Xavi Antonio Tom

José, Lina, Jorge, Ulises, Yingying, Cécile, Mehrez, Paul, Youse Wen Mehdi

Cyril

Gérard, Fouzia, Marie, ... Audrey

Kiki

Dorian Baptiste

Mickaël, ... Pierre Valérie

of the natural ventilation air ow rate North Openings at Shed-roof Leaks Openings North Height

Keywords: Natural ventilation, heat ux measurement, sensible energy charge-discharge, air ow simulations, airtightness tests, superposition of wind and buoyancy e ects

energy balance and in (2) the concrete slab by non-uniform heat conduction, as well as, of representing (3) the natural air ow rate accounting for wind and thermal buoyancy e ects simultaneously via a semi-empirical model.

A

Couplage entre ventilation naturelle et stockage-déstockage d'énergie sensible en bâtiments : approche expérimentale et modélisation As part of the searching for solutions to reduce the energy consumption related to the cooling in buildings, a naturally ventilated test platform, located in Southwest France, has been heavily instrumented in terms of heat ux and temperature measurements.

Here, we are interested in contributing to the improvement of the passive management of the thermal comfort of an existing building during the summertime, by controlling the mobile elements of its envelope, that is to say, the solar protections and the opening natural ventilation. These two mobile elements allow a priori to control the radiative and convective contributions, respectively. Then, the control of these two mobile elements vis-à-vis the dynamics of the thermal mass of the building (which in particular is subject to the charge/discharge process), will make more appropriate selections of natural ventilation strategies, this which will also minimize the need for air conditioning. Thus, such type of control should have the characteristic of being in function of the meteorology and the instantaneous thermal state of the building in order to be able to envisage a control in real time. For this type of control, it is necessary to de ne the necessary metrology and the control variables, as well as to describe the system to be controlled. This description must be su ciently simple and light to solve in order to consider the implementation of such type of control. Thus, in this context, this thesis aims rst of all to comprehend and highlight the charge/discharge process and its coupling with natural ventilation, and then to construct a simple model to describe this coupling.

The test platform is a Plus Energy House prototype, called Sumbiosi, created to participate in the inter-university competition Solar Decathlon Europe 2012. It was designed in such a way as to promote the passive storage of daytime energy in the winter and the semi-passive night storage in summer. Three main elements allow a priori these functions of energy storage and discharge: a thermally heavy-weighted oor slab located behind of the South-facing glazed-facade, xed or mobiles and programmable solar protections and openings on the South and North facades.

On the one hand, three measurement campaigns were carried out in the summertime to characterize the energy charge-discharge process and identify their nature. For this, a semi-empirical model is developed for decoupling the super cial heat transfer into its convective and radiative components, using couples of black and shiny heat ux meters. Correlation analysis is employed, to spot relevant heat-transfer couplings between the indoor and outdoor environment. On the other hand, the natural ventilation in the platform is characterized in terms of the air ow capacity of the openings and the natural air ow rate. The former is determined in situ by performing airtightness tests, and the latter, by transient air ow simulation using CONTAM software.

Finally, a thermal model is developed to describe the behavior of the platform, based on its thermal characterization. This model consists of representing the heat transfers in (1) the indoor air via a global R Couplage entre ventilation naturelle et stockage-déstockage d'énergie sensible en bâtiments : approche expérimentale et modélisation Dans le cadre de la recherche de solutions visant à réduire la consommation d'énergie liée au rafraîchissement des bâtiments, une plateforme expérimentale, située dans le Sud-ouest de la France, a été fortement instrumentée en termes de ux thermique et de température.

Ici, on s'intéresse à contribuer à l'amélioration de la gestion passive du confort thermique d'un bâtiment existant en période estivale, par pilotage des éléments mobiles de son enveloppe, c'est-à-dire, les occultations solaires et les ouvrants de ventilation naturelle. Ces deux éléments mobiles permettent a priori de contrôler les apports radiatifs et convectifs, respectivement. Alors, le pilotage de ces deux éléments mobiles vis-à-vis de la dynamique de la masse thermique du bâtiment (qui notamment est soumise au processus de stockage/déstockage), permettra de faire des sélections plus adéquates des stratégies de ventilation naturelle, ce qui permettra aussi de minimiser le recours à la climatisation.

Alors, un tel pilotage devrait avoir la caractéristique d'être en fonction de la météorologie et l'état thermique instantané du bâtiment a n de pouvoir envisager un contrôle en temps réel. Pour ce type de contrôle, il y a besoin de dé nir la métrologie nécessaire et les variables de contrôle, ainsi que de décrire le système à piloter. Cette description doit être su samment simple et légère à résoudre a n d'envisager de faire un tel type de contrôle. Ainsi, dans ce cadre, les travaux de cette thèse ont pour objectif tout d'abord de comprendre et mettre en évidence le processus de stockage/déstockage et son couplage avec la ventilation naturelle, et puis de modéliser ce couplage de façon simple.

La plate-forme d'essai est un prototype BEPos, appelé Sumbiosi, réalisée par un consortium rassemblé autour du campus de Bordeaux dans le cadre de sa participation à la compétition interuniversitaire Solar Decathlon Europe 2012. Elle a notamment été conçue de manière à favoriser le stockage passif de l'énergie diurne en hiver et le déstockage semi-passive nocturne en été. Trois éléments principaux permettent a priori ces fonctions de stockage et de déstockage d'énergie : une dalle à forte inertie thermique située derrière la façade vitrée orientée au Sud, des protections solaires xes ou mobiles et programmables et des ouvertures mobiles et programmables en façades Sud et Nord. D'une part, trois campagnes de mesures ont été réalisées en été pour caractériser le processus de charge-décharge et identi er sa nature. Pour cela, un modèle semi-empirique est développé pour découpler le transfert thermique super ciel dans ses composantes convectives et radiatives, en utilisant des couples de uxmètres noirs et brillants. L'analyse de corrélation est utilisée pour repérer les couplages de transfert de chaleur pertinents entre l'environnement intérieur et extérieur du bâtiment. D'autre part, la ventilation naturelle dans la plate-forme est caractérisée en termes de l'aéraulique des ouvertures et le débit d'air. Le premier est déterminé in situ par des tests d'étanchéité à l'air, et le second par simulation de ux d'air transitoires à l'aide du logiciel CONTAM.

En n, un modèle thermique est développé pour décrire le comportement de la plate-forme, basé sur vi sa caractérisation thermique. Ce modèle consiste à représenter les transferts de chaleur sur (1) l'air intérieur via un bilan énergétique global et sur (2) la dalle de béton par conduction thermique nonuniforme, ainsi qu'à représenter le débit d'air entrant en prenant en compte les e ets de vent et du tirage thermique simultanément via une approche semi-empirique.

Mots-clés: Ventilation naturelle, mesure de ux thermique, stockage-déstockage d'énergie sensible, simulations aéraulique, essais d'étanchéité à l'air, superposition des e ets du vent et du tirage thermique. L'augmentation de la consommation énergétique mondiale constitue aujourd'hui une préoccupation vitale puisque, en 2015, environ 82 % de la production d'énergie était encore basée sur des combustibles fossiles. Environ 22 % de cette consommation était due au secteur résidentiel. Ce 22 % était associé à 17 % des émissions de CO 2 [START_REF]Key World Energy Statistics[END_REF]. La majorité de la demande en énergie pour ce secteur appartient aux applications de chau age, de ventilation et de climatisation (CVC), ce qui en fait un contributeur important aux émissions mondiales de gaz à e et de serre. L'équilibre de la situation actuelle accentue la pression pour prendre des mesures, telles que celles mises en place récemment lors de la Conférence de Paris sur le climat (COP21). En conséquence, la réduction de la consommation d'énergie liée au système CVC et l'amélioration de l'e cacité des technologies utilisées dans ces applications, sont une tendance dominante de nos jours.

Unité de recherche

Sur ce sujet, dans le cadre de la recherche de solutions visant à réduire la consommation d'énergie dans les bâtiments, la réglementation thermique 2020 (RT 2020) vise à réduire cette consommation d'énergie de 50 kW•h•m -2 •an -1 en 2012 à 15 kW•h•m -2 •an -1 d'ici 2020 par le développement des systèmes énergétiques plus e caces. Ces systèmes doivent être passifs ou semi-passifs, ce qui permet d'atteindre des bâtiments à énergie nulle ou à énergie positive. Ici, on s'intéresse à contribuer à l'amélioration de la gestion passive du confort thermique d'un bâtiment existant en période estivale, par pilotage des éléments mobiles de son enveloppe, c'est-à-dire, les occultations solaires et les ouvrants de ventilation naturelle. Ces deux éléments mobiles permettent a priori de contrôler les apports radiatifs et convectifs, respectivement. Alors, le pilotage de ces deux éléments mobiles vis-à-vis de la dynamique de la masse thermique du bâtiment (qui notamment est soumise au processus de stockage/déstockage), permettra de faire des sélections plus adéquates des stratégies de ventilation naturelle, ce qui permet aussi de minimiser le recours à la climatisation. Alors, un tel pilotage devrait avoir la caractéristique d'être en fonction de la météorologie et l'état thermique instantané du bâtiment a n de pouvoir envisager un contrôle en temps réel. Pour ce type de contrôle, il y a besoin de dé nir la métrologie nécessaire et les variables de contrôle, ainsi que de décrire le système à piloter. Cette description doit être su samment simple et légère à résoudre a n d'envisager de faire un tel type de contrôle.

Ainsi, dans ce cadre, les travaux de cette thèse ont pour objectif tout d'abord de comprendre et mettre en évidence le processus de stockage/déstockage et son couplage avec la ventilation naturelle, et puis de modéliser ce couplage de façon simple. Donc, la première partie du manuscrit est dédiée à décrire l'approche expérimentale employée a n d'accomplir ces objectifs.

La mise en oeuvre d'études expérimentales permettant, en générale, d'améliorer la compréhension des phénomènes physiques, il est décidé de caractériser le transfert de chaleur dans le processus de stockage/déstockage de l'énergie sensible dans une plate-forme expérimentale à l'échelle 1 in situ. Cette vii viii plateforme fait l'objet d'un prototype de bâtiment à énergie positive (BEPos), nommé Sumbiosi, construite par un consortium ressemblé autour du campus de l'Université de Bordeaux, dans le cadre de sa participation au concours interuniversitaire Solar Décathlon Europe 2012, qui est actuellement installée sur le site de l'IUT de Bordeaux ( gures i-ii). Cette plateforme a été conçue de manière à favoriser le stockage passif diurne en hiver et le déstockage semi-passif nocturne en été. Elle présente trois caractéristiques architecturales principales qui favorisent ces fonctions de stockage et de déstockage, à savoir : une dalle de béton derrière la façade vitrée au Sud, des occultations solaires xes et programmables, et des ouvrants de ventilation naturelle programmables au Sud, au Nord et au shed. Pour adopter une stratégie de recherche visant à atteindre les objectifs spéci ques mentionés, nous devons d'abord obtenir une meilleure compréhension des phénomènes physiques qui sous-tendent le comportement thermique des bâtiments et des processus de stockage/déstockage associés à une ventilation naturelle. De même, la compréhension du rôle de l'enveloppe et de la ventilation, ainsi que des techniques expérimentales d'identi cation concernant la modélisation pour la prévision, sont essentielles. Ainsi, le premier chapitre est consacré à l'exploration et à la détermination des approches expérimentales et de modélisation les mieux adaptées à notre cas. Comme un modèle physique est recherché, nous avons également ciblé cette étude bibliographique sur les approches de modélisation pour les modèles physiques détaillés. Cette étude comprendre : le comportement thermique des bâtiments, la ventilation naturelle et la métrologie de la mesure du ux thermique sur les surfaces rigides et les procédures pour leur étalonnage. L'intérêt de ce dernier sujet peut être justi é par le fait que la ventilation naturelle interagit avec le processus de déstockage d'énergie sous forme de transfert de chaleur par convection. Comme leur couplage direct est à étudier, les mesures directes du ux convectif semblent convenir, car elles permettent de quanti er et de mettre en évidence les processus de stockage et de déstockage.

Cette étude bibliographique a permis de noter les remarques suivantes : d'abord, le couplage entre la ventilation naturelle et la masse thermique d'un bâtiment peut être étudié en considérant seulement deux bilans énergétiques simples, l'un sur l'air intérieur et l'autre sur la masse thermique, et l'équation du débit d'air de ventilation. Deuxième, l'emplacement des in ltrations doit être analysé attentivement a n d'éviter une surestimation ou une sous-estimation du taux de fuite d'air. Et troisième, l'utilisation de uxmètre à plaques plates (comme Captec®) est une bonne technique expérimentale pour estimer ix les échanges convectifs sur des parois lourdes et les modules thermoélectriques sont beaucoup plus attractifs que les uxmètres classiques en ce qui concerne leurs sensibilités et coûts.

En ce qui concerne les techniques expérimentales et de modélisation permettant d'estimer le débit d'air de ventilation naturelle, une limite s'applique à leur applicabilité à notre cas particulier : par rapport aux techniques expérimentales, qui notamment peuvent conduire à une meilleure compréhension des phénomènes impliqués, nécessitent une instrumentation lourde (souvent coûteuse) des ouvertures en termes de vitesse et de pression (locales). Et aussi, les techniques de modélisation telles que CFD nécessitent un temps de calcul important en fonction de la puissance de l'ordinateur et des modèles eux-mêmes. Les modèles basés sur des observations empiriques requièrent la connaissance des modèles de circulation d'air dans le bâtiment. Ainsi, la technique de modélisation plus adaptée à notre cas semble être l'implémentation de modèles de ux d'air réseau (network air ow models) via des simulations aérauliques directes e ectuées par un logiciel tel que CONTAM, car la connaissance du parcour de circulation de l'air n'est pas requise. La technique expérimentale la plus appropriée semble être les tests d'étanchéité à l'air, car elle permet d'obtenir des expressions empiriques reliant directement le débit d'air de ventilation à la di érence de pression dans le bâtiment dans les deux cas : in ltrations (ouvrants fermées) et ouvrants ouvertes. En outre, l'emplacement des in ltrations peut être identi é sans complications, et cette technique a le potentiel d'estimer in situ la capacité de ux d'air et les caractéristiques aérauliques ouvertures. L'étude expérimentale réalisée dans la plate-forme pour caractériser les processus de stockage et de déstockage, et leur couplage aux sollicitations thermiques extérieures, en particulier la ventilation naturelle en été, est décrite au chapitre 2. La caractérisation du stockage/déstockage vise à comprendre le comportement thermique de la plate-forme et à déterminer les phénomènes de transfert de chaleur impliqués dans chaque processus. Ils conduiront nalement à construire un modèle physique de la plate-forme qui ne considère que les paramètres clés pour décrire le comportement thermique de l'environnement intérieur.

Dans le but d'estimer les échanges convectifs et radiatifs par expérimentation, nous proposons un simple dispositif de mesure, basé sur les travaux d'autres chercheurs concernant les approches expérimentales de découplage du transfert thermique super ciel. Ce dispositif comprend les éléments suivants : un couple noir/brillant de modules Peltier, un thermocouple type T pour la mesure de température d'air, et un thermocouple type T inséré dedans le module Peltier brillant pour mesurer la température de surface ( gure iii). x Après un étalonnage judicieux des modules Peltier et thermocouples, plusieurs de ce dispositif de mesure ont été mis en place sur l'ensemble de la surface de dalle ( gure iv), sur la surface du plafond et celle du vitrage en façade Sud.

I(t) = ϕ s (t) ε s -ε b - ϕ b (t) ε s -ε b + σ • ε s • T 4 s (t) -ε b • T 4 b (t) ε s -ε b W•m -2 (1)
h C (t) = ε b ε b -ε s • ϕ s (t) ∆T s (t) - ε s ε b -ε s • ϕ b (t) ∆T s (t) W•m -2 •K -1 (2) ϕ C (t) = ε s ε s -ε b • ϕ b (t) - ε b ε s -ε b • ϕ s (t) W•m -2 (3) xi ϕ R (t) = ε b ε b -ε s • ϕ b (t) - ε b ε b -ε s • ϕ s (t) W•m -2 (4)
où ϕ C et ϕ R représentent les densités du ux convectif et radiatif, respectivement, et ∆T est la différence de température entre l'air (T ia ) et la surface. Ce dispositif de mesure et hypothèses, permettent aussi la mise en place d'une autre expression qui relie la température des environs radiatifs (T surr ) aux mesures directes de ux (ϕ b , ϕ s ) et de température de surface (T s ), donnant le suivant :

T surr (t) = 4 ϕ b (t) -ϕ s (t) [ε b -ε s ] • σ + T 4 s (t) [K] . (5)
A n d'estimer au mieu ces cinq grandeurs (eqs. [1][2][3][4][START_REF]Handbook -Fundamentals[END_REF], une étude de sensibilité par la méthode de dérivés a montré que la certitude dans la valeur d'émissivité de la surface brillante (ε s ) est la plus importante, ce qu'amène à la mesurer de façon très précise. Ce dernier fait l'objet d'un des travaux menés dans [START_REF] Yang | Innovative non-destructive methodology for energy diagnosis of building envelope[END_REF] ; les valeurs des émissivités ont été déterminées avec une certitude satisfaisante, donnant 0,069 ± 0,014 pour ε s , et 0,953 ± 0,012 pour ε b .

Une fois les trois surfaces instrumentées, trois campagnes de mesures ont été menées a n d'observer le comportement de la plateforme sous trois con gurations (où scénarios) d'ouverture/fermeture des ouvrants de ventilation naturelle (ceux en façade Sud et en shed) : ouvrants fermés en permanence (con guration 1), ouvrants ouverts en permanence (con guration 3), et n'ouvrir les ouvrants que si la température d'air extérieur est inférieure à l'air intérieur (con guration 2). Les occultations solaires programmables sont restées fermées pendant toutes les campagnes de mesures. Les résultats de ces campagnes nous ont permis de mettre en évidence les processus de stockage et déstockage dans les di érentes surfaces instrumentées, ainsi que de les quali er en ses parts convectifs et radiatifs. Par exemple, pour la con guration 2, on a pu constater que le stockage en surface de dalle est dominé par des échanges radiatifs et que son déstockage est dominé par les échanges convectifs notamment lors des moments d'ouverture des ouvrants de ventilation naturelle ( gure v). Au contraire, en surface de plafond, le stockage est dominé par les échanges convectifs et aucun déstockage a lieu vers l'ambiance intérieur.

Ces résultats de densité de ux convectif et radiatif ont été quali és à travers une comparaison avec des uxmètres classiques du type Captec® qui ont été aussi recouverts avec de revêtements noir et brillant. Une particularité sur la densité du ux convectif estimée a été trouvée, il s'agit d'une di érence récurrente de l'ordre de 2, entre la densité du ux convectif estimée à partir des mesures des modules Peltier et celle estimé à partir des mesures des uxmètres Captec® (présenté aux annexes). Ensuite, une étude à l'aide d'une analyse statistique de corrélation et des nombres adimensionnels a été mise en place a n de déterminer la nature des échanges convectifs au niveau de la surface de dalle. Les résultats de cette étude montrent qu'il n'y a pas une a nité assez forte a n de spéci er cette nature en convection naturelle ou forcée, ce qui amène à conclure qu'une convection mixte a lieu. En n, une analyse de confort thermique a été réalisée avec les données de mesures, a n de quanti er la performance de la plateforme sous une ventilation naturelle nocturne (con guration 2), à travers des indicateurs recommandés par la norme ISO 7730. Cette analyse a permis de constater que l'implémentation de cette stratégie a amené à maintenir le confort thermique d'une durée de 29 jours sur 34 journées. ces essais ont été menés à l'aide de deux portes sou antes. Dans ce cas, le coe cient de décharge de chaque ouvrant a été estimé par une égalisation de la dé nition théorique du débit d'air à travers une ouverture et des lois débit-pression obtenues des essais d'étanchéité. Puis, en vue que la valeur de ce coe cient varie pour de pressions assez faibles (notamment dans le cas où les mouvements d'air sont conduits par tirage thermique) et en attendant une valeur constante, la moyenne des valeurs résultantes pour ceux qui appartient aux pressions assez importantes a été prise. Ceci a donné : 0,40 ± 0,01 pour les ouvrants en façade Sud ; 0,31 ± 0,002 pour ceux en bas de façade Nord ; 0,28 ± 0,01 pour ceux en shed.

Une fois le modèle mono-zone construit et alimenté par les résultats de la caractérisation aéraulique expérimentale, l'emplacement des in ltrations a été dé ni. Pour cela, les simulations ont été réalisées avec deux emplacements di érentes à la fois : in ltrations equitativement réparties à la mi-hauteur des xiii façades contenantes le plus d'ouvrants et portes (dans notre cas, les façades Sud et Nord), et in ltrations concentrées sur l'armoire technique en façade Ouest. Le premier emplacement est issu d'une hypothèse faite dans le cas où on ne connaît pas la distribution réelle (suivant di cile à déterminer [20,[START_REF] Etheridge | The prediction of ventilation rates in houses and the implications for energy conservation[END_REF]). Le deuxième emplacement est issu des essais d'étanchéité, où en utilisant la poire à fumés, on a pu constater qu'y se concentrent la majorité d'in ltrations d'air.

A la n de ce chapitre, se présentent les résultats des simulations distinctes qu'ont été réalisées d'une part pour déterminer séparément le taux du renouvellement de l'air (ach) en fonction des e ets du tirage thermique et du vent, et d'autre part pour tester les deux emplacements di érents d'in ltrations. Par rapport à ce dernier, les résultats ont montré que la valeur de ach est indistincte de l'emplacement des in ltrations dans notre cas. En ce qui concerne à la valeur de ach en fonction des e ets du tirage thermique uniquement, les résultats ont été approximés par des régressions de loi de puissance, donnant l'expression générale suivante : ach ∆T = A • [∆T/T] x où les coe cients A et x ont de valeurs di érentes pour les cas d'ouvrants seuls que pour le cas d'in ltrations. De même, en ce qui concerne à la valeur de ach en fonction des e ets du vent uniquement, les résultats ont été aussi approximés par des régressions de loi de puissance, donnant l'expression générale suivante : ach W = B • [V W ] y où les coe cients B et y ont aussi de valeurs di érentes pour les cas d'ouvrants seuls que pour les in ltrations. En vue que la valeur du coe cient B dépende de la direction du vent (ϕ W ), cette valeur a été tracées en fonction de la direction du vent, et son comportement a pu être approximé par de séries de Fourier à 5 % près. La dernière partie de ce chapitre, se concentre sur le cas où les e ets du tirage thermique et du vent se trouvent simultanément (cas de convection mixte). Dans ce cas, les résultats de simulations ont pu démontrer que la superposition de ces deux e ets n'est pas dé nie par juste une addition ou reste des e ets. Ce qui amène à rechercher puis à proposer de modèles de superposition, ceci fait l'objet du début du chapitre 4.

Ainsi, le quatrième chapitre est consacré à l'identi cation d'un modèle semi-empirique permettant de décrire le comportement thermique de l'environnement intérieur, en se concentrant tout d'abord sur le modèle de l'air intérieur et puis sur le choix d'un modèle pour la masse thermique (la dalle en béton). Ce chapitre commence par le choix d'un modèle d'entre plusieurs modèles de superposition reportés dans la littérature. Pour ceci, la « vraie » valeur de ach a été identi ée en utilisant un bilan sur l'air intérieur complété par une expression de la température moyenne radiative et alimenté par les mesures de la densité du ux convectif et de températures. En comparant cette identi cation avec les modèles proposés par la littérature, on a constaté que ces modèles sous-estiment souvent la valeur identi ée de ach. Ceci amène à proposer un autre modèle de superposition, dans notre cas on a choisi un modèle de superposition multiplicative de la forme : ach = C • ach a ∆T • ach b W , inspiré d'après les travaux qui gèrent les nombres adimensionnels pour prendre en compte des phénomènes distincts sur une même grandeur. Dans notre cas, les termes ach ∆T et ach W représentent les phénomènes liés aux e ets du tirage thermique et du vent ; leurs intensités ou bien leurs in uences sur la valeur de ach est considéré à travers la valeur des exposants a et b, respectivement. A n d'identi er les valeurs de ces trois coe cients, la méthode classique d'optimisation qui cherche à minimiser la valeur de RMSE entre le modèle et la mesure a été employée. Ici, on cherche à minimiser la valeur RMSE entre la mesure de la température d'air intérieur T ia et son résultat numérique, en variant les valeurs des coe cients C, a et b, par « essais et erreur ». Après cette identi cation, on a pu constater qu'il semble exister une relation xiv forte entre les signes (positif ou négatif) des exposants et la direction du vent la plus fréquent (ou bien dominante).

La deuxième partie de ce chapitre 4 est dédiée au choix d'un modèle pour la dalle en béton. Après une évaluation avec le nombre de Biot et les résultats numériques pour un modèle 0D et un modèle 1D, un modèle de conduction unidirectionnelle qui discrétise cette dalle a été retenu, car ceci a donné une meilleure valeur RMSE respectant la température de surface de dalle (modèle et mesure). En n, ce deux modèles (air et dalle) ont été couplés faisant l'objet ultérieurement de notre modèle du coulage proposé (voir résultats en gure vi) :

                                                                                                   1) ρ(T ia ) • V ia • c p (T ia ) • dT ia (t) dt = h C D (t) • S D • T S D (t) -T ia (t) + h C P (t) • S P • T S P (t) -T ia (t) + h Cg (t) • S g • T Sg (t) -T ia (t) + V ia • ach(t) 3600 • ρ(T oa ) • c p (T oa ) • T oa (t) -ρ(T ia ) • c p (T ia ) • T ia (t) 2) ρ D • ∆z • c p D • dT D N (t) dt = T D N-1 (t) -2 • T D N (t) + T D N+1 (t) ∆z with ρ D • ∆z 2 • c p D • dT D 1 (t) dt = h C D (t) • T ia (t) -T D 1 (t) + ε D • σ • T 4 surr (t) -T 4 D 1 (t) + λ D • T D 2 -T D 1 ∆z and ρ D • ∆z 2 • c p D • dT D M (t) dt = λ D • T D M-1 -T D M ∆z 3) T Sg (t) = 1 F g→D 4 T 4 surr (t) -F P→D • T 4 S P (t) -1 -F P→D -F g→D • T 4 ia (t) -273, 15
4) ach(t) =                              C l • 4 • T ia (t) -T oa (t) T oa (t)
0,58 a l

; when NV openings closed

C v • A • T ia (t) -T oa (t) T oa (t) 1/2 av • [B v (φ) • V met (t)
] bv ; when NV openings opened

C v • A • T ia (t) -T oa (t) T oa (t)
1/2 av : If V met (t) = 0; when NV openings opened [START_REF] Chen | Evaluation expérimentale d'une stratégie domotique de pilotage des éléments mobiles : vers un contrôle semi-passif simple du confort d'été en BEPos[END_REF] En conclusion, ce modèle, basé sur la revue de la littérature concernant l'étude théorique du couplage entre ventilation naturelle et masse thermique, nous n'avons été intéressés que pour rendre compte du transfert de chaleur en deux éléments : l'air intérieur et la masse thermique (supposée être concentré dans le plancher dalle-béton). En plus de ces deux éléments, un troisième élément a été inclus : le débit d'air de ventilation naturelle. Une di érence entre notre choix de modélisation et ceux trouvés dans la littérature, tient compte les aspects suivants, issus de la caractérisation des processus de stockage/déstockage d'énergie, ainsi que sur le débit d'air de ventilation naturelle au sein de la plate-forme :

• L'intégration de la température radiante moyenne de l'environnement intérieur de la plate-forme.

• La nécessité de comptabiliser séparément les échanges de chaleur par convection entre le volume d'air intérieur ventilé et les surfaces de la dalle de béton, du plafond et de la façade vitrée, dans la représentation du transfert de chaleur air intérieur en plus des termes de ventilation et de stockage d'énergie (première expression en eq. 6).

xv

• La masse volumique (ρ) et la capacité thermique spéci que (c p ), sont dépendant de la température de l'air.

• La prise en compte des e ets à la fois du vent et du tirage thermique via un modèle de superposition multiplicative pour le débit d'air de ventilation.

• Des coe cients de transfert de chaleur par convection qui varient dans le temps. Concernant le modèle de superposition multiplicative pour le débit d'air de ventilation, une particularité a été observée : le signe des exposants pourrait devoir être ajusté en fonction de la direction du vent. Cependant, la relation entre la valeur de ces coe cients et l'in uence des e ets du tirage thermique et du vent est encore inconnue. D'autres modèles de superposition trouvés dans la littérature se sont avérés inappropriés, car ils ont été développés pour des trajectoires de circulation d'air spéci ques, dans des stratégies de ventilation naturelle simples telles que la ventilation unilatérale, transversale et tirage assisté par le vent avec un nombre réduit d'ouvertures. En n, la caractérisation thermique de la plate-forme a contribué à promouvoir la mise en oeuvre de modules thermoélectriques, en alternative aux uxmètres classiques, pour estimer les échanges convectifs et radiatifs dans le domaine du bâtiment. Les caractéristiques les plus attrayantes à prendre en compte dans l'implémentation de ces derniers, sont les suivantes :

• Le budget nécessaire, puisque le coût des modules thermoélectriques, est environ dix fois inférieur à celui des uxmètres classiques, tels que Captec®.

• Sensibilité/précision/taille, car les modules thermoélectriques génèrent un potentiel électrique plus élevé que les uxmètres classiques, pour la même taille de surface. Ce potentiel plus élevé peut permettre une estimation plus précise du ux thermique mesuré avec la même chaîne de mesure (capteur + système d'acquisition). Cette estimation précise pourrait être essentielle pour mesurer les faibles niveaux de ux thermique dans les environnements passifs.

Mots

I "The big picture"

The increase of the world energy consumption represents a vital concern nowadays since, in 2015, around 82% of the energy production was still based on fossil fuels (cf. g. 1). Around 22% of this consumption was due to the residential sector. This 22% was associated with a 17% of CO 2 emissions [START_REF]Key World Energy Statistics[END_REF].

The majority of the energy demand for this sector belongs to heating, ventilation and air-conditioning applications (HVAC), making them a signi cant contributor to global greenhouse gas emissions. The balance of the current situation increases the pressure to take action, such as those established recently at the Paris Climate Conference (COP21). They aim to restrict the increase of the greenhouse gas emissions, by holding the global average temperature rise to well below 2 • C [START_REF] Burleson | Paris Agreement and Consensus to Address Climate Challenge[END_REF]. Therefore, the reduction of energy consumption related to HVAC, and the improvement of the e ciency of technologies used in these applications is a prevailing trend nowadays.

In this matter, as part of the searching for solutions to reduce the energy consumption in buildings, in France, the 2020 Thermal Regulation (RT 2020) aims to reduce this energy consumption, from 50 kWh•m -2 •an -1 in 2012 to 15 kWh•m -2 •an -1 by 2020, through the development of more e cient energy systems (cf. g. 2). These systems are required to be either passive or semi-passive, leading to attaining zero-energy or positive energy buildings. Here, it is intended to contribute to the improvement of the "passive" management of the summer thermal comfort in an existing building, by controlling the moving parts of its envelope: the programmable solar protections, e.g., window blinds, shutters, and natural ventilation openings, e.g., windows type. These moving parts allow, in principle, to control the radiative and convective interactions between the indoor and outdoor environments. If such control of these moving parts is wanted to be a real-time controller, the description of the system being controlled needs to be su ciently simple and light Figure 1: 2015 world total primary energy production according to IEA [START_REF]Key World Energy Statistics[END_REF].

Thesis statement and speci c objectives

In this regard, we intend to verify that by performing a deep-comprehensive study of the physical phenomena regarding the coupling between the energy charge-discharge process and natural ventilation in a building, a suitable selection of a natural ventilation strategy leads to minimizing air conditioner usage regarding thermal comfort needs. This thesis focuses on rst on the comprehension and highlighting of this coupling and after the construction of a simple physical model able to describe the thermal behavior of the building under di erent weather conditions and various natural ventilation strategies. We propose to address this statement by pursuing the following speci c objectives:

1. To characterize (comprehension + highlighting) the coupling between the sensible energy chargedischarge process and natural ventilation.

2. To construct a model for describing the thermal behavior of the building considering the key parameters underlying this coupling, along with the outdoor conditions.

Since a better understanding of such coupling between these physical phenomena can be acquired by implementing experimental-based studies, it is decided to perform the characterization of the heat transfer, in the sensible energy charge-discharge process, in a full-scale test building under in situ conditions.

Charge and discharge processes and natural ventilation

So what do we call charge and discharge processes? In a 24h day-night cycle in the summertime, the building can be said to be submitted to di erent thermal stresses that are specially presented in two separate periods: the daytime and nighttime, in which the indoor environment of the building might behave di erently.

During the daytime, the building experiences a "charge process" in which the principal heat source, or more accurately yet, the only source is the solar power; which manifests in the form of solar radiation (direct and di use) and is the leading cause of wind and the rising of the outdoor air temperature [START_REF] David | Natural Science for practical use in every household[END_REF].

During this process, a passive building, a PEH, for instance, might choose to reduce the heat gains by closing the window openings and solar shades, in order to increase the total thermal resistance (and thus, increasing the building time constant), which may result in a su cient attenuation of the outdoor "heat wave" (cf. g. 3 (a)). In this case, such attenuation is primarily driven by the thermal mass of the envelope, where a poor attenuation will result in buildings with light-weight materials than in buildings with heavy-weight materials such as concrete.

During nighttime, the solar power "vanishes" causing a drop in the outdoor air temperature and the building experiences a "discharge process" (cf. g. 3 (b)). During this process, the building might choose to evacuate, as much as possible, the heat stored during the previous charge process by cooling down the indoor environment, in order to provide suitable initial conditions to attenuate the incoming heat of the following charge process. Among passive buildings, a common way to evacuate the heat stored is through natural ventilation, which will successfully cool down the indoor air and the structure, if the outdoor conditions are suitable (windy nighttime, no rain, no unbearable noises) and the heavy-weight materials are correctly placed.

Charge period

Wind

Natural ventilation in buildings is a subject that has been exhaustively studied over more than 50 years. Still, the mechanics of such physical problem hasn't been fully understood, despite the development of many descriptive models and software for air ow simulation coupled with heat transfer, to aid such an understanding. Many factors in uence the adequate implementation of natural ventilation strategies regarding the occupant's comfort needs and thus a ecting the energy consumption of the building. Among these factors, the behavior, knowledge, and tolerance of the occupants play an essential role.

In this regard, our starting hypothesis, is that the nature of these charge and discharge processes manifest in the form of convective and radiative heat transfer within the indoor environment of the building, and these processes can be decoupled into their convective and radiative parts (cf. g. 3 (c) top). For instance, in the discharge period, since the outdoor air is usually colder than the indoor air, the implementation of natural ventilation might drag in denser air, and thus, this air will enter the building by the lower parts (near the oor). In cases where a concrete slab is part of the oor as shown in gure 3, the oor will experience a discharging in the form of convection when the outdoor air interacts with the oor surface.

The test building

The building employed for implementing the experimental-based study is a Plus Energy House (PEH) prototype, named Sumbiosi (cf. gs. 4-5), built by a consortium gathered around the campus of the University of Bordeaux, as part of its participation in the inter-university Solar Decathlon Europe 2012 competition. This prototype was designed in such a way as to promote the passive energy storage in winter daytime and the semi-passive energy discharge in summer nighttime. After the competi-tion, Sumbiosi was installed in the campus of the University of Bordeaux; becoming an experimental platform for research purposes [START_REF] Madeleine | Projet SUMBIOSI -Domotique/Pilotage/Métrologie[END_REF][START_REF] Girón | Implantation de la domotique sur SUMBIOSI[END_REF][START_REF] Rouault | Système intégré de rafraîchissement d'air pour le bâtiment à base de matériaux à changement de phase[END_REF][START_REF] Rouxel | Projet SUMBIOSI[END_REF][START_REF] Serrault | Intégration et Pilotage d'un système de refroidissement d'air à Matériaux à Changement de Phase dans un bâtiment à énergie positive : le cas de Sumbiosi[END_REF]. The experimental platform is equipped with various systems helping to produce its own energy.

The solar panels and collectors with position-tracking strategies, are some of the active systems. The natural ventilation openings, a PCM heat exchanger and solar shades, are some of the semi-passive systems. Also, these semi-passive energy storage systems are intended to be coupled with the platform thermal mass. Such coupling allows the platform to enabling energy storage and discharge strategies aiming to control the thermal comfort of the indoor environment. This strategies can be automatize thanks to the home automation system (KNX and Domovea), destined to continuously monitoring the indoor air quality, and the outdoor environment.

Research strategy and organization of the manuscript

To adopt a research strategy for accomplishing these speci c objectives, we must rst obtain a better understanding of the physical phenomena behind the thermal behavior of buildings, and they chargedischarge process coupled with natural ventilation. Also, the understanding of the role of the envelope and ventilation, as well as, the experimental techniques for identi cation regarding the modeling for forecasting and the natural air ow rate, is essential.

Thus, the rst chapter is dedicated to explore and determine which experimental and modeling approaches are the more suitable for our case. Since a physical model is wanted, we also have focused this literature study on the modeling approaches for detailed physical models. This literature review will comprise: the thermal behavior of buildings, general aspects of natural ventilation, and the metrology in heat ux measurement on rigid surfaces and calibration procedures. The interest of this last topic can be justi ed by the fact that natural ventilation interacts with the energy discharge process in the form of convective heat transfer. Since their direct coupling is wanted to be studied, direct convective heat ux measurements appear to be suitable, because they allow to quantify and highlight the charge and discharge processes, as it will be shown later in this manuscript.

The second and third chapters involve an experimental part, regarding heat transfer and air ow, respectively. The second chapter is committed to characterizing the charge and discharge processes along with the phenomenology involved, within the test building, by implementing an experimental approach with heavy instrumentation in terms of heat ux and temperature. The third chapter is devoted to modeling the natural air ow rate in the test building.

Finally, the fourth chapter is dedicated to identifying a semi-empirical model for describing the thermal behavior of the indoor environment, by focusing only on the main elements of the building:

the indoor air and the thermal mass.

Scope

This chapter is devoted to comprehending the natural ventilation concept, and to assess the experimental and modeling techniques already implemented for past researchers, in the estimation of the ventilation air ow rate due to the wind and thermal buoyancy e ects. This will provide a strong theoretical grasp of the natural ventilation process as part of the main elements in the thermal behavior of buildings. These bases will help to choose the most suitable techniques to estimate the natural ventilation air ow rate in our platform. Also, regarding the coupling between natural ventilation and the energy charge-discharge process presented earlier, the techniques for estimating the convective heat ux on rigid surfaces are also assessed. Then, this chapter consists of the following four main sections:

• Natural ventilation concept in buildings, including experimental and modeling techniques.

• Building thermal behavior modeling and identi cation approaches.

• Coupling between natural ventilation and thermal mass.

• Heat ux measurement techniques for rigid surfaces.

Chapter 1 -Theoretical background and state of the art

Natural ventilation in buildings

Natural ventilation is the process of renewing the air of a room by natural means by either from in ltrations (unavoidable) or window openings (on purpose). In general, there are three leading causes 1.1. Natural ventilation in buildings

The role of natural ventilation

In a building, the role of ventilation is crucial concerning two major points: the indoor air quality (comfort and minimum air renewal rate) and the energy consumption. In this regard, natural ventilation is wanted to e ciently provide a minimum air renewal rate to keep the air stale out from the room, and thus, avoiding the use of mechanical ventilation, leading to minimizing the energy consumption.

In the present research work, we are only interested in the thermal aspects of comfort; no other aspect of comfort will be considered in further analysis.

(A) Thermal comfort:

The adequate implementation of natural ventilation in buildings strongly depends on the occupants' behavior, which is usually driven by their hygrothermal comfort needs. Many parameters in uence these comfort needs, and can be classi ed into three categories: physical, physiological, and external;

the indoor and outdoor conditions (air temperature, relative humidity, air currents), are among the physical parameters; the level of metabolic activity perform and the level of clothing, are some of the most important physiological parameters [2].

Thermal comfort indicators

Several comfort indicators can be found in the literature. In summer, the standard ISO 7730 recommend the use of the following values for comfortable indoor conditions:

• A room temperature between 23 and 26 • C,

• The di erence in vertical temperature must be less than 3 • C,

• An average indoor air speed less than 0,25 m•s -1 ,

• The degree of discomfort that measures thermal dissatisfaction.

Another parameter very evoked in the literature, is the di erence between the temperature of the interior air and the mean radiant temperature of the surrounding walls, that according to [START_REF] Ricaud | Construire une maison à énergie positive[END_REF]: a feeling of discomfort can appear beyond a temperature di erence higher than 2 • C, between the indoor air temperature and that of the ceiling, and 3 • C with that of the walls.

Nighttime ventilation as thermal comfort assistance

In regions with a signi cant temperature gradient between nighttime and daytime, night natural ventilation, if implemented adequately, arises as a good solution for the attenuation of the "heat wave" associated with the daytime period, leading to maintaining the thermal comfort for longer periods. Its application may be more attractive in o ce buildings, due to the absence of occupancy during nighttime.

Its principle consists of cooling down the structure of the building when it is not occupied (nighttime), providing a heat sink that is available during the occupancy period (daytime). This heat sink absorbs the heat gains related to occupancy or equipment and maintains acceptable indoor conditions As observed in gure 1.2, during nighttime, the temperature of the walls is higher than the air inside the o ce; therefore heat transfer will occur outwardly (from the walls to the surrounding air), successfully cooling down the walls. In detail, the temperature di erence between the indoor air and the wall surfaces is the consequence of the building interaction among other parameters, such as the outdoor air and the sky temperature, the surface temperature of the surrounding buildings, and wind e ects. A review of the night natural ventilation strategies was recently published by Solgi et al. [START_REF] Solgi | A literature review of night ventilation strategies in buildings[END_REF].

However, di erent limitations are encountered depending on the site where the building is located; urban or suburban. Also, depending, on the periods of occupancy in the building, implying that this strategy is useful for o ce buildings.

Limitations in applicability and usage

One of the most critical limitations of natural ventilation usage lays in its understanding. Some of the advantages (1-5) and limitations (6-9) regarding its applicability are [START_REF] Roulet | Santé et qualité de l'environnement intérieur dans les bâtiments[END_REF]:

1. Well accepted by occupants who understand it and control it very easily.

2. The investment required is very low or zero.

3. The energy required for air transport is free.

4. It allows high ow rates, especially for passive cooling. Air in ltrations and leakages are the unavoidable part of the natural ventilation process, due to imperfections in the envelope or joinery. They are important for indoor air quality, but if not controlled properly they could become the leading cause of heating losses. Therefore, the quanti cation of the air-leakage rate represents an important issue for prediction of the heat losses. Also, regarding the nature of the air leakages, their distribution around the envelope is often complicated to be determined [20,[START_REF] Etheridge | The prediction of ventilation rates in houses and the implications for energy conservation[END_REF].

(C) Impact in energy consumption and performance of natural ventilation strategies:

Despite it is known that the use of natural ventilation systems might reduce the overall power consumption if we applied them correctly, how much will it reduce, depends on many parameters. When applicable, natural ventilation can compensate cooling energy consumption and its energy costs and carbon dioxide emissions. The potential cooling energy that may be saved depends, of course, on the climate conditions of the building location and the internal and external heat gains [START_REF] Emmerich | Natural Ventilation Review and Plan for Design and Analysis Tools[END_REF].

When having not quite favorable climate conditions for the implementation of natural ventilation, coupling it to a mechanic system remains possible, which is accomplished in Hybrid Natural Ventilation systems. Among the performance indicators of natural ventilation strategies; a good indicator for evaluating the ventilation power is the level of air change per hour reached. Regarding the energy consumption, a good indicator is the percentage of occupied hours where minimum mechanical ventilation rates are met [START_REF] Belleri | Natural ventilation design: An analysis of predicted and measured performance[END_REF].

The natural ventilation concept

For a better understanding of the natural ventilation process, three essential aspects are introduced to de ne the concept of natural ventilation: How is it created? In which way it can be implemented in buildings? And, which architectural features can be employed? This can be illustrated in gure 1.3.

Natural ventilation is created by either buoyancy forces, wind forces, or a combination of both. These two forces can be exploited to ventilate a space by "promoting" the implementation of some strategies: single-sided ventilation, cross ventilation, or stack ventilation; and this, through some architectural features such as wind towers, wind scoops, chimneys, double facades, atria, among others [START_REF] Kleiven | Natural Ventilation in Buildings -Architectural concepts, consequences and possibilities[END_REF]. Finally, the determination of the natural air ow rate depends on the strategies implemented.

Driving forces

(A) Air ow due to wind forces:

In the case of wind driven ventilation, to bene t the most from this natural force, it is recommended that the facade with openings of a building located in a windy place must be oriented perpendicularly to the wind direction, although not strictly necessary [START_REF] Givoni | Man, Climate and Architecture[END_REF]. When the wind currents nd in their path a building, a high-pressure zone is created over the windward side (or upside) of the building, and the leeward side (or downside) experiences an under-pressure zone (cf. g. 1.4 (a)). The other sides of the building (those in the wind direction) will also experience an under-pressure status (cf. g. 1.4 (b)) [START_REF] Kleiven | Natural Ventilation in Buildings -Architectural concepts, consequences and possibilities[END_REF]. In general, the resulting dynamic pressure over the windward facade can be de ned as a function of the wind speed using Bernoulli's principle, as follows:

P v (t) = 1 2 • ρ • V 2 v (t) [Pa] (1.1)
where ρ represents the air density at outdoor temperature, and V v is the wind speed at the opening height on the windward side. The resulting air ow rate inside the building due to wind e ects depends on the windward-leeward pressure di erence, as follows:

∆P(t) = 1 2 • C p • ρ • V 2 (t) [Pa] (1.2)
where C p is known as the pressure coe cient. This pressure coe cient is introduced in the building domain to account for the pressure di erences induced by the air ow over the building envelope. A simpli ed representation of these pressure di erences is presented in gure 1.4 (a), where the windward facade of the building experiences an overpressure, while the leeward facade experiences a pressure drop with respect to the static pressure of the freestream, named dynamic pressure (P ∞ ), de ned by equation 1.1. Thus, an expression for C p 1.1. Natural ventilation in buildings can be written as follows [START_REF] Anderson | Fundamentals of Aerodynamics[END_REF]:

(b) (a)

C p ≡ P -P ∞ 1 2 • ρ ∞ • V 2 ∞ [-]
where P is the value of the pressure where the coe cient is being evaluated. ρ ∞ and V ∞ represent the density and velocity of the air ow on the freestream region, respectively. The windward facade will present positive values of C p , while the leeward facade, negative values. An overview of acceptable models to predict C p values in buildings are presented in §1.1.3.3.

