Investigation on the optical and energy performances of different kinds of monolithic aerogel glazing systems

Applied Energy 261 (2020) 114487

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Investigation on the optical and energy performances of different kinds of monolithic aerogel glazing systems

T

Yang Liua,b, Lin Lub, , Youming Chena, , Bin Luc ⁎

⁎

a

College of Civil Engineering, Hunan University, Changsha, Hunan 410082, China Department of Building Services Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong Special Administrative Region c College of Materials Science and Engineering, Central South University, Changsha 410083, China b

HIGHLIGHTS

solar extinction coefficient of monolithic aerogel is newly calculated. • The energy performances of different aerogel glazing systems are simulated. • The has greater influence than diameter on the solar extinction coefficient. • Porosity • Aerogel with small nanoparticle and low porosity can save more energy in Hong Kong. ARTICLE INFO

ABSTRACT

Keywords: Mie scattering Solar extinction coefficient Solar radiation Energy performance Aerogel glazing system

Aerogel glazing system is an advanced energy-efficient glazing system designed to reduce the building energy consumption. However, there is no study focused on the energy performances of aerogel glazing systems filled with different aerogels. To analyse the energy performance, the solar extinction coefficient is an indispensable parameter, which is unknown yet. In this research, the solar extinction coefficient is calculated by Mie scattering and Monte Carlo method. The spectral distribution of solar irradiance is taken into account. The influences of porosity and nano-particle’s size are discussed. Then, the solar heat gain coefficients of different aerogel glazing systems versus incidence angle are calculated. Finally, a dynamic heat transfer model is used to simulate the energy performances of different aerogel glazing systems. A case study is carried out for Hong Kong. The results indicated that the porosity of monolithic aerogel has greater influence than the diameter, and the reciprocal effect between the porosity and the diameter is negligible. It is also figured that aerogel with small nano-particle and low porosity will lead to a better energy conservation performance in cooling dominated region.

1. Introduction It is always declared that up to 40% of the total primary energy is consumed by buildings, which exceeds the consumption of industry and transportation parts in developed countries [1]. The proportion is increasing steadily due to the higher expectations for indoor comfort and the rapid urbanization. HVAC (heating, ventilation and air-conditioning) system expends over 40% of the building energy consumption [2], and a large amount is utilized to cover the load caused by heat transfer through building envelopes. Windows are the weakest point of thermal insulation, which are responsible for about 40% of the heat gain or loss through building envelopes. Optimizing the energy performance of windows is regarded as a promising way to reduce the energy consumption of HVAC system and energy conservation,

⁎

therefore becomes a hot research area with many researchers involved in. Aerogel glazing system (AGS) is an advanced energy-efficient glazing system designed to reduce the heat transfer through window. The structure of AGS is similar with the double-glazing system where the air-gap between double glazing system is filled with aerogel. It draws many researchers’ attentions due to the aerogel. Aerogel is regarded as one of the most promising materials in the 21st century. The thermal conductivity of aerogel can be as low as 0.013 W/(m·K), resulting from a well-balanced relationship among the low solid conductivity, the low gaseous conductivity, and the low radiative infrared transmission [3]. Aerogel is also a solid material with high visible transmittance of about 90%. Some light will be scattered when transmitting through the aerogel, so aerogel is called blue smoke as well.

Corresponding authors. E-mail addresses: [email protected] (L. Lu), [email protected] (Y. Chen).

https://doi.org/10.1016/j.apenergy.2019.114487 Received 10 September 2019; Received in revised form 28 December 2019; Accepted 31 December 2019 Available online 11 January 2020 0306-2619/ © 2020 Elsevier Ltd. All rights reserved.

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Nomenclature an bn d D0 Di Es h i k K L m n Pn

Q R V(λ) z

expansion coefficients Mie coefficients diameter of silica nano-particle (nm) cores distribution probability directional growth probability solar spectral irradiance function (W/(m2·nm)) convective heat transfer coefficient (W/(m2·K)) imaginary unit extinction coefficient (/mm) optical coefficient (/mm) optical path (mm) complex refractive index index of refraction inward flowing fraction

extinction or scattering cross section (mm2) thermal resistance (m2·K/W) photopic response function of the eye size parameter calculated by πd/λ

Greek symbols α τ λ ρ

absorptance transmittance Wavelength (nm) volume fraction of the generation phase

