Analysis of the temperature dependence of the thermal conductivity in Vacuum Insulation Panels

Accepted Manuscript

Analysis of the temperature dependence of the thermal conductivity in Vacuum Insulation Panels Stefano Fantucci , Alice Lorenzati , Alfonso Capozzoli , Marco Perino PII: DOI: Reference:

S0378-7788(18)31385-9 https://doi.org/10.1016/j.enbuild.2018.10.002 ENB 8831

To appear in:

Energy & Buildings

Received date: Revised date: Accepted date:

4 May 2018 2 October 2018 3 October 2018

Please cite this article as: Stefano Fantucci , Alice Lorenzati , Alfonso Capozzoli , Marco Perino , Analysis of the temperature dependence of the thermal conductivity in Vacuum Insulation Panels, Energy & Buildings (2018), doi: https://doi.org/10.1016/j.enbuild.2018.10.002

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Highlights Analysis of the average temperature dependency of thermal conductivity in VIPs



Analysis of the heat transfer contributions that affect thermal conductivity in VIPs



Evaluation of the combined effect of ageing and temperature on thermal conductivity



Impact of thermal conductivity variation on thermal behaviour of a VIP-based roof



Measures to mitigate severe conditions for VIP-based components were introduced

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

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Analysis of the temperature dependence of the thermal conductivity in Vacuum Insulation Panels Stefano Fantucci a, Alice Lorenzati a, Alfonso Capozzoli a*, Marco Perino a a

Department of Energy, TEBE Research Group, Politecnico di Torino, Corso Duca degli

Abruzzi 24, Torino 10129, Italy

Tel.: +39 011 0904413 E-mail address: [email protected] Abstract

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* Corresponding author: Alfonso Capozzoli

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Over the last few years, the adoption of Vacuum Insulation Panels (VIPs) in building envelopes has increased. However, in order to obtain a correct implementation of VIPs in buildings, it is crucial to conduct a proper analysis of the thermal bridging, the service life and the ageing effects at both the design stage and during building operation. A further factor that should be considered is the dependency of thermal conductivity on temperature.

In this paper, an experimental campaign has been carried out to evaluate the variation in the thermal

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conductivity of VIPs with the average temperature and to qualitatively assess the heat transfer contributions that affect this variation. The study has also been devoted to evaluating the effect of a

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variation in the thermal conductivity considering various VIP ageing stages. Moreover, dynamic heat transfer simulations have been performed, using a validated model, to investigate the impact of considering a temperature dependent thermal conductivity on the overall thermal behaviour of a building

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Keywords

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roof with VIP-based insulation.

Vacuum Insulation Panels; thermal conductivity; fumed silica; temperature dependency;

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experimental analysis; ageing.

Highlights 

Analysis of the average temperature dependency of thermal conductivity in VIPs



Analysis of the heat transfer contributions that affect thermal conductivity in VIPs



Evaluation of the combined effect of ageing and temperature on thermal conductivity



Impact of thermal conductivity variation on thermal behaviour of a VIP-based roof



Measures to mitigate severe conditions for VIP-based components were introduced

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Nomenclature solid thermal conductivity

[W/mK]

λr

radiative thermal conductivity

[W/mK]

λg

gaseous thermal conductivity

[W/mK]

λcpl

thermal conductivity (coupling effect)

[W/mK]

λ

overall thermal conductivity

[W/mK]

λCOP

centre of panel thermal conductivity

[W/mK]

λ(ϑ)

temperature dependent overall thermal conductivity

[W/mK]

∆λ

variation in the thermal conductivity

[W/mK]

ϑavg

average temperature

ϑi

different measuring temperatures

ϑ0

lowest measuring temperature

Δϑ

temperature difference

φ

specific heat flux

fcal(ϑ)

calibration factor of the measuring plate

e

measurement of the electric signal

t

specimen thickness

hi

internal surface heat transfer coefficient

[W/m2K]

he

external surface heat transfer coefficient

[W/m2K]

hc

external convective heat transfer coefficient

[W/m2K]

hr

external radiative heat transfer coefficient

[W/m2K]

ΔQlosses

heat losses

[Wh/m2]

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λs

[°C] [°C] [°C] [°C]

[W/m2µV] [V] [m]

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[W/m2]

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1. Introduction Over the last few years, the penetration of the Vacuum Insulation Panel (VIP) technology in the building sector has rapidly increased, especially as far as energy refurbishment applications are concerned. VIPs are composed of an evacuated core material, enclosed within a sealing multilayer envelope. The core is made up of nano- or micro-porous materials that usually consist of fumed silica powder and polyurethane foams or glass/mineral fibres, as summarised in Wang et al. [1]. The type of material and its

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characteristic pore size affect the required internal vacuum degree (which usually ranges between 0.1 and 10 mbar). Moreover, owing to the relatively high cost of VIPs, a great deal of effort has been made in the last few years to study novel and low cost core materials (e.g. expanded cork and cellulosic-crystal, as described in Zhuang et al. [2]; Chang et al. [3]; Liang et al.[4]; Tetlow et al. [5] and Gangåssæter et al.

