation available on the island. The latter divides the territory into three Cumulative pass (%)

Aggregate size (mm)

Fine sand Rough sand Gravel

Fine Agregates (FA) Coarse Agregates (CA) 3-4mm

Medium sand climatic zones: the low zone (altitude < 400 m), the mid-height zone (400 m < altitude < 600 m), and the high zone (altitude > 600 m).

In our case, we were interested in the high-altitude zone represented in particular by the city of La Plaine des Cafres (altitude 1560 m) located in the commune of Le Tampon (France). We conducted a brief climatic study of where the cells are positioned representative of the zone of high altitude, a cold and wet climate. This analysis consisted in measuring the outdoor air temperature with a thermometer under shelter and registering its evolution during a period long enough to be representative of the winter season. The corresponding data, presented in Figure 4, group the meteorological data from August 1 to September 17, 2020, divided into 6 periods.

The column on the left shows the magnitude of daylight duration while the different colors illustrate the range of registered outdoor air temperatures. These values clearly show that the site is in the winter period. Indeed, the days are short (less than 10 hours) and temperatures do not exceed 16 °C until midday to finally drop as early as 4:00 p.m. At the beginning and end of the day, average temperatures are below 6 °C.

The period of experimental data acquisition with the cells extended from August 18 to September 11, 2020.

Results and discussion

Impact of LFPW on surface temperatures

We analyzed the surface temperature 𝑇 !,#$%&%'( at the bottom of the plasterboard and compare the cell equipped with LFPW with the reference cell. This measurement allowed us to evaluate the attenuation power of the LFPW on the conductive exchanges between the roof and the cell enclosure.

12 AM ### ### 1,6 1,4 6,5 2,3 2,5 6,5 9,9 3,5 0,8 2,3 6,3 ### 6,0 8,8 7,6 9,4 9,6 ### 6,7 5,7 7,3 8,3 7,6 6,7 8,8 5,9 ### ### ### 9,9 4,7 8,3 7,9 8,2 9,9 8,4 ### ### 8,7 ### ### 5,7 7,8 5,6 5,0 4,6 1 AM ### 9,9 2,7 2,3 6,0 1,9 6,0 4,5 9,5 4,5 1,8 2,4 6,1 ### 5,4 9,0 7,6 9,7 9,9 ### 5,1 5,4 8,0 7,4 7,6 6,1 9,1 5,5 9,7 ### 9,7 9,9 3,9 9,0 6,2 8,1 9,9 9,6 ### ### 8,5 ### ### 5,6 8,6 2,8 5,5 2,7 2 AM 9,7 9,0 3,3 2,2 5,9 2,3 6,3 3,1 8,4 4,2 2,0 1,2 4,1 ### 5,8 9,3 7,1 9,4 9,5 ### 4,9 5,5 8,1 7,2 6,7 6,5 9,1 6,0 9,9 ### 9,7 9,8 3,9 9,6 6,2 8,4 ### 9,2 ### ### 8,7 ### ### 5,7 7,7 3,6 3,4 6,3 3 AM 9,0 5,0 4,2 2,2 5,6 2,8 5,4 3,6 7,5 1,8 2,3 0,5 4,9 ### 6,8 9,4 6,9 8,4 9,2 7,8 4,3 5,5 5,5 6,8 5,6 5,6 6,4 5,9 9,6 ### 9,8 ### 4,4 7,8 7,0 8,7 9,3 9,7 ### ### 8,8 ### 9,9 5,6 7,8 4,2 3,8 7,2 4 AM 9,6 3,9 4,3 4,7 5,9 1,1 4,0 3,3 7,0 0,7 2,8 0,2 4,1 ### 6,7 9,1 7,1 8,2 9,1 8,4 3,8 5,3 6,8 7,3 6,4 6,7 6,8 5,7 7,5 ### 9,9 ### 4,6 8,2 6,3 8,7 8,2 9,9 ### ### 8,8 ### 9,5 5,2 7,0 4,2 4,4 6,2 5 AM 9,7 5,1 1,9 6,0 5,5 1,8 3,2 3,7 7,0 2,3 1,8 0,5 3,2 9,7 5,2 8,3 7,2 7,2 9,0 9,3 3,9 5,1 5,8 8,1 6,9 6,1 6,0 5,7 7,0 ### 9,0 ### 7,3 8,8 6,5 9,0 7,2 9,8 ### ### 8,7 ### 8,7 5,4 8,1 4,6 4,1 5,4 6 AM 7,7 4,5 1,6 6,3 5,3 3,1 1,5 3,9 6,2 3,5 0,5 0,6 4,1 9,0 4,5 ### 8,0 8,5 8,8 9,7 3,8 4,9 6,2 8,1 7,4 6,8 9,2 6,7 7,2 8,6 9,6 ### 8,0 7,8 7,3 9,2 6,5 ### ### ### 8,6 ### 8,1 4,8 8,4 3,8 3,5 5,2 7 AM 7,3 2,3 1,9 6,1 3,3 4,8 2,2 4,6 6,8 4,5 0,6 0,7 4,1 9,2 4,0 ### 8,3 9,0 8,8 ### 4,5 4,9 7,3 8,0 7,4 8,2 9,0 6,0 8,1 8,4 ### ### 9,5 8,4 8,0 9,5 7,3 ### ### ### 9,6 ### ### 7,5 9,5 5,7 6,2 6,4 8 AM ### 6,7 8,1 9,6 5,6 7,3 6,2 8,9 6,5 6,2 4,7 5,8 7,7