(B) Air ow due to buoyancy forces:

A density gradient can induce air movement between two regions (buoyancy forces). This gradient can be created by either di erent gas concentrations, a temperature di erence, a humidity di erence, or a combination of these three. In buildings, this mentioned before can cause air movement within the same zone, between di erent zones within the building, between two facades [START_REF] Roulet | Santé et qualité de l'environnement intérieur dans les bâtiments[END_REF], and between the inside and outside of the building (cf. g. 1.5). The reason lays in that this density gradient creates a pressure di erence between the zones, normally referred to as static pressure. In this case, the overall pressure di erence can be de ned as a function of the air density of two zones (indoor and outdoor air), by Bernoulli's principle as follows:

∆P(t) = ∆ρ • g • Z = [ρ oa -ρ ia ] • g • Z [Pa] (1.3)
where g is the gravitational acceleration, and Z is the height between an upper and a lower openings (cf. g. 1.5 (a)). Note that this expression is under the assumption that the air entering the building is at outdoor air density (ρ oa ) and the air leaving the building is at indoor air density (ρ ia ). Also, in equation 1.3 it is considered that the openings height is negligible with respect to their separation (Z). However, when the openings height is not negligible (case of large openings), the use of equation 1.3 might lead to either an underestimation or an overestimation of this overall pressure di erence. In this case, the overall pressure di erence can be de ned as in equation 1.4, for the outgoing air ow [START_REF] Flourentzou | Natural ventilation for passive cooling: measurement of discharge coe cients[END_REF][START_REF] Li | Buoyancy-driven natural ventilation of a room with large opennings[END_REF]:

∆P = Z-Z NPL Z-Z NPL -z U ∆ρ • g • dz [Pa] (1.4)
where Z represents the vertical distance from the lower edge of the lower opening (L) to the upper edge of the upper opening (U); with height z U (cf. g. 1.5 (b)). The vertical distance Z NPL represents the height of the "neutral pressure level" (NPL), where the indoor-outdoor pressure di erence is equal to zero, with respect to the oor. Di erent ways to determine this height have been reported in the literature [3,[START_REF] Li | Buoyancy-driven natural ventilation of a room with large opennings[END_REF][START_REF] Roulet | Santé et qualité de l'environnement intérieur dans les bâtiments[END_REF]. For instance, the value of Z NPL can be determine by the following expression [START_REF] Li | Buoyancy-driven natural ventilation of a room with large opennings[END_REF]:

Z NPL = γ 2 1 + γ 2 • Z [m] (1.5)
where γ is the opening ratio, as follows:

γ = C d U • S U C d L • S L [-]
where C d and S represent the discharge coe cient and the opening e ective area, respectively. This vertical distance depends on the position and height of the openings. For an enclosure with a single opening, the NPL will established at half the height of this opening. For the same enclosure with another opening over the previous one at the same side, the NPL will established at half the distance between these openings, if they are of the same size. However, if they di er in size, the NPL will tend to get closer to the larger openings; and the height of the NPL is proportionally to the square of the opening surface [START_REF] Roulet | Santé et qualité de l'environnement intérieur dans les bâtiments[END_REF].

(C) Air ow due to a combined e ect:

If placing the openings at the correct location, wind e ects will join the thermal buoyancy e ect, reinforcing the ventilation air ow rate. On the contrary, not placing them correctly or if the building is not correctly oriented, the wind will mitigate the thermal buoyancy e ect reducing the building ventilation. This can be observed in gure 1.6 (a), where the openings are correctly located improving the air ow traversing the building. However, in (b), the openings are not correctly located, causing zero air ow (neutralizing both e ects) at a speci c wind speed value [START_REF] Roulet | Santé et qualité de l'environnement intérieur dans les bâtiments[END_REF].

In this interaction the wind turbulence e ect is more important than in cross-ventilation con guration [START_REF] Gładyszewska | E ect of wind on stack ventilation performance[END_REF]. However, signi cant di erences can be observed concerning the complexity of this interaction regarding theoretical or experimental approaches [START_REF] Wang | Interaction between wind-driven and buoyancy-driven natural ventilation[END_REF].

Assessment techniques for the natural ventilation air ow rate

Depending on the natural ventilation strategy implemented, the natural air ow rate can be assessed using di erent methods. Such methods can be grouped into two categories: Modeling and experimental techniques. For the determination of the air ow rate, all modeling techniques require the knowledge of the air ow capacity of the openings employed. Thus, hereafter, we address this matter in the following section. A theoretical expression describing the air ow rate caused by a pressure di erence between the upstream and downstream of an opening, can be written using Bernoulli's equation as follows:

V(t) = S • 2 • ∆P(t) ρ m 3 •s -1 (1.6)
where V represents the air ow rate in m 3 •s -1 and S represents the area of free gap sections of the opening m 2 (usually called e ective area S e f f ). This expression considers a non-frictional fully developed turbulent uid ow through the opening. If needed, the friction characteristics of the opening can be grouped in a single coe cient named the discharge coe cient (C d ) which multiples expression 1.6 here before.

For any type of uid ow through an opening, the air ow rate caused by a pressure di erence between the upstream and downstream of an opening, has been shown to follow expression 1.7:

V(t) = C • [∆P(t)] n m 3 •s -1 (1.7)
where C is called the air ow rate coe cient in m 3 •s -1 •Pa -n . Its value depends on the e ective area of the opening, and also considers its friction characteristics. The exponent n is called the ow exponent:

it takes the value of 0,5 for a fully developed turbulent ow and 1 for a laminar ow [START_REF] Sherman | Estimation of in ltration from leakage and climate indicators[END_REF] ; for values in between, the ow is said to be partially developed. It has been shown that expression 1.7 describes the best, the air-leakages rate of a room or a building, where it can be small and big holes due to imperfections [START_REF] Ghiaus | Natural Ventilation in the Urban Environment: Assessment and Design[END_REF].

Daler et al. in 1982, as found in [START_REF] Judet | Aéraulique : Principes de l'aéraulique appliqués au génie climatique. Collection des guides thématiques de l'AICVF[END_REF], reported the air ow capacity of bottom and side hung openings, for di erent opening degrees and as a function of a room indoor-outdoor temperature di erence (cf.

gs. 1.7-1.8). One of these types of openings, the bottom-hung window (also known as tilted window), is the same as the ones implemented in our test building. This coe cient can be de ned as the ratio of the empirical (or real) air ow rate to the theoretical (or ideal) air ow rate, translating the fact that the free gap area (or jet section) is smaller than the total area of the opening [START_REF] Hebbar | Performance of conical jet nozzles in terms of discharge coe cient[END_REF]. Various experimental studies have been interested in the dependence the discharge coe cient presents when the pressure around the opening varies. Flourentzou et al. in 1998 [START_REF] Flourentzou | Natural ventilation for passive cooling: measurement of discharge coe cients[END_REF] performed tracer gas and velocity measurements in situ in a three-level stack ventilated building to determine the C d . A value of 0,6±0,1 was found, and thus, it was stated that: "the accepted value for the discharge coe cient was con rmed once again" (cf. g. 1.9). with the e ective area and the type of opening, as well as, with the temperature di erence. Also, for for either still air, or wind-assisted (0 • and 180 • ) strategies; similar to those in gures 1.10 and 1.9.

However, for the stack opening, C d values changed considerable depending on the Reynolds number as shown in gures 1.11 and 1.12, for still air and wind-assisted strategies, respectively. In the case of the still air strategy, the average C d value was used, and in the case of the wind-assisted strategy, an average value from the constant region (from a Re of about 600) was taken. By determining the friction factor ξ v of the opening (S e f f = 0,377 m 2 ) to be equal to 28,9, a C d value of 0,67 was determined using the following expression:

C d = 1 1 + ξ v • S e f f S f o 2 [-] (1.8)
where S f o stands for the area of the entire section of the opening (1,82 m 2 ). S e f f represents the e ective area of the opening. Van Paassen et al. in 1998 [START_REF] Van Paassen | Control of Night Cooling with Natural Ventilation: Sensitivity Analysis of Control Stratégies and Vent Openings[END_REF] proposed the following expression to de ned the e ective area S e f f as a function of the opening angle, for tilted windows (bottom hung or side hung):

S e f f = 1 1 (z•w) 2 + 1 [2•z•w•sin( φ 2 )+z 2 •sin φ] 2 m 2 (1.9)
where z and w represent the height and width of the opening, respectively, and φ represents the opening-angle (0 -90 • ). The same expression was used latter by Krzaczek et al. in 2015 [60] for bottom hung openings. Other ways to calculate this area can be encountered in [START_REF] Caciolo | Analyse expérimentale et simulation de la ventilation naturelle mono-façade pour le rafraîchissement des immeubles de bureaux[END_REF][START_REF] Teppner | Air change rates driven by the ow around and through a building storey with fully open or tilted windows: An experimental and numerical study[END_REF].

Other models have been reported for the estimation of the discharge coe cient. Pelletret in 1991 [START_REF] Pelletret | Modelling of large openings[END_REF], proposed an empirical model for C d as a function of the ratio between the heights of the opening (z) and the room (Z), as follows:

C d = 0,609 • z Z -0,066 if 0,2 ≤ z Z ≤ 0,9 (1.10)
On the contrary, Kiel and Wilson in 2009 [START_REF]Handbook -Fundamentals[END_REF], proposed another empirical model for C d as a function of the indoor-outdoor temperature di erence, accounting for thermal buoyancy e ects, as follows:

C d = 0,4 + 0,0045 • |T ia -T oa | for 0,5 ≤ |T ia -T oa | ≤ 40 (1.11)
Moreover, a comparison of implementing these models, showing their impact on the natural air ow rate can be found in [START_REF] Stephan | Modélisation de la Ventilation Naturelle pour l'Optimisation du Rafraîchissement Passif des Bâtiments[END_REF], concluding that the estimation of this coe cient should be performed attentively. Nevertheless, to determine either the air ow capacity or the discharge coe cient of an opening, experimental data is needed. Thus, hereafter the experimental and modeling techniques employed to determine such characteristics of the openings.

Experimental techniques and empirical correlations

Many experimental techniques have been developed/employed to determine the air ow rate in naturally ventilated buildings for the case of openings closed or opened. From the literature we can cite the well known and accepted methods with few reference work (since the list is very vast):

• Direct air velocity measurements [33,[START_REF] Teppner | Air change rates driven by the ow around and through a building storey with fully open or tilted windows: An experimental and numerical study[END_REF].

• Direct air ow rate measurements [START_REF] Per | Windows: measurements of air ow capacity[END_REF].

• Tracer gas method [33,[START_REF] Flourentzou | Natural ventilation for passive cooling: measurement of discharge coe cients[END_REF].

Natural ventilation in buildings

• Particle image velocimetry [START_REF] Caciolo | Analyse expérimentale et simulation de la ventilation naturelle mono-façade pour le rafraîchissement des immeubles de bureaux[END_REF][START_REF] Heiselberg | Characteristics of air ow from open windows[END_REF].

• Wind tunnel for scaled room models [START_REF] Teppner | Air change rates driven by the ow around and through a building storey with fully open or tilted windows: An experimental and numerical study[END_REF][START_REF] Steen Larsen | Analysis and Design of Single-Sided Natural Ventilation[END_REF].

• Saline solutions for scaled dimensional analysis [START_REF] Hunt | The uid mechanics of natural ventilation-displacement ventilation by buoyancy-driven ows assisted by wind[END_REF].

• Blower door tests (or airtightness tests) [55].

In this section it is intended to present information about the air ow rate levels attained by implementing merely natural ventilation strategies. Thus, the following studies do not necessarily employ buildings and openings similar, in type and size, as our test building. Instead, we are interested in the reported air ow rate levels attained for given wind speed and direction, temperature di erence, and the experimental technique employed. Nevertheless, we include the size and type of the building and openings. Finally, to determine the air ow rate, these experimental techniques are often complemented with empirical correlations or statistical methods, but they will not be presented here in detail.

Since the majority of the studies in the literature employed these techniques for cases with simple con gurations, where the air ow path is well known (single-sided, cross or stack ventilation), and since our test building has a quite number of openings (rendering moot the assumption of a speci c air ow path, with an inlet and outlet far away from each other), the same air ow rate levels reported might not be attained in our platform.

Kronvall and Persily between 1980 and 1985, developed the K-P model, as found in Sherman 1987 [START_REF] Sherman | Estimation of in ltration from leakage and climate indicators[END_REF], to estimate the annual natural air-leakage rate of a building using airtightness tests as follows:

ach natural ≡ ach 50 20
h -1 (1.12)
which later employed data from tests performed in more than 40 houses, and achieved the following linear regression:

ach natural ≈ ach 50 18 -0, 08 h -1
where ach 50 referred to the value of ach at a pressure di erence of 50 Pa measured via blower door tests.

Gładyszewska-Fiedoruk and Gajewski in 2012 [START_REF] Gładyszewska | E ect of wind on stack ventilation performance[END_REF], studied the e ect of wind on the performance of stack ventilation by performing air speed measurements, proving that wind e ects has a considerable in uence that could change up to 350%. Freire et al. in 2013 [START_REF] Freire | Single-sided natural ventilation driven by wind pressure and temperature di erence[END_REF] (in an enclosure of 748 m 3 ) and Larsen et al. in 2003 [61] (in an enclosure of 93 m 3 ), compared measured data, from wind tunnel experiments, with di erent existing models, aiming to evaluate and improve the existing models for the case of single-sided ventilation (cf. gs. 1.14-1.15).

On the other hand, R. Jack et al. in 2015 [55], performed nine in situ airtightness tests (or blower door tests) for estimate the air change rate at natural pressure levels of a full-scale building of volume.

The air in ltration rate, for either windows closed and opened, was determined using the K-P model in equation 1.12 (cf. g. 1.16).

Models and numerical techniques

The local estimation of the impact of wind e ects on the natural air ow rate remains complicated in buildings with "non-standard" architectural features. These devices, forming part of the building enve-20 1.1. Natural ventilation in buildings lope and being either openings or entire facades with a "non-standard" morphology, make it di cult to accurately take into account the e ects of the wind on the instantaneous air ow rate. The reason lies in the needs to know the values of the external pressure coe cients and the discharge coe cients of its opening, which are not found always in the literature, for their consideration in the use of numerical air ow simulation tools.

Many researches have been undertaken for the estimation of this coe cient [START_REF] Cóstola | Overview of pressure coe cient data in building energy simulation and air ow network programs[END_REF][START_REF] Freire | Single-sided natural ventilation driven by wind pressure and temperature di erence[END_REF]. Walton in 1982 [START_REF] Walton | Air ow and multiroom thermal analysis[END_REF], presented the following empirical models for the determination of this coe cient as a function of the wind direction (φ):

C p = 0,75 -1,05 • φ 90 if φ ≤ 90 • (1.13) C p = -0,45 + 1,05 • φ 90 if φ ≥ 90 • .
On the other hand, Swami and Chandra in 1988 [START_REF] Swami | Correlations for pressure distribution of buildings and calculation of natural-ventilation air ow[END_REF], and Grosso in 1992 [START_REF] Grosso | Wind pressure distribution around buildings: a parametrical model[END_REF], proposed guidelines to determine the model for this coe cient depending on various geometrical parameters of the building and the wind incident angle. Swami and Chandra reported the following model:

C p = C p (φ = 0) • ln 1,248 -0,703 • sin φ 2 -1,175 • sin 2 φ 2 + 0,131 • sin 3 (2 • φ • G) +0,769 • cos φ 2 + 0,07 • G 2 • sin 2 φ 2 + 0,717 • cos 2 φ 2 [-] (1.14)
where φ goes from 0 to 180 • ; for higher angles are obtained by symmetry. G corresponds to the natural logarithm of the side ratio (ratio of the lengths of adjacent walls). For vertical walls, Swami and Chandra recommend using a value of 0,6 for the pressure coe cient at zero incidence angle [START_REF] Freire | Single-sided natural ventilation driven by wind pressure and temperature di erence[END_REF].

Mathews and Rousseau in 1996 [START_REF] Rousseau | A new integrated design tool for naturally ventilated buildings[END_REF], in their proposition for developing a new integrated design tool for naturally ventilated buildings, the wind e ect on the proposed ventilation model took into consideration a tted regression model for predicting C p values for each angle (cf. g. 1.17). This regression model was tted over C p values computed using experimental data from pressure measurements and the expression for this coe cient presented in §1.1.2.1. This regression model is similar to equation 1.14, but without considering logarithms, the parameter G, and the whole angle was con- Bernoulli's equation is then applied to relate every pressure node (taking into account a reference level).

For instance, in the case of zone 1 (pressure node 1) assuming that the reference level is at the hight of the ow path between nodes 1 and 2 , and the pressure is constant on the zone of each node, Bernoulli's general equations yield:

P 2 + 1 2 • ρ 2 • V 2 2 = P 1 [Pa]
and in the case where the ow path between nodes 1 and 2 is located at a hight of Z 2 with respect to the ow path between nodes 1 and 2 , then:

P 1 + g • ρ 2 • Z 2 = P 2 + 1 2 • ρ 2 • V 2 2 [Pa]
1.2. Thermal behavior modeling and identi cation approaches both expressions yield:

P 2 + 1 2 • ρ 2 • V 2 2 + g • ρ 2 • Z 2 = P 2 + 1 2 • ρ 2 • V 2 2 [Pa] .
Finally, all ow paths of one zone are related by writing the ow conservation equation. For instance, if a steady state is considered, for pressure node 1 results in:

ṁ12 = ṁ12 kg•s -1 .
The previous equation can be expressed in terms of pressure by using the expression relating the ow rate through an opening at the power of "n. " The most common numerical method to solve the system of equations is Newton-Raphson's method. Various software implementing network air ow models exists, where the most commonly used are COMIS, CONTAM, EnergyPlus, and ESP-r [START_REF] Zhiqiang (john) Zhai | Review of Natural Ventilation Models[END_REF].

1.2 Thermal behavior modeling and identi cation approaches 1.2.1 Thermal behavior of a passive building: the role of the envelope

The thermal behavior of a building can be de ned as how the building indoor environment responses to the changes in the outdoor environment. This response is represented by the dynamics of the indoor environment temperature. The performance of a building can be characterized by the following parameters:

1.2.1.1 The thermal lag (TL)

The thermal lag (sometimes referred as time shift) is de ned as the time between the maximum temperature value reached by the outdoor and indoor temperatures [38], as shown in gure 1.20. The building is characterized as to have good thermal inertia when presenting large TL values. This parameter is reported in over 24 h day-night cycle, and its values normally correspond to a few hours.

Outdoor air temperature

Indoor air temperature

Damping factor: 50%

Time lag: 6 h The damping factor is de ned as the attenuation of the outdoor temperature amplitude re ected in the indoor temperature amplitude. For instance, a value of 0,7 for the damping factor can be interpreted as the 70% of the outdoor "heat wave" is transmitted to the indoor environment; the weaker the damping factor, the building structure performance is better for the thermal comfort in the summertime [START_REF]Déphasage et amortissement[END_REF].

The time constant (TTL)

The time constant is de ned as the product of the total heat storage capacity of the structure, and the global thermal resistance which accounts for transmission losses, i.e., ventilation and conduction through the envelope [START_REF] Hedbrant | On the thermal inertia and time constant of singl-family houses[END_REF]. This before under the hypothesis that the building response is represented by the solution of a rst order di erential equation.

TTL = ∑ m • c p 1/R [h] (1.15)
where the heat storage capacity is represented by the product of the mass m and speci c heat capacity c p of the materials of the envelope. The magnitudes reported in the literature for this parameter, correspond to values larger than the thermal lag up to 100 h; about 147-184 h for thermally heavyweight houses, and about 20 h for light construction [4,[START_REF] Bonilauri | What's the "time constant" of a building?[END_REF][START_REF] Hedbrant | On the thermal inertia and time constant of singl-family houses[END_REF].

This parameter relates explicitly the thermal mass of the building envelope m • c p and the heat losses by ventilation. Thus, if the heat storage capacity of a building is wanted to be increased, to attenuate the most the outdoor "heat wave", the time constant needs to be increased. Equation (1.15) indicates that this before can be accomplished by either increasing the thermal mass or limiting the heat losses by ventilation. In this matter and regarding the cooling in passive buildings, di erent strategies might be applied, to attenuate the outdoor "heat wave", when it is the most suitable period in the 24 h day-night cycle.

Modeling approaches for forecasting in buildings

Di erent approaches exists for the construction of models regarding the forecasting of the thermal behavior of a building. Depending on the level of physical phenomena considered, these approaches can be classi ed as: black, gray and white box models (cf. table 1.1). Where the physical sense is not taken into account whatsoever (black box models), is somewhat taken into account (gray box models), and is fully taken into account (white box models).

The most common modeling approaches in building thermal application are: thermal network models (or RC models, electrical analogy), and the use of thermal dynamic simulation tools such as TRNSYS, EnergyPlus, COMFIE, among others. These modeling approaches are often implemented with a sensibility analysis (such as Morris 1991 [START_REF] Morris | Factorial sampling plans for preliminary computational experiments[END_REF]) and optimization algorithms to identify the parameters of the model, such as the thermal capacities and thermal resistances. These parameters are estimated by tting the numerical results over large sets of experimental data, minimizing the RMSE value [START_REF] Berthou | Développement de modèles de bâtiment pour la prévision de charge de climatisation et l'élaboration de stratégies d'optimisation énergétique et d'e acement[END_REF][START_REF] Recht | Analyse de la abilité de COMFIE par comparaison à des mesures: Application à un bâtiment passif[END_REF][START_REF] Viot | Fast on-Site Measurement Campaigns and Simple Building Models Identication for Heating Control[END_REF]. Non-sensitivity to the set of parameters chosen

Coupling between natural ventilation and thermal mass

The coupling between natural ventilation and the thermal mass of the building, has been study for either design purposes [START_REF] Zhou | Coupling of thermal mass and natural ventilation in buildings[END_REF], night ventilation assessment [16,[START_REF] Feuermann | On the potential and e ectiveness of passive night ventilation cooling[END_REF], merely theoretical purposes on the thermal behavior [START_REF] Zhou | Coupling of thermal mass and natural ventilation in buildings[END_REF][START_REF] Yang | Fluctuation of natural ventilation induced by nonlinear coupling between buoyancy and thermal mass[END_REF][START_REF] Yam | Nonlinear coupling between thermal mass and natural ventilation in buildings[END_REF], or a combination of these before [38].

From these studies we will detail those who aid to the understanding of such coupling since it is the primarily topic of our present work. As found in the literature, the study of such coupling is based mainly on three key elements: the heat transfer in the indoor air, the heat transfer in the thermal mass, and the ventilation air ow rate. In this regard, Feuermann and Hawthorne in 1991 [START_REF] Feuermann | On the potential and e ectiveness of passive night ventilation cooling[END_REF], and Along with the following equation:

ρ • c p • V • [T o -T i ] + R i • S • [T W -T i ] + E = M • ρ M • c p M • ∂T i ∂t [W]
where T W corresponds to the inner surface temperature, expressed by:

T W = TW + S sol-air v e • cos(ω • t -φ sol-air -φ e ) + S i v f • cos ω • t -φ i -φ f [ • C]
where TW corresponds to the average inner surface temperature, the second term on the right refers to the uctuation of the inner surface temperature caused by the variation of solar-air temperature under constant indoor air temperature conditions. The third is similar to the second term but induced by the variation of the indoor air temperature under constant outdoor air temperature conditions. The coe cients (v e , v f ) and angles (φ sol-air , φ e , φ i , φ f ), refer to the damping factors and phase shift for the external walls respectively, with respect to the outdoor air temperature and indoor air temperature.

From this analysis, although theoretically, the latter developed a simple tool to estimate the amount of internal thermal mass needed, i.e., furniture, in order to maintain a desirable indoor air temperature by increasing the time constant.

On the other hand, Yam et al. in 2003 [111], by assuming a natural air ow rate only driven by thermal buoyancy forces, studied the nonlinear coupling between natural ventilation and the thermal mass by considering the main uctuation frequency of the variables. The nonlinearity is due to the air ow rate dependence on the temperature di erence at the power of 1/2. This research studied the behavior of the indoor air using indicators such as the phase shift, for two cases (cf. g. 1.22): (a) the indoor thermal mass is not in equilibrium with the indoor air (2C2R), and (b) both are in equilibrium (1C2R).

For the case (a) where the thermal mass is not in equilibrium with the indoor air the equations employed were as follows:

ρ • c p • V • [T o -T i ] + h M • S M • [T M -T i ] + E = 0 [W] M • ρ • c p • ∂T M ∂t + h M • S M • [T M -T i ] = 0 [W] V = C d • A * • sgn (T i -T o ) • 2 • g • h • T i -T o To m 3 •s -1 1.3.
Coupling between natural ventilation and thermal mass where M represents the mass of the thermal mass, and A * represents the equivalent free airstream area of the two-openings con guration. For the case (b) where the thermal mass is in equilibrium with the indoor air the equation employed was the following:

ω • M • ρ • c p • ∂T i ∂(ωt) + ρ • c p • V • [T o -T i ] = E [W]
where ω is the frequency of the outdoor temperature variation in h -1 . Finally, in each case, the solar radiation was not included because no heat transfer through the envelope was considered, and the outdoor temperature was assumed to be represented by the sum of sinusoidal components of a 24 hours

period (T o = To + ∆ To • sin(ω • t)
). This analysis and numerical results showed that the consideration of the nonlinearity does neither change the behavior of the system, nor the behavior of the indoor air temperature phase shift, when a periodic (ideal) outdoor air temperature pro le is considered.

Finally, the most recent theoretical study of such coupling was performed by Yang and Guo in 2016 [START_REF] Yang | Fluctuation of natural ventilation induced by nonlinear coupling between buoyancy and thermal mass[END_REF]. This study was focused on the harmonically uctuation introduced by natural ventilation into the thermal behavior of an enclosure experiencing ventilation by buoyancy forces only. The model considered an indoor air not in equilibrium with the internal thermal mass (2C4R). In this case, where the thermal mass is not in equilibrium with the indoor air, the equations employed were as follows:

ρ • c p • V • [T o -T i ] + R e • S e • [T o -T i ] + E = ρ • c p • V • ∂T i ∂t + h M • S M • [T i -T M ] [W] M • ρ • c p • ∂T M ∂t + h M • S M • [T M -T i ] = 0 [W]
where the subscript e indicates "envelope. " Here, it was assumed that the heat source is large enough as to avoid downward ows (inverse sense with respect to the one shown in gure 1.23); thus the air ow rate is expressed by:

V = C d • A * • 2 • g • h • T i -T o To m 3 •s -1 .
The nonlinear coupling was rst decomposed into the corresponding multi-frequency uctuations, decoupled and solved, and then, recomposed for the indoor air temperature and the resulting air ow rate. For this study, an experimental apparatus that ts the theoretical enclosure conditions was constructed to validate the theoretical analysis; air temperature and airspeed measurements were performed (cf. g. 1.25). Both analytical and experimental results showed that coupling between thermal mass and buoyancy inside a building could lead to multi-frequency (or an-harmonic) uctuation of natural ventilation (cf.

g. 1.25). The phase shifts of the high-order indoor air temperature uctuation terms (with respect to the 1 st -order outdoor air temperature uctuation term) can exceed π/2 [START_REF] Yang | Fluctuation of natural ventilation induced by nonlinear coupling between buoyancy and thermal mass[END_REF].

Note that all these studies mentioned above, considered the lumped-capacitance approximation for the heat transfer in the thermal mass, i.e., null temperature gradients. In contrast, Holford and Woods in 2007 [START_REF] Holford | On the thermal bu ering of naturally ventilated buildings through internal thermal mass[END_REF], considered uniform and non-uniform conduction heat transfer in the thermal mass in their study, and showed that the uniformity assumption could be very applicable to the fully-mixed spaces and thermal mass with thin layers. For thermally strati ed spaces, this assumption may have limitations. For the thermal mass with thick layers, the temperature uctuation could be only concentrated at the surface. However, the lumped-capacitance approximation is useful for fundamental investigation of the thermal balance in a naturally ventilated space [START_REF] Holford | On the thermal bu ering of naturally ventilated buildings through internal thermal mass[END_REF].

In summary:

The coupling between natural ventilation and the thermal mass of a building can be studied by only considering two simple energy balances, one on the indoor air and another on the thermal mass, along with the equation for the ventilation air ow rate.

Heat ux measurement techniques for rigid surfaces

This section rst brie y describes the heat ux measurement theory for a at-plate-type of heat ux sensor, the Théry-type (referred here as FGT), and for another kind of sensor, the thermoelectric module (also known as Peltier modules, referred here as TEM). Second, a brief review concerning experimental techniques that have been used for heat ux detection or measurement is presented along with proposed approaches for decoupling the convection and radiation parts of the heat ux measured. Third, the perturbations introduced by heat ux sensors, spotted by past researches, are discussed. Finally, experimental techniques for at-plate heat ux sensors are described. The quanti cation of the heat ow rate is essential for a large variety of thermal applications, as it is for the presented work. The measurement of this type of sensors is based on the Seebeck e ect. Several and very small thermocouple junctions are connected in series, i.e., as a thermopile, distributed all over the surface of an insulated support (based on the printed circuit board technique). This support is then covered by two plates of copper, on each side. When both plates of this embedded element are submitted to di erent temperatures, each of the thermocouple junctions generates a potential di erence due to the temperature gradient. This potential di erence (U) is proportional to the heat ux traversing the sensor (ϕ), and they are related by a thermoelectric coe cient [START_REF] Cherif | Super cial heat transfer by forced convection and radiation in a horizontal channel[END_REF][START_REF] Thureau | Fluxmètres thermiques[END_REF][START_REF] Wu | Thermal characteristics in situ monitoring of detached house wall constituted by raw clay[END_REF] (cf. g. 1.26). These sensors are also able to measure the temperature of the surface where they are being placed. This before can be represented by a simple equation as follows:

ϕ(t) = U(t) K W•m -2 (1.16)
where U is normally expressed in µV and ϕ is the heat ux measured or traversing the sensor. U can take positive and negative values, depending on the heat ux direction and on the polarity connection of the sensor. The coe cient K groups the thermoelectric properties of the sensor, e.g., the Seebeck coe cient, the total number of thermocouple junctions and the thermal conductivity, normally expressed in µV•m 2 •W -1 and it is usually determined by calibration techniques. It could be demonstrated to be equal to the following expression:

K = N • a eq • e λ eq µV•m 2 •W -1 (1.17)
where N corresponds to the number of thermocouples junctions, e the thickness of the active section of the sensor, a eq the equivalent Seebeck coe cient, and λ eq the equivalent thermal conductivity.

Moreover, the coe cient K does not vary with temperature due to the thermoelectric properties of the materials used for this kind of sensors; their thickness is around a tenth of a millimeter. For example, the Captec® enterprise, o ers square heat ux meters with a dimension range between 5x5 mm 2 and 300x300 mm 2 of surface area with a thickness of 0,5 mm. Depending on these dimensions, their sensibility value can vary from some µV•m 2 •W -1 to a around a hundred of µV•m 2 •W -1 , for instance, a 50x50 mm 2 presents a sensibility of around 20 µV•m 2 •W -1 , and a 150x150 mm 2 presents a sensibility of around 120 µV•m 2 •W -1 ; where the cost of the latter may reach the 400€ each.

Thermoelectric modules

The thermoelectric modules, also known as Peltier modules, are composed of several thermocouple junctions connected electrically in series and thermally in parallel, integrated between two ceramic plates [START_REF] Rowe | CRC Handbook of Thermoelectrics[END_REF] (cf. g. 1.27). These thermocouple junctions consist of a n-and a p-type semiconductor materials connected by small and thin copper tabs. These modules are widely available in the market, normally used in electronics for cooling purposes, where the most common semiconductor materials

(2) However, these modules can also be used for power generation [START_REF] David | Caractérisation des propriétés thermoélectriques des composants en régime harmonique : Techniques et Modélisation[END_REF]. For heat ux measurement or heat ux detection, they work in an open circuit con guration when connected to a multimeter or an acquisition system for data collection [68]. In this case, they follow a similar relation between the potential di erence generated when a heat ux is traversing the module (cf. eq. 1.16). Even though they may have the particularity of a K coe cient dependent on temperature due to the semiconductor materials of the thermocouples junctions, and the time response is about one minute. The dimensions availability for this type of module is limited, but for the same dimensions a TEM presents a sensibility value of about a hundred times larger than the sensibility value of a conventional heat ux meter; their cost lays around the twentieth of euros.

1.4.2 Implementation of heat ux meters for measuring the super cial heat exchanges

1.4.2.

Estimation of the convection and radiation heat exchanges

The measurement of super cial heat exchanges, i.e., convection and radiation, using FGT sensors and thermoelectric modules, have been a topic of interest of various researchers [START_REF] Vultaggio | Les méthodes de la théorie du signal appliquées à l'analyse des transferts thermiques sur la surface d'une paroi opaque en régime variable[END_REF][START_REF] Herin | Conception et caractérisation de capteurs de ux radiatif et convectif : application aux mesures « in situ[END_REF][START_REF] Lassue | Analyse des échanges radiatifs et convectifs à la surface d'une paroi opaque : application à la commande optimale du système habitat[END_REF][START_REF] Harzli | Etude et réalisation d'un nouveau capteur de rayonnement thermique : Application à la detection du rayonnement provenant de sources lointaines[END_REF][START_REF] Douiri | Instrumentation dun four pilote pour la cuisson de genoise[END_REF][START_REF] Cherif | Super cial heat transfer by forced convection and radiation in a horizontal channel[END_REF][START_REF] Wu | Thermal characteristics in situ monitoring of detached house wall constituted by raw clay[END_REF][START_REF] Azerou | Conception, réalisation et mise en oeuvre de uxmètre thermiques passif et dynamique à base de couches minces[END_REF][START_REF] Yang | Innovative non-destructive methodology for energy diagnosis of building envelope[END_REF]. The interest lays in the possibility of splitting the convection and radiation parts from the heat ux measurement. This brings us to the question: can convection and radiation heat exchanges be separated from a heat ux measurement in a mixed environment? Thus, this review is focused on the implementation of such sensors for the estimation of both super cial heat exchanges; any other case was excluded. However, other research works have been found regarding the implementation of such sensors in the thermal characterization of walls, among which we have [START_REF] Lassue | Mesures uxmétriques et notion d'impédance thermique appliquées à la caractérisation d'une paroi de bâtiment soumise à des sollicitations naturelles[END_REF][START_REF] Legloanec | Non-intrusive thermal measurement methods adapted to painted cave walls[END_REF][START_REF] Vultaggio | Les méthodes de la théorie du signal appliquées à l'analyse des transferts thermiques sur la surface d'une paroi opaque en régime variable[END_REF].

In the late 80s, a technique to estimate the convection and radiation heat exchanges on a surface was implemented, consisting of using two FGT sensors, where one was to be coated with a black surface and the other with a shiny surface. Then, under the premise that the black and shiny surfaces had Chapter 1 -Theoretical background and state of the art emissivities close to 1 and 0 respectively, the former was said to estimate the total heat ux (convection + radiation) and the latter to estimate the convection heat ux on the rigid surface where they installed the sensors, e.g., heavyweight and lightweight walls, and isolate-type wall. Herin in 1988 [START_REF] Herin | Conception et caractérisation de capteurs de ux radiatif et convectif : application aux mesures « in situ[END_REF] worked on the design and characterization of convective and radiative heat ux meters applied to in situ measurements. The heat ux meters (25 x 25 x 0,02 cm and 30 µV•m 2 •W -1 ), coated with foils with contrasted emissivities, were tested with the objective of separating the convective and radiative components when installed inside a climatic chamber (cf. g. 1.28). The heat ux and temperature measurements were validated, allowing the separation of the convective and radiative components on heavyweight and lightweight walls, and also the determination of the thermophysical properties of such walls. In the early 90s, Lassue et al. in 1992 [START_REF] Lassue | A Convective and Radiative Flux Sensor for Designing Thermal Comfort Controllers[END_REF], implemented the estimation of the convective and radiative heat ux, using at-plate heat ux meters (0,01 cm thick and 20 µV•m 2 •W -1 ), for the design of thermal comfort controllers (cf. g. 1.29). These heat ux meters, coated with thin foils of contrasted emissivities (near 1 and near 0), were placed in the concrete wall of the enclosure (cf. g. (b)).

In principle, the comfort control was proposed to be done by using the radiative heat ux as the control variable, in addition to the room temperature, for controlling four radiative panels installed on the ceiling, leading to achieve low cost controllers (taking into account the time delay of the room) with the permanent installation need of heat ux meters.

Moreover, Lassue et al. in 1993 [START_REF] Lassue | CONTRIBUTION TO THE EXPERIMENTAL STUDY OF NATURAL CONVEC-TION BY HEAT FLUX MEASUREMENT AND ANEMOMETRY USING THERMOELECTRIC EF-FECTS[END_REF], used heat ux meters (25 x 25 x 0,02 cm and ∼3 µV•m 2 •W -1 ) coated with a thin polished aluminum foil and a prototype of airspeed/temperature sensor both based on the use of thermoelectric e ects (designed to measure very small airspeeds), as to propose a new experimental approach for measuring the convective heat transfer coe cient on heavyweight walls.

Results were found to agree with values reported in the literature for the case of laminar free convection along a vertical and isotherm heated plate.

One decade later or so, similar experiments were performed using FGT sensors: Douiri in 2007 [START_REF] Douiri | Instrumentation dun four pilote pour la cuisson de genoise[END_REF][START_REF] Sommier | Characterization of sponge cake baking in an instrumented pilot oven[END_REF] (Captec®, 2 x 2 x 0,04 cm and ∼3 µV•m 2 •W -1 ), for measuring the heat exchanges that an object will experience inside a particular type of oven for drying purposes (cf. g. 1.30). The front face of the wall was submitted to solar radiation heat ux and the rear face, to indoor air conditions. A heat dissipater (or heat sink) was installed on the sensor's surface in contact with the indoor air, to increase the heat ow rate through the sensor. Experimental results were compared with simulation, nding an average absolute di erence of 6,7±2,7% with maximum and minimum values of 10,5% and 0,1%, respectively. The other experiment consisted of coating the thermoelectric module surface in black to measure solar radiation heat ux (cf. g. 1.33 (b)); this was compared latter with a pyrometer. From this second experiment, it was pointed out that satisfactory results were encountered as the average of the absolute di erences was 4,8±3,9%, which lead to conclude that the sensor 1.4. Heat ux measurement techniques for rigid surfaces measurement can be used for radiation heat ux without knowing the exact emissivity value.

Recently, in 2017, Yang [START_REF] Yang | Innovative non-destructive methodology for energy diagnosis of building envelope[END_REF] used both types of sensors: Captec®, 5 x 5 x 0,04 cm and ∼18 µV•m 2 •W -1 , and thermoelectric modules, 3 x 3 x 0,35 cm and ∼0,39T+139 µV•m 2 •W -1 . The experiments were designed to characterize the thermal properties of a multilayer wall, placing a group of sensors on the front and rear faces, in two cases: in situ and under laboratory conditions (cf. g. 1.34). In the laboratory case, a black and shiny pair of FGT and TEM were installed at the front face of the wall which was latter heated by 6 halogen lamps (cf. g. 1.34 (a)); the rear face was maintained at room temperature.

In the in situ case, only black and shiny FGT sensors were employed (cf. In summary:

The studies reviewed show that the implementation of the heat ux meters di ered in geometry and arrangement, i.e., black and shiny sensors installed with one of their sides always in contact [START_REF] Cherif | Super cial heat transfer by forced convection and radiation in a horizontal channel[END_REF][START_REF] Douiri | Instrumentation dun four pilote pour la cuisson de genoise[END_REF] and installed with a separation between them [START_REF] Lassue | A Convective and Radiative Flux Sensor for Designing Thermal Comfort Controllers[END_REF][START_REF] Wu | Formalisme des impedances thermiques généralisées. Application à la caractérisation thermique de parois de bâtiments[END_REF][START_REF] Yang | Innovative non-destructive methodology for energy diagnosis of building envelope[END_REF]. The silicon thermal grease is used to reduce the contact thermal resistance when placing the heat ux sensors on walls.

Also, the heat ux and temperature measurements when using conventional heat ux meters for estimating the convective heat transfer coe cient on non-isolated walls type, have been shown

to be in strong accordance with the values reported in the literature.

Analytical approaches for splitting the convective and radiative heat exchanges

Cherif et al. [START_REF] Cherif | Super cial heat transfer by forced convection and radiation in a horizontal channel[END_REF] proposed a way to separate the convective and radiative parts from the heat ux measurement. The principle is based on a heat energy balance on the surface of the heat ux sensor, well-placed onto a wall surface, which is submitted to convection (ϕ C ) and radiation (ϕ R ) heat exchanges. The total heat ux (ϕ T ) on the sensor's surface is equal to the sum of ϕ C and ϕ R . Also, this is equal to the heat ux traversing the sensor (ϕ). This before could be expressed for any surface i as follows:

ϕ i (t) = ϕ C i (t) + ϕ R i (t) W•m -2 (1.18)
Chapter 1 -Theoretical background and state of the art It was stated that the heat ux measurement, on both sensors (black and shiny), would have a convection and radiation part, owing to the emissivity value of the black and shiny coating they used: a black paint (0,98) and a thin aluminum foil (0,1), respectively. Thus, the convection heat ux was determined by subtracting the radiation part from the shiny sensor measurement. This radiation part was computed using the "classical radiosity method" and also by numerical simulation on the Fluent software.

Going further on the emissivity issue, they analyzed numerically if the results depended on the emissivity value of the black coating. Changing the emissivity value from 0,9 to 1 (a perfect black body), it was found that increasing the emissivity yield to an increase in the total heat ux. Finally, it was concluded that the experimental procedure allows uncoupling the convection and radiation parts from the measurement since the relative error obtained was 5% maximum between the experimentation and numerical results. It is worth mentioning that the heat ux levels in this experiment reached up to 350 W•m -2 , as it will in uence later the permissible error range for the present work.

Hereafter, we will referred to the measurement of the black and shiny heat ux meters as ϕ b and ϕ s , respectively. The heat balance on the black and shiny sensors, using equation 1.18, results in:

ϕ b (t) = ϕ C b (t) + ϕ R b (t) W•m -2 (1.19) ϕ s (t) = ϕ C s (t) + ϕ R s (t) W•m -2 .
(1.20) Douiri [START_REF] Douiri | Instrumentation dun four pilote pour la cuisson de genoise[END_REF] based the analysis in equations 1.19 and 1.20, but wanted to estimate the heat convection coe cient (h C ) and the mean radiant temperature (here referred as T surr ). This consisted of de ning the convection part using Fourier's convection equation. For the radiation part, the Kirchho 's hypothesis for radiation heat transfer was employed. This two magnitudes depended on several parameters, in which the temperatures (T b , T s ) and emissivities (ε b , ε s : 0,93 and 0,1, respectively) of both sensors played an important role:

ϕ b (t) = h C (t) • [T air (t) -T b (t)] + ε b • σ • T 4 surr (t) -T 4 b (t) W•m -2 (1.21) ϕ s (t) = h C (t) • [T air (t) -T s (t)] + ε s • σ • T 4 surr (t) -T 4 s (t) W•m -2 . (1.22)
It should be noted here, that this approach is under two hypotheses: (i) having only one convection coe cient for both sensors and (ii) the temperature measured by the sensor is that of its surface. The working heat ux ranges were of the order of 1500 W•m -2 for the convection and 500 W•m -2 for the radiation heat uxes.

Yang [START_REF] Yang | Innovative non-destructive methodology for energy diagnosis of building envelope[END_REF], also based the analysis on the heat balance equations presented previously for determining the convective heat transfer coe cient (h C ), with the di erence that the emissivity values of each coating were determined, with good precision, by using the emissivity measurement method proposed in the standard ISO 18434-1:2008(E). After separating the convection and radiation heat uxes from sensors measurement, good concordance was found when comparing the estimated radiation heat ux with a pyrometer. Moreover, a signi cant di erence was found between the convective coe cient h C . From this, it was inferred that the di erence encountered was strongly related to the di erence in the sensors thickness, but no further studies were reported (the thickness of the TEM was 8,75 times greater than the FGT thickness).

Radiative heat ux meters

More e ort has been put into the estimation of the radiative heat ux. For instance, Herin in 1988 [START_REF] Herin | Conception et caractérisation de capteurs de ux radiatif et convectif : application aux mesures « in situ[END_REF] and El Harzli in 1993 [START_REF] Harzli | Etude et réalisation d'un nouveau capteur de rayonnement thermique : Application à la detection du rayonnement provenant de sources lointaines[END_REF] worked in the development of a radiative heat ux sensor, based on the same reasoning mentioned in the previous paragraphs. In this case, several black and shiny strips are placed next to each other intercalated and carefully wired as to superposed the electric potential given by each strip (cf. g. 1.36). One advantage of this type of sensor is that it allows to estimate the radiative heat ux directly from the sensor electrical response. This type of sensors is widely available in the market, e.g., Captec enterprises.

Perturbations and uncertainties introduced by the heat ux meter

Herin [START_REF] Herin | Conception et caractérisation de capteurs de ux radiatif et convectif : application aux mesures « in situ[END_REF] compared its measurements with simulation results for two di erent cases, to estimate the errors in steady state: (i) the heat ux sensors (25 x 25 x 0,02 cm and ∼35 µV•m 2 •W -1 ) placed on a vertical concrete wall (thermally heavyweight), (ii) the heat ux sensors placed on a polystyrene wall (thermal isolation). For the rst case, the convection heat ux was encountered to be overestimated by near 26% and the radiation heat ux to be underestimated by practically 35% (cf. g. 1.37 (a)). For the second case, the error on the radiation heat ux was around the -79% and on the convection heat ux was between 250 and 350% (cf. g. 1.37 (b)). For the case of isolate wall types, it was concluded that the estimation of the convective and radiative components is complexed and a temperature correction under the sensors is needed (in the sensor-wall interface, T s ), where errors were said to be mainly this was also pointed out in [START_REF] Thureau | Fluxmètres thermiques[END_REF] and [START_REF] Lassue | Analyse des échanges radiatifs et convectifs à la surface d'une paroi opaque : application à la commande optimale du système habitat[END_REF].