Subscripts s v

Besides, aerogel is one of the lightest solid material in the world because the nano-pores occupy a volume of more than 90% of the total volume. The density of monolithic aerogel is about 80 kg/m3 [4] and the specific surface area is up to l000 m2/g [5]. So aerogel can be used as absorbing material for rapidly oil-water separation [6] and emulsions separation [7]. Moreover, aerogel is also nontoxic, durable, low flammable, and air-permeable [8]. Garrido et al. [9] carried out the economic and energy life cycle assessment of aerogel-based thermal renders. It is concluded that renders with commercial aerogel are the least expensive. De Guinoa et al. [10] investigated the environmental impact of the aerogel-based panel and the results indicated that the use of the aerogel-based panel in a location with higher heating degree-days leads to better environmental performances, mainly in terms of global warming. Considering so many merits of aerogel, aerogel glazing system is regarded as a promising solution to energy conservation and greenhouse gas emission reduction. Some researches investigate the thermal and optical performance of AGS by experiments. Buratti et al. [11] measured the main optical characteristics of the samples, and then the light transmittance and solar factor are calculated. The results showed that the performance of monolithic aerogel is the best. Yang et al. [12] experiment the thermal and optical performance of 8 aerogel glazing samples. The results showed the envelope heat gain was reduced by 31% by replacing the single glazing with aerogel glazing at skylight in Guangdong. Cotana et al. [13] carried out an in-field experiment to analyze the thermalenergy, lighting and acoustic performance of aerogel glazing system. It is indicated that aerogel glazing system is an innovative solution for energy saving in winter. Lv et al. [14] measured the spectral transmittance and reflectivity of the different aerogel glazing system and discussed the influences of filling thickness and granule’s size. Moretti et al. [15] measured the thermal performances of different AGS under different weather conditions. Through experimental method, it is easy to figure out the thermal and optical performance of the determined sample. But it is hard and time-consuming to carry out the energy performances of different aerogel glazing systems. Some studies modelled the energy performance of AGS by building simulation software, such as EnergyPlus. Huang et al. [16,17] simulated the energy and visual performance of the monolithic aerogel glazing system in Hong Kong by two building energy simulation programs namely Radiance and EnergyPlus. The results showed that the energy consumption of the HVAC system was reduced by 4–7% compared with conventional single clear glazing. Ihara et al. [18] simulated the building energy consumption used granular aerogel glazing systems at spandrels through a simplified model. Granular aerogel glazing systems have the potential to become a solution in different climates. Gao et al. [19] simulated the thermal and energy performance of AGSs and calculated the payback time. It indicated that the aerogel glazing system

solar transmittance visible transmittance

can reduce about 21% reduction energy consumptions compared to the double-glazing systems. But aerogel is a new material discovered in 1930s by Kistler [20]. Some basic parameters, such as solar extinction coefficient, are unknown yet. A simplified model is utilized to model the energy performance. Only two parameters, thermal conductivity (K value or U value) and solar heat gain coefficient (SHGC), are used to simulate their energy performance. The SHGC is obtained at normal incidence, which should vary with the incidence angle. However, the incidence angle of solar radiation is barely vertical for the windows of most buildings in practice. For a normal 3 mm glass, the transmittance could be changed from 88% to 0% while the incident angle ranging from 0° to 90° [21]. What’s more, it’s also hard to calculate the SHGC of AGS. To obtain the SHGC, it is needed to calculate the transmittance of the AGS and the absorptance of each layer first. But the absorptance and transmittance are influenced by the solar extinction coefficient which is unknown yet. In a word, K-SC model is not suitable for simulating the thermal and energy performance of AGSs hourly. To model the energy performance of AGS accurately, Chen et al. [22] developed a dynamic heat transfer model and an optical model to predict the total heat gain or loss through the aerogel glazing system in a whole year. The results show that aerogel glazing system is suitable for buildings in Cold Region and in the south and north orientations of Hot-Summer Cold-Winter Region. Zhou et al. [23] proposed a surrogate model based on machine-learning to predict the energy performance of AGS. But a lot of experimental data are needed to train the model. For windows, optical performance and thermal performance influence the energy performance together. The solar extinction coefficient is a significant parameter that influences the optical performance (transmittance and absorptance), and the thermal conductivity influences the thermal performance (heat transfer). There are many studies focused on the thermal conductivity. The mechanism of heat transfer has been studied. Bi et al. [24] proposed a modified model to predict the effective thermal conductivity of aerogel the superlattice nanowire model. Zhu et al. [25] used the gray Boltzmann transport equation and Laplace heat conduction equation to predict the thermal conductivity of aerogel solid backbone. Guo et al. [26] proposed a theoretical model for gas-contributed thermal conductivity. The results indicated that the coupling effect of local solid-gas interaction is in a dominant position. Zhao et al. [27] developed a model to simulate the spectral transmittance of monolithic aerogel over the wavelength range from 1 μm to 25 μm, and then predict the radiative thermal conductivity. Lu et al. [28] measured the spectral transmittance of the monolithic aerogel in near infrared region (2.3–45 μm), and calculated the radiative thermal conductivity discussed. The impact of temperature is also discussed. Yu et al. [29,30] used T matrix code to simulate the optical properties of opacified aerogel over the wavelength range from 1 μm to 8 μm. 2

