Thermochromic materials for indoor thermal comfort improvement: Finite difference modeling and validation in a real case-study building

Applied Energy 262 (2020) 114147

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Thermochromic materials for indoor thermal comfort improvement: Finite difference modeling and validation in a real case-study building C. Fabiania,b, V.L. Castaldoa, A.L. Piselloa,b, a b

T

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CIRIAF – Interuniversity Research Center, University of Perugia, Via G. Duranti 67, 06125 Perugia, Italy Department of Engineering, University of Perugia, Via G. Duranti 97, 06125 Perugia, Italy

H I GH L IG H T S

G R A P H I C A L A B S T R A C T

continuous monitoring and a novel • Aanalytical model are elaborated. paint is developed • Thermochromic and tested for passive cooling purposes.

Thermochromic benefits in summer • and winter are assessed in the indoors. allow 0.5 K passive • Thermochromics cooling without winter penalties. effect of building envelope • The thermal insulation is not negligible.

A R T I C LE I N FO

A B S T R A C T

Keywords: Heat balance Energy efficiency in buildings Thermochromic materials Adaptive material properties Indoor thermal comfort Albedo

In recent years, a huge research effort aimed at developing adaptive materials for improving building indoor thermal comfort has been detected. Yet, only a few analytic and dynamic approaches have been implemented to predict building materials thermal performance. In this study, an analytic model is elaborated to evaluate the thermal performance of a well insulated case study prototype building equipped with a thermochromic envelope, and bench-mark it against cool-only and dark-only applications. Therefore, the effect of the selected thermochromic solutions on the indoor environment of the building in terms of surface and indoor air temperature is evaluated both in summer and winter conditions. Results show that the application of the thermochromic membrane and wall paint represents a win-to-win solution combining the well-established passive cooling effect of high reflectance materials in summer with desirable solar gains produced by dark surfaces in winter. Average indoor air temperature reductions up to 0.2 and 0.5 K were found in summer, while a 0.5 and 0.6 K increase was registered in winter, for the low and high insulation configuration, respectively, when compared to more common dark and cool solution.

1. Introduction In the last decades, several scientific contributions provided strong evidence that microclimate conditions in urban areas significantly

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differ from those of their rural surroundings. In particular, air temperatures are usually higher due to the urban heat island (UHI) effect and the wind speed tends to be lower due to sheltering reasons [1]. The UHI phenomenon, which is mainly caused by increased radiative

Corresponding author. E-mail address: [email protected] (A.L. Pisello).

https://doi.org/10.1016/j.apenergy.2019.114147 Received 20 June 2019; Received in revised form 23 October 2019; Accepted 12 November 2019 0306-2619/ © 2020 Elsevier Ltd. All rights reserved.

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Nomenclature

TT V x Z

Acronyms ASTM CFD EPS FTBS UHI NIR

American Society for Testing and Materials Computational Fluid Dynamics Expanded Polystyrene Forward Time-Backward Space Urban Heat Island Near Infrared

Subscripts External layer of the envelope Air Clouds Convection Counting function tracking the time elapsed from the beginning of a thermochromic transition d Direct solar beam dH Horizontal component of the direct solar beam dV Vertical component of the direct solar beam erf Error function i-th discrete element of the wall, with i being 0, 1 … d i in Indoor n n-th surface, with n being N,S,W,E N , S, W , E North, South, West, East building wall norm Normalization with respect to the thermochromic transition time interval out Outdoor Constant pressure p r Building roof rad, LW , gr Longwave radiation to the ground rad, LWsk Longwave radiation to the sky rad, LWwalls Internal longwave radiation exchanged among the different walls Sky sk solSW Incoming shortwave radiation w Building walls

0 a cl conv count

Greek symbols

α β ∊ λ ρ σ θ

Thermal diffusivity [m2 ·s−1] Slope of the wall [° ] Thermal emissivity Thermal conductivity [W·m−1·K−1] Density [kg·m−3 ] Boltzmann constant [J·K−1] Solar altitude [° ]

Roman symbols

A a c cc d dt h h q t

Transition temperature Volume [m3 ] x direction Solar Azimuth [°]

Area [m2 ] Supplementary angle of the solar Azimuth (π − Z ) Specific heat [J·kg−1·K−1] cloud cover Thickness [m] Simulation time interval Angle between the incoming solar beam and the horizontal direction Convection coefficient [W·m−2·K−1] Heat flux [W·m−2 ] Time [s]

comfort improvement in the built environment [9–11]. However, although numerous research contributions demonstrated the beneficial effect of vegetated roofs and walls in buildings, these applications also require extensive maintainance efforts. On top of that, designing an adequate irrigation system is of paramount importance for producing an effective green roof application [12], whose final mitigation outcome is utterly influenced by both substrate [13] and greenery water content [14]. Given the above, several researchers worldwide have focused their attention on the production and use of innovative cool building envelope components, characterized by optimized solar reflectance and thermal emittance capability. Said surface treatments usually require less maintenance than classic green roofs and produce lower impacts in terms of life cycle costs. In this context, different UHI mitigation techniques with similar energy saving performance to green roof