(

(2)

(a) (b) (3) (4)
Figure 1.37: Simulation results in steady state conditions [START_REF] Herin | Conception et caractérisation de capteurs de ux radiatif et convectif : application aux mesures « in situ[END_REF]. (a) In the case of a shiny heat ux meter place on a concrete wall submitted to:

(1) ϕ R = 20 W•m -2 , (2) ϕ R = 20 W•m -2 and ϕ C = 4 • [20 -T s ] W•m -2 . (b)
In the case of a shiny heat ux meter place on a polystyrene wall submitted to the same heat uxes as in case (a): ( 3) and ( 4), respectively. For the case of errors caused by the local temperature modi cations on the wall surface, a correction needed for the temperature of the shiny heat ux meter was also evoked in [START_REF] Lassue | Analyse des échanges radiatifs et convectifs à la surface d'une paroi opaque : application à la commande optimale du système habitat[END_REF][START_REF] Lassue | A Convective and Radiative Flux Sensor for Designing Thermal Comfort Controllers[END_REF], for cases when these sensors are placed onto an isolated-type wall.

In transient state, when a heat ux sensor is placed onto a surface, it will absorb the heat ow at the same rate as the wall if their thermal e usivities are the same. Also, the condition that the sensor's heat storage capacity is negligible concerning the heat ow traversing it must be veri ed to perform measurements in a transient state. Finally, he stated that the measurement error is proportional to the mismatching between the sensor and the wall, i.e., the di erence between the e usivities λ • ρ • c p and C/R of both, the sensor and the wall [START_REF] Herin | Conception et caractérisation de capteurs de ux radiatif et convectif : application aux mesures « in situ[END_REF].

Leephakpreeda [68] pointed out that the amount of the detected heat ux through the wall was not identical to the amount that would be detected without the sensor. Two reasons were given to explain this di erence: (i) the changes in the wall boundary conditions and (ii) the e ect of the thermal contact resistance between the thermoelectric module and the wall. The same reasons were stated years before, for at-plate sensors, by Thureau [START_REF] Thureau | Fluxmètres thermiques[END_REF] in 1996 in a technical report describing rst the theory of various types of heat ux sensors, a few calibrations methods and then giving various causes of perturbation introduced by the used of these sensors. Concerning the latter, one of them that haven't already be cited here, is the modi cation of the nature of the tested object surface: the thermal radiation properties, regarding the radiation heat transfer, and the roughness and thickness added to the tested surface, in regard of the convection heat transfer.

In summary:

From the aforementioned, it can be concluded that the scrupulously design and characterization of the conventional heat ux meters allow the estimation of the convective and radiative heat ux and the convective heat transfer coe cient, on heavyweight and lightweight walls, with great accuracy. The estimation of these parameters seems to be improved by the knowledge of the contrasted emissivity values, as the analytical approaches shown that the latter plays an important role in the accuracy of the estimated heat uxes. However, for the case of Peltier modules, when used for heat ux measurement, a di culty arises when trying to estimate the convective heat ux and convective coe cient. This might be strongly related to the very design of these devices (geometry and materials), which does not involve any problem for their natural application but seems to a ect the estimation of such parameters as accurate as the conventional heat ux meters. Nevertheless, no other study has been encountered concerning this last remarked.

Calibration techniques for at-plate type of heat ux sensors

The calibration process for heat ux sensors is usually employed to determine the sensor sensibility value K and the perturbations it introduces, regarding its equivalent speci c thermal capacity C and its equivalent thermal resistance R [START_REF] Oter-Duthoit | Application des méthodes de la théorie des systèmes à la simulation de l'évolution des ux thermiques sur les faces dd'entrée et de sortie d'une parois multicouche[END_REF]. The most common technique implemented for calibration has been the zero-ux method. Used by many researchers, some of them have been cited here before [START_REF] Oter-Duthoit | Application des méthodes de la théorie des systèmes à la simulation de l'évolution des ux thermiques sur les faces dd'entrée et de sortie d'une parois multicouche[END_REF][START_REF] Oiry | Etude thermique àpprofondie d'un uxmètre à gradient tangentiel[END_REF][START_REF] Vultaggio | Les méthodes de la théorie du signal appliquées à l'analyse des transferts thermiques sur la surface d'une paroi opaque en régime variable[END_REF][START_REF] Herin | Conception et caractérisation de capteurs de ux radiatif et convectif : application aux mesures « in situ[END_REF][START_REF] Lassue | Analyse des échanges radiatifs et convectifs à la surface d'une paroi opaque : application à la commande optimale du système habitat[END_REF][START_REF] Harzli | Etude et réalisation d'un nouveau capteur de rayonnement thermique : Application à la detection du rayonnement provenant de sources lointaines[END_REF][START_REF] Douiri | Instrumentation dun four pilote pour la cuisson de genoise[END_REF][START_REF] Cherif | Super cial heat transfer by forced convection and radiation in a horizontal channel[END_REF][START_REF] Wu | Thermal characteristics in situ monitoring of detached house wall constituted by raw clay[END_REF].

This technique consists, basically, in having the heat ux sensor inside a well-isolated-chamber

Chapter 1 -Theoretical background and state of the art device, which contains (cf. g. 1.39): two at heater resistors (having the same surface area as the sensor), a second heat ux sensor (usually no necessarily calibrated) and two water-recirculation-plates connected to a thermostatically-controlled water bath (used as heat sink). The sensor to be calibrated is placed over one of the water-recirculation-plates, and one of the heaters is placed over the sensor.

The second sensor is placed over the heater to detect heat dissipation in the opposite desired direction (towards the rst sensor). The other heater is placed over the second sensor, serving as heat ux compensation, which power is regulated to maintain a null signal response from the second sensor, ergo, ensuring a zero heat ux through this sensor (wherefore the name zero-ux method).

Figure 1.39: Schematic of the calibration apparatus employed for the zero-ux technique [START_REF] Wu | Thermal characteristics in situ monitoring of detached house wall constituted by raw clay[END_REF].

A profound study was conducted by Oiry [START_REF] Oiry | Etude thermique àpprofondie d'un uxmètre à gradient tangentiel[END_REF] in 1985. This study aimed to verify the sensibility value K, estimated by this calibration procedure for the FGT, implementing two numerical models of the multilayer system using the governing equations of the physical phenomena that take place. By using this calibration technique, a sensibility value of 6,19 µV•m 2 •W -1 and a contact resistance of 5,9x10 -4 K•m 2 •W -1 were found. The simulation results showed the following: 1. The in uence of some parameters can be neglected (<7%) when confronted with the conduction heat ux.

2. Only 39% of the sensibility value could be explained when using the perfect thermal-contact hypothesis between the copper and constantan layers.

A value of the order of 1x10

-6 K•m 2 •W -1
for the latter was enough to obtain a sensibility value identical to the one obtained by calibration.

4. The value of the contact resistance between the copper and constantan layers had a small in uence on the sensor internal resistance R calculated, being consistent with the value obtained by calibration.

On the other hand, [68] performed a di erent approach for the calibration of thermoelectric modules.

The sensibility value was determined indirectly by estimating the total Seebeck coe cient and the equivalent thermal conductivity as in equation (1.17). For the total Seebeck coe cient, the module was energized with a DC power source. Then, the electrical response of the module and the temperature di erence between its both sides, were measured after turning o the DC power; the Seebeck coe cient results from the slope of a tted linear regression. The thermal conductivity was estimated by the 1.5. Concluding remarks and perspectives classical conductive methods.

Concluding remarks and perspectives

In this chapter, we have covered the basics for comprehending the natural ventilation concept.

We have brie y reviewed the experimental and modeling techniques already implemented for past researchers, in the estimation of the ventilation air ow rate due to the wind and thermal buoyancy e ects. Also, a brief reviewed of the experimental and modeling techniques concerning the heat ux measurement and the estimation of the convective and radiative heat ux, have been presented. These literature review has allowed noticing the following remarks:

• The coupling between natural ventilation and the thermal mass of a building can be studied by only considering two simple energy balances, one on the indoor air and another on the thermal mass, and the equation for the ventilation air ow rate.

• The location of the air-leakage/in ltrations must be analyzed attentively, to avoid overestimation or underestimation of the air-leakage rate.

• The use of at-plate heat ux meters arises as a good experimental technique for estimating the convective heat exchanges, and more importantly, thermoelectric modules are considerably more attractive than conventional heat ux meters regarding their sensitivity.

Regarding this last remark, in the studies reviewed, the implementation of the heat ux meters di ered in geometry and arrangement, i.e., black and shiny sensors installed with one of their sides always in contact [START_REF] Cherif | Super cial heat transfer by forced convection and radiation in a horizontal channel[END_REF][START_REF] Douiri | Instrumentation dun four pilote pour la cuisson de genoise[END_REF] and installed with a separation between them [START_REF] Lassue | A Convective and Radiative Flux Sensor for Designing Thermal Comfort Controllers[END_REF][START_REF] Wu | Formalisme des impedances thermiques généralisées. Application à la caractérisation thermique de parois de bâtiments[END_REF][START_REF] Yang | Innovative non-destructive methodology for energy diagnosis of building envelope[END_REF]. The selection of the heat ux meter depends mainly on the heat ux levels to be measured, the accuracy wanted in the heat ux measured and the measuring system employed in the measurement.

Regarding the experimental and modeling techniques for estimating the ventilation air ow rate, a limitation arises in their applicability to our speci c case, since:

• The experimental techniques require heavy instrumentation (often expensive) of the openings in terms of airspeed and pressure measurements (local), being the ones that could lead to a better understanding of the phenomena involved in the ventilation process.

• The modeling techniques such as CFD requires large computation time depending on the computer power and the models itself. The models based on empirical observations require the knowledge of the air ow patterns within the building.

Thus, the modeling technique more suitable for our case seems to be the implementation of network air ow models via direct air ow simulations performed by software such as CONTAM, since the knowledge of the air ow patterns is not required.

The more suitable experimental technique seems to be the airtightness tests since it allows us to obtain empirical expressions relating the ventilation air ow directly to the pressure di erence in the building for both cases: in ltrations (openings closed) and openings opened. Also, the location of the leakages can be identi ed without complications, and this technique has the potential to estimate in situ the air ow capacity and friction characteristics of the openings.

In summary, it has been highlighted that in the literature, the coupling between natural ventilation and the thermal mass can be considered by only two energy balances. Then, if we want to consider a thermal behavior model as simple as those, a good characterization of the heat transfer within the test building is needed. With this, the key parameters in both the charge and discharge processes can be determined to later develop a model with the least quantity of parameters that accurately describe the thermal behavior of the building.

C Scope

This chapter describes the experimental study carried out on the platform for characterizing the energy charge and discharge processes, and their coupling to the outdoor thermal stresses, especially natural ventilation in the summertime. The characterization of both charge and discharge processes aims to understand the thermal behavior of the platform, and to determine the heat transfer phenomena involved in each process. They will ultimately, lead to construct a physical model of the platform that only considers the key parameters to describe the thermal behavior of the indoor environment.

This chapter is organized as follows: rst, a detailed description of the platform, the experimental approach and measuring systems implemented for data acquisition are presented. Second, an analytical model to qualify and quantify the charge and discharge processes in terms of convective and radiative heat uxes is presented. Third, the protocol followed for implementing di erent con gurations of the natural ventilation system during the measurement campaigns is presented. Finally, the experimental results showing the thermal behavior of the platform and the heat exchanges highlighted on the slab surface, as well as, evidence of the coupling between the energy charge-discharge process and the natural ventilation strategies implemented, are analyzed and discussed.

Description of the experimental platform

The current state of the experimental platform can be seen in gure 2.1 (a). As said before, the three main architectural features that aid to promote the strategies of passive energy storage and semi-passive

Passive strategies for the charge-discharge process in summer

In summer daytime, the platform employs its three architectural features for attenuating the incoming heat, which can be presented in the form of convective and radiative heat exchanges due to solar gains, wind and air temperature, by closing both the solar shades and the natural ventilation openings. This attenuation of the incoming heat will results in, nonetheless, an indoor temperature rise (cf. g. 2.2 (a)). Note here that the solar eave on the platform roof prevents solar rays from entering 2.2. Experimental approach and protocol the indoor environment, as the position of the sun is higher during the summer daytime. Then, in the summer nighttime, the platform con gures its natural ventilation system as to promote the releasing (or discharging) of the heat stored during the daytime, depending on the weather conditions of wind, air temperature, and rain. This results in a decrease of the temperature of both the indoor air and indoor surface of the structure (cf. g. 2.2 (b)). Given its characteristic and the intention of the platform design, the oor concrete-slab plays an important role in the energy charge-discharge process. Since this slab is the thermally heavier-weighted element in the platform envelope, it is considered as starting hypothesis, that majority of the thermal mass is concentrated in the concrete-slab.

Natural ventilation system and openings

The natural ventilation system of the platform controlled by the home automation system which allows automating the opening-closing con gurations of the natural ventilation openings. This natural ventilation system is equipped with ten programmable openings of the type "horizontal-axis-tilted window" (also known as tilt windows or bottom-hung windows), restricted to a maximum inwardly opening-angle of 20

Experimental approach and protocol

In order to study the energy charge and discharge processes experienced by the platform, resulting of the outdoor thermal stresses (inputs) re ected in the indoor environment, the platform was instrumented in terms of temperature, heat ux and airspeed measurements. This experimental approach aims to observe, comprehend and quantify the thermal response of the platform and of its oor Similarly, the thermal response of the thermal mass domain (cf. g. 2.4 (bottom)) can be studied by focusing on the convective and radiative heat exchanges, resulting of the interaction between the building domain and the outdoor thermal stresses. Thus, the thermal mass domain can be de ned by the interactions between the oor concrete-slab (thermal mass) and the following inputs:

• the indoor air (in the form of convection due to air temperature and speed)

• the surrounding (in the form of radiation due to solar radiation and temperature of other surfaces).

Thus, its behavior can be studied by the following outputs (cf. g. 2.4, outputs in red):

• the oor concrete-slab surface temperature

• the convective heat ux • the radiative heat ux

• the heat stored in the slab.

Finally, this level of instrumentation leads to the possibility of relating the convective heat ux to the natural air ow, and the radiative heat ux to the surrounding surfaces of the indoor environment. In addition, regarding the radiative heat transfer between the oor and surrounding surfaces, the ceiling and glazed-facade surfaces have been also instrumented in terms of temperature and heat ux.

Instrumentation of the thermal mass domain 2.2.1.1 The "measurement device" for decoupling the convective and radiative parts

With the objective of estimating the convection and radiation heat exchanges through experimentation, in the present work, we propose a simple experimental set-up named "measurement device", based on the reported ndings from past researchers concerning the experimental approaches for decoupling the super cial heat transfer (cf. §1.4.2). As this chapter develops, it will be show that such "device" allows to quantify directly the variables highlighted in red in gure 2.4. This "device" consists of the following:

A) A couple of black and shiny coated thermoelectric modules:

To measure the total heat ux and its convective part. These two modules were installed with a small separation between them (cf. g. 2.5), as to expose all their sides to the air. These sensors were properly placed onto the surface studied using a silicon-based thermal grease with thermal conductivity of 5

W•m -1 •K -1 .

B) A type T thermocouple:

To measure the air temperature near the surface studied (without radiation shield); in each measurement zone, this thermocouple was installed as to measure the temperature at a distance of 10 cm over the surface studied.

C) A type T thermocouple inserted into the shiny thermoelectric module:

To measure the temperature of the surface studied. This thermocouple was coated with nail polish, for electrical insulation purposes, before inserting it into the shiny module. The decision of inserting a thermocouple only inside the shiny thermoelectric module was inspired and justi ed after conducting several preliminary experiments. This experiments showed that the di erence between the temperature of the black and shiny thermoelectric modules lays inside the uncertainty interval of the instruments employed; thus leading to conclude that the temperature of the black and shiny modules cannot be experimentally distinguished when accounting for the measurement errors (cf. Appendix A.2). A representation of the convective and radiative heat exchanges over a "measurement device" containing a couple of black and shiny thermoelectric modules, and two thermocouples to measure the air and surface temperatures.

Floor concrete-slab surface

The oor surface of the platform consists of a concrete-slab located in the living room, behind the South-facing glazed-facade as presented in gure 2.1 (b). On the concrete-slab surface, nine "measurement devices" were installed as shown in gure 2.6. Here, to complement the main goal, the "measurement devices" were distributed all over the concrete-slab surface to also observe the local distribution of the convection and radiation heat uxes. 2.2. Experimental approach and protocol

Airspeed measurements

As complementary measurements, the airspeed were performed using omnidirectional hot-wire anemometers to monitor the air movement in two di erent locations in the platform (cf. g. 2.6, blue circles). One anemometer was installed at 10 cm over the concrete-slab oor, as shown in gure 2.7. The other anemometer was installed at the same location where the indoor air temperature measurement was performed (cf. g. 2.11 (a)).

Figure 2.7: Image of the installation for airspeed measurement near the concrete-slab surface.

Ceiling and glazed-facade surfaces

As mentioned earlier, another "measurement device" was installed at the center of the ceiling and glazed-facade surfaces with the purpose of motorizing the convection and radiation heat exchanges, air temperature, and surface temperature. An image of both "measurement devices" and their location within the platform are presented in gures 2.8, 2.9, and 2.10, respectively. It is worth mentioning that the importance of having instrumented these two surfaces is highlighted in the results and analysis part.

Instrumentation of the building

The instrumentation of the building domain allows to quantify the variables in italic font in gure 2.4: (i) wind speed, (ii) direct solar radiation, (iii) outdoor air temperature, (iv) indoor air temperature, and (v) the mean radiant temperature.

Indoor and outdoor air temperature measurement

A type T thermocouple was installed at the center of the concrete-slab oor at 1,70 m height to measure the indoor air temperature (see location in g. 2.6, middle blue circle and g.

Infrared measurements

The experimental set-up for infrared measurements is presented in gure 2.12. These measurements were performed during the main measurement campaign with the following objectives: (i) to measure the indoor mean radiant temperature, (ii) to measure the concrete-slab surface temperature, and (iii) to determine the concrete-slab surface emissivity value. These rst two points were performed

Wind and solar radiation measurements

Weather conditions data were obtained from a 10 m height meteorological station located near the platform at approximately 1,5 km (cf. g.2.13), from which the direct solar radiation, wind speed and wind direction were recovered for the study. This meteorological data was continuously registered every 10 minutes.

Supplementary indoor air temperature measurements

The vertical distribution of the air temperature inside a building is important when studying the natural airstreams due to thermal buoyancy. Therefore, supplementary type T thermocouples were distributed inside the platform at di erent heights for monitoring the vertical thermal strati cation inside the platform. The location of all thermocouples is shown in gure 2.14.

Measuring system and calibration 2.2.3.1 Measuring system for heat ux sensors

The two types of heat ux meters employed in this experimental study were thermoelectric modules and conventional heat ux meters. Both sensors were connected to the National Instrument acquisition board NI 9205, which is a very precise voltmeter with an uncertainty of ±174 µV.

A) Conventional heat ux meters:

The conventional heat ux meters are from Captec® company; their surface area is 225 cm 2 (15 x 15 cm) and their thickness is 0,05 cm. Their response time is about 0,3 s, and they have an integrated type T thermocouple. These sensors were precalibrated by the company at room temperature, using a stationary conductivity measurement method, but with a very thin sample, and since the conductivity of the sample is known, the ux passing through the sensor can be deducted. The sensitivity value K does not change with the temperature of the sensor (cf. table 2.1) at ±3% of error. In table 2.1, the number of the Captec® sensors corresponds to their location on the concrete-slab surface (cf. g. 2.6).

B) Thermoelectric modules:

The thermoelectric modules have a 9 cm 2 (3 x 3 cm) surface area and a 0,48 cm thickness (cf. g.2.15).

The surface of each thermoelectric module was covered with either black or shiny coatings, and their edge-sides were covered with concrete-colored silicon to isolate the semiconductor-joints from contact to surrounding air, before any implementation (cf. g.2.15 (c)).

Calibration of the thermoelectric modules A) Calibration set-up:

The experimental set-up depicted in gure 2.16 was implemented to determine the characteristics of the thermoelectric modules, such as the sensitivity value K, the response time, and the thermal conductivity λ, along with the uncertainty in the heat ux measurement. This set-up consisted of the use of the following items:

1. A at heating resistance of 20±0,05 Ω and a surface area of 1 cm 2 (1 x 1 cm): element number 1 in gure 2.16 (a), and in (b) at the top left square image. Note here that this surface area is smaller than the thermoelectric modules surface area.

2. Two at thermocouples of type K: elements number 2 in gure 2.16 (a).

3. A thermoelectric module: number 3 in gure 2.16 (a). 4. A type T thermocouple inside the thermoelectric module: number 4 in gure 2.16 (a). 5. Two type of isolating materials of color black and white: number 5 in gure 2.16 (a), and also showed in (b). The white was used to isolate precisely the thermoelectric module, and the black was used to isolate the chamber. [START_REF] Chen | Evaluation expérimentale d'une stratégie domotique de pilotage des éléments mobiles : vers un contrôle semi-passif simple du confort d'été en BEPos[END_REF]. A steel block that serves as a heat sink: number 6 in gure 2.16 (a). 7. A concrete block was used to keep the sensors steady inside the chamber: number 7 in gure 2.16 (a).

B) Calibration procedure:

The calibration procedure consisted of submitting the thermoelectric module to di erent constant heat loads and recording its thermal response, in steady state conditions. The heat loads were applied by the heating resistance and adjusted by a variable DC power source. Once the heating resistance was energized, approximately 20 minutes were awaited for the thermoelectric module response to stabilized (this time interval was chosen after previous observation of their behavior). After stabilization, the heating resistance was de-energized for 5 minutes, waiting until the module reaches its equilibrium.

The entire procedure was recorded, and the same process was performed for every heat load applied.

An example of the electrical response of the black coated thermoelectric module n o 8 measured when a heat load of 20 W•m -2 was applied, is presented in gure 2.17. After the electrical response was stabilized (at standard deviation of ±20 µV), it can be observed that the time response is approximately 2 minutes (calculated at 90% of the maximum tension value).

(C) Results and analysis:

The di erent heat loads applied in the calibration procedure and the electrical response of the Thermo-Electric Module (TEM) n heat load or setpoint ϕ setpoint , the voltage U and current I applied to the at heating resistance, the resulting heat load applied ϕ real by the at heating resistance, the electrical response U of the thermoelectric module, and its corresponding corrected response U corrected . The real heat loads applied ϕ real were calculated by the following expression:

ϕ real = U • I S W•m -2 (2.1)
where S represents the surface area of the thermoelectric module.

ϕ setpoint [W•m -2 ] U [V] I [A] ϕ real [W•m -2 ] U [µV] U corrected [µV] 0 0 0 - -59,61 -the procedure.
This implies that when a heat load was applied, the latter must have been greater than the opposite heat ux created by the inequality in the temperature of the sensor sides, and a correction is required (cf. table 2.2, U corrected column). This correction can be generalized as follows:

U corrected (ϕ setpoint ) = U(ϕ setpoint ) -U(ϕ setpoint = 0).
For the calculation of the sensitivity value K of the thermoelectric module, the corrected electrical response U corrected was plotted against the applied heat load ϕ real ; the sensitivity value was determined then, by tting a linear regression forced to cross the origin (see g. 2.18 here above).

This calibration procedure was performed again for the black coated thermoelectric module n Apart from the fabrication errors, the only visible di erence between the black and shiny modules is the type of coating used (texture and color). Not enough experiments have been performed to declare that these di erent coatings could explain the approximately 20 µV•m 2 •W -1 di erence encountered between the K values: the uncertainty analysis has shown that this di erence appears to be indistinguishable when accounting for the uncertainty of the instrument we have employed.

(D) Uncertainty in the heat ux measurement:

The uncertainty in the heat ux measurement of the black and shiny thermoelectric modules (δ ϕ ), was determined using the Constant Odds Combination (COC) method. Thus, to calculate the uncertainty in the heat ux measurement the COC method was applied to equation 1.16, as follows:

δ ϕ = δ U K 2 + U • δ K K 2 2 W•m -2 (2.2)
where δ U is the uncertainty in the TEM response measured by the acquisition system and δ K is the uncertainty in the sensitivity of the TEM. For the latter, by equating expressions 1.16 and 2.1, an expression for the sensitivity value K, yields

K = U • S U • I µV•m 2 •W -1 (2.3)
and thus, applying the COC method to the previous equation, results in:

δ K = S • δ U U • I 2 + U • δ S U • I 2 + U • S • δ U U 2 • I 2 + U • S • δ I U • I 2 2 µV•m 2 •W -1 (2.4)
It can be observed from equation 2.4 that the uncertainties in U and S, being constant values depending on the instruments employed, could make vary the uncertainty in K, depending on the value of the thermoelectric module response U, along with the value of the voltage and current applied to the heating resistance. The uncertainties of the instruments employed to measure each parameter are given in table 2.3. 7493,68 0,033 0,276 -0,0003 -0,007 0,074 0,004 36,49 50,61 12490,57 0,020 0,274 -0,0003 -0,005 0,095 0,005 36,02 99,87 24575,92 0,010 0,273 -0,0002 -0,004 0,134 0,007 35,80 200,24 49312,52 0,005 0,274 -0,0001 -0,003 0,190 0,010 [START_REF] Feuermann | On the potential and e ectiveness of passive night ventilation cooling[END_REF][START_REF] David | Caractérisation des propriétés thermoélectriques des composants en régime harmonique : Techniques et Modélisation[END_REF] In order to account for the uncertainty in the sensitivity K, we have now to choose whether to consider δ K as an average value or as a value that varies with the heat ux applied. Thus, by evaluating equation (2.2), the di erence between choosing one upon the other is presented graphically in gure 2. [START_REF] Caciolo | Analyse expérimentale et simulation de la ventilation naturelle mono-façade pour le rafraîchissement des immeubles de bureaux[END_REF]. In this gure it is clear that larger uncertainties are obtained when using δ K as an average value (cf. g. 2.19, color red), instead of using δ K as a heat-ux-applied dependent value (cf. g. 2.19, color blue).

ϕ real U S U•I U U•I U•S U 2 •I U•S U•I 2 δ U δ I δ K 0 0 - - - - - - - 1,

(E) Conclusion:

An estimation of the heat ux measured with the thermoelectric modules can be achieved, as precise as possible, by considering uncertainty values that depend on the heat ux measured instead of an average uncertainty value. Finally, the following expressions will be implemented when reporting the estimated heat ux measurement from the black and shiny thermoelectric modules, respectively: where ϕ b and ϕ s represent the heat ux measurement from the black and shiny thermoelectric modules, respectively.

ϕ b = U b 247 ± δ ϕ b = U b 247 ± 0,14 • U b 247 + 0,35 W•m -2 (2.5) ϕ s = U s 267 ± δ ϕ s = U s 267 ± 0,14 • U s 267 + 0,65 W•m -2 (2.6)

Measuring system for thermocouples and calibration

Several type T thermocouples were calibrated using a thermostatic bath (LAUDA RE 415) with a temperature accuracy of ±0,3 • C and ±0,5% of the temperature value displayed, and a stability of ±0,01 • C, assured by an integrated PT100. All thermocouples were connected to the NI 9213 acquisition card with a measurement sensitivity of ±0,02 • C, and a measurement error of ±0,8 • C for our temperature ranges.

The goal of the calibration procedure was to increase the accuracy of our thermocouples by correcting our measuring system (thermocouple + acquisition system) using a more accurate temperature measuring instrument as a reference; in this case, the thermostatic bath was used (see Appendix A.1 for full report).

Results showed that the maximum deviation between the thermocouples themselves before correction did not exceed the 0,3 • C when submerged in a stable medium (water in this case, cf. g. 2.20).

After correction, this maximum deviation was reduced to 0,07 • C (cf. g. 2.21). Results also showed that the measurement stability of the thermocouples is ±0,02 • C with a 95% of con dence.

Semi-empirical models for data processing 2.3.1 Decoupling the convection and radiation heat exchanges

A semi-empirical model is proposed here to distinguish the convection and radiation parts from the heat ux measurement. This model is based on a heat ux balance written for the considered surface i.

A heat ux balance of the convective and radiative heat exchanges over this surface, as represented in gure 2.22, can be written as follows:

ϕ i (t) = ϕ R i (t) + ϕ C i (t) = I(t) -I re f i (t) -E i (t) + ϕ C i (t) W•m -2 (2.7)
where ϕ i is the total heat ux entering the surface i. Together I, I re f , and E i , represent the net radiation heat ux (ϕ R i ) exchanged between the surface i and the surrounding environment, where I is the total incident radiation heat ux (short + long wavelength), I re f is the re ected part of the total incident radiation, E i is the emitted radiation heat ux, and ϕ C i is the convective heat ux. The term I -I re f of equation 2.7 is equal to the absorbed part of the total incident radiation (I abs ), which also can be written as α i • I, where α i is the total thermal absorptivity. By considering the following four assumptions:

• In a single measurement zone, both black and shiny heat ux meters (and the surface they are placed on) are submitted to the same total incident radiation,

• he convective heat ux follows Fourier's law of convection and is di erent for each heat ux meter (accounting for any di erence in their temperatures),

• the convective heat transfer coe cient is the same for both heat ux meters,

• the emitted radiation follows the Stefan-Boltzmann law for the radiative power emitted by a black body (supposing gray surfaces), equation 2.7 can be rewritten as follows for the black and shiny heat ux meters, respectively:

ϕ b (t) = ϕ R b (t) + ϕ C b (t) = α b • I(t) -ε b • σ • T 4 b (t) + h C • ∆T b (t) W•m -2 (2.8) ϕ s (t) = ϕ R s (t) + ϕ C s (t) = α s • I(t) -ε s • σ • T 4 s (t) + h C • ∆T s (t) W•m -2 (2.9)
where ϕ b and ϕ s represent the heat ux measurement of the black and shiny heat ux meters, respectively. The thermal emissivity is represented by ε, and σ represents the Stefan-Boltzmann constant

in W•m -2 •K -4 .
The convective coe cient is represented by h C , and ∆T represents the temperature di erence between the air and the heat ux meter.

Then, by solving together equations 2.8 and 2.9, for I and h C yields:

I(t) = ∆T b (t) • ϕ s (t) + ε s • σ • T 4 s (t) -∆T s (t) • ϕ b (t) + ε b • σ • T 4 b (t) α s • ∆T b (t) -α b • ∆T s (t) W•m -2 (2.10) h C (t) = α s • ϕ b (t) + ε b • σ • T 4 b (t) -α b • ϕ s (t) + ε s • σ • T 4 s (t) α s • ∆T b (t) -α b • ∆T s (t) W•m -2 •K -1 . (2.11)
Note that in the previous equation, the estimation of the convective heat transfer coe cient does not, explicitly, depends on the roughness of the surface, the airspeed over the surface, the thickness of the sensors, or any other intrinsic characteristic regarding the convective coe cient as reported in the literature. In turn, the in uence of all these characteristics are implicitly taken into account by the heat ux measurement itself from each heat ux meter.

Thus, by replacing equation 2.11 into Fourier's law of convection for the shiny heat ux meter, the convective heat ux ϕ C s , yields:

ϕ C s (t) = α b • ∆T s (t) α b • ∆T s (t) -α s • ∆T b (t) • ϕ s (t) - α s • ∆T s (t) α b • ∆T s (t) -α s • ∆T b (t) • ϕ b (t) + ∆T s (t) • σ • α b • ε s • T 4 s (t) -α s • ε b • T 4 b (t) α b • ∆T s (t) -α s • ∆T b (t) W•m -2 .
(2.12)

A similar expression can be obtained for the convective heat ux for the black heat ux meter ϕ C b , just by replacing ∆T s for ∆T b in each numerator:

ϕ C b (t) = α b • ∆T b (t) α b • ∆T s (t) -α s • ∆T b (t) • ϕ s (t) - α s • ∆T b (t) α b • ∆T s (t) -α s • ∆T b (t) • ϕ b (t) + ∆T b (t) • σ • α b • ε s • T 4 s (t) -α s • ε b • T 4 b (t) α b • ∆T s (t) -α s • ∆T b (t) W•m -2 .
(2.13)

It can be inferred from equation 2.12 that the assumption considering that the convective heat ux is entirely determined by the measurement of a heat ux meter coated with a shiny-foil (ϕ s ), might lead to an overestimation or an underestimation of this heat ux; depending on the radiative properties of the surface and the air-surface temperature di erence for each sensor.

Semi-empirical models for data processing

In turn, this equation implies that the convective heat ux would be determined by a shiny heat ux meter only if the following holds:

1. Both sensors are at the same temperature (∆T s = ∆T b ), 2. the shiny coating is a perfect re ector (ε s = 0, α s = 0), 3. the emissivity values are considered to be equal to the absorptivity values (ε = α), i.e., Kirchho 's hypothesis for enclosures with non-participating medium.

Note here that if the latter holds, the knowledge of the radiative properties of the black coating is not important, which seems fairly straightforward to conceived, because in such case, a black heat ux meter would not be needed to measure the convective heat ux. Now, if only item (1.) holds, the convective component for both heat ux meters would be the same (cf. eqs. 2.12-2.13), and if in addition to this, item (3.) holds, the last term of equation 2.12 would be null and the convective heat ux would only depend on the emissivity values.

Moreover, for surfaces with radiative properties similar to the black heat ux meter, an expression for the radiative heat ux (ϕ R b ), can be obtained using the previous results, where ϕ R b will result by subtracting ϕ C b from ϕ b (because ϕ b accounts for the entire radiative heat ux with respect to ϕ s , which only accounts for a small part of it), yields:

ϕ R b (t) = α b • ∆T s (t) α b • ∆T s (t) -α s • ∆T b (t) • ϕ b (t) - α b • ∆T b (t) α b • ∆T s (t) -α s • ∆T b (t) • ϕ s (t) + ∆T b (t) • σ • α b • ε s • T 4 s (t) -α s • ε b • T 4 b (t) α b • ∆T s (t) -α s • ∆T b (t) W•m -2 (2.14)
Note that from expression 2.14, if item (2.) holds, it might be assumed that the value of the net radiation heat ux ϕ R b would depend on the radiative properties of the black coating. However, in such case, it can be shown that the knowledge of the radiative properties of the black coating becomes unnecessary.

In turn, the value of the net radiative heat ux would depend on the value of ∆T b and ∆T s , resulting

in: ϕ R b = ϕ b -∆T b ∆T s • ϕ s .
This last remark is worth mentioning, in regard of the assumption made by former researchers before the 21 st century (cf. §1.4.2): the shiny and black sensors measure the convective and total heat ux, respectively, and the radiative heat ux will result from a simple subtraction of both measurements.

This assumption is proven to be only plausible, when ∆T b is equal to ∆T s or, in other words, T b is equal to T s . Note here that this last remark refers to the inquiry of whether the temperature of both black and shiny heat ux meters is the same or not, and not whether the temperatures of the interface "sensor's upper surface -air" and of the interface "sensor's lower surface -wall" are the same or not.

The inquiry regarding the di erence between these two temperatures is not treated here, as in [START_REF] Lassue | Analyse des échanges radiatifs et convectifs à la surface d'une paroi opaque : application à la commande optimale du système habitat[END_REF],p.38

or in [START_REF] Lassue | A Convective and Radiative Flux Sensor for Designing Thermal Comfort Controllers[END_REF],p.297.

Furthermore, for surfaces with radiative properties which values lay between ε s and ε b , an expression for the net radiative heat ux can be determined by ϕ

R i = α i • I -ε i • σ • T 4
S i , using expression 2.10.

Experimental-based simpli cations

Given that, during our experimental study, the temperature ranges encountered within the indoor environment were entirely in typical room temperature ranges, and since the window shades were kept always closed, Kirchho 's hypothesis was admitted and retained (cf. Table 2.5, hyp. n • 1 and n • 2).

T b = T s Experimentation (cf. Appendix A.2)
4) Temperature of shiny sensor has the same as the surface i

T b = T s = T S i Simpli cation
Results from measurement campaigns carried out previously, allow us to establish that the temperature di erence between the shiny and black thermoelectric modules always lays in 0,175±0,075

• C (T s -T b = 0,175±0,075 • C)
, and since the absolute uncertainty in our temperature measurements lays around ±0,4 • C, it was concluded that no signi cant di erence can be detected, and thus, both heat ux meters are considered to have the same temperature (cf. Table 2.5, hyp. n • 3). Therefore, equations 2.10 and 2.11 can be simpli ed as follows:

I(t) = 1 ε s -ε b • ϕ s (t) - 1 ε s -ε b • ϕ b (t) + σ • ε s • T 4 s (t) -ε b • T 4 b (t) ε s -ε b W•m -2 (2.15) h C (t) = ε b ε b -ε s • ϕ s (t) ∆T s (t) - ε s ε b -ε s • ϕ b (t) ∆T s (t) W•m -2 •K -1 . (2.16)
Note that in equation 2.15 the temperatures at the power of fourth have not been simpli ed, because their di erence becomes important in this case (around 5%), as encountered when using experimental results for computing the total incident radiation. However, for equation 2.16 when using experimental results no signi cant di erence were encountered whether or not the temperatures at the power of fourth are removed.

Thus, the convective and radiative heat uxes (cf. eqs. 2.12-2.14), after considering the previous hypotheses, result in the following:

ϕ C s (t) = ϕ C b (t) = ϕ C (t) = ε s ε s -ε b • ϕ b (t) - ε b ε s -ε b • ϕ s (t) W•m -2 (2.17) ϕ R b (t) = ε b ε b -ε s • ϕ b (t) - ε b ε b -ε s • ϕ s (t) W•m -2 . (2.18)
Finally, an expression for the net radiative heat exchange on a given surface i with an emissivity value between ε b and ε s , can be obtained using the following de nition where ϕ R i (t) is equal to

α i • I(t) minus ε i • σ • T 4 i (t)
. This before, along with Kirchho 's hypothesis, results in:

ϕ R i (t) = ε i • 1 ε b -ε s • ϕ b (t) - 1 ε b -ε s • ϕ s (t) + σ • T 4 s (t) -T 4 i (t) W•m -2 . (2.19)
Note here that if the surface studied i were to have the same emissivity value of the black coating, expression 2.19 would become the same as expression 2.18. Moreover, these simpli cations have reduced the number of instruments needed in our experiments, along with the budget for instrumentation: ten thermocouples type T and another acquisition card NI 9213 have been saved. Thus, it is recommended to perform preliminary experiments with few instruments regarding the simpli cations presented, before going further.

Determination of the emissivity

A sensitivity analysis showed that the estimation of the convective (cf. eq. 2.17) and radiative (cf. eq.

2.18) heat uxes is strongly in uenced by the uncertainty in the emissivity values of the shiny coating.

Thus, a precise determination of the emissivity is required, with an uncertainty value around or smaller than 1x10 -2 .

The emissivity values for the black and shiny coatings used here were determined by following the methodology recommended in the standard ISO 18434-1:2008(E) for emissivity measurements. The emissivity values obtained for the black (ε b ) and shiny (ε s ) coatings were 0,953±0,012 and 0,069±0,014, respectively [START_REF] Yang | Innovative non-destructive methodology for energy diagnosis of building envelope[END_REF]. The hypotheses considered were: (a) the emissivity of the crumpled aluminum foil is zero and (b) the temperature of the reference is the same as the temperature of the object studied; hypothesis (a) is justi ed by the fact that a crumpled aluminum foil can be considered as a perfect re ector; hypothesis (b) was retained for simpli cation issues.

Mean radiant temperature of surrounding surfaces

A well estimation of the mean radiant temperature T surr is needed when analyzing net radiative heat exchanges in buildings. Therefore, another way to estimate this temperature is proposed here by using the heat ux measurements, instead of an infrared camera. An expression to estimate the mean radiant temperature in terms of heat ux measurements in a measurement zone can be derived by subtracting equations 1.19 and 1.20 and assuming the same convection part for both sensors, results in:

ϕ b (t) -ϕ s (t) = ϕ R b (t) -ϕ R s (t) W•m -2 (2.20)
Now, having these small heat ux meters enclosed by a bigger environment and a non radiation inuence medium in between. The net radiation heat transfer ϕ R for each sensor can be estimated by following Kirchho 's hypothesis, resulting in:

ϕ b (t) -ϕ s (t) = ε b • σ • T 4 surr (t) -T 4 b (t) -ε s • σ • T 4 surr (t) -T 4 s (t) W•m -2 (2.21) T surr (t) = 4 ϕ b (t) -ϕ s (t) [ε b -ε s ] • σ + ε b • T 4 b (t) -ε s • T 4 s (t) ε b -ε s [K] . (2.22)
Finally, considering hypothesis n o 4 in table 2.5 (where T b is considered as same as T s ), the following expression for the mean radiant temperature is obtained:

T surr (t) = 4 ϕ b (t) -ϕ s (t) [ε b -ε s ] • σ + T 4 s (t) [K] . (2.23)

Smoothing of experimental data

All experimental data collected have been smoothed before implementation in the analytical models for data processing. Since all experimental data is processed using the software R, the function smooth.spline, with default smoothing parameters, is employed.

Experimental plan implemented in the measurement campaigns

Since the objective of the experimental approach is to highlight and to understand the energy charge and discharge processes of the platform submitted to the outdoor thermal stresses in the summertime, the experimental plan for the measurement campaign in 2016, consisted of the following points:

• All data from the instruments described before in §2.2.2, except for the IR camera, were set to be collected continuously at a sample time of one minute, regarding the acquisition systems limits in handling a signi cant amount of instruments and the time response of the sensors. This corresponds to a total of 63 observations registered each minute: 30 heat ux meters, 21 thermocouples for surface temperature, two anemometers, and ten thermocouples for air temperature.

The data from the IR camera was set to be collected at a sample time of 30 minutes, regarding the computer storage limit.

• The solar shades were kept permanently closed during the entire measurement campaign, to lter the most of the solar radiation. The natural ventilation openings were programmed with the home automation system, by following the owchart presented in gure 2.23: the openings will open when the indoor air temperature T ia is higher than the outdoor air temperature T oa and will close otherwise and when is raining. Only the openings at the South facade and shedroof were functional, due to technical problems; the openings at the north facade have remained closed.

• The platform was unoccupied during the entire measurement campaign, and the lights remained turned o . On the contrary, two computers remained operational: one for data collection and one for controlling the platform home automation system.

• Since the inside of the platform is divided into four zones (the living room, bedroom, bathroom, and toilet), all doors dividing these zones were kept open, with the intention of mixing the air of all four zones. Another measurement campaign was performed in the summertime of 2017, in which the natural ventilation openings were programmed to implementing other con gurations of the natural ventilation openings, where they were kept always opened and always closed during a short period. All measurement campaigns carried out during the summertime of 2016 and 2017 are summarized in table 2.6. It is worth mentioning that this experimental plan was also implemented in other measurement campaign carried out in the summertime in 2015. However, the data collected had only served for a qualitative study of the thermal behavior of the platform and the heat exchanges on the oor surface. The data collected from the measurement campaign in 2016 will be classi ed to analyze the thermal behavior of the indoor environment of the platform under di erent meteorological conditions. This classi cation organizes the ongoing meteorological conditions in terms of wind (windy and no-windy), and in terms of the sky state (clear and cloudy), in two distinguishable periods: when natural ventilation openings are opened, which happened mostly during nighttime, and when natural ventilation openings remained closed, which happened mainly during the daytime. Most days have presented no-windy nighttime, as expected for summer periods. Various days had similar meteorological conditions; these days were grouped, for no windy nighttime, as follows:

• July 28 th and 29 th , with a cloudy and windy daytime, and a clear and no-windy nighttime.

• August 15 th and 16 th , with a sunny and windy daytime, and a cloudy and no-windy nighttime.

• August 19 th and 20 th , with a cloudy and windy daytime, and a cloudy and no-windy nighttime.

• August 22 nd and 23 rd , with a sunny and windy daytime, and a clear and no-windy nighttime.

and for windy nighttime:

• July 27 th and August 17 th , with a cloudy and windy daytime, and a cloudy and windy nighttime.

• August 26 th and September 8 th , with a cloudy and no windy and windy daytime, respectively, and a clear and windy nighttime.

Therefore, since eight days presented no-windy nighttime and only four presented windy nighttime, two days of each group will be chosen for further analysis. The most reasonable pair of days are those that presented typical summer weather conditions: sunny days and clear nights. On the other hand, the entire data collected from the measurement campaigns in 2017 will be used for the analysis, since it comprised a short period.

Thermal behavior of the platform under di erent opening con gurations and outdoor conditions

Before going further in the analysis of the experimental results, the thermal behavior of the platform, under di erent meteorological conditions during the measurement campaigns, is presented and analyzed rst, for the con gurations presented in Wind speed and wind direction presented anticyclonic behavior and weak values, as also expected for this season.

Di erent behaviors of the indoor environment can be observed for each con guration. For instance, the lower day-night maximum indoor temperature gap is encountered for con guration n • 1 (cf. g.

2.24)

, which is also reasonable since both environments are, in principle, not allowed to interact with each other. Conversely, the higher day-night maximum indoor temperature gap is encountered during con guration n • 3 (cf. g. 2.26), which is reasonable since the indoor environment is permitted to interact the most with the outdoor environment.

Moreover, the mean radiant temperature (mean temperature of surrounding surfaces) appears to be very close to the indoor air temperature, which suggests that the LWL radiation heat transfer is weak in the indoor environment. Depending on the con guration, the mean radiant temperature appears to be slightly higher or slightly lower than the indoor air temperature as follows:

• In con guration n • 1, the indoor air is hotter than the surrounding surfaces during nighttime (cf.

g. 2.24); the opposite is encountered during the daytime.

• In con guration n • 2, the indoor air appear to be slightly colder than the surrounding surfaces during nighttime, as expected; during the daytime, the indoor air is hotter than the surrounding surfaces, as in agreement with con guration n • 1 for this period (cf. g. 2.25).