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However, there are a few papers focused on the solar extinction coefficient. Liu et al. [31] developed an experimental method to determine the solar extinction coefficient of granular aerogel layer from the experimental data. The results indicated that the aerogel layer’s solar extinction coefficient is influenced by weather conditions. Lv et al. [14] measured the spectral transmittance and reflectivity of the different aerogel glazing system, but solar extinction coefficient of monolithic aerogel is not calculated. Some papers [27–30] calculated the infrared radiative transmittance when calculated the thermal conductivity. There is an intersection with our research. However, they focused on the property of infrared ray. The influence of spectral distribution of solar irradiance is not discussed in their studies. Besides, the property of visible light is not discussed, which takes more than 45% of solar radiation. As a consequence, there is no study investigated the energy performances of AGS filled with different kinds of aerogels, since no paper studied the optical performance of monolithic aerogel. The influences of the porosity and the nano-particle’s size on energy performance are not discussed neither. To analyse the energy performances of different AGS accurately, it is needed to calculate the solar extinction coefficient of aerogel first, which is unknow yet. In this study, the solar extinction coefficients of different aerogels are calculated by Mie scattering and Monte Carlo method. The spectral distribution of solar irradiance is taken into account. Then, the solar heat gain coefficients versus incidence angle are predicted and the influences of porosity and nano-particle’s size are discussed. Once the solar extinction coefficient is fixed, the energy performances of AGS filled with different aerogels can be simulated by the dynamic heat transfer model. A case study for Hong Kong is carried out. The energy performances of aerogel glazing systems filled with different aerogels are simulated. The results indicated that the aerogel with small nanoparticle and low porosity will lead to a better energy conservation performance in Hong Kong.

Snell’s Law, and the extinction coefficient will influence the transmittance according to the Beer-Bouguer’s Law. These two constants are functions of wavelength. In this research, the refractive index of silica [32] is calculated by Eq. (2),

n2

1=

2

0.6961663 2 + 0.06840432

2

0.4079426 2 + 0.11624142

0.8974794 2 9.8961612

2

where λ is the wavelength, nm. The extinction coefficient of silica is calculated from the spectral transmittance of silica. The spectral transmittance of silica is measured by UH4150 Spectrophotometer produced by Hitachi as shown in Fig. 2. The measured range is from 300 nm to 2500 nm which takes more than 97.7% of the solar irradiance. The interval is 2 nm. The photometric accuracy of transmittance is less than ± 0.3%. The wavelength accuracy is less than ± 0.2 nm in UV and visible regions, less than ± 1.0 nm in near infrared region. The spectral extinction coefficient of silica is calculated according to Beer-Bouguer’s Law and interface energy balance method [31]. Interface energy balance method is widely used in China to simulate the optical performance of multi-layer transparent system, such as double glazing. 2.2. Mie scattering Given the scattering phenomena happening in the aerogel, the optical properties of the silica particle are different from bulk silica. In general, there are two solutions of electromagnetic scattering, i.e. Mie theory [33] and Rayleigh approximation [34]. For particle smaller than λ/10, Rayleigh scattering can be utilized. When the particle size d increases to λ or greater, Mie scattering can be applied. Bohren et al. [33] has shown that when the particle size is much smaller than the incident wavelength, the results derived by Rayleigh approximation and the one by Mie theory are equivalent. Because of the broader scope of application of Mie scattering, Mie scattering is selected to calculate the optical properties of the nano-particle. The Mie scattering is an analytical solution to Maxwell’s equations to describe the scattering of an electromagnetic plane wave by a homogeneous sphere. The scattering and