### 8,8 ### ### 9,9 ### ### 9,8 ### ### ### ### ### ### ### ### ### ### ### ### ### 9,1 ### ### ### ### ### ### ### ### ### ### 9,1 ### ### 9 AM ### ### ### ### ### ### ### ### 8,5 8,5 7,9 ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### 10 AM ### ### ### ### ### ### ### ### 9,6 ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### 11 AM ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### 12 PM ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### 1 PM ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### 2 PM ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### 3 PM ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### 4 PM ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### 5 PM ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### 6 PM ### ### 9,8 ### 9,3 9,4 9,4 ### 7,4 8,4 9,1 ### ### ### 9,6 9,2 ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### 8,8 9,5 ### ### ### ### ### ### ### ### ### ### 9,4 9,2 ### 7 PM ### 9,

(winter season)

To get an overview of the weather conditions, we plotted the evolution of the outdoor air temperature 𝑇 4,256 as well as the global solar radiation 𝐺𝐿𝑂 256 (Figures 5 and7). The latter parameter was representative of the energy transmitted by the sun and could be correlated to the cloud density. For instance, a clear sky is characterized by the daily profile of its radiation similar to a Gaussian. Such situation was observed on August 22, 23, and 29. In this case, the global solar radiation was close to the direct solar radiation, with nominal values close to 1050 W/m 2 (September 6). In contrast, the overall solar radiation profile on overcast (cloudy) days is up and down, as was the case on August 25 or September 4, when the nominal values were around 500 W/m 2 . The outdoor air temperatures were only slightly affected, given the density of the surrounding vegetation and the seasonal temperatures at this altitude. Indeed, they ranged from 4 to 17 °C. The examination of the surface temperatures of the ceiling (Figures 6 and8) shows that the presence of the loose-fill insulation reduced the value of maximum temperature during the day. Overnight, the temperatures of the two cells were similar. The influence of solar irradiation is probably the reason for this equality. During the day, the sun irradiated the dark roof that raised the temperature of this metallic panel. Then, the temperature of the air gap increased faster than that of the outside environment. However, the LFPW, whose thermal conductivity results from the combination of the plastic's insulating power and the air trapped between the chips, attenuated the conductive and radiative effects of the air/sheet complex. On August 22 nd , under clear sky, the maximum global solar nearly 850 W/m 2 at p.m (Figure 5). The maximum surface temperature in the reference cell reached 35.3 °C almost two hours later (3:10 p.m.) against 23.2 °C simultaneously in the cell equipped with the LFPW (Figure 6). The maximum surface temperature in the test cell was reached was attained 140 minutes later with a nominal value of about 26°C. Thus, from the peak of maximum solar irradiation, the cell equipped with the LFPW reached its maximum surface temperature not less than 270 minutes later with an attenuation factor of the order of 0.73 compared to the reference cell. The thermal inertia of the LFPW wall is also visible in the rate of the variability of the surface temperatures. On a cloudy day, when the global irradiation has evolved in a sawtooth pattern, the surface temperature of the ceiling of the reference cell undergoes a multitude of temperature amplitudes. On the opposite, the LFPW wall reduced the variations of the surface temperature. This observation highlights the increase of thermal inertia by simply adding the LFPW.

LFPW performance on 2 typical days

Let's focus now our attention on other typical days.

The day of August 22 nd , for example, was the day with the most important difference in the surface temperature of the reference and test cells, respectively. As shown in Figure 5, the weather conditions were typical of a clear sky day with a nominal irradiance of nearly 873 W/m 2 and a temperature of 17.7 °C. Figure 9 shows the evolution of both surface temperatures throughout the day. At night, the values registered with both ceilings were quite similar. As soon as the sun rose, the roof of the cells absorbed the solar irradiation. Then, in the reference cell, the surface temperature The evolution of solar irradiance for September 7 presented in Figure 7 is characteristic of a cloudy day, with a maximum value of 654 W/m 2 for a maximum temperature at the same time of 14.5 °C. For the day with the smallest surface temperature difference between the two cells, a significant phase shift was observed with the use of LFPW (70 minutes). Inside the cells, the peak temperature was reduced by 4.3 °C between the reference and test cell, as shown in Figure 10. The added value of LFPW on the thermal inertia of the ceiling could also be observed by comparing the slopes of surface temperature evolution of each cell.

LFPW performance on the whole periods

Table 1 summarizes the data over the entire measurement period (from August 18 to September 11), including those from the thermohygrometric sensors. The average difference in air temperature between the two cells was about 4.9°C with the advantage for the LFPW cell. The temperatures were more stable there, even if the deployment of the LFPW on all the walls, (i.e., horizontal and vertical), would make it possible to increase the benefits due to its use. The air temperatures reached in the test cell are largely within the comfort range defined by ASHRAE. The maximum temperature did not exceed 26.6°C, while the reference cell reached 30.7°C. The observation is the same for the surface temperatures, where the average difference was about 5.4°C. The presence of the LFPW also reduced the amplitude of variation of the relative humidity due to a higher value of the minimum measured. Indeed, in the test cell, the relative humidity remained 57.6%, while without insulation, it could decrease down to 44.8%. A similar hierarchy was observed as concerns the average RH value but both values (test and reference) remained below that registered outdoor. The LFPW seems able to regulate the hygrometric exchanges between the ceiling and the airspace. This insulating complex containing air will tend to "trap" water in the bulk of plastic chips.