trapping, heighteined heat capacity of engineered materials, released anthropogenic heat, lack of evapotranspiration and reduced turbulent convection [2], negatively affects human comfort level during hot periods, contributing to human diseases [3] and health risks [4]. Additionally, beyond their health and environmental impacts, heat islands also have important implications on buildings energy consumption [5], since increased air temperatures exacerbate building cooling loads [6] and increase peak electricity demand [7]. All this considered, in recent years, several research contributions have been focusing on the effect of specific UHI mitigation strategies such as shading of buildings, use of green and high albedo surfaces, introduction of water bodies and air ventilation improvement, on the magnitude of the local heat island in different cities worldwide [8]. In this view, the introduction of green and cool roofing applications was shown to produce significant benefits in terms of summer thermal

Fig. 1. Case study prototype building at Perugia University. 2

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smart packaging, security printing and textile colouring [23], avantgarde applications for buildings have been focusing on the use of thermochromic pigments, i.e. parcels capable of reversibly changing their color from darker (more absorbing) to lighter (less absorbing) in response to temperature variations [24]. The result is innovative building coatings capable of tuning their solar reflectivity as a function of the local temperature boundary conditions [25]. According to Garshasbi and Santamouris [26], thermochromic materials can be considered the forth generation of cool solutions for building applications. Based on their transition mechanism, these materials are divided in non-dye-based, and dye-based applications. The former, uses a temperature-driven nano-scale or molecular transition mechanism, so the single component does not possess any thermochromic properties [26]. The latter, is either composed by a pH-indicator dye and a polymer matrix or by a ternary composite (a color former (the leuco dye), a color developer and a co-solvent), capable of switching from the colorless (leuco) to the colored (zwitterionic) state through the temperature change [27]. This last kind of application, in particular, has been used to produce different types of adaptive building coatings capable of tuning their solar reflectivity as a function of the local temperature boundary conditions in the attempt to optimnize their potential use in passive building applications [25]. Despite the large literature bachground at the component scale, the investigation of the potential benefits derived from the integration of these materials in real building applications is still in its infancy [28]. In the meantime, computational fluid dynamic (CFD) tools, are increasingly beign used for studying environmental flows in urban areas [29] and quantifying uncertainties in the inflow direction and intensity [30], both inside and outside buildings [31]. Therefore, in addition to full-scale in-field measurements, CFD simulations represent one of the most suitable tools to develop predictive models of the urban built environment [32]. Along with numerical approaches, experimentally validated analytic analyses and modeling represent an effective mean to predict buildings thermal-energy performance. In this scenario, many different box models able to properly predict the heat dynamics of buildings by using stochastic differential equations have been proposed [33]. A

Table 1 Building characteristics in terms of materials and main thermal properties of the envelope. Envelope component

Material type

Thickness (m)

Thermal conductivity (W·(m·K))

Thermal transmittance

(W·(m2·K)−1)

Walls

Plaster EPS Brickwork Plaster

0.020 0.090 0.300 0.020

0.50 0.04 0.27 0.40

0.49

Roof

Waterproof membrane Mineral wool Concrete slab Plaster

0.010

0.50

0.25

0.100 0.200 0.015

0.04 0.16 0.40

Cast concrete Stone wool Linoleum

0.200 0.080 0.015

1.13 0.04 0.17

Floor

0.38

solutions [15] have been developed so far, e.g. innovative coatings, paintings, and shingles [16]. Al-Obaidi et al. [17], for example, developed and investigated the effect of an innovative roofing system combining day-lighting and passive cooling on the indoor air temperature and the mean radiant temperature of an attic, while Yew et al. [18] obtained a 13 °C reduction on the air temperature of an attic, by combining cool roof, thermal insulation and moving air cavity. The use of roof paintings and coatings composed of transparent polymers and white pigments such as titanium dioxide was also shown to produce significant roof overheating reductions [19]. However, reflecting most of the incoming solar radiation, cool applications were also found to reduce winter solar gains through the building walls and roof [20], and consequently, increase the building energy use for heating purposes [21], although the presence of snow was shown to scale down such an increase [22]. Therefore, in recent years, the scientific community has been trying to develop advanced materials, capable of reducing the wellknown winter penalty of such kind of applications. In particular, building upon existing studies in

Fig. 2. Comparison between the weighted optic response of the thermochromic coating in the colored and non-colored phase. 3

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Fig. 3. (a) Outdoor air temperature and relative humidity, and (b) Global and direct radiation on the horizontal plane for the selected summer (August 2–4th 2018), autumn (November 24–26th 2017) and winter days (December 22–24th 2017).

small-scale material prototyping and its in-field integration in existing case study buildings, ergo guiding the development of the aforementioned adaptive solutions for improving indoor thermal comfort conditions in the built environment. The next section describes in further details the methodology applied in this research, the case study building and the thermochromic finishing with its experimental characterization. Section 3 presents the analytic model and its validation procedure. Finally, Section 4 presents and discusses the obtained results comparing them to a traditional dark roof configuration and a more common cool roof application.