2. Methodology In this study, Monte Carlo method is used to calculate the spectral transmittance of the monolithic aerogel. The random 3-D porous structure of aerogel is generated by quartet structure generation set method, and the properties of the nano-particles which compose the aerogel are calculated by Mie scattering. The calculated spectral transmittance is compared with the experimental results to verify the model. Further, the other optical properties (such as solar extinction coefficient and solar heat gain coefficient) are calculated according to the solar irradiance distribution. The influences of the porosity and the nano-particle’s size on the solar extinction coefficient are also discussed in this paper. Finally, the solar heat gain coefficients of the aerogel glazing systems with different types of aerogels are calculated. The relationships among the solar heat gain coefficient, visible transmittance and the solar extinction coefficient are revealed. The energy performances of the AGS with different aerogel are also simulated by the dynamic heat transfer model to figure out the optimal structure of aerogel. The detailed flowchart is given in Fig. 1. 2.1. Complex refractive index The complex refractive index of the silica is a significant input of this model which dramatically influences the optical properties of the material. As mentioned before, the aerogel is composed of silica nanoparticles. The complex refractive index of the silica is used as the input in this study, which is calculated by Eq. (1)

m = n + ki

(2)

(1)

where n is the refractive index, k is the extinction coefficient, i is an imaginary unit which satisfies i2 = − 1. In general, the refractive index will influence the reflectance of the material according to the

Fig. 1. Flowchart of the research. 3

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Fig. 2. The Spectrophotometer UH4150.

extinction cross sections of the nano-particle can be expressed as [35],

Qext =

2 z2 2 z2

Qsca =

N

(2n + 1) Re (an + bn) n= 1

(3) Fig. 3. Flowchart of the Quartet Structure Generation Set.

N

(2n + 1) Re (|an |2 + |bn |2 ) n= 1

(4)

where K is the optical coefficient, such as extinction coefficient and scattering coefficient, V is the volume of the nano-particle.

where Qext and Qsca is the extinction cross section and scattering cross section, the an and bn are the expansion coefficients and the Mie coefficients expressed in terms of the Riccatty-Bessel functions, z is the size parameter calculated by πd/λ. The absorption cross section is expressed as,

Qabs = Qext

2.3. Quartet structure generation set Before operating the Monte Carlo method, it is needed to construct the random structure of the aerogel. In this research, quartet structure generation set (QSGS) [36] is used to construct the structure of aerogel. Four parameters are used to control the generation process, which are cores distribution probability (D0), directional growth probability (Di), volume fraction of the generation phase (ρ) and phase interaction growth probability (P). The phase interaction growth probability P is out of concern in this research because there are only two phases in the aerogel, i.e. gas and solid. The flowchart of the QSGS is shown in Fig. 3. The length of the 3D cubic grid is 100d nm, where d is the diameter of the nano-particle. In the initialization of the generation, constants D0 and Di (i = surface, edge and vertex) should be fixed. The 26 growth directions are shown in Fig. 4. The black ball in the centre is the growth core; the 6 blue balls in the middle of six surfaces mean the first 6 growth directions, Dsurface; the 12 yellow balls on the edge of the cube mean the next 12 growth directions, Dedge; and the 8 red balls at the vertex of the cube mean the final 8 growth directions, Dvertex. So, there are 26 growth directions totally. The porous structure of the aerogel will be generated through the following algorithm: (1) Some cores are located in the grid stochastically according to the core distribution probability D0. The core distribution probability is compared with a random number (0, 1) at each node. If the core distribution probability is greater than the random number, a core will locate at this node. Note D0 is no greater than the volume fraction. (2) The directional growth probability Di is compared with a random number (0, 1) to determine whether the core will grow along this direction. If Di is greater than the random number,

(5)

Qsca

The an and bn in Eqs. (3) and (4) are expressed as follows,

an =

bn =

m n (mz ) m n (mz )

n (z )

n (z )

n (mz )

n (z )

n (z )

n (mz )

m n (z ) m n (z )

n (mz )

n (mz )

n (z )

n (mz )

n (z )

n (mz )

(6) (7)

where ψn and ξn are the Riccatty-Bessel functions. n (z )

=

z [Jn+ 1/2 (z ) + iYn + 1/2 (z )] 2

(8)

n (z )

=

z Jn + 1/2 (z ) 2

(9)

where Jn+1/2(z) is the half-integer-order Bessel function of the first kind, Yn+1/2(z) is the half-integer-order Bessel function of the second kind. It is indicated that most of the terms are a function of z, indicating Mie scattering is highly dependent on the size parameter. When d is smaller than λ, the Mie scattering can be simplified to Rayleigh scattering. The code of Mie scattering in MATLAB is proposed by Mätzler [35]. Once the cross sections are fixed, the spectral coefficients are expressed as Eq. (10),