• In con guration n • 3, the indoor air is slightly colder than the surrounding surfaces during nighttime, which agrees with what has been encountered for con guration n • 2; the opposite is encountered during the daytime, as expected since the openings remained open (cf. g. 2.26).

These last three remarks are rendered moot when accounting for the uncertainties of our instruments in the temperature measurement since both temperatures became indistinguishable. In other words, the di erence between the temperature of the indoor air and surrounding surfaces lays within the uncertainty interval of the instruments employed. Nevertheless, these remarks are worth mentioning since the results encountered agree with the expected behavior of both temperatures for each con guration.

Regarding the thermal inertia of the platform, the indoor environment presents a higher thermal lag TL (or temporal phase shift) with respect to the outdoor air temperature during the daytime in increasing order as follows: con gurations n • 2, n • 1 and n • 3. This behavior can be simply explained by the fact that the platform attenuates the outdoor thermal stresses when the openings and solar shades are closed (con g. n • 1), and the platform attenuates them the most, when its indoor environment is cooldown the night before (con g. n • 2). As the openings remained open during the day for con guration n • 3, the indoor environment of the platform opposes the least to the outdoor thermal stresses.

On the other hand, during nighttime the platform presents a thermal lag (TL) in decreasing order as follows: n • 1, and n • 2/n • 3 with slightly the same values, which is also expected.

In summary:

The previous analysis highlights the e ects of the coupling between natural ventilation and the energy charge-discharge process by focusing only on the outdoor and indoor environments temperatures.

2.5. Results and discussion on the coupling between the energy charge-discharge and natural ventilation

Coupling of the charge-discharge process with natural ventilation within the indoor environment

Now let us focus on the charge-discharge process in the indoor environment (thermal mass domain).

The rst evidence of the coupling is merely qualitative, and it can be observed at a glance since the behavior of the convective heat ux on each surface ( oor and ceiling) is di erent depending on which opening con guration is being implemented. Here, we speak about the convective heat ux, because it is directly related to the energy ow caused by air movement.

In order to verify that the changes in the behavior of the convective heat ux are caused by the opening and closing of the natural ventilation openings, we take the behavior encountered in con g.

n • 1 as a reference since the openings remained close. In this way, when the convective heat ux reaches signi cant values (with respect to con g. n • 1), it will be considered directly as a consequence of natural ventilation, and thus, highlighting the coupling between the latter and the charge-discharge process in the form of convection. This charge-discharge process is analyzed individually by focusing rst on the convective heat ux, and after on the radiative heat ux. Also, sometimes its more accessible to referrer to these processes as charge and discharge period, and thus, the reader is wanted to note that both terms will be used interchangeably.

Charge and discharge by convection

The results of the convective heat ux and the corresponding air-surface temperatures for con gurations n • 1, n • 2, n • 3 are presented in gures 2.27-2.32. For visual purposes, the uncertainties are only presented for convective heat ux, since the temperature range is very narrow. Also, for the graphics where heat uxes are presented, a horizontal dashed line will be drawn on zero to well separate the charge period, i.e., positive values (mostly during the daytime), and the discharge period, i.e., negative values (mostly during nighttime). These positive or negative values can also be regarded as if the heat ux is entering or leaving the surface, respectively. Note that, as a convective heat ux presenting positive values indicates that the surface is being charged, this also indicates that the air near this surface is experimenting a "discharging. " Conversely, if the heat ux presents negative values (indicating that the surface is being discharged), the air near this surface is experimenting a "charging. " With this in mind, during the charge period, the behavior observed in gures 2.27 and 2.29 indicates that the glazed-facade (brown line) contributes the most to the charging of the indoor air (by convection). On the other hand, in gures 2.27, 2.28 and 2.29, the behavior of both the oor (black line) and ceiling (purple line), during the charge period, indicates that they contribute to discharging the indoor air, while these two surfaces are being charged. This statement only appears to apply to the rst day (23/5) in con g. n • 1, as expected, due to the outdoor conditions of the following days (cf. g. 2.24). It seems that the magnitude of the convective heat ux on the oor surface is signi cantly higher when the openings were kept open (cf. g. 2.28, gray zones), than when they were kept closed. The same can be said for the airspeed measurements (brown circled lines). On the other hand, the magnitude of the convective heat ux on the ceiling surface appears to be signi cantly lower (almost null) when the openings were kept opened than when they were kept closed (white zones). This can be explained by the fact that when the openings remained open (mostly in nighttime), the outdoor air temperature was lower than the indoor air (cf. g. 2.24). And since cold air is denser than warm air, outdoor air was entering at the lower part of the platform through the lower openings, and thus air currents near the oor surface is stronger. It will be shown later, that this is an essential result regarding the nature and modeling of the convective heat transfer coe cient on both surfaces. The values and signs adopted by the convective heat ux on both surfaces imply that, during nighttime, the oor is vigorously discharged, while the ceiling presents a weak discharge or none at all.

Charge

Regarding the temperatures, it can be observed from gures 2.30 and 2.32 that the glazed-facade surface (brown line) always presents the highest temperature of these three surfaces and its behavior appears to be synchronized with the behavior of the outdoor air temperature (no temporal phase shift appears to be present between them). This is expected since the glazed-facade has a weak heat capacity, and might suggest that the in uence of direct solar radiation, in the heating of this surface, can be neglected.

Finally, it can be observe that when the heat ux at the glazed-facade is positive, i.e., a heat ux entering this surface (cf. g. 2.27, brown solid line), its temperature (cf. g. 2.30, brown line) appears to be lower than the near air, which air temperature is measured at 0,1 m (cf. g. 2.30, brown circles). This indicates that the air near the surface is charging it. This last remark is worth mentioning, since this behavior, as logic as it may seem, was encountered to correspond only between the temperatures of the surface and the air at 0,1 m, but not between this surface and the air temperature measured at 1,70 paigns) at 0,02 m from the oor. This measurement presented lower values than the temperature measured at 0,10 m during nighttime. This before highlights the in uence of the vertical thermal stratication of the indoor air, and also, that at the height of 0,10 m is the better location for measuring the air-surface temperature that better corresponds to the behavior of the convective heat ux.

Charge and discharge by radiation

The results of the radiative heat ux for con gurations n appears to be weak, with negative values, in comparison with the other surfaces. This might imply that the surrounding surfaces (as viewed from the ceiling: oor, glazed-facade, internal partitions, among others) are always at a temperature slightly lower than the ceiling surface. However, gures 2.30 and 2.32 show that the glazed-facade always presents higher temperatures than the ceiling, and the oor surface always presents a lower temperature. It can be inferred from this, that the radiative heat ux responds to a mean temperature of the surrounding surfaces (also depending on the corresponding view factors), as expected. Moreover, the radiative heat ux at the oor surface (black line) presents the largest values, during this period. This implies that the oor surface is the coldest surface, and thus, all surrounding surfaces are discharged towards it; indicating that the oor helps to attenuate the temperature rise of the other elements of the envelope.

Characterization of the energy charge and discharge processes

During the discharge period, comparing gures 2.34 and 2.35 with 2.33, there appear to be no signi cant changes in the radiative heat ux between con gurations n • 1, n • 2 and n • 3, and therefore, the opening and closing of the natural ventilation openings do not seem to have a direct and explicit e ect on the radiative environment. However, it is clear that if the oor surface has been cool down the night before (by leaving the openings opened), this surface will experience a stronger charging by radiation the following day, than if it was not cooled down the night before. This seems fairly straightforward to conceive since the concrete slab might be able to bear stronger heat loads the next daytime if it is cooling down enough the night before.

In summary:

The coupling between the charge-discharge and natural ventilation has been qualitatively highlighted by the behavior of the convective heat ux at each surface, for con guration. From the previous analysis it can be infer the following:

• The oor and ceiling play an essential role in the attenuation of the rising of the indoor air temperature, while the glazed-facade contributes the most to the heating of the indoor air.

• The role of the elements of the envelope appears to change places, depending on the periods of charge and discharge.

• The oor surface plays an essential role in the attenuation of the temperature rising of the elements of the envelope, since the latter discharge by radiation towards the oor.

• The opening and closing of the natural ventilation openings do not seem to have a direct e ect on the radiative environment, since no changes in the radiative heat ux.

Characterization of the energy charge and discharge processes

The characterization of both energy charge and discharge processes aims to describe and determine the heat transfer phenomena involved in each process. This characterization will permit a full knowledge of the thermal behavior of the platform, which will ultimately, lead to construct a physical model that only considers the key parameters for the forecasting of the behavior of the indoor environment.

Impact of the outdoor environment upon the indoor environment via correlation analysis

To complement the characterization of both, the energy charge and discharge processes, we analyze the correlation between the data collected from the outdoor and indoor environments, to determine the relevance (or impact or in uence) of the former over the latter via correlation analyses. Such analysis will allow us later in the modeling, whether to consider or not some parameters, for instance:

• Does the solar radiation reaching the platform indoor environment have a signi cant impact?

• Can the e ect of solar radiation be neglected when modeling the heat transfer in the oor concreteslab?

Data collection and sample rate

During the measurement campaign (34 days in the summertime), data were collected from the indoor environment (including the outdoor temperature) at a sample rate of an observation every one minute, equivalent to 1440 observations per day. From the outdoor environment, data were collected at a sample rate of an observation every ten minutes, equivalent to 144 observations per day. Here, a reduction for the indoor environment data was performed to be match with the outdoor environment sample rate:

only 144 observations per day will be used for the indoor environment data.

Correlation analysis

A correlation analysis based on the Pearson correlation coe cient R was implemented to evaluate how strong is the relationship between indoor and outdoor variables, and also to understand better the coupling between the heat transfer and air ow e ects in the platform.

Since the implementation of a correlation analysis of such physical problem via only the correlation coe cient may lead to subjective inferences, the statistical signi cance of the relationships between to variables is further analyzed using other approaches concerning its interpretation. To do this, we have implemented the following three approaches as presented in [START_REF] Schumacker | Understanding Statistics Using R[END_REF]:

1. The veri cation of the null and alternative hypothesis state via the p-value (we will assume 0,95 as con dence level).

2. The explained variability of the data via the squared value of the Pearson's correlation coe cient R (R 2 ).

3. The visual trend that veri es the linear or curvilinear relationship via scattering plots.

Regarding the rst approach (1.), the null hypothesis states, as default, that there is no signi cant relationship between the two variables studied (a p-value greater than or equal to 0,05). Once the pvalue of the supposed correlated data is determined, if its value lays under 0,05, it is said that the null hypothesis is rejected and the alternative hypothesis holds: there is a signi cant correlation between the two variables studied.

Regarding the second approach (2.), as stated in [START_REF] Schumacker | Understanding Statistics Using R[END_REF], the value of R 2 indicates the percentage of the variability that can be explained by the knowledge of the correlated variables.

Regarding the third approach (3.), the visualization of the two correlated variables will verify their relationship subjected by R. In the case where values near zero are encountered (indicating no linear relationship exists), the visual trend can help us to determine whether to accept the "no correlation" implied by the value of or to consider the determination of another correlation coe cient that allows evaluating the strength in the trend encountered.

Finally, regarding this third approach, the Spearman's coe cient (or Spearman's rank-order correlation coe cient) will be determined, since it allows evaluating monotonic relationships. In such relationships, the variables tend to change together, but not necessarily at a constant rate. It is worth mentioning that it is possible to meet a situation where Pearson's coe cient is negative while Spearman's coe cient is positive or vice versa, which might lead to infer that such situation is an inconsistency. However, with a logical understanding of the di erence between these two coe cients, such "inconsistencies" are justi ed [START_REF] Hauke | Comparison of values of Pearson's and Spearman's correlation coe cients on the same sets of data[END_REF].

In addition to correlation plots, to present the results with Spearman's coe cient, we use correlation matrices using the software R, as they allow us to group the three approaches mentioned earlier.

Distinguishing strong from weak correlations

Here, we establish a threshold for the value of R that could help us to distinguish, as unbiased as possible, strong from weak correlations. This threshold is chosen based on the statistical interpretation of R 2 , described earlier in §2.6.1.2.

As a value of R 2 greater than 0,51 indicates that the 51% of the variability of variable A is explained by a variable B, we extend this to the following: the variable B can explain the variability of variable A at least 51% of the times, which represents the majority. Thus, the threshold value for R results in 0,71

(the squared root of 0,51).

Then, a correlation will be classi ed as strong if the R value is greater than 0,71, and as weak if the R value is lower or equal to 0,71. Similar threshold or critical values were proposed by Cohen in 1988, as encountered in [START_REF] Randolph | Basic Statistics in Multivariate Analysis[END_REF].

Day/nighttime criteria for data sorting

As the aspects we wish to analyze here are the impacts of external sources on the indoor environment and the impact of the night natural ventilation strategy implemented, the experimental data collected will be analyzed separately in the daytime and nighttime. To do this, we have sorted the data using the following criteria:

• Nighttime: Solar radiation = 0 & indoor-outdoor temperature di erence > 0.

• Daytime: Solar radiation = 0 & indoor-outdoor temperature di erence < 0.

Here, we have included the condition of the temperature di erence, only for con guration n • 2.

Classi cation of the correlation results as strong or weak

The results from the meteorological station have shown that the majority of days presented cloudy and windy daytime conditions, and clear and no-windy nighttime conditions. Nevertheless, rst, we decided to apply the statistical approach to days with similar meteorological conditions: sunny and windy daytime and no-windy nighttime (August 15 th , 16 th , 22 nd , and 23 rd ); a total sample size of 576: corresponding to 144 observations in four days. The correlation analysis results based on the Pearson's coe cient, are presented in gures 2.36 and 2.37, for no-windy nighttime (sample size of 196), and sunny and windy daytime (sample size of 271), respectively, using the criteria presented in §2. Also, the temperature di erence between (g) the indoor and outdoor air, and (h) the air near the oor and the oor surface. The airspeed at (i) the location where the indoor air temperature was measured To read these graphs, we can assign to each segment (frames containing numbers) a pair of variables: (vertical-axis variable, "stairs"-axis variable). For example, in gure 2.37, the Pearson's coe cient 2.6. Characterization of the energy charge and discharge processes between indoor and outdoor air temperatures is the cross value between letter "b" in the vertical axis the letter "a" in the "stairs" axis, namely R = 0,64. Additionally, segments presenting an "X" indicates no signi cant statistical correlation, since the computed p-values resulted in being greater than 0,05.

Before going further, to evaluate if the proposed correlation analysis can be considered as acceptable or not, it is applied to correlate variables that normally, in agreement with the physical laws, should present strong correlations coe cients. For instance, consider the convective heat ux (m) and the temperature di erence between the air near the oor surface and the oor surface (h). Since these variables are known to be directly related, as stated by Fourier's law of convection, a strong R value should be expected; this can be observed in segment (m,h) in gures 2.36 and 2.37, which R values are 0,99 and 0,86. These values indicate that the correlation between m and h are both strong (R > 0,71) and positively correlated, as expected.

The di erence in the previous R values for each period (daytime and nighttime), can be explained by the fact that convective heat ux values are stronger when the openings are opened than when they are closed. Another fair and obvious example can be the solar radiation heat ux (k) during nighttime.

Since this variable usually is zero during this period, no correlation whatsoever should be encountered between this and other variables; this can be observed in gure 2.36, of which every R value related to the variable k resulted in a question mark (?) (in other words: "NA"). Moreover, other fair example, not as obvious as those presented before, is that all the temperatures from the indoor environment (b,c,d,e, f ) should present strong correlations between one-another all the time. This can be observed in both gures 2.36 and 2.37, as expected. From those above, the statistical method proposed here, a priori, seems to be a reliable method to evaluate the strengths of correlated variables.

Correlation between the outdoor and indoor environments

The variables from the outdoor environment selected for the correlation analysis are the following: the air temperature (a), the direct solar radiation (k), and the wind speed (n). To evaluate the in uence that these three variables have on the indoor environment, we choose the following variables for the indoor environment: the air temperature (b), the oor surface temperature (c), the total incident radiation on the oor surface (l), and the airspeed (i) and (j). In this way, we can evaluate, speci cally, the contribution of the direct solar radiation to the thermal behavior of the oor surface temperature, and also the contribution of the wind speed to the air movement inside the platform.

First, from the variables mentioned here before we depurate by focusing on the R values greater than 0,71, and the "X" presented in both gures 2.36 and 2.37. Every segment presenting an R value lower or equal to 0,71 and an "X, " is eliminated from the analysis. This allows us to obtain the relevant variables and to consider the third approach mentioned in §2.6.1.2, using correlation matrices with the Spearman's coe cient (cf. gs. 2.38 and 2.39). The correlation matrices include the following:

• The graphs of each pair of correlated variables, as well as their magnitudes (visual trends),

• the distribution of each corresponding sample (represented by histograms),

• The statistical signi cance due to the p-value with red asterisks; where three asterisks ( * * * )

indicate that the p-value is very close to zero, two asterisks ( * * ) that are very close to 0,001, and one asterisk ( * ) that is very close to 0,01. A point (.) indicates that the p-value is very close to 0,1, and nothing ( ) indicates that is very close to 1.

The interest in using Spearman's coe cient is for comparison purposes as the Pearson's coe cient are already presented before. This type of graph (refer to Figs. 6 and 2.39) can be read in the same way as gures 2.36 and 2.37, but here the correlation coe cients of two correlated variables are presented above the diagonal with histograms; under this diagonal are the scatter plots of those variables showing their trend.

Wind speed and indoor air movements

In gures 2.38 and 2.39, for the wind speed (variable n), it is clear that there is no strong correlation presented between variable n and those representing the air movement in the indoor environment (i and j). This is fairly expected for the nighttime period (cf. g. 2.38) since they presented no-windy conditions. In daytime (cf. g. 2.39), the weak correlations encountered between variables n, i and j, might be explained by the fact that the openings remained closed; as a consequence, the air in ltrations are minimal. It is worth mentioning that for a no-windy nighttime, thermal buoyancy dominates the ventilation air ow in the platform.

Therefore, it can be inferred that the air movements in the indoor environment may be strongly correlated with a speci c temperature di erence. In this matter, gure 2.38 shows that there are strong correlations between the air movements (i and j), and the temperature di erences: g and h. Between the segments (g,i), (g, j) and (h, j), which are the strongest ones, higher R values were encountered when using Spearman's coe cient (cf. g. 2.38), than when using Pearson's (cf. g. 2.36). This indicates that the relationship between these correlated variables is rather curvilinear than linear. In fact, based on the physical laws of natural convection and thermal buoyancy, relating the temperature di erence and the resulting airspeed, a 1/2 power law trend is expected to be encountered (cf. g. 2.38, visual trends).

Outdoor solar radiation and the indoor radiative environment

Results from correlation analysis showed that the direct solar radiation heat ux does not play an essential role in the indoor radiative environment, whether using the Pearson's coe cient (cf. g.

2.37, segment (l,k): R = 0,24) or Spearman's (cf. g. 2.39, segment (l,k): R = -0,25). In fact, the solar radiation heat ux (k) is not strongly correlated with any other variable, when considering the R threshold criterion proposed. This a priori means that the implemented double-glazed windows with blinds, reduce the incoming solar radiation heat ux, which lead to suspect that the indoor radiative environment is driven by internal long wavelength (LWL) radiation. This implies that the oor surface is heated by the surrounding surfaces, i.e., the glazed-facade and ceiling, among others.

However, the fact that no strong correlations have been encountered for the variable k can also be explained by the position of the Sun in the summertime and the solar eave facing south, on the ceiling.

As the Sun position is higher, the solar eave prevents the sun rays from reaching the glazed-facade, and thus, the indoor oor surface. Also, a consequence of the orientation of the platform, the windows at the north facade will not be heated by direct solar radiation. It is worth mentioning that this analysis was rst applied to data from only one day (sample size of 144), and greater correlation coe cient values have been encountered when larger sample size was used.

So far we have analyzed data from days with similar meteorological conditions. In addition to this, the same analysis was applied to days with mixed meteorological conditions, to observe if the correlation results hold: July 28 th and 29 th , and August 15 th , 16 th , 19 th , 20 th , 22 nd , and 23 rd . The R values were encountered to be lower than those found in the analysis presented before. This lead to conclude that if the variability of a variable "A" wants to be statistically studied regarding a variable "B", data from experiments with similar conditions should be used, rather than mixing data from experiments under di erent conditions together, as expected.

Characterization of the energy charge and discharge processes

In summary:

The correlation analysis strongly suggests that indoor direct solar radiation is well attenuated by the double-glazed windows with blinds, which implies that the LWL radiation dominates the indoor radiative heat exchanges. Therefore, the direct solar radiation heat ux will be neglected in further analyses.

2.6.2 Identi cation of the heat transfer phenomena involved 2.6.2.1 Convective heat transfer coe cient in the charge and discharge

The periods of charge and discharge can also be highlighted by the behavior of the convective heat transfer coe cient. Since our experimental results allow us to determine this coe cient in two ways based on Fourier's law of convection:

• by confronting the convective heat ux with the corresponding air-surface temperature di erence: ϕ C ∝ ∆T the resulting slope corresponds to the convective heat transfer coe cient (cf.

gs. 2.40, 2.41 and 2.42).

• by dividing the convective heat ux (ϕ C S i ) with the corresponding air-surface temperature difference:

h C S i = ϕ C S i T ia S i -T S i W•m -2 •K -1 (2.24)
where S i is the corresponding surface where the coe cient is been determined: concrete-slab (D), ceiling (P), glazed-facade (g). Note that the air temperature employed here (T ia ) is that measured at 0,1 m above the surface. In each gure, the colors black, purple and brown are assigned to the oor surface, ceiling surface, and glazed-facade, respectively. From gures 2.41 and 2.42, two di erent regions can be distinguished by the changes in the slopes.

For instances, in gure 2.41 for the oor (black dotted line), the slope appears to have an in ection point around the origin (∆T = 0 and ϕ C = 0); the ceiling (purple dotted line) appears to have the same in ection point. This before may imply that the convective heat transfer coe cient adopts di erent values in two di erent periods: the charge (ϕ C > 0) and discharge (ϕ C < 0). This remark can be con rmed by plotting the convective heat transfer coe cient with respect to time as in gures 2.44 and 2.45.

In these gures, the convective heat transfer coe cient for the oor (black circles) presents larger 2.6. Characterization of the energy charge and discharge processes values than for the ceiling, during the discharge period (nighttime). The opposite is observed during the charge period (daytime). This agrees with what was found for the case of their convective heat uxes (cf. gs. 2.28 and 2.29).

Moreover, the value of the slope for either the oor or ceiling appears to be slightly di erent depending on the day, i.e., the slope for the 22/8 is not the same as for the [START_REF] Cherif | Super cial heat transfer by forced convection and radiation in a horizontal channel[END_REF] In summary:

The implementation of a constant value might not be a suitable choice for modeling purposes, in order to enhance prediction accuracy. Thus, the determination of this coe cient as a function of other parameters might be necessary, for the case when the heat transfer phenomena involved is wanted to be taking into account explicitly. In this regard, the same statistical analysis performed earlier was employed here only for the oor concrete-slab surface, to determine the heat transfer phenomena involved in both charge and discharge periods.

Convection and conduction heat transfer phenomena at the oor concrete-slab surface

In order to determine the nature of the heat transfer phenomena involved in the most heavyweighted element of the platform envelope, only the results for the oor concrete-slab are presented.

In the case of convective heat transfer, we recur to the classic four dimensionless numbers frequently employed for this kind of analysis: Nu, Re, Gr , Ri, Bi and Fr (referred to the last nomenclature page for mathematical de nitions). Nu number is employed to determine the strength of convective over conductive heat transfer, Re and Gr are employed to associate the nature of the convective heat transfer to present more a nity to forced or natural convection. Ri number is employed to determine the importance of either force or natural component that might be involved in the convective heat transfer.

Bi number is employed to determine if a uniform or non-uniform heat conduction occurs through the slab thickness. Finally, the Fr number is employed in regard to natural ventilation forces to determine the importance of either the shear stress or thermal buoyancy.

The characteristic length L c employed in Nu number is the height at where the air temperature is measured above the oor surface 0,1 m. For Re number, the characteristic length is the horizontal distance between the openings at the glazed-facade and the location where the airspeed is measured at 0,1 m above the surface: 1 m. The same distance was employed for Gr number to be in agree-ment with Re number at the moment of comparison. Finally, for Bi number, the slab slab thickness is used 0,068 m [START_REF] Çengel | Heat Transfer: A Practical Approach[END_REF][START_REF] Özisik | Heat Transfer: A Basic Approach[END_REF]. The values implemented in all dimensionless number are presented in table 2.7. Color key: Moments where openings remained opened (gray zones). These results are from the thermoelectric modules.

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

The results for Bi, Nu, Re and Gr for con gurations n • 2 and n • 3, are presented in table 2.8. Despite the low values of Bi number encountered for each con guration, they suggest that a non-uniform heat conduction is most likely to happen (Bi > 0,1) during both the charge and discharge periods (cf. gs. 2.46 and 2.48). As Bi number presented in these gures accounts only for the convective heat transfer coe cient, it is clear that the consideration of a modi ed Bi number, including the radiative heat transfer coe cient, will also yield to the same conclusion.

A correlation matrix, with Spearman's coe cient, is employed here for the analysis of the convective heat transfer phenomena over the oor surface, during the discharge period only (cf. gs.2.47 and 2.49).

By implementing the threshold value (R > 0,71) presented in earlier in §2.6.1.3 to distinguish strong from weak correlations between two variables, from gure 2.47 it can be observed that the Nu number presents strong correlation with Gr and Re numbers, in both correlation coe cient R (0,89 and 0,92, respectively), and in trend. This implies that a mixed convection takes place during the discharge period. The trend between both dimensionless numbers is expected since both Gr and Re, are related to the Nu number by a power law [START_REF] Çengel | Heat Transfer: A Practical Approach[END_REF][START_REF] Özisik | Heat Transfer: A Basic Approach[END_REF].

Moreover, a strong correlation (R = 0,80) is also encountered between Gr and Re number. Since both numbers depend on di erent parameters from which may not have a direct relationship: temperature di erence, and airspeed, respectively, the R value may be surprising at rst sight. However, this might not be surprising at all, if we recall the pair (h, j) from gure 2.38 (p.81), where a strong correlation was encountered between the air-surface temperature di erence at oor surface and the airspeed near it. This suggests that the airspeed detected is a consequence of the air movement caused by a temperature di erence. In fact, by assuming Boussinesq approximation, an expression relating the airspeed ( V) with the air-surface temperature di erence (∆T) can be obtained as follows [34]:

V = 2 • g • L c • β • ∆T m•s -1 (2.25)
where β represents the expansion coe cient of the air. It can be inferred from this analysis, that the convective heat transfer has a dominant nature: natural convection.

On the other hand, the levels of the Ri number encountered (cf. g.2.50, black circles), suggest that mixed convection is most likely to happen during the discharge period (gray zones), as these values are between 0,1 and 10.

Regardless, the consideration of the uncertainty in this analysis might lead to di erent inferences. Also, in this gure, it can be observed that during the rst three discharge periods the Fr number presents a value of zero (brown circles) due to the absence of wind, suggesting that stack ventilation occurs [START_REF] Hunt | The uid mechanics of natural ventilation-displacement ventilation by buoyancy-driven ows assisted by wind[END_REF][START_REF] Linden | The uid mechanics of natural ventilation[END_REF]. For the fourth day (8/9), an inconsistency appears to happen: as the Fr number gets larger, the Ri number also presents more signi cant values. The former indicates that wind e ects are getting stronger, and the two-layer strati cation established (stack ventilation) due to the absence of wind, is being disturbed, and mixing occurs. Values of Fr number large enough indicates that wind e ects dominate. On the contrary, large values of Ri number indicates that natural convection dominates. In summary, we can retain the following:

Characterization of the energy charge and discharge processes

Ri

• The heat conduction through the concrete-slab thickness might be best described when considering no-uniform heat conduction, for both charge and discharge periods.

• During the discharge period, it is strongly suggested that natural convection dominates the convective heat transfer at the oor surface. Regardless, there appear to be not enough evidence to completely neglect the forced convection component.

Air temperature distribution within the platform

Regarding the air thermal strati cation within the platform, the air temperature measurements from con guration n • 2 are presented in gure 2.51. From the point of view of thermal buoyancy or stack forces, the important gradients to analyze are: (i) between the air near the shed-roof and the air near the concrete slab (red solid line), and (ii) between the air near the ceiling and the air near the concrete slab (brown solid line).

Note that a maximum temperature di erence of around 3 • C is encountered during the rst discharge period (22/8 nighttime), and a decreasing trend is presented for the following days; indicating that thermal buoyancy gets weaker. This is in agreement with the behavior observed for the Fr number in gure 2.50, which presents larger values for the following days; indicating that wind e ects gets stronger, and thus, mixing occurs faster. The latter may also explain the fact that both temperature gradients (cf. g.2.51, red and brown lines) appear to get similar values. However, during the entire measurement campaign (where only con guration n • 2 was implemented) the most frequent air temperature di erence between the shed and the oor (cf. g. 2.51 A-D) was encountered to be 0,47 • C. This might indicates that a weak thermal strati cation is more probably to happen (cf. g. 2.52). However, this last remark is can be rendered moot since 0,47 • C falls inside the uncertainty in our temperature measurements (0,48 • C).

Distribution of the heat exchanges over the oor concrete-slab surface

Only as an illustrative mode, the experimental set-up implemented in the very rst measurement campaign carried out in the summertime of 2015, is presented hereafter in gure 2.53, with the purpose of determining the locations where the total heat ux presents the most signi cant values over the oor concrete-slab. During this measurement campaign, all "measurement devices" were distributed to cover half of the concrete-slab surface near the glazed-facade.

Such "discrete" arrangement had allowed us to observe the distribution of the heat ux near the natural ventilation openings; an illustration of the total heat ux distribution results during the discharge period is presented in gure 2.54. It is worth recalling that since during this period, the radiative heat ux does not present signi cant values with respect to the convective heat ux, and thus, the most part 90 of the total heat ux measured is by convection.

In this gure 2.54, it can be observed that the total heat ux presents larger values near the openings, as expected. This heat ux appears to get smaller as we move away from the openings, which can be explained by the fact that after the air currents, at outdoor temperature, enter the platform and mixed with air, at indoor temperature (higher than the outdoor air), they reach the rst row of "measurement devices" [START_REF] Azerou | Conception, réalisation et mise en oeuvre de uxmètre thermiques passif et dynamique à base de couches minces[END_REF][START_REF] Chen | Statistical analysis of architectural features e ects on indoor environmental conditions in a Plus Energy House prototype[END_REF][START_REF] Chen | In uence des e ets du vent et du tirage thermique sur le taux de renouvellement de l'air d'un bâtiment ventilé naturellement : estimations par simulation aéraulique directe et par validation expérimentale d'une modélisation thermique[END_REF]7,[START_REF] Chen | Evaluation expérimentale d'une stratégie domotique de pilotage des éléments mobiles : vers un contrôle semi-passif simple du confort d'été en BEPos[END_REF]. Here, the air currents are heated as they get in contact with the concrete-slab surface between the rst and second row of "measurement devices". Then, before reaching the second row (5, 4, 3, 2, 1): (i) some groups of air particles might get lighter enough, after heated, to detaching from the rest of the groups towards the upper parts of the platform, weakening the air currents towards the second row, or (ii) the concrete-slab surface roughness (including the sensors) may be important enough as to weaken the air currents. This scenario might happen slowly since the airspeed detected were signi cantly low (cf. g. 2.28, brown line, similar airspeed levels were encountered by [START_REF] Dascalaki | On the combination of air velocity and ow measurements in single-sided natural ventilation con gurations[END_REF]).

This behavior was studied for a similar scenario (a buoyant cold ow dropping into the oor region), concluding, as expected, that it causes a radial air movement into the zone, and the airspeed is reduced as it moves away from the air jet from the opening [START_REF] Peter | Characteristics of buoyant ow from open windows in naturally ventilated rooms[END_REF].

Note that placing measurement devices exactly behind the openings results in an average underestimation of the total heat ux, and placing them too close to the glazed-facade, results in an average overestimation of this heat ux. This highlights the zones where the total heat ux distribution presents the most signi cant values, and this measurement point or zone will be employed for further analysis, regarding the modeling.

Contribution of the envelope to the charge process via infrared thermography

The impact that the outdoor environment has on the indoor environment can also be highlighted during the charging process using infrared thermography [START_REF] Balaras | Infrared thermography for building diagnostics[END_REF]. To illustrate this statement, thermo- Since all thermograms were not all taken at the same moment, the color bar serves only to relatively distinguishing between "hot", and "not hot" surfaces, i.e., the color yellow might not indicate the same temperature level in all thermograms). measurements; the others are directly measured.

For the calculation of the room temperature inside the platform, an expression given by ISO 7726

(1998) will be used. Regarding the estimation of discomfort, it is proposed to use the daily degree-hours of discomfort indicator (DDH). In addition, the di erence between the temperature of the interior air and the mean radiant temperature of the surrounding walls, will be also evaluated (cf. §1.1.1(A)).

Room temperature according to the standard ISO7726

The room temperature takes into account both the temperature of the air, the average temperature of the walls, as well as the air velocity; all three being measured at the same location. It is described, according to ISO 7726 (1998), by the following equation:

T op (t) = T ia (t) + [1 -A k (t)] • [T surr (t) -T ia (t)] [ • C] (2.26)
Where the parameter A k is a function of the air velocity, A k (t) = 0,73V(t) 0,2 .

Daily degree-hour of discomfort (DDH)

Having chosen a comfort interval (23 -26

= day T op (t) -T com f ort max (t) • dt [ • C•h] (2.27)
under the restriction that T op is greater than T com f ort max (T op > T com f ort max ).

Impact of a passive night ventilation strategy on internal thermal comfort

During this measurement campaign, the evolution of the outside air temperature (black line) and Usually, the room temperature should be in the comfort range during the daytime period of a typical day. Thus we can see in gure 2.56 that the majority of the peaks of the room temperature were in agreement with the comfort interval.

Figure 2.57 shows the degree-hour of days with T op (cf. eq. 24) greater than T com f ort max (T op > T com f ort max ), and the di erence in temperature maximum (∆T max ) between these last two. There are also the maximum values of the outdoor temperature and room temperature.

In more detail, the comfort interval was exceeded by the room temperature 13% of the total duration of the measurement campaign (6862 times out of 51398 data). Here we observe that the more frequent exceeding degrees are less than 2 • C (6397 times out of 6862: 93,22% of the exceeding). This corresponds to a value of approximately 120 degree-hour of discomfort over the 34 days. In order to know if this value is signi cant, it should be compared with the results of degree-hour for similar weather days, without the implementation of night natural ventilation strategy. In the daytime, we can observe that the speed levels are visibly lower than 25 cm•s -1 ; which is also consistent with the norm.

In addition, gure 2.59 shows the resulting mean radiant temperature of the surrounding walls (black line with "+"). It can be observe that this temperature is confused with the line of the room temperature (blue dotted line) and likewise with that of the air temperature (black solid line). Among this results, the di erence between the air temperature and the mean radiant temperature has never reached a gap as large as 3 • C. It can also be inferred that because the mean radiant temperature is very close to that of the indoor air, the level of radiation inside the platform is very low. This low level may be the result of good insulation of the building envelope and the fact that the solar shades always remained close.

In summary:

The results showed that this platform, under typical summer weather conditions, was able to maintain the comfort during the daytime of most days of this measurement campaign (87%, equivalent to 29 out of 34 days) this by allowing a night natural ventilation strategy and keeping the solar shades closed. This allows us to rea rm that an adequate coupling between the thermal inertia of a building, programmable solar protection, and openings allowing natural night ventilation, can ensure an integral thermal comfort of the indoor environment during the period day of a typical day in the summer season. It should be noted that the natural ventilation strategy implemented throughout the campaign did not use all the openings of the platform; thus, implementing all the openings, for the days that have presented discomfort, might reduce the risk of discomfort.

2.8. Concluding remarks

Concluding remarks

The exhaustive experimental study presented in this chapter has allowed characterizing, in detail, the thermal aspects of the experimental platform, suggesting the following major points:

1. It is not enough to take the convective coe cients as constant values when the openings are open. It would be necessary to model or to identify them in another way.

2. The convection inside the platform does not appear to have a dominant nature, natural or forced, both may occur when the openings are open.

3. The direct solar radiation does not heat directly the indoor environment of the platform.

4. The most representative measuring location on the slab surface is between the two groups of openings and in the middle of the platform, close to the south facade.

5. It is necessary to take into account the convective e ects on the slab surface, on the ceiling, and on the glazed-facade individually, due to their behavior.

6. It is clear that there are some vertical walls that contribute the most to the heating of the indoor air; taking them all when describing the indoor air heat gains might lead to overestimations.

7. The vertical thermal strati cation of the indoor air within the platform, can be neglected regarding the thermal comfort of the indoor environment. However, regarding buoyancy driven ventilation, it is suggested that neglecting these thermal gradients may be a suitable choice for larger values of Fr number, than the ones encountered. 8. The values of Bi number encountered suggest that a non-uniform heat conduction might give a precise description of the heat transfer through the concrete-slab thickness.

These last remarks have allowed us to highlight the key elements involved in the energy chargedischarge process in our experimental platform: the indoor air, the concrete slab (as the thermal mass), the glazed-facade, the air ow rate, and the ceiling, in terms of heat transfer.

Nevertheless, the characterization of the thermal aspects of the experimental platform should also consider the heat transfer associated with the exchanges in mass (air) between the indoor and outdoor environments. This consideration requires the knowledge of the natural air ow rate within the platform. Thus, we address the following chapter to characterize the ventilation air ow rate.

Furthermore, this characterization has endorsed the consideration of including, later in the modeling, the key elements mentioned here before. Also, to consider not to include the direct solar radiation in the modeling of the heat transfer in the concrete slab.

C Scope

This chapter is dedicated to characterizing the natural ventilation air ow rate in the platform, in terms of air change rate per hour (ach). This characterization aims to determine an expression relating the net ach as a function of the wind speed and direction, and the indoor-outdoor temperature di erence. To do this, direct air ow simulations were performed for a single-zone model of the platform via network air ow models in CONTAM, to account for wind and temperature e ects on the net ach. Air leakages are also included. These simulations require the knowledge of the air ow characteristics of the openings and leakages, i.e., discharge coe cient, air ow rate coe cient, ow exponent and e ective area. These characteristics were estimated using experimental data from airtightness tests. Since these tests allow us to determined an expression for the discharge coe cient that depends on the pressure di erence, pressure measurements were carried out to observe the pressure levels attained in the platform. Finally, the distribution of the air-leakage is studied for two particular cases, and the combined e ects of wind and temperature are also studied.

Chapter 3 -Characterization of the natural ventilation air ow rate

Initial considerations and air ow pattern recognition

After assessing the experimental and modeling techniques that have been developed and implemented for the determination of the natural air ow rate (cf. §1. 1.3, p.14), and since we are interested in taking into account those with deep consideration of the physical phenomena, the most attractive options are CFD simulations, heavy instrumentation, or both. Since the computation time expend by CFD simulations can become excessively large very promptly, such modeling techniques are rendered as inconvenient. Complicated and expensive experimental methods such as tracer gas, particle image velocimetry, or heavy instrumentation in terms of airspeed measurements using complex algorithms as in [START_REF] Caciolo | Analyse expérimentale et simulation de la ventilation naturelle mono-façade pour le rafraîchissement des immeubles de bureaux[END_REF]33,[START_REF] Teppner | Air change rates driven by the ow around and through a building storey with fully open or tilted windows: An experimental and numerical study[END_REF], are neither suitable nor accessible techniques for our particular case. The reasons are attributed to the non-generic distribution and the number of natural ventilation openings in our platform.

At rst sight, the most plausible appears to be the implementation of empirical modeling techniques, speci cally using air ow path with the electrical analogy, because these models do not require heavy experimental equipment or simulation tools, or both, and their use is largely acceptable among this eld of study. However, an essential obstacle for such models is the precise knowledge of the air ow path within the building. In this matter, instead of assuming a hypothetical air ow path, several small ags were installed at all the openings, as well as, at other parts within the platform, to identify visually On the other hand, in gure 3.1 (c), the ag on the bottom right opening appears to be tilted inwardly, and the ag on the bottom left opening appears to be tilted outwardly, while both ags on the top openings appear to be steady. The behavior of the bottom openings might be expected regarding the wind direction. However, the behavior of the top openings with respect to those of the bottom might be unexpected when only considering the wind direction. Also, accounting for this particular behavior in the air ow path electrical analogy modeling, might not be convenient. In such cases, stochastic studies on air ow pattern recognition might lead to determine the most likely air ow path to happen, before considering the implementation of such models. Only as an illustrative purpose, in gure 3.1 (d), the ags appear to be tilted outwardly (air ow leaving the platform, green arrows); another behavior easily to account for in air ow path models.

Therefore, this air ow pattern recognition, rather simple, led us to consider another modeling method. In this regard, the choice of air ow network models seems the most suitable option, since a deep consideration of the physical laws is taken into account. However, instead of solving the sys- tem of equations that might result from the implementation of such model, CONTAM software was decided to be employed. This software allows to perform transient air ow simulations, and includes several kinds of air ow models; having di erent options for air-leakages and openings. Also, as it employs the Newton-Raphson numerical method, low errors are to be expected in the numerical solution [START_REF] Dols | CONTAM User Guide and Program Documentation Version 3.2[END_REF].

Modeling of the natural air ow rate in the platform

The natural air ow rate in the platform, as a function of wind and thermal buoyancy e ects, is proposed to be determined using the air ow simulation software CONTAM. This software is, dedicated to performing air ow simulations by solving the ow conservation equation, in either steady and transitory conditions, coupled with Bernoulli's equation, without accounting for any heat exchanges inside the given building (convection, radiation, conduction). The simulation calculates the pressure di erence and air ow rate at every opening in the building, along with the ow direction. Also, the air ow rate of a speci c zone of the building can be calculated.

The interest in the implementation of this software lays especially in the possibility to determine simple expressions linking the wind and thermal buoyancy e ects individually to the natural air ow rate in the platform. Here, the natural air ow rate will be represented in the form of air change per hour or ach, since it is a standard way to refer to the ventilation air ow rate when considering natural ventilation in buildings.

Since this software allows to design the given enclosure only by visualizing the top view, some modi cations are made to the geometry of the platform. The modeling process is presented in gure Here, the two di erent heights of the south and north facades are distinguished on the software with their corresponding heights: 3,7 m and 4,9 m, respectively with respect to the ground. To do this, we followed the next six steps to design the model on CONTAM: After drawing the four walls of the enclosure, on the project con guration properties window, in the sketchpad dimensions label, the width, and height are set to 70 and 66 cells with a scaling factor of 0,1 m, to account for the real dimensions in meters of the zone limited by the south facade and the shed-roof (a 7 x 6,6 m surface area). Then, on the zone properties window, a normal-zone type is created inside the four walls, where the volume of the enclosure is included. Finally, the temperature and pressure are set to vary instead of remain constant, and no temperature schedule is considered. To account for the height of the enclosure, on the level data window, the distance to level above is set to 3,47 m which is the height from the oor of the platform to its highest point. (

2) Location of the natural ventilation openings

The openings or as the software called them, air ow paths, are created onto the walls of the enclosure (cf. g. 3.2, domain modeling box on the right-hand side). Four air ow paths are created onto the wall facing south (bottom wall) and six onto the wall facing north (top wall). As two of the openings at the south facade are located above the other two, the relative elevation of these openings is set at 1,2 m in the ow path label on the air ow path properties window. In the same label, the location of the opening is terminated by setting the value of the x coordinate to their real relative distance on the facade, and nally, no limitations for pressure or ow capacity are considered for each opening.

(

3) Location of the air-leakages

The location or distribution of the air in ltrations on the envelope is a delicate topic due to the imprecisions that might arise when estimating the air ow rate through modeling techniques [20,[START_REF] Etheridge | The prediction of ventilation rates in houses and the implications for energy conservation[END_REF].

According to the CETE de Lyon in its report regarding the generalities and sensitization of the enve-lope airtightness in buildings [START_REF] Carrié | Perméabilité à l'air de l'enveloppe des bâtiments -Généralités et sensibilisation[END_REF], the regions most likely to attend air-leakages are: (i) facades and oors, (ii) external furnishings, (iii) electrical equipment, and (iv) traps and elements crossing the walls.

Therefore, the following two scenarios gured as the most likely locations and should be analyzed: Both scenarios can be simulated on CONTAM without complications (refer to §3.4 for results).

(4) Air ow models for the openings and in ltrations

For each air ow path created, a ow element is required by the software. Therefore, by accessing the ow element label on the air ow path properties window and then selecting new element, the air ow path can be created by choosing the appropriated air ow element model. This air ow element model describes the air ow through the opening. In our case, a one-way ow using power law models in the form of Q = C(dP) n is chosen for the air ow paths symbolizing the air leakages and in ltrations; a two-way ow models in the form of one opening is chosen for the air ow paths symbolizing the natural ventilation openings.

Regarding the air leakages and in ltrations, the dimensions of the ori ces are generally small and often unmeasurable, which a priori justify the assumption of only admitting a unidirectional ow.

Regarding the natural ventilation openings, the air ow element model chosen is based on previous studies done by [START_REF] Caciolo | Analyse expérimentale et simulation de la ventilation naturelle mono-façade pour le rafraîchissement des immeubles de bureaux[END_REF][START_REF] Dascalaki | On the combination of air velocity and ow measurements in single-sided natural ventilation con gurations[END_REF][START_REF] Flourentzou | Natural ventilation for passive cooling: measurement of discharge coe cients[END_REF][START_REF] Li | Buoyancy-driven natural ventilation of a room with large opennings[END_REF] Individually they do not meet the requirements to consider them as large openings (where bidirectional ows are most likely to occur), but together they behave as a large opening. Note that this consideration might be rendered moot when including wind e ects, which might break the neutral plane established.

