Daylighting performance simulation and analysis of translucent concrete building envelopes

Renewable Energy 154 (2020) 754e766

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Daylighting performance simulation and analysis of translucent concrete building envelopes Xiaosong Su a, b, Ling Zhang a, b, *, Zhongbing Liu a, b, Yongqiang Luo c, **, Jinbu Lian a, b, Ping Liang a, b a b c

College of Civil Engineering, Hunan University, Changsha, Hunan, 410082, PR China Key Laboratory of Building Safety and Energy Efficiency of Ministry of Education, Hunan University, Changsha, 410082, PR China School of Environmental Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, PR China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 12 November 2019 Received in revised form 26 February 2020 Accepted 8 March 2020 Available online 11 March 2020

A novel optical fiber (OF) embedded building envelope, namely translucent concrete (TC), was proposed and popularized for its light transmission property and unique artistic features, but there is still a lack of in-depth research on its daylighting performance analysis. To reveal the impacts of multi-factors on TC daylighting performance, an optical model of TC was established based on a ray-tracing method. In the model validation, both the simulated transmittance of OFs and illuminance of translucent concrete were in a good agreement with the experimental results. The simulation results showed when the numerical aperture (NA) of the OFs increased from 0.51 to 0.70, the annual average luminous flux of TC under seven cities conditions could be enhanced by up to 40.62%. In terms of effective illuminance, the optimum fiber volume ratio of the seven cities was determined, respectively. Besides, it was found that the corecladding interface losses could lead to a relative deviation over 5% when the length of 1-mm OFs with 0.51 NA exceeded 259 mm, and the deviation could be larger with the decrease in diameter of OFs and the increase both in length and NA of OFs. © 2020 Elsevier Ltd. All rights reserved.

Keywords: Daylighting analysis Optical fiber Transmittance Translucent concrete Optimum tilt angle Numerical aperture

1. Introduction Daylight plays an indispensable part both in biological and psychological need in modern architecture. Sunlight is used to illuminate building interiors to affect the indoor environment, health, lighting quality, and energy efficiency [1]. Research shows that the use of daylight not only reduces artificial lighting expenses, but also offers a sense of cheeriness and brightness, contributes to a healthier working space and improves work performance [2e4]. This might be an explanation for the increasing application of large windows and highly glazed facades in new buildings, which admits light for indoor environment with a pleasing atmosphere and allows people to maintain visual contact with the outside world [5,6]. However, the use of substantial amounts of glazing facades or windows leads to large heat gains in summer and heat losses in

* Corresponding author. College of Civil Engineering, Hunan University, Changsha, Hunan, 410082, PR China. ** Corresponding author. E-mail addresses: [email protected] (X. Su), [email protected] (L. Zhang), [email protected] (Z. Liu), [email protected] (Y. Luo). https://doi.org/10.1016/j.renene.2020.03.041 0960-1481/© 2020 Elsevier Ltd. All rights reserved.

winter, which will influence building energy efficiency [7,8]. Extensive research indicates that conventional window or glazing façade is responsible for about 40% of the total building energy consumption [9]. Therefore, a novel method which can transmit sunlight to improve indoor visual comfort without sacrificing the thermal insulation of building envelope is needed. Fiber optic daylighting system might be a possible solution to this dilemma because it has a high transmittance of light and only takes up a little space. Previously, many studies were conducted to investigate the performance of optical fiber daylighting systems [1,10e15]. In those studies, the sun concentrator is incorporated with optical fibers to concentrate sunlight, and distribute the daylight to the building interior. However, such active daylighting systems are complex because they required a sun-tracking system with a tiny sun-tracking error and power to drive them [12,14]. Besides, multi-stage focusing devices are needed to minimize nonuniformity of focused sunlight [11]. The complex process of coupling sunlight in optical fibers reduces the coupling efficiency [10]. Due to the possibility of creating fascinating lighting effect and unique artistic features by optical fibers, a novel optical fiber

X. Su et al. / Renewable Energy 154 (2020) 754e766

Nomenclature DHI DNI DTI NA PMMA OF TC TIR TMY TTI FVR AL Ev e L l NTIR n RTIR r T(L) VðlÞ

diffuse horizontal irradiance on a horizontal plane direct normal irradiance total diffuse hemispherical irradiance on a tilted surface numerical aperture polymethyl methacrylate optical fiber translucent concrete total internal reflection typical meteorological year total transmitted irradiance fiber volume ratio attenuation loss (dB/km) illuminance (lux) Euler’s number (
) distance of a light ray transmitting in an OF (km) length of an OF (m) the number of total internal reflections (
) refractive index (
) reflectivity of total internal reflection (
) radius (mm) transmission over distance L (
) value of the photopic response curve at wavelength l (
)