K = Q /V

(10) 4

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aerogel. The spectral-average solar transmittance of the monolithic aerogel is expressed as Eq. (11) and the spectral-average visible transmittance of the monolithic aerogel is expressed as Eq. (12) s

=

v

=

( ) Es ( ) d Es ( ) d

(11)

( ) Es ( ) V ( ) d Es ( ) V ( ) d

(12)

where τ is the transmittance, Es(λ) is the solar spectral irradiance function, V(λ) is the photopic response function of the eye [38], and subscripts s and v mean the solar and visible transmittance. Finally, the solar extinction coefficient of the monolithic aerogel is derived from the spectral-average solar transmittance. Since the refractive index of aerogel is similar with air, the multi-reflection phenomena happened in the aerogel are negligible. The solar extinction coefficient is expressed as Eq. (13),

ks =

Fig. 4. The 26 growth directions of each core.

(13)

ln s / L

where L is the optical path. The solar extinction coefficient of aerogel is the final object of our research. Once the solar extinction coefficient of aerogel is known, the energy performance of AGS can be analysed and the aerogel can be optimized according to the energy performance.

a new core will grow along this direction and locate at the node. (3) If the volume fraction is less than the threshold value, repeat step (2) until the volume fraction satisfies the target. Fig. 5 illustrates a sample generated by QSGS. The length of the grid are 700 nm and the volume fraction of the aerogel is 0.1. In this case, D0 = 0.06, Dsurface = 0.1, Dedge = 0.05 and Dvertex = 0.025. By setting different value of the D0 and Di, the microstructure will be changed. The anisotropic microstructure can also be simulated by setting different values in different directions.

2.5. Evaluation criteria 2.5.1. Solar heat gain coefficient Due to the weak mechanical strength of monolithic aerogel pane, the aerogel is always filled in the cavity between the double-glazing which is called aerogel glazing system (AGS) [1,4,16]. For the fenestration, the transmitted irradiance is absorbed by interior zone surfaces and, therefore, contributing to the zone heat balance. As for the absorbed part, a fraction of the absorbed irradiance will release inward, and the other part will release outward. The energy performance of window is a joint result of the transmittance, absorptance and thermal resistance. If a simple process is required, the solar heat gain coefficient (SHGC) is selected to indicate the energy performance. The SHGC is the fraction of incident solar radiation admitted through a window, both directly transmitted and absorbed and subsequently released inward. SHGC is expressed as a number between 0 and 1. The lower a window's SHGC is, the less solar heat it transmits. However, the required energy

2.4. Monte Carlo method After knowing the properties of the silica particle and the structure of aerogel, it is available to run the Monte Carlo (MC) method to calculate the transmittance of aerogel (simulated grid). The MC method is of advantages in calculating radiation transfer in 3D porous medium, by which the scattering and absorption in the material can be captured. Fig. 6 shows the flowchart of the MC method. A beam of radiation is emitted from a random place (decided by two random numbers) of a fixed surface (i.e. surface x = 0) with a random direction vector. Then, trace the radiation and figure out whether there is an intersection with the silica particles or the boundary. If there is an intersection with the boundary, it will be assumed that this beam of radiation is transmitted through the material. If there is an intersection with the nano-particle, a random number (0 ≤ RN ≤ 1) will be compared with the rate of scattering and absorptance to determine whether this beam of radiation is scattered, absorbed or transmitted. If RN is smaller than the transmittance of the nano-particle (0 ≤ RN ≤ τnano), this beam of radiation will transmit through the nano-particle; If RN is smaller than the sum of transmittance and the rate of scattering and greater than the transmittance (τnano < RN ≤ τnano+ɛnano), this beam of radiation will be scattered; If RN is greater than the sum of transmittance and the rate of scattering (τnano + ɛnano < RN ≤ 1), this beam of radiation will be absorbed by the nano-particle. In addition, if this beam of radiation transmitted through the nano-particle, this beam of radiation will move along the original direction vector. If this beam of radiation is scattered, this beam of radiation will move along the new direction vector. The new direction vector is calculated according to Henyey-Greenstein phase function [37]. Finally, count the number of the radiation that transmitted through the simulated grid and absorbed by the nanoparticles. The number of transmitted radiation (absorbed) divided by the total radiation is the final transmittance (absorptance) of the aerogel (simulated grid). After knowing the spectral transmittance of the monolithic aerogel, it is available to calculate the other optical properties of the monolithic

Fig. 5. The porous structure of the silica aerogel. 5

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Fig. 6. The flowchart of the Monte Carlo method.