simplified and accurate building model based on electrical analogy was developed, for instance, by Fraisse et al. [34] to describe the thermal behavior of a building, by transforming a multi-layer wall into a threeresistances and four-capacities model. Pepper et al. developed a numerical model dealing with 3-D natural convection in an air-filled cavity oriented at three different angles and experimentally validated considering three different angles and four Rayleigh numbers [35]. Ouakarrouch et al. produced a numerical code coupling heat transfers by conduction, convection, and radiation and used it to investigate two kinds of alveolar structures used in the construction sector [36]. In this panorama, the purpose of the present research is to evaluate the thermal performance of a case study prototype building equipped with an adaptive solution consisting of thermochromic roof membrane and thermochromic wall paintings, and benchmark it against cool-only and dark-only solutions. In particular, an analytic box model is implemented to predict the indoor thermal environment of a case study building by taking into account heat transfer by (i) convection, (ii) conduction, and (iii) radiation. The model is later used the compare the effect of the selected thermochromic solutions on the indoor environment of the building in terms of surface and indoor air temperature both in summer and winter conditions. Therefore, the analytic analyses are critically examined and the expected benefits deriving from the introduction of thermochromic solutions in the built environment are evaluated. The final aim of the research is to bridge the gap between the

2. Materials and methods 2.1. Methodology The methodology applied in this work consists of the following main steps: – continuous monitoring of indoor-outdoor microclimate parameters, e.g. surface temperature and air temperature during autumn and winter 2017 and summer 2018; – production and thermo-optic characterization of the thermochromic coating; – implementation and experimental validation of an analytic box 4

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Table 2 Geometrical parameter.

Table 3 Direct solar radiation on the differently oriented building walls and roof.

Geometrical parameters

Symbol

Value

Unit [m2 ] [m]

North wall area

AN

11.038

North wall thickness South wall area

dN AS

0.430 11.038

South wall thickness East wall area

dS AE

0.430 8.520

East wall thickness West wall area

dE AW

0.430 8.520

West wall thickness Roof area

dW Ar

0.430

Roof thickness

dr

0.330

[m]

Thermophysical parameters

Symbol

Value

Unit

Thermal conductivity of the walls

λw

0.290

[W·m−1·K−1]

Thermal conductivity of the roof

0.261

[W·m−1·K−1]

Specific heat of the walls

λr cp, w

958

[J·kg−1·K−1]

Specific heat of the roof

cp, r

911

[J·kg−1·K−1]

Density of the walls

ρw

956

[kg·m−3 ]

Density of the roof

ρr

444

Thermal emissivity of the walls Thermal emissivity of the roof Volume of the indoor air

∊w ∊r Va

0.9 444 24.899

[kg·m−3 ] [–] [–]

Density of the indoor air

ρa

1.200

[kg·m−3 ]

Specific heat of the indoor air

ca

1005

[J·kg−1·K−1]

Outdoor convection coefficient

hconv, out

20

[W·m−2·K−1]

Indoor convection coefficient

hconv, in

11

[W·m−2·K−1]

North wall

In = −IdV ·cos(θ) In = 0

[m2 ] [m]

South wall

Is = 0

if − 90° > a ⩽ 90° if a > 90°

East wall

[m2 ] [m]

Ie = IdV ·sin(θ) Ie = 0

West wall

Iw = 0

if − 90° > a ⩽ 90° if a > 90°

[m2 ] [m]

if − 90° > a ⩽ 90° if a > 90°

Is = IdV ·cos(θ)

Iw = −IdV ·sin(θ)

if − 90° > a ⩽ 90° if a > 90°

Roof

[m2 ]

Ir = IdH

∀

a

2.2. Description of the case study The selected case study building is a dedicated and fully instrumented test-room (3.8 × 3.8 m2) [21,37,38] situated inside the Engineering campus of Perugia, central Italy (Fig. 1). The main construction technologies and materials are summarized in Table 1. All the real thermal properties and characteristics of the building envelope components have been used as input data in the box model. More in detail, a simplified building geometry has been implemented, by assuming a single solid layer for each envelope component. Therefore, the “equivalent” thermal properties of the one-layer simulated configuration have been accurately calculated by considering realistic multi-layer components connected in series.

[m3 ]

model of the test-room building; – analysis of the thermal energy performance of a highly insulated case study building and of a typical low insulation building.

2.3. Field monitoring The continuous monitoring of the test-room building, equipped with a cool roof membrane and cool paintings on the walls, was carried out between September 2017 and September 2018, i.e. for one whole year. A complete weather station [39] situated on the roof of a building in the proximity of the test-room was used to measure the main outdoor micro-climate parameters i.e. dry bulb air temperature (K), air relative humidity (%), wind speed (m·s−1) and direction (° ), global and direct solar radiation (W·m−2 ), and rain fall (mm). Additionally, a dedicated microclimate monitoring station situated inside the test-room was used

In more detail, the experimental monitoring carried out from September 2017 to September 2018 was here used for the validation of the implemented models. In the following sub-sections, the different experimental and analytic approaches applied are further described.