Greek symbols a attenuation coefficient (km
1) b absorptivity (
) r reflectivity (
)

embedded building envelope was proposed by architects, which can transmit natural light indoor through embedding an array of OFs into conventional concrete. The mixture of optical fibers and concrete material is called as translucent concrete (TC). Without sun concentrator and sun-tracking system, it may be less efficient but simpler and cheaper. Besides, TC can be used as walls or roof to directly transmit sunlight indoor and, to some extent, create an artistic visual environment as decorations. The concept of transparent concrete was first put forward by Hungarian architect AronLosonzi in 2001, and the first transparent concrete block was successfully produced by mixing large amount of glass fiber into concrete in 2003, named as LiTraCon [16,17]. In the following years, this innovative concrete was widely spread and accepted by architects around the world for its pleasing aesthetics. For instance, the Italian Pavilion shown in Shanghai Expo 2010 drew a wide attention through its amazing lighting effects and unique artistic features created by TC [18]. With wide application of TC, relevant researches and experiments followed. Daylighting performance and energy saving potential are two of the main research fields on TC. In this field, studies mainly focus on lighting transmission, thermal insulation properties and the potential of reducing artificial lighting and air conditioning expenses. He et al. [19] studied the light guiding property of smart transparent concrete with the plastic OF volume ratio from 1% to 6% by using the halogen lamp and incandescent lamp and found the plastic OF volume ratio to concrete is proportional to the transmission. Momin et al. [20] produced the concrete specimens by reinforcing glass rods and OFs with different percentage and concluded that the transparency of concrete specimens with glass fibers was more as compared to the specimens

s h f

q1 q2 qac qcr qn qz t l ∅

F g gs Subscripts 1 2 cir clad core e hor iso R rp

755

roughness height at the core-cladding interface (Å) the fraction of light rays which undergo total internal reflection inside the OF (
) tilt angle of an inclined working plane (Rad) incidence angle (Rad) transmission angle (Rad) acceptance angle (Rad) critical angle of an OF (Rad) the respect angle to the local normal of the corecladding interface (Rad) solar zenith angle (Rad) transmittance (
) wavelength (nm) diameter of optical fibers (mm) luminous flux (lm) surface azimuth angle (Rad) solar azimuth angle (Rad) the number of total internal

interface 1 or incident media interface 2 or transmission media circumsolar diffuse irradiance cladding of an optical fiber core of an optical fiber electronic transition horizon-brightening diffuse irradiance isotropic diffuse irradiance Rayleigh scatter a representative process

with glass rods. Both Li et al. [21] and Henriques et al. [22] found when the number of fibers was a certain value, optical power decreased with an increasing distance from the light source and the specimen. For specimens at the same distance, the optical power increased gradually as the fiber content increased. The experiments above discovered how the basic factors like fiber volume ratio and distance affecting light transmission property of TC. However, the use of artificial light source instead of sunlight cannot completely represent the light transmission property of TC as a building envelope. There is a difference of spectrum between sunlight and artificial light source and each optical wavelength has a different transmittance in OFs. What matters most is that the incidence angle of sunlight projected onto TC changed with time while it remained constant refer to artificial light source in the experiments above. Apart from experiments, some numerical simulations on TC were carried out [23e26]. With the help of Autodesk Ecotect Analysis software, it was reported that after using the lighttransmitting concrete products, the average daylight factor of the room could be increased by 30%; lighting uniformity upgrade 51%; the close time of artificial lighting devices within the natural light service period increased from 23% to 39% [23]. Literature [24] indicated that using resin TC as building envelope reduced about 14% building energy consumption comparing with single clear glass windows. However, the simulations above replaced the fibers embedded in TC with windows of the same area and with the same light transmittance because there was a shortage of OFs modular in simulation software. Literature [26] simulated the lighting energy savings of TC walls with models for occupancy and light switching in Radiance software. However, the core-cladding interface of OFs is

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X. Su et al. / Renewable Energy 154 (2020) 754e766

usually regarded as perfect and the reflectivity of total internal reflection (RTIR ) at this ideal interface is assumed as 1 [25e27], but this is hard to achieve in practical application and it will overestimate the transmittance of OFs. Literature review shows that a research gap exists in daylighting analysis of TC based on the entire solar spectrum and the transmission characteristics of OFs with imperfect core-cladding interface. This research aims to bridge the research gaps through investigating the annual transmission property of TC under sunlight source instead of an artificial light source and provide a useful tool to evaluate and analyze the daylighting performance of TC based building envelope. Numerical investigation was also carried out to reveal the influence of tilt angle of TC panel and NA of OFs on light transmission property of TC. Besides, the optical model of TC can be served as a solid foundation for the thermal modeling and optimal design of TC in the future. The main structure of this paper is as follows: Section 2 describes the modeling process of translucent concrete; Section 3 validates the model with experimental data; Section 4 provides discussions related to system performance and Section 5 gives concluding remarks and outlooks.

