En effet, l'Union Européenne s'est fixée l'objectif de satisfaire 20% de sa consommation finale d'énergie par les énergies renouvelables à l'horizon 2020. Cette ambition se traduit par une cible de 23% pour la France déclinée par filière : chaleur (géothermie, biomasse, solaire, pompes à chaleur, part renouvelable des déchets) à 33%, électricité à 27% et transports à 10,5%. Le développement de la filière biomasse entraîne donc de plus en plus de production de cendres. La société DALKIA, Bois Energie France, possède 450 chaudières biomasse en France. Celles-ci produisent de la chaleur (chauffage et eau chaude sanitaire) à partir de la combustion de bois de palettes non traitées ou de broyat avec pour conséquence directe une production d'environ 50 000 tonnes de cendres de deux types : les cendres sous-foyers (90%) et les cendres volantes 10%). La filière agricole est actuellement la principale voie de valorisation. Mais les coûts de stockage ou les frais d'épandage conduisent à trouver d'autres voies d'utilisation. La filière BTP serait une possibilité pour valoriser ces sous-produits.

Un consortium s'est créé avec trois laboratoires, un centre technique industriel et deux entreprises : l'ER3 du LGCgE (Université d'Artois), le Laboratoire Cyclann de l'EME (Bretagne), le pôle Sciences des Matériaux de la Faculté Polytechnique de Mons (Belgique), le CERIB (Centre d'Etudes et de Recherches de l'Industrie du Béton), l'entreprise Biallais Industries fabricant de blocs béton et Dalkia Bois Energie Nord-Ouest leader du service énergique. Le pilotage du projet est assuré par l'équipe ER3 - Université d'Artois (Pr. Chafika Djelal et Dr. Laurent Libessart).

Je me suis particulièrement investi dans les LOT 4 et LOT 5 qui correspondent à la caractérisation des mortiers et des bétons secs à base de cendres volantes de biomasse (CVB). L'ingénieur de recherche Issam Laiymani et un collègue, nommé en septembre 2018, (Dr. Jonathan Page) ont également participé à cette étude. Les formulations de mortiers ont été caractérisées aux états frais et durci à des taux de 0 à 100% de substitution de ciment par les cendres (**Stage de M2 de Manh-Hung Nguyen**). De plus, durant ce stage de Master, l'étude a été également orientée sur la demande en eau des cendres, sur les essais calorimétriques et sur l'ouvrabilité des mortiers. La partie sur les blocs de béton a été développée avec le Post-doc de Vincent Dappe.

Pour continuer sur la thématique, en 2020, un second projet a été déposé par Pr. Chafika Djelal et Dr. Jonathan Page à l'ADEME GRAINE et accepté sous l'intitulé "Valorisation des cendres de biomasse en tant que granulats et filler dans des blocs de construction" et la **thèse de Florian Schlupp** (T4) a démarré le 1 octobre 2020 sur cette même problématique. Le but étant de valoriser les cendres de sous-foyers des centrales biomasse bois en substituant une partie du sable des formulations de blocs de bétons creux.

Pour ces études, les équipement utilisés pour les caractérisations minéralogiques et chimiques des matières premières sont donnés dans le tableau 2.2. La majeure partie des analyses minéralogiques et chimiques ont été faites à UMONS par l'intermédiaire du Pr. Maurice Gonon. Mais, au vu des appareils utilisés et des projets en cours, notre équipe a investi, en 2019, dans l'achat d'un ATG 2500 Regulus de NETSCH afin de pouvoir réaliser les mesures directement au laboratoire.
<table><caption>TABLE 2.2 – Dispositifs de caractérisations minéralogique et chimique utilisés</caption><thead><tr><td>Appareil</td><td>Paramètre mesuré</td></tr></thead><tbody><tr><td>DRX - Diffractométrie de Rayons X</td><td>Analyse minéralogique</td></tr><tr><td>ATG - Analyse Thermo Gravimétrique</td><td>Analyse de la variation de masse</td></tr><tr><td>Blaine</td><td>Surface spécifique des poudres</td></tr><tr><td>MEB - Microscope Electronique à Balayage</td><td>Analyse d'images</td></tr><tr><td>MEB - EDS (Energy Dispersive Spectroscopy)</td><td>Analyse chimique élémentaire</td></tr></tbody></table>

Le tableau 2.3 présente, quant à lui, les équipements nécessaires pour la caractérisation des pâtes et des mortiers à l'état frais et à l'état durci.

<table><caption>TABLE 2.3 – Dispositifs de caractérisation des pâtes et des mortiers à base de sous-produit</caption><thead><tr><td>Appareil</td><td>Paramètre mesuré</td></tr></thead><tbody><tr><td>Sonde Vicat</td><td>Temps de prise et demande en eau</td></tr><tr><td>Essai La Chapelle "Modifié"</td><td>Activité pouzzolanique</td></tr><tr><td>Table à secousses</td><td>Ouvrabilité des mélanges cimentaires</td></tr><tr><td>Calorimètre isotherme</td><td>Temps de début et fin de prise</td></tr><tr><td>Presse hydraulique</td><td>Résistances à la traction et la compression</td></tr><tr><td>MEB - EDS</td><td>Analyse chimique élémentaire</td></tr><tr><td>ATG - Analyse ThermoGravimétrique</td><td>Analyse de la variation de masse</td></tr></tbody></table>

Pour résumer, la première étude consiste à mettre au point un co-produit argile et hydroxyde d'aluminium afin de valoriser une partie des produits locaux du Cameroun enrichi en minéraux argileux (gibbsite) dont le diamètre est inférieur à 20 µm sans calcination. Deux types de kaolins, l'un commercial acheté en France et l'autre prélevé à l'état brut au Cameroun, ont été caractérisés par des analyses chimiques, minéralogiques et thermiques avant d'être enrichis en hydroxyde d'aluminium amorphe à des substitutions de 10% et 20%.

La deuxième étude porte sur les cendres volantes de biomasse pour les incorporer dans une matrice cimentaire. Les méthodes de formulations basées sur la substitution au ciment ou l'addition ont été analysées afin de trouver le meilleur taux d'incorporation de cendre. Comme pour les argiles, les cendres volantes ont été caractérisées par des analyses chimiques, minéralogiques, thermiques et mécaniques.

## 3.1 Etude des propriétés minéralogiques et chimiques des sous-produits

Suite à l'arrivée d'une nouvelle économie basée sur l'utilisation des ressources naturelles pour limiter la pollution environnementale, la valorisation des matériaux argileux apparaît comme une solution économique et durable à ce problème dans le domaine de la construction depuis quelques décennies.
Au Cameroun, il existe de vastes gisements de minéraux argileux et plus particu-
lièrement de kaolins qui n'ont pas encore été étudiés comme matériaux de construction
[117, 118, 119, 120]. Certains gisements contenant du kaolin/gibbsite sont déjà utilisés dans
la fabrication des matériaux réfractaires. Les argiles kaolinites, par la réactivité qu'offre
leur structure lorsqu'elle se trouve à l'état amorphe, sont les matériaux les plus utilisés
pour l'élaboration de ciment. Les argiles kaolinitiques du Cameroun enrichies en gibbsite
possèdent une structure quasi amorphe. Cette structure leur confère de fortes propriétés
mécaniques qui atteignent les valeurs proches de leurs produits calcinés à 700°C [117, 121].

En France, la valorisation de sous-produits industriels fait partie intégrante du paysage du Génie Civil. En effet, les apports de ses composés améliorent nettement les performances du béton comme par exemple l'emploi des cendres volantes des centrales thermoélectriques [125]. En effet, elles peuvent être intégrées en tant que granulats, dans les bétons et mortiers, et venir en substitution du ciment [126]. Dans le cadre de cet usage, elles doivent répondre aux exigences de qualité proposées par la norme NF EN 450 – Octobre 1995 – (Classement P18-050) et son annexe nationale – « Cendres volantes pour béton – Définition, exigences et contrôle de qualité ». Elles sont employées avec un taux de l'ordre de 80 à 100 kg/m³ de béton. En effet, du fait de leur activité pouzzolanique consommant la portlandite, les cendres volantes augmentent les résistances mécaniques à long terme des bétons, améliorant de fait leurs résistances aux attaques chimiques et donc leur durabilité. Ces deux avantages proviennent également de la compacité que fournit au béton leur ajout (effet filler) [127].

Au vu des recherches faites sur les cendres, l'utilisation des cendres volantes de bio-
masse peut donc être une source intéressante de valorisation pour le Génie Civil. Par
exemple, un groupe de chercheurs du département Génie Civil de l'Université de Grenade
vient de développer un béton autocompactant à partir de cendres provenant de la com-
bustion de granulés fabriqués avec les restes d'élagages d'oliviers [128]. Ils pensent au vu
des résultats de cette étude que l'utilisation de cendres volantes de biomasse en tant que
filler dans le béton autocompactant est possible.

En France, en 2016, le CERIB [129] a réalisé une étude sur une valorisation croisée de co-produits industriels (papeterie et fonderie). Une cendre de biomasse était présente. Ils ont montré l'intérêt de son emploi sur l'amélioration de la rhéologie des mortiers ainsi qu'en tant que liant sur une substitution du ciment à des taux inférieurs à 10% en confection de béton auto-plaçant. Une dernière étude récente a été réalisée au Québec (Sherbrooke) [130] en 2016 sur l'optimisation des cendres volantes et grossières de biomasse pour les bétons compactés au rouleau et dans les bétons moulés à sec. Ils ont réalisé des substitutions de 15% à 30% de cendres dans diverses compositions.

Quelles que soient les études menées, il est important au départ de connaître les com-
positions minéralogiques et chimiques des composés présents dans le co-produit à valoriser.

Au vue de la bibliographie, nous nous sommes basés, dans un premier temps, sur
la norme ASTM C618 pour connaître les caractérisations nécessaires pour définir si les
matériaux sont pouzzolaniques :

— % SiO₂ + % Al₂O₃ + % Fe₂O₃ > 70 %;

— Son indice d'activité I est : 0,67 < I < 1 ;

— Sa teneur en verre > 34 %.
Pour identifier les phases cristallines présentes dans les matériaux, la diffraction des rayons X (DRX) a été utilisée par comparaison avec un fichier de références J.C.P.D.S. (Joint Committee on Powder Diffraction Standard). Il est également possible de calculer leur degré de cristallinité et les paramètres de mailles associés. La diffractométrie de Rayons X a été faite par l'intermédiaire du Pr. Maurice Gonon à UMon sur les échantillons K, Kc, et $AH_3$ à l'état brut et sur les matériaux cimentaires obtenus à partir des différents échantillons bruts [122, 123]. La figure 2.68 présente les mesures obtenues sur les trois échantillons étudiés dans la thèse de CC Tchamo Leussa.

<figure><img src="image_64.png" /><figcaption>FIGURE 2.68 – Exemple de diffractogrammes (DRX) du Kaolin commercial, du Kaolin du Cameroun et de l'Hydroxyde d'aluminium [122]</figcaption></figure>

Il ressort que le kaolin commercial K et le kaolin du Cameroun Kc contiennent d'après les fiches J.C.P.D.S comme minéral principal, la Kaolinite. Les minéraux secondaires sont la Muscovite et le Quartz pour le kaolin commercial et la Gibbsite et le Quartz pour le kaolin du Cameroun. L'analyse chimique faite par analyse EDS-MEB a également montré une somme des oxydes ($SiO_2 + % Al_2O_3 + % Fe_2O_3$) de 97,49% et 97,94% respectivement pour K et Kc. Ainsi, ces matériaux peuvent convenir pour une réaction pouzzolanique. Les oxydes $Al_2O_3$ et $SiO_2$ sont les ingrédients fondamentaux pour une réaction pouzzolanique. Durant cette réponse, ces oxydes réagissent avec le $CaO$ du ciment ou de la chaux pour donner les gels de CSH ou de CASH qui provoquent une compacité du matériau et le rend ainsi plus résistant.

Concernant les cendres volantes de biomasse, les analyses DRX des échantillons de cendres provenant de la chaufferie biomasse de la ville de Calais (62) ont révélé la présence de phases cristallines attendues pour ce type de cendres, à savoir majoritairement $CaO$ (39 – 55%), $CaCO_3$ (37 – 50%) et $SiO_2$ (8 – 12%). D'autres phases cristallines sont également présentes dans des proportions bien moindres ($Ca_{10}K(PO_4)_7; Mg_2P_2O_7; Ca_3(PO_4)_2; Ca_2SiO_4$). L'allure du diffractogramme (Figure 2.69) ne laisse pas présumer la présence d'une quantité significative de phase amorphe (pas de dôme amorphe nettement visible).
<figure><img src="image_65.png" /><figcaption>FIGURE 2.69 – Exemple de diffractogrammes (DRX) des cendres volantes de biomasse étudiée</figcaption></figure>

Pour compléter les connaissances sur les matériaux, une acquisition d'image de la
morphologie des cendres a été réalisée par microscopie électronique à balayage (UMons),
la figure 2.70 présente un exemple sur les cendres volantes de la biomasse de Calais.

<figure><img src="image_66.png" /></figure>

<table><caption>FIGURE 2.70 – Images SEM et analyses EDS des cendres provenant de la chaufferie de Calais</caption>
  <thead>
    <tr>
      <th></th>
      <th>A</th>
      <th>B</th>
      <th>C</th>
    </tr>
    <tr>
      <th>Élément</th>
      <th>% masse</th>
      <th>% masse</th>
      <th>% masse</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>C</td>
      <td>0,00</td>
      <td>94,57</td>
      <td>22,58</td>
    </tr>
    <tr>
      <td>Mg</td>
      <td>5,27</td>
      <td>0,32</td>
      <td>11,97</td>
    </tr>
    <tr>
      <td>Al</td>
      <td>0,66</td>
      <td>0,04</td>
      <td>0,08</td>
    </tr>
    <tr>
      <td>Si</td>
      <td>4,91</td>
      <td>0,07</td>
      <td>0,29</td>
    </tr>
    <tr>
      <td>P</td>
      <td>2,94</td>
      <td>0,05</td>
      <td>3,21</td>
    </tr>
    <tr>
      <td>S</td>
      <td>2,02</td>
      <td>0,07</td>
      <td>0,48</td>
    </tr>
    <tr>
      <td>K</td>
      <td>8,38</td>
      <td>3,02</td>
      <td>1,95</td>
    </tr>
    <tr>
      <td>Ca</td>
      <td>75,81</td>
      <td>1,87</td>
      <td>59,44</td>
    </tr>
  </tbody>
  <tfoot>
    <tr>
      <td>Total:</td>
      <td>100,00</td>
      <td>100,00</td>
      <td>100,00</td>
    </tr>
  </tfoot>
</table>
La figure 2.70 montre bien la présence importante de calcium (Ca) et la présence d'imbrulés (en B).

Dans notre cas, au vu des analyses ICP (UMons), les cendres volantes étudiées ont un très faible effet pouzzolanique ($SiO_2 + \% Al_2O_3 + \% Fe_2O_3 = 21,6\%$). Elles pourraient avoir un effet d'hydraulicité latente à long terme de part la présence de chaux (CaO). De même, il est important de contrôler la présence de métaux lourds et pour nos cendres, la somme des éléments As, Ba, Cd, Cr, Cu, Mo, Ni, Pb, Sb, Se, Zn, Hg est inférieure à 0,103%.

Pour confirmer certains résultats sur les matériaux argileux, des analyses thermogravimétriques ont été réalisées à l'aide d'un appareil NETZSCH STA 409 sous flux d'air de 75 L min⁻¹ avec élévation de température de 5°C min⁻¹. Sur la figure 2.71, nous pouvons voir les courbes obtenues sur les argiles K et Kc, qui présentent la perte de masse de 5,5% due à la décomposition de la gibbsite autour de 300-350°C en Kc et la perte de masse caractéristique liée à la kaolinite entre 400 et 700°C qui est de 11,5% pour K et 10,5% pour Kc.

<figure><img src="image_67.png" /><figcaption>FIGURE 2.71 – Courbes ATG pour les argiles K et Kc</figcaption></figure>

Il ressort que la composition minéralogique du Kaolin du Cameroun diffère de celui commercialisé par la présence de 8% de gibbsite dans sa structure et d'une kaolinite à l'état semi-amorphe.

Concernant l'étude des cendres volantes de biomasse et pour compléter ces mesures minéralogiques, il peut être intéressant de déterminer des paramètres physiques importants pour la composition du béton tels que la masse volumique absolue, la surface spécifique et la demande en eau. En effet, pour avoir une idée de la demande en eau des cendres, la connaissance de la surface spécifique Blaine (cm²/g) est impérative. Elle représente la surface totale par unité de masse du produit accessible aux atomes et aux molécules. La demande en eau croit proportionnellement à la surface spécifique. Le perméabilimètre de Blaine permet la mesure de la surface spécifique des ciments selon les normes EN 196-6 et ASTM C204.
Avant la mesure, il est nécessaire de déterminer la masse volumique absolue des cendres par le densitomètre "Le Chatelier". Le liquide employé ne doit pas être réactif avec le ciment (chaux). La moyenne de la masse volumique absolue mesurée après trois essais est de 2,54 g/cm³. Cette valeur est proche de celle des cendres volantes de charbon (2,6 g/cm³).

Concernant les cendres volantes étudiées, la surface spécifique Blaine mesurée est de 6290 cm²/g. Elle est plus de deux fois supérieures à celle du ciment (3000cm²/g pour un CEMI 42.5) ce qui indique une forte demande en eau. Il est important dans un premier temps de déduire la quantité d'eau absorbée par les cendres volantes pour en prendre compte lors des formulations sur mortiers [131].

Afin de déterminer la courbe granulométrique des cendres volantes de biomasse de Calais, une granulométrie laser a été faite à l'Ethanol. La figure 2.72 montre la répartition des diamètres. En comparaison au ciment, les cendres volantes utilisées sont dans la même gamme de diamètre. Les CVB peuvent donc intéressantes dans le cas de la substitution du ciment.

<figure><img src="image_68.png" /><figcaption>FIGURE 2.72 – Courbe granulométrique laser des cendres volantes de biomasse</figcaption></figure>

## 3.2 Valorisation des sous-produits dans les matériaux cimentaires

### Caractérisation des matériaux en laboratoire

Il est désormais important de comprendre comment les sous-produits vont se mettre en œuvre dans les matrices cimentaires.

Pour la valorisation des cendres volantes de biomasse (CVB), la norme NF EN 450 d'octobre 2005, « Cendres volantes pour béton - Partie 2 : Evaluation de la conformité » va nous servir de base pour vérifier leur conformité. Cette norme est accompagnée du fascicule de documentation FD CEN/TR 15840, qui date de février 2009. La suite des études a été réalisée sur des pâtes et des mortiers. **Issam Laiymani et Manh-Hung Nguyen** ont participé à cette partie.
Dans un premier temps et comme vu précédemment, la valeur de la perméabilité de Blaine nous indique que les cendres de biomasse auront une plus forte demande en eau que le ciment. Il est donc nécessaire de déterminer la demande en eau des cendres volantes de biomasse (CVB) avec la norme EN 193-3 avec la sonde Vicat sur des pâtes de ciment. L'essai consiste à varier la quantité d'eau jusqu'à obtenir un enfoncement de la tige tel que $d= 6\text{mm} \pm 1\text{mm}$. Ceci permet d'atteindre une consistance dite normalisée. Dans notre cas, nous avons déterminé une correction d'eau de 22,1% pour les différents taux de substitution [132]. Ensuite, les formulations de mortiers ont été basées sur la norme NF EN 196-1. Pour chaque étude, une formulation de référence est créée (MR ou Mc) qui correspond à un mortier dont la formulation est calquée sur celle d'un mortier normalisé. Les formulations de mortiers à base de cendres volantes sont créées avec un $E_{tot}/\text{L} = 0,5$ et des taux de substitution de ciment par les CVB de 10%, 20%, 30%, 40% et 50%. Pour l'étude sur l'argile du Cameroun, l'incorporation du kaolin et de l'hydroxyde d'aluminium est faite par substitution massique du ciment. Par exemple, le mortier M(Ka)b signifie que le ciment a été substitué à hauteur de b% par le kaolin de référence substitué lui-même à hauteur de a% par l'hydroxyde d'aluminium amorphe. Plusieurs auteurs ont indiqué que la substitution optimale du ciment avec du Métakaolin dans le mortier est de 20% avec des rapports $E_{tot}/\text{L}$ de 0,5 à 0,55 [132]. Il a été décidé de prendre pour nos formulations un $E_{tot}/\text{L}$ égal à 0,55 sans correction d'eau.