Study of the thermal gradient within the LFPW

The time has come to look at the evolution of the thermal gradient within the loose-fill plastic. Indeed, it is important to know if the thermal behavior of the bulk can be considered proportional to its thickness. To this end, two types of days were studied.

The first one, September 4 th , was the coldest day of our measurement period, i.e., when the maximum temperature presented the lowest value registered as shown in Figure 7. Figure 11 represents the evolution of the thermal gradient for this day at different times. A first examination of these data indicated that the temperature profile could vary depending on the time of day due to the variations of sunshine. Then, different characteristic hours were examined with much attention. At 6:00 a.m., at the beginning of the day, the cell has not yet received any heat, which justifies that the temperatures within the material, the air gap, and the sheet remained stable at

6.5 °C. At 9:00 a.m., the temperature 𝑇 (,/ was 6.4 °C higher than the temperature 𝑇 (,1 close to the plywood. However, the temperature of the sheet metal reached 18 °C. This is because the outside air temperature remained low, but the cell received the first irradiation from the sun. The vertical walls and the sheet metal heated up, while the bulk plastic and the air gap maintained their temperatures. This demonstrates the low thermal conductivity of the wall, in contrast to the steel roof. At noon, temperatures continued to rise with the maintenance of a thermal phase shift within the LFPW. At 6:00 p.m., the trend was reversed. When the solar radiation became zero, the temperature near the plasterboard and the temperature of the metallic sheet stabilized at 11 °C, while the temperature within the LFPW was 3.3 °C higher. At 11:00 p.m. and midnight, the temperature difference outside the LFPW was reduced but remained positive: the thermal inertia of the LFPW was deemed sufficient to induce a remarkable thermal phase shift. The maximum amplitude of the thermal gradient was notable. Indeed, the temperature difference between the upper and lower nodes could reach more than 5 °C over 8 cm. Also, in the middle of the day, the closer you get to the interior (i.e. towards the ceiling), the more the temperature increases which proves the insulating ability of this loose-fill plastic waste.

Conclusion and perspectives

The literature revealed that plastic waste as loose insulation has not yet been studied. Most of the articles refer to valorization as aggregate for concrete or mortar or as raw material for the realization of insulating or massive building materials (brick, paving stone). As for loose insulation, it is generally of vegetable or mineral origin, but no study mentions polymeric materials and even less waste. Our study is, therefore, the first on the potential of LFPW.

To demonstrate the potential of this technology, we conducted an experimental study on small-scale cells over 24 days during the winter season on Reunion Island. The testing platform was located in the town of La Plaine des Cafres in the island's heights, at an altitude of 1560 m. A cold and humid tropical climate marks this place.

Our data showed that the loose-fill insulation increased the thermal mass of the cell and largely limited the conductive exchanges between the roof and the air zone. The use of a thickness of 8 cm of loose-fill plastic wastes reduced the ceiling temperature by nearly 5.4 °C on average, with a maximum difference of nearly 16.5 °C. The time lag on the ceiling surface temperatures was also found worth of interest with a value comprised between 70 and 150 minutes.

The use of LFPW also impacted the relative humidity inside the cell. The insulation acted as a water barrier and did not allow moisture to escape. This explains why the reference cell showed better results. In a real situation, the use of minimum air exchange rates is likely to prevent this problem.

We also studied the thermal behavior within the material by measuring the thermal gradient. The maximum amplitude was notable since the temperature difference between the upper and lower nodes could reach more than 5°C over 8 cm during the day. The related profile was found to be no linear and probably depended on the chips' relative moisture and the bulk density variability.

The attenuation of temperatures by the insulation was minimized when the outside temperatures were low (for a low stress, there is a low impact).

These findings supported a follow-up to this first study. Measurements are still in progress to evaluate the behavior of the LFPW in summer in a hot and humid climate.

The impact of chip settling on the global conductivity of LFPW will also be investigated. Indeed, when used as insulation in attics, an additional quantity of loose-fill insulation is usually added beyond the level required for insulation to solve the problem of settlement associated with material creep. Since this creep is generally related to changes in relative humidity, the use of plastic material could be an asset since it is hydrophobic.

The optimal chip size also deserves to be studied with further attention to get the best performance of this class of insulating substrate. The improvement of the wall efficiency could also be achieved by the coupled use of PCM microcapsules, as described in a previous study combining loose-fill cellulose fibers [START_REF] Kosny | Performance of thermal insulation containing microencapsulated phase change material[END_REF].

All these leads that the deployment of LFPW walls considering is a technical solution that is interesting considering the thermal efficiency for energy management and building efficiency improvement. At the same time, both simplicity of implementation and nature of raw material lead to a cost-effective technical solution that is accessible to all.

  .

4

 4

Figure 1 :

 1 Figure 1: Schematic representation of the ISOTEST, location of the experiment and view of the LFPW wall

Figure 2 :

 2 Figure 2: Detail of the LFPW wall and sensor placement

8 th

 8 International Conference on Green Computing and Engineering Technologies (ICGCET®) 22 Sep -23 Sep 2022 Port Louis, Mauritius 7

Figure 4 :

 4 Figure 4: Temporal evolution of air temperature from August 1 to September 17, 2020

8 th 9 Figure 5 :

 895 Figure 5: Evolution of outdoor meteorological parameters (𝑇 4,256 and 𝐺𝐿𝑂 256 ) during period 1 (winter season)

2 )Figure 6 :

 26 Figure 6: Evolution of the surface temperature of the ceiling during period 1 (winter season)

Figure 7 :