2. Modeling of translucent concrete

It is the OFs that makes TC light-transmitting. Therefore, it is essential to investigate the characteristics of OFs to make a better understanding of TC. According to previous research [19,21,25], bare OFs without a layer of jacket were used in the production of TC. Hence, a numerical model of a bare optical fiber was built. (1) Reflectivity on the end surfaces of a bare fiber Reflectivity on the two end surfaces of a bare fiber can be obtained from Fresnel’s equations [29] as shown in Eq. (2):

8
 n1
n2 2 > > > ; if q1 ¼ 0 ; > < n1 þ n2 " # r¼ > > 1 sin2 ðq1
q2 Þ tan2 ðq1
q2 Þ > > ; if q1 s0 : þ : 2 sin2 ðq1
q2 Þ tan2 ðq1 þ q2 Þ

As showed in Fig. 1, TC is a novel kind concrete embedding with optical fibers. Embedded OFs act as a light guide in the concrete and make the TC light-transmitting. As light channels through an OF, the phenomenon of total internal reflection (TIR) occurs. In this phenomenon, if a light ray travels from a denser medium to a relatively rarer medium having an incidence angle larger than critical angle, it is conventionally regarded as totally reflecting back into the same medium without any loss under ideal conditions [28]. Therefore, TC has a good light transmission property, which can be used to reinforce natural daylighting and reduce artificial lighting consumption. The critical angle can be calculated as Eq. (1), where qcr is the critical angle of an OF; ncore and nclad are the refractive index of core and cladding of the OF.

(1)

(2)

where q1 and q2 are the incident and transmission angles; n1 and n2 are the refractive indexes of incident and transmission media. The incidence angle of sunlight for a inclined working plane can be derived from Eq. (3) [30].

q1 ¼ Arccos½cos qz $ cos f þ sin qz $ sin f $ cosðgs
gÞ

2.1. Description of translucent concrete


n qcr ¼ Arcsin clad ncore

2.2. Numerical model of a bare optical fiber

(3)

where qz is the solar zenith angle; f is the tilt angle of an inclined working plane; gs is the solar azimuth angle, g is the surface azimuth angle. The transmission angle can be derived from Snell’s law as shown in Eq. (4).



q2 ¼ Arcsin

n1 $sin ðq1 Þ n2

 (4)

(2) Transmittance The attenuation of the solar radiation energy along the optical fiber is estimated readily by defining the transmission T(L) as Eq. (5), which is the ratio of solar radiation energy between l1 and l2 transmitted over distance L to the incident solar radiation energy for the same wavelength interval [31].

Fig. 1. Translucent concrete panel: (a) a top view; (b) a TC panel with a tilt angle of f.

X. Su et al. / Renewable Energy 154 (2020) 754e766

ð l2 TðLÞ ¼

l1

b¼1
r
t

E0 ðlÞexp½
ðaR þ ae ÞLdl E0 ðlÞ dl

(4) Numerical aperture

where L is the distance of a light ray transmitting in an OF, km, which is a function of both the incidence angle and the length of OFs; l1 and l2 are the minimum and maximum wavelength of a light source with a continuous spectral spectrum, nm; aR and ae are the Rayleigh scattering and electronic transitional attenuation coefficients, km
1; E0 ðlÞ is the solar spectral energy with a wavelength of l, W/(m2 ,nm). The attenuation coefficient a can be expressed in terms of attenuation loss, shown in Eq. (6) [32].

AL 10 log e

(6)

where AL is attenuation loss, dB/km and e is the Euler’s number. The attenuation loss of Rayleigh scatter (ALR ) and electronic transition (ALe ) can be derived from Eq. (7) and Eq. (8) [31,33]:

ALR ¼


8 633 4 > < 13  ; for polymethyl methacrylate ðPMMAÞ

l

> :

1:727  1011 ,l
4 ; for fused silica (7)

ALe ¼

8 > > > <

1:58  10
12 exp

1:15  104

l

! ; for PMMA

! > 3 > > : 1:58  10
12 exp 2:246  10 ; for fused silica

(8)

l

For simplicity, the solar spectral energy with a wavelength of l can be derived from Eq. (9) [31]:

E0 ðlÞ ¼

C1

(9)

l5 ½expðC2 =ðlÞÞ
1

where C1 ¼ 8:097  10
21 W$m2 ; C2 ¼ 2:497  10
6 m. Losses that are due to roughness at the core-cladding interface are taken into account. According to Ref. [34], RTIR can be related to the roughness at the core-cladding interface shown in Eq. (10).

" RTIR ¼ exp





(12)

(5)

ð l2 l1

a¼

757

4psncore cos qn

2 #

l

(10)

where s is the roughness height at the core-cladding interface, a mean value of 50 Е is used here; qn is the respect angle to the local normal of the core-cladding interface. The transmittance of an OF including Fresnel losses of reflection at the entrance and exit apertures can be defined as Eq. (11).

t ¼ ð1
rÞ2 $ TðLÞ$ðRTIR ÞNTIR

(11)

where NTIR is the number of TIRs. (3) Absorptivity The absorptivity of an OF can be calculated as Eq. (12) based on the law of energy conservation.