Le mélange de mortier est ensuite coulé dans un moule pour la préparation de trois éprouvettes prismatiques de dimension 4x4x16cm. Les éprouvettes sont démoulées 24h après leur fabrication et sont conservées hermétiquement dans une armoire humide main tenue à une température de 20°C ± 1°C et une humidité relative supérieure à 90%. Les éprouvettes prismatiques obtenues peuvent être ensuite être testées à la flexion et à la compression à 7, 14, 28 et 90 jours suivant les conditions de l'étude. L'essai de rupture est réalisé selon la norme NF EN 196-1 sur trois éprouvettes identiques.

Pour l'étude sur le kaolin du Cameroun (Kc), l'activité pouzzolanique des différentes formulations a été évaluée par méthode indirecte en mesurant l'indice d'activité (Rapport de la résistance à la compression des formulations avec la résistance du mortier de référence) des différents échantillons, les résultats sont présentés à la figure 2.73.

<figure><img src="image_69.png" /><figcaption>FIGURE 2.73 – Activité pouzzolanique par la méthode de l'indice d'activité à 28 jours [123]</figcaption></figure>
La méthode directe est réalisée par l'essai «Chapelle modifié» [123]. Il révèle que les deux kaolins (Figure 2.74), lorsqu'ils sont enrichis en hydroxyde d'aluminium amorphe présentent une activité pouzzolanique. De même, le kaolin du Cameroun (Kc) substitué à 10% d'hydroxyde d'aluminium est plus pouzzolanique [121].

<figure><img src="image_70.png" /><figcaption>FIGURE 2.74 – Activité pouzzolanique par essai de Chapelle des argiles (K et Kc) et des mélanges d'argiles - 10% en poids d'hydroxyde d'aluminium amorphe (K10 et Kc10) [123]</figcaption></figure>

Concernant les essais mécaniques, ils ont montré que la substitution du ciment par le kaolin commercial (K) contenant 10% d'hydroxyde d'aluminium amorphe améliore les propriétés mécaniques des mortiers au 28ième jour par rapport à ceux faits de kaolin commercial seul ou substitué à 20% d'hydroxyde d'aluminium amorphe. Il confirme l'existence d'un seuil maximal d'hydroxyde d'aluminium à introduire dans les formulations. Le kaolin du Cameroun (Kc) quant à lui présente une activité pouzzolanique à 7 et 28 jours et des indices d'activité supérieurs à la formulation enrichit à 10% d'hydroxyde d'aluminium.

Pour compléter l'analyse des sous-produits argileux, les mesures à la Diffractométrie de Rayons X et à la Microscopie Electronique à Balayage faites sur les mortiers (Figure 2.75) ont montré que plus l'hydroxyde d'aluminium amorphe est substitué au ciment, plus il bloque la formation de C-S-H dans les mortiers. Celui-ci en se libérant plus tard augmente les résistances en compression des mortiers à long terme. Je conseille au lecteur de se référer à l'annexe 4 article G pour davantage de détails.

Il a donc été montré que l'incorporation d'hydroxyde d'aluminium amorphe a favorisé l'amélioration de l'activité pouzzolanique des argiles kaolinitiques. Elle était plus grande lorsque l'argile contenait à l'origine du gibbsite. L'hydroxyde d'aluminium amorphe a stimulé la formation de phases hydratées métastables en inhibant temporairement les réactions d'hydratation du ciment à un âge précoce. Avec le temps, le processus de transformation graduelle a conduit à la formation de phases hydratées plus stables. Les argiles kaolinitiques brutes contenant de l'hydroxyde d'aluminium sont des matériaux de remplacement prometteurs lorsqu'ils sont mélangés avec du ciment Portland.
<figure><img src="image_71.png" /><figcaption>FIGURE 2.75 – Images MEB du mortier de ciment poli de MK10 (a) et MKc10 (b) avec courbe EDX des zones de la matrice. [123]</figcaption></figure>

Pour l'étude sur les cendres volantes de biomasse (CVB), les essais à la compression sur les éprouvettes prismatiques ont eu lieu à 7, 28 et 90 jours [131, 133]. La figure 2.76 illustre les ruptures obtenues pour des taux de substitution de 10% et 20%. La figure 2.77 présente les résultats à la compression de mortiers faits à base de CVB avec et sans correction d'eau. Pour les mortiers sans correction de l'eau, la résistance à la compression diminue de 30% pour un taux de substitution de 20% de CVB, et de 79% pour 40% de CVB. Ainsi, plus le taux de substitution de cendres volantes augmente, plus la diminution de la résistance est importante. Dans le cas des mortiers avec la correction d'eau, la chute de résistance est davantage prononcée pour les faibles taux de substitution (10% et 20%). Par comparaison, la résistance à la compression diminue de 40% pour un taux de CVB de 20%, et de 63% pour 40% de CVB. Par ailleurs, la correction d'eau permet d'aller jusqu'à un taux d'incorporation de 50% de cendres de biomasse, ce qui était impossible sans la correction d'eau, du fait de la consistance du mortier [133].

<figure><img src="image_72.png" /><figcaption>FIGURE 2.76 – Photos de la rupture d'une éprouvette prismatique composée de cendre de biomasse à 10% et 20% (MC10 et MC20)</figcaption></figure>
Au vu de ces résultats, les conclusions sont de limiter le taux de substitution à 25%, de ne pas corriger la quantité d'eau et de réaliser des essais sur béton en substitution et en addition avec des pourcentages de 10% et 20%.

<figure><img src="image_73.png" /><figcaption>FIGURE 2.77 – Évolution résistance à la compression des formulations à base de CVB sans (a) et avec correction d'eau (b) [132]</figcaption></figure>

## Valorisation industrielle de sous-produits

Pour la suite de l'étude sur les cendres de biomasse, des essais sur des blocs creux de béton ont été réalisés. La formulation de ce type de béton pour du bloc vibrocompacté est très différente de celle d'un béton coulé en place. Elle se fait en conformité avec la norme NF EN 771-3 CN. C'est pourquoi le CERIB apporte son expertise sur la formulation des bétons. La formulation est basée sur celle de l'entreprise Biallais pour la confection de blocs B60 c'est à dire que les blocs doivent atteindre plus de 6 MPa de résistance à 7 jours. L'étude venant de se finir (janvier 2021), je ne pourrai pas présenter tous les résultats obtenus mais j'essaierai de donner les principales conclusions.

Dans un premier temps, le béton est mis en forme par vibocompactage au laboratoire avec l'arrivée de **Vincent Dappe**. Au vu des résultats sur mortier, les taux d'addition (A) ou de substitution (S) de CVB de 10% et 20% ont été retenus. Une dernière formulation composée d'une substitution de 10% de CVB couplé avec 20% d'addition de CVB a été également étudiée. Les formulations seront nommées S10, S20, A10, A20 et S10/A20).

La fréquence, la durée de vibration et la force de compression ont été optimisées afin de respecter au mieux les conditions de fabrication industrielle [114]. Les paramètres étudiés sont un temps de vibration de 5s, 10s et 15s et une force de compression de 1kN, 2kN et 4kN avec 3 éprouvettes par condition. Pour notre étude, il a été retenu un temps de vibration de 10s et une force de compression de 2kN (Figure 2.78). La confection des éprouvettes est basée sur la masse volumique des blocs industriels.
<figure><img src="image_74.png" /><figcaption>FIGURE 2.78 – Dispositif de vibrocompactage (gauche) - Eprouvettes réalisées (droite)</figcaption></figure>

Pour finir, la chaîne de production de l'entreprise Biallais a été utilisée pour valider ce couple formulation/process (Figure 2.79). La production des blocs de béton est entièrement automatisée. Les différents matériaux nécessaires à la formulation des bétons (gravillons, sable et ciment) sont acheminés via des trémies équipées de pesons, ce qui permet de délivrer la quantité nécessaire de chaque matériau dans le malaxeur. Un panneau de contrôle permet d'introduire les quantités désirées de chaque matériau.

Le mélange est effectué à sec (sans rajout d'eau) dans un premier temps afin d'homogénéiser l'ensemble. En effet, les différents matériaux étant stockés à l'extérieur des bâtiments, ils possèdent déjà une teneur en eau initiale. A la fin de cette première étape de malaxage, une partie du mélange présent dans le malaxeur est prélevé par un opérateur afin de déterminer la teneur en eau du mélange. La teneur finale en eau devant être de 5%, il est donc nécessaire de rajouter (dans la plupart des cas) un complément d'eau afin d'atteindre cette valeur. Un temps de malaxage de 45 secondes après ajout d'eau a été choisi suite à l'ajout des cendres pour permettre une hydratation homogène et complète du mélange.

<figure><img src="image_75.png" /><figcaption>FIGURE 2.79 – Presse vibrante Biallais Ind. (gauche) - Blocs réalisés (droite)</figcaption></figure>

Au laboratoire la rectification des éprouvettes testées est réalisée avec des membranes en caoutchouc (Figure 80a). Chez Biallais Ind., les essais de compression sont réalisés sur des blocs dont les surfaces sont rectifiées au soufre (Figure 80b) afin de les rendre planes.
Le surfaçage permet d'exercer une force uniforme sur l'ensemble de la surface du bloc.

<figure><img src="image_76.png" /><figcaption>FIGURE 2.80 – Eprouvette cylindrique de laboratoire (a) - Bloc de béton industriel (b)</figcaption></figure>

Les mesures réalisées après confection sur la presse vibrante de Biallais Ind. présentent les même variations en terme de réduction des résistances par rapport au témoin. Plusieurs mélanges ont atteint les 6MPa de résistance demandée à 7 jours. Sur les cinq formula-tions étudiées seule la S20 ne remplit pas le critère des 6MPa à 7 jours. Les premiers retours montrent une tendance similaire au laboratoire (Figure 2.81) sur les résistances à la compression. Néanmoins, les résistances des éprouvettes vibrocompactées en laboratoire sont supérieures à celles obtenus sur les blocs en industrie. En effet, certains paramètres industriels sont différents du laboratoire (Blocs creux vs éprouvette cylindrique pleine, vibration verticale en industrie vs vibration horizontale au laboratoire, ...).

<figure><img src="image_77.png" /><figcaption>FIGURE 2.81 – Résistances à la compression des éprouvettes vibrocompactées en laboratoire</figcaption></figure>
Pour finir, les mesures de variations dimensionnelles réalisées au CERIB montrent une stabilité des blocs dans le temps, aucun bloc n'a dépassé la valeur seuil de 0,45mm/m (gonflement - retrait) de la norme NF EN 772-14. L'étude vient de se terminer et les premières conclusions sont positives. En effet, il a été possible de mettre en forme en filière industrielle des blocs de béton creux à base de cendre volante de biomasse. Cette étude pourrait être également étendue à d'autres sous-produits plus complexes (hétérogénéité élevée). A cette date, le rapport a été finalisé et envoyé à l'ADEME. Une étude économique est à réaliser plus en détail afin de chiffrer l'impact de l'incorporation de CVB dans les blocs de béton.

Comme énoncé précédemment, pour développer cette thématique, un dossier ADEME GRAINE 2020 a été déposé et accepté. De même, une thèse a débuté en octobre 2020 par le recrutement de Florian Schlupp, "Valorisation des cendres de biomasse en tant que granulats et fillers dans des blocs de construction" sous la direction de Pr. Chafika Djelal et avec les co-encadrements de Dr. Laurent Libessart et de Dr. Jonathan Page. Pour ces suites, nous nous orientons davantage sur les cendres de sous-foyers en les utilisant comme substitution au sable dans le béton.
# Chapitre 3

# Conclusion et perspectives

Ce chapitre a pour but de résumer les apports de mes travaux tout en essayant de dégager les perspectives envisagées à plus ou moins longs termes. En effet, les travaux menés au cours de ces dernières années ont été consacrés, comme vous l'avez lu, à trois thèmes dans deux équipes de recherche du LGCgE (ER3 et ER5). Le premier est basé sur des recherches en thermique de l'habitat, par l'étude des matériaux fibreux et des murs végétalisés. Le deuxième thème s'intéresse à l'interface coffrage/béton et le décoffrage du béton. Le dernier porte sur la valorisation de sous-produits pour les matériaux cimentaires.

Dans le premier thème, j'ai présenté mes travaux en thermique de l'habitat. Les deux thèmes de recherche traités au cours de mon poste à HEI sont les matériaux fibreux et les murs végétalisés. L'aspect expérimental est très présent associé à de la modélisation. Pour les caractériser, j'ai pu participer à la mise en place de dispositifs expérimentaux en laboratoire et in-situ, au développement de modèles numériques et de protocoles d'essais et à l'analyse de données.

Les travaux sur les murs végétalisés ont permis des avancées sur la compréhension des composants formant les murs végétalisés complexes et sur les échanges thermiques entre le mur et la paroi d'un bâtiment. La mise en oeuvre et le développement de moyens expérimentaux permettant la mesure des paramètres des échanges thermiques ont été un apport important de cette recherche. De plus, des valeurs concrètes des conductivités thermiques ont pu être déterminées grâce à un dispositif simple. Les résultats publiés ont déjà été repris une dizaine de fois par des auteurs. Ensuite, la création de dispositifs expérimentaux en extérieur comportant du Lierre ou de la Vigne vierge ont donné de nombreux résultats et informations utilisables pour les bureaux d'études et les poseurs de murs végétalisés. Ils possèdent des atouts indéniables pour réduire la surchauffe durant l'été. Les modèles développés et la modélisation réalisée ont confirmé ces tendances et permettent maintenant de prédire et d'évaluer les apports des murs végétalisés sur un bilan thermique global. Finalement, il est conseillé, en cas de façade exposé au Sud, de disposer de la végétation à feuilles caduques afin de protéger la façade de la surchauffe l'été et de récupérer la chaleur du soleil en hiver.

Pour compléter cette étude, il faudrait instrumenter d'une habitation réelle avec murs végétalisés sur une période longue, prendre en compte les phénomènes convectifs par le modèle de prédiction, évaluer l'impact de rafraîchissement des plantes dû aux autres phénomènes (évapotranspiration, photosynthèse,...) et modéliser de l'influence des murs végétalisés à l'échelle urbaine.
Les travaux sur les **matériaux fibreux** ont servi à développer des compétences sur la **caractérisation du rayonnement thermique** par des méthodes optiques. Il a été possible de quantifier la proportion de rayonnement suivant différentes épaisseurs de matériaux par l'utilisation de la méthode inverse au moyen de mesures expérimentales infrarouge de réflexion et de transmission dans les longueurs d'ondes 2-20 µm. Cette technique a été utilisée sur différents matériaux : chanvre, laine de verre, ouate de polyester, textile recyclé et PMMA et il a été montré que la participation moyenne de la conductivité radiative au sein de la ouate de polyester est de 26% par rapport à la conductivité totale, celle de la laine de verre est de 23% et pour la laine de chanvre de 4%.

Pour développer ces résultats, l'étude pourrait se poursuivre sur l'exploitation des résultats des mesures bidirectionnelles pour identifier les paramètres de la fonction de phase (g1λ, g2λ, f1λ, f2λ), sur la comparaison de nos résultats avec la méthode directe qui consiste à utiliser la théorie de Mie.

Dans le deuxième thème, j'ai exposé mes travaux sur l'interface coffrage/béton et plus particulièrement sur les agents de démoulage. Beaucoup d'outils expérimentaux ont été utilisés et valorisés. J'ai pu participer à la mise en place de protocoles d'essais et d'analyses de données sur la **caractérisation des agents de démoulage** (huile et émulsion). Malgré la complexité des phénomènes se déroulant à l'interface, des mécanismes ont été présentés et développés pour les huiles entières d'origine minérale ou végétale grâce à l'utilisation d'un tribomètre plan/plan associé à des mesures de spectroscopie d'impédance électrochimique. Il a été montré qu'il est important de maîtriser l'application des agents de démoulage et de respecter les recommandations des fournisseurs pour les formulations en émulsions. Nous avons vu qu'une épaisseur de 3 à 5 µm d'huile de décoffrage suffit pour obtenir un **décoffrage de qualité**. De même, le film des émulsions est performant malgré une épaisseur plus faible (1 à 2 µm) car il s'intègre parfaitement dans les aspérités du coffrage (Etat de Wenzel). Ces avancées constituent un guide pour les formulateurs et les industriels afin d'optimiser la mise en oeuvre des agents de décoffrage sur les chantiers.

Mes travaux ont aussi contribué à mieux comprendre **l'interaction des agents de démoulage sur le coffrage**. Des outils simples de caractérisation (Tensiomètre et Goniomètre) ont permis d'émettre des recommandations pour la formulation des produits de décoffrage afin de rendre le film déposé plus résistant aux passages du béton dans les coffrages. De même, pour l'évaluation de la qualité esthétique des parements et des surfaces de coffrage, une grille de notation a été créée et développée ainsi qu'une méthode par analyse d'images.

Au niveau des perspectives, à court terme, des études sont à mener sur la **valori-sation d'huile recyclée industrielle ou agro-alimentaire** pour formuler des agents de décoffrage. En effet, une première étude avec l'entreprise CILA a déjà montré des propriétés intéressantes de ces huiles pour le décoffrage du béton. Une deuxième étude se développe avec l'entreprise GECCO pour valoriser des huiles de fritures. Un stage de Master 2 va débuter début mai 2021. Pour ce projet, les connaissances acquises durant les recherches vont nous permettre de créer des formulations efficaces. D'un point de vue physico-chimique, il sera nécessaire d'avoir une viscosité dynamique entre 25 et 50 mPa.s, une tension de superficielle L/V supérieure à 30 mN/m et un angle de goutte inférieur à 30 °. Sa performance lors de la mise en oeuvre du béton dans le coffrage pourra être
validée par des essais de frottement au tribomètre plan/plan. De plus, il serait important de prendre en compte d'autres propriétés des agents de décoffrage tels que la pureté du produit, la protection contre la corrosion ou la maîtrise de l'application sur le coffrage.

De même, afin d'avoir une meilleure compréhension de l'adhésion des agents de démoulage sur leur support, une étude à l'échelle microscopique voire nanoscopique associée à la rugosité des parois de coffrage est à développer pour mieux **appréhender les phénomènes de mouillabilité** des agents de décoffrage par rapport aux états de Cassie ou de Wenzel. Une collaboration avec l'Unité de Chimie et de Catalyse su Solide de Lens pourrait être intéressante à développer.

De plus, dans la continuité des travaux menés sur la qualité esthétique des parements, l'élaboration de bétons biosourcés, de bétons avec granulats recyclés ou encore de bétons avec cendres de biomasse nécessite une étude sur la **qualité et la durabilité des parements** associée à l'interaction avec les agents de décoffrage.

A moyen terme et malgré l'utilisation efficace des agents de décoffrage, il sera intéressant de **développer d'autres systèmes de décoffrage** par des matrices imperméables facile à mettre en oeuvre sur chantier et pouvant durer dans le temps. Le tribomètre a montré son intérêt durant la collaboration avec l'ENSAM d'Aix en Provence sur les travaux de N. Spitz. Un article est en soumission à la revue *Construction Building Materials*. Un paramètre important à étudier avec le tribomètre plan/plan sera la reproduction du frottement du béton en mode cyclique sur la paroi. En effet, il sera possible d'analyser et de prédire l'usure du revêtement. Le développement de notre collaboration avec l'ENSAM avec mesures par interférométrie pourrait nous donner des informations précises sur l'évolution de la rugosité après passage du béton. Pour débuter dans ce domaine, des contacts ont été pris avec les entreprises "FIBERTEX" et "MAXFRANK", des essais de caractérisation sont prévus sur des matrices existantes de type "Formtex" ou "Zemdrain".