 7 Figure 7: Evolution of outdoor weather parameters (Ta and GLO) during period 2 (winter season)

2 )Figure 8 :

 28 Figure 8: Evolution of the surface temperature of the ceiling during period 2 (winter season)

Figure 9 :

 9 Figure 9: Evolution of the surface temperature of the ceiling for the day with the highest deviation (22/08) (winter season)

  1560m ∆" !"#$%#&' = 16.5°) ! = 150 '() 8 th International Conference on Green Computing and Engineering Technologies (ICGCET®) 22 Sep -23 Sep 2022 Port Louis, Mauritius 13 increased rapidly and stabilized at 12:50 p.m., reaching a maximum value of 35.4 °C at 3:10 p.m. With the days being short at this time of year, the surface temperature decreased in two phases: a gentle until 5:00 p.m., then a rapid drop to 7 °C by nightfall. The cell equipped with the LFPW showed different behavior. The surface temperature increased slowly from 8:00 a.m. (i.e., 30 minutes later than in the reference cell) to reach a maximum temperature of 26 °C at 5:40 p.m. The difference in maximum temperatures reached 16.5 °C. The peak temperature of the cell with LFPW was reached 150 minutes after that of the reference cell. As with conventional insulation, the air trapped between plastic chips reduces the thermal conductivity of the material. In other words, the presence of LFPW significantly increased the thermal inertia of the horizontal wall.However, nighttime data show that the vertical walls and floor of the cells exchanged with their surroundings, and the solar energy stored by the thermal mass is quickly lost.

Figure 10 :

 10 Figure 10: Evolution of the surface temperature of the ceiling on the day with the lowest deviation (07/09) (winter season)

  ceiling,REF Plaine des Cafres 1560m ∆" !"#$%#&' = 4.3°( ! = 70 &'(

Figure 11 :

 11 Figure 11: Evolution of the thermal gradient of the roof for the coldest day (with the lowest 𝑇 7,89:,;7< ) (September 4)

Table 1 :

 1 Summary of measurements in La Plaine des Cafres

		Plaine des Cafres	Average Minimum Maximum
		𝑇 7,89:	11,1	3,8	19,1
		𝑇 23,)*+	13,7	1,9	30,7
	Air temperature	𝑇 23,,+-.	12,9	1,7	26,6
	(°C)	∆ 𝑇 !" (%&'()'*+)	0,8	0,2	4,1
		Average deviation 𝑇 !" (%&'()'*+)		4,9
		𝑇 !,#$%&%'(,)*+	14,2	1,5	37,2
	Surface	𝑇 !,#$%&%'(,,+-.	12,0	1,3	26,0
	temperature	∆ 𝑇 -(%&'()'*+)	2,2	0,2	11,2
	(°C)	Average deviation 𝑇 -(%&'()'*+)		5,4
		𝐻𝑅 89:	88,4	43,0	100,0
		𝐻𝑅 )*+	77,4	44,8	99,9
	Relative	𝐻𝑅 ,+-.	79,9	57,6	98,3
	humidity (%)	∆ 𝐻𝑅 % (%&'()'*+)	-2,5	-12,8	1,6
		Average deviation 𝐻𝑅 % (%&'()'*+)		6,8

th International Conference on Green Computing and Engineering Technologies (ICGCET®) 22 Sep -23 Sep 2022 Port Louis, Mauritius

ACKNOWLEDGEMENTS

We thank the PIMENT laboratory technician, Mr. Jérôme VIGNERON, for having actively contributed to the deployment of the experiment and the reliability of the data.

Authors


Dimitri Bigot
email: dimitri.bigot@univ-reunion.fr

Bruno Malet-Damour

Lionel Trovalet

Lisa Liu

Nadia Hammami

Jean-Pierre Habas

Potential of PCM Materials in Building Walls in La Reunion Island: A Numerical Study

Keywords: PCM, thermal modeling, thermal regulation, comfort

The French government has set up thermal regulation policy to minimize building energy consumption and ensure occupant's comfort in residential buildings, named RTAADOM in Reunion Island for "Acoustic, Aeraulic and Thermal Regulation applied to French overseas countries". It is used to design building walls, particularly the insulation materials they are made of, according to the building environment, which is described by four major climatic zones in the island. The present work highlights the potential of using phase change materials (PCM) as a candidate to improve insulation solutions traditionally used to comply with the regulation. The paper focuses on building's indoor temperatures to show that using a PCM can be an excellent solution to improve building thermal behavior in compliance with regulation needs. A reference building based on previous works on the development of a local insulating material is used to run a set of numerical thermal modeling in EnergyPlus. The results show differences between the thermal behavior of the reference building to ones with traditional regulation insulation and with three types of PCM material (a manufactured one and two imagined). Those two lasts were imagined from studies carried out within the framework of the MCP-iBAT FEDER project. The review shows that it is necessary to adapt the PCM properties (phase change temperature and range) to the building environment and uses. The present paper results show that the three PCMs can be used to partly or completely replace an insulation as recommended in the regulation. However, each environment needs a particular PCM configuration to optimize its impact on the building behavior. These results support the need to carry out additional studies to design the PCM material according to the building environment and its uses.