NA of an OF is a parameter that characterizes the range of angles over which the OF can accept light. The NA of an OF can be derived from Eq. (13):

NA ¼ nqac ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   ncore 2
nclad 2

(13)

where n is the refractive index of the medium around the fiber, here it is the refractive index of air, namely 1.0; qac is the acceptance angle. (5) The fraction of total internal reflection TIR occurs when a light ray strikes the coreecladding interface at an angle greater than the critical angle. The fraction of light rays which undergo TIR inside an OF when striking the OF entrance interface, h, can be calculated with ray tracing method. Taking direct normal irradiance (DNI) as an example, hDNI can be directly derived from Eq. (14) and Eq. (15). According to the Perez diffuse irradiance model, total diffuse hemispherical irradiance on a tilted surface (DTI) can be divided as three components including isotropic, circumsolar and horizon-brightening diffuse irradiance, which are assumed to be uniformly distributed over the sky vault, a cone with a half-angle of 25 centered on the position of sun and a horizon band with an elevation of 6.5 , respectively [35,36]. Based on this, each diffuse irradiance can be regarded as a combination of light rays with the same energy density but various incidence angles uniformly distributed in its corresponding region. Each light ray of diffuse irradiance can be treated with the same method for DNI and thus the TIR fraction of each diffuse irradiance is the fraction of its light rays meet the criteria of TIR.

hDNI ¼ 1


B¼

2h

p

ArccosðBÞ þ B $


 n1 n cos Arcsin 2 sin q1 n1

pffiffiffiffiffiffiffiffiffiffiffiffiffiffi i 1
B2

(14)

(15)

Light rays that do not meet the criteria of TIR will leak out from the core and undergo multiple refraction and reflection along the OF, which is shown in Fig. 2. Usually these light rays are regarded to dissipate as heat inside the OF. However, the TC is thin and the length of OFs is short in application. Therefore, it is possible for some of these light rays to transmit out from the OF. To take this into account, this study proposes a simplified method based on the spatial energy distribution of reflected light rays to avoid huge calculation of multiple refraction and reflection. All the reflected light rays (and their optical energy) are assumed to concentrate on the reflected light ray with the highest energy. Fig. 3 shows this simplification. If a light ray propagates in the core, part of it will transmit into the cladding and then reflect back to the core and this process will repeat until the light ray exits from the OF. Taking this as a representative process, the optical property of the whole transmitting process can be simplified as the study of the reflectivity and absorptivity of a representative process. The Reflectivity and absorptivity of a representative process can be derived from Eq. (16) and Eq. (17). The sum of rrp and brp is equal to 1, which satisfies the law of energy conservation.

758

X. Su et al. / Renewable Energy 154 (2020) 754e766

Fig. 2. A schematic of multiple reflection and refraction of light rays transmitting in an OF.

Fig. 3. Light rays transmitting processes in an OF: (a) a TIR process; (b) a no TIR process; (c) The simplification of a no TIR process.

rrp ¼ 2t21 þ

r1 t21 þ r2 t21 t22
2t21 1
r1 r2 t22

brp ¼ 1
2t21 þ

2t21
r1 t21
r2 t21 t22 1
r1 r2 t22

(16)

(2) Total diffuse hemispherical irradiance on a tilted surface is divided as isotropic, circumsolar and horizon-brightening diffuse irradiance according to the Perez diffuse irradiance model [35,36]. It can be derived from Eq. (18).

(17)

where r1 and r2 are the reflectivity of interface 1 and 2; b1 and b2 are the transmittance of interface 1 and 2; Moreover, ri þ bi ¼ 1, i ¼ 1, 2; t1 and t2 are the transmittance of material 1 and 2 (or the core and cladding).

  1 þ cos f cos q1 þ F1 DTIðfÞ ¼ DHI ð1
F1 Þ þ F2 sin f 2 cos qz

(18)

where f is the tilt angle of an inclined working plane, Rad; DHI is the diffuse horizontal irradiance on a horizontal plane, W=m2 ; the coefficients F1 , F2 can be obtained from Ref. [37].

2.3. Assumptions in the numerical model of translucent concrete (1) For simplicity, only specular reflection instead of diffuse reflection is considered in this study to utilize ray tracing methods.

(3) As bare OFs are used in the TC panel and its numerical model, an assumption that there is no airgap between the cladding and concrete is made. The reflectivity of the interface between the cladding and concrete is supposed to be 0.2.

X. Su et al. / Renewable Energy 154 (2020) 754e766

2.4. Total transmitted irradiance and indoor illuminance Total transmitted irradiance (TTI) though an OF can be calculated from Eq. (19):

be also reflected at the appearance of inflection point before or after the qac of nominal NA. For example, in Fig. 5 (b) the inflection point of experimental relative transmission curve appears at about qac ¼ sin
1 ð0:64Þ but not at qac ¼ sin
1 ð0:66Þ. On the whole,

ptTTI ¼ DNI$½hDNI $tDNI þ ð1
hDNI Þ$t’DNI    1 þ cos f cos q1 þ hcir $tcir $F1 þ hhor $thor $F2 sin f þDHI hiso $tiso $ð1
F1 Þ 2 cos qz   1 þ cos f cos q1 þ ð1
hcir Þ$t’cir $F1 þ ð1
hhor Þ$t’hor $F2 sin f þDHI ð1
hiso Þ$t’iso $ð1
F1 Þ 2 cos qz

where t is the transmittance of the corresponding solar irradiance in an OF through TIR processes; t’ is the transmittance of the corresponding solar irradiance in an OF through representative processes; subscript DNI refers to direct normal irradiance and subscripts iso, cir and hor refer to isotropic, circumsolar and horizon-brightening diffuse irradiance, respectively. Based on the assumption that the spectral distribution of solar irradiance refers to ASTM G173-03(2012) [38], TTI can be transformed to indoor illuminance according to Eq. (20) [37]: 780 ð