Concernant les travaux sur la rhéologie des bétons et dans la suite du RILEM Round Robin Test 2018 (RRT 2018) réalisés à Béthune, les perspectives de recherche portent sur l'utilisation du tribomètre plan/plan. En effet, en plus d'avoir améliorer mes connaissances en rhéologie des bétons, les premiers résultats obtenus sont prometteurs. Le tribomètre pourrait comme le rhéomètre **déterminer la thixotropie des bétons**. Des essais complémentaires seront tout de même à effectuer pour faire varier les paramètres de vitesse et de pression, réaliser des essais de répétabilité sur d'autres formulations de bétons thixotropiques et corréler les résultats avec des rhéomètres (ICAR, RhéoCad).

Dans ce domaine, un article est en cours de finalisation avec les membres de la RILEM TC-266 : RRT sur les essais réalisés lors du RRT 2018. De même, je participe à la rédaction d'un chapitre d'ouvrage : TC-266 : MRP Members RILEM, "Procedures and Interpretation" - Chapitre 7, "State of knowledge of interface rheometry". J'interviens dans les deux cas sur la partie tribologie.

Pour finir, **avec le dernier thème**, j'ai présenté mes avancées sur la valorisation du kaolin et des cendres volantes de biomasse. L'ajout de sous-produits ou d'éco-produits dans les matrices cimentaires est depuis plusieurs années une habitude des industriels. En effet, ils peuvent apporter des performances intéressantes pour les bétons (cendre volante de charbon, fumée de silice, laitier de haut fourneaux, ...). Dans notre cas, nous
nous sommes intéressés au kaolin (et hydroxyde d'aluminum) et aux cendres volantes de biomasse. Grâce aux recherches effectuées, j'ai ainsi pu développer des connaissances sur les **analyses minéralogiques et chimiques** ainsi que la formulation et la caractérisation de mortiers et de blocs de béton. La force de ces recherches est la possibilité d'associer l'échelle laboratoire et l'échelle industrielle. De plus, l'utilisation de différentes techniques issues de la chimie et du génie civil nous permet de mieux appréhender les réactions d'hydratation pouvant se dérouler dans les matrices cimentaires à base de sous-produits. De même, il est possible de déterminer l'activité pouzzolanique soit par l'essai Chapelle soit par mesure indirecte (Indice d'activité). Des collaborations seront à développer avec nos collègues du département de Chimie de Béthune et de Lens.

Les perspectives de recherches dans ce thème sont nombreuses. A court terme, l'étude sur les cendres volantes de biomasse est à développer pour affiner les premiers résultats obtenus et permettre la commercialisation de blocs de bétons. La rédaction du rapport ADEME Graine "BIMGC" est finalisé et il a été envoyé à l'ADEME. De même, la valorisation des cendres de biomasse issue des sous-foyers va être étudiée en substitution des granulats. Cette étude sera développée par l'obtention d'une thèse qui a démarrée en octobre 2020 et par l'acceptation du second projet ADEME Graine "BIOGRAFIC" (2021-2024). Des études de formulations de béton (fluide ou blocs) seront à mettre au point. Les cendres de sous-foyers étant souvent récupérées sous forme d'agglomérats. L'équipe s'est dotée d'un broyeur afin de créer les courbes granulométriques les plus efficaces dans le mélange. Une étude morphologique des cendres sera à prévoir pour déterminer leur interaction dans le squelette granulaire. Dans le cas de béton fluide, l'étude pourra se poursuivre sur des analyses rhéologiques et tribologiques. L'analyse de la qualité esthétique est également à prévoir du fait de la teinte noire des cendres de sous-foyers.

Des études seront également à réaliser sur la **qualité des cendres** obtenues. En effet, suivant le combustible, les cendres peuvent apportées des performances intéressantes. L'étude réalisée en 2012 de GODBOUT et al. «Avenues pour la valorisation des cendres de combustion de la biomasse agricole» a montré que les cendres de la graminée Panic Erigé pourraient avoir des compositions similaires à celles issues des centrales à charbon. En associant les chaufferies alimentées en biomasse et les usines de fabrication de béton, tout une économie locale pourrait se développer.

A moyen terme, une suite porterait sur l'étude des **formulations innovantes par extrusion**. L'incorporation de sous-produit ou d'éco-produit dans des mélanges ternaires à base de kaolin et de ciment serait une voie à explorer pour les valoriser. La compréhension de la mise en forme et des frottements ainsi que l'étude de la durabilité des produits finis pourrait être intéressant à explorer et développer.

Dans cette même voie, des **projets transversaux** entre les équipes ER3 "Matériaux" et ER5 "Thermique de l'habitat" pourraient se mettre en place associant les produits finis (brique, blocs ou béton), l'esthétique des parements et la performance thermique, par l'étude :

- de matériaux à base d'éco-produit,

- de parements de façade en matériaux biosourcés,

- de bétons plus isolants,

- ...
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Table des figures

<table>
  <tbody>
    <tr>
      <td>2.1</td>
      <td>Dispositif expérimental en conditions extérieures [1]</td>
      <td>39</td>
    </tr>
    <tr>
      <td>2.2</td>
      <td>Courbes des valeurs brutes de flux et températures [1]</td>
      <td>40</td>
    </tr>
    <tr>
      <td>2.3</td>
      <td>Positionnement de nos corrélations par rapport aux relations existantes [1]</td>
      <td>41</td>
    </tr>
    <tr>
      <td>2.4</td>
      <td>Objectifs du projet Bâti et Biodiversité Positive</td>
      <td>43</td>
    </tr>
    <tr>
      <td>2.5</td>
      <td>Schéma de principe d'un mur simple</td>
      <td>44</td>
    </tr>
    <tr>
      <td>2.6</td>
      <td>Schéma de principe d'un mur complexe</td>
      <td>44</td>
    </tr>
    <tr>
      <td>2.7</td>
      <td>Box des mesures de conductivités thermiques</td>
      <td>46</td>
    </tr>
    <tr>
      <td>2.8</td>
      <td>Principe de mesure</td>
      <td>47</td>
    </tr>
    <tr>
      <td>2.9</td>
      <td>Photos dispositif avec la vigne vierge et le lierre</td>
      <td>48</td>
    </tr>
    <tr>
      <td>2.10</td>
      <td>Conductivité du compost, de la mousse de sphaine et du substrat CVF en fonction de la teneur en eau [19]</td>
      <td>48</td>
    </tr>
    <tr>
      <td>2.11</td>
      <td>Montage du box in-situ</td>
      <td>50</td>
    </tr>
    <tr>
      <td>2.12</td>
      <td>Isolation par l'intérieur de l'enveloppe et montage de la paroi Sud</td>
      <td>50</td>
    </tr>
    <tr>
      <td>2.13</td>
      <td>Test d'occultation par la végétation; (a) : vue générale; (b) : répartition des parois végétalisées; (c) : disposition des capteurs</td>
      <td>50</td>
    </tr>
    <tr>
      <td>2.14</td>
      <td>Flux thermique externe sur les trois box [20]</td>
      <td>51</td>
    </tr>
    <tr>
      <td>2.15</td>
      <td>Température de surface extérieure sur les trois box [20]</td>
      <td>52</td>
    </tr>
    <tr>
      <td>2.16</td>
      <td>Éléments du bilan énergétique; (a) cas l'occultation artificiel; (b) cas du masquage par la végétation [25]</td>
      <td>52</td>
    </tr>
    <tr>
      <td>2.17</td>
      <td>Occultation controlée [24]</td>
      <td>53</td>
    </tr>
    <tr>
      <td>2.18</td>
      <td>Comparaison entre les températures théoriques et mesurées (occ50%) [25]</td>
      <td>53</td>
    </tr>
    <tr>
      <td>2.19</td>
      <td>Analyse d'images (a) Pré-traitement des couleurs; (b) binarisation [25]</td>
      <td>54</td>
    </tr>
    <tr>
      <td>2.20</td>
      <td>Comparaison des températures des surfaces extérieures (référence / VW1 / VW2) en été [24]</td>
      <td>54</td>
    </tr>
    <tr>
      <td>2.21</td>
      <td>Modélisation d'une maison [19]</td>
      <td>55</td>
    </tr>
    <tr>
      <td>2.22</td>
      <td>Modélisation d'une maison en brique [31]</td>
      <td>56</td>
    </tr>
    <tr>
      <td>2.23</td>
      <td>Principe du couplage entre le modèle du mur végétalisé et le modèle multizone du bâtiment</td>
      <td>57</td>
    </tr>
    <tr>
      <td>2.24</td>
      <td>Comparaison des besoins en énergie de chauffage entre une maison ordinaire et une maison avec murs végétalisés pour le Lierre (a) [31]</td>
      <td>58</td>
    </tr>
    <tr>
      <td>2.25</td>
      <td>Comparaison des besoins en énergie de chauffage entre une maison ordinaire et une maison avec murs végétalisés pour la Vigne vierge (b) [31]</td>
      <td>58</td>
    </tr>
    <tr>
      <td>2.26</td>
      <td>Micrographies électroniques à balayage de fibre d'échantillon d'isolant en ouate de polyester</td>
      <td>60</td>
    </tr>
    <tr>
      <td>2.27</td>
      <td>(a) Photo MEB de la ouate de polyester, (b) Image binarisée, (c) Images simulées en augmentant le diamètre de fibre, (d) Images maillées sous Abaqus CAE [41]</td>
      <td>61</td>
    </tr>
    <tr>
      <td>2.28</td>
      <td>(a) Mode d'investigation, position de l'échantillon dans la sphère d'intégration et (b) mesure de transmittance directe au LEMTA.</td>
      <td>62</td>
    </tr>
  </tbody>
</table>
<table>
  <tbody>
    <tr>
      <td>2.29</td>
      <td>(a) DHTk;exp, (b) DHRk;exp and (c) DTk;exp de la ouate de polyester en fonction de la longueur d'onde pour différentes épaisseurs [44]</td>
      <td>63</td>
    </tr>
    <tr>
      <td>2.30</td>
      <td>Schéma du montage expérimental LGCgE</td>
      <td>64</td>
    </tr>
    <tr>
      <td>2.31</td>
      <td>Micrographies électroniques à balayage de fibres d'échantillons d'isolants en textile recyclé à des grossissements de 100× (a, b), 200× (c) et 500x (d)[46]</td>
      <td>64</td>
    </tr>
    <tr>
      <td>2.32</td>
      <td>(a) La conductivité thermique radiative du textile recyclé en fonction de l'épaisseur des échantillons, (b) l'effet de l'épaisseur sur la conductivité thermique radiative et phonique [46]</td>
      <td>65</td>
    </tr>
    <tr>
      <td>2.33</td>
      <td>Schéma du dispositif cône/plan [68]</td>
      <td>69</td>
    </tr>
    <tr>
      <td>2.34</td>
      <td>Evolution de la viscosité dynamique suivant la température pour quatre agents de décoffrage [68]</td>
      <td>70</td>
    </tr>
    <tr>
      <td>2.35</td>
      <td>Représentation vectorielle de Young [76]</td>
      <td>70</td>
    </tr>
    <tr>
      <td>2.36</td>
      <td>Tensiomètre - TensioCad [71]</td>
      <td>71</td>
    </tr>
    <tr>
      <td>2.37</td>
      <td>Goniomètre PGX</td>
      <td>72</td>
    </tr>
    <tr>
      <td>2.38</td>
      <td>Représentation schématique des profils de rugosité en fonction de l'angle de contact [76]</td>
      <td>73</td>
    </tr>
    <tr>
      <td>2.39</td>
      <td>Evolution schématique des émulsions directes dans l'état de Wenzel [79]</td>
      <td>73</td>
    </tr>
    <tr>
      <td>2.40</td>
      <td>Evolution schématique des émulsions inverses dans l'état de Wenzel [79]</td>
      <td>73</td>
    </tr>
    <tr>
      <td>2.41</td>
      <td>Evolution du film après pulvérisation (a) d'une huile à base végétale (V) et (b) de l'émulsion EDV [79]</td>
      <td>74</td>
    </tr>
    <tr>
      <td>2.42</td>
      <td>Evolution de la mouillabilité des émulsions dans le temps [71]</td>
      <td>75</td>
    </tr>
    <tr>
      <td>2.43</td>
      <td>Valeurs des énergies d'adhésion (mN/m) pour les formulations en émulsion dans le temps [71]</td>
      <td>75</td>
    </tr>
    <tr>
      <td>2.44</td>
      <td>Etat de surface après pulvérisation [79]</td>
      <td>76</td>
    </tr>
    <tr>
      <td>2.45</td>
      <td>Cinétique d'évaporation de l'eau pour les émulsions étudiées [79]</td>
      <td>76</td>
    </tr>
    <tr>
      <td>2.46</td>
      <td>Schéma de principe du tribomètre plan/plan [99]</td>
      <td>78</td>
    </tr>
    <tr>
      <td>2.47</td>
      <td>Représentation schématique de l'interface béton/coffrage métallique [105]</td>
      <td>79</td>
    </tr>
    <tr>
      <td>2.48</td>
      <td>Application de l'émulsion sur la plaque</td>
      <td>80</td>
    </tr>
    <tr>
      <td>2.49</td>
      <td>Contraintes de frottement dynamique en fonction de la pression de contact pour les agents de démoulage étudiés (v = 0.84 mm/s) [79]</td>
      <td>80</td>
    </tr>
    <tr>
      <td>2.50</td>
      <td>Contraintes de frottement dynamique du béton standard en fonction des surfaces de coffrage étudiés [54]</td>
      <td>81</td>
    </tr>
    <tr>
      <td>2.51</td>
      <td>Contraintes de frottement dynamique en fonction de la pression de contact des bétons auto-plaçants SCC2 et SCC3 à t= 10min et t= 40min (v=0,84 mm/s)</td>
      <td>82</td>
    </tr>
    <tr>
      <td>2.52</td>
      <td>Montage SIE [68]</td>
      <td>84</td>
    </tr>
    <tr>
      <td>2.53</td>
      <td>Diagrammes SIE obtenus au potentiel de corrosion après 1 h d'immersion dans l'électrolyte [68]</td>
      <td>84</td>
    </tr>
    <tr>
      <td>2.54</td>
      <td>Schéma représentant le glissement du béton sur le film d'huile [100]</td>
      <td>85</td>
    </tr>
    <tr>
      <td>2.55</td>
      <td>Organisation d'un film de savon à l'interface béton/coffrage [100]</td>
      <td>85</td>
    </tr>
    <tr>
      <td>2.56</td>
      <td>Organisation de l'interface savon/huile [68]</td>
      <td>86</td>
    </tr>
    <tr>
      <td>2.57</td>
      <td>Organisation de l'interface superplastifiant/savon/huile [82]</td>
      <td>86</td>
    </tr>
    <tr>
      <td>2.58</td>
      <td>Moule fabriqué par OUTINORD</td>
      <td>87</td>
    </tr>
    <tr>
      <td>2.59</td>
      <td>Application des huiles (a) Pulvérisation directe, (b) Pulvérisation suivi d'un raclement</td>
      <td>87</td>
    </tr>
    <tr>
      <td>2.60</td>
      <td>Protocole de malaxage pour un béton traditionnel</td>
      <td>88</td>
    </tr>
    <tr>
      <td>2.61</td>
      <td>Protocole de malaxage pour un béton auto-plaçant (BAP)</td>
      <td>88</td>
    </tr>
    <tr>
      <td>2.62</td>
      <td>Abréviations utilisées pour évaluer les performances de démoulage</td>
      <td>89</td>
    </tr>
    <tr>
      <td>2.63</td>
      <td>Critères de notation utilisés en 2006 [112]</td>
      <td>89</td>
    </tr>
    <tr>
      <td>2.64</td>
      <td>Critères de notation utilisés à partir de 2012 [68]</td>
      <td>90</td>
    </tr>
  </tbody>
</table>
<table>
  <tbody>
    <tr>
      <td>2.65</td>
      <td>Critères de notation utilisés à partir de 2015</td>
      <td>90</td>
    </tr>
    <tr>
      <td>2.66</td>
      <td>Exemple d'une analyse d'image pour une émulsion directe à 1 jour (a), 3 jours (b) et 7 jours (c) [71]</td>
      <td>91</td>
    </tr>
    <tr>
      <td>2.67</td>
      <td>Exemple d'une analyse d'image pour une huile végétale recyclée à 1 jour (a), 3 jours (b) et 7 jours (c) [72]</td>
      <td>91</td>
    </tr>
    <tr>
      <td>2.68</td>
      <td>Exemple de diffractogrammes (DRX) du Kaolin commercial, du Kaolin du Cameroun et de l'Hydroxyde d'aluminium [122]</td>
      <td>96</td>
    </tr>
    <tr>
      <td>2.69</td>
      <td>Exemple de diffractogrammes (DRX) des cendres volantes de biomasse étudiée</td>
      <td>97</td>
    </tr>
    <tr>
      <td>2.70</td>
      <td>Images SEM et analyses EDS des cendres provenant de la chaufferie de Calais</td>
      <td>97</td>
    </tr>
    <tr>
      <td>2.71</td>
      <td>Courbes ATG pour les argiles K et Kc</td>
      <td>98</td>
    </tr>
    <tr>
      <td>2.72</td>
      <td>Courbe granulométrique laser des cendres volantes de biomasse</td>
      <td>99</td>
    </tr>
    <tr>
      <td>2.73</td>
      <td>Activité pouzzolanique par la méthode de l'indice d'activité à 28 jours [123]</td>
      <td>100</td>
    </tr>
    <tr>
      <td>2.74</td>
      <td>Activité pouzzolanique par essai de Chapelle des argiles (K et Kc) et des mélanges d'argiles - 10% en poids d'hydroxyde d'aluminium amorphe (K10 et Kc10) [123]</td>
      <td>101</td>
    </tr>
    <tr>
      <td>2.75</td>
      <td>Images MEB du mortier de ciment poli de MK10 (a) et MKc10 (b) avec courbe EDX des zones de la matrice. [123]</td>
      <td>102</td>
    </tr>
    <tr>
      <td>2.76</td>
      <td>Photos de la rupture d'une éprouvette prismatique composée de cendre de biomasse à 10% et 20% (MC10 et MC20)</td>
      <td>102</td>
    </tr>
    <tr>
      <td>2.77</td>
      <td>Évolution résistance à la compression des formulations à base de CVB sans (a) et avec correction d'eau (b) [132]</td>
      <td>103</td>
    </tr>
    <tr>
      <td>2.78</td>
      <td>Dispositif de vibrocompactage (gauche) - Eprouvettes réalisées (droite)</td>
      <td>104</td>
    </tr>
    <tr>
      <td>2.79</td>
      <td>Presse vibrante Biallais Ind. (gauche) - Blocs réalisés (droite)</td>
      <td>104</td>
    </tr>
    <tr>
      <td>2.80</td>
      <td>Eprouvette cylindrique de laboratoire (a) - Bloc de béton industriel (b)</td>
      <td>105</td>
    </tr>
    <tr>
      <td>2.81</td>
      <td>Résistances à la compression des éprouvettes vibrocompactées en laboratoire</td>
      <td>105</td>
    </tr>
  </tbody>
</table>
# Liste des tableaux

<table><tr><td>1.1</td><td>Détail des matières et des modules du domaine de formation EHE pour l'année 2009-2010</td><td>18</td></tr><tr><td>2.1</td><td>Principaux appareils de caractérisation physico-chimique utilisés</td><td>68</td></tr><tr><td>2.2</td><td>Dispositifs de caractérisations minéralogique et chimique utilisés</td><td>94</td></tr><tr><td>2.3</td><td>Dispositifs de caractérisation des pâtes et des mortiers à base de sous-produit</td><td>94</td></tr></table>
# Annexes

Afin de compléter ce mémoire, j’ai sélectionné dans les annexes suivantes les articles les plus représentatifs de mes travaux de recherche. j’ai découpé en 4 parties.