Introduction

The French government has set up a thermal regulation policy to minimize building energy consumption and ensure occupant's comfort in residential buildings. In French Overseas Countries, such as Reunion Island, this regulation is named RTAADOM for "Acoustic, Aeraulic and Thermal Regulation applied to French overseas country" [1]. The design offices of the building industry need to verify the compliance of the different building systems with 1 this regulation to ensure the comfort of the building and minimize its energy consumption. For example, it is necessary to verify wall insulation according to the environment of the building. In that purpose, Reunion Island is divided into four climatic zones defined by the altitudes: 0-400 m, 400-600m, 400-600m, and more than 800m, as shown in Figure 1. For low altitudes, the regulation aims to minimize the absorption of solar radiation through walls or windows. In contrast, for high altitudes, heat transfer through the walls needs to be minimized due to outdoor cold air. To ensure low heat transfers through opaque walls, a standard solution is to set up an insulation material inside the wall system. To help the Reunion Island building industry, the Center of Innovation and Research on Tropical Building (CIRBAT) set up a tool for insulation design according to different wall systems commonly used on the island [START_REF] Castelnau | Guide de pose des Isolants à La Réunion[END_REF].

Traditional insulation materials included rock wool, glass wool, polystyrene, and polyurethane. All these materials need to be imported from the European or Asian continents. However, the recent geopolitical conditions of the island increased the cost of materials' importation. Local authorities, through the Reunion Region, have shown that it is very urgent to find solutions and to develop new building materials on the island [START_REF] Ceser | et vision pour un usage raisonné et concerté des matériaux de construction nécessaires à un aménagement durable de La Réunion[END_REF].

In that respect, the University of Reunion Island has developed the European research project MCP-iBat, which aims at developing an innovative insulating material based on a phase change material from local biobased resources. In this paper, we propose to study the potential of using PCM materials as a candidate to improve insulation solutions traditionally used to comply with the regulation.

In the first part, a brief presentation of the regulation is proposed to identify the parameters that must be achieved in compliance with the regulations and those achievable in the case of a PCM wall. In a second step, we describe the building and its environment through the four climatic zones and their modeling. In a third step, we present the results of the simulation (or modeling) and conclude with the interest of the technology according to each climatic zone and regulation objectives.

Thermal regulation and its limitations

Compliance with RTAADOM regulations requires that the walls have solar transmittance factors S or thermal transmittances U below the regulatory thresholds depending on the type of wall and the climatic zone. Figure 1 shows the island's division into four climatic zones and the cities chosen for this work. These cities are representative of the climatic zones and meteorological data are available for the numerical study. To conform to the thermal regulation, two parameters must be checked: the global heat transfer coefficient through the wall and its solar factor, respectively U and S. The global heat transfer coefficient U corresponds to the amount of heat transferred through the wall from the outside to the inside of the building. The solar factor S corresponds to the proportion of solar radiation transferred through the wall to the indoor environment. Under 600m altitude, the walls have to comply with the global heat transfer coefficient of the regulation (see Table 1), whereas above the solar factors have to be matched (see Table 2).

Table 1. Maximum values of global heat transfer coefficient U [1]

Vertical walls Roofs

U ≤ 2 W.m -2 .K -1 U ≤ 0.5 W. m -2 .K -1
According to the traditional method, the global heat transfer coefficient U of a wall is obtained with the reverse of the global thermal resistance. The global thermal resistance is simply the addition of the thermal resistance of each wall layer and thethermal surface resistances due to convective exchanges with air on both sides of the wall. In this paper, the global heat transfer coefficient U was obtained from the heat density transfer equation ( 1)

𝑈 = φ 𝑤𝑎𝑙𝑙 ∆𝑇 (1)
being the heat density through the wall and the temperature difference between φ 𝑤𝑎𝑙𝑙 ∆𝑇 the two air points on either side of this wall.

The wall solar factor can be obtained by dividing the thermal heat that passes through it by its incident solar radiation [START_REF] Castelnau | Guide de pose des Isolants à La Réunion[END_REF].

𝑆 = φ 𝑤𝑎𝑙𝑙 φ 𝑖,𝑠𝑜𝑙𝑎𝑟 (2)
being the incident solar radiation on the considered wall. φ 𝑖,𝑠𝑜𝑙𝑎𝑟

Table 2. Maximum values of solar factor S [1]

Vertical walls Roofs S ≤ 0.09 S ≤ 0.03

As the physical principle of the PCM is based on its phase change from solid to liquid, and inversely, , the two regulatory constraints U and S are impossible two comply with directly by calculation or estimation. So, it is necessary to compare the thermal behavior of the building with and without PCMon walls to evaluate its efficiency in comparison with traditional insulation materials.

Problem description

To be able to quantify the impact of the PCM on the thermal behavior of the building, we chose to model it with a building energy simulation code, validated by the scientific community and used by local design offices. A reference building has been chosen and several scenarios have been defined to highlight the use of PCM in buildings in compliance with the thermal regulation.

Building description

The chosen building is a residential one defined by previous local studies as in [START_REF] Castelnau | Guide de pose des Isolants à La Réunion[END_REF] and as shown in Figure 2. It can accommodate a family of four people (two parents and two children) with an inside volume of about 286 m 3 and a floor area of 80.5 m². An air renewing of one volume per hour (1 m 3 /h ?) has been considered and internal loads due to standard equipment have been taken into account for sensible and latent heat [START_REF] Castelnau | Guide de pose des Isolants à La Réunion[END_REF]. For heat gains due to the occupants, a total power of 162 W has been considered, of which 70% for the latent part [START_REF] Castelnau | Guide de pose des Isolants à La Réunion[END_REF]. Furthermore, two types of heat gain due to electrical equipment have been defined. The first one is a base power of 250W for common electrical equipment throughout the day (television or computer for example). The second one consists of two power peaks at cooking times (12 am and 18 pm) of about 1000W for sensible heat and latent heat each. A door of 2 m² and two windows of 3 m² facing north and south respectively were also integrated in the model. The composition of the walls is given later in this paper in the description of the different studied scenarios. The heat transfer through the floor has been neglected by making it adiabatic. The roof of the building was made of two equal sides inclined at 21°, one facing north and the other south.