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[6]).

The heat transfer mechanism in VIPs, as well as in general porous materials, is generally described by equation (1) as the sum of the contributions of the solid thermal conductivity (λs), the radiative thermal conductivity (λr), the gaseous thermal conductivity (λg), and a coupling thermal conductivity(λcpl), which takes into account the interactions between gas and the solid core material particles (Beatens et al. [7];

(1)

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tot  s  r  g  cpl 

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Bouquerel et al. [8]; Alam et al. [9]; Singh et al. [10]).

The core material of a VIP is evacuated in order to reach internal residual pressure values that are low

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enough to obtain the Knudsten number Kn ≥ 1. The Knudsten number is defined as the ratio of the gas molecular mean free path length to a representative physical length scale (the size of the porous media).

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Because of the low internal pressure, the gaseous thermal conductivity (λg) and the coupling thermal conductivity (λcpl) are usually neglected, and this results in the total VIP thermal conductivity which is

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mainly dependent on the solid conduction and radiative contribution of the pores. The use of VIPs in practical building applications could lead to a series of issues which would need to be faced at both the design stage and during building operations. In particular, the actual thermal conductivity of VIPs, when they are applied in building construction, could be very different from the centre of panel thermal conductivity (λCOP) measured in the laboratory on new panels. This is mainly due to two main factors: i) the thermal bridging effect determined by the high conductive envelope material and the construction joints, and ii) the service life and ageing effects of VIPs.

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The effect of thermal bridges in VIPs has been widely investigated and discussed in literature at both the material/component level (Lorenzati et al., 2014 [11]; Lorenzati et al., 2016 [12] ; Sprengard et al., [13]) and at the building level (Ghazi Wakili et al., 2011 [14]; Capozzoli et al., 2015 [15]; Isaia et al., 2016 [16]). However, the service life of VIPs remains a key issue that has to be dealt with when considering that the material may be subjected to severe external conditions during building operations and, as a consequence,

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its total thermal conductivity may increase rapidly as a result of the growing pressure and internal moisture content (the increase in pressure and humidity inside a panel over time is one of the main ageing mechanisms, as observable, for instance, in Shwab et al., 2005 [17]; Simmler et al., 2005 [18]). Several works have focused on the prediction of the service life of VIPs and on the development of linear models

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to determine their moisture content (as described in Beck et al., 2007 [19]), and to predict their long-term performances by means of an accelerated ageing test (Kim et al., 2017 [20]). Moreover, long-term in situ monitoring campaigns have been performed for VIP insulated façades in order to evaluate the effect on the actual thermal performances (MacLean et al., 2016 [21]; Johansson et al., 2016 [22]). A further important factor that should be taken into account for the characterization of VIPs when exposed

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to an external environment, is the temperature dependency of the thermal conductivity (Quénard et al.,

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2005 [23]; Lorenzati et al., 2015 [24]; Lorenzati et al., 2017 [25]). By performing VIP thermal conductivity measurements at various temperatures, it is possible to isolate the different heat transfer

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contributions (radiative and solid conductive), because of their different temperature dependence. The main factor that influences the increase in the total thermal conductivity, at a constant pressure, is

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assumed to be the radiative contribution, which increase linearly with the cube of the average temperature (Bouquerel et al., 2012 [8]; Alam et al., 2014 [9]; Jang et al., 2013 [26]). The λs contribution is instead

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less sensitive to increases in temperature (Caps et al., 2000 [27]; Caps et al., 2001 [28]), while the gaseous thermal conductivity (λg) depends to a great extent on the pressure, due to the Knudsen effect. However, an increase in the temperature in a confined volume also determines an increase in the internal pressure (Sprengard et al., 2017 [30]) as well as in the partial vapour saturation pressure pvs(θ), and hence in the gaseous thermal conductivity. The relationship between temperature and thermal conductivity can be neglected for most of the insulating materials that operate over the typical temperature range of buildings. Nevertheless, for a few materials, including VIPs (Lorenzati et al. [24][25]) and polyisocyanurate (Berardi 2017 [31] and Berardi