Fig. 4. Real and simplified (a) wall and (b) roof scheme with the adopted finite difference discretization. 5

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Fig. 5. (a) Main components of direct solar radiation received by a horizontal and vertical surface; (b) sun position over the earth surface.

2.5. Analytic experiments design

to collect the main indoor microclimate parameters for the validation of the model, e.g. indoor air temperature (K), mean radiant temperature (K), air relative humidity (%) and velocity (m·s−1), surface temperature (K), and thermal flux (W·m−2 ).

As anticipated in Section 2.1, in this research, two different models were developed and used to investigate the effect of the considered thermochromic applications at the single building scale. First, an analytic box model of the test-room building was defined and validated with respect to the monitored data considering three different configurations: (i) clear sky days in summer, i.e. August 2–4th 2018, (ii) overcast sky days in autumn, i.e. November 24–26th 2017, and (iii) clear sky days in winter, i.e. December 22–24th 2017. A spin up day was also considered in each simulation. Fig. 3 shows the outdoor relative humidity, air temperature, and the global and direct radiation on the horizontal plane, in summer, autumn and winter conditions, for the three selected days of each configuration. The same validated model was later used to investigate the potential benefit of a thermochromic application (α = 0.35 → 0.55) when applied to the case study building described in Section 2.2 and to a fictitious construction with the same geometrical characteristics but lower thermal performance. Thermal transmittance values of 1.01 and 0.82 (W·(m2·K)−1) were considered for the building roof and walls, respectively, for reproducing the effect of the temperature responsive material when applied to a typical Italian building. In particular, according to the Italian Building Typology Brochure [42], the values above can be considered as representative of a concrete and masonry flat roof construction produced between 1970s and 1990s. The obtained results were bench-marked against a traditional low albedo (α = 0.35) and a soiled high albedo configuration (α = 0.55), in both summer (August 2–4th 2018) and winter conditions (December 22–24th 2017).

2.4. Advanced thermochromic roof coating: development and testing 2.4.1. Thermochromic coating production In this work, 5 μm -large microencapsulated leuco-based thermochromic pigments were used to produce an innovative solvent-based coating for roofing applications. Said pigments, capable of switching from black to translucent once their surface temperature exceeds the threshold of 303 K, i.e. about 30 °C, were used to produce a finishing paint to be applied over a soiled polyurethane-based membrane to provide the existing cool solution with a dynamic optic behavior. The thermochromic paint was produced using: – 50 wt% of a toluene–xylene based solvent; – 30 wt% of petroleum-derived resins; – 20 wt% of thermochromic pigment. A double layer of thermochromic paint was sprayed over the polyurethane membrane, to ensure a more uniform result (see Fig. 2).

2.4.2. Thermo-optic characterization of the coating A solar spectrophotometer (SolidSpec-3700) equipped with a 60 mm-diameter integrating sphere with a wavelength accuracy of 0.1 nm was used to characterize the membrane in terms of total reflection coefficient according to the ASTM E 903-96 [40] standard, over the spectral range of 300–2500 nm. The solar reflectance values were defined by weighting wavelength with respect to reference solar spectra (according to reference values [41]). In order to accurately describe the thermo-optic behavior of the advanced coating, both the colored and non-colored phase, i.e. below and above the reference transition temperature of 303 K, were characterized in the spectrophotometer. As can be seen in Fig. 2, the thermochromic coating shows a variable optic response in the range 400–780 nm. However, almost negligible variations can be noticed in the NIR region as a function of the colored state. Globally, the average reflection coefficient of the membrane switches between 0.35 (colored phase) and 0.55 (non-colored phase).

3. Analytic model 3.1. Implementation of the analytic model The analytic model was implemented through an open calculation environment with the aim of predicting the external/internal surface temperatures and the building indoor air temperature by only using the initial values (i.e. at t = 0) of the experimentally measured outdoor/ indoor air temperatures and envelope surface temperatures as input data. The model considers two different kinds of input data, i.e. geometrical and thermophysical properties of the building which are resumed in Table 2, and is driven by specific weather forcing such as the 6

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Fig. 6. Measured and simulated external surface temperatures and global solar radiation on each surface of the building envelope, i.e. North, South, East, West walls and roof, for the three simulated summer days (August 2–4th 2018). 5

incoming solar radiation (direct and diffuse), solar position (solar altitude and latitude) and outdoor air temperature. Additionally, it takes into account the most important heat transfer phenomena taking place between the building envelope and outdoor and indoor environment, and of course, within the envelope itself: – – – – – –

Ta (t + 1) = t

− ∑n = 1 qconv, in Va ρa cp, a

+ Ta (t ) (m3 ),

(2) (kg·m−3 ),

ρa is the air density where Va is the indoor air volume c p, a is the specific heat of the air (J·(kg·K)−1), qconv, in is the heat flux by convection towards the indoor (W·m−2 ), n represents the n-th surface, i.e. North, South, East and West oriented and roof, while Ta is the simulated indoor air temperature (K). Therefore, the temperature of the n-th thermal mass temperature is calculated by solving the transient heat conduction equation:

longwave radiation from outdoor walls to sky and ground; longwave radiation from indoor walls to indoor air; short-wave solar radiation from sun to walls; outdoor convection heat transfer; indoor convection heat transfer; conduction heat transfer.