Studied scenarios

Five building scenarios have been set up according to a type of wall to compare PCM material to traditional thermal insulation material. The first one is a reference building without thermal insulation in walls and obtained by the simplification of the second one. The second one is a traditional insulation type building based on previous local works [START_REF] Castelnau | Guide de pose des Isolants à La Réunion[END_REF]. The third one is the reference building where walls have been equipped with a commercial microencapsulatedPCM from Winco Technologies. The two last ones are imaginary PCMs that could be produced locally and based on the experimental observations of the MCP-iBAT project. These five scenarios are summed up in Table 3 with the abbreviations that are used to identify the results. The composition of each wall is given in Table 4 and Table 5 from the outer to the inner layer. The thermal properties of each material are presented in Table 6, and the particular properties of PCMsin Table 7 and Table 8. As can be seen in Table 8, the PCMs differ in their phase change properties. The properties of the two imagined PCMs were chosen to match the diversity of the climatic zones of the island. Indeed, several studies carried out in tropical climates showed that many different PCM types can be used to improve building thermal behavior according to their environment and the wall where it is installed [START_REF] Boobalakrishnan | Thermal management of metal roof building using phase change material (PCM)[END_REF][START_REF] Song | Review on building energy performance improvement using phase change materials[END_REF][START_REF] Bimaganbetova | Performance evaluation of phase change materials suitable for cities representing the whole tropical savanna climate region[END_REF][START_REF] Lei | Energy performance of building envelopes integrated with phase change materials for cooling load reduction in tropical Singapore[END_REF][START_REF] Sheriyev | Effect of phase change materials on the thermal performance of residential building located in different cities of a tropical rainforest climate zone[END_REF]. The properties of the two fictitious PCMs were defined based on the experimental results of the MCP-iBAT project [START_REF] Malet-Damour | MCP-iBAT project reports[END_REF]. This work has been achieved using a standard building energy simulation code EnergyPlus [START_REF] Crawley | EnergyPlus: Energy simulation program[END_REF]. The PCM model is the one by NREL Laboratory and implemented in EnergyPlus [START_REF] Lee | EnergyPlus Hysteresis PCM Model: Cooperative Research and Development Final Report[END_REF] and named "EnergyPlus Hysteresis PCM Model".

The previous building and scenarios have been implemented in EnergyPlus and simulated in each of the four climatic zones. This has been achieved by setting up a building description file each scenario and simulating it with meteorological data corresponding to each reference city. These simulations led to five simulation result files for each climatic zone presented below.

Results and discussion

The simulation results have been analyzed and separated into three parts to show both the impact of the different materials on the building temperatures.The interest was to study the PCM solutions from the thermal comfort point of view and for their ability to comply or not with the thermal regulations in use in Reunion Island. The first part focuses on the behavior of the building's indoor air temperatures. The second part focuses on solar factors of walls for a building located in a climatic zone below an altitude of 600m. The last part shows the compliance of the results with the other requirements of the thermal regulation for a building located above an altitude of 600m.

For the three following parts, we analyzed two representative days of the year: a hot day in the summer (March 22 nd ) and a cold day in the winter (August 7 th ). As the compliance of solar factors is needed for an altitude below an altitude of 600m, we chose to present the meteorological data of Saint-Denis and Piton Saint-Leu on March 22, in Figure 3. Similarly, we decided to show the meteorological data of Colimaçons and Plaine Des Cafres on August 7 th to study global heat transfer coefficients (Figure 4). The aim of studying the thermal behavior of the building's indoor air temperature in such work is to verify the impact of the insulation and of the PCM. Figure 5 compares the reference building (without insulation PCM) with regulation-complying insulation and the three studied PCM materials for a hot day. As it can be observed, insulation and PCM materials all allow the decrease of the building's indoor air temperature. In all cases, PCMs are at least as effective as thermal insulation. Below 600m altitudes (Saint-Denis and Piton-Saint-Leu), the manufactured PCM seems to be the more effective in decreasing the temperature, with a maximum difference of about compared the reference building. Between 600m and altitudes, PCM1 seems more effective in decreasing the temperature on hot days, with a maximum difference of 8.5°C with reference building. Above 800m altitudes, the most effective PCM material is PCM1, with a maximum difference of 9°C with reference building. These results are in agreement with literature reviews [START_REF] Faraj | A review on phase change materials for thermal energy storage in buildings: Heating and hybrid applications[END_REF][13][14][15] [START_REF] Lamrani | Phase change materials integrated into building walls: An updated review[END_REF].

Figure 8 also shows that the manufactured PCM can improve heat conservation inside the building at night, whereas PCM1 has the opposite effect. PCM2 has the same behavior as traditional insulation at night. Figure 9 presents building's indoor air behavior for a cold day (August 7 th ). Considering the need to maximize heat gains above 800m altitudes (Plaine Des Cafres), PCM1 seems to be the best candidate, followed by PCM2. At lower altitudes, the manufactured PCM seems to be more efficient. Experimentally, results obtained with the MCP-iBAT project have shown that the manufactured PCM could not produce the same effect above 600m altitudes [START_REF] Malet-Damour | MCP-iBAT project reports[END_REF]. This was undoubted because the experimental building was not subjected to such significant heat loads. It is necessary to reach RTAADOM regulation thresholds such as solar factor and global heat transfer coefficient to use PCM in buildings to replace traditional insulation materials.