<table><thead><tr><th>Article</th><th>Code</th></tr></thead><tbody><tr><td><strong>Annexe 1 : Etude des murs végétalisés</strong></td><td></td></tr><tr><td>Measuring thermal conductivity of green-walls components in controlled conditions</td><td>A</td></tr><tr><td>Kenai M.A., Libessart L., Lassue S., Defer D., "Impact of plants occultation on energy balance : Theoretical and numerical study"</td><td>B</td></tr><tr><td><strong>Annexe 2 : Etude des matériaux fibreux et semi-transparents</strong></td><td></td></tr><tr><td>Determination of radiative properties of polyester batting insulation material from hemispherical transmittance and reflectance measurements</td><td>D</td></tr><tr><td>Characterization of the thermal properties of fibrous insulation materials made from recycled textile fibers for building applications : Theoretical and experimental analyses</td><td>E</td></tr><tr><td><strong>Annexe 3 : Etude de l'interface béton/huile/coffrage</strong></td><td></td></tr><tr><td>Influence of the type of release oil on steel formwork corrosion and facings aesthetics</td><td>F</td></tr><tr><td>Comparative study of the tribological behaviour of emulsions and demoulding oils at the concrete/formwork interface</td><td>H</td></tr><tr><td><strong>Annexe 4 : Etude des éco-matériaux</strong></td><td></td></tr><tr><td>Pozzolanic activity of kaolins containing aluminum hydroxide</td><td>J</td></tr><tr><td>Feasibility of Using Biomass Fly Ash in Cementitious Materials</td><td>K</td></tr></tbody></table>
# Annexe 1

Cette annexe présente les articles :

(A) Libessart L., Kenai M.A., "Measuring thermal conductivity of green-walls components in controlled conditions", *Journal of Building Engineering*, 19, 258-265, 2018

(B) Kenai M.A., Libessart L., Lassue S., Defer D., "Impact of plants occultation on energy balance : Theoretical and numerical study", *Journal of Building Engineering*, 29, 101112, 2020

Ces articles illustrent les apports faits sur les murs végétalisés tant sur la caractérisation thermique des constituants que sur leurs échanges thermiques avec un bâti extérieur. J'indique par la suite, les mots clefs importants associés aux références des articles.

Mots clefs : Conduction (A, B), Conductivité thermique (A), Convection (B), Flux-mètre (A, B), Indice foliaire (B), Milieux poreux (A), Modèle numérique (B), Modélisation (A), Murs extensifs (A, B), Murs intensifs (A), Occultation (B), Rayonnement solaire (B), Substrats (A), Température de surface (B), Thermocouple (A, B).
# Measuring thermal conductivity of green-walls components in controlled conditions

Laurent Libessart<sup>a,*</sup>, Mohamed Amine Kenai<sup>b</sup>

<figure><img src="image_78.png" /></figure>

Check for
updates

## ARTICLE INFO

**Keywords:**

Thermal conductivity

Green wall

Living wall

Humidity

Substratum

Insulation

Thermal simulation

## ABSTRACT

This study is the first stage of a larger multidisciplinary research program about the environmental performances and functions of green walls in urban ecosystems. It aims to determine how green-walls contribute to the thermal insulation of buildings by measuring the thermal conductivities of green-walls' components in controlled conditions. The study focused on complex green-wall systems, i.e. with a structure containing substrate in opposition with green-walls based on climbing plants. The four substrates were materials found in commercial substrate combinations. To compare, the thermal conductivities on two plants are carried out. In dry conditions, they showed conductivities of 0.062 W/m °C for sphagnum moss (*Sphagnum cristatum*), 0.060 W/m °C for outdoor planting mix, and 0.105 W/m °C for clay balls and 0.051 W/m °C for substrate from a green-wall. Vegetation conductivities were also measured for ivy (*Hedera helix*) and Virginia creeper (*Parthenocissus quinquefolia*). As expected, conductivities were quite high (between 0.220 and 0.274 W/m °C). With the building thermal simulation, green-walls are technically able to improve buildings' insulation.

## 1. Introduction

There exist two types of green-walls: simple green-walls (intensive) and complex green-walls (extensive) [1]. The simple green-walls use climbing plants of standard ivy which come “to invade” the wall. It is necessary to wait several years to get the desired result. The complex green-walls, generally claiming an intensive maintenance technique, are working in terms of design. In fact, there exist several processes of implementation. Several manufacturers dispute the market and propose various construction processes. But overall, the principle remains the same one: a system of reinforcement is fixed on the wall, leaving a blade of air between this one and the wall. These reinforcements make it possible to place a substrate in the structure to accommodate the plants.

The concept of reconciliation ecology represents one of the major challenges for the future of urban areas [2]. The ecological engineering techniques of living roofs and walls represent a great potential for reconciliation ecology [2]. But, this task is not easy because it faces two main socioeconomic barriers to their constructions: the cost and the cultural perception of nature [2]. Moreover, a French study [3] showed conflicting interests among citizens. Urban populations express a need for natural spaces and intimacy as well as a need for social contacts with a surrounding environment providing many services such as stores, recreation activities or transport network. Several studies

examined the effects of green walls on the temperatures of façades [4]. They have a certain cooling efficiency on the immediate environment [5]: they decrease the temperatures more than on a control facade without vegetation [6–8]. Several factors influence the observed differences of temperatures. They are grouped around three basic mechanisms. The first is the sunlight ray blocked by the vegetation, which creates a shadow and influences facade temperatures. The importance of this mechanism depends on the density and homogeneity of the foliage. The second is the thermal insulation induced by plants and substrate. The thickness, the density and moisture content of the substrate, the foliage density, the air movement in the intermediate spaces, and the capacity to stop the wind are all factors that affect this mechanism. The third is the facade protection against wind. The effectiveness of this last mechanism depends on the facades orientation, the direction and speed of the wind, and the foliage density [5,6,9–12]. Precisions on their component's thermal behavior were given by a model on the thermodynamic transmission process of the vertical ecosystem [13]. But no measurements were found in the literature. The screening effect by the plants of a building was studied recently [14]. The process developed by prediction of the thermal behavior of buildings envelopes in the presence of simple green-walls was applied to a virtual house located at Lille.

The green-walls are put up more and more on the buildings

<footnote><sup>a</sup> Univ. Artois, EA 4515, Laboratoire de Génie Civil et géo-Environnement (LGCgE), F-62400 Béthune, France</footnote>

<footnote><sup>b</sup> YNCREA-Ecole des Hautes Etudes d'Ingénieur, LGCgE, F-59000 Lille, France</footnote>

<footnote>* Correspondence to: IUT, 1230 rue de l'université, 62408 Béthune Cedex, France.
E-mail address: laurent.libessart@univ-artois.fr (L. Libessart).</footnote>
<table><caption>**Table 1**

Models developed for the simple granular mediums.</caption><tr><td>Parallel</td><td>λ<sub>app</sub> = Σε<sub>i</sub>λ<sub>i</sub></td><td>Medium made up in several states parallel between them</td></tr><tr><td>Series</td><td>λ<sub>app</sub> = Σ(ε<sub>j</sub>/λ<sub>j</sub>)<sup>-1</sup></td><td>Medium made up in several states in series between them</td></tr><tr><td>Hashin-Shtrikman</td><td>(λ<sub>app</sub>)<sub>min</sub> = λ<sub>f</sub> + ε(1/λ<sub>f</sub> - ε(1/λ<sub>s</sub> - ε(1/λ<sub>f</sub>)))</td><td>The medium is isotropic</td></tr><tr><td>Maxwell</td><td>(λ<sub>app</sub>)<sub>max</sub> = 1 + ε(1/λ<sub>f</sub> - ε(1/λ<sub>s</sub> - ε(1/λ<sub>f</sub>)))</td><td>Particles are spherical and no mutual interaction between the particles</td></tr><tr><td>Hamilton</td><td>λ<sub>app</sub> = ελ<sub>f</sub>(2λ<sub>f</sub> + λ<sub>s</sub>) + 3αλ<sub>s</sub>λ<sub>f</sub>ε(2λ<sub>f</sub> + λ<sub>s</sub>) + 3αλ<sub>f</sub></td><td>An extension of the Maxwell model to particles ellipsoidal</td></tr><tr><td></td><td>(λ<sub>app</sub>)<sub>f</sub> = λ<sub>s</sub>(n<sub>h</sub> - 1)λ<sub>f</sub> - (n<sub>h</sub> - 1)ε(λ<sub>f</sub> - λ<sub>s</sub>)λ<sub>s</sub>(n<sub>h</sub> - 1)λ<sub>f</sub> + α(λ<sub>f</sub> - λ<sub>s</sub>)</td><td></td></tr></table>

Where.

n = Number of contact per particle.

ε = Porosity of the granular layer.

α = Relative density.

λ<sub>i</sub>, λ<sub>app</sub> = Apparent thermal conductivity of porous media, W/m K.

λ<sub>s</sub> = Thermal conductivity of the solid phase, W/m K.

λ<sub>f</sub> = Thermal conductivity of the fluid to the atmospheric pressure, W/m K.

ψ = Sphericity referring to the spherical geometry with n<sub>h</sub> = 3/ψ.

frontages. As this background shows, green-walls are creating a growing interest in research, and they are approached using different methods and scales. Nevertheless, their thermal benefit still not yet completely mastered in thermal simulation. They are always more used for their aesthetic aspect. Many gaps still remain about their ecological and environmental value. More generally, the required design to optimize their ecological, thermal, acoustic and sensory functions still has to be elucidated. Finally the suppliers of green-walls are interested by the determination of the thermal conductivities values to develop their products.

The aim of this study is to develop the integration of the green-walls on the building and to show its benefits on the building frontage. Firstly, the measurement of the thermal conductivity of different substrates for extensive green-wall (sphagnum moss (*Sphagnum cristatum*), clay balls and substrate of a green-wall CVF are made for manufacturers. Secondly, many walls in France are covered with ivy (*Hedera helix*) or Virginia creeper (*Parthenocissus quinquefolia*), it is interesting to look at their thermal interest. Can the green-wall replace a standard thermal insulation? Which thickness of green-walls is it necessary to allow a profitable insulation? Finally, the thermal conductivities knowledge is an asset to develop the databases of the software and thus create more precise thermal simulations.

## 2. Methodology and theory

### 2.1. Conduction and conductivity

The thermal transfer through an environment is made possible thanks to three different heating transfer reactions: conduction, convection, and radiation [15]. For the conductivity measurements, the transfer reaction by conduction was used.

The term of conduction describes the distribution inherent to the internal shocks without transport of material. For example, when two solids with different temperatures enter into contact, the element which the highest temperature is placed into the one with a lower temperature.

Such a transfer always shows itself when a material is subject to a gradient of temperature. A heat flux goes across the region where the temperature is the highest towards the region where the temperature is the lowest. The conduction theory rests on the Fourier law. The flow density is proportional in the temperature gradient:

$$ \vec{\phi} = -\lambda \overline{grad} (T) \qquad (1) $$

Where

φ = Flux density (W/m²)

λ = Thermal conductivity (W/m K)

T = temperature (Kelvin)

The energy preservation depends on thermal properties: the thermal conductivity, the thermal diffusivity, and the geometry of the environment. Heat transfer in an opaque, homogeneous solid, without term of source and isotropic is translated by the following equation:

$$ \frac{1}{a} \frac{\partial T}{\partial t} = \nabla^2 T \qquad (2) $$

Such as: 'a' represents the thermal diffusivity which is only a function of λ (thermal conductivity) and ρCp (heat volume).

To resolve the heat equation of any environment, it is indispensable to know two parameters; the thermal conductivity and the heat volume. They characterize the thermal transfer in the environment. This project relied on the measurement of thermal properties, especially thermal conductivity of the porous media. The measure is complex because it depends on more parameters as the material, the contact resistance, the measurement time and the thickness.

### 2.2. Thermal conductivity of porous media

From the resolution of the energy equation [16,17] many models of calculations of thermal conductivity were developed (Table 1). The models found in literature can give good results for the calculation of the apparent thermal conductivity of porous media. They are predictions tools developed to know the mechanisms of thermal transfer in porous media. It is necessary to specify that the models suggested relate to only the diphasic granular mediums. The solid phase consists of only one phase represented by solid particles. In addition, the fluid is represented by pores filled exclusively with air.

The problem is complex. It is necessary to develop models, bringing in different physical phenomena (transfer / condensation, contact law between particles, conduction, and convection) and to verify the microstructure of the environment (size, shape of the particles) and to study the state of the constituents of the environment (conductive phase).

Not knowing the thermal conductivity of materials, the bibliographical references validated the experimental models. The measurement of apparent thermal conductivity is interested in taking into account two phases: solid and fluid. It is necessary to consider the problem of resistance to contact which can intervene during the measurement.
<figure><img src="image_79.png" /><figcaption>Fig. 1. Overview of the wood box and the device of measure.</figcaption></figure>

## 2.3. Experimentation

To characterize materials, the used device is a horizontal system by the guarded hot plate method [18,19]. It is an experiment in permanent transfer mode (ISO 8302) where one imposes on a plane sample a one-way heat flow, and measures the difference in temperature at the boundaries of the sample. This method rests on the use of a thin plate compared to the dimensions of the sample. The implementation of materials tested is easier. The purpose of this experimentation is to measure thermal conductivities. It is necessary to prevent the thermal transfer by convection by the creation of closed wood box (Fig. 1). Its composition is detailed below.

The sensors used are a " tangential gradient type ". The tangential gradient fluxmeter intrinsically generates temperature variations in the plane of measurements. Then, these gradients are detected by a great number of thermoelectric junctions connected in a series. Indeed, the sensor generates a Seebeck electro motive forces (EMF) which is proportional to the heat flow. These fluxmeters have a highly conductive copper surface which tends to homogenize the surface temperature and thus to provide average values.

Two fluxmeters with a sensitive area of 30 × 30 cm² are used for this experiment. A first fluxmeter (Φ1) measures the flow, which enters (Fig. 2) and the second (Φ2) measures the flow, which goes out. The average calibration is 262 µV/(W/m²) for the first and 258 µV/(W/m²) for the second, where Φ is the flux density (W/m²).

To measure the temperature difference in the borders of the samples, K type thermocouples are used. Its composition is Chromel (alloy nickel + chrome) and Alumel (alloy nickel + aluminum (5%) + siliceous). It allows a measure in a range of wide temperature from –250 to 1372 °C. It is stuck on the surface to measure the temperature (T1).

To allow a unidirectional flow and to avoid the flow loss on the sides, a guard zone was installed around each sensor (Fig. 3).

After the second thermocouple is arranged on its surface (T2), the

<figure><img src="image_80.png" /><figcaption>Fig. 2. Detail of the device of measure.</figcaption></figure>

<figure><img src="image_81.png" /><figcaption>Fig. 3. Principal plan.</figcaption></figure>

temperature difference can be measured for the Fourier Law resolution.

To generate the heat flow two devices are necessary. Heating plates heat the surface of concrete to a maximal temperature of 40 °C. And a heating resistance homogenizes the temperature of the surface. Furthermore, it will serve for the delicate measurements of plants to obtain a lower temperature (20 °C) to avoid the drying of the plants. As a reminder, the measure of conductivity is based on the principle of the guarded warm plate method and the fluxmetric method. It is realized in steady state. The heat flow must be constant in time and uniform in space.

The conductivity value (λ) is calculated by using Fourier Law (3). For it, two temperatures have been measured on the borders of the sample (ΔT) for a surface (S) of 1 m² and with a thickness (e) gives the following equation [20,21]:

$$ \lambda = \frac{\phi \cdot e}{\Delta T \cdot S} (\text{W/mK}) \qquad (3) $$

The measurements are carried out with a portable multimeter and are correct when the device reached the steady state.

The experimental protocol is carried out in the following manner:

* To put on the hotplates and it is necessary to wait a few hours to reach the steady state.

* To make sure of the uniformity of the temperature of the concrete slab. The ΔT should not exceed 1 °C. Three thermocouples are distributed on the concrete slab.

* To place the fluxmeter in the center of the concrete slab (a layout is envisaged)

* To place material to be studied with the top of the fluxmeter.

* For a solid material

To place the material directly at the top of the fluxmeter.

* For a granular material

To place the polyurethane framework of which the interior is covered with geotextile. To put the material to be studied within the framework, to fill it to the brim without packing (the material should beforehand be weighed).

To cover the framework with a film of geotextile in order to avoid resistances of contact

* To place the second fluxmeter at the top

* Lastly, to close the box and to expect the steady state.

## 2.4. Green-wall components

The substrate characterization for complex green-wall are presented in Table 2 and in Table 3 for the two climbing plants (Ivy, Virginia creeper).
<table><caption>**Table 2**

Substrate characterization.</caption><tr><td><strong>Universal potting substrate</strong></td><td>Composition: composted bark, fair peat, plant compost<br>Material dries / total : 35%<br>Material organic/dries : 55%<br>Capacity of retention in water : 600ml/l of substrate<br>pH : 6.5</td><td></td></tr><tr><td><strong>Clay balls</strong></td><td>The expanded clay is industrially made from natural clay which will successively be dried, reduced to flour, will in some water then will in ovens what gives after all balls or blocks with clay balls. This material has a density between 350 and 700 kg/m³.</td><td></td></tr><tr><td><strong>Sphagnum moss</strong></td><td>It possesses a big absorption capacity and retention of the water, the sphagnum moss is a moss which can store 20× its volume in water grace to its very light texture.<br>It is antibacterial what allows a protection against the decay, the diseases and the parasites and it has a pH naturally acid of 4.8.</td><td></td></tr><tr><td><strong>Substrate CVF</strong></td><td>Industrial composition:<br>Approximately 90 % coconut matting, approximately 10 % of perlite, fertilizer of synthesis</td><td></td></tr></table>

<figure><img src="image_82.png" /></figure>

<figure><img src="image_83.png" /></figure>

<figure><img src="image_84.png" /></figure>

<figure><img src="image_85.png" /></figure>

## 2.5. Thermal simulation

To complete this study, a modeling was carried out in order to look at the influence of the thermal conductivity of the ivy on consumption energy of a standard house. To determine the influence of the green-wall of a dwelling, the thermal software of simulation instigates TRNSYS 17 has been used. The study case considered thereafter is a house on under floor space. This house is called “House MOZART”: it is a “standard” house representing the average of the French houses in

main home. It was defined by EDF in 1994 in co-operation with the CSTB (French Scientific and Technical Center for Building) and GDF.

The thermal simulation is based on the thesis of Mr. Gossard [22] and a study carried out by the CSTB [23] (for comparison purposes) and to have the data necessary to model the “House Mozart”. The total space of this house is of 100.86 m² with a height under ceiling of 2.3 m. The results are presented in paragraph 3.5.
<table><caption>**Table 3**
The vegetal palet.</caption><thead><tr><th>Vegetal (%)</th><th>Pictures</th></tr></thead><tbody><tr><td>Ivy</td><td></td></tr><tr><td>Virginia creeper</td><td></td></tr></tbody></table>

# 3. Results and discussion

## 3.1. Device validation

To validate the device, two materials have been used: a plain plate extruded polystyrene and sand. The extruded polystyrene has a conductivity value (supplied by the manufacturer) of $\lambda = 0.036$ W/m.K. The measurement gives a conductivity value of $\lambda_{measured} = 0.0377$ W/m K. For this validation, an error of the conductivity value of the polystyrene extruded is about 4%. Furthermore, $\Delta T$ must be higher for 20 °C as required by the trial standard [20]. For the sand, Fillali [16] found a value of thermal conductivity of dry sand of $\lambda = 0.225$ W/m K. The measurement gives a conductivity value of $\lambda_{measured} = 0.229$ W/m K. The thermal conductivity of sand was measured. The experimental device is validated for porous media.

## 3.2. Dry substrate

Every material was allowed to dry for 48 h in a steam room. The basic materials of green-walls were chosen as well as a composition used directly as substrate.

Table 4 presents the results obtained by the measurement of thermal conductivity for an average of three tests. The thickness of the samples is 4 centimeters. The steady state was obtained after 10 h.