∂T ∂ 2T =α 2 ∂t ∂x

More in details, the average indoor air temperature is calculated according to the following balance equations:

where α is the thermal diffusivity of the material λ .

(3) (m2 ·s−1),

defined as

ρcp

In particular, Eq. (3) is solved in time, according to the Forward Time-Backward Space (FTBS) finite difference resolution accounting for i sub-layers in the building envelope, and assuming single layer

5

Va ρa cp, a

dTa = − ∑ qconv, in dt n=1

(1) 7

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Fig. 7. Measured and simulated indoor surface temperatures and indoor air temperature, for the three simulated summer days (August 2–4th 2018).

⎛ ∂T ⎞ = qn ⎝ ∂x ⎠ x = d

envelope components with equivalent thermal properties (Fig. 4):

Ti + 1, t − 2Ti, t + Ti − 1, t Ti, t + 1 − Ti, t =α Δt Δx 2

(4)

α Δt α Δt Ti, t + 1 = ⎛1 − 2 2 ⎞ Ti, t + (Ti + 1, t + Ti − 1, t ) Δx ⎠ Δx 2 ⎝

(5)

x d

T − Tl q0 = 0 Δx

(8)

(9)

All the external and internal heat flux balance laws are defined based on the previous equations and on the input weather data, i.e. the incoming direct and diffuse solar radiation, and the outdoor temperature according to:

(6)

Tl = T0 − q0 Δx

Tr = Tn + qn Δx

α Δt α Δt t Tnt +, i 1 = ⎛1 − 2 2 ⎞ Tnt , i + (Tn, i + 1 + Tnt , i − 1) Δx ⎠ Δx 2 ⎝

where Ta, in is the monitored indoor air temperature (K), Ta, out is the monitored outdoor air temperature (K), x is the discretization layer (m) and d is the total wall or roof thickness (m). The following boundary conditions are imposed while solving the model:

⎛ ∂T ⎞ = q0 ⎝ ∂x ⎠ x = 0

Tr − Tn Δx

where T0 and Tn are the outdoor and the indoor thermal mass temperature (K), while q0 and qn are the outward and inward heat flux (W·m−2 ), respectively. Therefore, the conduction equation is discretized in time and space according to Eq. (9):

The initial outdoor and indoor air temperatures were used to define a suited initial condition for each wall and roof sub-layer, according to:

Ti, t = 0 = Ta, in + (Ta, in − Ta, out )

qn =

q0 = qconv, out + qrad, LWsk + qrad, LWgr + qsol, SW

(10)

qn = qconv, in + qrad, LWwalls

(11)

where qconv, in and qconv, out are the heat flux due to indoor and outdoor convection, respectively, qrad, LWsk and qradLWgr are the heat flux due to

(7) 8

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Fig. 8. Measured and simulated external surface temperatures and global solar radiation on each surface of the building envelope, i.e. North, South, East, West walls and roof, for the three simulated autumn days (November 24–26th 2017).

the longwave radiation to the sky and the ground, qsol, SW is the heat flux generated by the incoming shortwave solar radiation, while qrad, LWwalls is the internal longwave radiation flux exchanged among the different walls in the indoor environment. All of these fluxes are of course measured in W·m−2 . In the model the heat fluxes due to indoor and outdoor convection are calculated by using the internal and the external convection coefficient, hconv, i and hconv, e , respectively, according to:

qconv, out = hconv, out (Ta, out − T0)

(12)

qconv, in = hconv, i (Ta, in − Tn )

(13)

(14)

qrad, LWgr = hsk (Tsk − T0)

(15)

(16)

β T + Tsk 3 ⎞ hsk = 4 ∊ σ ⎛1 − cos ⎛ ⎞ ⎞ ⎛ 0 2 2 ⎠ ⎝ ⎠⎠⎝ ⎝

(17)

Tsk = (9.3655746 (1 − cc ) Ta6, out + Ta4, out ·cc·ecl )1/4

(18)

8.45 ⎛1 − 273 ⎞ ⎞ ⎛ ∊cl = (1 − 0.84·cc ) ⎜0.527 + 0.161·∊ ⎝ Ta, out ⎠ ⎟ + 0.84·cc ⎠ ⎝

(19)

⎜

⎜

⎟

⎟

where cc is the cloudiness level, ∊cl is the cloud emissivity (–), σ is the Boltzmann constant (J·K−1), ∊ is the thermal emissivity (–), and β is the wall slope (° ), i.e. 90° for the walls and 0° for the roof. Similarly, to calculate the internal longwave radiation among the walls, the following equation is considered:

The longwave radiation to the sky and the ground, on the other hand, are calculated as follows:

qrad, LWsk = hgr (Ta, out − T0)

T0 + Ta, out 3 β ⎞ hgr = 4 ∊ σ ⎛1 − cos ⎛ ⎞ ⎞ ⎛ 2 ⎠ ⎝ 2 ⎠⎠⎝ ⎝

qrad, LWwalls = hr (Ta, in − Tn )

where, as reported in the work by Fraisse et al. [43]: 9

(20)

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Fig. 9. Measured and simulated indoor surface temperatures and indoor air temperature, for the three simulated autumn days (November 24–26th 2017).

associated to surface temperatures below the thermochromic transition temperature (TT); rcool is the reflectance associated to surface temperatures above the thermochromic transition temperature (TT); erf (tnorm) is the error function; and tnorm is the normalized time, defined as:

where:

hr = 4 ∊

σTn3

(21)

The heat flux generated by the shortwave solar radiation on each building surface is defined as the fraction of the direct radiation acting on a vertical or horizontal surface, i.e. building walls and roof, respectively, according to Eq. (23):

IdV = Id ·cos(h)

(22)

IdH = Id ·sin(h)

(23)

tnorm = count (t )

rcool − rdark (1 + erf (tnorm)) 2

(25)

where tTT represents the thermochromic transition time interval (set to 1200 s [44]) and count(t) is a counting function that tracks the time elapsed from the beginning of a given thermochromic transition, defined as:

Therefore, the fraction of solar radiation received by each building envelope surface can be defined as in Table 3 where a = π − Z (see Fig. 5 for the reference angular system): Finally, in order to represent the a albedo of the thermochromic coating the following function was considered:

r (T ) = rdark +

2π tTT

⎧tTT ⎪ count (t − 1) − dt count (t ) = ⎨0 ⎪ count (t − 1) + dt ⎩

if if if if

T (t T (t T (t T (t

− − − −

1) 1) 1) 1)

< TT & count (t − 1) > tTT < TT & count (t − 1) ⩽ tTT ⩾ TT & count (t − 1) < tT 0 ⩾ TT & count (t − 1) ⩾ tT 0

(24)

(26)

where r (T ) is the reflectance at temperature T; rdark is the reflectance

where tT0 is equal to 0, and dt is the simulation time interval, i.e. 10 s. 10

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Fig. 10. Measured and simulated external surface temperatures and global solar radiation on each surface of the building envelope, i.e. North, South, East, West walls and roof, for the three simulated winter days (December 22–24th 2017).

outdoor walls to sky and ground, (ii) longwave radiation in the indoor, (iii) short-wave solar radiation from the sun, (iv) outdoor and indoor convection heat transfer; – Air properties do not change significantly in the investigated temperature and time domain; – Latent and mass transport phenomena are neglected.

3.2. Model assumptions and limitations The analytic model described in Section 3.1 is based on the following main geometrical and thermo-physical assumptions: – The prototype building is composed by perfectly flat surfaces; – Opening in the building envelope such as windows and doors are not modeled; – The thickness of the building envelope is much smaller than the width and height of each surface; – The building envelope can be simplified by using homogeneous materials characterized by uniform, equivalent properties as described in further details in Section 3.1; – Heat conduction through the building envelope is mono-dimensional (in the x-direction); – No heat is generated in the air domain or within the building walls; – Local boundary conditions can be described by means of simplified heat flux equations taking into account (i) longwave radiation from

Just like any other analytic solution method, the present model is limited to a highly simplified problem and considers a straightforward geometry. Also, the main thermo-physical phenomena taking place in the investigated domain are parametrized by acknowledged schemes such as the thermal-electrical analogy, and the Newton’s law of cooling. Finally, mass transport and latent phenomena are not taken into account, which could result in non linear deviations from the experimentally monitored data. Still, the model can represent the most important heat transfer phenomena taking place both between the building envelope and the indoor and the outdoor environment. Based on a limited number of initial values at time zero, i.e. surface 11

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Fig. 11. Measured and simulated indoor surface temperatures and indoor air temperature, for the three simulated winter days (December 22–24th 2017).

(Figs. 10 and 11). The validation of the model was carried out comparing air temperature and surface temperature values for each surface of the case study building both summer and autumn, however, surface data from the East and West walls were not available in winter. In more detail, Fig. 6 shows the comparison between the simulation outputs and the in-field measurements in terms of external surface temperature for the different building surfaces, i.e. the four vertical walls (North, South, East, West) and the roof. Additionally, the amount of global solar radiation heating each of these surfaces is also plotted during the three considered days. The graphs highlight the good capability of the implemented model to replicate the monitored temperature trends and values in the three investigated summer-clear sky days. As a matter of fact, the discrepancies between the compared trends is usually within the experimental error associated to the selected temperature sensors, i.e. 0.5 °C, with the exception of local high peaks probably due to experimental outliers. Similar considerations can also be made when comparing the simulated and the monitored external surface temperature profiles (only 3 of them are available in this case, i.e. North and South walls and roof)