Ev ¼ 683

TTIðlÞ$VðlÞdl

(19)

the simulation results are in a good agreement with those of the experiment, which indicates the effectiveness of the model. The

(20)

380

where Ev is illuminance, lux; the value of 683 lm/W is the maximal luminous efficacy of radiation at 555 nm; TTI(l) is the spectral irradiance at wavelength l; VðlÞ is the value of the photopic response curve at wavelength l. Main steps in the simulation show in Fig. 4. The inputs DNI and DHI are obtained from typical meteorological year (TMY) files. The length of OFs, l, is equal to the thickness of TC panel.

3. Model validation 3.1. Comparison with experimental results of transmittance To validate the optical model of an OF, experimental data from literature [39] was used for comparison. In that experiment, a quartz-halogen lamp with two collimating lenses was used as a light point source irradiating collimated light onto the front end of an OF. A calibrated integrating box with a silicon photodiode sensor was fixed at the back end of the OF to measure the emitted radiation intensity. To achieve the angular response an OF, the incidence angle, q, was varied by rotating the OF as well as the integrating box with an uncertainty of ±0.5 while the light source was kept in static. It should be noted that the experimental results in literature [39] were only presented as relative transmission, tðqÞ=tð0Þ, which was the ratio of transmittance at q to that value at normal incidence. Therefore, relative transmission is also used as the comparison criterion in this section. The experimental relative transmission values with uncertainties are shown in Fig. 5. Besides, literature [39] made a check for NA values for the reason that some experimental results were lager than the theoretical values under ideal conditions. It is reported that the nominal NA values of OFs has an uncertainty of ±0:02 according to manufacturers. The inconsistency between nominal NA and actual NA can

759

Fig. 4. The flow chart of simulation processes.

760

X. Su et al. / Renewable Energy 154 (2020) 754e766

3.2. Comparison with experimental results of illuminance This section aims to make a simulation and compare the results with the experimental data obtained from Test 1 and Test 2, in Mosalam and Casquero-Modrego [40]. The experiment was conducted on July 1, 2013, on the University of California, Berkeley, California campus. OFs of different diameter (3 mm, 6 mm and 10 mm) were embedded in TC panels (with dimensions of 0:203 m  0:203 m  0:019 m) in a 7  7 grid, which placed horizontally on a cubic box with interior clear dimensions of 0.203 m  0.203 m  0.203 m. The experimental illuminance values were recorded by a light meter installed at the center of the floor of the box. With respect to test panels with 10-mm OFs, more transmitting area was near the boundary of the test box and this resulted in a decrease in light transmission in the middle of the day [38], which was contrary to practical application. Therefore, only TC panels with 3-mm and 6-mm OFs are simulated and compared with experimental results, and light rays that projected on the side walls of the box are perceived as being completely absorbed without reflection in the simulation. The weather conditions can be obtained from National Solar Radiation Database (Location ID: 122886). Other simulation inputs are listed in Table 2, which are identical to that in the experiment. The average illuminance on the interior floor of the box shows in Fig. 6. For TC panels with 3-mm OFs, the average relative deviation is 11.93% to fiber volume ratio (FVR) of 0.84% and 15.43% to FVR of 1.71%. For TC panels with 6-mm OFs, the average relative deviation is 5.48% to FVR of 0.84% and 7.45% to FVR of 1.71%. The cause of deviation might be that the experimental results were the illuminance values on the area where the light meter was set, at the center of the bottom floor, while the simulation results were the average illuminance. But an average illuminance can be representative enough in an application of full-size TC panels, where the distribution illuminance will be more even and the boundary influence of the panels can be neglected. 4. Results and analysis

Fig. 5. Angular response of an OF: (a) NA ¼ 0.39; (b) NA ¼ 0.66.

simulation inputs are listed in Table 1, which are identical to that in the experiment.

In this chapter, we aim to investigate the daylighting performance of unit area translucent concrete as external building envelope, which makes it possible to predict the daylighting performance of any other size of translucent concrete under the same circumstance. The following simulations are based on a south-facing TC panel with dimensions of 1:000 m  1:000 m  0:100 m. According to literature [19], OF volume ratio is proportional to the transmission. It is assumed that OF volume ratio is 10.00% in the TC panel model. Other parameters of the OFs are listed in Table 3. The NA is an important parameter of OFs, which represents the acceptance cone of the fiber. The larger the NA of OFs

Table 1 The inputs of Angular response simulation of an OF [39]. NA -

Core -

Core index -

Core diameter mm

Cladding diameter mm

Length mm

0.39 0.66

Fused silica Fused silica

1.45 1.45

1.000 1.000

1.035 1.040

133 166

Table 2 The simulation inputs of Test 2 in Literature [40]. Type-

NA-

Core diameter mm

Cladding diameter mm

Separation mm

Fiber volume ratio %

∅3 ∅6

0.51 0.51

2.95 5.88

3.00 6.00

26.90 23.90

0.84 and 1.71 1.71 and 3.36

X. Su et al. / Renewable Energy 154 (2020) 754e766

761

Fig. 7. The average illuminance at different tilt angles in Beijing, China (NA ¼ 0.51, ∅5).