According to the French standards, an insulating material is recognized as a heat insulator if its thermal conductivity is lower than 0.06 W/m K. In our case and in the dry state, the outdoor planting mix, the sphagnum moss and the substrate CVF can be considered as heat insulators. But, numerous heat insulators with lower thermal conductivity are available on the market. In fact, the traditional heat insulators have a thermal conductivity included generally between 0.035

<table><caption>**Table 4**
Values of thermal conductivity for substrate testing.</caption><thead><tr><th>Substrate</th><th>Thermal conductivity (W/m K)</th></tr></thead><tbody><tr><td>Sand</td><td>0.225</td></tr><tr><td>Universal plant mix</td><td>0.062</td></tr><tr><td>Clay balls</td><td>0.105</td></tr><tr><td>Sphagnum</td><td>0.060</td></tr><tr><td>Substrate CVF</td><td>0.051</td></tr></tbody></table>

<figure><img src="image_86.png" /><figcaption>**Fig. 4.** Mix ball of clay and plant mix.</figcaption></figure>

and 0.045 W/m K. Furthermore, if the substrate is dry, it is very likely that no plant can push above.

### Mixture of outdoor planting mix and clay balls

Formulations of substrate of green-walls can contain clay balls. A mixture of outdoor planting mix and clay balls has been realized in the dry state. The results obtained are presented in the following figures (Figs. 4 and 5).

The graph gives us as relation (4):

$$ \lambda_{\text{mixture}} = 0.00025 (\%_{\text{Clayballs}} - \%_{\text{Plantmix}}) + 0.08675 \quad (4) $$

## 3.3. Wet substrate

The next stage consists of studying the substrate in the wet state, here are the results obtained for the outdoor planting mix (Fig. 6) and the sphagnum moss for a 4-centimeter thickness (Fig. 7). The steady state was obtained after 13 h.

The water presence makes the visible density of some compost decrease. Between 150 kg/m³ and 250 kg/m³, a decline of conductivity of about 33% is noted by 50 kg/m³.

$$ \text{Apparent density}_{\text{plantmix}} = -0.6851 \times w_{\text{plantmix}}(\%) + 260.89 \quad (5) $$

What a moisture content $w > 10\%$ as average relation gives us (6):

$$ \lambda_{\text{Plantmix}} = 0.0013 \times w_{\text{Plantmix}}(\%) + 0.07737 \quad (6) $$

And for the sphagnum moss relation (7):

$$ \lambda_{\text{sphagnum\_moss}} = 0.000206 \times w_{\text{sphagnum\_moss}}(\%) + 0.071892 \quad (7) $$

And for the substrate CVF relation (8):

<figure><img src="image_87.png" /><figcaption>**Fig. 5.** Variation of the conductivity according to the % of plant mix and clay balls.</figcaption></figure>
<figure><img src="image_88.png" /><figcaption>Fig. 6. Apparent densities of the plant mix according to moisture content.</figcaption></figure>

<figure><img src="image_89.png" /><figcaption>Fig. 7. Conductivity of the compost, the sphagnum moss and substrate CVF according to moisture content.</figcaption></figure>

$$ \lambda_{substrateCSV} = 0.000540 \times w_{substrateCVS}(\%) + 0.04328 \quad (8) $$

Despite the important water presence, the sphagnum moss preserves a low thermal conductivity. Indeed, for a 890% moisture content, its conductivity is equal to 0.28 W/m °C, compared with the outdoor planting mix, it corresponds approximately to a 150% moisture content. These results show the importance of the choice of the substrate for the green-wall creation. It is important to control moisture content.

With the relations (3 and 4), the thermal conductivity of materials can be determined with a measure of moisture content (Fig. 8).

The separation between the measured and calculated conductivities can result from the measure of the moisture content, where a sampling is taken from the global mass.

### 3.4. Plant palette

To avoid the dry out of plants and to avoid the loss of moisture, the paving concrete was warmed slightly to create a temperature difference

<figure><img src="image_90.png" /><figcaption>Fig. 8. Comparison between thermal conductivity measured and calculated.</figcaption></figure>

<table><caption>Table 5
Measure of the vegetal palet.</caption><thead><tr><td>Vegetal (%)</td><td>Thermal conductivity (W/m K)</td></tr></thead><tbody><tr><td>Ivy</td><td>0.239–0.265</td></tr><tr><td>Virginia creeper</td><td>0.220–0.274</td></tr></tbody></table>

of about 10 °C. After measurement, the plant was always in the same state. The plant arrangement was realized so as to reproduce a green-wall thickness of 10 centimeters. The foliage implementation is realized to feign a green-wall consisted of sheets and air. Measured thermal conductivities are presented Table 5.

It is not easy to reproduce the test with the plants. Five tests were carried out to have this measurement range. The results show that the plants don’t bring real thermal insulation. On the other hand, they can help to reduce overheating on the walls in summer [14]. In order to quantify the contribution of a green-wall on a dwelling a modeling on TRNSYS is carried out.

### 3.5. Thermal simulation

The modeling of the house Mozart was carried out on SketchUp in order to export it on TRNSYS 17 (Fig. 9).

To take into account the green-wall (Fig. 10), TRNBuild determined these specific properties (λ = 0.25 W/m °C, ρ = 16 kg/m³ and a heat capacity of 150 W h/m³ K).

The assumptions of simulation are

**Heating:**

* 19 °C except for garage, roofs and underfloor space

* Power = limited to 7.5 kW per zone

* Radiative share = 70%

**Occupation:**

* 3 people present of 17:00 at 8:00 the week and all the day the safe weekend in the garage, roofs and underfloor space

**Internalloads:**

* Illumination: 5 W/m², leaves convective = 40% fluorescent tube

* Use cooks: 240W, radiative share 90% to 777.6 kJ/h (from 19:00 to 20:00 the week and 11:00–12:00 the weekend)

**Not air-conditioning**

**Ventilation**

* Kitchen: 0.4 vol/h

* Bathroom: 0.2 vol/h

<figure><img src="image_91.png" /><figcaption>Fig. 9. Modeling of the house Mozart on SketchUp.</figcaption></figure>
<figure><img src="image_92.png" /><figcaption>Fig. 10. Modeling of the green-wall of the house Mozart on SketchUp.</figcaption></figure>

<table><caption>**Table 6**
Comparison of the annual statements with and without ivy.</caption><caption>House Mozart<br>Annual statement in kWh/h/an</caption><thead><tr><th>Needs for heating</th><th>Solar contributions</th><th>Internal contributions</th><th>Losses by the walls</th><th>Losses by ventilation</th><th>Losses by the infiltrations</th></tr></thead><tbody><tr><td colspan="6">Without green-wall</td></tr><tr><td>8454</td><td>3147</td><td>1442</td><td>-8734</td><td>0</td><td>-4309</td></tr><tr><td colspan="6">Green-wall in the south (5 cm of Ivy)</td></tr><tr><td>8204</td><td>3147</td><td>1442</td><td>-8449</td><td>0</td><td>-4344</td></tr><tr><td colspan="6">Green-wall in the south (10 cm of Ivy)</td></tr><tr><td>8167</td><td>3147</td><td>1442</td><td>-8417</td><td>0</td><td>-4340</td></tr></tbody></table>

<figure><img src="image_93.png" /><figcaption>Fig. 11. Comparison for heating with or without ivy.</figcaption></figure>

## Infiltration

* Heated zones: 0.1 vol/h

* Not heated zones: 1 vol/h

The results are given in Table 6.

Fig. 11 presents the reduction of heating of housing with presence of a green-wall.

By modeling the green-wall, a reduction in the production of heating of 3% has been noted which remains low. An ivy addition of 5 cm does not make it possible to have a better performance in insulation. It is necessary to do a more complete study of the thermal performances of the green-walls and integrated the influences of the other phenomena related to the presence of the vegetation [4,14,24].

## 4. Conclusion

This study gives concrete values of thermal conductivity of the components of the complex green-walls for manufacturers. This preliminary study enabled us to find conductivity apparent being able

made up a green-wall. This approach remains in conditions controlled with measurements in the laboratory. The measures bring thermal knowledge for the manufacturing of complex green-walls. The manufacturers can develop their product. The green-walls made up of sphagnum have the best thermal conductivities in wet condition. Moreover, it is important to control the moisture of the substrates to obtain the best thermal conductivity. The manufacturers can add sensors moisture in the substrate to find a balance between thermal conductivity, moisture and growth of the plants.

The green-wall materials cannot be used as a replacement to classic types of insulation. On the other hand, they can be used to complement other types of insulation. Their presence controls the solar thermal radiations and thus to avoid overheating in summer.

Concerning the simple green-wall, to obtain a wall respecting the wall insulation ($R = 3 m^2 K/W$) with 20 cm of ivy or Virginia creeper and with a veil in concrete of 20 cm would be to add a complementary insulation ($λ = 0.04 W/m K$) of:

* For the Virginia creeper : 8.2 cm

* For the Ivy : 8 cm

The thermal insulation investigation shows that 5 cm of ivy makes it possible to reduce the needs for heating. The increase of the ivy thickness to 10 cm does not make real improvement of the insulation. The first results of thermal simulation show the interest of the green-walls on the building. It is important to take them into account in thermal simulations in design offices.

Furthermore, the measure of thermal conductivity is realized on rough materials and provides an intrinsic value of the material; it does not take into account its use. It would be necessary to pursue experiments on exposed sites to measure its influence on the thermal comfort of the house.

## References

[1] M.A. Kenai, L. Libessart, S. Lassue, D. Defer, Impact énergétique d'un mur végétalisé sur les performances thermiques d'une paroi de bâtiment, XIIIème Colloque Interuniversitaire Franco-Québécois sur la thermique des Systèmes, Saint-Lô.

[2] R.A. Francis, J. Lorimer, Urban reconciliation ecology: the potential of living roofs and walls, J. Environ. Manag. 92 (2011) 1429–1437.

[3] T.N.S. SOFRES Les français et leur Habitat : perception de la densité et des formes d'habitat. Observatoire de la ville, <http://www.observatoire-de-la-ville.com/publications/les-etudes-tns-sofres.html>.

[4] R. Djedjig, R. Belarbi, E. Bozonnet, Experimental study of green walls impact son buildings in summer and winter under an oceanic climate, Energy Build. 150 (2017) 403–411.

[5] N. Hien Wong, A. Yong Kwang Tan, Y. Chen, et al., Thermal evaluation of vertical greenery systems for building walls, Build. Environ. 45 (2010) 663–672.

[6] C.Y. Cheng, K.K.S. Cheung, L.M. Chu, Thermal performance of a vegetable cladding system on façade walls, Build. Environ. 45 (2010) 1779–1787.

[7] T. Sternberg, H. Viles, A. Cathersides, Evaluating the role of ivy (Hedera helix) in moderating wall surface microclimates and contributing to the bioprotection of historic buildings, Build. Environ. 46 (2011) 293–297.

[8] N. Hien Wong, A. Yong Kwang Tan, P. Yok Tan, K. Chiang, N. Chung Wong, Acoustics evaluation of vertical greenery systems for building walls, Build. Environ. 45 (2010) 411–420.

[9] E. Alexandri, P. Jones, Temperature decreases in an urban canyon due to green walls and green roofs in diverse climates, Build. Environ. 43 (2006) 480–493.

[10] K.L. Geter, B. Rowe, The role of extensive green roofs sustainable development, Hortscience 41 (2006) 1276–1285.

[11] H.F. Castleton, V. Stovin, S.B.M. Beck, J.B. Davison, Green roofs, building energy savings and the potential for retrofit, Energy Build. 42 (2010) 1582–1591.

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[13] C.Y. Jim, H. He, Estimating heat flux transmission of vertical greenery ecosystem, Ecol. Eng. 37 (2011) 1112–1122.

[14] M.A. Kenai, L. Libessart, S. Lassue, D. Defer, Impact of plants occultation on energy balance: experimental study, Energy Build. 162 (2018) 208–218.

[15] Y. Cherif, A. Joulin, L. Zalewski, S. Lassue, Superficial heat transfer by forced convection and radiation in a horizontal channel, Int. J. Therm. Sci. 48 (9) (2009) 1696–1706.

[16] M. Filali, Conductivité thermique apparente des milieux granulaires soumis à des contraintes mécaniques: modélisation et mesures (Ph.D. Thesis), Polytechnic Institut of Toulouse, 2006.
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[18] S. Lassue, L. Zalewski, L. Libessart, P. Herin, Instrumentation for experimental study on heat transfer coefficient for external surface of building. Intern. Conf. Urban Engin., Lille, 2005.

[19] B. Martin, J.F. Durastanti, B. Peureux, Méthode d'identification de la conductivité thermique des matériaux isolants, Entrop 147 (1994) 47-52.

[20] SD EN 12667 et SD EN 12664 Normes caractérisation de la conductivité thermique des matériaux.

[21] F. De Pont, S. Klarsfeld, Conductivité thermique des isolants, Technique de l'ingénieur, 2002.

[22] D. Gossart, Impact de l'enveloppe sur la performance énergétique des bâtiments : de la caractérisation jusqu'à l'optimisation (Ph.D. Thesis) 3 University of Toulouse, 2011.

[23] CSTB, «Inertie thermique des logements et confort d'été, Collect. Techn. Cimbéton, 2001.

[24] M.A. Kenai, Caractérisation, analyse et modélisation des échanges énergétiques entre un mur végétalisé intensif et son environnement (Ph.D. Thesis), University of Artois, 2016.
<figure><img src="image_94.png" /></figure>

# Impact of plants obscuration on energy balance: Theoretical and numerical study

Mohamed-Amine Kenai<sup>a</sup>, Laurent Libessart<sup>b, *</sup>, Stephane Lassue<sup>b</sup>, Didier Defer<sup>b</sup>

## ARTICLE INFO

**Keywords:**

Green walls

Obscuration effect

Model adaptation

Thermal effect analysis

## ABSTRACT

This article presents the numerical simulation of the energy effect of a solar mask created by a green wall on the thermal performance of a building envelope in a temperate climate in order to integrate it into thermal calculation codes. The document describes primarily the adaptation of a simplified prediction model. The simplified model was developed and validated on the basis of tests carried out with an experimental controlled occultation device by integrating all external parameters influencing heat exchanges (conduction, convection and radiation). A first validation of the numeric resolution algorithm of the preliminary model was realised. Then the model was supplemented by considerations related to the characteristics of the selected plants: ivy and Virginia creeper, such as the semi-transparent appearance of foliage plants and their geometric distribution. The numerical prediction was very close to the experimental values, and the mean error was about 1 °C. This difference makes it possible to validate the developed model.

## 1. Introduction

The issue of reducing energy consumption is a major factor in solving contemporary environmental problems. From the first world conference on the environment (Stockholm, 1972) to the recent climate conference (Cop 21, Paris 2015), passing by the Kyoto agreements (1997) and the various inter-state negotiations around the world, the building sector has been identified as one of the most important targets on which energy saving efforts must be made [1]. The vegetation of building envelop by creating Green Walls (GW) or Vegetal Walls (VW) is among the various solutions for the optimization of energy consumption in buildings [2-5] and some well publicized projects have given a very good image of the process (Quai Branly Museum in Paris for example [6]). This tendency mainly came from Germany in the early 1970s. Although it is a very old technique, the main driver of its development remains, to this day, the aesthetic aspect and the desire to provide originality to buildings [7]. However, green walls can also have very positive effects on the improvement of the sound insulation [8-10] and the thermal performance of buildings [11-20]. According to numerous studies, green walls contribute to the improvement of air quality [21-26], bring biodiversity to urban centres and limit the development of the heat island phenomenon [27-30]. In addition to the described properties that are

common to both types of green walls, the complex types (Substrate + Plants) introduce evapotranspiration phenomena that give them a cooling capacity [31-34]. In this case, the substrate, if it is regularly irrigated, is the seat of an evaporation phenomenon and feeds the transpiration of the plants. This transformation of water from its liquid phase to its gaseous phase requires energy that contributes to the consumption of heat flux at the outer surface area of the wall. The energy required to convert 1 m³ of water (at 20 °C) to steam is equivalent to about 680 kWh (latent heat). The transpiration of the plants is a function of the stomata resistance, it is a characteristic peculiar to the plants which allows them to self-regulate physiologically. Stomata give plants the ability to adjust the flow of water through them, so these flows are regulated according to the size of the stomata opening, which in turn depends on the different atmospheric conditions and physiological state of the plant. In case of water deficit the stomata close to compensate for the lack of water supply. Jim and He [35] evaluated the process of transmitting green walls using a solar projection principle. The results showed that the thermal efficiency of the shading effects varies with the orientation, in the case of the south-facing wall the latter had reached a higher coefficient (0.31) compared to the north-facing wall. The south wall exchanged lower heat flows (in both directions) than the north wall. It was more effective than the north wall due to amplification of the effects of canopy evapotranspiration [35]. In the case of "simple"

<footnote><sup>a</sup> YNCREA-Ecole des Hautes Etudes d'Ingénieur, LGCgE, F-59000, Lille, France</footnote>

<footnote><sup>b</sup> Univ. Artois, Laboratoire de Génie Civil et géo-Environnement (LGCgE), EA 4515, F-62400, Béthune, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: laurent.libessart@univ-artois.fr (L. Libessart).</footnote>
Nomenclature

Symbols

T temperature, K

GW green wall

$Is^↓$ incident solar radiation, W/m²

$Ir^↓$ infrared radiation, W/m²

$c_p$ specific heat, J.kg⁻¹.K⁻¹

$d_0$ height of movement, m

$df$ average leaf thickness, m

$F$ leaf cover index

$h_{cv}$ convective exchange coefficient, W.m⁻².K⁻¹

$hf$ height of vegetal canopy, m

$k$ constant of Von Karman

$ra$ aerodynamic resistance, s.m⁻¹

$rc$ « resistance » to sensible thermal transfer, s.m⁻¹

$uc$ flow velocity within the plant layer, m/s

$U_m$ wind speed, m/s

$z_{0H}$ roughness lengths « sensitive heat », m

$z_{0m}$ roughness lengths « amount of movement», m

Greek letters

$A$ solar absorption coefficient

$\beta_{zen}$ solar zenith angle

$\phi$ flux density, W/m²

$\sigma$ constant of Stefan-Boltzmann 5.67 × 10⁻⁸W/m².K⁴

$\sigma_{occ}$ coverage rate, [0,1]

$\varepsilon$ emissivity, [0,1]

$\tau$ transmissivity, [0,1]

$\sigma_{vw}$ coverage rate, [0,1]

$\mu^*$ solar extinction coefficient

Indices / Exponents

$CC$ cellular concrete

$vw$ vegetal wall

$Eq$ equivalent

$sol$ solar

$R_{env}$ infrared exchanges with the environment

$R_{occ}$ infrared exchanges with the GW

$R_{env}$ infrared exchanges with the environment

$R_{occ}$ infrared exchanges with the GW

$R_{env-vw}$ infrared exchanges with the environment

$R_{cc-vw}$ infrared exchanges with the green wall

$Cv$ convection

$Tr$ transmitted

$Th$ theoretical

$AG$ air gap

$SWR$ short-wave radiation, W/m²

$LWR$ long-wave radiation, W/m²

green walls that will be addressed in this work (low transpiration, lack of substrate), this cooling effect is negligible compared to the impacts on short wavelengths and long wavelengths radiation and on thermal convection.

To complete the aim of the study, there are very few studies proposing numerical and analytical tools for evaluating the thermal effects of green walls on buildings [36]. Dynamics simulation software's don't take into account the effect of green walls on the thermal balance. Some experimental studies have shown the beneficial effect of masking made by plants [37]. In order to develop digital thermal simulation tools, it is necessary to create a code integrating the parameters of the green walls. A simplified model was therefore developed on artificial masking to determine the theoretical evaluation of the thermal impact according to its coverage rate. The numerical code has been developed from the balance of energy exchanges through the integration of radiative and convective parameters. The introduction of the envelope characteristics and the meteorological data enabled the equations to be solved. The artificial masking device was then replaced by real vegetation (Ivy and Virginia creeper) and the theoretical study was supplemented by the integration of plant properties: the semi-transparent appearance of foliage plants and their geometric distribution. The differences between artificial masking and plants are discussed and interpreted as new parameters in the different equations. This work aims to evaluate the thermal impact of the “simple” green walls by digital and theoretical tools. The paper presents modelling of the thermal effect of plants. Prototype-scale validation was then presented to pave the way for the creation of a real-scale predictive thermal model.