Solar factors

To verify the compliance of our walls with regulations, we focused on two solar exposed walls: the east vertical wall and the north roof. As explained before, only results of climatic zones above 600 m altitudes are interesting to study. Figure 3 shows that solar radiation was more critical at Saint-Denis on March 22 nd . This allows us to focus on solar factor analysis in this city. Furthermore, the following figures are centered on the moment of the day where the incident solar radiation is sufficient to calculate their solar factor.

Global heat transfer coefficients

Like solar factors, the global heat transfer coefficient study can be limited to the cities above 600m altitude. We chose to show the results obtained at Des Cafres in Figures 9 and10. Figure 9 shows the vertical walls and the of PCM with RTAA DOM Figure 10 shows only the manufactured PCM and PCM1 comply with RTAADOM thresholds. During the day, when solar radiation increases, the global heat transfer coefficient threshold is not respected. Indeed, this method of evaluation of the global heat transfer coefficient is only valid when the solar radiation is low or close to zero, i.e. before 7 a.m. and after 7 p.m. according to meteorological data presented in Figure 4.

Conclusion and perspectives

A numerical study of 3 PCMs has been presented in comparison with a reference building and an insulation material complying with the thermal regulation in use at Reunion Island. The regulations thresholds and the island's climatic context have been explained. After describing the studied building and the modeling methodology, the simulation results have been discussed.

These results have shown that they can help improve indoor comfort conditions by positively influencing the building's indoor air temperature. On hot days, the use of PCMs can lead to a reduction up to 10°C, similarly to traditional insulation. On cold days, the same benefits have been observed to keep the heat in the building.

The three types of PCM, with different temperature ranges of melting (or freezing) and different latent heats, from 19 to 29°C and 138 to 195 kJ.kg-1 respectively have shown various advantages and disadvantages. According to these parameters and climatic zone, each type of PCM can be helpful. It also seems that the building thermal loads can impact the choice of the best PCM. Future studies should highlight the impact of building thermal loads on PCM design, particularly from a comfort point of view. It will also be interesting to study the combination of several different layers of PCM to achieve better building energy consumption, thermal regulation thresholds and user's comfort.

ACKNOWLEDGEMENTS

Figure 1 :

 1 Figure 1: Climate zoning of the thermal regulation in La Réunion Island and location of the meteorological data [1].

Figure 2 :

 2 Figure 2: Plan view of the studied building [2].

Figure 3 :

 3 Figure 3: Meteorological data below 600m altitude (March 22).

Figure 4 : 4 . 1 .

 441 Figure 4: Meteorological data above 600m altitude (August 7).4.1. Impact of insulation material on building thermal behavior

Figure 5 :

 5 Figure 5: Building inside air thermal behavior on March 22.

Figure 6 :

 6 Figure 6: Building inside air thermal behavior on August 7.

Figure 7 :

 7 Figure 7: Solar factor of east vertical walls on March 22 nd .

Figure 7

 7 Figure 7 presents the solar factors of east vertical walls at Saint-Denis March 22 nd . The RTAADOM threshold is also represented on Figure 8. As it can be seen, every studied PCM solutions enabled to reach the RTAADOM requirements.

Figure 8

 8 Figure8presents the solar factors of north roofs at Saint-Denis on March 22 nd . Except for 8 a.m. slot, where the incident radiation is too weak compared to the convective exchanges to correctly evaluate the solar factor, it can be seen that every studied PCM solutions also allow reaching the RTAADOM thresholds for roofs.

Figure 8 :

 8 Figure 8: Solar factor of North roofs on March 22.

Figure 9 :

 9 Figure 9: Global heat transfer coefficient of east vertical walls on March 22 nd .

8

  th International Conference on Green Computing and Engineering Technologies (ICGCET®) 22 Sep -23 Sep 2022 Port Louis, Mauritius

Figure 10 :

 10 Figure 10: Global heat transfer coefficient of North roofs on March 22.

Table 3 . List of the simulated scenarios and the corresponding abbreviations

 3

	Scenario	Wall type	Insulation or PCM name	Abbreviation
	number
	1	Reference	-	ref
	2	Insulated	Polystyrene	ins
	3	Manufactured PCM	Paraffin PCM	com
	4	Imagined PCM	PCM to design	PCM1
	5	Imagined PCM	PCM to design	PCM2

Table 4 . Composition of vertical walls from the outside layer to the internal one.

 4

	Scenario	Composition from the outer to the inner layer
	number
	1	Cinder block	Air gap	Plasterboard
		(200mm)	(20mm)	(13mm)
	2	Cinder block	Polystyrene	Plasterboard
		(200mm)	(20mm)	(13mm)
	3	Cinder block	Air gap	Plasterboard	PCM Coated
		(200mm)	(20mm)	(13mm)	(4mm)
	4	Cinder block	Air gap	PCM1	Plasterboard
		(200mm)	(16mm)	(4mm)	(13mm)
	5	Cinder block	Air gap	PCM2	Plasterboard
		(200mm)	(16mm)	(4mm)	(13mm)

Table 5 . Composition of roofs from the outer to the inner layer.