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et al. 2018 [32]), the general assumptions of temperature-independent thermal conductivity can lead to potential inaccuracies in the assessment of the building energy performance (Berardi et al. 2018 [32]). The dependency of VIP thermal conductivity on the average temperature has not been thoroughly investigated so far, and its influence on the overall energy performance has frequently been overlooked. For example, several numerical simulations have been performed on insulated components at the building scale, in order to evaluate the real operating conditions of VIPs, and the thermo-economic advantages of

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using VIPs instead of traditional insulating solutions (Kim et al., 2017 [33]; Mujeebu et al., 2016 [34]; Ascione et al., 2017 [35]). However, none of them has considered the temperature dependency of the VIP thermal conductivity on the real VIP operating temperatures. On the basis of these considerations, two different investigations have been performed in this paper.

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Firstly, an experimental campaign, conducted by means of a Heat Flux Meter apparatus (HFM) on a fumed silica-based VIP and on a fumed silica board, was carried out, as a follow-up of the results presented in Lorenzati et al. (2017) [25]. This investigation has been aimed at assessing the dependency of thermal conductivity on the average temperatures, in order to qualitatively identify the different heat transfer contributions that affect the variation in the thermal performance of VIPs with temperature.

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Moreover, the effects of temperature on the thermal conductivity of a VIP at different ageing stages were

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also studied.

In addition, numerical dynamic heat transfer simulations were performed, in order to investigate the

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effects of a thermal conductivity variation of the VIP on the overall thermal behaviour of a building roof. Finally, guidelines that are useful to mitigate the VIP operating conditions were discussed on the basis of

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the obtained results.

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2. Fumed silica-based VIPs - Features Nanoporous silica materials (fumed silica, precipitated silica and granular aerogel) are the most commonly used materials for VIP cores. In the case of Fumed Silica (FS), the gas conduction λg is quite low, even at atmospheric pressure, because the pores (~ 300 nm) have the same order of magnitude as the mean free path of the air molecule at ambient temperature and pressure (Caps et al., 2000 [27]; Beatens et al., 2010 [7]). This fact, combined with the effect of the opacifiers inside the core (silicon carbide powder, or titanium dioxide), makes it

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possible to reach a thermal conductivity of the core of the order of 0.019 - 0.020 W/mK (Caps et al., 2001 [28]). Once the core has been evacuated, the VIP is characterised by an equivalent thermal conductivity value of around 0.004 W/mK. Owing to the small size of the pore, a gas pressure below 10 mbar is generally sufficient to greatly reduce the λg contribution, while, in the case of other core materials (foams and fibres), a pressure value of below 0.2 mbar is needed (Caps et al., 2001 [28]).

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Fumed Silica (FS) based VIPs are particularly suitable for building applications because they offer several advantages over VIPs made with other kinds of cores (Bouquerel et al., 2012 [8]). Among these advantages, the following are worth mentioning: the relatively long service life expectancy, (since the component is less sensitive to any increase in the internal pressure) and the relatively low thermal

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conductivity in the case of a complete loss of vacuum (punctured VIP).

For all these reasons, FS-based VIPs have been investigated in depth in the scientific literature, from different perspectives. In particular, the heat transfer mechanism has been described by Caps et al. 2000 [27], Caps et al. 2001 [28], Quénard et al. 2005 [23], Shwab et al. 2005 [17] and Heinemann 2008 [29]. The dependence of thermal conductivity on the internal gas pressure was analysed in Simmler et al. 2005

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[18], while the variation in the thermal conductivity over time was investigated by Wegger et al. 2011

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[36] for different VIP envelope typologies. In all these studies, λs+r values ranging between 0.0036 and 0.0044 W/mK were found. Moreover, as specified in Bouquerel et al. 2012 [8], λg assumes a value of about 0.00004 W/mK at a pressure level of 1 mbar.

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However, most manufacturers declare a λtot ≤ 0.005 W/mK value for FS-based VIPs, which is a typical

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value at a pressure of 10 mbar (Kalnæs et al., 2014 [37]).

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3. Laboratory characterisation This work has been aimed at assessing, through experimental investigations, the variation in the thermal conductivity for various average1 boundary temperature values (the typical building applications range of temperatures). The investigation was carried out on a fumed silica-based VIP (10 mm thickness) and a fumed silica pressed board (VIP core material). The obtained results extend those reported in Lorenzati et al. 2017 [25].

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In the paper, the “average temperature” is intended as the mean value between the temperatures of the two sides of the VIP.

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Furthermore, the combined effect of the average temperature and of the ageing stage (0, 20, 32 and 40 months) on the thermal conductivity of a VIP was also investigated to establish their impact. A transient heat transfer simulation was then performed on a building component, in order to evaluate the VIP thermal performance when a temperature dependent thermal conductivity was taken into account in the simulation.