temperatures and indoor/outdoor air temperature, it can predict the thermal behavior of the case study building in an acceptable way. 4. Results and discussions In this Section, results from the novel box model are firstly presented and validated against the experimental data from the monitoring campaign. Secondly, the potential thermal effect of the innovative thermochromic envelope is bench-marked against a traditional dark configuration and the monitored cool envelope in the reference highinsulation configuration. Lastly, the results from the low-insulation investigation are shown, both in summer and winter conditions. 4.1. Validation of the model Figs. 6–11 show the comparison between the simulated and the monitored data for each of the investigated cool envelope configurations, i.e. (i) clear-sky days in summer (Figs. 6 and 7), (ii) overcast-sky days in autumn (Figs. 8 and 9), and (iii) clear-sky days in winter 12

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Fig. 12. External surface temperature for the different vertical walls, i.e. North, South, East and West, and for the roof of the high insulation case study building, August 2–4th 2018.

Fig. 13. External surface temperature for the different vertical walls, i.e. North, South, East and West, and for the roof of the high insulation case study building, December 22–24th 2017.

compared to the experimental values, however, they are always lower in the absolute value. This could be due to the additional thermal load produced by the indoor monitoring system, which is not taken into account in the model. A continuous functioning regime could, indeed, produce a non-negligible effect, particularly, in the small air volume of the case study building in winter free floating conditions. However, the higher discrepancies found in the external surface temperature profiles in winter produce deviations as high as 1.1 °C between the monitored and the calculated values (see Fig. 11). Finally, consistently with the above findings, the model is able to accurately predict the indoor thermal performance of the building. As a matter of fact, by comparing the indoor air temperature simulation outputs with the available data from the monitoring campaign (see Figs. 7, 9 and 11) a maximum gap of 0.5 K can be found in the investigated configurations. In particular, the obtained results show a general, even though acceptable underestimation of the indoor temperature profile in both summer and autumn, and an overestimation in winter. This once again could be a consequence of one of the main simplifications in this model, namely, not considering latent phenomena both in the indoor and the outdoor environment, particularly

in autumn and winter conditions. Figs. 8 and 10 show higher differences between the simulated and the experimental trends, however, temperature waves with almost identical shapes are always registered. These discrepancies are more evident in winter conditions (Fig. 10) where probably, the combination of higher wind speeds and non-negligible condensation phenomena, which are not directly taken into account in the model, produces relatively less accurate, but still acceptable, simulation outputs. Concerning the indoor temperature trends, the model allows to almost perfectly reproduce the registered profiles, i.e. differences well below 0.5 °C, in summer-clear sky and autumnovercast sky conditions (see Figs. 7 and 9). A slight derivation of the obtained surface temperature profile can be found in the hottest surfaces in summer. This is a consequence of the fixed convective and radiative heat transfer coefficients used in the model. As a matter of fact, this derivation is mostly affecting the heating ramp, while in the cooling one the simulated trends more closely approach the experimental results. A possible future development of the code could regard the implementation of variable coefficients, defined as a function of the local boundary conditions. As for winter conditions, the simulated indoor surface temperature profiles, present a very similar trend 13

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Fig. 14. Indoor air and surface temperature for the different vertical walls, i.e. North, South, East and West, and for the roof of the high insulation case study building, August 2–4th 2018.

Fig. 15. Indoor air and surface temperature for the different vertical walls, i.e. North, South, East and West, and for the roof of the high insulation case study building, December 22–24th 2017.

differences in the case of the indoor surface temperature profiles and the average indoor air temperature for the case study building. As can be seen, both the thermochromic and cool application allow to significantly reduce the superficial solar heat gains during daylight hours in Summer, reaching up to 10 K temperature reduction in the East wall profile with respect to the reference, lower albedo application (Fig. 12). However, thanks to its temperature responsive nature, the thermochromic solution is capable of absorbing most of the incoming solar radiation in winter, reproducing the positive behavior of the traditional dark envelope and completely canceling the detrimental winter penalty that affects the common cool configuration (up to 4 K temperature reduction in South wall and roof surface during the daylight hours as seen in Fig. 13). Given the significant thermal inertia and insulation capability of the prototype test-room, the huge temperature differences registered in Summer at the outermost layer of the building envelope produce small temperature fluctuations in the indoors where the superficial thermal profile of the different surfaces, although always cooler than that of the dark solution, oscillates reaching a peak difference of 0.16 K during the night (see Fig. 14).

surface condensation processes. 4.2. Bechmarking of the innovative thermochromic envelope The analytic model developed and validated in this work was used to investigate the potential of an innovative building envelope, i.e. thermochromic wall paint and roof membrane, characterized by an adaptive response to the local temperature boundary. As previously described in Section 2.5, two different configurations were explored, i.e. the real case study building, characterized by high insulation capability, and a more common solution, associated to lower thermal performance. 4.2.1. High insulation configuration Results from the High insulation configuration are presented in this Section. Figs. 12 and 13 show the difference between the external surface temperature profiles of the traditional dark and the innovative thermochromic configuration (dashed orange line in the graphs) and the soiled cool roof application (solid blue line in the graphs), for the selected summer and winter days. Similarly, Figs. 14 and 15 depict such 14

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Fig. 16. Comparison between the indoor surface temperature for the different vertical walls, i.e. North, South, East and West, and for the roof of the high and low insulation configuration, August 2–4th 2018.