## 2. Methods

### 2.1. Experimental approach

This part presents the evaluation of the energy effect of a solar mask created by a GW as described in Ref. [37]. The aim was to evaluate the impact of vegetation on the thermal performance of building envelope under a temperate climate, in summer and winter. This wall was equipped with a device simulating the masking effect of a vegetal cover

by an artificial material. This approach allowed the listing and evaluation of the principal transfer phenomena that occur between the wall and its environment. Thus, a relatively simplified model was validated from the comparison between numerical simulations and experimental results obtained for the thermal labs which are under natural constraints. These cubic cells of reduced size each consisted of five thermally insulated walls and a test wall, facing south, equipped with heat flux and temperature sensors (as described in Refs. [1,37]) which were then equipped with green walls (Fig. 1). The central prototype “Lab 1” serves as a reference, while Lab 2 and Lab 3 are respectively equipped with an evergreen (Ivy) plant and a deciduous plant (Virginia creeper).

The experimental results [37] showed clearly the effect of masking on reducing surface and air temperatures. It was found a significant decrease in the thermal heat flux through the south oriented wall depending on the increase of the coverage rates.

### 2.2. Preliminary theoretical model

A preliminary theoretical model was developed to identify the parameters that affect the heat flow received by an occult wall. This model was created by performing an energy balance to determine the heat flux resulting from various transfer phenomena between the outer wall and the environment, which are conditioned by the presence of a partial occultation (Fig. 2).

#### 2.2.1. Energy exchange balance

The heat flux at the outer wall ($\phi_{cc}$) obtained by the balance of the radiative and convective exchanges SWR and LWR, can be written in the following form:

$$ \phi_{cc} = \phi_{sol} - \phi_{R_{env}} - \phi_{R_{occ}} - \phi_{cv} \quad (1) $$

The different terms of the energy exchange balance at the CC wall are detailed below (2.2.2. to 2.2.4.). The transfer equations used are relatively standard in the bibliography [38], the characteristic term of the coverage rate was added here. The radiative characteristics of each of the materials used are given in Table 1.

Calculations were made using meteorological records and measured
<figure><img src="image_95.png" /><figcaption>Fig. 1. Test of masking by the vegetation; (a) general view; (b) distribution of vegetated walls; (c) sensors disposition.</figcaption></figure>

<figure><img src="image_96.png" /><figcaption>Fig. 2. Energy balance at the outer surface of the CC wall.</figcaption></figure>

<table><caption>**Table 1**
Radiative properties.</caption><thead><tr><th>Radiative Properties</th><th>α [0/1]</th><th>ε [0/1]</th><th>τ [0/1]</th><th>r [0/1]</th></tr></thead><tbody><tr><td>Wall CC</td><td>0.9</td><td>0.9</td><td>0</td><td>0.1</td></tr><tr><td>Masking</td><td>0.9</td><td>0.9</td><td>0</td><td>0.1</td></tr></tbody></table>

temperatures on the CC wall surfaces, within the shading device and the air gap.

### 2.2.2. Solar radiation

The radiation absorbed by the outer surface of the wall is equal to the difference between the radiation which passes through the uncovered part of the occultation $Is^↓(1 - σ_{occ})$ and the radiation reflected by the wall.

$$ \phi_{sol} = α_{CC}(1 - σ_{occ}) × Is^↓ \quad (2) $$

The SWR radiative exchanges between the masking and the outer surface of the cellular concrete are represented by the solar radiation of equation (2) whereas equation (3) takes into account possible multiple reflections between the wall and the inner surface of the masking.

$$ \phi_{sol_{(occ-CC)}} = Is^↓.α_{CC} \left(1 - σ_{occ}\right) \times \sum_{n=2}^{∞} r_{CC}^n(σ_{occ} \cdot r_{occ})^{n-1} \quad (3) $$

The value of n = 2 is largely sufficient here, the surfaces having high solar absorption coefficients (close to 0.9).

### 2.2.3. Infrared radiation

The radiation (LWR) at the CC wall is the sum of the exchanges between the wall and the environment is ($φ_{Renv}$), and between the wall and the masking is ($φ_{Rocc}$).

$$ \phi_{Renv} = \frac{ε_{CC}σ. (T_{CC}^↓ - T_{EQ}^↓) × (1 - σ_{occ})}{1 - σ_{occ} × (1 - ε_{CC})} \quad (4) $$

The exchanges between the CC wall and the environment are calculated from an equivalent temperature determined using a pyrgeometer placed on a vertical wall and which integrates the combined effect of the “surfaces” constituting the radiative environment at low temperatures (sky, ground, etc.). The equivalent temperature is
obtained by equation (5).

$$T_{EQ} = \left(\frac{Ir}{\sigma}\right)^{\frac{1}{4}} \qquad (5)$$

The radiative exchanges LWR between the masking and the CC wall are represented by the following equation:

$$\phi_{R_{occ}} = \frac{\sigma \cdot (T_{CC}^4 - T_{occ}^4)}{\frac{1-\varepsilon_{CC}}{\varepsilon_{CC}} + \frac{1}{\sigma_{occ}} + \frac{1-\varepsilon_{occ}}{\varepsilon_{occ}} \times \frac{1}{\sigma_{occ}}} \qquad (6)$$

### 2.2.4. Convection

The heat flux exchanged by convection ($\phi_{cv}$) is given by the following equation:

$$\phi_{cv} = h_{cv} \cdot (T_{CC} - T_{AG}) \qquad (7)$$

The convective heat exchange coefficient $h_c$ was determined from the correlation used by Ref. [39]:

$$h_{cv} = 1.31 \cdot |T_{CC} - T_{AG}|^{\frac{1}{4}} + 9 \qquad (8)$$

The constant 9 of equation (8) is an experimental factor recommended to take into account the effect of the average wind speed.

## 2.3. Equations resolution

The equations composing the energy balance at the outer surface of the cellular concrete wall (4), (6) and (8) involve nonlinear terms according to the surface temperature of the cellular concrete wall ($T_{cc}$).

A resolution of the energy balance equations was performed under Matlab using the Newton-Raphson method. Thus, for each time step, the “theoretical” calculated temperature of the wall surface is evaluated numerically with an iterative calculation. Once this temperature is approximated with an error deemed as acceptable, the program resets the inputs to make the approximation in the next time step and so on, until the last time step entered for the end of the calculations (Fig. 3).

For the functioning of the algorithm (Fig. 3), it is necessary to introduce the characteristics of the envelope and the meteorological data. The heat flux on the outer surface of the cellular concrete wall must also be provided at each time step in order to evaluate the temperature. The temperatures evaluated with this algorithm are validated

<figure><img src="image_97.png" /><figcaption>Fig. 3. Diagram of the resolution algorithm.</figcaption></figure>

experimentally in the following section.

## 2.4. Preliminary model validation

A comparison between the theoretical temperatures, represented in orange (T°_theoretical) and the measured temperatures, in blue (T°_measured) was carried out for the different coverage rates (0–100%) in order to validate the preliminary model based on the energy balance equations in the artificial occultation test (Fig. 4).

For all coverage rates, the theoretical model closely reproduces the measured temperature. For example, in the case of coverage rates of 100%, the mean deviation between the theoretical temperatures curve and the experimental curve for a period of 6 days was 0.54 °C.

A typical day was selected to better illustrate the comparison between the numerical results and the experimental results. The coverage rate during this typical day (May 12, 2014) was 50% on the lab3, and the meteorological data used for the chosen day are shown in Fig. 5.

This typical day was selected according to the maximum temperature values and the solar radiation recorded during the period of the test of the controlled occultation rate. The peak of solar radiation was 786 W/m² at 16h00, while the ambient air temperature was around a maximum of 16.6 °C for the period and a minimum of 8.1 °C recorded at 5h00. No precipitation was observed during this day, but high humidity values were recorded during the night and in the morning (82%–90% between 1h00 and 10h00). The wind speed was relatively low during the selected sequence (0.9–3.6 m/s).

The results of validation of the theoretical model during the typical sequence are illustrated in Fig. 6.

In this figure, it is observed that the calculated heat flux is globally similar to that measured. The mean deviation between the theoretical and measured temperature is of the order of 1.3 °C. Deviations of up to 3.8 °C were recorded during peaks and in the rapid changes in solar radiation. These deviations coincide with the period when solar radiation is rapidly changing from 500 to 786 W/m². During the night and in the morning, the deviations are relatively higher than the mean values, they correspond perfectly to the sequence in which, the relative humidity was very high and the solar radiation not exceeding 200 W/m².

Despite these few deviations corresponding to particular sequences (high humidity and rapid change of solar radiation), the influence of the coverage rate was reproduced fairly accurately throughout the test.

The good similarity obtained, between the theoretical model and the experimental results, allowed an appropriate validation of the controlled occultation model. The equations of this model will be used as a basis for the modelling of the behaviour of the green walls.

## 2.5. Adaptation of equations to the case of vegetation

The energy balance at a wall obscured by vegetation is based on the balance equations of solar radiation exchanges, infrared exchanges and convective exchanges (Equation (9)).

$$\phi_{cc} = \phi_{sol} - \phi_{R_{env-cc}} - \phi_{R_{w-cc}} - \phi_{cv} \qquad (9)$$

Among the major differences between the two types of occultation is the semi-transparent foliage aspect of plants. This involves a new equation quantifying the solar flux ($\phi_{sol-tr}$) which crosses the “vegetation cover” and involves several and numerous parameters (only parameters related to the obscuration effect are treated) (Fig. 7).

The second important difference is related to the geometry of the occultation. In the experiment, realised with artificial occultation, the objective was to master the role of the coverage rate. This has been possible by using a relatively simple structure where each of the meshes of the occultation lies in the same plane and thus in two dimensions (2D). In the case of vegetation, the leaves of the plants replace the square meshes. The distribution of plant leaves is not limited by a 2D plan. The thickness of the leaf layer, the density and the number of leaves are new
<figure><img src="image_98.png" /><figcaption>Fig. 4. Comparison of numerical and experimental results.</figcaption></figure>

parameters to be integrated into the energy balance equations. This last aspect requires modification of the transmitted and absorbed solar radiation and an adaptation of the equations of convective exchanges. These convective exchanges are considered in the case of the artificial occultation to be similar to exchanges between two flat surfaces. They are more complex in the case of plants, and it is then necessary to take into account an aerodynamic resistance in the external surface area of the leaf layer and a resistance to the sensible heat transfer within the canopy layer, following its thickness, and the density of leaves.

### 2.5.1. Radiative exchanges

The radiative exchanges balance was adapted according to the characteristics of the plants, no change was made to the infrared radiation equations between the cellular concrete wall (W<sub>CC</sub>) and the environment (Equation (10)) on one hand and between the GW and the W<sub>CC</sub> on the other hand (Equation (11)):

$$ \phi_{RCC-env} = \frac{\epsilon_{BC}\sigma \times (T_{CC}^{\perp} - T_{EQ}^{\perp}) \times (1 - \sigma_{vw})}{1 - \sigma_{vw} \times (1 - \epsilon_{CC})} \quad (10) $$
<figure><img src="image_99.png" /><figcaption>Fig. 5. Meteorological data.</figcaption></figure>

<figure><img src="image_100.png" /><figcaption>Fig. 6. Comparison between theoretical and measured temperatures (σocc = 50%).</figcaption></figure>

<figure><img src="image_101.png" /><figcaption>Fig. 7. Elements of the energy balance; (a) case of artificial obscuration; (b) case of masking by the vegetation.</figcaption></figure>
$$ \phi_{R_{vw-cc}} = \frac{\sigma \times (T_{cc}^4 - T_{vw}^4)}{\frac{1-\epsilon_{cc}}{\epsilon_{cc}} + \frac{1}{\sigma_{vw}} + \frac{1-\epsilon_{vw}}{\epsilon_{vw}} \times \frac{1}{\sigma_{vw}}} \quad (11) $$

Since the leaf layer of plants is considered semi-transparent to solar radiation, a transmitted flux term has been added ($\phi_{sol-tr}$). This adds to the direct solar flux and to those exchanged between the masking and the WCC have been expressed respectively by ($\phi_{sol}$) and ($\phi_{sol(vw-cc)}$) in equations 12 and 13.

$$ \phi_{sol} = \alpha_{cc}(1 - \sigma_{vw}) \times Is \quad (12) $$

$$ \phi_{sol(vw-cc)} = Is^1 \times \alpha_{cc}(1 - \sigma_{vw}) \times \sum_{n=2}^{\infty} r_{cc}^n (\sigma_{vw} \times r_{vw})^{n-1} \quad (13) $$

The radiative flux transmitted by the foliar layer of plants ($\phi_{sol-tr}$), is obtained as a function of the incident solar radiation, the WCC absorption coefficient, the coverage rate of the plant layer and the solar transmission coefficient of the leaf layer (Equation (14)).

$$ \phi_{sol-tr} = Is^1 \times \alpha_{cc} \times \sigma_{cc} \times \tau_{vw} \quad (14) $$

The foliar solar transmission coefficient $\tau$, is determined according to a simplified approach which consists in assuming the foliar layer as a homogeneous medium in which the radiation is absorbed and not diffused. With this assumption, the Beer-Lambert law can then describe the exponential attenuation of the radiation passing through the leaf layer [28,40]. Thus, the coefficient ($\tau_{vw}$) is calculated as a function of the solar zenith angle ($\beta_{zen}$), the leaf coverage index ($F$) and a solar extinction coefficient ($\mu^*$) which vary according to the radiative properties of the leaves and their mean inclination (Equation (15)).

$$ \tau_{vw} = \exp(-\mu^* \times \beta_{zen} \times F) \quad (15) $$

The inclination of the leaves and the radiative properties of the plants ($\mu^*$) determine the depth up to which direct solar radiation (of $\beta$) zenith angle) can penetrate in the leaf layer without being intercepted. The foliar cover index ($F$), for its part, is a dimensionless quantity, representing the spatial distribution of the leaf structure in three dimensions. In other words, the index $F$ is taken to be equal to the coverage rate in the case of a spatial distribution in 2D only (case of artificial occultation). It is defined as the ratio between half of the total surface area of the leaves (up and down seeds) and the total surface area (CC wall). Unlike the coverage rate, which is limited to the ratio between the covered area and the total area, the index $F$ is calculated taking into account the total number of leaves, even if they are superimposed (Equation (16)).

$$ F = \frac{1/2 \text{ Total leaf area}}{W_{cc} \text{ area}} \quad (16) $$

### 2.5.2. Convective exchanges

The new model of convective exchanges is inspired by the model validated by Ref. [28]. It is expressed as a function of an aerodynamic resistance of the top layer of the plants (ra) and a resistance to the sensible heat transfer (rc) within the foliage. The introduction of the two “resistances” (in s.m⁻¹) is similar to that which is generally used for the modelling of heat transfer by electrical analogy. The new convective flux at the level of the leaf layer, involving these two resistances, is given by the following equation:

$$ \phi_c = \frac{\rho_{air} \times c p_{air}}{rc + ra} (T_{cc} - T_f) \quad (17) $$

The aerodynamic resistance (ra) is defined by the variation of the wind speed above a rough surface. It is determined according to a general model often used by climatologists to describe the wind velocity profile at the upper boundary layer of a plant canopy [41,42]. According to Ref. [28], the aerodynamic resistance (ra) which takes into account the very small deviations between the ambient air temperature and the foliage temperature can be calculated by equation (18):

$$ ra = \frac{\left[ \ln \left( \frac{z_U - d_0}{z_{0m}} \right) \right] \times \left[ \ln \left( \frac{z_U - d_0}{z_{0H}} \right) \right]}{k^2 um} \quad (18) $$

With (k) the Von Karman constant (k≈ 0.40) and ($u_m$) the wind speed measured at the distance ($z_U$). Whereas, the displacement height ($d_0$) and the roughness lengths ($z_{0H}$) and ($z_{0m}$) are calculated, according to Ref. [43], as a function of the height of the plant canopy ($hf$):

$$ \begin{aligned} d_0 &= 0.701hf^{0.975} \\ z_{0m} &= 0.131hf^{0.997} \\ z_{0H} &= 0.1z_{0m} \end{aligned} \quad (19) $$

The resistance to sensible heat transfer (rc) intervenes inside the plant layer. It is determined as a function of the velocity of the air flow within the plant canopy (uc) using the relationship below [44–46]:

$$ rc = \frac{1}{0.004 + 0.012 uc} \quad (20) $$

The air flow velocity within the plant layer (uc) is reduced as function of a specific coefficient of the vegetation layer (a) and is determined according to the following equation:

$$ uc = \left[ um \cdot \ln \left( \frac{(hf - d_0)}{z_{0m}} \right) / \ln \left( \frac{(z_U - d_0)}{z_{0H}} \right) \right] \cdot e^{-a \left( 1 - \frac{0.05}{hf} \right)} \quad (21) $$

The coefficient (a) (in eq (21)) is calculated according to the foliar surface index (F), the height of the plant canopy ($hf$) and the average leaves thickness ($df$):

$$ a = \sqrt{0.2F \frac{hf}{df}} \quad (22) $$

Henceforth, the different equations used in the first part have been adapted to the case of vegetation. They were validated after the determination of the coverage rate by an image analysis method.

### 3. Experimental validation

The different equations having the wall surface temperature ($T_{cc}$) as unknown parameter were solved using the Newton Raphson method. Then, in order to verify the relevance of the theoretical model, the results of the calculations were compared with the experimental measurements [37]. The parameters used in the theoretical modelling are grouped in Table 2.

The experimental data used for validation were recorded by the mini thermal lab at the end of the summer period of 2014. The meteorological data entered as inputs to the program are: ambient air temperature, short-wave solar radiation, equivalent environmental temperature and wind speed. In addition, data on precipitation and relative humidity are given only for information. These additional data may be useful for understanding numerical prediction errors, which generally coincide with possible rapid changes in the values for these two parameters (Fig. 8).

During the sequence selected for experimental validation, the air temperature varied between 9 and 24 °C. While the wind speed never

<table><caption>**Table 2**

Parameters for experimental validation.</caption><thead><tr><th>Parameters</th><th>Value</th><th>Parameters</th><th>Value</th></tr></thead><tbody><tr><td>a<sub>cc</sub></td><td>0.90</td><td>ε<sub>cc</sub></td><td>0.96</td></tr><tr><td>σ<sub>wv</sub></td><td>0.45</td><td>σ</td><td>5.67 10<sup>-8</sup></td></tr><tr><td>r<sub>cc</sub></td><td>0.1</td><td>ε<sub>wv</sub></td><td>0.95</td></tr><tr><td>r<sub>wv</sub></td><td>0.3</td><td>hf</td><td>0.15</td></tr><tr><td>μ<sup>*</sup></td><td>0.75</td><td>d<sub>f</sub></td><td>0.001</td></tr><tr><td>F</td><td>3</td><td></td><td></td></tr></tbody></table>
<figure><img src="image_102.png" /><figcaption>Fig. 8. Meteorological data of the validation sequence.</figcaption></figure>

<figure><img src="image_103.png" /><figcaption>Fig. 9. Comparison of theoretical and measured temperatures.</figcaption></figure>

exceeded 3.6 m/s over the entire validation sequence. As for solar radiation, the maximum values ranged between 400 and 700 W/m² with very rapid oscillations during the first three days of validation because of frequent cloud crossings.

The theoretical temperatures obtained for the surface of the CC wall were then compared with the outside surface temperatures recorded by the "Lab 2" (Fig. 9).

From the comparison, it appears that the numerical prediction is generally very close to the experimental values. The temperatures from the numerical calculations correspond to the experimental temperatures within about 1.5 °C.