performances of the windows are different in different climates and different orientations. For example, the high SHGC can be utilised to provide cost and pollution free heat from the sun in cold climate such as northern Europe. But, the high SHGC will also add large amounts of unwanted heat to the room in hot climate such as Hong Kong. In consequence, the optimal SHGC is not a fixed value which should depend on the climates and the orientations. The SHGC of AGS is expressed as Eq. (14),

3

SHGC =

+

n Pn n=1

(14)

where αn is absorptance of layer n, and Pn is the inward flowing fraction of layer n. The transmittance of the AGS and the absorptance of each layer are calculated by interface energy balance method [31]. The inward flowing fraction of layer n is defined as the sum of the resistances up to a given node divided by the sum of all the resistances which expressed as Eq. (15) [39],

6

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Pn =

n i=1

agreements are obtained though there are some errors at the turning points. These errors may be caused by the impurities of the material. It is also noticed that the curve of the calculated results is fluctuant, which is caused by the MC method. The MC method is a statistical method, therefore the calculated results fluctuated around the true value. Our research aims to obtain the solar properties of aerogel which are influenced by the solar spectral irradiance. However, the interval of measurement and interval of the solar spectral irradiance do not match. The interval of measurement is 2 nm and the intervals of solar spectral irradiance are 1 nm (wavelength shorter than 1700 nm) and 5 nm (wavelength longer than 1700 nm). As a consequence, there are more points plotted in shorter wavelength range. The curve in long wavelength seems smoother than that in short wavelength. As a result, the solar transmittance of the 10 mm-thick aerogel sample is about 89.6% and the visible transmittance is 90.9% approximately. The solar extinction coefficient of the aerogel is 0.0108/ mm and the visible extinction coefficient is 0.00960/mm. The solar extinction coefficient is a lumped parameter which can be used in calculating the angular solar transmittance and absorptance of aerogel glazing system with different thickness of aerogel. Furthermore, the angular transmittance and absorptance can be used in the dynamic heat transfer model to simulate the energy performances of aerogel glazing system with different thicknesses of aerogel under different climates [22].

Ri (15)

Rtotal

where Rtotal is the total thermal resistance of the AGS, Ri is the thermal resistance of the layer i. The total thermal resistance of the AGS is expressed as Eq. (16)

Rtotal =

1 1 1 = + + K hi ho

3

Ri 1

(16)

where hi and ho are the convective heat transfer coefficient at the interior and exterior surface of window. 2.5.2. Dynamic heat transfer model If a precise result is required, the solar extinction coefficient can be utilized. The solar extinction coefficient is used to calculate the angular absorptance of each layer (according to Beer-Bouguer’s Law) and the refractive index is used to calculate the angular reflectance (according to Snell’s Law). Then, interface energy balance is applied to simulate the angular transmittance and absorptance of AGS varied with incidence angle [31]. The angular properties can be used in the dynamic heat transfer model to simulate the hourly energy performance [22]. The dynamic heat transfer model is based on the differential equations of Fourier's law, in which the thermal conductivity, heat convection, solar irradiance and the long-wavelength heat exchange are all taken into account. The influences of porosity and nano-particle’s size on the thermal conductivity and solar extinction coefficient are taken into account as well. The energy performance of AGS filled with different aerogels are simulated.

3.3. The influence of physical property In the above paragraph, a model is proposed to calculate the spectral transmittance of the monolithic aerogel. The calculated results are compared with the experimental results. Good agreements are obtained. According to the solar spectral irradiance, the other optical properties of the aerogel are calculated, such as the solar extinction coefficient and visible extinction coefficient. In this part, the influences of the porosity and the nano-particle’s size on the solar extinction coefficient are discussed. The porosities of the aerogel are 84.9%, 89.9%, 93.8 and 96.9%, separately. The diameters of the nano-particle are 4 nm, 7 nm, 10 nm and 12 nm, separately. The calculated results are illustrated in Fig. 10. It is noticed that the greater the diameter and porosity are, the lower the solar extinction efficient is. As a result, lower solar extinction coefficient will lead to higher transmittance and lower absorptance. Since two parameters influence the solar extinction coefficient of the aerogel, a sensibility analysis is carried out in this part, which is shown in Fig. 11. The influence of the diameter is revealed in Fig. 11(a). The baseline diameter used as a benchmark is 7 nm. Similar trends are shown in Fig. 11(a), which means the porosity almost has no influence