 5

	Scenario	Composition from the outer to the inner layer
	number
	1	Ribbed steel sheet	Air gap	Plasterboard
		(1mm)	(80mm)	(13mm)
	2	Ribbed steel sheet	Polystyrene	Plasterboard
		(1mm)	(80mm)	(13mm)
	3	Ribbed steel sheet	Air gap	Plasterboard	PCM Coated
		(1mm)	(80mm)	(13mm)	(4mm)
	4	Ribbed steel sheet	Air gap	PCM1	Plasterboard
		(1mm)	(76mm)	(4mm)	(13mm)
	5	Ribbed steel sheet	Air gap	PCM2	Plasterboard
		(1mm)	(76mm)	(4mm)	(13mm)

Table 6 . Thermal properties of wall materials.

 6

	Material	Conductivity	Density	Specific heat
		(W.m -1 .K -1 )	(kg.m -3 )	(J.kg -1 .K -1 )
	Cinder Block			1250
	Air gap	Calculation of thermal resistance based on air gap thickness
	Polystyrene	0,042	18	1450
	Plasterboard	0,16	850	940
	Ribbed steel sheet	16	8000	480

Table 7 . Thermal properties of PCM materials.

 7

	Material	State	Conductivit	Density	Specific
			y	(kg.m -3 )	heat
			(W.m -1 .K -1 )		(J.kg -1 .K -1 )
	PCM	Liquid	0.053	640	1100
	coating	Solid	0.037	940	1100
	PCM1	Liquid	0.13	640	1100
		Solid	0.2	940	1100
	PCM2	Liquid	0.13	640	1100
		Solid	0.2	940	1100
	3.3. Numerical modeling

Table 8 . Phase change properties of PCM materials.

 8

	Material	Latent heat of	Phase	PCR 1	PCT 2
		phase change	change
		(J.kg -1 )	type	(°C)	(°C)
	PCM	138000	Melting	26.9-29.9	29
	coating		Freezing	26.4-22.8	24.4
	PCM1	195000	Melting	19.5-22	21
			Freezing	19.5-18.5	19
	PCM2	145000	Melting	17.5-28.5	24.5
			Freezing	21.5-14.5	20.5

th International Conference on Green Computing and Engineering Technologies (ICGCET®) 22 Sep -23 Sep 2022 Port Louis, Mauritius

This work was carried out within the framework of the FEDER MCP-iBAT project funded by Region Réunion and Europe. The authors would also like to thank them warmly for their trust.

Authors


Fabien Gelat

Michaël Coffinet

Stephane Lebrun

Francine Agbossou-Niedercorn

Christophe Michon

Eric Deniau

Total synthesis of (-)-herbaric acid. Organocatalyzed asymmetric halolactonization of acrylate-type carboxylic acids

Organocatalyzed asymmetric halolactonization of acrylate-type carboxylic acids. Total synthesis of (-)-herbaric acid. Examples of synthetic pharmacologically active isobenzofuranones

  Artois, UMR 8181-UCCS-Unité de Catalyse et Chimie du Solide, F-59000 Lille, France

	Synthesis of acrylate-type carboxylic acids 4
	Entry		R		Yield (%)		Yield (%)
	1		(+)-Menthyl		3a (66)		4a (97)
	2		(-)-Menthyl		3b (68)		4b (96)
	3		(-)-Borneyl		3c (59)		4c (89)
	4		(+)-Isopinocampheyl	3d (64)		4d (91)
	5		(+)-Fenchyl		3e (60)		4e (91)
	Entry		R	Catalyst	Additive	Yield (%)	D.e. (%)
	1	4a	(+)-Menthyl	-	-	5a (83)	28
	2	4a	(+)-Menthyl	QDTC 4-OMe	-	5a (85)	18
	3	4a	(+)-Menthyl	QTC 2,4-OMe	-	5a (88)	58
	4	4a	(+)-Menthyl	QDTC 4-OMe	PhCO 2 H	5a (85)	10
	5	4a	(+)-Menthyl	QTC 2,4-OMe	PhCO 2 H	5a (83)	76
	6	4b	(-)-Menthyl	QDTC 4-OMe	PhCO 2 H	5b (82)	74
	7	4b	(-)-Menthyl	QDTC 4-OMe	PhCO 2 H	5b (85)	79
	8	4b	(-)-Menthyl	QDTC 4-OMe	PhCO 2 H	5b (88) (X=I)	54
	9	4b	(-)-Menthyl	QTC 2,4-OMe	PhCO 2 H	5b (88)	32
	10	4c	(-)-Borneyl	QDTC 4-OMe	PhCO 2 H	5c (91)	45
	11	4c	(-)-Borneyl	QTC 2,4-OMe	PhCO 2 H	5c (88)	15
	12	4d	(+)-Isopinocampheyl	QDTC 4-OMe	PhCO 2 H	5d (93)	51
	13	4d	(+)-Isopinocampheyl	QTC 2,4-OMe	PhCO 2 H	5d (90)	32
	14	4e	(+)-Fenchyl	QDTC 4-OMe	PhCO 2 H	5e (93)	56
	15	4e	(+)-Fenchyl	QTC 2,4-OMe	PhCO 2 H	5e (90)	37

GELAT Fabien, COFFINET Michaël, LEBRUN Stéphane, AGBOSSOU-NIEDERCORN Francine, MICHON Christophe, DENIAU Eric Univ. Lille, CNRS, Centale Lille, ENSCL, Univ.

Organocatalyzed regio and diastereoselective halolactonization of 4

Total synthesis of (-)-herbaric acid