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3.1 Methodology

The experimental campaign was performed by means of a Heat Flux Meter apparatus (“Lasercomp FOX600”), in accordance with EN ISO 12667:2001 [39]. The thermal conductivity was measured by means of the following equation:

     f cal (test )  e  t 

(2)

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    

where: φ is the measured heat flux density through the sample [W/m2], λ is the thermal conductivity of the sample that has to be determined [W/mK], t is the sample thickness [m] measured by means of the apparatus and Δϑ is the temperature difference between the two sides of the specimen [K].

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The contribution of λg is usually negligible in fumed silica-based VIPs, due to the small size of the pore

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(microporous structure), as discussed in Section 1. However, the magnitude of this contribution is affected by the temperature level, and it is usually limited by the typical temperature variations that occur during building operations and at atmospheric pressure (Bouquerel et al., 2012 [8]; Heinemann, 2008

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[29]).

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The assumption mentioned in Section 1 about the heat transfer contributions, allows the increment in the thermal conductivity to be analysed while focusing on the variation of the radiative and gaseous

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contributions due to the increase in temperature. The variation of the thermal conductivity (Δλ(ϑi)) at temperature i (ϑi) in a VIP and in a fumed silica core was compared with the thermal conductivity obtained at the lowest measured temperature (ϑ0):

 (i )   (i )   (0 )

(3)

where: λ(ϑi) is the thermal conductivity measured at temperature i, while λ(ϑ0) corresponds to the thermal conductivity measured at the lowest tested temperature (-7.5°C). The main nominal features of the measured VIP sample are shown in Table 1.

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As mentioned in Section 2, experimental measurements were also performed on a non-evacuated Fumed Silica pressed board (VIP core material), with dimensions of 600 x 500 x 25 (thickness) mm and a density of ~ 198 kg/m3. Table 1. Characteristics of the fumed silica FS-based VIP (nominal values)

Area

Composition t

SiO2

Properties (as stated by the manufacturer)

SiC

Other

ρ 3

[mm]

[mm]

[%]

[%]

[%]

[kg/m ]

600 x 600

10

80

15

5

150 - 300

3.2 Analysis and discussion of the results

λCOP - (22.5°C)

p

[W/mK]

[mbar]

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Dimensions

≤ 0.005

≤5

The results of the experimental laboratory analyses, conducted on both the VIP and the fumed silica board

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that constitutes the VIP core at the material level, are presented in the following sections. The thermal conductivity was measured for a wide range of average temperature values. Furthermore, a similar analysis was performed on a VIP at different stages of ageing (stored in laboratory environmental conditions for 0, 20, 32, and 40 months) in order to identify the combined effect of ageing and working

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temperature on the thermal performance of the VIP.

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3.2.1. The effect of temperature on thermal conductivity Different experimental tests were carried out for the 10 mm thick VIP panel and the FS core board, kept at ambient pressure and measured under different average temperatures. A VIP that had been stored in the

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laboratory for 32 months was used for these tests. Ten average temperatures, ranging from -7.5°C to

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55.5°C, were selected in order to accurately analyse the non-linear variation of the VIP thermal conductivity from the average temperature. A constant difference between the temperatures at the sides of

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the VIP (e.g., plates of HFM) of 15° C was considered for each test, as reported in Table 2 in order to assure reliable measurements with low uncertainties, according to [24]. The selected range of experimental average temperatures was constrained by the lowest and highest temperature which can be reached at the plates of the HFM apparatus and by the imposed temperature difference between them. This range of average temperatures is representative of the majority of actual conditions at which VIPs generally operates, considering also that the VIP layers in building components are usually not exposed directly to the outdoor environment. However, in very severe weather conditions

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with poor protected VIP based component, the VIP layer could be subjected to average temperatures lower than the lowest value considered in this study (-7.5 °C). The obtained results highlight a 53% increase (~ 0.0026 W/mK) in the VIP thermal conductivity (from ~0.0049 to ~0.0075 W/mK) over the range of average temperatures between -7.5 °C and 55.5 °C (Figure 2); the increase in thermal conductivity over the same range of average temperatures for the FS core (Figure 3) is considerably lower (around 0.0017 W/mK).

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Considering that the radiative contribution λr is linearly dependent on the third power of the absolute temperature, the thermal conductivity of the VIP and FS core were plotted against ϑ 3 [K] in Figures 2 and 3, respectively.