Fig. 17. Comparison between the indoor surface temperature for the different vertical walls, i.e. North, South, East and West, and for the roof of the high and low insulation configuration, December 22–24th 2017.

Fig. 18. Indoor air and surface temperature for the different vertical walls, i.e. North, South, East and West, and for the roof of the low insulation case study building, August 2–4th 2018. 15

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Fig. 19. Indoor air and surface temperature for the different vertical walls, i.e. North, South, East and West, and for the roof of the low insulation case study building, December 22–24th 2017.

Higher fluctuations are registered in winter by the cool envelope, i.e. up to 0.5 K during the night in the case of the South wall and the roof surface (see Fig. 15). However, the adaptive response of the thermochromic solution allows to reduce such differences to 0 K, increasing the amount of heat released within the unconditioned environment as a consequence of the incoming solar heat gains. As a result, the indoor air temperature profile is positively affected by the adaptive albedo variation, which maintains higher temperatures in winter, while keeping lower values in summer (see Figs. 14 and 15). Of course, the data presented in this Section concern a case study building characterized by high insulation performance. Consequently, the amount of heat which is transferred through the envelope relatively low. However, the application of the same material on a more common, low insulation configuration is more effective, as described in the next Section.

5. Concluding remarks In this work, the potential effect of an innovative adaptive thermochromic application on the thermal performance of a prototype building is assessed and bench-marked against a traditional dark envelope configuration and a soiled cool envelope application. In detail, a simplified analytical model of a real test-room building was developed and validated against experimental data from a continuous field monitoring. The model, which implements the main heat transfer phenomena taking place between the building envelope and the indoor and outdoor environment, was used to investigate the effect of the three applications on the indoor air and surface temperatures during summer and winter conditions. Results show that the application of the thermochromic membrane and wall paint allows to combine the positive summer passive cooling effect of the high albedo solution, with the desirable heat gains produced by dark surfaces in winter. In particular, introducing such adaptive, temperature-responsive materials as the outermost layer of the case-study building allows to mimic the thermal behavior of the cool solution in summer, while preserving the positive interaction with the incoming solar radiation characterizing a traditional dark finishing in winter. A reduction of about 0.2 K and 0.5 K were found on the average indoor air temperature in summer for the high and low insulation configuration, respectively. Additionally, a maximum temperature increase of about 0.5 K and 0.6 K were registered in winter, for the high and low insulation configuration, respectively, when compared to a common cool solution. Consequently, the introduction of the thermochromics, could represent a win-to-win approach to combine the well established passive cooling effect of high reflectance materials with the positive solar gains perceived by the most common dark solutions. This is particularly true in the case of a typical building with low thermal insulation performance, for which the benefits deriving from the modeled adaptive material on cooling and heating loads are significantly higher. In conclusion, using temperature responsive materials such as thermochromic coatings in buildings can indeed be considered a promising solution to mitigate the increase of indoor air temperatures in the built environment during summer overheated conditions, while maintaining the positive absorption of solar radiation in winter. All this considered, further research is needed to examine the effect of these solutions on the indoor air circulation, to more closely investigate their effect on the local thermal comfort conditions.

4.2.2. Low insulation configuration As previously mentioned, the proposed passive technique is also implemented into the same building model, with relatively minor thermal insulation performance, which may be more realistically representing European construction typicality of recent decades [42]. Figs. 16 and 17 compare the indoor surface temperature profiles of the previously presented high insulation and the low insulation configuration. As expected, higher temperature fluctuations are registered on the indoor surface profiles, as a consequence of the reduced thermalenergy performance. Given the higher amount of heat transferred through the envelope with lower insulation capability, similar external surface temperatures produce fairly different indoor profiles as shown in Figs. 18 and 19. In particular, both the thermochromic and cool application allow to reduce the superficial solar heat gains through the roof of about 0.9 K in Summer, (Fig. 18). While the detrimental 2 K winter penalty registered on the ceiling was completely removed by the temperature responsive nature of the thermochromic solution as seen in Fig. 19). The result, as shown in the last panel in Figs. 18 and 19, is an improved indoor air temperature trend, characterized by milder winter profiles (up to 0.6 K, and reduced overheating in summer (about 0.5 K lower values were registered at 6 PM in both the cool and thermochromic solution). Of course, the data presented in this work concern the average air temperature of the case study building, and a more detailed investigation of the air temperature distribution should be carried out. 16

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Acknowledgment [22]

The first author’s acknowledgments are due to the PhD school in Energy and Sustainable Development. All the authors also thank H2CU for the great international cooperation opportunities and Fondazione Cassa di Risparmio di Perugia for supporting the project SOS CITTA’ 2018.0499.026.

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