The average deviation observed corresponds to an average error of ±6.4% throughout the validation sequence. However, it should be noted that the differences between the calculated and the measured temperatures are less than 1 °C over 90% of the values. The error calculated on 90% of the values, which does not take into account the deviations due to the rapid variations of the solar radiation, is less than 4.7% (less than 1 °C). This difference is very acceptable for validations under external conditions.

## 4. Conclusion

This work presents a new contribution to the numerical evaluation of the thermal effects of green walls. A preliminary theoretical model has been established and the overall behaviour of the heat flux according to

the imposed coverage rates has been reproduced very correctly. Modelling of the effects of occultation by a plant screen was introduced by presenting the differences between a plant screen and occultation by an artificial material. New equations incorporating these changes have been added to the established preliminary model. The results of the new model were then compared to the experimental results. The relevance of the numerical model was discussed and confronted to the experimental results. The comparison between theoretical and experimental temperatures made it possible to validate the proposed model on a small scale. This will help predict the effect of plants on the thermal behaviour of a real building in different climates.

The experimental and theoretical approaches demonstrated the thermal interest of simple green walls and highlighted the complexity of transfer phenomena in a plant layer. This will allow for future modelling of the thermal effect of plants on buildings on a real scale. The digital tool has been developed to provide more accuracy on the effects of plants in temperate climate regions and can now be integrated into thermal building simulation software. It will also permit studying the thermal effects of simple green walls in other climates and for different types of constructions.

## Acknowledgement

This research was conducted out at the Laboratory of Civil Engineering and Geo-Environment of University of Artois, the Graduate
School of Engineering HEI of Lille in the context of the project "Building and Positive Biodiversity" (2012-2015), supported by the Catholic University of Lille, the "Nord-Pas-de-Calais" Regional Council and the European Metropolis of Lille.

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# Annexe 2

Cette annexe présente les articles :

(C) Tilioua A., Libessart L., Jeandel G., Lassue S., “Determination of radiative properties of polyester batting insulation material from hemispherical transmittance and reflectance measurement”, *Applied Thermal Engineering*, 105, 594,- 604, 2016

(D) Tilioua A., Libessart L., Lassue S., “Characterization of the thermal properties of fibrous insulation materials made from recycled textile fibers for building applications : Theoretical and experimental analyse”, *Applied Thermal Engineering*, 142, 56-67, 2018

Ces articles illustrent les apports faits sur les matériaux fibreux et semi-transparents (ouate de polyester, matériau textile et plexiglas) sur leurs propriétés optiques et sur leur caractérisation thermique par rayonnement.

Mots clefs : Conductivité radiative effective (C, D), Conductivité thermique (C, D), Epaisseur (C, D), Flux (C, D), Isolant (C, D), Méthode inverse (C, D), Ouate de polyester (C), Propriétés radiatives (C, D), Réflectance (C, D), Transmittance (C, D), Textile recyclé (D).
<figure><img src="image_104.png" /></figure>

<figure><img src="image_105.png" /></figure>

Research Paper

# Determination of radiative properties of polyester batting insulation material from hemispherical transmittance and reflectance measurements

<figure><img src="image_106.png" /></figure>

CrossMark

Amine Tilioua<sup>a,b,*</sup>, Laurent Libessart<sup>c</sup>, Gérard Jeandel<sup>d</sup>, Stéphane Lassue<sup>e</sup>

## HIGHLIGHTS

* The radiative properties of the polyester batting material have been investigated.

* The radiative conductivity was determined with the Rosseland approximation.

* The radiative properties of polyester batting insulation depend mainly on the wavelength.

* The radiative conductivity depends on the material thickness.

## GRAPHICAL ABSTRACT

<figure><img src="image_107.png" /></figure>

## ARTICLE INFO

**Article history:**

Received 13 October 2015

Accepted 9 March 2016

Available online 21 March 2016

**Keywords:**

Insulation

Polyester batting

Radiative properties

Inverse method

Radiative conductivity

## ABSTRACT

This work presents a study on the thermal characterization of semi-transparent polyester batting insulation material for building application. This material is consisting of recycled plastic waste based polyester fibers with constant diameters. Thus, the effective thermal conductivity of this material is determined using fluxmeter devices. The radiative properties of the polyester batting (i.e. albedo, optical thickness, absorptance, etc.) have been obtained for different thicknesses of the material with the inverse method, which is based on infrared experimental measurements of reflection and transmission in the wavelengths range of 2–21 µm using a Fourier Transform Infrared Spectrometer. Thus, the radiative conductivity is determined by the Rosseland model. The radiative conductivity varies as a function of material thickness; this variation is due to the fiber density effect.

© 2016 Elsevier Ltd. All rights reserved.

## 1. Introduction

The sustainable development and the energy efficiency concepts remain of a great interest for researchers community in

particular in the thermal building field. Thus, the main objective is to bring new solutions the environment protection as well as to reduce the high energy consumption involved for the buildings process. In addition, the optimization and adoption of new alternative materials may offer important advantages for building applications. Indeed, recycled plastic can be used as potential candidate for insulation materials, since the plastic waste production

<footnote><sup>a</sup>LPSMS, Department of Physics, Faculté des Sciences et Techniques d'Errachidia, Université Moulay Ismaïl, BP 509, Boutalamine, Errachidia, Morocco</footnote>

<footnote><sup>b</sup>MMESA, Department of Physics, Faculté des Sciences et Techniques d'Errachidia, Université Moulay Ismaïl, BP 509, Boutalamine, Errachidia, Morocco</footnote>

<footnote><sup>c</sup>Laboratoire Génie Civil et géo-Environnement (LGCgE)-Lille Nord de France (EA 4515), IUT de Béthune, 1230 Rue de l'Université, F-62400 Béthune, France</footnote>

<footnote><sup>d</sup>LEMTA, Université de Lorraine, 54500 Vandoeuvre-lès-Nancy Cedex, France</footnote>

<footnote><sup>e</sup>Laboratoire Génie Civil et géo-Environnement (EA-4515), Faculté des Sciences Appliquées-Université d'Artois, Technoparc Futura, 62400 Béthune, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: tiliouamine@yahoo.fr, a.tilioua@fste.umi.ac.ma (A. Tilioua).</footnote>
Nomenclature

<table><tr><td>C<sub>p</sub></td><td>specific heat capacity of the medium, J kg<sup>-1</sup> K<sup>-1</sup></td></tr><tr><td>T</td><td>temperature, K</td></tr><tr><td>&Delta;T</td><td>temperature difference, K</td></tr><tr><td>t</td><td>temps, s</td></tr><tr><td>k<sub>e</sub></td><td>effective thermal conductivity, W m<sup>-1</sup> K<sup>-1</sup></td></tr><tr><td>k<sub>c</sub></td><td>phonic thermal conductivity, W m<sup>-1</sup> K<sup>-1</sup></td></tr><tr><td>k<sub>c&nu;</sub></td><td>convective thermal conductivity, W m<sup>-1</sup> K<sup>-1</sup></td></tr><tr><td>k<sub>r</sub></td><td>radiative thermal conductivity, W m<sup>-1</sup> K<sup>-1</sup></td></tr><tr><td>k<sub>g</sub></td><td>gas thermal conductivity, W m<sup>-1</sup> K<sup>-1</sup></td></tr><tr><td>k<sub>s</sub></td><td>solid thermal conductivity, W m<sup>-1</sup> K<sup>-1</sup></td></tr><tr><td>k<sub>s&nu;</sub></td><td>thermal conductivity of the fibers, W m<sup>-1</sup> K<sup>-1</sup></td></tr><tr><td>k<sub>g</sub><sup>*</sup></td><td>thermal conductivity of the gas at atmospheric pressure, W m<sup>-1</sup> K<sup>-1</sup></td></tr><tr><td>Q<sub>t</sub></td><td>total heat flux, W m<sup>-2</sup></td></tr><tr><td>Q<sub>g</sub></td><td>gas heat flux, W m<sup>-2</sup></td></tr><tr><td>Q<sub>s</sub></td><td>solid heat flux, W m<sup>-2</sup></td></tr><tr><td>Q<sub>r</sub></td><td>radiative heat flux, W m<sup>-2</sup></td></tr><tr><td>f</td><td>fiber volume fraction</td></tr><tr><td>f<sub>v</sub></td><td>solid fraction ratio</td></tr><tr><td>L<sub>c</sub></td><td>characteristic length, m</td></tr><tr><td>p<sub>r</sub></td><td>reflective power, %</td></tr><tr><td>d<sub>f</sub></td><td>fiber diameter, m</td></tr><tr><td>d<sub>g</sub></td><td>gas collision diameter, m</td></tr><tr><td>Pr</td><td>Prandtl number</td></tr><tr><td>Kn</td><td>Knudsen number</td></tr><tr><td>P</td><td>pressure, Pa</td></tr><tr><td>P<sub>&lambda;</sub></td><td>spectral phase function</td></tr><tr><td>L<sub>&lambda;</sub></td><td>spectral radiation intensity, W m<sup>-2</sup> &mu;m<sup>-1</sup> sr<sup>-1</sup></td></tr><tr><td>L<sub>0</sub></td><td>incident radiation intensity, W m<sup>-2</sup></td></tr><tr><td>L<sup>&deg;</sup></td><td>blackbody radiation intensity, W m<sup>-2</sup></td></tr><tr><td>T<sub>&lambda;</sub></td><td>spectral transmittance</td></tr></table>

Greek symbols

<table><tr><td>&alpha;</td><td>thermal accommodation coefficient</td></tr><tr><td>&beta;<sub>&lambda;</sub></td><td>spectral extinction coefficient, m<sup>-1</sup></td></tr><tr><td>&beta;<sub>&lambda;</sub><sup>*</sup></td><td>weighted extinction coefficient, m<sup>-1</sup></td></tr><tr><td>&sigma;<sub>&lambda;</sub></td><td>scattering coefficient, m<sup>-1</sup></td></tr><tr><td>&tau;<sub>&lambda;</sub></td><td>optical thickness of the medium</td></tr><tr><td>&omega;<sub>&lambda;</sub></td><td>albedo</td></tr><tr><td>&kappa;<sub>&lambda;</sub></td><td>absorption coefficient, m<sup>-1</sup></td></tr><tr><td>&alpha;<sub>&lambda;,exp</sub></td><td>spectral absorptance, %</td></tr><tr><td>&lambda;</td><td>wavelength, m</td></tr><tr><td>&mu;</td><td>cosine of the polar angle</td></tr><tr><td>&mu;<sub>1</sub></td><td>first direction</td></tr><tr><td>&gamma;</td><td>specific heat ratio</td></tr><tr><td>&rho;</td><td>density of the medium, kg m<sup>-3</sup></td></tr><tr><td>&rho;<sub>s</sub></td><td>density of the solid constituting the fibers, kg m<sup>-3</sup></td></tr><tr><td>d&Omega;<sub>0</sub></td><td>solid angle, sr</td></tr><tr><td>&Sigma; &phi;</td><td>sum of flux, W m<sup>-2</sup></td></tr></table>

Superscripts

* weighted coefficient

Subscripts

<table><tr><td>&lambda;</td><td>spectral</td></tr><tr><td>E</td><td>thickness, m</td></tr></table>

Physical constants

<table><tr><td>&sigma;</td><td>Stefan–Boltzmann constant, 5.67040 &times; 10<sup>-8</sup> W m<sup>-2</sup> K<sup>-4</sup></td></tr><tr><td>C<sub>1</sub></td><td>radiation constant, 1.19 &times; 10<sup>-16</sup> W m<sup>-2</sup></td></tr><tr><td>C<sub>2</sub></td><td>radiation constant, 1.4388 &times; 10<sup>-2</sup> m K</td></tr></table>

in of great increases is all countries [1]. The performances optimization of these new materials requires a good knowledge of basic phenomena on the heat and mass transfer that coexist in a complex medium geometrically. The fibrous materials traditionally used for building insulation are of porous media family, where the contribution of the convection can be often neglected [2]. In order to optimize the energy efficiency of the insulation materials, in particular the fibrous insulating material, it is important to control the radiative as well as conductive heat transfer. Thus, the heat transfer by radiation can play an important role in fibrous media with low density. In addition, several research works have been reported concerning the problem of radiative transfer inside the porous materials in order to determine the radiative parameters based on the inverse method that allows to study different types of complex materials [3–6]. Moreover, two approaches for determining the radiative properties have been proposed by Baillis and Sacadura [7]; the microscopic approach based on Maxwell’s equations solutions and geometric optics combined with diffraction theory, and the macroscopic approach based on the minimization of the quadratic differences between the theoretical values and measurements of directional reflectance and transmittance combined with of the radiative transfer equation (RTE) solutions. Thus, several studies have focused on the modeling of radiative properties of fibrous media for insulation. Indeed, Milandri et al. [8] calculated the radiative properties of the silica wool from the Mie theory applied to an infinity long circular cylinders for the fibers that are distributed randomly in planes parallel to the boundaries of the sample. The determined radiative properties were compared to those obtained by inverse method based on

experimental measurements of bidirectional reflection and transmission of silica wool samples taking into account several simplifying assumptions axial symmetry (i.e. axial symmetry, no emission, medium considered as being isotropic and the limits of the phase function usually used Henyey–Greenstein phase function associated with the function of Lorentz). Thus, Sacadura [9] presented a method combining both theoretical prediction and experimental identification of the radiative properties of semi-transparent materials. Moreover, a few works have been reported for the heat transfer through the polyester insulating; McKay et al. [10] have been used the Mie theory to determine the extinction coefficient and absorption of the polyester fiber with randomly oriented fibers. Also the refractive index of the fibers were determined from transmittance and reflectance measurements on the material in thin films form. Thus, the radiative properties obtained are used to determine the radiative thermal conductivity with the Rosseland approximation and have allowed to estimate the total heat flux through the medium between two parallel plane plates at different temperatures. In addition, Zhao et al. [11] have used the macroscopic approach based on Monte Carlo method for the modified radiative properties, such as the extinction coefficient, the scattering albedo and phase function, by estimation analysis parameters using measured transient temperature data taken from the fibrous sample, which one surface of the sample is heated by graphite radiant; it was found that the estimated radiative properties become time-independent after about t = 3000 s. However, Nicolau et al. [12] proposed an inverse method to determine the radiative properties of fiber glass and silica fibers-cellulose with random distribution, considering the
<figure><img src="image_108.png" /><figcaption>Fig. 1. (a) Scanning electron micrographs of fibrous insulation sample polyester fiber and (b) scanning electron micrographs of fibrous insulation sample polyester fiber showing the diameter fiber.</figcaption></figure>

following simplifying assumptions (i.e. azimuthal symmetry without emission term). The radiative properties are determined by minimizing the square of the differences between measured and calculated bidirectional transmittances, which the phase function is represented with Henyey and Greenstein. Baillis et al. [13] have been reported the radiative properties of open cell polyurethane foam from directional-directional transmittance, directional-hemispherical transmittances and reflectances measurements in the wavelength infrared region of 2–15 µm. The discrete ordinates method is used to solve the radiative transfer equation. Moreover, Zhao et al. [14] have determined the modified factor of extinction coefficient and the equivalent albedo of scattering taking into account anisotropic scattering in fibrous insulation, and a modified factor of extinction coefficient and equivalent albedo of scattering are defined. Thus, Lee and Cunnington [15] presented an improved theoretical model that predict the radiative properties and heat transfer by radiation in fibrous thermal insulation with high porosity. The investigated radiation heat-transfer model is based on the diffusion approximation using a modified Rosseland mean coefficient. This model was validated comparing numerical predictions with spectral transmittance and reflectance experiments data. Then, Lee [16] have developed a radiation model based on the two-flux approximation for fibrous media with fibers spatial orientation. The radiation model is developed in order to evaluate the effect of fiber orientation on the radiative heat transfer through fibrous media between parallel planar diffuse boundaries. Thus, the analysis of this study reveals that the polar orientation of the fibers strongly affects both the backscatter factor and radiative heat transfer, and the radiative heat transfer is independent of the azimuthal direction of the fibers. Kaemmerlen et al. [17] presented the radiative properties of the wood wool with inverse method based on infrared experimental measurements of reflection and transmission, which have taken into account some hypotheses to solve the Radiative Transfer Equation (RTE). The emitted radiation by the medium is not taken into account in the RTE, because the incident radiation is modulated at the FTIR spectrometer source output. It was assumed that there is an axial symmetry in the distribution of fibers in the planes parallel to the boundaries and in the radiative boundary conditions (i.e. quasi-normal incidence); the azimuthal dependence in the RTE was neglected.

The aim of this work is to study mainly the conductive and radiative heat transfer inside a polyester batting particular material, and to determine the contribution of each mode of heat transfer. The studied material was obtained from the recycled post-consumer polyethylene terephthalate (PET) bottles [18]. This

material is composed of the cylindrical fibers distributed more or less randomly in plane (Fig. 1), which is considered as the semi-transparent, absorbing and scattering material. To our knowledge this is the first time that the inverse method was used to investigate the radiative properties of the polyester batting. For the thermophysical measurements of materials, we have used the fluxmeter devices. The radiative properties of materials will be determined by the inverse method from the directional-hemispherical transmittance and reflectance measurements with FTIR spectrometer.

## 2. Physical model

The large majority of the fibrous materials generally used for the buildings insulation are of the family of porous media. The total thermal conductivity (i.e. effective conductivity) within the fibrous materials is consisting of conduction, convection and radiation [8]:

$$k_e = k_c + k_{cv} + k_r \quad (1)$$

The investigated fibrous media in the present work are made of two phases, solid matrix containing fibers and gas phase formed of air. Indeed, the thermal transfer can take place by conduction, natural convection and radiation. However, at ambient temperature, the air may be considered at rest, and consequently no convection movement; the heat transfer by convection through the fibrous material can be neglected at room temperature, and the heat exchange is governed only by conduction and radiation. Therefore, two modes of heat transfer occur simultaneously for the fibrous medium; the conductive transfer through the fibrous matrix and gas phase (i.e. Qs and Qg), and the radiative heat transfer (i.e. Qr). Indeed, the total heat flux becomes [19]:

$$Q_t = Q_g + Q_s + Q_r \quad (2)$$

The conduction and radiation heat transfers are governed by the conservation of energy and radiative transfer equations. The total thermal equilibrium can result from energy conservation equation that defines the coupling between the conductive heat transfer and radiative one, which is obtained from an energy balance in a volume element associated to the total thermal energy conservation. For only conductive and radiative heat transfers, the energy conservation equation can be written as the following formula:

$$\rho C_p \frac{\partial T}{\partial t} = \frac{\partial}{\partial x} \left( k_c \frac{\partial T}{\partial x} \right) - \frac{\partial Q_r}{\partial x} \quad (3)$$
$$Q_r = -k_r \frac{\partial T}{\partial x} \qquad (4)$$

$$\rho C_p \frac{\partial T}{\partial t} = \frac{\partial}{\partial x} \left( k_c \frac{\partial T}{\partial x} \right) \qquad (5)$$

$$k_e = k_c + k_r \qquad (6)$$

$$\begin{aligned} \rho C_p \frac{\partial T}{\partial t} &= -\operatorname{div}(Q_t) = -(\operatorname{div}(Q_c) + \operatorname{div}(Q_r)) \\ &= -\frac{\partial}{\partial x} \left( k_c \frac{\partial T}{\partial x} \right) - \frac{\partial Q_r}{\partial x} \end{aligned} \qquad (7)$$