Table 2. Test conditions and thermal conductivity results (32 months aged VIP) λcop

ϑupper plate

ϑlower plate

ϑavg

[°C]

[°C]

[°C]

[W/mK]

0

-7.5

0.00488

7

-0.5

0.00499

14

6.5

0.00509

21

13.5

0.00524

28

20.5

0.00545

35

27.5

0.00570

42

34.5

0.00599

49

41.5

0.00637

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Test n°

-15

2

-8

3

-1

4

6

5

13

6

20

7

27

8

34

9

41

56

48.5

0.00686

10

48

63

55.5

0.00746

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1

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The difference in thermal conductivity between the two samples (VIP and FS board) for each testing temperature Δλ(ϑi) can be attributed to an increase in the gaseous conduction and the coupling

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contribution (λg+λcpl), both of which are relevant in the VIP (variation of the internal pressure) and negligible in the FS core (atmospheric pressure).

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Nevertheless, it is important to remark that the analysis of the separate contributions of λg, λr, λc, λcpl to the overall thermal conductivity, is characterised by a certain degree of uncertainty2, because it is impossible to completely suppress the influence of three factors while analysing the effect of the fourth one. The present analysis only has the scope of qualitatively analysing the phenomena that are responsible for the increment in the thermal conductivity as a result of changes in the temperature.

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A ~2.5% measurement uncertainty on λtot (error bars in Figure 2, Figure 3 and Figure 4) were determined according to UNI CEI 70098-3:2016 [38].

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As it is possible to observe in Figure 2, a linear increment in the thermal conductivity, as a function of the third power of the average temperature [K], can be observed in the range between -7.5 and 27.5° C. This means that λr is dominant over the analysed range of temperatures and the gaseous conduction, λg, can be considered negligible. Moreover, as proposed by Kobari et al. 2015 [40], the solid thermal conductivity can be estimated as the intercept of this regression line on the y-axis, where the gaseous contribution can be neglected.

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The increment in thermal conductivity from -7.5 to 55.5 °C, pointed out by the dotted line in Figure 2 (~0.0016 W/mK), is in agreement with the one measured in the FS board and which is represented in Figure 3 (~0.0017 W/mK). Considering that the contribution of λg+ λcpl to the variation of thermal conductivity in the FS board is negligible, it can be inferred that the increment in thermal conductivity

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related to the dotted line in Figure 2 for a VIP is mainly due to the increment in λs+ λr.

When the temperature is higher than 27.5°C, a significant change in the slope in Figure 2 occurs, thus demonstrating that the contribution of λg + λcpl becomes more significant at a high temperature. This change in the slope (from linear to quadratic) may be related to the internal pressure of the VIP, which exceeds the critical pressure for which the gaseous contribution can be considered suppressed (5 < p < 10

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mbar in the fumed silica core, Simmler et al., 2005 [41], Sprengard et al., 2017 [30]), as a consequence of

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the temperature increment.

By plotting the linear regression line of the measured points between -7.5 °C and 27.5°C (dotted line in Figure 2), it is possible to highlight the contribution of the λg+ λcpl terms (that is, the difference between

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the λ(θ) continuous line and the dotted line).

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This representation allows the gaseous and the coupling contributions to be qualitatively isolated from the solid and the radiative contributions. The results confirm that the increment in the gaseous contribution

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over the range of temperatures to which the VIP could be exposed in building applications, in plant and storage system insulation, determines a non-negligible reduction of the performance, which should be carefully accounted during the design phase. 3.2.2. The effect of ageing on thermal conductivity The measured thermal conductivities on a pristine VIP (0 months) and on the same VIP stored for 20, 32 and 40 months in the lab, are summarised in Table 3 and shown in Figure 4 for three different average test temperatures (10, 25 and 40°C), together with the corresponding thermal conductivities, which are denoted as: λ10, λ25, and λ40.

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Table 3. Measured thermal conductivities for various test temperatures and ageing times ϑavg [°C] 10 25 40

Ageing period 0 (pristine) λ [W/mK] 0.00483 0.00520 0.00581

20 (months) λ [W/mK] 0.00512 0.00549 0.00614

Δλ (aged – prist.) [W/mK] 0.00029 0.00030 0.00032

32 (months) λ [W/mK] 0.00517 0.00550 0.00629

Δλ (aged – prist.) [W/mK] 0.00034 0.00039 0.00048

40 (months) λ [W/mK] 0.00520 0.00555 0.00638

Δλ (aged – prist.) [W/mK] 0.00037 0.00043 0.00057

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The results show a rapid increase in the thermal conductivity during the first 20 months, while a slower increment was observed between the 20th and the 40th months. This phenomenon can be explained by analysing the effect of the air and water vapour permeation mechanisms across the laminated envelope. In the first period (0 - 20 months), the magnitude of the gas and vapour transport is driven by a high pressure difference, which determines a rapid increase in the internal pressure of the VIP. In the second period,

the lower variation of the thermal conductivity.