Furthermore, this before also leads to consider the following two inquiries: (1.) does the neutral plane remained at this xed position during the entire opening period? (cf. g. 3.4 (a)) Or (2.) does the neutral plane behave as a moving boundary implying that stack ventilation occurs? (for instance, starting as in gure 3.4 (c), then moving up to location as in gure 3.4 (a), and continuing). CONTAM does seem to account for inquiry (2.), since it is allowed to perform transient simulations. However, a dimensionless analysis implementing the Froude number can help to determine the moments when wind e ects become strong enough to break this neutral plane (NPL) established [START_REF] Linden | The uid mechanics of natural ventilation[END_REF]. The analysis presented in chapter 2 implies that inquiry (2.) should be considered, since most days presented absence of wind.

Finally, by choosing a two-way ow model, CONTAM only allows the user to provide the opening dimensions, as well as, the value of the corresponding discharge coe cient C d (where the default value is set to 0,78). The ow exponent n is xed at a value of 0,5 (theoretical value established by Bernoulli's law); refer to §1.1.3.1 for de nitions. In turn, the methodology to determine the value of the discharge coe cient and the ow exponent, is presented later in §3.3.

(5) Accounting for wind and thermal buoyancy e ects Wind e ects are taking into account by an expression relating the relative dynamic pressure at the building height with the wind speed. The following equation computes the relative wind pressure at each facade:

P(t) = 1 2 • ρ • V 2 met (t) • C f • C p (φ W S ) [Pa] (3.1)
where V met represents the wind speed measured at a free height of 10 m by a meteorological station.

The coe cient C f , named wind speed modi er, considers the e ects of the terrain where the building is installed regarding elevation and roughness, as follows:

C f = V 2 f V 2 met = A 2 o • Z f Z met 2•γ [-] (3.2)
where V f represents the wind speed at the facades height Z f containing openings, and Z met is the height where the meteorological station measures the wind speed. The factor A o and exponent γ depend on the terrain type as shown in table 3.1.

A view of the terrain where our platform was installed, is presented in gure 3.5. From gure 3.5 (a), it can be inferred that the terrain surrounding the platform does not t the characteristics of an urban terrain type, according to [101]; in this regard, a suburban terrain type seems an adequate classi cation for our case, and it will be considered in the simulations. The resulting C f values for North and South Finally, in equation 3.1 the coe cient C p (φ W f ) represents the external pressure coe cient which depends on the relative wind direction φ W with respect to the azimuth angle of the facade φ f , as:

φ W f = φ W -φ f .
The e ects of thermal buoyancy are taken into account on the software by allowing to di erentiate the temperature inside and outside of the zone. The transient conditions are considered by enabling the variation of the air density with temperature, but the air temperature of each zone is considered uniform throughout its volume.

C p = e/5 d • C p A + 4 • e/5 d • C p B + d -e d • C p C [-] (3.3)
Therefore, for the case where the North facade is the windward facade, the C p values are assigned as follows: +0,76 for 0 • and 360 • ; -0,856 for 90 • and 270 • ; and -0,42 for 180 • (the leeward facade). For intermediate angles, on CONTAM, the user has the option to choose between linear or polynomial interpolation on the wind pressure pro le window; a polynomial interpolation have been chosen here, refer to gure 3.7. In summary:

In order to perform the air ow simulation on CONTAM, the following requirements are still needed:

1. The air ow characteristics of both the openings and the tightness of the building envelope.

2. the location of the air in ltrations/leakages.

Air ow characteristics of the openings

In order to determine the air ow characteristics of the air-leakage and openings, to complete the air ow model on the software, airtightness tests (also known as blower door tests or fan pressurization tests) are implemented. For the air-leakage (openings closed), the airtightness tests are performed following the procedure recommended by the standard NF EN 13829. For the openings, we proposed to follow the same procedure as for the latter, but with the openings opened (similar to [55]).

We decided to characterize the air ow capacity of the platform openings in terms of discharge coe cient and air ow rate, instead of using the values reported in the literature (cf. §1. 1.3.1). The reason lays in the morphology of the openings in the platform, which are equipped with a high tightness level (cf. g. 3.9).

Recovery of the envelope tightness and airtightness tests

Since the platform had been a ected due to various phases of assembly and transport, its envelope was carefully examined by pressurizing the platform with the ventilator and using the smoke pencil 109 to identify the regions most likely to attend air-leakages, based on [START_REF] Carrié | Perméabilité à l'air de l'enveloppe des bâtiments -Généralités et sensibilisation[END_REF]. Before this, all air-conducts related to the mechanical ventilation and PCM system were sealed (cf. g. 3.10 (a)-(b)).

After identi cation, polyurethane foam in aerosol (with a traction resistance up to 175 kPa and density of 1,09 g•cm -3 ) and the "special tightness adhesive", were employed to close the big holes and to reinforce the joinery (cf. g. 3.10 (c)-(f)). Consecutively, airtightness test were performed to see how each hole sealed and joinery reinforced, reduces the air-leakage rate, and evaluate if it met the regulated air-leakage rate (cf. g. 3.12, and table 3.4). It appears that only around 27% of the air-leakage were reduced by performing the actions in table 3.4. Finally, after these actions, the majority of the air-leakages were identi ed to be located at the West facade due several electrical networks (cf. g.

(e))

; location of part of the home automation system. (

1) Airtightness tests with openings closed

Considering that the outdoor conditions can strongly in uence the variability of the outcome of each test, two measurement campaigns were carried out in 2015 and 2016 to repeat the tests as many as possible. In 2015, 34 tests were performed in ten di erent days from June 17 th to October 30 th , e.g., (

2) Airtightness tests with openings opened

Part of the tests performed during the measurement campaigns consisted of opening a set of openings and performing the same test as for the case of openings closed. In this case, depending on the opening con guration one blower door could not achieve the pressure di erence levels recommended by the standard, and thus, two blower doors were implemented simultaneously, as shown in gure 3.12. For this the software TECLOG was used.

Discharge coe cient of the openings

For the determination of the discharge coe cient, the following expression arises by equalizing the theoretical and empirical de nitions of the air ow capacity of an opening (cf. eq.1.6 and eq.1.7

C d (∆P) = C S e f f • ρ 2 1/2 • [∆P] n-1/2 [-] (3.4)
where, S e f f represents the e ective area of the opening and is calculated for the tilted window type using equation 1.9 (p.18), by knowing the opening dimensions and their opening-angle. In our case, the latter is equal to 20 • , which corresponds to the maximum opening-angle of all the openings in the platform. A similar expression for C d can be obtained by the de nition given in [START_REF] Hebbar | Performance of conical jet nozzles in terms of discharge coe cient[END_REF], but it involves other characteristics of the openings in addition to those in equation 3.4. Therefore, we only require the value of the air ow rate coe cient C and the ow exponent n, for each opening to determine an expression of their corresponding discharge coe cient as a function of the pressure di erence.

Finally, since equation 3.4 depends on the pressure di erence, it is condensed to the following expression in order to evaluate the discharge coe cient at each pressure di erence to decide whether an average value can be used or not, over the working pressure levels:

C d v (∆P) = C d v • [∆P] n dv [-] (3.5)
where, as example for the openings at the South facade,

C d south is equal to C south S e f f south • ρ 2 1/2
, and the exponent n d south is equal to n south -1/2.

Results and analysis

Identi cation of C and n for each opening

Here, the subscript "v" will be used to refer to the openings and "l" to refer to the air-leakage or in ltrations, i.e., C south and n south for the opening at the south facade, C north and n north for the opening at the north facade, and C shed and n shed for the opening at the shed-roof. In order to identify the values of C and n for the openings, the following is considered for processing the results from the airtightness tests with openings opened:

• The air-leakage are present in every test.

• The openings at the South and North facades are programmed by default to open and close all four simultaneously. On the other hand, the two openings at the shed-roof can both be opened simultaneously or individually. Therefore, the coe cient C South includes all four openings; this coe cient must be divided by four to know the value of only one opening.

Then, with the airtightness tests results, an expression similar to equation (1.7) (p.15) is obtained by tting a power law regression to the air ow rate results with respect to the pressure di erence. In general, the tted regression for each test with openings opened, yield:

Vv+l (∆P) = C v+l • [∆P] n v+l m 3 •s -1 (3.6)
where Vv+l represents the total air ow rate through the openings and leakages, e.g., Vsouth+l = C south+l (∆P) n south+l , for the test where the openings at the South facade remained open. Now, the air ow rate only through the openings can be either obtained by using directly, the air ow rate measurements:

Vv = Vv+l -Vl m 3 •s -1 (3.7)
or by employing the tted regression as follows:

Vv (∆P) = C v+l • [∆P] n v+l -C l • [∆P] n l m 3 •s -1 (3.8)
which, ultimately, corresponds to the following expression for only the openings:

Vv (∆P) = C v • [∆P] n v m 3 •s -1 . (3.9)
3.4 Results and analysis

Airtightness tests and discharge coe cient identi cation

The linear regressions resulting after processing the data from airtightness tests, for identi cation of the air ow rate coe cient ( C) and ow exponent (n) of each opening with the procedure developed in §3.3.3, are grouped in table 3.5. Also, the parameters needed to identify the value of the discharge coe cients through equation 3.5, for each opening, are included (cf. table 3.5, three last rows).

Since we obtained an expression for the discharge coe cient which depends on the pressure difference (∆P), instead of a constant value, the working pressure di erence must be known in order to determine the values of the discharge coe cient. In order to have an estimate of the working range for ∆P, the pressure di erence was measured at two points during a short period (from July 9 th to 11 th ); the values encountered are shown in gure 3.13 (a). Also in this gure, the following is presented:

(a) The pressure measurements at two point in the platform, where P1 is located at the South facade (green line), and the P2 is located at the North facade (red line).

(b) Location of these measurement , P1 and P2.

(c) A zone presenting an absence of wind.

(d) Another zone presenting an absence of wind.

(e) An schematic of the platform, where the prevalent wind direction is indicated (250 • ).

(f) The corresponding wind speed (red) and wind direction (blue).

The corresponding wind speed and direction from the meteorological station and the location of the two points of measurement are also presented in this gure (cf. g. 3.13 (b) and (f). During these measurements, only the openings at the South and shed-roof were functional.

The behavior of both P1 and P2 are in agreement with the dynamics of the wind speed and direction; the levels of P1 and P2 encountered might seem rather high for typical values encountered in situ measurements. However, similar pressure levels were encountered when performing wind tunnel tests for similar wind speed levels [START_REF] Teppner | Air change rates driven by the ow around and through a building storey with fully open or tilted windows: An experimental and numerical study[END_REF]. Nevertheless, we used these pressure ranges to evaluate the discharge coe cients.

The resulting air ow rates through the openings (cf. eq. 3.9) and their discharge coe cient (cf. eq.

3.5), for the pressure ranges, are presented in gures 3.14 and 3.15, respectively. In these gures, the results of both parameters, are presented for each group of openings: the set of four openings at the South facade (black lines), the set of four opening at the North facade (red lines), and the set of two openings at the shed-roof (blue lines). The interest of showing the air ow rate for each set of openings is merely for comparison purposes with what has been found in the literature for the same type of openings. Let's take gure 1.1 for instance, the air ow rate is reported as a function of the opening degree in centimeters: 200 m 3 •h -1 for an opening degree of 12 cm. In our case, the opening degrees are: 16 cm for the openings at the shed-roof, 22 cm for those at the South facade, and 23 cm for those at the North facade. We can infer from this gure, that each of our openings must bare an air ow capacity larger than 200 m 3 •h -1 at least. In gure 3.14, it can be observe that the air ow capacity of each set of openings is larger than

200 m 3 •h -1 (0,056 m 3 •s -1
). Note that the values in this gure correspond to a set of openings; for one opening, the values must be divided by the total number of openings: for one opening at the South Second, we use the K-P model (cf. eq. 1.12, p.19) to determine both the ach with openings closed and opened. The results are presented here after in table 3.6. The last row of this table presents the resulted ach for a speci c opening con guration. Third, we compare these results with the values reported by R. Jack et. al [55] as shown in gure 3.16. In gure 3.16, it can be observe that the greater the opening area, the greater the ach value, as expected.

Opening effective area (m^2

However, it can be observe that the con guration "South+shed" appears to have a smaller opening area than the "South" opening con guration.

Air ow simulation results

An schematic of the single-zone model constructed on CONTAM is presented in gure 3.17

Air change per hour due to thermal buoyancy e ects only

The simulation results for the air change per hour due to thermal buoyancy only ach ∆T are presented in gure 3.18, for the case of air-leakage only (blue line), openings at the South and shed-roof opened with no leakages (red line), and all openings opened with no leakages (black line). The results are presented with respect to the indoor-outdoor temperature di erence range employed in the simulations.

From these results, an expression relating the ach ∆T and ∆T directly, can be obtained by tting a power law regression as follows:

ach ∆T = A • T ia -T oa T oa x h -1 (3.10)
where the values of A and x depend on the opening con guration. The values obtained for di erent con gurations are presented in table 3.7. The interest of such expression lays in the facility to determine the value of ach ∆T without repeating the simulations. The resulting regression models are in agreement with the theoretical description of the air ow rate due to a temperature di erence (cf. eq. 1.3). These results are important since no knowledge of the air ow path is needed, and the simulation accessibility is very high.

Table 3.7: Regression results for ach ∆T as a function of temperature. In gure 3.19, the resulting ach W for the case of air-leakage only (openings closed) with respect to the wind speed are presented for di erent wind directions. In gure 3.20, the resulting ach W for the case of openings opened with no leakages with respect to the wind speed are presented for di erent wind directions.

Leaks Equally distributed Leaks at the West facade Openings opened

A h -1 Exponent x R 2 A h -1 Exponent x R 2 None (leakages) 4
Similarly, a linear regression can be obtained for the resulting ach as a function of the wind speed, as follows:

ach W = B(φ W ) • V y met h -1 (3.11)
where y depends on the opening con guration: leaks only (cf. table 3.8) or openings with no leaks (y = 1). B is the slope of each line in gures 3.19 and 3.20, which value depends on the wind direction φ W , and also, on the opening con guration. By plotting each slope B(φ W ) with respect to φ W , results in the points presented in gure 3.21. The blue squares represent the di erent slopes from gure 3.19

(air-leakages), and the red squares represent the slopes from gure 3.20.

This behavior, exhibit by B(φ W ), can be approximated by a Fourier's series regression (cf. g. 3.21, dashed lines). A three cycles Fourier's series was encountered to t this behavior at less than 5% of relative error, resulting in:

B(φ W ) = A + B • cos[ω • φ W ] + C • sin[ω • φ W ] + D • cos[2 • ω • φ W ] + E • sin[2 • ω • φ W ] + F • cos[3 • ω • φ W ] -G • sin[3 • ω • φ W ] h -1 •m -y •s y (3.12)
where the values of the coe cients A to G and ω, are presented in table 3.8. Note that only these values are presented for the opening con guration South+shed-roof since they were the only functional openings during the measurement campaigns, as mentioned earlier.

Regarding the resulting ach W for the two locations of air-leakages, the value of B(φ W ) for "South + shed + leaks" (cf. table 3.8), appears to have only a slight di erence. Also, a slight di erence is presented between B(φ W ) for the case of "South+shed+leaks" (at the West facade) and "South+shed" (no leakages). This di erences indicate that the consideration of either the case of openings opened without leaks or the case of openings opened with leaks at the West facade, will not have a signi cant in uence in the resulting net ach W . However, having the leaks equally distributed at the facades with openings slightly increases the net ach W , and this for openings at the South and North facades. The results for the leaks located at the West facade are presented in the following.

Leaks Equally distributed

Openings y A B C D E F G ω
Leakages 1,16 0,328 0,1367 -0,0415 -0,0398 0,0237 0,0129 -0,01702 0,03307 South + shed 1,00 4,234 1,5620 -0,4756 -0,4890 0,2869 0,1585 -0,2150 0,03305 South + shed + leaks 1,00 4,611 1,7160 -0,5226 -0,5343 0,3139 0,1732 -0,2344 0,03305 Leaks at the West facade South + shed + leaks 1,00 4,471 1,6380 -0,5668 -0,4582 0,2971 0,1191 -0,23430 0,03272 b) With leakages located at the West facade:

The simulation results for the ach W as a function of the wind speed and the coe cient B as a function of the wind direction are presented in gures 3.24 and 3.25, respectively. It can be observe, that in gures 3.25 and 3.24, and 3.26 and 3.25, that only a slight di erence is presented for ach w and B, respectively as mentioned before. Similar behavior as in gures 3.21, 3.25 and 3.29, has been reported in the literature [START_REF] Freire | Single-sided natural ventilation driven by wind pressure and temperature di erence[END_REF][START_REF] Steen Larsen | Analysis and Design of Single-Sided Natural Ventilation[END_REF][START_REF] Larsen | Single-sided natural ventilation driven by wind pressure and temperature di erence[END_REF], specically, in [START_REF] Larsen | Single-sided natural ventilation driven by wind pressure and temperature di erence[END_REF] (cf. g. 1.18, p.21). However, the applicability of obtaining the regression models presented here before (cf. eqs. 3.10-3.12), is rather less complicated than those propose by other researchers [START_REF] Larsen | Single-sided natural ventilation driven by wind pressure and temperature di erence[END_REF]121 Chapter 3 -Characterization of the natural ventilation air ow rate 97].

In summary:

The location of the air-leakages has no apparent in uence on the results given by the CONTAM software.

Consistency of air ow simulation results

This section is dedicated to give explanation about the correlations draw from the simulation results.

For instance, take expression (3.10); a similar expression can be easily conceived by replacing equation

(1.
3) into equation (1.6), and assuming Boussinesq's approximation. The di culty lays in the determination of the air ow rate coe cient C, since the common expressions for the e ective area reported in the literature does not applied for out platform due to the required knowledge of the air ow paths [2]. On the contrary, the determination of the air ow ow exponent might not be complicated, since for the case of openings opened only (no leaks) the expected value of n is 0,5. For the case of leaks only (openings closed), the value of n remained unknown without performing experiments.

Regarding equation (3.11) can be easily identi ed by replacing equation (1.2) on page 12 into equation (1.5) on page 15. Here, the di culty also lays in the determination of the coe cient C, since it depends on the air ow path and on the wind direction. The ow exponent n, for the case of openings opened only, the expected value is one; for the case of opening closed, the value of y is two times the value of n (y = 2 • n), but also the n value can only be determined by experimental techniques.

Combined e ects: assistance and opposition

In order to understand the superposition of both e ects (wind and buoyancy), air ow simulations were performed by maintaining constant one e ect and varying the other. For instance, gure 3.26

presents the resulting net ach value for a wind speed of 1 m•s -1 ( V met = 1 m•s -1 ) at di erent temperature di erences and di erent wind directions. For the temperature di erences, the outdoor air temperature was varied; maintaining the indoor air temperature constant at 22 • C.

In this gure, it can be observe that for a wind direction within the rst and fourth quadrant (namely

90 • > φ W > 270 •
), the ach value appears to decrease rst and then increase, where the threshold appears to be a temperature di erence (∆T) depending on the direction: 2 K for 0 • and 20 • , 1 K for 60 • , 1 K for 320 • . For wind directions greater than or equal to 90 • , this behavior disappears. Such behavior is consistent with the case where the wind e ect opposes and assists a stack ventilation strategy (cf. g.

1.6, p.15). Thus, the behavior for wind directions between 0 • and 90 • indicates that wind and buoyancy e ects oppose to each other; for wind directions greater than or equal to 90 • , both e ects assist each other.

This can be explained by assuming plausible air ow path, for instance, since the indoor air temperature is higher than than the outdoor air, the air ow path established should be: outdoor air enters the building from the lower openings and leaves the building through the upper openings. In this case, the only lower openings opened are at the South facade, because at the North facade, only the openings at the shed-roof are opened. Therefore, for a wind direction of between 0 • (wind towards the South pole), the wind encounters the outgoing ow through the openings at the shed-roof (windward facade), and thus, both ows are opposed to each other, decreasing the net air ow rate in the building. Conversely, for an opposite wind direction, say 180 • , the wind encounters the outgoing ow at the upper openings at the South facade (windward facade) and the ingoing ow at the lower openings. For this case, it appears that the net air ow rate is assisted, which indicates that the wind reinforces the ingoing ow due to buoyancy e ects. Additionally, for wind direction of 90 • or 270 • , a assisting e ect is expected, since the wind encounters outgoing ow through four upper openings, and thus, enhancing the net air ow rate (cf. g. 3.26).

Concluding remarks on the air ow characteristics of the platform and perspectives

The undertaken work in this chapter was devoted to characterizing the natural air ow rate in the platform via air ow simulation on CONTAM. This characterization aimed to determine an expression relating the net ach as a function of the wind speed and direction, and the indoor-outdoor temperature di erence. Thus, we can retain the following remarks:

• For the buildings or enclosures, where the air ow path is di cult to be determined due to a large number of openings, focusing on estimating the net air ow rate by using network air ow models, can lead to avoiding unnecessary di culties.

• The assumption of air-leakage equally distributed at the facades with openings seems to be appropriate, instead of identifying them rst by performing airtightness tests with the smoke pencil, when focusing on the global e ect of wind and buoyancy via the net air change rate.

• Performing in situ airtightness tests for the estimation of the friction characteristics of openings, might not be the most suitable choice due to the presence of internal obstructions, such as furniture, partition-walls, doors, among others. However, the implementation of these tests for the 123 Chapter 3 -Characterization of the natural ventilation air ow rate estimation of the air ow capacity in terms of air ow rate levels appears to agree with the values reported in the literature.

• Finally, from the air ow simulations for the combined wind and buoyancy e ects, these e ects appear to oppose to each other only in a speci c range of wind direction.

At the moment, we may conclude that the real value of the natural air change rate in the platform remains uncertain. However, since our results have been compared with values reported in the literature, we may state that the values encountered may be a reasonable estimation of this parameter when an annual-averaged value is needed.

Moreover, the last part of this chapter has shown that we are not yet capable of reporting an expression that combines both wind and buoyancy e ects directly, since: The net value of ach does not appear to be a simple addition when both e ects are assisted, nor a simple subtraction when both e ects are opposed. Therefore, an expression able to superpose both e ects is still needed. In order to choose from the superposition models reported in the literature and to avoid any possible overestimation or underestimation of the ach value, it is necessary to determine its real value. For the latter, we are able to identify the value of ach by employing the heat ux and temperature measurements performed during the measurement campaigns (presented in chapter 2), and a global energy balance in the indoor air.

The rst part of the following chapter is dedicated to identify and compare the ach value.

I Scope

This chapter is dedicated to constructing a thermal model with the aim of describing the behavior of the platform. This behavior is represented by three main elements: the indoor air temperature, the natural ventilation air ow rate, and the concrete-slab surface temperature. These three main elements are represented, respectively, through an energy balance for the indoor air, a semi-empirical expression for the natural air ow rate, and a non-uniform conduction heat transfer model for the concrete slab.

The two rst elements were identi ed together over experimental data. The last element was chosen after comparing the case of uniform and non-uniform heat conduction.

Such thermal model is wanted to contemplate the following aspects:

• To account, as much as possible, for the physical sense.

• To describe the thermal behavior accurately.

• To be able to adapt itself when the opening con guration strategy changes.

Thus, it is decided to implement a semi-empirical modeling approach by taking into account all analyses, data, and hypotheses, presented in previous chapters. Hereafter, we will refer to this model as the "coupled model. " The "control surfaces" (CS) of this control volume (CV) consist of two types of thermodynamic boundaries: impermeable and permeable; this way to distinguish the type of boundary is introduced to separate the boundaries where heat and mass transfer are allowed (permeable) from those where only heat transfer is allowed (impermeable) [START_REF] Wark | Termodinámica[END_REF]. The elements of the envelope: ceiling, oor, and walls (including windows) and natural ventilation openings (only when close), are considered as impermeable control surfaces (ICS). The natural ventilation openings, only when open, are considered as permeable control surfaces (PCS). A schematic representation of the exchanges in mass and heat between the indoor air volume and these CS is presented in gure 4.1.

Theoretically, since we consider a xed control volume, the changes in the enthalpy of the indoor air can be written as follows [START_REF] Wark | Termodinámica[END_REF]:

dH(t) dt CV = d dt CS -→ q(t) • -→ dS + Φ gen (t) + ∑ in ṁin (t) • H(t) + V(t) 2 2 + g • Z in -∑ out ṁout (t) • H(t) + V(t) 2 2 + g • Z out [W] (4.1)
where H(t) given in J represents the enthalpy. On the right-hand side of equation 4.1, the rst term represents the heat exchanged between the impermeable control surfaces and the indoor air in the form of convection. This heat exchanged is represented by q(t) in J•m -2 (cf. g. 4.1, blue lines). A power generation term Φ gen in W represents any heat source within the CV, e.g., occupancy, lights, household appliances. The last two terms in equation 4.1 represent the heat exchanged with the air ow entering and leaving the control volume, respectively, where ṁ(t), V(t), g, and Z, represent the mass ow, the relative airstream speed, the gravitational constant, and the relative height of the airstream source, respectively.

Equation 4.1 can be simpli ed, after examine some considerations (explained hereafter), as follows:

ρ(T ia ) • V ia • c p (T ia ) • dT ia (t) dt = h C D (t) • S D • [T S D (t) -T ia (t)] + h C P (t) • S P • [T S P (t) -T ia (t)] + h C g (t) • S g • T S g (t) -T ia (t) + V ia • ach(t) 3600 • ρ(T oa ) • c p (T oa ) • T oa (t) -V ia • ach(t) 3600 • ρ(T ia ) • c p (T ia ) • T ia (t) [W] (4.2)
where the mass and speci c heat capacity of the indoor air is represented by ρ(T ia ) • V ia and c p (T ia ), respectively, which together represent the heat capacity of the indoor air volume. The temperatures of the indoor and outdoor air are represented by T ia (t) and T oa (t), respectively. The surface temperature of the oor concrete-slab, ceiling and glazed-facade are represented by T S D (t), T S P (t), and T S g (t), respectively; those surfaces in contact with the indoor air. Finally, the convective heat transfer coecient is represented by h C (t). Also, in equation 4.2, the resulting net air ow rate, due to the airstreams entering and leaving the control volume through the permeable control surfaces, is represented by the term ach(t)•V ia /3600 in m 3 •s -1 , where ach(t) is the air change rate per hour in h -1 , V ia is the indoor air volume, and the factor 1/3600 is for dimension agreement, which converts the magnitude hours into seconds. Finally, the heat transfer associated with the airstreams entering and leaving the CV, are represented by ρ(T oa )•c p (T oa )•T oa (t) and ρ(T ia )•c p (T ia )•T ia (t), respectively.

In order to simplify equation 4.1 into equation 4.2, the following considerations were taken into account, along with the hypothesis in table 4.1:

(a) No heat generation within the platform is considered since it remained unoccupied during all measurement campaigns (cf. table 4.1, hyp. n • 3).

(b) The indoor air behaves as an ideal gas (cf. table 4.1, hyp. n • 4). This hypothesis might be justi ed to be retained by the working temperature ranges in our experiments. Also, based on this hypothesis, the sensible part of the enthalpy can be expressed in terms of the speci c heat capacity c p and temperature [START_REF] Bejan | Convection Heat Transfer[END_REF].

(c) The assumption of a uniform temperature was retained, regarding the most frequent vertical temperature gradient encountered in our experimental results, between the air near the shedroof and the air near the oor, of about 0,47 (e) The heat transfer through in ltrations and leakages are taking into account indirectly in the term ach(t), also via the natural air ow rate characterization in chapter 3.

(f) The indoor furniture is considered to be in thermal equilibrium with the air (cf. table 4.1, hyp. n • 6), as well as, any internal partition-walls, doors, and shelves, thus being always at temperature T ia . ). In these gures the coe cient h C was computed using the air temperature measured at 10 cm (recall the "measurement device").

∆H = ρ • V • c p • ∆T
However, to consider hypothesis n • 5 (cf. table 4.1), it is necessary to compute this coe cient using the air temperature measured at 1,70 m above the oor instead (refer to remark (c) here before). This convective coe cient will be named here as h C and is de ned as follows:

h C S i = ϕ C S i T ia -T S i W•m -2 •K -1 (4.3)
where S i represents any of the three surfaces: oor, ceiling and glazed-facade. Thus, the convective coe cient for each surface is represented, respectively, by: h the same for each days. This before leads to state the following remarks:

• During nighttime, when the openings are opened, h C D is larger enough with respect to h C P , that the e ect of the latter becomes imperceptible or, even yet, negligible.

• During the daytime, when the openings are either closed or opened, h C P is larger enough with respect to h C D , that the e ect of the latter also becomes imperceptible or, even yet, negligible.

However, for con guration n • 1 in gure 4.2, it seems that a similar remark, as those mentioned above, regarding the behavior of the oor and ceiling, can only be said for the rst day (May 23 rd ), but not for the others. This might be explained by the fact that the temperature levels encountered in mid-September were not of typical summertime temperature values; unfortunately con guration n • 1 was not implemented in any other time. The temperature of the glazed-facade surface is of interest because results showed that, it always presents the highest temperature values in comparison with the oor and ceiling surfaces (cf. §2.5.3, p.69). Thus, the analysis above leads to retain the following:

In summary:

It is necessary to account for the convective heat transfer individually for each surface: a vertical wall, a horizontal wall at the bottom ( oor), and a horizontal wall at the top (ceiling). The most important vertical wall seems to be the glazed-facade, due to its thermal behavior and contact with the indoor air.

At this point, by using experimental data, equation 4.2 can only be solved for con gurations n • 1 and n • 3 since the glazed-facade surface temperature was not measured for con guration n • 2. For the latter it is necessary to represent the glazed-facade temperature surface T S g in a way as to include experimental data. For this, we propose to represent T S g in terms of the surrounding surface temperatures (SST) measured on the oor surface. An average value of SST can be obtained by approximating its value using the de nition of the mean radiant temperature (MRT). The de nition of MRT is based on a weighted-superposition to the fourth power, as follows [START_REF] Herin | Conception et caractérisation de capteurs de ux radiatif et convectif : application aux mesures « in situ[END_REF][START_REF] Tredre | Assessment of mean radiant temperature in indoor environments[END_REF]:

T 4 surr (t) ≈ F P→D • T 4 S P (t) + F g→D • T 4 S g (t) + F w→D • T 4 S w (t) K 4 (4.4)
F P→D + F g→D + F w→D = 1 [-] (4.5)
where T surr represents the mean radiant temperature. The subscript w represents the rest of the vertical walls surrounding the oor concrete-slab other than the glazed-facade. Note here, that equation 4.4

only holds for a long-wavelength environment. The coe cients F P→D , F g→D and F w→D , represent the di use view factor, respectively, between the following surfaces: ceiling, glazed-facade and remain walls; and the oor surface. Then, by equating together, equations 4.4 and 4.5, the following expression can be obtained for the temperature of the glazed-facade surface T S g :

T S g (t) ≈ 1 F g→D 4 T 4 surr (t) -F P→D • T 4 S P (t) -1 -F P→D -F g→D • T 4 S w (t) [K] . (4.6)
The vertical walls, other than the glazed-facade, are considered to be in thermal equilibrium with the indoor air, and thus, they are assumed as to have the same temperature as the indoor air: T S w ≈ T ia .

Estimation of the natural air ow rate via heat ux and temperature measurements

At the end of chapter 3, the searching for an expression able to relate both the wind and buoyancy e ects showed that when both e ects are considered simultaneously, the resulting value of net ach appears not to be a simple superposition of both individual e ects, e.g., addition or subtraction. Thus, an expression able to relate both e ects is still necessary to determine the value of ach, for the case when neither e ects dominate. For such a case, various superposition models (empirical and theoretical) have been reported in the literature [START_REF] Oropeza-Perez | Model of natural ventilation by using a coupled thermal-air ow simulation program[END_REF][START_REF] Klems | Methods of estimating air in ltration through windows[END_REF][START_REF] Shaw | Wind and temperature induced pressure di erentials and an equivalent pressure di erence model for predicting air in ltration in schools[END_REF][START_REF] Walker | Field Validation of Algebraic Equations for Stack and Wind Driven Air In ltration Calculations[END_REF][START_REF] Walker | Evaluating models for superposition of wind and stack e ect in air in ltration[END_REF][START_REF] Max | Superposition in In ltration Modeling[END_REF]. Despite that these models have been determined

for simple opening con gurations, we decided to evaluate them with the intention of choosing a model for ach, relating both e ects, that can estimate the real value of the ach in our platform.

However, to evaluate which of the reported models t the best to our particular case, the real value of ach should be known to avoid any overestimations or underestimations of this parameter. To do this, the value of ach was determine indirectly through the energy balance considered before (cf. eq. 4.2).

From this energy balance, we can draw an expression for the ach in terms of the internal convective heat exchanges, as follows:

ach(t) = 3600 V ia • ρ(T oa ) • c p (T oa ) • T oa (t) -ρ(T ia ) • c p (T ia ) • T ia (t) ρ(T ia ) • V ia • c p (T ia ) • dT ia (t) dt -h C D (t) • S D • [T S D (t) -T ia (t)] -h C P (t) • S P • [T S P (t) -T ia (t)] -h C g (t) • S g • T S g (t) -T ia (t) h -1 (4.7)
where the variable T S g (t) is replaced by equation 4.6. Note that, since equation 4.7 carries the experimental error from each of the variables, the resulting ach might present inconsistencies, e.g., negative values. Consequently, the absolute value of ach will be presented. Hereafter, we will referred to it as ach ϕ C since this ach is determined from the convective heat exchanges. The resulting ach ϕ C is presented in gures 4.5-4.7 (blue dots), for each opening con guration: n In gures 4.5-4.7, it can be observed that as the indoor air temperature (brown dashed line) approaches the outdoor air temperature (brown dots), the resulting ach ϕ C (blue dots) presents a rather Moreover, in each gure, it can be observed that considering either the wind e ects (yellow line) alone or the buoyancy e ects alone (red dots), leads to an overestimation of ach ϕ C (blue dots). The superposition model ach n=2 (green line) and the ach K-P model (cyan line), also seems to overestimate the value of ach ϕ C . Conversely, the superposition model ach m=2 overestimates the value of ach ϕ C for con guration n • 1, but underestimates it for con guration n • 2 and n • 3. Table 4.2 summarizes the results of this comparison. The reasons of such overestimations may lay in the following aspects:

• The air ow simulations performed on CONTAM might overestimate the value of ach W , due to the approximations regarding the wind e ects, e.g., the value of the pressure coe cients, the wind pro le power law, among others. But also, because both buoyancy and wind e ects are opposed.

For the cases of absence of wind, the value of ach ∆T might overestimate the value of ach ϕ C , since neither any internal heat exchanges (convection with walls) nor thermal strati cation is considered on CONTAM.

• The overestimation and underestimation of ach ϕ C by the models ach n and ach m , maybe because these models account for a situation where either wind and buoyancy are always assisted or always opposed, but not both interchangeably.

• The overestimation by the model ach K-P maybe because it is said to give the annual-averaged value of the natural air change rate per hour. The equations of the model were solved using the software R with the package dsolve. The time step employed was the same as the meteorological station sample rate: one time-iteration every ten minutes, and the method chosen for the numerical solution was "Radau" (implicit Runge-Kutta), which is a fth order solution method. The values of the constant parameters and coe cients employed in Model A, are presented in table 4.3. The adaptability of Model A can be highlighted regarding the changing of the opening con guration since the RMSE converges to similar values on each con guration: 0,31 • C for con g. n • 1; 0,24 • C for con g. n • 2; and 0,24 • C for con g. n • 3. This indicates that model A works best for describing a night ventilation strategy, such as con guration n • 2 (cf. g.4.13 (a)). Additionally, its adaptability is also highlighted in con guration n • 1 (cf. g.4.11 (a)), since the dataset implemented, is not from consecutive days as in con gurations n • 2 and n • 3. Thereby, the following remarks can be said about the performance of model A in terms of dynamics and accuracy, for each con guration:

F P→D F g→D F w→D h C g A Dimensions m 3 m 2 m 2 m 2 [-] [-] [-] W•m -2 •K -1 h -1
• For the case where the openings remained close, as in gure 4.11 (entire day) and in gure 4.13 • Finally, a slight phase shift appears to be presented between T ia model and T ia measured, and is longer in the daytime than in nighttime.

However, the results from identi cation in table 4.4, show that the best values for all con gurations are not the best values for each con guration alone, apart from con guration n • 3. For instance, the best values for con guration n • 2 that minimizes the RMSE value for T ia , are di erent. Moreover, the best values for con guration n • 1, indicates that the ventilation term in equation 4.2 does not seem to be signi cant (C l = 0,1). This may imply that the in ltrations are very low, which may seem contradictory with the values found for con guration n • 2 (C l = 1). Nevertheless, in con guration n • 2, both strategies (openings opened and closed) are tested, whereas in con guration for n • 1 there is only one strategy (openings closed).

Furthermore, the identi ed superposition model for ach, implies that wind e ects does not in uence at all or there was a prevalence absence of wind, for the case of openings closed (b l = 0). The latter is highlighted in gure 4.17; expected for weather conditions in the summertime. Likewise, this statement seems to hold also for the case of openings opened during the daytime in conguration n • 3, even with a strong presence of wind all along this measurement campaign (cf. g. 4.15 (c)). From this analysis, we may conclude that the values of the exponents, clearly respond to the most frequent or dominant situation taking place. However, these low exponent values may be subjected to the superposition arrangement (the product of ach ∆T and ach W ), and that the coe cients C l and C v were xed to one in the identi cation process for all con gurations. Then, if we recall the characterization of the natural air ow rate presented in chapter 3, it indicated that for a wind direction between 90 expected to be assisted. This agrees with the positive values of the exponents (a l = 0,2 ; a v = 0,5 ; b v = 0,2). This agreement is also encountered for con gurations n • 1 and n • 2, respectively:

• a l = 0,2 and φ W = 245 • .

• a l = 0,1 ; a v = 0,4 ; b l = 0,2 ; b v = 0,1 and φ W = 289 • . A physical explanation for this, was given in §3. 4.33.4.3.4 (p.122). On the other hand, for con guration n • 3 the most frequent wind direction encountered is 87 • , although this angle is near 91 • , an exponent with a negative value might be expected. However, every exponent resulted to be positive: a v = 0,5 ; b v = 0,2. A better relationship between ... might be identi ed if the moments were the openings remained close are separated from the moments were they remained open, and also, if separating the daytime from nighttime.

Physical signi cance of the identi ed superposition natural air ow model ach (∆TxW)

A superposition model ach (∆TxW) in the form of C • ach a ∆T • ach b W was inspired by the usual way that heat transfer phenomena is accounted for in convective heat transfer (for instance: Nu = C • Re n • Pr m ). Likewise, if a similar expression is chosen for ach, the phenomena involved in natural ventilation might also be accounted for. A di erence and limitation may lay regarding dimensions, since the coe cient C should have dimensions such as h a •h b •h -1 , which does not have a physical meaning. However, regardless of the heat transfer phenomena studied, the value of the exponents (associated to a speci c phenomena, e.g., Re for force convection and ach ∆T for air movement due to thermal buoyancy) gives indications about how strong is the phenomenon (the value of the exponent), and if such phenomenon opposes to another (the sign of the exponent: if negative, decreases, and if positive, increases). This last remark is essential to the physical signi cance of the identi ed model ach (∆TxW) .

Finally, the superposition model ach (∆TxW) can be expressed in a dimensionless form, by the following analysis. Recalling the expression for the superposition model:

ach = C • ach a ∆T • ach b W h -1 (4.9)
where the expression of ach ∆T and ach W were presented in chapter 3 (cf. eqs. 3. 10-3.11). By replacing these two expressions into equation 4.9, yields:

ach = C • A a • B b • T ia -T oa T oa 0,5•a • V b met h -1 (4.10)
Now, multiplying the entire previous equation by 1/ V b f , using the expression for the wind speed modi er C h (cf. eq. 3.2, p.105), and equating expression 4.10, yields:

ach C • A a • B b • V b f = T ia -T oa T oa 0,5•a • 1 √ C h b [-] (4.11)
where the left-hand side term is a variation of the dimensionless ow rate number F [START_REF] Caciolo | Analyse expérimentale et simulation de la ventilation naturelle mono-façade pour le rafraîchissement des immeubles de bureaux[END_REF]:

F = T ia -T oa T oa 0,5•a • 1 C h -0,5•b [-] (4.12)
to which, we can give a more practical expression in terms of V met , to be:

F = ach C • A a • B b • V met • √ C h b [-] . (4.13)
In addition, an expression can be given to A and B, based on the equations presented in chapter 1, as follows for A (when considering small openings):

A = 3600 • C d • S e f f eq V ia • 2 • g • Z h -1 (4.14)
and for B:

B = 3600 • C d • S e f f eq V ia • ∆C p s•h -1 •m -1 (4.15)
where the term C d • S e f f eq is the equivalent air ow resistance for any given air ow path within the building.

heat transfer, i.e., short wavelength, is neglected. Also, despite the several layers included in the oor slab (cf. g. 4.22), only the concrete layer will be considered for the modeling and computation.

Physical domain Domain modeling

Global domain modeling

Spatial discretization via nite di erences

The physical domain to be discretized is presented in gure 4.22, where the top surface of the concrete slab is submitted to convective and radiative heat exchanges with the indoor environment only.

The bottom surface of the concrete layer is considered to be isolated, as well as its other ends in the XY plane. For this, following the nite di erence method, the concrete-slab thickness is divided into several N small control volumes (CV N ) as showed in gure 4.23 with a thickness of ∆z, where each CV N is considered to be at a uniform temperature T D N , represented by a single point N ("node") located at the center of the control volume.

Therefore, the classic transitory one-dimensional heat conduction equation in cardinal coordinates can be written by using the nite di erence method for spatial discretization only [START_REF] Çengel | Heat Transfer: A Practical Approach[END_REF], as follows:

ρ D • ∆z • c p D • dT D N (t) dt = T D N-1 (t) -2 • T D N (t) + T D N+1 (t) ∆z [W] (4.17)
where T D N represents the temperature of the node N. The temperatures T D N-1 and T D N+1 , when analyzing node N, represent the temperature of the nodes before and after, or in our case, the nodes above and below node N in the z-direction, respectively. The distance ∆z is calculated by dividing the considered thickness e D with a desired number of nodes M.

The boundary conditions of our modeling domain can be written for the top node (N = 1) or CV 1 (submitted to convection an radiation heat transfer), being at temperature T D 1 , where the CV 1 has a thickness of half ∆z, as follows:

ρ D • ∆z 2 • c p D • dT D 1 (t) dt = h C D (t) • [T ia (t) -T D 1 (t)] + ε D • σ • T 4 surr (t) -T 4 D 1 (t) + λ D • T D 2 -T D 1 ∆z [W] (4.18)
where λ D represents the thermal conductivity of the concrete slab, considered to have a constant value through the slab. The last term on the right-hand side of equation 4.18 represents the conductive heat ux from the CV 2 to the CV 1 .

The boundary condition for the bottom node N = M or CV M , can be written as follows:

ρ D • ∆z 2 • c p D • dT D M (t) dt = λ D • T D M-1 -T D M ∆z [W] . (4.19)
For the intermediate control volumes, i.e., CV 2 to CV M-1 , the heat conduction equation is the same as equation 4.17.

Choice of a Model B for all opening con guration

Model B1 with the lumped-capacitance approximation, and Model B2 with the discretization of the concrete slab, have been de ned here before. The dataset for the comparison process and validation criteria is the same as described in §4. . The values of the former are computed with the heat ux measurement from thermoelectric modules (TEM), and the values of the latter are computed with the heat ux measurement from Captec heat ux meters (FGT), which was encountered to be around half of the value from the thermoelectric modules (cf. Appendix A.3). Note here that this was also found by Yang [START_REF] Yang | Innovative non-destructive methodology for energy diagnosis of building envelope[END_REF] as presented previously at the end of §1.4.2.2. Moreover, in gure 4.24 (a), it can be observed that the red line reproduces more accurately the behavior of T S D (blue circles) in comparison with the yellow line. Where the latter slightly underestimates the temperature during nighttime.

S D ρ D ε D M ∆z λ D Dimensions [mm] J•kg -1 •K -1 m 2 kg•m -3 [-] [-] [mm] W•m -1
The resulting mean absolute error between the blue circles and the red line is 0,14 • C (brown line), with a RMSE value of 0,18 • C (cf. g. 4.25). The RMSE value is about 0,24 when using h C D-TEM . This implies that the overestimation caused by the thermoelectric modules in the estimated convective heat ux appears to have an impact (a di erence of about 0,06 in terms of RMSE) on the prediction of the surface temperature of the concrete slab. Although, the importance of this impact is rather subjected to the application and purpose of the model, the value of h C D-FGT or just h C D /2 will be employed in the next simulations. Finally, lower RMSE values were encountered, when employing a larger value of ∆z and holding the total number of nodes, for any given number of nodes chosen. In other words, a slightly bigger thickness than the real value, gives better results in terms of dynamics and errors.

In summary:

Although not big di erences are encountered between Models B1 and B2 in terms of RMSE and dynamics, the best representation of T S D appears to be achieved by Model B2. This indicates that considering a no-uniform conduction heat transfer through the slab thickness leads to better prediction of its thermal behavior (also suggested by the values of Biot's number encountered).

Despite lower RMSE values were encountered when employing a bigger value for the concrete slab thickness (e D ), this was rejected due to the inconsistency with the real physical domain. Data from experiments: T oa , T surr , T S P , h C P , h C D , h C g .

Data from meteorological station: V met , φ W .

Variables in "the coupled model"

= T D N-1 (t) -2 • T D N (t) + T D N+1 (t) ∆z with ρ D • ∆z 2 • c p D • dT D 1 (t) dt = h C D (t) • T ia (t) -T D 1 (t) + ε D • σ • T 4 surr (t) -T 4 D 1 (t) + λ D • T D 2 -T D 1 ∆z and ρ D • ∆z 2 • c p D • dT D M (t) dt = λ D • T D M-1 -T D M ∆z 3) T Sg (t) = 1 F g→D 4 T 4 surr (t) -F P→D • T 4 S P (t) -1 -F P→D -F g→D • T 4 ia (t) -273, 15
4) ach(t) =                              C l • 4 • T ia (t) -T oa (t) T oa (t) 0,58 a l
; when NV openings closed • RMSE values for T ia of 0,24 and 0,28 • C, from Model A and "the coupled model", respectively.