Fig. 6. The comparison of illuminance between experiment and simulation results: (a) ∅3; (b) ∅6.

is, the more lights can be channeled by the TC panels. At present, the NA of OFs sold on the market is usually not larger than 0.51, but OFs with larger NA can be anticipated in the future. Through changing the refractive index of the cladding, OFs with a NA of 0.60 and 0.70 are created, shown in Table 3. The weather files of TMY were obtained from EnergyPlus [41]. 4.1. Optimum tilt angle of translucent concrete

Lanzhou, Beijing, Harbin and Bugt were taken as examples to explore the optimum tilt angle of TC only in terms of daylighting performance. The measurement index is the average transmitted illuminance on a plane parallel to TC panels with the same area of TC, which is the ratio of the total luminous flux transmitted through TC to the area of TC. First, an array of tilt angles was set in the interval of 10 to find the possible range of optimum tilt angle. Taking Beijing as an example, the optimum tilt angle of TC panels falls within the range from 30 to 40 with NA ¼ 0.51 and ∅ ¼ 5 mm as shown in Fig. 7. Then the interval was narrowed down as 1 and the optimum tilt angle was obtained. The optimum tilt angles of TC panels in the seven cities were shown in Fig. 8 with an auxiliary dashed line representing y ¼ x. It can be found that the optimum tilt angle of TC panels deviates with the value of local latitude, especially in low or high latitude area. The deviation can be as large as about 7 (like Beijing, NA ¼ 0.51). Moreover, when keeping the NA of OFs in constant, the optimum tilt angle of TC panels increases with the increment of latitude, while it also increases with the increment of NA in the same latitude. To some extent, the optimum tilt angle is proportional to latitude and NA. To make it convenient for predicting the optimum tilt angle, a bivariate nonlinear regression equation is proposed based on the assumption that the optimum tilt angle is linear to latitude and NA, respectively, as shown in Eq. (21) where y, x1 , x2 stand for optimum tilt angle [Degree], latitude [Degree] and NA, respectively; a, b, c, d are partial regression coefficients. Eq. (21) can be transformed into a ternary linear regression equation as Eq. (22), where X1 ¼ x1 , X2 ¼ x2 , X3 ¼ x1 $x2 , A0 ¼ a$c, A1 ¼ b$c, A2 ¼ a$d,A3 ¼ b$d. The simulated results with a total number of 21 shown in Fig. 8 are used as fitting samples. The optimum fitting result of Eq. (22) can be solved as Eq. (23), where R, R2 , R2a are multiple correlation coefficient, determination coefficient, and adjusted determination coefficient,

Seven cities in China including Shenzhen, Changsha, Shanghai,

Table 3 Parameters of OFs. Parameters

Core Cladding

Refractive index

Diameter

NA ¼ 0.51

NA ¼ 0.60

NA ¼ 0.70

∅1/mm

∅3/mm

∅5/mm

1.490 1.400

1.490 1.365

1.490 1.315

0.980 1.000

2.939 3.000

4.899 5.000

762

X. Su et al. / Renewable Energy 154 (2020) 754e766

Fig. 8. The optimum tilt angles of TC panel in the seven cities.

Fig. 10. The change of illuminance values on representative days in Beijing: (a) January 3rd; (b) July 3rd.

y ¼ A0 þ A1 $X1 þ A2 $X2 þ A3 $X3 8 > > < y ¼
5:1446 þ 0:8694 X1 þ 29:7028 X2
0:4874 X3 R2 ¼ 0:9328 ðR ¼ 0:9658Þ > > : R2 ¼ 0:9209

Fig. 9. A comparison between the regressive and simulation results.

(22)

(23)

a

respectively. If the confidence level is set as 0.05, the critical multiple correlation coefficient Rcr is 0.601 in this case. Since R>Rcr , it can be concluded that Eq. (23) is well fitted with the simulation results. A comparison between the regressive and simulation results is shown in Fig. 9. The average relative error is 3.19% and the maximum relative error is 8.45%. It is worth noting that Eq. (23) is obtained based on the simulation results of seven cities in China, which can be used as a reference to determine the optimum tilt angle at different latitude, but additional calculations are needed to obtain a precise value of optimum tilt angle especially when NA is out of the range from 0.51 to 0.70.

y ¼ ða þ b $ x1 Þðc þ d $ x2 Þ

(21)

To investigate the impact of NA on TC panel daylighting performance, January 3rd and July 3rd, two sunny days, are chosen from TMY as the representative days in winter and summer in Beijing, respectively. Fig. 10 shows the change of illuminance values at the optimum tilt angle. It is found that when the incidence angle of sunlight exceeds the acceptance angle, the illuminance values decrease sharply. The larger the NA, the longer the high lighttransmitting time span is. Therefore, TC panels with high-NA OFs have a greater potential to provide a long-time daylighting with a relative stabler illuminance level. The average illuminance values for the TMY at the optimum tilt angle are listed in Table 4. It is found that when the NA of the OFs is increased from 0.51 to 0.60 and from 0.51 to 0.70, the average illuminance can be enhanced by up to 21.80% and 40.62%. Therefore, the method of increasing the NA of OFs has a great potential to improve the light-transmitting capabilities of TC panel. It is worth noting that the potential varies with different cities as different latitudes and weather conditions.