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that is, between the 20th and the 40th months, the pressure gradient becomes lower, and this can explain

The above-mentioned behaviour of the thermal conductivity is clearly observable for the measurement at 10°C and 25°C, while a less evident variation of the slope in the evolution of λ over time occurs at 40° C.

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This fact can be explained considering that the internal pressure is higher for a high testing temperature, even in pristine VIPs. The internal pressure in the 40 months aged VIP is higher at 40°C than at 10°C

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(Sprengard et al., 2017 [30]) and, as a consequence, λg is higher.

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4. Performance at the building component scale In real building applications, the VIP insulating layer is usually located inside a multilayer structure.

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Therefore, the variability of its centre of panel (COP) thermal conductivity with the working temperatures influences the overall energy performance of the building envelope component. In order to study the

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impact of the variation of λCOP, due to the working temperature at the building component scale, the thermal behaviour of a roof in which a VIP layer had been introduced was analysed through numerical dynamic heat transfer simulations, performed by means of WUFI® Pro software [42]. A pitched roof was selected as a case study, considering that it can be subjected to higher temperature variations than a vertical wall, and the effect on the variation on the thermal conductivity should, therefore, be more relevant. In some cases, referred to a single room in attic space, the estimated peak demand could be

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significantly underestimated when the temperature dependent thermal conductivity is not accounted for a VIP insulated roof component. However, the heat loss and gain through a roof component generally account for a limited part of the total heat losses and gains which occur through the building envelope. In addition, the whole energy performance of a building is influenced by other factors including ventilation, infiltration, solar radiation, internal heat, and so on.

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The selected component that was analysed was a timber frame pitched roof. The selected roof has already been used to test different retrofitting solutions for an attic space by Elarga et al. 2017 [43] and Fantucci et al. 2017 [44]. The roof is located in San Francesco al Campo (Torino – Italy), and it is characterised by a south - south - west orientation and 28° slope (Figures 5(a) and 5(b)).

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Simulations were carried out on two different design alternatives (Figure 5(c)). The monitored one (configuration A) is composed, from the inside to the outside, of: 1) a gypsum board layer, 2) an extruded polystyrene XPS layer, 3) a Vacuum Insulation Panel, 4) a slightly ventilated air layer and 5) clay roof tiles. In the second one (configuration B), the position of the VIP and the XPS layers are reversed so as to analyse the influence of the position of the VIP layer. The thermal and physical properties are listed in

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Table 4.

Material

1 2 3 4 5

Gypsum board XPS VIP Air layer Roof tiles

t (mm) 9.5 30 10 100 30

ρ (kg/m3) 800 32 200 1.2 1700

λ (W/mK) 0.200 0.036 0.005* 0.700

C (J/kgK) 1000 1500 800 1020 840

α (-) 0.55

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Layer

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Table 4: The roof layers from inside to outside (configuration A). (*data retrieved from [45])

4.1 Numerical simulations

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The dynamic heat transfer simulations were carried out using WUFI® Pro. The software allows simulations that include the dependence of the thermal conductivity to be performed as a function of the temperature and moisture content (in this study, the moisture based analysis was disabled). The data collected during the experimental campaign (32 months aged VIP) were used to validate the simulation model. The experimentally determined polynomial fitting curve used to model the temperature-dependent variation of the thermal conductivity in the WUFI® Pro simulations is reported in Equation 4. Moreover,

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the fixed thermal conductivity adopted for the simulations was the one that was measured at 10°C (λ10) at month 32 (Table 3). (4) The roof was modelled as a simplified 1D multilayer roof structure, and the effect of thermal bridges and 2D heat transfer phenomena were not taken into account, as was the water vapour transport phenomena.

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Heating season (15th October- 15th April): ϑ = 20 °C

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Cooling season (15th April- 15th October): ϑ = 25 °C.

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The indoor climate conditions defined in EN 15026:2007 [46] were assumed for the analysis:

The weather data for Torino implemented in the WUFI® 6.0 database (Torino - year 2004) were used for the outdoor climate.

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Simulations were performed with a time-step of 15 min, while the “fine grid” option was used for the spatial discretisation.