C v • A • T ia (t) -T oa (t) T oa (t) 1/2 av • [B v (φ) • V met (t)] bv ; when NV openings opened C v • A • T ia (t) -T oa (t) T oa (t)
• RMSE values for T S D of 0,18 and 0,25

Evaluation of the model with data outside the identi cation process

The coupled model was also tested using data from outside the identi cation process. The only data remaining from the measurement campaigns with typical summertime weather conditions, for consecutive days, was for con guration n

Concluding remarks

In this chapter, we had addressed the problem of identifying a thermal model that describes the behavior of the platform. At the moment, the identi ed model (namely the "coupled model") seems to thoroughly describe the behavior of the indoor air temperature and the surface temperature of the concrete slab, for the measurement campaigns implemented in the identi cation process. However, this model still employs experimental data as inputs (other than those from the meteorological station):

the convective heat transfer coe cient at the oor and ceiling surfaces, the mean radiant temperature, and the ceiling surface temperature. The couple model can be represented in a simple schematic by highlighting the three main elements (indoor air, air ow rate, concrete-slab), and the components that are still needed (in purple):

(𝑻 𝒊𝒂 ) Nevertheless, this identi cation has allowed us to notice the following: and the oor and ceiling, apart from the vertical walls.

• The consideration of only two capacities seems to be enough for a good description of the thermal behavior. However, in this case, since a small number of parameters is involved in the model, this model is more sensitive to all those parameters, and thus, they need to be represented attentively. Moreover, the fact that only two thermal capacitances, in any given coupled model with natural ventilation, are enough to well described the behavior of the indoor air temperature of the platform is in agreement with the models reported in the literature concerning the coupling of natural ventilation with the thermal mass.

• The value of the exponents' signs in the superposition model for ach is related to the phenomena involved, i.e., buoyancy and wind forces are assisted or opposed to each other, being strongly dependent on the wind direction. Such phenomena encourage to nd an expression that can link both parameters directly.

• The determination of the net ach, indirectly, via an energy balance with heat ux and temperature measurements, arises as a suitable identi cation methodology for cases where costs reduction is far more important than accuracy requirements, in comparison to other experimental techniques.

Nevertheless, it has been demonstrated that instead of focusing on the local e ects of wind and buoyancy, the natural air ow rate can be well estimated by focusing only on the global in uence of both e ects.

G Recapitulation of the undertaken work

Throughout this study, we are interested in characterizing the thermal and air ow aspects of an experimental platform, which stands as a prototype of Plus Energy House (PEH), to identify a thermal model that describes its behavior under typical weather conditions of southwest France in the summertime.

For this model, based on the literature review concerning the theoretical study on the coupling between natural ventilation and the thermal mass, we have been interested in only account for the heat transfer in two elements: the indoor air and the thermal mass (assumed to be concentrated in the oor concrete-slab). Also, in addition to these two elements, a third element was included in the model: the natural ventilation air ow rate.

A di erence between our modeling choice and those found in the literature, lays in consideration of the following aspects:

• The incorporation of the mean radiant temperature of the indoor environment of the platform.

• The prevalence necessity of accounting for the convective heat exchanges between the indoor air ventilated-volume, and the surfaces of the oor concrete-slab, the ceiling, and the glazed-facade, separately, in the representation of the heat transfer in the indoor air. Apart from the ventilation and energy storage terms.

• The temperature dependence of the air density and speci c heat capacity.

• The accounting for both wind and thermal buoyancy e ects via a product superposition model for the ventilation air ow rate.

• Time-dependent convective heat transfer coe cients.

Such considerations are based on the characterization of both, the energy charge and discharge processes, and the natural ventilation air ow rate within the platform.

As a result, the identi ed thermal behavior model, the "couple model", accounts for the heat transfer in the three main elements mentioned earlier by: • An energy balance for the indoor air, complemented with the representation of the mean radiant temperature as the weighted sum of the absolute temperature of the surrounding surfaces.

• The representation of the concrete-slab temperature through a non-uniform conduction heat transfer approximation, via the nite di erences discretization method.

• A superposition model, for the ventilation air ow rate, that allows to accounting individually for the e ects of wind and thermal buoyancy. Moreover, concerning this last element, the ventilation air ow rate, a particularity was observed in the superposition model: the sign of the exponents might need to be adjusted depending on the wind direction. However, the relationship between the magnitude of these coe cients/exponents and the dominance of wind and buoyancy e ects is still unknown. Other superposition models found in the literature have been proven not to be suitable, since they were developed for simple air ow path/patterns, in simple natural ventilation strategies such as single-sided, cross and stack ventilation, with a reduced number of openings. Thus, network air ow models were implemented via direct air ow simulations through the software CONTAM, because the knowledge of an air ow path/pattern is not necessary. Also, because of the number and distribution (location) of the openings in our experimental platform, which might be judged as rather complicated for a one-story building of 70 m 2 . These air ow simulations considered the following: the location of the air-leakage within the platform, a single-zone model, and transient conditions with no consideration of any contaminants and humidity.

In this regard, the characterization of the air ow rate in the platform included the in situ estimation of the air ow capacity of the openings and their friction characteristics via the discharge coe cient.

Finally, the thermal characterization of the platform has also contributed to promoting the implementation of thermoelectric modules, as an alternative to conventional heat ux meters, for estimating the convective and radiative heat exchanges in the building domain. The most attractive characteristic to consider the implementation lays in the following aspects:

• Budget, since the cost of thermoelectric modules, is around ten times lower than the cost of conventional heat ux meters, such as Captec®.

• Sensitivity/accuracy/size, since thermoelectric modules generate a higher electric potential than conventional heat ux meters, for the same device size. This higher potential can allow a more accurate estimation of the heat ux measured with the same measuring system (sensor + acquisition system). This accurate estimation might be essential for measuring weak heat ux levels in passive environments.

Speci c remarks from chapter one

In this chapter, we have covered the basics for comprehending the natural ventilation concept.

We have brie y reviewed the experimental and modeling techniques already implemented for past researchers, in the estimation of the ventilation air ow rate due to the wind and thermal buoyancy e ects. Also, a brief reviewed of the experimental and modeling techniques concerning the heat ux measurement and the estimation of the convective and radiative heat ux, have been presented. These literature review has allowed noticing the following remarks:

• The coupling between natural ventilation and the thermal mass of a building can be studied by only considering two simple energy balances, one on the indoor air and another on the thermal mass, and the equation for the ventilation air ow rate.

• The location of the air-leakage/in ltrations must be analyzed attentively, to avoid overestimation or underestimation of the air-leakage rate.

• The use of at-plate heat ux meters arises as a good experimental technique for estimating the convective heat exchanges, and more importantly, thermoelectric modules are considerably more attractive than conventional heat ux meters regarding their sensitivity.

Regarding this last remark, in the studies reviewed, the implementation of the heat ux meters di ered in geometry and arrangement, i.e., black and shiny sensors installed with one of their sides always in contact [START_REF] Cherif | Super cial heat transfer by forced convection and radiation in a horizontal channel[END_REF][START_REF] Douiri | Instrumentation dun four pilote pour la cuisson de genoise[END_REF] and installed with a separation between them [START_REF] Lassue | A Convective and Radiative Flux Sensor for Designing Thermal Comfort Controllers[END_REF][START_REF] Wu | Formalisme des impedances thermiques généralisées. Application à la caractérisation thermique de parois de bâtiments[END_REF][START_REF] Yang | Innovative non-destructive methodology for energy diagnosis of building envelope[END_REF]. The selection of the heat ux meter depends mainly on the heat ux levels to be measured, the accuracy wanted in the heat ux measured and the measuring system employed in the measurement.

Regarding the experimental and modeling techniques for estimating the ventilation air ow rate, a limitation arises in their applicability to our speci c case, since:

• The experimental techniques require heavy instrumentation (often expensive) of the openings in terms of airspeed and pressure measurements (local), being the ones that could lead to a better understanding of the phenomena involved in the ventilation process.

• The modeling techniques such as CFD requires large computation time depending on the computer power and the models itself. The models based on empirical observations require the knowledge of the air ow patterns within the building. Thus, the modeling technique more suitable for our case seems to be the implementation of network air ow models via direct air ow simulations performed by software such as CONTAM, since the knowledge of the air ow patterns is not required.

The more suitable experimental technique seems to be the airtightness tests since it allows us to obtain empirical expressions relating the ventilation air ow directly to the pressure di erence in the building for both cases: in ltrations (openings closed) and openings opened. Also, the location of the leakages can be identi ed without complications, and this technique has the potential to estimate in situ the air ow capacity and friction characteristics of the openings.

Speci c remarks from chapter two

The exhaustive experimental study presented in chapter two has allowed characterizing, in detail, the thermal aspects of the experimental platform, suggesting the following major points:

• It is not enough to take the convective coe cients as constant values when the openings are open. It would be necessary to model or to identify them in another way.

• The convection inside the platform does not appear to have a dominant nature, natural or forced, both may occur when the openings are open.

• The direct solar radiation does not heat directly the indoor environment of the platform.

• The most representative measuring location on the slab surface is between the two groups of openings and in the middle of the platform, close to the south facade.

• It is necessary to take into account the convective e ects on the slab surface, on the ceiling, and on the glazed-facade individually, due to their behavior.

• It is clear that there are some vertical walls that contribute the most to the heating of the indoor air; taking them all when describing the indoor air heat gains might lead to overestimations.

• The vertical thermal strati cation of the indoor air within the platform, can be neglected regarding the thermal comfort of the indoor environment. However, regarding buoyancy driven ventilation, it is suggested that neglecting these thermal gradients may be a suitable choice for larger values of Fr number, than the ones encountered.

• The values of Bi number encountered suggest that a non-uniform heat conduction might give a precise description of the heat transfer through the concrete-slab thickness.

These last remarks have allowed us to highlight the key elements involved in the energy chargedischarge process in our experimental platform: the indoor air, the concrete slab (as the thermal mass), the glazed-facade, the air ow rate, and the ceiling, in terms of heat transfer.

Nevertheless, the characterization of the thermal aspects of the experimental platform should also consider the heat transfer associated with the exchanges in mass (air) between the indoor and outdoor environments. This consideration requires the knowledge of the natural air ow rate within the platform. Thus, we address the following chapter to characterize the ventilation air ow rate.

Furthermore, this characterization has endorsed the consideration of including, later in the modeling, the key elements mentioned here before. Also, to consider not to include the direct solar radiation in the modeling of the heat transfer in the concrete slab.

Speci c remarks from chapter three

The undertaken work in this chapter was devoted to characterizing the natural air ow rate in the platform via air ow simulation on CONTAM. This characterization aimed to determine an expression relating the net ach as a function of the wind speed and direction, and the indoor-outdoor temperature di erence. Thus, we can retain the following remarks:

• For the buildings or enclosures, where the air ow path is di cult to be determined due to a large number of openings, focusing on estimating the net air ow rate by using network air ow models, can lead to avoiding unnecessary di culties.

• The assumption of air-leakage equally distributed at the facades with openings seems to be appropriate, instead of identifying them rst by performing airtightness tests with the smoke pencil, when focusing on the global e ect of wind and buoyancy via the net air change rate.

• Performing in situ airtightness tests for the estimation of the friction characteristics of openings, might not be the most suitable choice due to the presence of internal obstructions, such as furniture, partition-walls, doors, among others. However, the implementation of these tests for the estimation of the air ow capacity in terms of air ow rate levels appears to agree with the values reported in the literature.

• Finally, from the air ow simulations for the combined wind and buoyancy e ects, these e ects appear to oppose to each other only in a speci c range of wind direction.

At the moment, we may conclude that the real value of the natural air change rate in the platform remains uncertain. However, since our results have been compared with values reported in the literature, we may state that the values encountered may be a reasonable estimation of this parameter when an annual-averaged value is needed.

Moreover, the last part of this chapter has shown that we are not yet capable of reporting an expression that combines both wind and buoyancy e ects directly, since: The net value of ach does not appear to be a simple addition when both e ects are assisted, nor a simple subtraction when both e ects are 4.4. Concluding remarks opposed. Therefore, an expression able to superpose both e ects is still needed. In order to choose from the superposition models reported in the literature and to avoid any possible overestimation or underestimation of the ach value, it is necessary to determine its real value. For the latter, we are able to identify the value of ach by employing the heat ux and temperature measurements performed during the measurement campaigns (presented in chapter 2), and a global energy balance in the indoor air.

The rst part of the following chapter is dedicated to identify and compare the ach value.

Speci c remarks from chapter four

In this chapter, we had addressed the problem of identifying a thermal model that describes the behavior of the platform. At the moment, the identi ed model (namely the "coupled model") seems to thoroughly describe the behavior of the indoor air temperature and the surface temperature of the concrete slab, for the measurement campaigns implemented in the identi cation process. However, this model still employs experimental data as inputs (other than those from the meteorological station):

the convective heat transfer coe cient at the oor and ceiling surfaces, the mean radiant temperature, and the ceiling surface temperature. The couple model can be represented in a simple schematic by highlighting the three main elements (indoor air, air ow rate, concrete-slab), and the components that are still needed (in purple):

(𝑻 𝒊𝒂 ) Nevertheless, this identi cation has allowed us to notice the following:

• It is necessary to account, separately, for the convective heat exchanged between the indoor air and the oor and ceiling, apart from the vertical walls.

• The consideration of only two capacities seems to be enough for a good description of the thermal behavior. However, in this case, since a small number of parameters is involved in the model, this model is more sensitive to all those parameters, and thus, they need to be represented attentively. Moreover, the fact that only two thermal capacitances, in any given coupled model with natural ventilation, are enough to well described the behavior of the indoor air temperature of the platform is in agreement with the models reported in the literature concerning the coupling of natural ventilation with the thermal mass.

• The value of the exponents' signs in the superposition model for ach is related to the phenomena involved, i.e., buoyancy and wind forces are assisted or opposed to each other, being strongly dependent on the wind direction. Such phenomena encourage to nd an expression that can link both parameters directly.

• The determination of the net ach, indirectly, via an energy balance with heat ux and temperature measurements, arises as a suitable identi cation methodology for cases where costs reduction is far more important than accuracy requirements, in comparison to other experimental techniques.

Nevertheless, it has been demonstrated that instead of focusing on the local e ects of wind and buoyancy, the natural air ow rate can be well estimated by focusing only on the global in uence of both e ects.

Future work

The experimental and modeling study developed/implemented throughout the present work has allowed us to conceive some of the subsequent activities in di erent research areas:

(1) Thermal characterization:

The fact that the discharge process of the indoor ceiling surface is not done by convection nor by radiation leads to reconsider our initial hypothesis of the concrete-slab as the most important element in the platform. Thus, if neither the convective nor the radiative heat exchanges discharge the ceiling to the indoor environment, the ceiling would be discharged by conduction through its thickness towards the roof surface. Such a case brings us to consider its speci c thermal behavior in the coupled model.

(2) Air ow characterization:

The apparent relationship between the exponents (values and signs) in the product superposition model for the net air change rate per hour and the wind direction, leads to perform further analysis aiming to nd an expression that can describe this relationship.

(3) Metrology:

The apparent overestimation of the convective heat transfer coe cient (h C ) by the thermoelectric modules, in comparison with Captec heat ux meters, also lead to perform further analysis with the objective of nally validating such devices in the estimation of the convective heat ux, and thus, the convective heat transfer coe cient.

(4) Forecasting and control:

The construction of a forecasting model able to accurately predict the behavior of the platform, in order to develop control systems that can supervise the opening-closing of the natural ventilation openings along with the home automation system, to reduce air conditioning usage. 1.1. Technical data of the measuring system As said before, several phases are needed to estimate a temperature measurement using thermocouples, these phases could be described as: rst, since thermocouples tension responses are as low as the electric noise that can be encountered in the environment medium, a tension signal ampli cation phase must be applied [1]. Second, once the signal is ampli ed, comes the ltration phase to reduce as much as possible the electric noise due to signal ampli cation process. Also, when connecting the thermocouple to an acquisition system, care should be taken concerning the connection terminals. The terminals must be electrically insulated. The third phase includes two steps: the cold junction compensation and the tension-temperature regression; as it is well known that the thermocouple response is proportional to the Seebeck coe cient and the temperature, the tension signal measured would not be a linear function of the temperature. Nowadays, many standards give us the regression between the temperature and the tension delivered by a thermocouple (i.e., NIST standards). In these standards, the polynomial coe cients for all types of thermocouples that exists are given, and because of the nonlinear response of the thermocouple, the polynomials errors is also given. This phase is called linearization (see gure A.1). These polynomial coe cients are determined within a range of temperature, depending on the operation range of the thermocouple. Also, the coe cients depend on the junction compensation of the thermocouple. The polynomials coe cients given by the NIST are determined using a cold junction compensation (maintaining the reference junction to zero degrees celcius) [1].

All the signal processing required for converting the thermocouple response in a temperature measurement causes systematic errors. Errors that will always be there when performing a temperature measurement with a speci c data acquisition system. Unfortunately, the error caused by the acquisition system does not account the thermocouple uncertainty or accuracy itself. The thermocouple accuracy is bound to the purity of the materials employed in its fabrication process.

In our experiments, the NI 9213 acquisition card and the Labview software have been used. The signal processing is already integrated into the National Instrument acquisition system. As so, the error committed when estimating a temperature measurement is given in the NI 9213 technical data. In our particular case, thermocouples type T have been used. The measurement errors, when using the NI 9213, are shown in gure A.2. As said, in addition to this error, comes the error of the thermocouple itself. Our thermocouples were acquired from the company TC Direct [2]. These thermocouples are second class thermocouples type T; this class gives us the thermocouple accuracy after it is manufactured under a speci c standard. TC Direct follows the NF EN 60584-2 (or IEC 584.2) standard when manufacturing thermocouples, as so the accuracy on our thermocouples is ±1 • C (this value is also mentioned in [3]). There two most common thermocouple classes and if they are not speci ed as rst class thermocouple, they are of second class. Consistent with our case.

Thermocouple calibration

The process of performing the junction metal-alloy, could a ect the thermocouple measurement. This e ect can be observed if the thermocouples (let's say 32) are immersed in a very stable temperature uid. It would be observed that thermocouple's temperature measurements are not quite the same, even if they were of the same type or were manufactured together. Here this e ect would be named as thermocouples natural deviation. This before could cause large errors in the estimation of a temperature di erence, because when subtracting two measurements, the result could lays inside the range of the two thermocouples natural deviation relative to each other. This, would not be the real value of the temperature di erence, thus, this must be corrected before performing any temperature di erence.

As in our particular case, we are also interested in the estimation of temperature di erences. As so, the aforementioned in the previous paragraph, was conducted using a thermostatic bath (model: LAUDA RE 415) with a temperature stability of ±0, 01 • C, and an accuracy of ±0, 3 • C and ±0, 5% • C of the relative temperature, assured by an integrated PT100 sensor [4]. The procedure will be described in the next section. Furthermore, we are also interested in reducing the bias error of our thermocouples. The thermostatic bath could help us to accomplish this before, as it has a smaller bias error value than our measuring system (thermocouple + acquisition system). As the technical data of the thermocouples and acquisition system subject the bias error may lays within a range of ±1, 8 • C in the worst case scenario, but it should be noted that it will not necessarily be exactly 1,8 • C. Here we proposed an experimental procedure to attempt to reduce this error interval or uncertainty, as shown graphically in gures A. In order to observed and quantify the thermocouples natural deviation, they were immersed into the bath lled with water in two groups of 16 (32 thermocouples in total) along with a NTC probe, as shown in gure A.6 in appendix. Seven di erent temperature setpoints (see Table A.1, rst and second columns from left to right) were set, in order to observe their stability, deviation to one another and to the bath temperature. Also, the average temperature of all thermocouples wanted to be observed.

The weirdness in the bath temperature values is because the bath temperature was adjusted so that the NTC temperature matches the setpoints values. Lately, it was found that the Bath temperature sensor is more accurate that the NTC probe [3], as so the NTC measurements were discarded. After the bath reached the setpoint (now, referring to the middle column of Table A.1) and stabilize it, the data acquisition was started for only 28 seconds with a sample rate acquisition of 4 seconds. A repetition of this experiment might be considered. Results are presented in the following section. In a steady-state medium: The thermocouples behavior at all seven temperature setpoints can be observed in gure A.7 and from gures A.10 to A.12, in appendix. The thermocouples measurement natural deviation when having the bath at 9, 89 • C could be observed in gure A.7. The maximum deviation between thermocouples is approximately 0, 3 • C. We proposed to reduce this deviation by correcting the thermocouples measurements as said in §2.1, which in other words means that we will try to nd a regression function that correlates the thermocouples measurement and the Bath temperature.

Furthermore, results showed that the higher the temperature setpoint, the closer the thermocouples measurement gets to the bath temperature (see gures from A.10 to A.12 in appendix) and the maximum deviation between the thermocouples changes at each setpoint (see Table A.2), being 0, 29 The regression function for the thermocouple 32 is shown in gure A.8 as an example. In a general way the regression function can be written as follows:

T Bath = a X T TCX + b X (21)
where a X and b X are the linear regression coe cients and the subscript X corresponds to the thermocouple number TCX. Coe cients units are: dimensionless and in degrees Celsius, respectively.

Regression coe cient values are shown in Table A.5.

Expression 21 could help us to make the thermocouples measurement to be equal to the Bath temperature. We can go further and rewrite this expression as a function of time, this will help us to correct the thermocouple measurement at any instant. However, it is known that the correlation should have an associated error, since no regression is perfect. Thus, the regression correct the thermocouple measurement to be equal to the bath temperature at e% of error. As so, we can think of the regression as being an estimation of the Bath temperature at e% near. Then, expression 21 can be rewrite as follows:

T * TCX (t) = a X T TCX (t) + b X [START_REF] Chen | Stockage/déstockage d'énergie sensible et ventilation naturelle en bâtiment : une approche expérimentale à l'échelle 1[END_REF] where T * TCX represents the estimated temperature from thermocouple X measurement. T TCX is the actual thermocouple measurement.

We can test our regression function to correct our thermocouples measurements by using the results from gure A.7. The result, after applying the correction, is shown in gure A.9. Also, data showed that the maximum deviation between thermocouples at this setpoint is reduced to 0, 04 • C, which is way lower than the value presented in Table A.2: 0, 28 • C (maximum deviations values at each setpoint are presented in Table A.4). As we will see in the next section, despite the correction we just made to the temperature magnitude of our thermocouples measurement, the thermocouples random error remained the same.

Before we go to the random error analysis, the regression function error in estimating a temperature must be treated. The plots showed in gure A.8 were computed using the software Matlab and its app: curve tting. As we can see it can also give us the residual plot, which plot the deviation of the predicted value by the regression function. So, we interpreted this plot as the error of the regression function.

These residuals can be gather all together to have a unique error value instead of 7 di erent ones, which would be convenient as we will not have to look for this plot in order to estimate the error. This unique error value is calculated by the root-mean-square error (RMSE) and luckily Matlab compute it for us.

RMSE values for each regression is also showed in Table A.5. However, it does not tell us whether the error in estimation made the prediction be higher than the temperature of the bath or lower. Now, we have to decide whether this error should be considered as a bias or as a random error. Well, we can deduct that this error should be consider as part of the bias error, since it is the error that the regression commit in the process to estimate the Bath temperature from the thermocouple measurement.

Determination of the temperature stability

The stability of the temperature measurement was calculated as the standard deviation of a continue sets of measurements at a given temperature setpoint value assured by the thermostatic bath, and using a con dence interval of 95 % in a normal distribution (meaning: 1, 96 times the standard deviation value) [3]. Data showed that the majority of the thermocouples presented a standard deviation of ±0, 01 • C, except for the TC10, which was ±0, 02 • C (see Table A .6). Therefore, the temperature stability or random error for all thermocouples would be, ±0, 02 • C (0,0196 • C), except for the TC10 which would be ±0, 04 • C (0,0392 Abstract: This experimental study aims to verify if the hypothesis consisting of both thermoelectric modules having the same temperature, due to a limitation in the uncertainty of our instruments, by performing complementary measurement campaigns.

Experimental set-up and measurement campaigns

The experimental set-up implemented here consists of a "measurement device" installed at the most signi cant location, in terms of heat ux, over the oor concrete-slab surface. This "measurement device" also includes a type T thermocouple inserted into the black coated thermoelectric module. The zone where the "measurement device" is installed, was submitted to two di erent conditions:

• Case 1: since the window shades were kept closed, the "measurement device" is submitted to a non-direct solar radiation heat transfer, carried out during the summertime. (cf. g. A.13).

• Case 2: since the window shades were kept opened, the "measurement device" is submitted to a direct solar radiation heat transfer, carried out during the wintertime. (cf. g. A.14).

Experimental results and analysis

The experimental results from the measurement campaigns carried out for each case, are presented hereafter. A.3 Assessment of thermoelectric modules as alternative to conventional heat ux meters for decoupling the super cial heat transfer Abstract: This experimental study aims to asses the performance of thermoelectric modules (TEM) in the estimation of the convective heat ux, by comparing their measurements with conventional heat ux meters (FGT); Captec heat ux meters. In this case, a couple of black and shiny of both heat ux meters (four sensors), TEM and FGT, have been installed near each other to submit them to the same conditions. Also, these couples were installed in two di erent locations within the platform, in order to submit them to a no-direct solar radiation environment and a direct solar radiation environment. Regression results showed that TEM always overestimate the estimated convective heat ux by a factor of around two.

In the summertime

In the wintertime

Introduction

Conventional heat ux meters are widely used for measure super cial heat ux, and as they are far expensive than thermoelectric modules, an experimental study has been conducted to compare the use of both types of heat ux sensors in the heat ux measurement. This experimental study was performed in a naturally ventilated Plus Energy House (PEH) prototype, in which only the natural ventilation semi-passive system was implemented. This system is controlled by the home automation system of the house, which controls the opening or closing of the natural ventilation openings depending on the relative conditions between the indoor and outdoor environment in regard of the thermal comfort in the summertime. However, the experimental study presented here was carried out during fall in November 2016, and the protocols for the opening and closing, of the natural ventilation openings, were chosen manually.

Until now no other research has been encountered in the literature regarding the comparison between the use of thermoelectric modules and the use of conventional heat ux meters for decoupling the convective and radiative parts in the heat ux measurement. Nevertheless, various researchers have reported perturbations induced by both types of sensors in the measured heat ux. Most of these 3. The platform was unoccupied during the measurement campaigns, and the lights remained turned o . However, two computers remained operational; one for data collection and one for controlling the natural ventilation openings.

4. Since the inside of the platform is divided into four zones: the living room, bedroom, bathroom, and toilet; all doors dividing these zones were kept opened.

Comparison analysis

With the objective of comparing the use of both types of heat ux meters, a comparison analysis was performed regarding the following aspects:

1. The electrical response of sensors of the same surface color will be compared and confronted,

where di erent values are expected since they are fabricated with di erent materials. Also, their corresponding heat ux measurement will be compared and confronted.

2. The temperature measurement from the integrated thermocouples inside both types of sensors will also be compared and confronted. These temperatures are expected two be the same, as the integrated thermocouples are meant to measure the temperature of the surface in which the heat ux meters are installed.

3. The convective and radiative heat uxes estimated by the the measurement of both types of sensors will be also compared and confronted, using a semi-empirical model presented in §2.3.1.

Experimental results and analysis

B Weather conditions from ENSAM meteorological station

  I2M-TREFLE, UMR CNRS 5295, Esplanade des Arts et Métiers 33405 Talence R Couplage entre ventilation naturelle et stockage-déstockage d'énergie sensible en bâtiments : approche expérimentale et modélisation

Figure i :

 i Figure i: Image of the experimental platform, Sumbiosi: South-facade view.

Figure ii :

 ii Figure ii: Image of the experimental platform, Sumbiosi: North-facade view.

Figure

  Figure iii: Echanges radiatifs et convectifs sur le dispositif de mesure destiné à observer et quanti er le stockage/déstockage.

Figure

  Figure iv: Instrumentation de l'ensemble de la surface de dalle : représentation schématique (a) et dispositif de mesure pour observer le stockage/déstockage (b).

Figure v :

 v Figure v: Résultats de la densité du ux thermique pour la con guration 2. En surface de dalle : échanges radiatifs (orange) et convectifs (noir). En surface du plafond : échanges radiatifs (vert) et convectifs (violet). Vitesse d'air en surface de dalle (rouge foncé, axe à droite). Moments d'ouverture des ouvrants (zones grises).

Figure vi :

 vi Figure vi: Résultats du modèle pour une con guration 2. A gauche : température d'air intérieur mesurée (noir) et simulée (rouge), température de surface de dalle mesurée (bleu) et simulée (orange premier noeud et vert dernier noeud). A droite : taux de renouvellement de l'air (noir) et températures d'air intérieur et extérieur (rouge).

1 A 1 BCF- 2 g 2 h 1 h 1 I- 2 R 1 δ

 11221121 Abbreviations

Figure 2 :

 2 Figure 2: Objectives in energy consumption of the regulation RT 2020 in France.

Figure 3 :

 3 Figure 3: Overview of the physical phenomena: (a) charge process, (b) discharge process, and (c) physical phenomena.

Figure 4 :

 4 Figure 4: Image of the experimental platform, Sumbiosi: South-facade view.

Figure 5 :Figure 6 :

 56 Figure 5: Image of the experimental platform, Sumbiosi: North-facade view.

Figure 1 . 1 :

 11 Figure 1.1: In uence factors and relations in the air movement domain inside and around the building [117].

Figure 1 . 2 :

 12 Figure 1.2: Cooling potential due to nighttime ventilation technique [2].

Chapter 1 -Figure 1 . 3 :

 113 Figure 1.3: The natural ventilation concept.

Figure 1 . 4 :

 14 Figure 1.4: Representation of wind forces (a), and pressure distribution induced by wind (b) [58].

Figure 1 . 5 :

 15 Figure 1.5: Air movement due to buoyancy forces: (a) small openings, (b) one large lower opening [70].

1. 1 . 3 . 1 Figure 1 . 6 :

 13116 Figure 1.6: Stack ventilation with: (a) assisting winds, and (b) opposing winds [58].

Figure 1 . 7 :

 17 Figure 1.7: Air ow capacity of bottom and side hung windows depending on the opening degree [57].

Figure 1 . 8 :

 18 Figure 1.8: Variation of the air ow capacity of bottom and side hung windows as a function the indoor-outdoor temperature [57].

Figure 1 . 9 :

 19 Figure 1.9: Values of discharge coe cient obtained by [36]. Heiselberg et al. in 2001 [49], performed air ow rate and pressure measurements at the opening in a laboratory set-up, and determined C d values for openings similar to ours, using equation 1.6 (cf. g. 1.10). It was concluded that "the use of a constant value could lead to serious errors in the prediction of air ow capacity", because their experimental results showed that the discharge coe cient changes

1. 1 .

 1 Natural ventilation in buildings the three types of opening they tested, the value of the discharge coe cient slightly decreases as the pressure di erence increases.

Figure 1 . 10 :

 110 Figure 1.10: Values of discharge coe cient obtained by [49].

Figure 1 . 11 :

 111 Figure 1.11: Values of stack discharge coecients for inward and outward ow in still air [25].

Figure 1 . 12 :Chapter 1 -

 1121 Figure 1.12: Values of stack discharge coecients for inward and outward ow with wind [25].

Figure 1 .

 1 13 (a) shows the reported air change rate values, for stack and wind only. They also reported the variation of the air change rate, with respect to the wind speed (cf. g.1.13 (b)).

Figure 1 .

 1 Figure 1.13: (a) In uence of wind on the e ciency of stack ventilation. (b) Air change rates in the investigated rooms as the function of the wind velocity [44].

Figure 1 . 14 :

 114 Figure 1.14: Comparisons between the experimental and simulation results performed into the PowerDomus software for the wind tunnel case [37].

Figure 1 . 15 :Figure 1 . 16 :

 115116 Figure 1.15: Measured and calculated volume ow rates: Warren & Parkins (black thin line), De Gids & Pha (black dotted line, ∆T = 0 • C), and De Gids & Pha (black thick line, ∆T = 5 • C) [61].

Figure 1 . 17 :

 117 Figure 1.17: Averaged facade pressure coecient as a function of azimuth angle [87].

Figure 1 . 18 :

 118 Figure 1.18: Fitted regression model over experimental data of a coe cient regarding wind effects as a function of the incident angle [62].

Figure 1 . 19 :

 119 Figure 1.19: Example of a network air ow modeling applied to a multi-zone building [39].

Thermal lag: 6 hFigure 1 . 20 :Chapter 1 -

 61201 Figure 1.20: Comparison of the temperature of the outdoor and indoor environments: thermal lag and damping factor [43].

1. 3 .

 3 Coupling between natural ventilation and thermal mass

Figure 1 . 21 :

 121 Figure 1.21: Schematic of the model [116].

Figure 1 . 22 :

 122 Figure 1.22: Schematic of the models for two cases: (a) the indoor thermal mass is not in equilibrium with the indoor air, and (b) both are in equilibrium [111].

Figure 1 . 23 :

 123 Figure 1.23: Schematic of the model [112].

Figure 1 . 24 :

 124 Figure 1.24: Experimental set-up: (a) Sketch, (b) inside the ventilated enclosure showing the heat source E and the thermal mass (steel balls), and (c) temperature and airspeed probes. [112].

1. 4 .Figure 1 . 25 :

 4125 Figure 1.25: Experimental and theoretical results for the ventilation ow rate ( V) and the indoor air temperature (T i ) when T o = 33 + 7 • cos 4,09x10 -4 • tπ [112].

1. 4 . 1

 41 Principles of the heat ux measurement 1.4.1.1 Théry-type heat ux sensors

Figure 1 . 26 :

 126 Figure 1.26: Structure of Captec® heat ux meter: (a) Composition, and (b) transversal side view with heat ux lines [23].

1. 4 .

 4 Heat ux measurement techniques for rigid surfaces employed is a quaternary alloy of bismuth, tellurium, selenium, and antimony, e.g., Bi 2 Te 3 . In the case of cooling applications when higher performance is needed, multistage Peltier modules can be found in the market (cf. g. 1.27 (b)).

Figure 1 . 27 :

 127 Figure 1.27: General structure of a Peltier module [89]: (a) a singular TEM, and (b) two multistage TEM con gurations.

Figure 1 . 28 :

 128 Figure 1.28: Experimental set-up in [51, 66]: (1) Air conditioning central, (2) Radiant panels, (3) a 12 cm heavyweight concrete wall, (4) air temperature probe, (5) room temperature probe, (6) a lightweight wall (isolation-wood), designed heat ux meters.

1. 4 .Figure 1 . 29 :

 4129 Figure 1.29: Proportional controller converted into a room temperature programmable device (a), and a schematic of the experimental room (b).

Figure 1 . 30 :

 130 Figure 1.30: Experimental set-up in Douiri 2007 [29]: Heat ux meters installed inside the oven.

Figure 1 . 31 :

 131 Figure 1.31: Experimental set-up in [23]: Heat ux meters black and shiny, installed inside the heat exchanger (a).

Chapter 1 -Figure 1 . 32 :Figure 1 . 33 :

 1132133 Figure 1.32: Experimental set-up in [109]: Heat ux meters installed at the (a) front and (b) rear faces of an external wall in a real residential building.

Figure 1 . 34 :

 134 Figure 1.34: Experimental set-up in [113]: (a) heat ux (Peltier or TEM and Captec) and temperature sensors installed on the wall front face (laboratory case), and (b) heat ux (Captec) and temperature sensors installed on the wall front face (in situ case).

1. 4 .

 4 Heat ux measurement techniques for rigid surfaces estimated by the TEM and the FGT; the former was approximately two times greater than the latter (cf. g. 1.35 (a), black and blue lines, respectively). The convective coe cient estimated with FGT measurements was veri ed with a well-known correlation for determining the convection coe cient on vertical walls under natural convection ([120] p.431) (cf. g. 1.35 (a) red line).

Figure 1 . 35 :

 135 Figure 1.35: Results for laboratory case: (a) Convective coe cient estimated for the TEM (black) and FGT (blue); coe cient estimated by correlation (red). (b) Surface temperatures: FGT (black), black TEM (red), shiny (TEM) blue. (c) Resulting convective heat ux for the black TEM (black), shiny TEM (red), and FGT (green) [113].

Chapter 1 -Figure 1 . 36 :

 1136 Figure 1.36: Schematic of the radiative heat ux designed by [30].

Figure 1 . 38 :

 138 Figure 1.38: Schematic representation of the resistive circuit when a heat ux meter is installed [51].

1. 4 .

 4 Heat ux measurement techniques for rigid surfaces

Figure 2 . 1 :

 21 Figure 2.1: Image of Sumbiosi current state (a). Architectural features: oor concrete-slab (b), and programmable solar shades and natural ventilation openings (inside red squares) at the South glazedfacade (c)-(d), (e) at the shed-roof and (f) at the North facade.

Figure 2 . 2 :

 22 Figure 2.2: Illustration of the platform employing its architectural features: passive energy storage in summer daytime (a), and semi-passive energy discharge in summer nighttime (b).

  . They are distributed in the South and North facades, and three manual door-like openings located in an internal wall that separates the living room and the bedroom (cf. g. 2.3 (a)-(d)). The South facade has four natural ventilation openings of the same dimensions, being of 119 x 35 cm 2 (height x width) (cf. g. 2.3 (a)), while the four openings in the North facade have di erent dimensions, all four being of 108 x 43 cm 2 (cf. g. 2.3 (b)),. Finally, the shed-roof contains two window openings, having dimensions of 55 x 222 cm 2 (cf. g. 2.3 (c)). A schematic of the west and top views of the platform architectural plans, showing the location of the natural ventilation openings and the oor concrete-slab, was presented earlier in gure 6 (p.4).

Figure 2 . 3 :

 23 Figure 2.3: Images of the natural ventilation openings: (a) at the South facade, (b) at the North facade, (c) at the shed-roof, and (d) between the living room and bed room.

Figure 2 . 4 :

 24 Figure 2.4: Domains and variables for the experimental approach. Top: inputs and outputs studied regarding the building domain (in italic letter). Bottom: inputs and outputs studied regarding the thermal mass domain (in red).

Figure 2 . 5 :

 25 Figure 2.5: A representation of the convective and radiative heat exchanges over a "measurement device" containing a couple of black and shiny thermoelectric modules, and two thermocouples to measure the air and surface temperatures.

  Additionally, ten conventional heat ux meters of the type Captec®, were included for comparison purposes, since they have been validated (cf. §1.4.2.2), in the "measurement devices" close to the southfacing natural ventilation openings. Complementary experiments, to study the use of a couple of black and shiny thermoelectric modules instead of the use of a couple of black and shiny Captec®, were carried out later on (cf. Appendix A.3).

Figure 2 . 6 :

 26 Figure 2.6: Instrumentation of the concrete-slab surface: (a) distribution of the "measurement devices", anemometers location (blue circles), and IR camera view section (purple square), (b) an image of the "measurement devices" near to the South facade openings.

Figure 2 . 8 :

 28 Figure 2.8: Location of the "measurement devices" at the ceiling and the glazed-facade (blue boxes): (a) West-side view and (b) top view.

Figure 2 . 9 :

 29 Figure 2.9: Image of the measurement zone on the ceiling surface.

Figure 2 . 10 :

 210 Figure 2.10: Image of the measurement zone on the glazed-facade surface.

Figure 2 . 11 :

 211 Figure 2.11: Image of the installation for temperature measurement: (a) indoor air and (b) outdoor air.

2. 2 .

 2 Experimental approach and protocol for comparison purposes, to validate the surface temperature measurement performed inside the thermoelectric modules §2.2.1.1.C), and to validate the estimation of the indoor mean radiant temperature obtained by heat ux measurement and an analytical model presented later in this chapter in §2.3.2.

Figure 2 . 12 :

 212 Figure 2.12: Experimental set-up for infrared measurements. On the left-hand side: Infrared camera. On the right-hand side: A fully crumbled aluminum foil (isotropic and di use re ector), a black foil placed on the concrete-slab surface (reference).

Figure 2 . 13 :

 213 Figure 2.13: Image of the meteorological station.

Figure 2 . 14 :

 214 Figure 2.14: Distribution of supplementary thermocouples for air temperature measurements inside the platform (in yellow).

Figure 2 .

 2 Figure 2.15: Images of a shiny thermoelectric module: (a) width, (b) thickness, and (c) a thermoelectric module installed with the silicon trail.

Figure 2 .

 2 Figure 2.16: A cross-section schematic representation and images of the calibration set-up, (a) and (b) respectively.

Figure 2 . 17 :

 217 Figure 2.17: Electrical response of the black coated thermoelectric module N o 8 after correction, when applying a heat load of 20 W•m -2 , along with the uncertainty of the voltmeter NI 9205.

Figure 2 . 19 :

 219 Figure2.19: Variation in the uncertainty δ ϕ in the heat ux measurement of the TEM N o 8: when using δ K (in red) and when using δ K depending on the heat ux applied (in blue).

Figure 2 . 20 :

 220 Figure 2.20: Thermocouples measurement when having the bath at 9, 89 • C, before correction.

Figure 2 . 21 :

 221 Figure 2.21: Thermocouples measurement when having the bath at 9, 89 • C, after correction.

Figure 2 . 22 :

 222 Figure 2.22: Schematic of a surface i submitted to super cial heat transfer.

2. 5 .

 5 Results and discussion on the coupling between the energy charge-discharge and natural ventilation

Figure 2 . 23 :

 223 Figure 2.23: Flowchart of the automation strategy for the natural ventilation openings during the measurement campaign in 2016.

Figure 2 . 27 :

 227 Figure 2.27: For con g. n • 1: Convective heat ux for the oor (black line), the ceiling (purple line), and for the glazed-facade (brown line). Moments where openings remained opened (gray zones).

Figure 2 . 28 :Figure 2 . 29 :

 228229 Figure 2.28: For con g. n • 2: Convective heat ux for the oor (black line), and the ceiling (purple line). Moments where openings remained opened (gray zones).

2. 5 .

 5 Results and discussion on the coupling between the energy charge-discharge and natural ventilation During the discharge period, the behavior of the convective heat ux at each surface indicates that their role in the charge-discharge has changed. The glazed-facade (brown line) contributes to the discharging of the indoor air, while the oor (black line) contributes to its charging. The magnitudes of the convective heat ux encountered, when the openings remained open (gray zones), at the oor surface (cf. gs. 2.28 and 2.29), with respect to the magnitude encountered for this surface when the openings remained close (cf. g. 2.27), clearly indicate that the increment is caused by the opening of the openings, and thus, a consequence of natural ventilation. Moreover, the heat ux at the ceiling surface (purple line) appears to not have a signi cant contribution neither to the charging nor the discharging of the indoor air during the discharge period, regardless of the opening con guration implemented (cf. g. 2.29).

Figure 2 . 33 :Figure 2 . 34 :Figure 2 . 35 :

 233234235 Figure 2.33: For con g. n • 1: Radiative heat ux for the oor (black line), the ceiling (purple line), and for the glazed-facade (brown line). Moments where openings remained opened (gray zones).

6 . 1 . 4 .

 614 The missing 109 observations laid outside the day/nighttime criteria established.The variables presented in gure 2.36 and 2.37 are: temperature of the (a) outdoor air, (b) indoor air, (c) oor surface, (d) ceiling surface, (e) averaged of surrounding surfaces and ( f ) air near oor surface.

Figure 2 . 36 :Figure 2 . 37 :

 236237 Figure 2.36: Correlation plot based on the Pearson coe cient for experimental results from no-windy nighttime: the sample size resulted in 196.

2. 6 .Figure 2 . 38 :

 6238 Figure 2.38: Correlation results for no-windy nighttime with Spearman's coe cient.

Figure 2 . 39 :

 239 Figure 2.39: Correlation results for sunny and windy daytime with Spearman's coe cient.

0 Figure 2 . 40 :

 0240 Figure 2.40: For each day in con g. n • 1, results of the convective heat ux vs air-surface temperature di erence: oor (black), ceiling (purple), and glazed-facade (brown).

Figure 2 . 41 :Figure 2 . 42 :

 241242 Figure 2.41: For each day in con g. n • 2, results of the convective heat ux vs air-surface temperature di erence: oor (black), ceiling (purple), and glazed-facade (brown).

Figure 2 . 51 :

 251 Figure 2.51: Air temperature vertical distribution within the platform. Air at the shed-roof (red circles).Indoor air (black dashed line). Floor: air (black circles), surface (black solid line). Ceiling: air (purple circles), surface (purple solid line). Air temperature di erences: indoor-outdoor (green), ceiling-indoor (yellow), indoor-oor (blue), ceiling-oor (brown), and shed-oor (red).

2. 6 .Figure 2 . 52 :

 6252 Figure 2.52: Occurrence distribution of the air temperature di erence between the shed and the oor (a vertical distance of around 3,5 m). Data employed: measurement campaign carried out in 2016; a total of 51398 samples.

Figure 2 . 53 :

 253 Figure 2.53: Experimental set-up implemented during the measurement campaign of 2015.

Figure 2 . 54 :

 254 Figure 2.54: Total heat ux (ϕ b ) distribution over the oor concrete-slab surface during the discharge period from the measurement campaign of 2015.

  grams of ve elements of the platform envelope (viewed from the inside of the platform) are presented in gure 2.55: (a) the glazed-facade and concrete-slab, (b) the concrete-slab and surroundings surfaces via the crumbled aluminum foil, (c) the North facade, (d) the shed-roof, and (e) the East-side door.

  the internal room temperature (cf. eq. 23, red line) are shown in gure 2.56. Two horizontal dashed lines represent the chosen comfort range (23 -26 • C).

94

 94

2. 7 .Figure 2 . 56 :

 7256 Figure 2.56: Outdoor (black line) and indoor (red line) air temperatures of the entire measurement campaign carried out during the summertime in 2016.

Figure 2 . 57 :

 257 Figure 2.57: Degrees of discomfort time of days whose T op is greater than T com f ort max .

Figure 2 . 58 :

 258 Figure 2.58: Left axis: T ia to 1,70 m, black line. T ia at 0,10 m, dotted with balls. Right axis: 1,70 m air velocity, black dotted line. Air velocity at 0,10 m, black line.

Figure 2 . 59 :

 259 Figure 2.59: Left axis: T ia black line. T surr black line with "+". T op dotted line in blue. Axis on the right: Air velocity, black dotted line. All measurements made at 1,70 m height.