## 2.1. The conductive heat transfer

The heat transfer by conduction in the fibrous media is a complex phenomenon, which the complicated structure of the media is constituted of a fluid as well as solid phase. However, when the fluid pore size is very small compared to the macroscopic dimensions of the medium, the propagation of conduction heat may be taken into account using a simple Fourier's law as that used for homogeneous materials. For 1-D heat transfer, the conductive heat flux density is expressed more simply by the following formula:

$$Q_c = -k_c \frac{\partial T}{\partial x} \qquad (8)$$

The heat transfer is effected by conduction through the solid fibrous matrix and the immobile interstitial gas (i.e. absence of natural convection), and by radiation. Thus, the phonic thermal conductivity $k_c$ of the fibrous medium depends strongly on the thermal conductivities of the two phases $k_s$ and $k_g$, which are the thermal conductivities of solid and gas inside the fibrous material, respectively. The phonic thermal conductivity may depends also on the morphology of the fibrous medium, in particular on the porosity, the degree of division of the solid phase and the thermal contact resistance between the fibers:

$$k_c = k_g + k_s \qquad (9)$$

The effective thermal conductivity $k_e$ is obtained by superposition of the thermal conductivities of solid conduction, gas conduction and radiation:

$$k_e = k_g + k_s + k_r \qquad (10)$$

In addition, the heat transfer by conduction depends on a large number of parameters such as the conductivity of solid and fluid phase, the morphology of the solid matrix, the proportion and distribution of each phase. Karamanos et al. [20] have reported the equation for calculating the total thermal conductivity by conduction as [21,22]:

$$k_c = k_s + \frac{k_g - k_s}{1 + \frac{f}{1+f} \cdot \left[ 1 + z \cdot \frac{k_g - k_s}{k_g + k_s} \right]} \qquad (11)$$

where f the fiber volume fraction and z a coefficient; z = 1 when the fibers are vertically oriented to the direction of the heat flux, z = 2/3 when the fibers are oriented at random, and z = 5/6 when 50% the fibers are vertically oriented to the direction of the heat flux and the 50% remaining randomly oriented. In addition, Daryabeigi [23] has reported the following formula:

$$k_c = (1 - f)k_g + f^3 k_{sf} \qquad (12)$$

## 2.2. Solid conduction

For solid conduction heat transfer, Karamanos et al. [20] have proposed a more interesting equation for the thermal conductivity across the fibers as:

$$k_s(T) = f^2 k_{sf}(T) \qquad (13)$$

f is the fiber volume fraction:

$$f = \frac{\rho}{\rho_s} \qquad (14)$$

## 2.3. Gas conduction

Daryabeigi et al. [24] presented a thermal conductivity of the gas, which is not pressure depending, and the exchange of heat from gas molecules to adjacent solid surfaces is influenced by the environmental pressure in the rarefied and transition flux transport regimes. Thus, the effective thermal conductivity of the gas is defined by the following formula:

$$k_g = \frac{k_g^*}{\Phi + 2 \cdot \frac{\Psi}{\rho_r} \cdot Kn} \qquad (15)$$

The parameter $\chi$ is defined as

$$\chi = \frac{2 - \alpha}{\alpha} \cdot \frac{2\gamma}{\gamma + 1} \qquad (16)$$

$Kn$ the Knudsen number, which is given as:

$$Kn = \frac{\Lambda}{L_c} \qquad (17)$$

While mean free path on gas is:

$$\Lambda = \frac{K_B T}{\sqrt{2\pi d_g^2 P}} \qquad (18)$$

The $\Phi$ and $\Psi$ parameters depend on the Knudsen number: $\Phi = 1$, $\Psi = 0$ for $K_n < 0.01$ (continuum regime), $\Phi = 1$, $\Psi = 1$ for $0.01 < K_n < 10$ (transition regime), $\Phi = 0$, $\Psi = 0$ for $K_n > 10$ (free molecular regime). To define the pore size $L_c$ as well as to estimate the gas conduction contribution in the fibrous insulation, we can use an empirical formulation as:

$$L_c = \frac{\xi}{f} \frac{df}{f_v} \qquad (19)$$

The value of the constant $\xi$ is of 0.524 for fibers randomly oriented in space, and of 0.785 for fibers randomly oriented in planes [24]. We can take the value 0.785 because the material fibers studied in or work are randomly oriented in a plane.

## 2.4. Determination of the radiative properties

The radiative properties provide informations on the behavior of the fibrous medium such as the optical thickness and albedo. For the radiative properties investigation, we have used the inverse method based on the experimental measurements. These radiative properties were identified from the three following physical quantities: directional hemispherical reflectance (DHR$_{\lambda,th}$) (Eq. (20)), directional hemispherical transmittance (DHT$_{\lambda,th}$) (Eq. (21)) and direct transmittance (DT$_{\lambda,th}$) (Eq. (22)). Thus, the radiative properties of the medium were characterized for each wavelength by in optical thickness (calculated for $x = E$ in Eq. (26)), the albedo and the phase function. DHR$_{\lambda,th}$, DHT$_{\lambda,th}$ and DT$_{\lambda,th}$ are theoretically given by:

$$\text{DHR}_{\lambda,\text{th}} = -2\pi \frac{\int_{-1}^{0} L_{\lambda}(0, \mu) \mu \, d\mu}{L_o \, d\Omega_o} \qquad (20)$$

$$\text{DHT}_{\lambda,\text{th}} = -2\pi \frac{\int_{0}^{1} L_{\lambda}(E, \mu) \mu \, d\mu}{L_o \, d\Omega_o} \qquad (21)$$
$$DT_{\lambda,\text{th}} = \frac{L_{\lambda}(E, \mu_1)}{L_0} \qquad (22)$$

In order to calculate the radiative intensity variation in directions characterized by $\mu$, we resolved the RTE equation (26). The radiative intensity variation depends on three parameters; optical thickness $\tau_{\lambda}$, albedo $\omega_{\lambda}$ and phase function $P$, which are defined as:

$$\tau_{\lambda} = \beta_{\lambda}z \qquad (23)$$

and

$$\omega_{\lambda} = \frac{\sigma_{\lambda}}{\beta_{\lambda}} \qquad (24)$$

The monochromatic extinction coefficient can be written as the sum of absorption $\kappa_{\lambda}$ and scattering coefficients $\sigma_{\lambda}$:

$$\beta_{\lambda} = \kappa_{\lambda} + \sigma_{\lambda} \qquad (25)$$

Several methods exist to solve the RTE equation and to determine the radiative properties; in our case we chosen the matrix method. For a non-gray absorbing, emitting, and anisotropic scattering medium of thickness $E$, assuming heat transfer in the x-direction, with an axial symmetry like that reported by Modest and Özışık [25,26]; the RTE becomes as follows:

$$\mu \frac{\partial L_{\lambda}(x, t)}{\partial x} = \kappa_{\lambda} L_{\lambda}^{0}(x, \mu) - \beta_{\lambda} L_{\lambda}(T) + \frac{\sigma_{\lambda}}{2} \int_{-1}^{1} P_{\lambda}(\mu' \to \mu) L_{\lambda}(x, \mu') d\mu' \qquad (26)$$

for $0 < x < E$, $\mu \in [-1, 1]$, $\lambda > 0$.

In this equation, the terms on the right hand side describe the internal emission, extinction phenomena and the intensity, respectively of the scattering in the $\mu$-direction. $L_{\lambda}^{0}(T)$ is the monochromatic intensity of the black body at the temperature $T$, given by Planck's law as:

$$L_{\lambda}^{0}(T) = \frac{C_{1}}{\lambda^{5}(\exp\left(\frac{E_{\lambda}}{T}\right) - 1)} \qquad (27)$$

$P(\mu', \mu)$ is the scattering phase function, which is the fraction of radiative energy scattered into the outgoing direction $\mu$ from the incoming direction $\mu'$. We have adapted this method to our problem neglecting the internal emission. The discretization of the RTE gives:

$$\mu_j \frac{\partial L_{\lambda}(\tau_{\lambda}, \mu_j)}{\partial \tau_{\lambda}} = -L_{\lambda}(\tau_{\lambda}, \mu_j) + \frac{\omega_{\lambda}}{2} \sum_{k=1}^{m} P_{\lambda}(\mu_k \rightarrow \mu_j) L_{\lambda}(\tau_k, \mu_k) C_k^{\mu} \qquad (28)$$

for $1 \le j \le m$. Where $C_k^{\mu}$ is the associated weight with the direction $\mu_k$ for the used quadrature. The hypotheses used are as follows:

- The symmetry is azimuthal at the level of the radiative boundary conditions (i.e. near normal incidence).

- The azimuthal angle $\phi$ is not depending in the radiative transfer equation.

- The internal emission of medium is neglected.

- The boundaries of the sample are supposed transparent due to the high porosity of the medium.

From simplifying hypotheses and introducing new quantities (albedo and optical thickness), the RTE may be written as:

$$\mu \frac{\partial L_{\lambda}(\tau_{\lambda}, \mu)}{\partial \tau_{\lambda}} = -L_{\lambda}(\tau_{\lambda}, \mu) + \frac{\omega_{\lambda}}{2} \int_{\mu'=-1}^{1} P_{\lambda}(\mu' \to \mu) L_{\lambda}(\tau_{\lambda}, \mu') d\mu' \qquad (29)$$

The boundary conditions are as follows:

At the front surface of the sample, $L_{\lambda}(z = 0, \mu > 0) = L_0$ for $\mu_0 < \mu < 1$ and $L_{\lambda}(z = 0, \mu > 0) = 0$ elsewhere. $\mu_0$ represents the direction of the incident beam, which depends on the experimental setup.

At the back of the sample, $L_{\lambda}(z = 0, \mu < 0) = 0$.

For the present calculations, isotropic scattering phase function $P$ was used for the numerical inversion taking into account the Henyey-Greenstein model and direct transmittance measurements. The inverse method consists of determining of the medium radiative properties by minimizing the average standard deviation between theoretical and experimental DHR. DHT and DT; the minimization is performed by the Lsqcurvefit method [27]. Thus, a method was developed with MATLAB software, which the minimization calculation involves the gradient of $F$ calculated from a derivation of the RTE compared to each sought parameters. The function to be minimized is then written as:

$$F = \left[ \frac{\text{DHR}_{\lambda,\text{th}} - \text{DHR}_{\lambda,\text{exp}}}{\text{DHR}_{\lambda,\text{exp}}} \right] + \left[ \frac{\text{DHT}_{\lambda,\text{th}} - \text{DHT}_{\lambda,\text{exp}}}{\text{DHT}_{\lambda,\text{exp}}} \right] + \left[ \frac{\text{DT}_{\lambda,\text{th}} - \text{DT}_{\lambda,\text{exp}}}{\text{DT}_{\lambda,\text{exp}}} \right] \qquad (30)$$

Theoretical values of DHR$_{\lambda,\text{th}}$, DHT$_{\lambda,\text{th}}$ and DT$_{\lambda,\text{th}}$ were calculated by solving Eq. (29) as a function of $\mu$ and wavelength $\lambda$. A numerical quadrature similar to the one used by Kaemmerlen et al. [17] was employed, using a Gauss quadrature with 44 points equally spaced between 0 and 180 for the angular discretization. Thus, the solid angle was determined with the bidirectional and hemispherical reflectances measurements. The calculation method of solid angle was described by Milandri et al. [8]. The solid angle of the beam was obtained by the following formula: $d\Omega = 2\pi(1 - \cos\theta_0) = 0.0038$, where $\theta_0 = 2.8$ being the divergence half-angle of the incident beam used for the sample illumination. The spectral absorption and scattering coefficients $\sigma_{\lambda}$ and $\kappa_{\lambda}$ could be recovered using Eqs. (24) and (23). The experimental data for the transmission and reflectance given by the FTIR were obtained for wavelengths of 2333. Moreover, we retained 50 values in order to present the total evolution of the experimental transmission and reflectance according to the spectrum.

## 2.5. The radiative conductivity

The spectral extinction coefficient can be obtained from Eq. (31) using the measured spectral transmittance; it is plotted as a function of wavelength. Experimental measurements on the spectral transmission with FTIR are performed for different thicknesses of polyester batting fibrous insulation material; radiative heat conductivity was determined by calculating extinction coefficient using Beer's Law as [28]:

$$T_{\lambda} = \exp \left( - \int_{0}^{E} \beta_{\lambda} dx \right) \qquad (31)$$

For a homogeneous sample, $\beta_{\lambda}$ is not depending on the sample thickness, then Eq. (31) can be reduced to $\beta_{\lambda}$:

$$\beta_{\lambda} = - \frac{\ln(T_{\lambda})}{E} \qquad (32)$$

And the radiative conductivity $k_r$ as:

$$k_r = \frac{16\sigma T_m^3}{3\beta_R} \qquad (33)$$

$\beta_R$ is the Rosseland mean extinction coefficient given by:

$$\frac{1}{\beta_R} = \int_{\lambda=0}^{\infty} \frac{1}{\beta_{\lambda}^*} \frac{dL_{\lambda}^{\circ}(T_m)}{dL_{\lambda}^{\circ}(T_m)} d\lambda \approx \int_{b}^{a} \frac{1}{\beta_{\lambda}^*} \frac{dL_{\lambda}^{\circ}(T_m)}{dL_{\lambda}^{\circ}(T_m)} d\lambda \qquad (34)$$

In order to take into account anisotropic scattering by insulation, a weighted spectral extinction coefficient $\beta_{\lambda}^*$ substitutes the real spectral extinction coefficient. The $\beta_{\lambda}^*$ was defined as $\beta_{\lambda}^* = \kappa_{\lambda} + \sigma_{\lambda}^*$ and $\sigma_{\lambda}^* = \sigma_{\lambda}(1 - g_{\lambda})$ [29]. The optical thickness and weighted spectral extinction coefficient can be given as:
$$ \tau_{\lambda}^{*} = \beta_{\lambda}^{*} z \quad \text{and} \quad \omega_{\lambda}^{*} = \frac{\sigma_{\lambda}^{*}}{\beta_{\lambda}^{*}} \qquad (35) $$

The radiative conductivity is conventionally calculated with the Rosseland mean.

$$ k_r = \frac{16\sigma T^3}{3} \int_{b}^{a} \frac{1}{\beta_{\lambda}^{*}} \frac{dL_{\lambda}^{\circ}(T_m)}{dL_{\lambda}^{\circ}(T_m)} d\lambda \qquad (36) $$

### 3. Experimental details

#### 3.1. The overall thermal conductivity

The used experimental device is based on fluxmeter measurements, which was developed and validated by Duthoit [30] in order to study the behavior of different types of materials for buildings construction field. This fluxmeters device allows to realize several tests on different temperature ranges. In our work, the operating temperature range of the experimental device can range from 10 °C to 60 °C, which allows us to characterize the heat transfer of our fibrous polyester batting material. Thus, through a developed program under LabVIEW environment the temperature may be imposed on two faces of the sample, each sample surface was contacted with an exchange plate connected to a thermostated bath. This latter allows to circulate a fluid coolant at fixed temperature inside the exchange plates. Each exchange plate (50 cm × 50 cm) is connected to a type T thermocouple, which have a sensitivity of the order of Θ = 40 μV/°C. These thermocouples gives us measured temperature values on each sample surface. The polyester batting was cut in the form of parallelepipedic plate (dimension 30 cm × 30 cm) with thickness E, which is placed between two plane plates compared temperatures (Tc and Tf). A heat flux settles then between the two plates. Indeed, we have used the following relationship:

$$ Q_t = -k_e \frac{\Delta T}{\Delta z} \Rightarrow k_e = \frac{|Q_t| \Delta z}{\Delta T} = \frac{|Q_t| E}{\Delta T} \qquad (37) $$

where Qt (W/m²) is the average surface heat flux Qtc and Qtf measured at the level of the hot and cold plates, respectively.

$$ Q_t = \frac{Q_{tc} + Q_{tf}}{2} \qquad (38) $$

<figure><img src="image_109.png" /><figcaption>Fig. 3. Thermal conductivity according to temperature.</figcaption></figure>

Concerning the heat flux measurements, two fluxmeter types “Tangential gradients” with a sensitivity of the order of 6.445 μV/(W/m²) and with surface of 15 × 15 cm² are placed on the two exchange plates. Fig. 2 shows an illustration of the experimental device. We have linked the fluxmeters and thermocouples to a multimeter (Keithley 2700) and a computer in order to visualize the measured signals. Before proceeding with the measurements we have achieved the calibration of fluxmeters as well as of the two fluxmeters that gives a sensitivity of the right fluxmeter equal to 154.4 μV/(W/m²) and the sensitivity of the left fluxmeter equal to 156.2 μV/(W/m²). For the fibrous material thermal conductivity estimation, we imposed a temperature difference between the two faces of the sample until a steady state, which the value of the apparent can be extracted the following relationship:

$$ k_e = \frac{E \sum \varphi}{2 \Delta T} \qquad (39) $$

where ΔT is the difference temperature, E is the thickness of the sample and Σφ the sum of flux. The uncertainty on the conductivity can be calculated from the following formula:

$$ \frac{\delta k}{k_e} = \left( \left( \frac{\delta Q}{Q} \right)^2 + \left( \frac{\delta E}{E} \right)^2 + \left( \frac{\delta \Delta T}{\Delta T} \right)^2 \right)^{0.5} \qquad (40) $$

The heat transfer which was established within the insulation was one-dimensional (1-D), and the edge effect is negligible. The parameters that can influence the measured value of the thermal conductivity are the error on the measurement of the

<figure><img src="image_110.png" /><figcaption>Fig. 2. Experimental fluxmeter device.</figcaption></figure>
temperatures of hot and cold plates, the spectral emissivity of the hot and cold plates, the thickness of the tested sample and the samples moisture content.

As expected, the overall conductivity can be deduced from the relation (39) that links $k_t$ to the total heat flux $Q_t$, the thickness of the sample E and the temperature difference between the two sides of the insulator. We noticed a value of $k_t = 0.036$ W/m K (Fig. 3), which is lower of 4% compared to the experimental one, due to the radiative conductivity that is underestimated by 4% when considering the radiative properties determined by the predictive model for the average size of the polyester batting; this has a little influence on the calculated heat flux.

## 3.2. Experiment details RDH & TDH

The spectroscopic properties of fibrous materials have been investigated in order to achieve our characterization, and to clarify the behavior of fibrous media for radiation. Indeed, we have performed measurements on different thicknesses of the fibrous polyester insulating material. Thus, we presented the transmission and reflection hemispherical measurements, which are made from 5000 averaged scans to limit the noise measurements. The measurements will be carried out on a range of wavelength 2–20 µm. The VERTEX 80 V Brucker Fourier Transform Spectrometer was used in the investigated study. The out beam from the spectrometer focused on the sample and then collected by an integrating sphere after transmission or reflection. The sphere is specifically dedicated to the infrared range with a coating of infragold with reflective power of 0.95 reflectivity (i.e. manufacturer specifications). The diameter of the sphere (15 cm) and the size of the beam

(the diameter of a circle is 1.8 cm) are widely superior to the observed inhomogeneities on samples (of the order of the mm). Thus, the detector is of MCT type, cooled with liquid nitrogen; the maximum wavelength range is 0.83–11.76 µm. The fibrous material has been placed in the sample holder ensuring their perpendicular holding to the input window of the integrating sphere. Indeed, the samples are kept in the rings at the edges and the measurements were made directly on the material without the need for maintaining by a transparent window, which avoids any parasitic reflection problem on the sample holder. The basic method include the measurements on open sphere in input without sample and is closed in output $\Phi_{reference}$, the measurements of “zero”: sphere open input and output without sample in reflection $\Phi_0$, and the measurements with sample in transmission and reflection ($\Phi_{sample}^r$ and $\Phi_{sample}^t$). The directional–hemispherical transmittances and reflectances DHT$_{λ,exp}$ and DHR$_{λ,exp}$ were then evaluated by:

$$ DHR_{λ,exp} = p_r \frac{\Phi_{sample}^r - \Phi_0}{\Phi_{reference}^r - \Phi_0} \qquad (41) $$

$$ DHT_{λ,exp} = \frac{\Phi_{sample}^t}{\Phi_{reference}^t} \qquad (42) $$

Two experiment types have been carried out for the specular and hemispheric measurements. Fig. 4(a) and (b) illustrates the protocols of hemispherical measurements for the three sizes DH, DHT and DT. At the detector level, we will retrieve the reflected or transmitted radiation through the sample in all directions, the deflector shown in Fig. 4(a) allows to avoid direct illumination of the detector. In order to obtain a value of absolute reflectivity, the evaluation of $\rho_λ$, the reflectivity value of 0.95 was introduced.

<figure><img src="image_111.png" /><figcaption>Fig. 4. (a) Investigation mode, sample position in the integrating sphere and (b) direct transmittance measurement.</figcaption></figure>