The internal surface heat transfer coefficient (hi) was assumed equal to 5.88 W/m2K, according to EN ISO 6946:2007 [47], while a wind dependent heat transfer coefficient was considered for the outside layer (he)

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according to Equation 5:

he  (hc  hr )  (a  v)

(5)

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where: hc is the convective heat transfer coefficient, which was assumed to be 4.5 W/m2K, hr is the radiative heat transfer coefficient, assumed equal to 6.5 W/m2K, a is the wind coefficient, which was

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taken equal to 1.6 Ws/m3K for windward conditions and 0.33 Ws/m3K for leeward conditions, respectively, while v is the wind velocity (m/s).

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The numerical model was validated through a comparison with the temperatures measured at the boundaries of the VIP (fifteen days of measurements – from Sept. 24th to Oct. 8th 2016). Figure 6 shows

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the measured and the simulated temperatures at interface 2-3 (between the VIP and the XPS board, see Table 3), together with the corresponding Root Mean Square Error - RMSE (between the VIP and the XPS board). Only three days of comparison are presented in Figure 6 in order to improve its readability. However, the RMSE values are related to the whole measurement period. As can be seen in Figure 6, the model that takes into account the temperature dependence of the thermal conductivity makes it possible to better fit the measured data.

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4.2. Results analysis and discussion In order to verify the impact of the dependency of thermal conductivity on the average temperature of the VIP, a set of simulations of the roof was performed with the validated numerical model. In short, the frequency distributions of thermal conductivity for the two roof configurations were analysed for a typical year. Figures 7(a) and 7(b) show the box plot of the average temperatures reached by the VIP for each month,

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while the corresponding VIP thermal conductivity values are shown in Figures 8(a) and 8(b).

The results pointed out that a proper protection of the VIP, by means of external insulation layers (configuration B), can significantly mitigate the effects of exposure to high temperatures in summer. As it is possible to see:

For configuration A, the VIP reaches higher temperatures than 32°C during summer (June-

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•

August) for 25% of the time (third quartile), with peak values of ~ 45°C (upper whisker), while in configuration B (VIP below the XPS layer), the maximum temperature reached is ~ 36°C (upper whisker); •

The variation in thermal conductivity, from the hottest summer peak to the coldest winter peak,

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can span from ~ 0.0050 to 0.0066 W/mK, with a variation of ~ 32% for configuration A. For

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configuration B, the thermal conductivity changes from 0.00520 to 0.00605 W/mK, with a decrease in the peak temperature of ~ 9°C, with respect to configuration A. This reduction of temperature can lead to a

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significant and positive impact on VIP durability. In fact, the VIP is less exposed to the high temperatures that are responsible for accelerating the gas permeation phenomena through the metallized envelope layer

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[48].

The monthly energy gains and losses across the roof component (configuration A) were assessed

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considering temperature-dependent thermal conductivity and constant thermal conductivity, respectively. Comparing the results of these two calculations (see Figure 9 and Figure 10), it emerged that: •

If a constant thermal conductivity is assumed for the energy calculation in winter, the heat losses

are slightly underestimated. Nevertheless, the maximum difference between the heat losses assessed considering a constant thermal conductivity and those obtained considering a value that depended on the temperature (ΔQlosses) is ~ 3 %, and it can be considered negligible;

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•

An underestimation of the monthly heat energy gains occurs in summer, with a maximum

difference of ~ 15% in July and August (Figure 9), while a difference of up to 21% of the maximum heat gains (Figure 10) was observed in summer. The proper evaluation of the peak temperature of a ceiling has a direct impact on the indoor comfort conditions. In fact, the ceiling temperature in an attic space is crucial to determine the mean radiant temperature of the room, and hence of the operative temperature. Figure 11 shows the effect of the

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different values of the VIP thermal conductivity on the interior surface temperature (ceiling) on the 11th August, which represent the hottest day of the year. It is possible to see that if a constant value of thermal conductivity (λ10) is considered, the peak ceiling temperature is underestimated by ~ 0.32 °C, compared to the case with a λ = f(ϑ), while during the night and in the coldest hours, the results are in good agreement

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with the ones calculated with the temperature-dependent thermal conductivity.

The difference in the calculation of the peak ceiling temperature is marginal, but this value is strictly dependent on the assumed indoor surface heat transfer coefficient. This value could be very different from the assumed hi = 5.88 W/m2K (EN ISO 6946:2017 [47]), especially for a transient condition. The lower the hi is, the higher the indoor surface temperature and the difference between the two simulation

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methods.

5. Conclusions

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The influence of combining the ageing effect and average temperature on the thermal conductivity of fumed silica based VIPs has been analysed in the present study. A preliminary experimental campaign

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was carried out at the material level. Moreover, in order to understand the implications, in terms of loss of performances, further analyses were performed on a roof using a numerical model at the building

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component level.