3. Results and discussion 3.1. The property of silica As shown in the Fig. 1, it is needed to obtain the spectral extinction coefficient of silica as input first. The spectral extinction coefficient of silica is derived from the spectral transmittance which is measured by Spectrophotometer UH4150. The spectral transmittance of a 1 mmthick silica sample is measured, and results are shown in Fig. 7. It is noticed that silica has high transmittance at short wavelength and comparatively low transmittance at long wavelength. The spectral extinction coefficient of silica is derived based on Beer-Lambert Law and interface energy balance. 3.2. Experimental validation The thickness of the aerogel sample (as shown in Fig. 8) is 10 mm. The diameter of the nano-particle is about 7 nm and the porosity is 93.8% approximately. So it is referred as D7P938, where D means the diameter of the nano-particle and P means the porosity. The spectral transmittance of aerogel is measured by Spectrophotometer UH4150. The transmittance of aerogel was measured 3 times at different portions. There is no big difference, and the difference is less than 1% during each measurement. The average measured transmittance of aerogel is used in this study. As mentioned before, the thickness of the simulated grid is 100d nm, where d is the diameter of the nano-particle. So, the thickness of the simulated grid is 700 nm, which differs from the aerogel sample. In our research, the spectral extinction coefficient of the simulated grid is calculated according to the Beer-Lambert Law (τ = exp(−kL)) where k is the extinction coefficient and L is the optical path. Since the refractive index of aerogel is similar to air, the multi-reflection phenomena happened in the aerogel are negligible. Then, the spectral transmittances of the 10 mm-thick aerogel are calculated according to the calculated spectral extinction coefficient. The calculated spectral transmittance is compared with the experimental results as shown in Fig. 9. Good

Fig. 7. The spectral transmittance of silica. 7

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Fig. 10. The solar extinction coefficient of monolithic aerogel under different porosities and different particle sizes.

4. Energy performance 4.1. Solar heat gain coefficient From the above paragraph, the solar extinction coefficient of the monolithic aerogel with different porosities and different particle sizes are calculated. So, in this part, the SHGC of the AGS filled with different kinds of aerogel are calculated. The porosities of the aerogel are 84.9%, 89.9%, 93.8 and 96.9%, separately. The diameters of the nano-particle are 4 nm, 7 nm, 10 nm and 12 nm, separately. The properties of the aerogel and glass are listed in Table 1. It is indicated that the diameter of the nano-particle has a slighter influence on the thermal conductivity compared to the porosity [38]. It is also noticed that when the porosity changed from 84.9% to 96.9%, the thermal conductivity changed from 0.01917 W/(m·K) to 0.0233 W/(m·K) [27]. So, the thermal conductivity of the aerogel used in this study is calculated according to Zhao’s research [27]. Besides, temperature is an important parameter that influence the thermal conductivity due to the radiative heat transfer. There is a slight temperature difference when the aerogel glazing system used in architecture. The calculated SHGCs of AGS with different aerogels are shown in Fig. 12. It is found that the lower the diameter and porosity is, the lower the SHGC is. Four typical AGSs (D4P849, D7P899, D10P938 and D12P968) are selected in this part to show the directional properties of the AGS as shown in Fig. 13. It is noticed that the curves show the same trend, and fall sharply after 45°. As shown in Eq. (14), the SHGC is dramatically influenced by the optical properties of AGS, such as the transmittance and absorptance. These two parameters are dramatically determined by the solar extinction coefficient. When the extinction coefficient of glass is fixed, the extinction coefficient is the only parameter that affects the transmittance and absorptance. Here, the relationship among the solar extinction coefficient of aerogel, the SHGC and the visible transmittance are illustrated in Fig. 14. It is noticed that quadratic function relationships exist among the solar heat gain coefficient, visible transmittance and the solar extinction coefficient. Finally, the optimal structure of the aerogel can be selected according to the comprehensive performance of both SHGC and visible transmittance.

Fig. 8. The 10 mm-thick aerogel sample. 1.0 0.9

Transmittance (%)

0.8 0.7 0.6

Visible

0.5

Experiment Calculation

0.4 0.3 300

600

900

1200

1500

1800

2100

2400

Wavelength (nm) Fig. 9. The comparison of the spectral transmittance between the calculated results and experimental results.

when thinking of the influence of the diameter. The solar extinction coefficient decreases by about 75% when the diameter increases by about 70%. But when the diameter decreases by about 40%, the solar extinction coefficient will increase by about 200%. As a consequence, the smaller the diameter is, the greater influence the diameter has. The influence of the porosity is revealed in Fig. 11(b). The baseline porosity used as a benchmark is 89.9%. Similar trends are shown in Fig. 11(b), which means the diameter almost has no influence when thinking of the influence of the porosity. It is noticed that the solar extinction coefficient decreases by about 75% when the porosity increases by about 8% (from 89.9% to 96.9%). As a result, the porosity has greater influence than the diameter on the solar extinction coefficient and the reciprocal effect between the porosity and the diameter is negligible.