(

  video recording) any possible air ow patterns. Though this could only be performed for one facade at a time, the behavior of the ags showed air ow patterns that could only be taken into account when performing numerical modeling techniques as CFD. For instance, let us look at some screenshots from a 17 mins video recorded on May 15 th , 2017 starting at 11 h, shown in gure 3.1 (a)-(c), and gure 3.1 (e) (f). During this recording, only the openings at the South facade and shed-roof remained open. In gure 3.1 (a), the ags on the openings at the South facade appear to be in a steady state (no air current appears to be detected by the ags), represented by the yellow arrow (reference state). In gure 3.1 (b), all four ags appear to be tilted inwardly (air ow entering the platform, green arrows). Based on the wind direction during the recording (cf. gure 3.1 (c), top right corner: blue line), the behavior in gure 3.1 (b) is expected, and can be easily considered in the air ow path electrical analogy modeling.

3. 1 .Figure 3 . 1 :

 131 Figure 3.1: Screenshots from a 17 mins video for air ow pattern recognition: a reference of the ags in steady position (yellow arrows) and ow direction indicated by the ags (green arrows). At the South facade: (a) all ags motionless, (b) all ags tilted inwardly, (c) both upper ags motionless while both lower ags tilted outwardly (left) and inwardly (right), (d) all ags tilted outwardly. At the shed-roof: (e) left ag tilted outwardly while right ag steady, (f) left ag tilted outwardly while right ag tilted inwardly.

3. 2 .Figure 3 . 2 :

 232 Figure 3.2: Schematic of the modeling process employed. Global domain modeling: Physical or real domain, and single-zone model in CONTAM (domain modeling). Local domain modeling: air ow models chosen for openings and in ltrations.

3. 2 .

 2 Modeling of the natural air ow rate in the platform (1) A single-zone enclosure represented by four walls

Figure 3 . 3 :

 33 Figure 3.3: Schematic showing the steps in the construction of the single-zone model on CONTAM: (1) single-zone area and volume, (2) location of the natural ventilation openings (South, North, shed-roof), (3) location of air-leakages (location 1 and location 2), (4) Air ow models selection for the openings and leakages.

  a. The in ltrations are equally distributed on the facades containing the natural ventilation openings: the location of the in ltrations is xed at half of each facade height. b. The in ltrations are not equally distributed and an in situ identi cation of their location is required: with the intention to recovery the tightness of the platform envelope, an in situ identication process has shown that the majority of the air-leakage are located behind the kitchen (at the West facade) (cf. §3.3.1).

Figure 3 . 4 :

 34 Figure 3.4: Considerations for a bidirectional ow: (a) when the NPL crosses an opening, (b) CONTAM simulation results for temperature di erence only, (c) when the NPL does not cross any opening.

Table 3 . 2 :Figure 3 . 5 :

 3235 Figure 3.5: (a) Surrounding around the platform, and (b) image of the platform [41].

( 6 ) 6 ( 106 3. 2 .Figure 3 . 6 : 42 For

 6610623642 Figure 3.6: Building morphology approximation implemented in the estimation of the external pressure coe cients (red boxes): (a) West view, and (b) Top view.Table 3.3: Recommended external pressure coe cient values for rectangular vertical walls.

Figure 3 . 7 :( 7 )

 377 Figure 3.7: External pressure coe cient C p pro le used on the simulations.(7) Air ow simulations on CONTAMThe air ow simulations can be performed by either considering weather data from an Energy Plus letype or manually changing the values of both the indoor and outdoor temperatures, and wind speed and direction, on the Edit weather data: weather and wind parameters window. To account separately for the in uence of wind and thermal buoyancy e ects on the air ow rate (in the form of ach), we followed the procedure illustrated in gure 3.8: a) Air ow rate due to wind e ects only: In order to isolate the in uence of wind e ects on the ach, both the indoor (T ia ) and outdoor (T oa ) air temperature are set to have the same value, and the simulations are performed by varying the wind speed ( V) and direction (φ W ), arbitrarily. The wind speed from 1 to 10 m•s -1 ; keeping the wind direction at a constant angle, and this was performed for di erent angle values, from 0 to 360 • . Since the resulting ach only depends on wind speed and direction, we referred to this air change per hour as ach W . b) Air ow rate due to thermal buoyancy e ects only: For isolating the e ects of thermal buoyancy on the ach, the wind speed is set to zero. Then, the simulations are performed by varying the indoor and outdoor air temperatures arbitrarily within the temperature range encountered in the measurement campaigns. We referred to the resulting air change per hour due only to thermal buoyancy as ach ∆T .

Figure 3 . 8 :

 38 Figure 3.8: Schematic of the simulation process employed.

Chapter 3 -Figure 3 . 9 :

 339 Figure 3.9: Tightness of the openings: (a) South, and (b) North facades.

Figure 3 . 10 :

 310 Figure 3.10: Sealing of air-conducts related to the mechanical ventilation and PCM system (a)-(b), indicated by red arrows. Reinforcement of joinery (c)-(d), red rectangles. Sealing holes due to electrical networks and water system (e)-(f), indicated by red arrows.

Figure 3 . 11 :

 311 Figure 3.11: Airtightness tests results performed on June 15 th , 2015.Table 3.4: ach results from airtightness tests performed on June 15 th , 2015. Test n • Color code ach 50 * h -1 Action 1 Red 13,07 After blocking all mechanical ventilation conducts 2 Green 12,99 After sealing the bedroom window-door (cf. g.3.10 (c)) 3 Blue 12,53 After sealing big holes found in electrical networks and hot water system (cf. g.3.10 (e)-(f)) 4 Olive 12,09 After sealing door joinery (cf. g.3.10 (d)) 5 Purple 11,72 After sealing the kitchen extractor *ach at a pressure di erence of 50 Pa.

Figure 3 . 12 :

 312 Figure 3.12: Experimental set-up for airtightness tests with openings opened. (a) Blower door installed at the West door. (b) Location of both blower doors. (c) Blower door installed at the East door.

Figure 3 .Figure 3 . 14 :Figure 3 . 15 :

 3314315 Figure 3.13: (a) Pressure measurements performed on July 8 th -11 th , 2017: at one point on the South (P1, green) and North (P2, red) facades with respect to the indoor environment (P o ). (b) Experimental set-up and points of measurements (P1, P2, P o ). (c)-(d) Moments of absence of wind. (e) A schematic representation of a wind direction of 250 • . (f) Corresponding wind speed (dark red) and direction (blue).

Figure 3 . 16 :

 316 Figure 3.16: ach results from the K-P model as a function of the opening e ective-area: work of [55] (red dashed line), and from our airtightness tests (black dots).

Figure 3 . 17 :

 317 Figure 3.17: Schematic of the single-zone model employed in the simulations with leakages: (a) equally distributed at the facades with openings, (b) at the West facade only.

*Figure 3 . 18 :

 318 Figure 3.18: Resulting ach due to thermal buoyancy only (ach ∆T ): air-leakages only (blue line), openings at the South and shed-roof opened with no leakages (red line), and all openings opened with no leakages (black line).

Chapter 3 -igure 3 . 19 :igure 3 . 20 :Figure 3 . 21 :igure 3 . 22 :

 3319320321322 Figure 3.21: Results of B(φ W ) for di erent wind direction and tted Fourier's regression: Openings south + shed without leakages (red) and In ltrations only (blue).

Figure 3 . 23 :

 323 Figure 3.23: Results of B(φ W ) for di erent wind direction and tted Fourier's regression: Openings south + shed + leakages.

3. 4 .

 4 Results and analysis

igure 3 . 24 :Figure 3 . 25 :

 324325 Figure 3.25: Results of B(φ W ) with leakages at the West facade for di erent wind direction and tted Fourier's regression: Openings south + shed + leakages.

3. 5 .Figure 3 .

 53 Figure 3.26: (a) Simulation results when combining wind an buoyancy e ects, for a constant wind speed of 1 m•s -1 and di erent wind directions. Indoor temperature was xed at 22 • C, while the outdoor temperature was decreased from 22 to 16 • C. (b) Illustration of the situations presented here at the right-hand side of this gure, for three four wind direction; showing the opposing and the assisting of both e ects.

4. 1

 1 Identi cation of a thermal behavior model for the indoor air using experimental data 4.1.1 Energy balance for the indoor air The thermal behavior of the indoor air is modeled by following the energy balance equation of a xed control volume in the case of an open thermodynamic system. This control volume (CV) is set to represent the entire volume of the experimental platform as a single-zone (cf. g. 4.1). This assumption might be justi ed by the fact that all internal partition-walls and doors remained open during the measurement campaigns. the platform: Approximate morphology of the platform:

Figure 4 . 1 :

 41 Figure 4.1: Schematic of the platform employed in the modeling. Left-hand side: physical domain (real domain). Right-hand side: domain modeling (approximation of the real domain). Airstreams (brown arrows), convective heat exchanges (blue arrows).

Working temperature range in experiments 5 ) 0 simpli cation 7 )P 9 )

 5079 Indoor air uniform in temperature ∆T ia (x, y, z) = 0 For simpli cation 6) Furniture, partition-walls and doors are in thermal equilibrium with the indoor air ϕ f urniture (λ,C,R) = For Physical properties are constant with temperature, except for ρ and c p Solar radiation reaching the indoor environment is negligible ϕ iSWL ∼ 0 Window shades closed and experimentation 10) The air speci c heat depends on the temperature c p (T) = 1009-1003 350-293 • [T -293] + 1003 Regarding the term relating the convective heat transfer in equation 4.1, it was decided to consider the convective heat transfer between the indoor air and the oor, ceiling and glazed-facade surfaces, individually in three terms, as in equation 4.2. The reason lays in hyp. n • 5 (cf.

Chapter 4 -Figure 4 . 4 :

 444 Figure 4.4: For con g. n • 3: oor h C D (black), ceiling h C P (purple), and glazed-facade h C g (brown).

, 7 achFigure 4 . 5 :

 745 Figure 4.5: Resulting air change rate per hour for con g. n • 1: ach ϕ C (blue), ach ∆T (red), ach W (yellow), ach n=2 (green), ach K-P (cyan), and ach m=2 (purple). The corresponding temperature measurements: indoor air (brown dashed line) and outdoor air (brown circles).

4. 1 .Figure 4 . 6 :Figure 4 . 7 :

 14647 Figure 4.6: Resulting air change rate per hour for con g. n • 2: ach ϕ C (blue), ach ∆T (red), ach W (yellow), ach n=2 (green), ach K-P (cyan), and ach m=2 (purple). The corresponding temperature measurements: indoor air (brown dashed line) and outdoor air (brown circles).

Figure 4 . 9 :

 49 Figure 4.9: For con g. n • 2. Convective heat ow for the oor (red) and ceiling (blue), and storage term (yellow), from the point of view of the air (negative values correspond to a discharge).

4. 1 .Figure 4 . 10 :

 1410 Figure 4.10: For con g. n • 3. Convective heat ow for the oor (red),ceiling (blue), glazed-facade (green), and storage term (yellow), from the point of view of the air (negative values correspond to a discharge).

(

  a) a comparison of the indoor air temperature T ia between the model (red line) and experimental data (black circles), along with the absolute error (brown line), (b) the resulting heat ow terms in equation 4.2 using T ia from the model: oor (red), ceiling (blue), glazed-facade (green), energy storage in air (yellow), and ventilation (purple), (c) the resulting air change rate per hour (ach) from the model solution (black dotted line).

Chapter 4 -

 4 Identi cation of a thermal model to describe the behavior of the platform

Figure 4 . 11 :Figure 4 . 12 :

 411412 Figure 4.11: Numerical results for con g. n • 1: (a) T ia model (red line), T ia measured (black dots), and absolute error (brown line); error bars ±0,48 • C. (b) Heat ows: oor (red), ceiling (blue), glazed-facade (green), energy storage in air (yellow), and ventilation (purple). (c) ach (black), V met (purple) and φ W (yellow), and T oa (brown).

Figure 4 . 13 :Figure 4 . 14 :

 413414 Figure 4.13: Numerical results for con g. n • 2: (a) T ia model (red line), T ia measured (black dots), and absolute error (brown line); error bars ±0,48 • C. (b) Heat ows: oor (red), ceiling (blue), glazed-facade (green), energy storage in air (yellow), and ventilation (purple). (c) ach (black), V met (purple) and φ W (yellow), and T oa (brown).

Figure 4 . 15 :Figure 4 . 16 :

 415416 Figure 4.15: Numerical results for con g. n • 3: (a) T ia model (red line), T ia measured (black dots), and absolute error (brown line); error bars ±0,48 • C. (b) Heat ows: oor (red), ceiling (blue), glazed-facade (green), energy storage in air (yellow), and ventilation (purple). (c) ach (black), V met (purple) and φ W (yellow), and T oa (brown).

(

  A) Accuracy and adaptability to di erent opening con gurations regarding the indoor air temperature The identi ed values are presented in table 4.4. For the results of model A, regarding the behavior (or dynamics) of T ia (cf. gs. 4.11 (a), 4.13 (a) and 4.15 (a), red line), satisfactory results are obtained since the values of the absolute error are very low (brown line), where the maximum RMSE value is 0,31 • C for con guration n • 1 (cf. gs. 4.11 (a) and 4.12).

(

  daytime only): model A appears to accurately describe the behavior of T ia in regard to the RMSE value, and the average absolute error; an average absolute error around 0,27 • C and 0,19 • C for con gs. n • 1 and n • 2, respectively.• For the case where the openings remained opened, as in gure 4.13 (nighttime only) and in gure 4.15 (entire day): model A appears to describe more accurately the behavior of T ia (with respect to the case of openings closed) in regard to the RMSE value, and the average absolute error; an average absolute error around 0,19 • C, for con guration n • 3, respectively.

Figure 4 . 17 :

 417 Figure 4.17: Wind speed occurrence distribution during the measurement campaigns for each opening con guration; a total of 2304 samples.

(

  B) Accuracy and adaptability to di erent opening con gurations regarding the convective heat ow termsRegarding the results for the convective heat ows and energy storage terms in equation 4.2: for conguration n • 1, the behavior of the heat ows in gure 4.11 (b) appear to be similar to those in gure 4.8. However, the magnitude of the oor slab (red) and ceiling (blue) terms not always agreed. For con guration n • 2 (comparing gures 4.9 and 4.13 (b)), a clear overestimation in the oor slab term is presented (red line) for only two of the days (nighttime of 12/8 ad 13/8), and this, also in the ceiling term only for three of the days (daytime 13/8, 14/8 and 15/8). For con guration n • 3, comparing gure 4.10 and 4.15 (b), the model presents an overestimation in the oor slab (red) and ceiling (blue) terms for 4.1. Identi cation of a thermal behavior model for the indoor air using experimental data three days out of four days in nighttime. In turn, the ceiling term (blue) in gure 4.15 (b), shows strong agreement with the values in gure 4.10, except for the 27/5 which is underestimated in the daytime. (C) Accuracy and adaptability to di erent opening con gurations regarding the air change rate per hour The resulting air change rate per hour ach (black dotted line) for each con guration is shown in gures

Figure 4 . 20 : 21 :

 42021 Figure 4.20: Resulting air change rate per hour for con g. n • 3: ach (∆TxW) (black), ach ϕ C (blue), ach ∆T (red), ach W (yellow), and ach K-P (cyan). The corresponding temperature measurements: indoor air (brown dashed line) and outdoor air (brown circles).

Figure 4 . 22 :

 422 Figure 4.22: Schematic employed in the modeling of the heat transfer through the concrete-slab.

Figure 4 . 23 :

 423 Figure 4.23: Schematic of the method employed in the discretization of the concrete-slab thickness.

and 4 . 25 .

 425 In the latter, a histogram is included to show the distribution of the absolute error between the model and measurement. The computation time (or running time) expended to solve the model for each con guration was less than a minute.

Figure 4 .

 4 24 presents the following two plots: (a) A comparison of the surface temperature of oor concrete-slab T S D between the model (yellow and red lines) and experimental data (blue circles), along with the absolute error (brown line) at every instant. This error is calculated between the temperature T S D measured (blue dots) and the model (red line). Also, the results of model B1 using h C D-TEM (yellow line, named TS_D model 1), and model B1 using h C D-FGT (red line, named TS_D model 2). For this Model, T S D ≡ T D . (b) The resulting heat ow on the oor for each term in equation 4.16 using T S D from the model: Convection (red), radiation (dark green), energy storage term (black).

Figure 4 .

 4 Figure 4.24 (a) shows the results from Model B1, when using h C D-TEM (yellow line) and h C D-FGT (red line). The values of the former are computed with the heat ux measurement from thermoelectric

Figure 4 . 24 :

 424 Figure 4.24: Model B1 for con g. n • 2. (a) concrete-slab surface temperature measured (blue dots), T D model with h C D-TEM (yellow line, TD_S model 1), and T D model with h C D-FGT (red line, TD_S model 2). Absolute error (brown) between red line and blue dots, and error bars ±0,48 • C. Recall that: T S D ≡ T D . (b) Terms on equation 4.16, from the point of view of the surface (negatives values correspond to a discharge).

Figure 4 . 25 :

 425 Figure 4.25: Associated error distribution for T S D in g. 4.24 (a), and the RMSE value.

Figure 4 .

 4 26 presents the following: (a) a comparison of the surface temperature of oor concrete-slab T S D between the model (yellow and red lines) and experimental data (blue circles), along with the absolute error (brown line) at every instant. This error is calculated between the temperature T S D measured (blue) and the model (red). We present two "sub-models" for T S D : one with h C D-TEM (yellow line, named TS D model 1), and another with h C D-FGT (red line, named TS D model 2). (b) the resulting heat ow on the oor for each term in equation 4.16 using T S D from the model: Convection (red), radiation (dark green), energy storage term (black).

Figure 4 . 26 :

 426 Figure 4.26: Model B2 for con g. n • 2. (a) Temperatures of the top node (yellow line, TD_S model N=1) and bottom node (red line, TD_S model N=M). Absolute error (brown) between top node and blue dots, and error bars ±0,48 • C. (b) heat ow terms on equation 4.17, from the point of view of the surface (negatives values correspond to a discharge).

Figure 4 . 27 :

 427 Figure 4.27: Associated error distribution for T D in g. 4.26 (a), and the RMSE value. Therefore, gure 4.26 (a) shows the results of Model B2 using h C D /2 only. In this gure, the temperature results for the top (N=1, yellow line) and bottom (N=M, red line) nodes are presented, where a

4. 3 A

 3 complete model for describing the coupling between the energy charge-discharge of the thermal mass and natural ventilation4.3.1 Evaluation of the model with data inside the identi cation processNow, by merging Model B2 with Model A, the temperature measurement of the concrete-slab surface is no longer needed, and the coupling between the energy charge-discharge of the thermal mass and natural ventilation is completed. This model is summarized in equation 4.20 and we will refer to it as "the coupled model. "The numerical results of "the coupled model" are presented in gures 4.28-4.31, for con guration n • 2 only. The computation time expended was about 13 minutes.Desired variables (unknowns): T ia , T S D , T D , ach.

Figure 4 . 28 :

 428 Figure 4.28: Results for con g. n • 2: (a) T ia model (red line), T ia measured (black dots), and absolute error (brown line). (b) Heat ows: oor (red), ceiling (blue), glazed-facade (green), energy storage in air (yellow), and ventilation (purple). (c) ach (black), V met (purple) and φ W (yellow), and T oa (brown).

4. 3 .Figure 4 . 29 :

 3429 Figure 4.29: Associated error distribution for g. 4.28 (a), and the RMSE value.

Figure 4 . 30 :

 430 Figure 4.30: Results for con g. n • 2. (a) Temperatures of the top node (yellow line, TD_S model N=1) and bottom node (red line, TD_S model N=M). Absolute error (brown) between red line and blue dots, and error bars ±0,48 • C. (b) heat ow terms, from the point of view of the surface (negatives values correspond to a discharge).

Figure 4 . 31 :

 431 Figure 4.31: Associated error distribution for g. 4.30 (a), and the RMSE value.

Figure 4 . 32 :

 432 Figure 4.32: Results for con g. n • 2 (data not part of identi cation): (a) T ia model (red line), T ia measured (black dots), and absolute error (brown line). (b) Heat ows: oor (red), ceiling (blue), glazed-facade (green), energy storage in air (yellow), and ventilation (purple). (c) ach (black), V met (purple) and φ W (yellow), and T oa (brown).

Figure 4 . 33 :

 433 Figure 4.33: For con g. n • 2 (data not part of identi cation). Associated error distribution for g. 4.32 (a), and the RMSE value.

Figure 4 . 34 :

 434 Figure 4.34: Results for con g. n • 2 (data not part of identi cation). (a) Temperatures of the top node (yellow line, TD_S model N=1) and bottom node (red line, TD_S model N=M). Absolute error (brown) between red line and blue dots, and error bars ±0,48 • C. (b) heat ow terms, from the point of view of the surface (negatives values correspond to a discharge).

Figure 4 . 35 :

 435 Figure 4.35: For con g. n • 2 (data not part of identi cation). Associated error distribution for g. 4.34 (a), and the RMSE value.

i 1 2 1 3 3 4 4 5 4 6 4 1. 1 8 1. 2 10 1. 3 12 1. 4 12 1. 5 13 1. 6 16 1. 9

 113444182103124125136169 Image of the experimental platform, Sumbiosi: South-facade view. . . . . . . . . . . . . viii ii Image of the experimental platform, Sumbiosi: North-facade view. . . . . . . . . . . . viii iii Echanges radiatifs et convectifs sur le dispositif de mesure destiné à observer et quanti er le stockage/déstockage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix iv Instrumentation de l'ensemble de la surface de dalle : représentation schématique (a) et dispositif de mesure pour observer le stockage/déstockage (b). . . . . . . . . . . . . . . x v Résultats de la densité du ux thermique pour la con guration 2. En surface de dalle : échanges radiatifs (orange) et convectifs (noir). En surface du plafond : échanges radiatifs (vert) et convectifs (violet). Vitesse d'air en surface de dalle (rouge foncé, axe à droite). Moments d'ouverture des ouvrants (zones grises). . . . . . . . . . . . . . . . . xii vi Résultats du modèle pour une con guration 2. A gauche : température d'air intérieur mesurée (noir) et simulée (rouge), température de surface de dalle mesurée (bleu) et simulée (orange premier noeud et vert dernier noeud). A droite : taux de renouvellement de l'air (noir) et températures d'air intérieur et extérieur (rouge). . . . . . . . . . . . . . xv 1 2015 world total primary energy production according to IEA [54]. . . . . . . . . . . . Objectives in energy consumption of the regulation RT 2020 in France. . . . . . . . . . Overview of the physical phenomena:(a) charge process, (b) discharge process, and (c) physical phenomena. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Image of the experimental platform, Sumbiosi: South-facade view. . . . . . . . . . . . . Image of the experimental platform, Sumbiosi: North-facade view. . . . . . . . . . . . Schematic of the architectural plan of the experimental platform: (a) West view and (b) top view. Values of the global heat transfer coe cients for external walls of the platform (dotted lines). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . In uence factors and relations in the air movement domain inside and around the building [117]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cooling potential due to nighttime ventilation technique [2]. . . . . . . . . . . . . . . . The natural ventilation concept. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Representation of wind forces (a), and pressure distribution induced by wind (b) [58]. . Air movement due to buoyancy forces: (a) small openings, (b) one large lower opening [70]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stack ventilation with: (a) assisting winds, and (b) opposing winds [58]. . . . . . . . . . 15 1.7 Air ow capacity of bottom and side hung windows depending on the opening degree [57]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.8 Variation of the air ow capacity of bottom and side hung windows as a function the indoor-outdoor temperature [57]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Values of discharge coe cient obtained by [36]. . . . . . . . . . . . . . . . . . . . . . . 1.10 Values of discharge coe cient obtained by [49]. . . . . . . . . . . . . . . . . . . . . . . 1.11 Values of stack discharge coe cients for inward and outward ow in still air [25]. . . 1.12 Values of stack discharge coe cients for inward and outward ow with wind [25]. . . 1.13 (a) In uence of wind on the e ciency of stack ventilation. (b) Air change rates in the investigated rooms as the function of the wind velocity [44]. . . . . . . . . . . . . . . . 1.14 Comparisons between the experi-mental and simulation results performed into the PowerDomus software for the wind tunnel case [37]. . . . . . . . . . . . . . . . . . . . 1.15 Measured and calculated volume ow rates: Warren & Parkins (black thin line), De Gids & Pha (black dotted line, ∆T = 0 • C), and De Gids & Pha (black thick line, ∆T = 5 • C) [61]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.16 Results of the blower door tests with window opening from [55]. . . . . . . . . . . . . 1.17 Averaged facade pressure coe cient as a function of azimuth angle [87]. . . . . . . . . 1.18 Fitted regression model over experimental data of a coe cient regarding wind e ects as a function of the incident angle [62]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.19 Example of a network air ow modeling applied to a multi-zone building [39]. . . . . . 1.20 Comparison of the temperature of the outdoor and indoor environments: thermal lag and damping factor [43]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.21 Schematic of the model [116]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.22 Schematic of the models for two cases: (a) the indoor thermal mass is not in equilibrium with the indoor air, and (b) both are in equilibrium [111]. . . . . . . . . . . . . . . . . . 1.23 Schematic of the model [112]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.24 Experimental set-up: (a) Sketch, (b) inside the ventilated enclosure showing the heat source E and the thermal mass (steel balls), and (c) temperature and airspeed probes. [112]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.25 Experimental and theoretical results for the ventilation ow rate ( V) and the indoor air temperature (T i ) when T o = 33 + 7 • cos 4,09x10 -4 • tπ [112]. . . . . . . . . . . . 1.26 Structure of Captec® heat ux meter: (a) Composition, and (b) transversal side view with heat ux lines [23]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.27 General structure of a Peltier module [89]: (a) a singular TEM, and (b) two multistage TEM con gurations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.28 Experimental set-up in [51, 66]: (1) Air conditioning central, (2) Radiant panels, (3) a 12 cm heavyweight concrete wall, (4) air temperature probe, (5) room temperature probe, (6) a lightweight wall (isolation-wood), designed heat ux meters. . . . . . . . . . . . . 1.29 Proportional controller converted into a room temperature programmable device (a), and a schematic of the experimental room (b). . . . . . . . . . . . . . . . . . . . . . . . 1.30 Experimental set-up in Douiri 2007 [29]: Heat ux meters installed inside the oven. . . 1.31 Experimental set-up in [23]: Heat ux meters black and shiny, installed inside the heat exchanger (a). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.32 Experimental set-up in [109]: Heat ux meters installed at the (a) front and (b) rear faces of an external wall in a real residential building. . . . . . . . . . . . . . . . . . . . thermocouples, several phases regarding its tension response must be accomplished. A simple explanation would be as follows:

Figure A. 1 :

 1 Figure A.1: NIST polynomials [NI_1].

Figure A. 2 :

 2 Figure A.2: Thermocouple type T errors when using a NI 9213 [NI_1].

3 and A. 4 .

 34 In the rst picture, the bias (β) and random (ζ) errors in the temperature estimation of both the thermostatic bath and our thermocouples (accounting the acquisition system). The second picture shows what we are trying to accomplish: made the thermocouples measurement bias error to be equal to that of the Bath temperature.

Figure A. 3 :

 3 Figure A.3: The temperature distribution for both measurements, the Bath and the thermocouples, along with the bias errors respect to a real temperature value and the random errors.

Figure A. 4 :

 4 Figure A.4: The temperature distribution for both measurements, the Bath and the thermocouples, after corrections are applied.

Figure A. 5 :Figure A. 6 :

 56 Figure A.5: Thermocouples calibration rig.

3. Results and data analysis 3 . 1 .

 31 Reduction of the thermocouples deviation from the true temperature

Figure A. 7 :

 7 Figure A.7: Thermocouples temperature measurement behavior when having the bath at 9, 89 • C. T Bath in red (with error bars) and the mean temperature in black.

Figure A. 8 :

 8 Figure A.8: Both axis in ( • C). The upper plot: Regression between the Bath temperature and TC32 measurement. The lower plot: Residuals values on predicting T Bath using TC32 measurement.

Figure A. 9 :

 9 Figure A.9: Thermocouples temperature measurement behavior after corrected using expression 22, when having the bath at 9, 89 • C. T Bath in red (with error bars) and the mean temperature in black.

Figure A. 10 :

 10 Figure A.10: Thermocouples measurement behavior when having the bath at 14, 71 • C (at the left side) and 19, 75 • C (at the right side). T Bath in red (with error bars) and the mean temperature in black.

Figure A. 11 :

 11 Figure A.11: Thermocouples measurement behavior when having the bath at 24, 79 • C (at the left side) and 29, 09 • C (at the right side). T Bath in red (with error bars) and the mean temperature in black.

Figure A. 12 :

 12 Figure A.12: Thermocouples measurement behavior when having the bath at 34, 78 • C (at the left side) and 39, 72 • C (at the right side). T Bath in red (with error bars) and the mean temperature in black.

11/5/ 2015 |A. 2

 20152 Graisse thermique, Silicone, RS, 5W/m•K | http://fr.rs-online.com/web/p/graisse-thermique/7074736/?searchTerm=707-4736&relevancy-data=636F3D3126696E3D4931384E525353746F636B4E756… 1/2 Accueil > Chauffage, ventilation et air conditionné > Systèmes de chauffage et refroidissement électronique > Graisse thermique Code commande RS 707-4736 Fabricant RS Graisse thermique, Silicone, RS, 5W/m•K Comparer ce produit Caractéristiques techniques Trouver des alternatives Détail produit Graisse au silicone -série RS Cette pâte de dissipateur de silicone a une durée de vie de 18 mois à compter de la date de fabrication lorsqu'elle est stockée dans le récipient d'origine non ouvert à 25° C ou à une température inférieure. Les applications incluent : composants électroniques par exemple CI, microprocesseur, MOS, LED, M/B, P/S, LCD-TV, PC portable, circuit de télécommunications, concentrateur sans fil ; module de DDRII ; applications DVD ; applications de combiné. Bonne conductivité thermique Facile à utiliser Stabilité élevée Ne durcit pas avec le temps Perte de poids <0,5 % Gravité spécifique 2,3 g/cm 3 Température d'utilisation : -40 → +180°C Résistance transversale >10 12 ohm-cm Dimensions du boîtier 80x80x40 mm Contenu du pot : 30 g L' ensemble des produits de la Marque RS sont approuvés par les professionnels. Notre gamme est testée par des ingénieurs pour vous donner la même qualité que les autres marques leaders et vous faire profiter des meilleurs prix..Isolateurs thermoconducteurs (dissipateurs)POur trouver un produit similaire, sélectionnez ses attributs. Comparing the temperature of black and shiny thermoelectric modules

Figure A. 13 :

 13 Figure A.13: Image of the experimental set-up: sensors submitted to a non-direct solar radiation environment during the summertime (case 1).

Figure A. 14 :

 14 Figure A.14: Image of the experimental set-up: sensors submitted to a direct solar radiation environment during the wintertime (case 2).

Figures A. 15

 15 Figures A.[START_REF] Berthou | Développement de modèles de bâtiment pour la prévision de charge de climatisation et l'élaboration de stratégies d'optimisation énergétique et d'e acement[END_REF] and A.16 present, respectively for case 1, the temperature measurements for both black (black dashed line) and shiny (red dotted line) thermoelectric modules, and a histogram to show the occurrence distribution of their temperature di erence.

Figure A. 15 :Figure A. 16 :

 1516 Figure A.15: Temperature measurements from black (black dashed line) and shiny (red dotted line) thermoelectric modules for case 1. Temperature di erence (brown line, axis at the right).

Figures A. 17

 17 Figures A.17and A.18 present, respectively for case 2, the temperature measurements for both black

Figure A. 17 :

 17 Figures A.[START_REF] Bonilauri | What's the "time constant" of a building?[END_REF] and A.18 present, respectively for case 2, the temperature measurements for both black (black dashed line) and shiny (red dotted line) thermoelectric modules, and a histogram to show the occurrence distribution of their temperature di erence.

Figure A. 18 :

 18 Figure A.18: Occurrence distribution of the temperature di erence between black and shiny thermoelectric modules for case 2.

NomenclatureFGT 1 K 1 s

 11 Sensitivity of heat ux metersµV•m 2 •W -Shiny

Figure A. 19 :

 19 Figure A.19: Schematic of the experimental set-up installed in November 2016, and their location inside the PEH: (a) Location 1 used from 2/11 to 7/11 and from 18/11 to 21/11, and (b) location 2 used from 22/11 to 25/11.

Figure A. 20 : 2 .

 202 Figure A.20: Images of the experimental set-up installed in November 2016, and their location inside the PEH: (a) Location 1 used from 2/11 to 7/11 and from 18/11 to 21/11, and (b) location 2 used from 22/11 to 25/11.

Figure A. 21 2 ]Figure A. 21 :

 21221 Figure A.21 presents the results obtained for the estimated convective heat ux using the heat ux data collected by the black and shiny thermoelectric modules ϕ C-TEM (black line) and using the heat ux data from the black and shiny conventional heat ux meters ϕ C-FGT (red line). A di erence can be observed at a glance in ϕ C estimated by both sensors, where larger values were obtained for ϕ C-TEM .

Figure A. 22 :

 22 Figure A.22: On location 1. Convection heat ux from TEM measurements against FGT measurements (red dots). Blue line: linear regression xed at the origin.

Figure A. 23 :

 23 Figure A.23: On location 2. Convection heat ux from TEM measurements (black dots) and from FGT measurements (red dots). Blue zone: the natural ventilation openings remained opened.

Figure A. 24 :

 24 Figure A.24: On location 2. Convection heat ux from TEM measurements against FGT measurements (red dots). Blue line: linear regression xed at the origin.

  Natural ventilation system and openings . . . . . . . . . . . . . . . . . . . . . . 2.2 Experimental approach and protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Instrumentation of the thermal mass domain . . . . . . . . . . . . . . . . . . . 2.2.2 Instrumentation of the building . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Measuring system and calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Semi-empirical models for data processing . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Decoupling the convection and radiation heat exchanges . . . . . . . . . . . . . 2.3.2 Mean radiant temperature of surrounding surfaces . . . . . . . . . . . . . . . . 2.4 Experimental plan implemented in the measurement campaigns . . . . . . . . . . . . .2.5 Results and discussion on the coupling between the energy charge-discharge and natural ventilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Classi cation of the experimental data . . . . . . . . . . . . . . . . . . . . . . . Estimation of the natural air ow rate via heat ux and temperature measurements 4.1.3 Identi cation of Model A for all opening con guration . . . . . . . . . . . . . . 4.2 Choice of a thermal behavior model for the thermal mass . . . . . . . . . . . . . . . . . 4.2.1 Lumped-capacitance approximation . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Spatial discretization via nite di erences . . . . . . . . . . . . . . . . . . . . . 4.2.3 Choice of a Model B for all opening con guration . . . . . . . . . . . . . . . . . 4.3 A complete model for describing the coupling between the energy charge-discharge of the thermal mass and natural ventilation . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Evaluation of the model with data inside the identi cation process . . . . . . . 4.3.2 Evaluation of the model with data outside the identi cation process . . . . . . 4.4 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

	CONTENTS	xxix
	4.1.2 General conclusion and future work
	Associated publications
	Bibliography
	Appendices

1.1.3 Assessment techniques for the natural ventilation air ow rate . . . . . . . . . . 1.2 Thermal behavior modeling and identi cation approaches . . . . . . . . . . . . . . . . 1.2.1 Thermal behavior of a passive building: the role of the envelope . . . . . . . . . 1.2.2 Modeling approaches for forecasting in buildings . . . . . . . . . . . . . . . . . 1.3 Coupling between natural ventilation and thermal mass . . . . . . . . . . . . . . . . . . 1.4 Heat ux measurement techniques for rigid surfaces . . . . . . . . . . . . . . . . . . . . 1.4.1 Principles of the heat ux measurement . . . . . . . . . . . . . . . . . . . . . . 1.4.2 Implementation of heat ux meters for measuring the super cial heat exchanges 1.4.3 Perturbations and uncertainties introduced by the heat ux meter . . . . . . . . 1.4.4 Calibration techniques for at-plate type of heat ux sensors . . . . . . . . . . 1.5 Concluding remarks and perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Characterization of the coupling of the energy charge-discharge process with natural ventilation 2.1 Description of the experimental platform . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Passive strategies for the charge-discharge process in summer . . . . . . . . . . xxvii xxviii CONTENTS 2.1.2 2.5.2 Thermal behavior of the platform under di erent opening con gurations and outdoor conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.3 Coupling of the charge-discharge process with natural ventilation within the indoor environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Characterization of the energy charge and discharge processes . . . . . . . . . . . . . . 2.6.1 Impact of the outdoor environment upon the indoor environment via correlation analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.2 Identi cation of the heat transfer phenomena involved . . . . . . . . . . . . . . 2.7 Thermal comfort assessment of a simple opening-closing strategy . . . . . . . . . . . . 2.7.1 Indicators employed in the assessment . . . . . . . . . . . . . . . . . . . . . . . 2.7.2 Impact of a passive night ventilation strategy on internal thermal comfort . . . 2.8 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Characterization of the natural ventilation air ow rate 3.1 Initial considerations and air ow pattern recognition . . . . . . . . . . . . . . . . . . . 3.2 Modeling of the natural air ow rate in the platform . . . . . . . . . . . . . . . . . . . . 3.3 Air ow characteristics of the openings . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Recovery of the envelope tightness and airtightness tests . . . . . . . . . . . . . 3.3.2 Discharge coe cient of the openings . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Identi cation of C and n for each opening . . . . . . . . . . . . . . . . . . . . . 3.4 Results and analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Airtightness tests and discharge coe cient identi cation . . . . . . . . . . . . . 3.4.2 Comparison of the air change rate per hour using airtightness tests . . . . . . . 3.4.3 Air ow simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Concluding remarks on the air ow characteristics of the platform and perspectives . . 4 Identi cation of a thermal model to describe the behavior of the platform 4.1 Identi cation of a thermal behavior model for the indoor air using experimental data . 4.1.1 Energy balance for the indoor air . . . . . . . . . . . . . . . . . . . . . . . . . . A Calibration and metrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.1 Experimental report: Calibration of thermocouples . . . . . . . . . . . . . . . . A.2 Comparing the temperature of black and shiny thermoelectric modules . . . . A.3 Assessment of thermoelectric modules as alternative to conventional heat ux meters for decoupling the super cial heat transfer . . . . . . . . . . . . . . . . B Weather conditions from ENSAM meteorological station . . . . . . . . . . . . . . . . . C Reports of airtightness tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 1 -

 1 Theoretical background and state of the art sidered. Moreover,Larsen et al. in 2006 [62], developed an empirical model for the estimation of C p as a function of the wind incident angle, by tting regression models as shown in gure 1.18. According to the network modeling concept, a building is represented by a grid composed of several pressure nodes and ow paths (cf. g. 1.19)[START_REF] Ghiaus | Natural Ventilation in the Urban Environment: Assessment and Design[END_REF]. These pressure nodes could represent the pressure of a single zone inside the building or the pressure of the exterior environment (cf. g. 1.19 black ovals). The ow paths represent each opening in the building, e.g., windows, doors, etc. (cf.

	Nevertheless, all these models are applicable for buildings with simple rectangular geometries. For
	cases where other geometries should be taken into account, the standard EN 1991-1-4:2005 (Euro code
	1) presents guidelines for the estimation of C p values.
	Di erent models have been developed and proposed for the determination of the natural air ow rate
	in terms of the driving forces, depending on the natural ventilation strategy implemented. Zhiqiang
	et al. in 2015 [114] and later in 2016 [115], reported a review of natural ventilation models for simple
	opening con gurations, and classi ed them in two groups: analytical and empirical models, and net-
	work models. The analytical models are developed by applying the conservation equations to a speci c
	con guration.

g. 1.19 squares).

Table 1 .

 1 1: Strengths and weaknesses of di erent forecasting model techniques[START_REF] Berthou | Développement de modèles de bâtiment pour la prévision de charge de climatisation et l'élaboration de stratégies d'optimisation énergétique et d'e acement[END_REF].

		Physical model	Inverse model	Inverse model
	Forecasting models
		("white box")	("black box")	("gray box")
	Parametrization speed	-	++	+
	Data access	-	++	+
	Execution speed	-	+	+
	Physical sense	++	-	+
	Forecasting accuracy	++	?	?
	Adaptability to changes	-	++	+
	in strategy
	For the validation of such models, a set of experimental data other than the one used for identi -
	cation, is employed to run the simulations again. The models are said to be validated if the numerical
	results meet certain criteria. For instance, on the deliverable n • 3.3.2 [67], it is stated that the model
	must be met the criteria presented in table 1.2 in order to be eligible for control applications.
	Table 1.2: Criteria for model validation [67].
	N o Quality	Observed/improved factors
	1) Fast when recalibration is needed Uncomplicated models: choice
		of the number of parameters
	2) Reliability	Behavior of the error: Convergence
		to the same value at each identi cation
	3) Accuracy	Error values
	4) Prediction and adaptability	Observation of results for another dataset
	5) Robustness

Table 2 .

 2 1: Sensitivity values of Captec® heat ux meters.

	N • Captec	1	2	3	4	5	6	7	8	9	10
	K [µV•m 2 •W -1 ] 123 123 124 126 117 127 128 128 108 122

Table 2 .

 2

2: Response of the TEM N • 8 to di erent heat loads.

  • 4 on the same day, giving a K value of 247,91 µV•m 2 •W -1 . It was also performed two times on July 8 th , 2016 for the shiny coated thermoelectric module N • 8, giving a K value of 267,53 µV•m 2 •W -1 the rst time, and 267,14 µV•m 2 •W -1 the second time.

Table 2 .

 2 3: Uncertainties of the instruments for the calibration procedure. .4 with the values in table 2.2 and those in table 2.3, the resulting uncertainties in K at each heat load applied are presented in table 2.4. Results showed that the uncertainty in K decreases when the heat load applied increases, resulting in an average value δ K of 48,49 µV•m 2 •W -1 .

	Instrument	Parameter Uncertainty δ
	NI 9205	U	174 µV
	Digital caliper	S	6,0x10 -6 m 2
	Digital DC power source	U	10%
	Digital DC power source	I	10%
	By evaluating equation 2

Table 2 .

 2 4: Components in the uncertainty of the sensitivity K.

Table 2 .

 2

	5: Hypotheses and assumptions for data processing
	N o Hypotheses/assumptions	Notation	Justi cation
	1) LWL dominates indoor
	radiant environment	Φ SWL = 0	Window shades closed
			Experimentation-based
	2) Kirchho 's hypothesis	α = ε
			simpli cation
	3) Couple black-shiny
	has the same temperature

Table 2 .

 2 6: Con gurations of the openings on each measurement campaign in summertime.

						Openings con gurations
				Diurnal (T ia < T oa )	Nocturnal (T ia > T oa )
		Dates	Duration North	South Shed-roof North	South Shed-roof
		23/5/17,
	N • 1)	12/9 -17/9	4 d	Closed Closed	Closed	Closed Closed	Closed
		0h00 -0h00
	N • 2)	27/7 -12/9/16	35 d	Closed Closed	Closed	Closed Opened	Opened
		0h00 -0h00
	N • 3)	25/5 -29/5/17	4 d	Closed Opened	Opened	Closed Opened	Opened
		0h00 -0h00
	2.5 Results and discussion on the coupling between the energy charge-
		discharge and natural ventilation
	2.5.1 Classi cation of the experimental data

table 2

 2 August 26 th and September 8 th ) are presented. Figures2.26 shows the indoor temperatures and weather results for con guration n • 3 from May 25 th to May 28 th . The outdoor air temperature and solar radiation presented typical summertime values as expected.

.6. Figures 2.

[START_REF] Chiu | External ow e ects on the discharge coe cients of two types of ventilation opening[END_REF]

to 2.26, show the indoor temperatures and weather results for con gurations n • 1, n • 2, and n • 3, respectively.

Figure 2.24 shows the indoor temperatures and weather results for con guration n • 1, which comprises May 23 rd , September 12 nd , and September 15 th to 16 th . Figures 2.25 shows the indoor temperatures and weather results for con guration n • 2, in which, only two days with no windy nights (August 22 nd and 23 rd ), and two days with windy nights (

  m (black dashed line). For instance, consider the rst day (22/8) for con guration n • 2 in gure 2.28, and the rst day (25/5) for con guration n • 3 in gure 2.27, and let us concentrate on the convective heat ux at the oor surface (black line): at 0,10 m the exact moment when the heat ux changes from Figure2.31: For con g. n • 2. Air temperatures (lines with small circles) measured at the: oor (black), and ceiling (purple). Indoor air (black dashed line) and mean radiant temperature (red dashed line).

		25
		24
		23
		22
	T (°C)	21
		20
		19
		18
		17
		23/5	12/9	15/9	16/9	17/9
		27
		25
	T (°C)	23
		21
		19
		17
		22/8	23/8	26/8	8/9	9/9
	Surface temperatures (solid lines) measured at the: oor (black), and ceiling (purple). Moments where
	openings remained opened (gray zones).

positive to negative values, the air temperature (cf. gs. 2.31 and 2.32, black circles) goes from being higher than the surface temperature (black solid line) to being lower. It can be observed that this does not apply if we perform the same exercise with the air temperature at 1,70 m. About this last remark, a temperature measurement was performed (after the measurement cam-Figure

2

.30: For con g. n • 1. Air temperatures (lines with small circles) measured at the: oor (black), ceiling (purple), and glazed-facade (brown). Indoor air (black dashed line) and mean radiant temperature (red dashed line). Surface temperatures (solid lines) measured at the: oor (black), ceiling (purple), and glazed-facade (brown). Moments where openings remained opened (gray zones).

°C) 20 21 22 23 24 25 26 27 28 29 30

	25/5	26/5	27/5	28/5	29/5

T (

Figure 2

.32: For con g. n • 3. Air temperatures (lines with small circles) measured at the: oor (black), ceiling (purple), and glazed-facade (brown). Indoor air (black dashed line) and mean radiant temperature (red dashed line). Surface temperatures (solid lines) measured at the: oor (black), ceiling (purple), and glazed-facade (brown). Moments where openings remained opened (gray zones).

m^-2.K^-1) 0 1 2 3 4 5 6 7 8 9 10 22

  /8 (cf. g. 2.41). On the other hand, from gures 2.40 (23/5) and 2.42 for the glazed-facade (brown dotted line), the slope appears to remain the same for either the charge and discharge periods. Figure 2.45: For each day in con g. n • 3, results of the convective heat transfer coe cient using equation 2.24: oor (black), ceiling (purple), and glazed-facade (brown).