Laboratory analyses were carried out to measure the variations in the thermal conductivity due to: i) the working temperature and ii) the ageing stage. The results demonstrate that: •

A significant variation was observed in the thermal conductivity over the first 20 months (~6%

of an increment for all the tested temperatures); •

The variation of the thermal conductivity (due to the temperature) measured on a sample with 32

months of ageing was about 53%, that is, it passed from an average tested temperature of -7.5°C to 55°C.

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•

The contribution of the gaseous conduction (λg) cannot be considered to be completely

suppressed. In fact, the study demonstrates that a significant increment in the thermal conductivity is observable for higher temperatures than 27.5° C; •

After 40 months, the increase in thermal conductivity ranged from between 8% (λ10) and 10%

(λ40), with respect to the pristine λ value, thus underlining that the influence of temperature on thermal conductivity is more significant for aged VIPs.

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The analyses at a building component level were carried out through numerical simulations on a case study that was considered to represent a possible retrofitting intervention of a pitched roof using a VIP layer. The variation in thermal conductivity resulting from changes in the temperature was accounted for (data measured in the lab were used as inputs):

The working temperature range, in the case of a pitched roof, has been found to be quite severe

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•

(between 3°C during winter and 45°C during summer) and may negatively influence both the performances of the VIP and its useful service life; •

In summer, if the variation of λ with the temperature is not taken into account, a non-negligible

underestimation of both the λ-values and the monthly heat energy gains is possible (up to 27% and 15%

The effect of temperature on the λ-value of VIPs can be considered negligible for heat losses

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•

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respectively). Moreover, a ~21% underestimation of the maximum summer heat gains was observed;

during the winter season in Torino. However, this effect could be higher in a colder climate.

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The present work has proved the importance of adequately considering the variation in the thermal conductivity of a VIP according to the temperature, especially when severe boundary conditions occur

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(after the change of the slope in Figure 2). Apart from a detrimental influence on the λ-value, these severe boundary conditions may also have a significant impact on the service life of a panel. Therefore, effective

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solutions are needed to mitigate the exposure of VIPs, for example by adopting additional insulating layers on the side characterised by the highest temperature variations. The protection of VIPs with an additional external insulating layer represents a general practical indication/guideline for the design of durable and well-performing insulating solutions that make use of VIPs. In fact, the results have demonstrated that configuration B (in which the VIP panel is more protected by external insulation layers) determines an increment in the performance (a reduction in thermal conductivity) of ~ 9% during the summer peak period as well as a reduction in the average

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temperature of the VIPs of up to 9°C, and also presents a significant and positive impact on VIP durability. As a future work, parametrical investigations at building level will be performed to identify the influence of the temperature-dependent thermal conductivity on the whole energy performance.

Acknowledgements

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The authors would like to thank Fraunhofer IBP for allowing the use of the WUFI® Pro free software license, and ENEA (Italian National Agency for New Technologies, Energy and Sustainable Economic Development) for supporting this research.

[1]

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Prediction of VIP in Building Applications (2005).

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Figure 1. Samples: (a) VIP 10 mm thick; (b) FS VIP core material.

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Figure 2. Measured thermal conductivity of VIP (λ(ϑi)VIP) as a function of the cube of average absolute

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temperature ϑavg [K].

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Figure 3. Measured λ(ϑi)core for the FS sample, and Δλ(ϑi) calculated as the difference between the λ(ϑi)core

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and the λ(ϑ0)core, as a function of the cube of average absolute temperature ϑavg [K].

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Figure 4. Evolution of the measured thermal conductivity over ageing time for different average

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temperature (λ10, λ25, λ40).

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Figure 5. (a) VIP mounted in roof component; (b) Roof insulation assembly; (c) Roof sections (Configurations A and B)

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Figure 6. Comparison between measured and simulated results. λ = f(ϑ) (temperature dependent thermal conductivity). λ10 (constant thermal conductivity measured at 10°C). RMSE values were calculated for the

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period 24/09/17 – 08/10/17

Figure 7. Box plot of the VIP average temperature (a) Configuration A (VIP above the XPS layer); (b) Configuration B (VIP below the XPS layer). Q1: first quartile, m: median value, Q3: third quartile.

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Figure 8. Box plot of the VIP actual thermal conductivity (temperature dependent) (a) Configuration A (VIP above the XPS layer); (b) Configuration B (VIP below the XPS layer). Q1: first quartile, m: median

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value, Q3: third quartile.

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roof component.

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Figure 9. Monthly energy heat gains (positive values) and heat energy losses (negative values) across the

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Figure 10. Monthly maximum heat gains across the roof component.

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Figure 11. Indoor surface temperature profile of 11 th August 2017

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