4.2. Dynamic heat transfer model The properties of the AGS are listed in Table 1. The aerogel selected in this part are D4P849, D7P899, D10P938 and D12P968, separately. 8

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Fig. 11. The sensibility analysis between the porosity and diameter: (a) Diameter (b) Porosity. Table 1 The properties of the aerogel and glass.

Thickness (mm) Thermal conductivity (W/(m·K)) Refractive index Extinction coefficient (/mm)

Aerogel

Glass

10 0.01917–0.0233 [27] 1.02 \

4 0.75 1.526 0.045

Fig. 13. The SHGCs of different AGSs versus incidence angle.

aerogel sample that provided by manufactory (D7P938) is about 21595.19 Wh/m2. It is noticed that the smaller the size of the nanoparticle and the porosity are, the lower heat will transfer through the AGS. In other words, the small size of nano-particle and porosity will lead to a high solar extinction coefficient and, therefore, block more solar radiation which is the major heat resource in cooling dominated regions such as Hong Kong. Finally, aerogel D4P849 can reduce about 25% heat gain compared to the aerogel sample (D7P938) provided by manufactory. 5. Conclusions

Fig. 12. The SHGC of AGS with different porosities and different diameters.

In this paper, a model is proposed to calculate the solar extinction coefficient of different kinds of aerogel. The influences of the porosity and the nano-particle’s size on the solar extinction coefficient are discussed. Further, the solar heat gain coefficients versus incidence angle are calculated. Finally, a case study for Hong Kong is carried out. The energy performance of AGS filled with different aerogels are simulated. Some conclusions are drawn as follows:

The energy performances of AGS of a typical week in H.K. are simulated (from Sept. 2 to Sept. 8). The weather data of Hong Kong is developed by Dr TT Chow and ALS Chan of the City University of Hong Kong which is also used in EnergyPlus. The AGS is placed horizontally. The indoor temperature is set at 23 °C. The heat gains through AGS with different aerogels are shown in Fig. 15. It is noticed that the energy performance of D4P849 is the best because of the greatest solar extinction coefficient. However, the visible transmittance (45.4%) is also the worst in this case. The total heat gains in this week are 16202.36 Wh/m2, 20761.33 Wh/m2, 22431.55 Wh/m2 and 23084.53 Wh/m2, separately, when the aerogels are D4P849, D7P899, D10P938 and D12P968, separately. The total heat gain of the AGS filled with the

1. The greater the nano-particle diameter and porosity of aerogel are, the lower the solar extinction efficient is. 2. The porosity of aerogel has greater influence than the diameter, and the reciprocal effect between the porosity and the diameter is negligible. 9

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Fig. 14. The relationships among the solar extinction coefficient of aerogel, solar heat gain coefficient and visible transmittance: (a) SHGC (b) Visible transmittance.

Fig. 15. The heat gain through AGS with different aerogel in a week (Sept. 2 to Sept. 8).

3. Aerogel (Diameter: 4 nm, Porosity: 84.9%) with small nano-particle and low porosity will reduce about 25% heat gain compared to the aerogel sample (Diameter: 7 nm, Porosity: 93.8%) in cooling dominated regions such as Hong Kong.

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

The new theoretical model can be employed to estimate the solar extinction coefficient of monolithic aerogel accurately. The research provides a method to achieve the structure optimization of aerogel glazing system under different weather conditions. The results provide a guideline for manufactory to produce the most adaptable aerogel when it is used in windows under different weather conditions, and therefore contributes to the energy conservation and greenhouse gas emission reduction.

Acknowledgement The authors would like to express their gratitude to the National Natural Science Foundation of China (No. 51678227), the China National Key R&D Program during the 13th Five-year Plan Period (Grant No. 2017YFC0702201) and Mainland University Joint Supervision Scheme (G-SB0N) for their financial support and Hunan Shangyifeng Advanced Material Technology Co., Ltd. for providing the aerogel sample.

CRediT authorship contribution statement Yang Liu: Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing - original draft, Visualization. Lin Lu: Resources, Supervision, Project administration, Funding acquisition. Youming Chen: Conceptualization, Methodology, Writing - review & editing, Supervision, Project administration, Funding acquisition. Bin Lu: Resources.

Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.apenergy.2019.114487.

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