	Convective coefficient (W.m^-2.K^-1)	2 4 6 8 10 12 14
		16 0
		25/5	26/5	27/5	28/5	29/5
		14
	Convective coefficient (W.m^-2.K^-1)	4 6 8 10 12
		2
		0
		25/5	26/5	27/5	28/5	29/5
		/8	23/8	26/8	8/9	9/9

Figure 2.43: For each day in con g. n • 1, results of the convective heat transfer coe cient using equation 2.24: oor (black), ceiling (purple), and glazed-facade (brown).

Convective coefficient (W.

Figure 2.44:

For each day in con g. n • 2, results of the convective heat transfer coe cient using equation 2.24: oor (black), and ceiling (purple).

Table 2 .

 2 7: Constant parameters employed in the dimensionless numbers.

	Parameter	Notation		Value
	Concrete thermal conductivity	λ D	1,8 W•m -1 •K -1
	Air thermal conductivity Air density	λ ia ρ	0,024 W•m -1 •K -1 1,2 kg•m -3
	Dynamic viscosity	µ	1,81x10 -5 m 2 •s -1
	Gravitational constant	g	9,81 m•s -2
	Upper to lower openings height	Z	3,72 m
	Parameter		Critical range
	Biot number (Bi)		Bi	0,1
	Richardson number (Ri)		0,1 < Ri < 10
	Froude number (Fr )		0,3 < Fr < 3

Table 2 .

 2 8: Dimensionless numbers evaluated at the concrete-slab surface for each con guration. Figure 2.46: Bi number. Nu, Gr and Re numbers.

	2: Open-Close Con g. n • Figure 2.47: Con g. n • Bi 0.00 0.10 0.20 0.40 0.0e+00 0.50 Density Nu 0.30 22/8 23/8 26/8 8/9 9/9 x 0.0e+00 2.0e+08 + + + + ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +++ +++ +++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +++ + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + +++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +++ + ++ ++ + + + + + + + + + + + + + + + + + + + +++ + + + + + + + + + + + + + + + + + + + + ++++ ++ ++ ++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +++ + + + + + + + + + + + + + + + ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +++ + + + + + + + + + + + + + + + + +++ + + + + + + + + + + + + + ++++++++ + + + + + + + + + + + + + + + ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++++ + + + + + + + + + + + + ++++ + + + + + + + + + + + + + + + + + + + + + + +++++ +++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + +++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +++++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +++ + + + + + + + + + ++++++ +++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + +++++ + ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +++ + + + + ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +++++ +++ + + + + + + + + + + + + +++ + + + +++ + + + + + + + + + + + + + + + + + + +++++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +++ + + + + + + + + + + + + + + + + + + + + + + + + + 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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +++++ + ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +++ + + + + ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++++++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +++++++++ + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + ++ + + + + + + +++ + + + + + + + + + + + + + + + + + + + + + + + + +++ + + + + + + +++ + + + + + + + + + + + + + + + + + + +++ + + + + + + +++ + + + + + + + + + + + + + + + + + + + + + + + + + ++++ + + + + +++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++++++++ + + + + + + + + ++++ + + + + + + + + + + + + + + + + + + +++ + + + + + + + + ++++ + + + + + + + + + + + +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +++++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +++ + + + + + ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +++++++ + + + + + + + + + + + + +++++++ + + + + + + + + + + + + +++++++++ + + + + + + + + + ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++++ + + + + + + + + + + + + + + + ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++++++ + + + + + + + + + + + + + ++++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + 2000 Density Figure 2.48: Bi number. Bi 0.30 0.40 0.50 Density Nu 0.0e+00 4.0e+09 0.69 *** 0.92 *** 0.80 *** 6000 10000 14000 Re x 8.0e+09 1.2e+10 0 0 10 20 30 40 2000 8000 16000 20 40 60 3: Open-Open 0.00 0.10 0.20 25/5 26/5 27/5 28/5 29/5 x 0 10 20 30 40 50 60 0.0e+00 8.0e+09 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

  Nu and Gr numbers.

																Gr
	+ + + + + + + + + + +	+ +	+	+	+	+	+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++++++ + + + + + + + + + + + + + + +	+ +	+	+	+	+	+	+ +	Density	+ +
	Figure 2.49:						x

Table 3 .

 3 1: Terrain type coe cients for the wind speed modi er[START_REF] Dols | CONTAM User Guide and Program Documentation Version 3.2[END_REF].

	Terrain type Factor (A o ) Exponent (γ)
	Urban	0,35	0,40
	Suburban	0,60	0,28
	Airport	1,00	0,15
	facades are presented in table 3.2.

Terrain type characteristics Façade azimuth Pressure Coefficients

		Domain modeling
						Openings	North
			Solar radiation	at Shed-roof
			Wind			𝐓 𝐨𝐚
						Shed-roof
					Openings
						𝐓 𝐢𝐚	North	Leaks	Openings
			South		Concrete-slab	𝓩 𝐍𝐍
				For each zone	𝒊
	NF EN 1991-1-4 (2005)	Governing on CONTAM equations	𝑷 = 𝑷 𝟏 +	𝝆 • 𝓥 𝟏 𝟐 𝝏𝒎 𝒊 𝝏𝒕	𝟐 = 𝝆 𝒊 • -𝑷 𝟐 + 𝝏𝑽 𝒊 𝝏𝒕 + 𝑽 𝒊 • 𝟐 𝝆 • 𝓥 𝟐 𝝏𝝆 𝒊 + 𝝆𝒈 • 𝒛 𝟏 -𝒛 𝟐 𝟐 𝝏𝒕
		Discretization method
		System of equations		𝑷 = 𝑷 𝟏 +	𝝏𝒎 𝒊 𝝏𝒕 𝝆 • 𝓥 𝟏 ≈ 𝟐 𝟐	𝟏 ∆𝒕 -𝑷 𝟐 + • 𝑷 𝒊 𝑽 𝒊 𝑹𝑻 𝒊 𝒕 𝝆 • 𝓥 𝟐 -𝒎 𝒊 𝒕-∆𝒕 𝟐 𝟐 + 𝝆𝒈 • 𝒛 𝟏 -𝒛 𝟐
		Solution method	Newton-Raphson
		Numerical	For each zone 𝒊	𝒂𝒄𝒉 𝒊
		solution	For each opening	∆𝑷, 𝒎
		Wind effects	Buoyancy effects
		𝒂𝒄𝒉 𝒘 = 𝒇 𝓥, 𝝓	𝒂𝒄𝒉 ∆𝑻 = 𝒇 𝑻 𝒊𝒂 , 𝑻 𝒐𝒂
		𝑻 𝒊𝒂 = 𝑻 𝒐𝒂	𝓥 , 𝝓	𝓥 = 𝟎 𝑻 𝒊𝒂 ≠ 𝑻 𝒐𝒂

Table 3 .

 3 5: Results of airtightness tests.

					Openings opened
		Shed-roof Shed-roof North South South+shed South+North+shed
	Number of openings 1 (West)	2	4	4	6	10
	C l m 3 •s -1 •Pa -n l	0,0325	0,0325	0,0353 0,0358	0,0861*	0,0375
	n l	0,6560	0,6560	0,6560 0,6500	0,5800*	0,6400
	R 2	0,9996	0,9997	0,9996 0,9998	0,9997	0,9991
	C l+v	0,1936	0,3547	0,5906 0,7078	1,3000	1,8220
	n l+v	0,5500	0,5430	0,5010 0,5340	0,4151	0,4727
	R 2	0,9957	0,9991	0,9996 0,9963	0,9972	0,9998
	C v	0,1619	0,3231	0,5619 0,6744	1,2250	1,7920
	n v	0,5133	0,5241	0,5048 0,5251	0,3955	04666
	R 2	0,9999	0,9999	0,9999 0,9999	0,9999	0,9999
	S v e f f m 2	0,4840	0,4840	0,3575 0,3473	-	-
	S total e f f m 2	0,4840	0,9680	1,4300 1,3890	1,2430**	2,1420**
	C d v	0,2591	0,3051	0,3792 0,4081	-	-
	n d v R 2	0,0133 0,9884	0,0241 0,9992	0,0048 0,0251 0,9972 0,9997	--	--

*The values of C l and n l changed due to a malfunction of the openings at the North facade. **Using the Canadian convention EqLA (Equivalent Leakage Area): pressure di erence of 10 Pa with a dicharge coe cient of 0,6 (hole with sharp edges).

Table 3 .

 3 6: Natural air ow rate (ach) with the standard.

	ach l with openings closed (leakages) h -1

*Refer to equation 1.12 on page 19.

Table 3 .

 3 8: Resulting values for B(φ W ).

  Identi cation of a thermal model to describe the behavior of the platform temperature is the one measured at the center of the platform at 1,70 m above the oor (cf. g.2.14, p.52).(d) Stack ventilation occurs at a uniform indoor and outdoor air temperatures, which is in agreement with the previous consideration and the natural air ow rate characterization presented in chapter 3.

• C (cf. §2.6.2.3). Therefore, in equation 4.2, T ia represents the temperature of the entire indoor air volume (cf. Table 4.1, hyp. n • 5), and this Chapter 4 -

Table 4 .

 4 1: Hypotheses employed in the modeling of the heat transfer in the platform.

	N • Hypotheses/Assumptions	Notation	Justi cation
	1) Single-zone approximation	-	For simpli cation
	2) Internal energy depends	E = f (H)	For simpli cation
	only on the enthalpy term
	3) No internal heat generation	Φ gen = 0	Unoccupied building
	4) Ideal gas approximation
	and only sensible heat is considers

table 4

 4

	.1) or consideration

10 15 20 25 30 35 40 45

  C D , h C P , and glazed-facade (h C g ). The resulting convective coe cients are presented in gures 4.2, 4.3, and 4.4: for the opening con gurations n • 1, n • 2, and n • 3, respectively. Recall here, that the temperature of the glazed-facade surface T S g was not measured for con guration n • 2, as mentioned in chapter 2. Thus, it will not be shown hereafter in gure 4.3.Figure 4.2: For con g. n • 1: oor h C D (black), ceiling h C P (purple), and glazed-facade h C g (brown).Figure 4.3: For con g. n • 2: oor h C D (black), and ceiling h C P (purple). For con gurations n • 2 and n • 3 (cf. gs. 4.3 and 4.4), a signi cant di erence in the behavior of h C can be observed for daytime and nighttime periods. For instance, in gure 4.3, the values of h C for the oor (h C D , black dots) are larger than the values for the ceiling (h C P , purple dots), and this during nighttime (gray zones, openings opened). The opposite is observed during the daytime (white zones, openings closed): h C P presents larger values than h C D . The same can be said for the daytime and nighttime in gure 4.4. On the other hand, in gures 4.4 and 4.4, it can be observed that h C g for the glazed-facade (brown dots) presents similar behavior during the daytime and nighttime, and its values appear to be

		70
	Convective coefficient (W.m^-2.K^-1)	10 20 30 40 50 60
		0
		23/5	12/9	15/9	16/9	17/9
	Convective coefficient (W.m^-2.K^-1)	0 5 22/8	23/8	26/8	8/9	9/9

Table 4 .

 4 2: Comparison between air change rate models.It appears that none of the models t the values of ach ϕ C for each con guration, and thus, other expression for determine the net ach should be proposed.Here in equation 4.8, the expressions for both buoyancy (red box) and wind (yellow box) e ects were presented in chapter 3 (cf. eqs. 3.10-3.11, pp.[START_REF] Çengel | Heat Transfer: A Practical Approach[END_REF][START_REF] Özisik | Heat conduction[END_REF]. Then, the coe cients C l , C v , a l , a v , b l and b v , will be determined by solving Model A for T ia , nding the values that minimizes the RMSE value between T ia model and T ia measured. This was done by trial and error. Only one set of values For con g. n • 1. Convective heat ow for the oor (red),ceiling (blue), glazed-facade (green), and storage term (yellow), from the point of view of the air (negative values correspond to a discharge).

	Model		Notation			Remarks regarding ach ϕ C
	Buoyancy e ects alone	ach ∆T			overestimation
	Wind e ects alone		ach W			overestimation
	K-P model [93]		ach K-P			overestimation
	Superposition as ach n for n = 2, 3, 5, 10	[76]	ach n = [ach n ∆T + ach n W ] 1/n	overestimation
	Superposition as ach m for m = 2		ach m = ach	1/m ∆T + ach	1/m W	1/m	overestimation and underestimation
	In summary:
	4.1.3 Identi cation of Model A for all opening con guration
	Now, let us propose a "Model A" consisting of equations 4.2 and 4.6, where the natural air ow rate
	or air change per hour ach in the platform, is considered to be a product superposition of wind and
	buoyancy e ects, as shown in equation 4.8.

Table 4 .

 4 3: Set of parameters for Model A.

	Parameters	V ia	S D	S P	S g

  P→D and F g→D were calculated by abacuses reported in[START_REF] Çengel | Heat Transfer: A Practical Approach[END_REF]; F w→D obtained by superposition. *** From experimental data. (*) From air ow simulations for ach ∆T (cf. table 3.7, p.118).Data from experiments:T S D , T S P , T oa , T surr , h C D , h C P , h C g . Data from meteorological station: V met , φ W .The solution of Model A, for each opening con guration (cf. table 2.6, p.65), is presented in gures 4.11-4.16, where a histogram is included to show the distribution of the absolute error of T ia model (|error| = |value measuredvalue simulated |). The computation time (or running time) expended to solve the model for each con guration was about 18 s, where a low computation time was expected since most variables in Model A were taken from experimental data. Thereby, each gure presents the following:

	Values	158*	46*	58*	17,4* 0,37** 0,14**	0,49	4,5***	67 (*)
					Variables in Model A
		Desired variable (unknown): T ia , ach.

* Dimensions of the single-zone model. ** F

  4.1. Identi cation of a thermal behavior model for the indoor air using experimental data

	T (°C)	18 21 24 27		12/8	13/8 Tia measured Tia model Error	14/8	15/8	16/8	17/8	18/8	19/8		20/8	0.0 0.3 0.6 0.9 |Error| (°C)
											(a)
				2.0
	Heat flow (kW)	-1.0 -0.5 0.0 0.5 1.0 1.5			Floor			Ceiling			Glazed
			-1.5	12/8	13/8	14/8	15/8	16/8	17/8	18/8	19/8		20/8
											(b)
	T (°C)	38 14 20 26 32	ach (h^-1)	0.0 2.0 4.0 6.0	12/8	13/8	14/8	15/8	16/8	17/8	18/8	19/8	20/8	0 2 4 6 8 V (m.s^-1)	0 150 350 Angle (°)
											(c)

Table 4 .

 4 4: Identi ed set of values for ach expression in Model A (cf. eq. 4.8). Between the model and experimental data for T ia ; only two signi cant gures to agree with the uncertainty in our temperature measurements.

			Best values for all con gurations	Wind direction φ W
	Con g. n • C l C v a l	a v b l b v	RMSE* |error|* [ • C] [ • C]	Most frequent	Average
	1							0,31	0,27
	2	1	1 0,2 0,5 0 0,2	0,24	0,19	91 •	175 •
	3							0,24	0,19
		Best values for each con gurations alone	Wind direction φ W
	Con g. n • C l C v a l	a v b l b v	RMSE* |error|* [ • C] [ • C]	Most frequent	Average
	1	0,1 0 0,2 0	0	0	0,12	0,10	245 •	232 •
	2	1	1 0,1 0,4 0,2 0,1	0,20	0,16	289 •	185 •
	3	0	1	0 0,5 0 0,2	0,24	0,19	87 •	114 •

*

  4.18-4.20, respectively, where ach ∆T (red line), ach W (yellow line), ach K-P (cyan line), and ach ϕ C (blue line) are included. Hereafter, we will refer to the identi ed superposition model for ach as "ach (∆TxW) . "At rst sight, it appears that ach (∆TxW) (black dotted line) is only in agreement with the ach experimentally determined (named ach ϕ C ) for con guration n • 3 in gure 4.20. For con guration n • 1 (cf. g. 4.18), the value of ach (∆TxW) clearly overestimates the value of ach ϕ C . For con guration n • 2 (cf. g.4.19), the value of ach (∆TxW) appears to underestimate the value of ach ϕ C by approximately 0,5 times, during the nighttime, but both behaviors appear to be similar. On the contrary, the value of ach (∆TxW) appears to overestimate the value of ach ϕ C by 2 times, during the daytime for con guration n • 2. For the latter, the behavior of ach (∆TxW) is clearly inversely proportional to ach ϕ C .All di erent behaviors for each con guration might be explained by the values of the identi ed coe cients presented in table 4.4. Only for con guration n • 3 the same values were identi ed to be the same, when alone as when being together with all the con gurations. In this case, both the behavior and magnitude of ach (∆TxW) and ach ϕ C appear to be the same. However, the values of the identi ed coe cients presented in table 4.4 changed for the other two con gurations n • 1 and n • 2, which might indicate that both wind and buoyancy are not assisted with the same force. Figure 4.18: Resulting air change rate per hour for con g. n • 1: ach (∆TxW) (black), ach ϕ C (blue), ach ∆T (red), ach W (yellow), and ach K-P (cyan). The corresponding temperature measurements: indoor air (brown dashed line) and outdoor air (brown circles). (D) Assessment of the identi ed natural air ow model Finally, we want to highlight the apparent relationship between the identi ed values of the exponents Chapter 4 -Identi cation of a thermal model to describe the behavior of the platformFigure 4.19: Resulting air change rate per hour for con g. n • 2: ach (∆TxW) (black), ach ϕ C (blue), ach ∆T (red), ach W (yellow), and ach K-P (cyan). The corresponding temperature measurements: indoor air (brown dashed line) and outdoor air (brown circles).

			18
			14
		ach (h^-1)	0 2 4 6 8 10			T (°C)
			22/8	23/8	26/8	8/9	9/9
	ach (h^-1)	ach (h^-1) 0 2 4 6 8 10 12 14 16 18 20 1.0 1.5 2.0 2.5 3.0			8 12 16 20 24 28	T (°C)	T (°C)
			0.5 25/5	26/5	27/5	28/5	4 29/5
			0.0			0
			23/5	12/9	15/9	16/9	17/9

  • and 270 • (namely 90 • > φ W >270 • ), wind and buoyancy e ects rst oppose, then are assisted depending on the temperature di erence level (cf. g. 3.26, p.123). For other wind directions, both e ects are assisted. Therefore, with this recall in mind, since the most frequent wind direction was encountered to be 91 • (cf. table 4.4), both wind and buoyancy e ects are

Table 4 .

 4 Desired variables (unknowns): T D , T D 1 and T D M . Data from experiments: T ia , T surr , h C D . 5: Set of parameters for Model B.

			Variables in Model B1 and B2
	Parameters	e D	c p D

1.3.1 (p.135)

. The method for solving Model B is the same as for Model A. However, since we employed our experimental data only (no meteorological data), the time step chosen is of one iteration every minute. The values employed, for Models B1 and B2, are presented in table 4.5.

  Retained total number of nodes; no signi cant di erence found for a larger number of nodes.4.2.3.1 Discussion and evaluation of results from Model B1 and B2The solution of Model B1, for con guration n • 2 only (cf. table 2.6, p.65), is presented in gures 4.[START_REF] Chiu | External ow e ects on the discharge coe cients of two types of ventilation opening[END_REF]

							•K -1
	Values	68**	1000*	46**	2300*	0,95* 64*** 1,06	1,8*
	* Standard physical properties for concrete [1].
	** Geometrical parameters of the concrete layer.
	***

18 22 26 30 12/8 13/8 14/8 15/8 16/8 17/8 18/8 19/8 20/8

		TS_D measured TS_D model N=1 TS_D model N=M Error						0.0 0.6 1.2 1.8	|Error| (°C)
	-0.5 0.0 0.5 Heat flow (kW) 1.0	Convection		Radiation		Storage
	-1.0
	12/8	13/8	14/8	15/8	16/8	17/8	18/8	19/8	20/8
					(b)

  Despite the accuracy encountered with the "the coupled model", a model with the least variables from experimental data or none not all, would be required for forecasting the thermal behavior of the platform under di erent outdoor conditions and di erent natural ventilation scenarios (other than those implemented during out measurement campaigns). In this matter, there are ve variables in the models that are taken from the measurement campaigns: T surr , T S P , h C P , h C D , h C g . Until now, a constant value was employed for h C g for all the models before, which indicates that the model is not particularly sensible to values admitted for this variable. Therefore, it can be said that only four variables, which values are taken from the measurement campaigns, remained: T surr , T S P , h C P , h C D .

•

C, from Model B and "the coupled model", respectively.

Regarding the heat ow terms, the resulting convective heat ow for the concrete slab in both gures 4.28 (b) (red) and 4.30 (b) (red), appear to agree with each other regarding the magnitudes, and also with the convective heat ow determined experimentally presented in gure 4.9 (red). Conversely, the resulting convective heat ow term for the ceiling in gure 4.28 (b) (blue), appears to overestimate this value for only three days (13/8 -15/8) in comparison with gure 4.9 (blue).

Regarding the air change rate per hour, the resulting ach values in gure 4.28 (c) (black), can not be compared directly with the values in gure 4.19 (black), since the experimental data employed is not from the same days. However, similar values are encountered between them.

  • 2: from July 27 th to 29 th . The numerical results are presented 4.3. A complete model for describing the coupling between the energy charge-discharge of the thermal mass and natural ventilation in gures 4.32-4.35. As expected, the accuracy of the model is reduced: a RMSE value of 0,53 • C and 0,43 • C, for T ia and T S D , respectively.Data from experiments: T oa , T surr , T S P , h C P , h C D .Data from meteorological station: V met , φ.Coe cients in ach model: same as in table4.4 for all con gurations.One of the leading causes for the accuracy reduction is that, for this dataset, the most frequent wind direction was approximately 300 • . From the analysis in chapter 3, for such wind direction, it is expected that wind and buoyancy e ects would oppose to each other, and since the values for the exponents have been xed to be the same as before (cf. table 4.4), the ach ∆TxW model for this case is not fully consistent with the phenomena involved; despite the RMSE values, which might be acceptable depending on the application.

	Variables in "the coupled model" tested with data outside identification

Glazed-facade Concrete slab Ceiling

	Wind (𝓥 𝑾 , 𝝓 𝑾 )	Outdoor air (𝑻 𝒐𝒂 )	(𝑻 𝑺 𝑷 )
	Air change rate
		per hour	𝒉 𝑪 𝑫
			Indoor air
		(𝑻 𝑺 𝒈 )		Mean radiant
			𝒉 𝑪 𝑷	𝑻 𝒔𝒖𝒓𝒓
		openings	Crumbled aluminum foil	IR cam
				(𝑻 𝑺 𝑫 )

(𝒂𝒄𝒉)

Table A .

 A 1: Temperature setpoints Setpoint ( • C) T Bath ( • C) T TC ( • C)

	10	9,89	9,58
	15	14,71	14,41
	20	19,75	19,46
	25	24,79	24,51
	30	29,09	28,83
	35	34,78	34,54
	40	39,72	39,51

  • C the mean value of them all. Table A.2: Maximum deviation values among thermocouples at each setpoint T Bath ( • C) Deviation ( • C)

	9,89	0,28
	14,71	0,33
	19,75	0,26
	24,79	0,27
	29,09	0,33
	34,78	0,26
	39,72	0,31

A slight part of the thermocouples measurements results is shown in Table A.3. The table presents the time average temperature for each thermocouple (only few of them are presented as example).

Table A .

 A 3: Raw thermocouples measurement results at each setpointT Bath ( • C) T TC ( • C) T TC1 ( • C) T TC16 ( • C) T TC17 ( • C) T TC32 ( • C)

	9,89	9,58	9,65		9,70	9,70	9,77
	14,71	14,41	14,49		14,48	14,56	14,61
	19,75	19,46	19,60	. . .	19,57	19,55	19,62
	24,79	24,51	24,63		24,62	24,60	24,67
	29,09	28,83	28,92		28,94	28,97	29,03
	34,78	34,54	34,67		34,70	34,65	34,71
	39,72	39,51	39,60		39,65	39,65	39,71

Table A . 4 :

 A4 Maximum deviation values among thermocouples at each setpoint, after applying the correctionT Bath ( • C) Deviation ( • C)

	9,89	0,04
	14,71	0,07
	19,75	0,07
	24,79	0,06
	29,09	0,05
	34,78	0,04
	39,72	0,04

Table A .

 A 5: Regression coe cients values for expression22. TCX a X (-) b X ( • C) RMSE X ( • C)

	TC1	0,9959	0,2674	0,0238
	TC2	0,9968	0,2942	0,0221
	TC3	0,9974	0,3116	0,0220
	TC4	0,9966	0,3601	0,0187
	TC5	0,9973	0,378	0,0185
	TC6	0,9976	0,3779	0,0189
	TC7	0,9967	0,4058	0,0165
	TC8	0,9966	0,4142	0,0164
	TC9	0,997	0,4304	0,0188
	TC10 0,9975	0,4315	0,0205
	TC11 0,9961	0,4622	0,0161
	TC12 0,9966	0,4548	0,0185
	TC13	0,997	0,4433	0,0203
	TC14 0,9955	0,4306	0,0196
	TC15 0,9951	0,3707	0,0240
	TC16	0,995	0,2742	0,0258
	TC17 0,9968	0,2287	0,0318
	TC18 0,9971	0,2504	0,0282
	TC19 0,9966	0,3124	0,0260
	TC20	0,997	0,3311	0,0240
	TC21 0,9972	0,3456	0,0209
	TC22 0,9969	0,3492	0,0177
	TC23 0,9969	0,3662	0,0275
	TC24	0,997	0,3609	0,0201
	TC25 0,9973	0,378	0,0173
	TC26 0,9951	0,4154	0,0193
	TC27 0,9964	0,3905	0,0224
	TC28 0,9985	0,3335	0,0241
	TC29 0,9958	0,3896	0,0213
	TC30 0,9954	0,3507	0,0235
	TC31 0,9962	0,2873	0,0212
	TC32 0,9967	0,1689	0,0243

  Thermal and Fluid Science. (6) ASME International. Policy on reporting uncertainties in experimental measurements and results (1990). Journal of Heat Transfer. 01 14,45±0, 01 14,42±0, 01 14,38±0, 01 14,36±0, 01 14,35±0, 01 14,34±0, 19,60±0, 01 19,56±0, 01 19,53±0, 01 19,49±0, 01 19,45±0, 01 19,44±0, 01 19,43±0, 24,63±0, 01 24,58±0, 01 24,54±0, 01 24,52±0, 01 24,48±0, 01 24,47±0, 01 24,47±0, 28,92±0, 01 28,87±0, 01 28,83±0, 01 28,81±0, 01 28,76±0, 01 28,75±0, 01 28,76±0, 34,67±0, 01 34,61±0, 01 34,57±0, 01 34,55±0, 01 34,51±0, 01 34,49±0, 01 34,50±0, 39,60±0, 01 39,55±0, 01 39,51±0, 01 39,49±0, 01 39,45±0, 01 39,44±0, 01 39,45±0, 30±0, 01 14,30±0, 01 14,28±0, 01 14,28±0, 01 14,29±0, 01 14,32±0, 01 14,38±0, 19,40±0, 01 19,38±0, 01 19,38±0, 01 19,37±0, 01 19,37±0, 01 19,41±0, 01 19,47±0, 24,43±0, 01 24,41±0, 01 24,42±0, 01 24,41±0, 01 24,41±0, 01 24,46±0, 01 24,52±0, 28,72±0, 01 28,70±0, 02 28,72±0, 01 28,72±0, 01 28,71±0, 01 28,78±0, 01 28,85±0, 34,47±0, 01 34,45±0, 02 34,47±0, 01 34,46±0, 01 34,46±0, 01 34,52±0, 01 34,60±0, 39,41±0, 01 39,40±0, 02 39,41±0, 01 39,40±0, 01 39,41±0, 01 39,47±0, 01 39,54±0, 56±0, 01 14,54±0, 01 14,48±0, 01 14,45±0, 01 14,43±0, 01 14,43±0, 01 14,42±0, 19,55±0, 01 19,53±0, 01 19,47±0, 01 19,45±0, 01 19,43±0, 01 19,43±0, 01 19,41±0, 24,60±0, 01 24,58±0, 01 24,54±0, 01 24,51±0, 01 24,51±0, 01 24,51±0, 01 24,48±0, 28,97±0, 01 28,94±0, 01 28,89±0, 01 28,86±0, 01 28,83±0, 01 28,84±0, 01 28,82±0, 34,65±0, 01 34,61±0, 01 34,57±0, 01 34,54+±0, 00 34,51±0, 01 34,52±0, 01 34,50±0, 39,65±0, 01 39,61±0, 01 39,56±0, 01 39,53±0, 01 39,50±0, 01 39,50±0, 00 39,50±0, 01 14,40±0, 01 14,43±0, 01 14,40±0, 01 14,45±0, 01 14,50±0, 01 14,40±0, 19,42±0, 01 19,40±0, 01 19,40±0, 01 19,42±0, 01 19,42±0, 01 19,46±0, 01 19,51±0, 24,49±0, 01 24,49±0, 01 24,47±0, 01 24,48±0, 01 24,49±0, 01 24,53±0, 01 24,58±0, 28,82±0, 01 28,83±0, 01 28,81±0, 00 28,81±0, 01 28,83±0, 01 28,88±0, 01 28,92±0, 34,50±0, 01 34,51±0, 01 34,50±0, 01 34,48±0, 00 34,52±0, 01 34,58±0, 01 34,61±0, 39,48±0, 01 39,51±0, 01 39,49±0, 01 39,47±0, 00 39,52±0, 01 39,57±0, 00 39,60±0, 208

	Table A.6: Temperature measurements of each thermocouple with their standard deviation
	TC1	TC2	TC3	TC4	TC5	TC6	TC7
	9,65±0, 01	9,62±0, 01	9,60±0, 01	9,56±0, 01	9,54±0, 01	9,54±0, 00	9,52±0, 00
	14,49±0, TC9	TC10	TC11	TC12	TC13	TC14	TC15
	9,50±0, 01	9,50±0, 01	9,48±0, 01	9,49±0, 01	9,50±0, 01	9,53±0, 01	9,60±0, 01
	14,TC17	TC18	TC19	TC20	TC21	TC22	TC23
	9,70±0, 01	9,67±0, 01	9,61±0, 01	9,59±0, 01	9,57±0, 01	9,57±0, 01	9,56±0, 01
	14,TC25	TC26	TC27	TC28	TC29	TC30	TC31
	9,56±0, 01	9,52±0, 01	9,54±0, 01	9,58±0, 01	9,55±0, 00	9,59±0, 01	9,65±0, 01
	14,41±0,

• C).

Table B .

 B 1: Meteorological conditions from ENSAM in 2016. Opened (T ia > T oa ) Closed (T ia < T oa )

			Mostly night	Mostly day
	Date Clear Cloudy Windy No windy Sunny Cloudy Windy No windy
	27/07	*	*	*	*
	28/07	*	*	*	*
	29/07	*	*	*	*
	12/08	*	*	*	*
	13/08		*
	14/08	*	*	*	*
	15/08	*	*	*	*
	16/08	*	*	*	*
	17/08	*	*	*	*
	18/08	*	*	*	*
	19/08	*	*	*	*
	20/08	*	*	*	*
	21/08	*	*	*	*
	22/08	*	*	*	*
	23/08	*	*	*	*
	24/08	*	*	*	*
	25/08	*	*	*	*
	26/08	*	*	*	*
	27/08	*		*
	28/08	*		*
	29/08	*		*
	30/08	*		*
	31/08	*		*
	01/09	*		*
	02/09	*		*
	03/09	*		*
	04/09	*		*
	05/09	*		*
	06/09	*		*
	07/09	*		*
	08/09	*	*	*	*
	09/09	*		*
	10/09	*		*
	11/09	*		*
	12/09	*		*

0,141 0,008 1,25

225,71 285,32 5 0,300 0,016 5,33 1209,03 1268,64 10 0,424 0,022 10,34 2414,33 2473,94 15 0,520 0,026 15,02 3697,61 3757,22 20 0,600 0,030 20,00 4942,00 5001,61 25 0,671 0,034 25,35 6191,85 6251,46 30 0,735 0,037 30,22 7434,07 7493,68 50 0,949 0,048 50,61 12430,96 12490,57 100 1,342 0,067 99,87 24516,31 24575,92 200 1,897 0,095 200,24 49252,91 49312,52 In table 2.2, note that the rst value in the column of the TEM response U, is negative (-59,61 µV).This may indicate two things:• when no heat load was applied, the TEM response had an opposite direction in comparison when the heat loads were applied (positive),• both sides of the thermoelectric module were not at the same temperature at the beginning of

2) ρ D • ∆z • c p D • dT D N (t) dt

pouvoir continuer de travailler (soit du côté académique soit du côté académique/

From thermogram (a) and (b) it can be observed that the concrete-slab surface appears to be less hot than the glazed-facade (a) and also less hot than the surrounding surfaces (b), which con rms the remark stated earlier in §2.5.3.2. Also, from the thermogram (b), it can be observed that the black foil placed on the concrete-slab surface (cf. g.2.12) appears to banished from the view of the IR camera.

This might indicate that the concrete-slab surface has similar emissivity value as the default set value of the camera, which resulted in being the case.

From thermogram (c), it can be observed that the opening (North facade) is hotter than the wallfacade (in purple). The little square stuck on the opening (a crumbled shiny foil), also indicates that the opening is hotter than the surrounding surfaces (partition-walls and doors separating the living room and the bedroom). This before may imply that, when in the modeling process, taking into account the entire surface of the north facade as to heat the indoor air, might yield to an overestimation of the heat gained by this air. A similar statement can be given by analyzing thermograms (d) and (c), regarding the shed-roof surface, and the East and West facades, respectively.

Thermal comfort assessment of a simple opening-closing strategy

Finally, since con guration n • 2 was implemented during the entire measurement campaign in the summertime 2016, an evaluation of the impact of passive night natural ventilation, in maintaining the thermal comfort within the indoor environment, is performed hereafter based on the indicators recommended by the standard ISO 7730 (cf. §1.1.1(A)).

Indicators employed in the assessment

In order to estimate such indicators, we are interested in determining the following parameters: (i) the air temperature and (ii) air velocity at di erent heights, (iii) the mean radiant temperature, (iv) the room temperature, and (v) the degree of discomfort. The last three parameters are calculated from the Chapter 3 -Characterization of the natural ventilation air ow rate facade yields about 900 m 3 •h -1 at a ∆P of about 2,5 Pa.

Regarding the discharge coe cients presented in gure 3.15, their values do not appear to change signi cantly within the pressure range. In fact, their mean values result in 0,40±0,01 for the openings at the South facade; 0,31±0,002 for the openings at the North facade; and around 0,28±0,01 for the openings at the shed-roof. These values are similar to those found by [25,[START_REF] Chiu | External ow e ects on the discharge coe cients of two types of ventilation opening[END_REF], but they are rather low, in comparison with those largely accepted in the literature, of around 0,6 -0,7 for a similar type of openings [START_REF] Flourentzou | Natural ventilation for passive cooling: measurement of discharge coe cients[END_REF][START_REF] Per | Windows: measurements of air ow capacity[END_REF]. This di erence (about 38%) might be explained by: (i) the tightness of the openings itself (cf. g.3.9), or (ii) by the obstructions within the air ow path between the fan and the opening when performing the airtightness tests.

For the case (i), the tightness might increase the friction losses, and thus, yield a decrement in the discharge coe cient. For the case (ii), if the obstruction is a contributing factor to reducing the discharge coe cient, the corresponding loss coe cient values should be encountered in a decrementing order as follows: the openings at the shed-roof, then those at the North facade, and nally, those at the South facade. The more obstructions, the more signi cant the pressure losses. The same can not be stated for the tightness of each opening since it appears to be the same level of tightness for all the openings.

Then, if we compute the loss coe cients for each opening by introducing the values of the discharge coe cient encountered and the corresponding fully and e ective opening areas into equation 1.8 (p.18), result in: 74,81 for the openings at the shed-roof; 17,06 for those at the North facade; and 7,55 for those at the South facade. These values are in agreement with the explanation given for the case (ii). The same equation was employed in [START_REF] Teppner | Air change rates driven by the ow around and through a building storey with fully open or tilted windows: An experimental and numerical study[END_REF], where, with a total and e ective opening area of 1,82 and 0,377, respectively, the loss coe cient resulted in 28,9 with a discharge coe cient of 0,67. Unfortunately, no other experiments have been performed in order to support statements (i) and (ii).

In summary:

Performing in situ airtightness tests for the estimation of the friction characteristics of openings, might not be the most suitable choice due to the presence of internal obstructions, such as furniture, partition-walls, doors, among others. However, the implementation of these tests for the estimation of the air ow capacity in terms of air ow rate levels appears to agree with the values reported in the literature.

Comparison of the air change rate per hour using airtightness tests

Since the only indicator of the natural air change rate per hour (ach) we have is the ach 50 , which only gives values for the in ltration rate, in this section we compare our results with a similar research work. To do this, we rst compute the ach 50 for each of the opening con gurations presented in table 3.5, for either the case of openings opened or closed. For the case of opening closed, we only took the C l and n l values reported for the "South+shed" column in table 3.5 (0,08611 and 0,58), because this was the current in ltration rate state. For the case of openings opened, we took C v and n v (openings opened only, no leakages).

4.1. Identi cation of a thermal behavior model for the indoor air using experimental data

; when NV openings closed

; when NV openings opened

Color-box code: Buoyancy e ect (red) and wind e ect (yellow).

is wanted for these coe cients that t the best all three con gurations. The reason of performing the identi cation by adjusting Model A to best t T ia (model) with T ia (measured), lays in the reliability of the air temperature measurement.

Selecting a dataset for the identi cation process

A dataset of consecutive days is chosen for the identi cation process. For such dataset, the experimental results from con gurations n • 2 and n • 3 can be employed. These two datasets allow us to evaluate Model A for accuracy. On the other hand, the dataset of experimental results from con guration n • 1, allows us to evaluate Model A in terms of adaptability, in addition to accuracy, since this con guration was not tested for consecutive days. The adaptability of the model can also be highlighted, by evaluating its accuracy under di erent opening con gurations.

Moreover, in addition to the criteria presented in chapter 1 in table 1.2 (p.24), the convective heat ow terms for the oor, ceiling, and the storage term on equation (4.2) will be computed using experimental results for each con guration (cf. gs. 4.8-4.10). In this way, we are also able to judge the numerical results by the accuracy of describing each of these terms. In other words, the model should also describe the magnitudes for each term in equation 4.2 in order to be retained.

In gures 4.8-4.10, it can be observed that the convective heat ow at the ceiling (blue line) appears to be one of the most important terms, i.e., presents large heat ow values with respect to the other terms, during the daytime (negative values), whether the openings are kept closed (see gure 4.8 on 23/5, and gure 4.9 (daytime)) or kept opened (cf. g.4.10). Conversely, during nighttime, the most important term appears to be the convective heat ow at the oor concrete-slab (red line). Note that in gure 4.8, this before does not applied from 12/9 to 17/9, as explained before.

Choice of a thermal behavior model for the thermal mass

In summary:

From the analysis above, Model A appears to be accurately and adaptable enough for describing the thermal behavior of the indoor air temperature, which indicates that wind and buoyancy e ects are most probably to be assisted by each other, due to the most frequent wind direction encountered; in agreement with what has been reported in §3.4.3(D). However, the identi ed values in table 4.4 also depends on the accuracy of the rst two equations in Model A, which is why the necessity of them to be consistent with the thermal characterization of the platform. In this regard, an analysis of the error of Model A due to the numerical solution method employed and the uncertainty of the experimental data introduce should be performed to assess its reliability.

Choice of a thermal behavior model for the thermal mass

As shown before, one of the most important terms in equation 4.2 is the convective heat ow at the oor concrete-slab. In order to reduce the experimental data required to run the model, the following is intended to choose a conduction heat transfer model to describe the surface temperature of the oor concrete-slab. Despite the values of Biot's number found in chapter 2 regarding the concrete-slab for each con guration (values around 0,1), the Biot's number critical value (Bi 0,1) suggests that uniform conduction heat transfer might not occur through the slab thickness. However, a "Model B" is proposed to consider both uniform and no-uniform conduction heat transfer. Thus, we introduced a Model B1 which considers uniform conduction heat transfer via a lumped-capacitance model, and a Model B2 which considers non-uniform conduction heat transfer via a space discretization over the slab thickness using nite di erence. Both models are solved using experimental data. Finally, the model that describes more accurately the behavior of the oor surface temperature will be coupled with the Model A.

Lumped-capacitance approximation

The assumption of uniform conduction heat transfer through the concrete-slab thickness implies that all temperature gradients are null or negligible, and thus, the entire slab is considered to have a uniform temperature. This assumption is often called "the lumped-capacitance model approximation" [START_REF] Özisik | Heat conduction[END_REF], and it is merely de ned by an energy balance of the super cial heat exchanges between the slab and its environment, similar to equation 4.2, as follows: The coupled model

Motivation for accomplishing the future work

The craving of the settlement of a uni ed methodology that proportions the su cient knowledge about the air ow characteristics of a building, in order to master the natural ventilation concept applied to such building, for boosting the thermal comfort and for reducing the usage of air conditioning systems.

Absolute error (brown) between red line and blue dots, and error bars ±0,48 • were calibrated using a thermostatic bath (LAUDA RE 415, temperature stability of ±0, 01 • C with temperature accuracy of ±0, 3 • C and ±0, 5% of the relative temperature, assured by an integrated PT100) and the NI 9213 acquisition card (measurement sensitivity of ±0, 02 • C with a measurement error of ±0, 8 • C for our temperature ranges). The goal is to increase the accuracy of our thermocouples by correcting our measurement system (thermocouple + acquisition) with a more accurate instrument (the thermostatic Bath). As results showed, the thermocouples maximum deviation to one another before correction, when measuring the temperature of a stable medium (water in this case) it does not exceed the 0, 3 • C. After correction, the maximum deviation does not exceed the 0, 07 • C. Their stability is ±0, 02 • C with 95 % of con dence. Following the ASME international journal of heat transfer Policy, on reporting uncertainties in experimental results, our best estimation on reporting the temperature overall uncertainty is presented at the end of this document.

Nomenclature

Introduction

The well-known thermocouple calibration process can be resume as nding the regression function that relates the temperature measured by the thermocouple and its tension response, and the determination of the calibration process uncertainties. To well estimate a temperature measurement using

Conclusion

In order to conclude, our best estimation in temperature measurement for experiments replication, would be as follows:

where u X is as the ASME [ASME] subjects:

where ζ TCX is equal to 0, 02 • C for all thermocouples, except for the TC10 which is 0, 04 • C.

If the temperature measurements are needed to be compared, using let's say the measurements from two of our thermocouples: TCX and TCY, in the same experiment. Only the random error of both thermocouples: ζ TCX and ζ TCY , must be used, instead of u TCX and u TCX (as interpreted from [START_REF]Handbook -Fundamentals[END_REF]).

A little example, in order to illustrate the use of expressions 23 to 25, is as follows: A medium is said to be at 10 ± 1 • C and let's say we measure its temperature with our thermocouple 32 (TC32). Our best estimation of the temperature of such medium, would be calculated rst by using the expression 23 and the a 32 and b 32 values from Table A.5. This give: 10, 14 • C. Second, we have to determine the uncertainty in the temperature measured. Expressions 24 and 25 will help us to to that, given: u TC32 = 0, 38 • C. Thus, our measurement would be reported as: 10, 14 ± 0, 38 • C. Finally, values are presented with 2 signi cant gures since the instrument we have used to calibrate our thermocouples can only display the temperature as so.

Furthermore, when temperature di erences are needed to be estimated, using our thermocouples (let's say TCX and TCY), we would have that the magnitude of the di erence, will be calculated as:

and the uncertainty in the temperature di erence, as follows:

where if the temperature di erence ∆T * encountered is lower than u ∆T * , the temperatures should be considered to be equal as we cannot be more accurate in our measurement estimation.

(1) T. Ferguson. Mesurer des temperatures par thermocouples (2001).

(2) Welded Tip Fiberglass Thermocouple, available at http://www.tcdirect.fr.

(3) T. Dupuis. Pratique de la mesure en genie climatique (2015). ISBN: 978-2-10-073762-8.

(4) Lauda. Eco Silver Operating instructions manual (2014). English version.

(5) R. J. Mo at. Describing the uncertainties in experimental results (1988). Elsevier: Experimental perturbations were encountered when comparing experimental results with simulation [START_REF] Herin | Conception et caractérisation de capteurs de ux radiatif et convectif : application aux mesures « in situ[END_REF][START_REF] Cherif | Super cial heat transfer by forced convection and radiation in a horizontal channel[END_REF]68],

and they have been given an explanation based on logic and current knowledge of the heat transfer analysis.

Methodology

In this experimental study, to compare the use of thermoelectric modules (TEM) over the use of conventional heat ux meters (FGT), a pair of each type of sensor was used: two thermoelectric modules and two conventional heat ux sensors. In this pair, one sensor was coated with a black-foil and the other with a shiny-foil. The properties of both types of sensors is presented in table A.7. The experimental set-up implemented here was installed on the oor concrete-slab surface in two di erent locations. The four sensors were installed on the oor concrete-slab surface using silicon-based thermal grease, and as the experimental set-up of the two locations slightly di ered from each other, regarding the sensors arrangement, the following presents both set-ups separately. The two locations where the experimental set-up was installed are presented in the following gures. Note here that the experimental set-up was used rst on location 1 and then was changed to location 2; they were not employed at the same time.

Protocol for the measurement campaigns

As the only functioning system of the PEH implemented in this study was the natural ventilation automated system, the experimental protocol implemented for the measurement campaigns during fall in November 2016, consisted of the following points:

1. Experimental data were collected continuously:

• From 2/11 to 7/11, at a sample time of one minute.

ESSAI DE PERMEABILITE A L'AIR DE BATIMENT