X. Su et al. / Renewable Energy 154 (2020) 754e766

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Table 4 The average illuminance for the TMY at the optimum tilt angle (∅5). NA

0.51 0.60 0.70

The average illuminance = lux Shenzhen

Changsha

Shanghai

Lanzhou

Beijing

Harbin

Bugt

2927 3330 (13.78%) 3713 (26.86%)

2608 2965 (13.69%) 3306 (26.78%)

2805 3206 (14.30%) 3571 (27.28%)

3305 3885 (17.56%) 4409 (33.39%)

3187 3826 (20.03%) 4307 (35.17%)

2870 3496 (21.80%) 3957 (37.88%)

2948 3574 (21.23%) 4146 (40.62%)

[42], a desire illuminance range of 500e2000 lux is used as the effective illuminance range. In the simulation, the TC panels tilt with an angle to achieve a greater light transmitting capacities, but illuminance is much more relative to a horizontal working plane. Therefore, cosine value of the tilt angle is employed with the simulation results to evaluate the horizontal illuminance. Fig. 11 shows us that though the increasement of NA can increase the fraction of illuminance exceeding 500 lux to 90% or more, it leads to a greater increasement of that exceeding 2000 lux, which in fact reduces the fraction of effective illuminance. Therefore, when the FVR is 10.00%, it is not suitable to improve the daylighting performance of TC in increasing the NA of OFs. Fig. 12 shows the fraction of effective illuminance at different OF volume ratio. It indicates that the OF volume ratio imposes a stronger impact on the fraction of effective illuminance than the NA does. In terms of effective illuminance, the optimum fiber volume ratio of the seven cities was determined according to Fig. 12, respectively. It is worth noting that the transmission is proportional to OF volume ratio [19] and a result similar to that in Fig. 12 can be anticipated even under different conditions of FVR. In the research scope, a FVR of about 3% can maintain the fraction of effective illuminance at a relative high level regardless of NA of OFs.

4.3. The influence of core-cladding interface losses

Fig. 11. The fraction of illuminance values (VR ¼ 10.00%): (a) > 500 lux; (b) > 2000 lux.

4.2. The fraction of effective illuminance To evaluate the daylighting performance of TC, it is necessary to investigate the fraction of effective illuminance, which is the fraction of time span under suitable illuminance. According to Sun et al.

A comparison was made on the deviation of whether taking core-cladding interface losses into account. Taking Beijing as an example, Table 5 and Table 6 list the average illuminance at optimum tilt angle in Beijing with different NA and diameters of OFs and thickness of TC panels. It is found that influence of corecladding interface losses becomes more and more stronger with the decrease in diameter and the increase in NA and length of OFs due to the increase in the number of TIRs. The influence of corecladding interface losses should not be neglected in the application of TC panels with small-diameter, high-NA and long OFs, which can reach up to 6% in the research scope. The deviation between the ideal and non-ideal models under various conditions was presented in Fig. 13 but the length of OFs was controlled within the range of 500 mm considering most of the representative wall and roof types listed in ASHRAE Fundamentals 2017 [43] with a thickness thinner than 500 mm. A linear relationship was shown between the thickness of TC panels and the deviation, because the optical losses was assumed to be proportional to the length of OFs. Fig. 13 can be used to estimate the deviation. For example, in Fig. 13 (a), if the maximum relative deviation is required to be within 5% in the design process, the effect of imperfect corecladding interface has to be considered when the length of 1-mm OFs with 0.51 NA exceeds 259 mm, or that with 0.60 NA exceeds 205 mm, or that with 0.70 NA exceeds 165 mm. It was found that the deviation could be larger with the decrease in diameter of OFs and the increase both in length and NA of OFs.

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X. Su et al. / Renewable Energy 154 (2020) 754e766 Table 5 A comparison on core-cladding interface losses (∅5). Thickness/mm

100

NA

0.51

0.6

0.7

200 0.51

0.6

0.7

non-ideal ideal

3187 3199 (0.37%)

3826 3844 (0.47%)

4307 4333 (0.59%)

3161 3186 (0.77%)

3791 3828 (0.97%)

4264 4315 (1.21%)

0.6 3650 3828 (4.87%)

0.7 4069 4315 (6.04%)

Table 6 A comparison on core-cladding interface losses (∅1). Thickness/mm

100

NA non-ideal ideal

0.51 3138 3199 (1.92%)

200 0.6 3752 3843 (2.42%)

0.7 4206 4333 (3.00%)

0.51 3067 3186 (3.86%)

5. Conclusion and outlooks A ray-tracing model for transmission of TC building envelope has been developed to reveal the impacts of multiple system factors on TC daylighting performance. Both the simulated transmittance of optical fibers and illuminance of translucent concrete were in a good agreement with the experimental results, which confirmed the accuracy of the model. By applying the model, the average illuminance values for the TMY were simulated. Seven cities from southern China to Northern China were selected to investigate the relationship among the optimum tilt angle of TC panels, numerical aperture and local latitude. The simulation results showed the optimum tilt angle of TC panels deviated with the value of local latitude, especially in low or high latitude area. The deviation could be as large as about 7. To make it convenient for predicting the optimum tilt angle at different latitude, a ternary linear regression equation based on latitude and NA was proposed. Besides, when the NA of the OFs increased from 0.51 to 0.60 and from 0.51 to 0.70, the annual average luminous flux of TC under seven cities conditions could be enhanced by up to 21.80% and 40.62%, respectively. Though the use of fibers with large NA is beneficial to increase the light-transmitting capability of TC, it can also lead to excessive daylighting. The results showed that the FVR imposed a stronger impact on the fraction of effective illuminance than the NA did. In terms of effective illuminance, the optimum FVRs of the seven cities were determined, respectively. In the research scope, an FVR of about 3% can maintain the fraction of effective illuminance at a relative high level regardless of NA of OFs. Besides, it was found that the core-cladding interface losses could lead to a relative deviation over 5% when the length of 1-mm OFs with 0.51 NA exceeded 259 mm, and the deviation could be larger with the decrease in diameter of OFs and the increase both in length and NA of OFs. However, there is still some space for improvements for the study of TC embedded envelopes. The core-cladding interface roughness should be further quantified by measurement. Extra experiments at different latitudes are needed to better validate the effectiveness of the TC numerical model, confirm the accuracy of the conclusion and find out the common rules behind the transmission of TC. Besides, TC panels should be integrated with a building entity or model to investigate the thermal performance and spatial illuminance values, which is also the focus of our future work. Fig. 12. The fraction of effective illuminance (500e2000 lux) at different OF volume ratio: (a) NA ¼ 0.51; (b) NA ¼ 0.60; (c) NA ¼ 0.70.

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Declaration of competing interest None. CRediT authorship contribution statement Xiaosong Su: Conceptualization, Methodology, Software, Validation, Writing - original draft. Ling Zhang: Conceptualization, Writing - review & editing, Project administration, Supervision, Funding acquisition. Zhongbing Liu: Methodology, Writing - review & editing. Yongqiang Luo: Methodology, Writing - review & editing, Funding acquisition. Jinbu Lian: Software, Data curation. Ping Liang: Validation, Visualization. Acknowledgements The work described in this paper is sponsored by the National Natural Science Foundation of China (Grant Number: 51878253) and the Fundamental Research Funds for the Central Universities (Grant Number: 2019kfyXJJS189). Appendix A. A case study of the simplification of light rays transmitting in optical fibers Taking a representative process as an example analysis, a case of calculation was carried out to analyze the rationality of the simplification described in section 2.2. It is assumed that a light ray with unit energy strikes on the entrance interface of an OF. The refractive index of the core and cladding are 1.49 and 1.40, respectively. It is supposed that the length and diameter of an OF are 100 mm and 10 mm. The energy distribution of the incident light ray and its subsidiary rays transmitting into an OF is calculated and the results are listed in Table A1 and Table A2.

Table A1 Energy distribution of reflective light rays. Incidence angle ðDegreeÞ

40

60

No.

value

proportion value (%)

proportion value (%)

proportion (%)

1 2 3 4∞ sum

0.0452 0.6616 0.0230 0.0008 0.7307

6.19 90.55 3.15 0.11 100.00

0.80 98.71 0.49 0.00 100.00

0.42 99.55 0.23 0.00 100.00

0.0064 0.7213 0.0036 0.0000 0.7313

80

0.0031 0.7274 0.0017 0.0000 0.7322

Table A2 The distance between two adjacent reflective light rays along the central axis of an OF

Fig. 13. The deviation between the ideal and non-ideal models with different TC panels embedded with OFs of different diameters: (a) ∅1; (b)∅ 3; (c)∅ 5.

Incidence angle [Degree]

y1 mm

y2 mm

2y2 mm

2ðy1 þy2 Þ mm

40 60 80

10.2470 6.8602 5.5634

0.3436 0.1732 0.1327

0.6871 0.3465 0.2654

21.1812 14.0669 11.3923

For one thing, the reflective ray 2 shown in Fig. 2 takes up over 90% energy among all the reflective rays in a representative process. This faction also increases with the increase of incidence angle. Besides, over 99% energy of all the reflective rays concentrates on

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the first three reflective rays, which are very close to each other. The distance between two adjacent reflective rays is less than 3.25% in axial direction compared with the axial distance of a representative process, while it is less than 0.69% compared with the length of an OF, which also decreases with the increase of incidence angle. To some extent, the optical model can be simplified while maintaining computational accuracy and efficiency if the assumption that energy of all the reflective rays are represented by a single light ray with the equal energy intensity is adopted.

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