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A solar fiber daylighting system without tracking component
Solar Energy 194 (2019) 461–470
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A solar fiber daylighting system without tracking component ⁎
T
Kaiyan He , Ziqian Chen, Shiuku Zhong, Yingda Qian, Haoyue Liu, Junhua Yin, Bangdi Zhou School of Physical Science and Technology, Guangxi University, Nanning 530004, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Solar light guiding Solar concentrating Non-tracking system Optical fiber daylighting
A fixed optical fiber solar system for long distance daylighting used in buildings is proposed. Its structure and working principle have been introduced. The proposed system takes the advantages of both light pipe and traditional optical fiber system and overcomes their shortcomings. The receiving surface of the new system is like a spherical sunflower. It has a simple structure, good integrity, flexible light transmission and light redistribution characteristics. Especially, it does not require a tracking device. Both the theoretical analysis and field test have proved that the system has the same reception feature as the traditional optical fiber system with a tracking device. Its graph of the illuminance roughly follows the fluctuation of the curve of the solar irradiance. A small test system with a solar receiving area of 1.69 × 10−2 m2 and receiving angle of 32° was made to verify the feasibility of the fixed optical fiber system. Experimental result had proved that the proposed system is feasible. On average, the output illuminance inside a small test room is up to about 180 lx in a distance of 0.4 m from the bundled end of the fibers with the solar irradiance being about 600 W/m2, approximately 300 lx under approximately 800 W/m2. The simple structure, expectable low cost, almost maintenance-free and a predictable long life of the new system will facilitate the mass production and the viable commercialization of daylighting systems.
1. Introduction Nowadays, two schemes of solar light guiding, light pipe and the optical fiber, are often adopted in long distance daylighting for buildings. The light pipe technology is relative mature and has been commercially used in buildings. Recently, there are still some researchers studying light pipe, but their looked only at the details of the application (Garcia-Hansen and Edmonds, 2015; Bruno Malet-Damour et al., 2016; Darula et al., 2010), or new analysis method (Petržala et al., 2018; Shuxiao et al., 2015; Kocifaj, et al., 2010). There is no major breakthrough in technical route so far. The technology of optical fiber light guiding is not yet very mature. Several technologies of optical fiber daylighting have been proposed in the past few decades (Schlegel et al., 2004; Feuermannt and Gordon, 1999; Tsangrassoulis et al., 2005; Kandilli et al., 2008; Sedki and Maaroufi, 2017; Lv et al., 2018; Obianuju and Chong, 2017; Vu and Shin, 2016). Several commercial products made with different technologies of the optical fiber daylighting, such as the Himawari (Japan), Hybrid lighting (USA) and SOLUX (Germany) was reported by Andre′ and Schade (2002). The differences in these optical fiber technologies mainly lie in light concentrating component which usually resorts to typical lens (or Fresnel lens) and parabolic concentrator to collect sunlight. A parabolic
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concentrator usually uses reflective surfaces to transmit solar energy, which is called the mirror surface reflection type (abbreviated as MSRT). An optical fiber system using a special designed compounded parabolic concentrator, called imaging CPC, as its light concentrating unit was introduced by Kaiyan et al. (2009a), , which still a MSRT type (Kaiyan et al. (2009b)). The idea of the special designed compounded parabolic concentrator was originally proposed in 2008 (Kaiyan et al., 2007). Since then, this type of concentrator has been studied further. Several papers involving its experimental results for two dimensions or three dimensions structure have been published subsequently (Kaiyan et al., 2009; Xiaodi et al., 2010; Tao et al., 2011). Especially in literature (Kaiyan et al., 2011), its working principle and several performance parameters have been theoretically studied in more detail. The schematic of its working principle is shown in Fig. 1. Tow parabolic line l1 and l2, with their symmetrical axes parallel to each other, are separated by a distance 2l. Take parabolic segments DA and CB, together with straight lines AE and BG, as the contour of the concentrator. When the contour is rotated around its symmetrical axis, a concentrator is formed, which looks like a funnel with a cylindrical lower portion. For a given solar ray as shown in Fig. 1, when it strikes on CB, parallel to the central axis of the parabola, it should be reflected to the focus F1, but
Corresponding author. E-mail address: [email protected] (K. He).
https://doi.org/10.1016/j.solener.2019.10.058 Received 10 July 2019; Received in revised form 18 October 2019; Accepted 23 October 2019 0038-092X/ © 2019 International Solar Energy Society. Published by Elsevier Ltd. All rights reserved.
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Nomenclature MSRT TIRT TET η
K P N α β
mirror surface reflection type total internal reflection type tracing error tolerance transmission efficiency
eigen parameter of the concentrator focal parameter of the parabola refractive index of the selected transparent material ratio of the width to the height of the concentrator ratio of the entrance width to exit width
daylighting system that integrates the advantages of both light pipe and the optical fiber system and overcomes their shortcomings, which is called a fixed optical fiber solar daylighting system. The proposed system has a simple, compact and integral structure, especially, without tracking system. In this paper, the system structure and its important components are first introduced, and then the conceptual design of components and their working principals are discussed. By computer simulation and field testing, the efficiency attenuation curves of a light concentrating unit and a five-unit daylighting system are researched.
due to the specular reflection of the AE, it will actually reach F, which is just the focus of the concentrator. The same physical process will happen for the opposite symmetrical side of the contour, namely DA l and BG. As long as F1 E = EF = FG = GF2 = 2 , all optical rays parallel to the central axis of the concentrator will converge on concentrator’s focus F. The light path pattern from a computer simulation of the concentrator is shown in Fig. 2. Some researchers have tried using A. Rabl and R. Winston’s CPC (non-imaging CPC) as concentrator in fiber optical daylighting systems. For example, Ngoc-Hai Vu and Seoyong Shin have come up with such a design with modified non-imaging CPCs, but still with a tracking system (Ngoc-Hai et al., 2016). Actually, for a normal non-imaging CPC, even when light is incident normally, the angle of divergence of the output light beam is colossal, let alone when the incident light is deflected from the normal line. Therefore, non-imaging CPC is unsuitable for connecting to a fiber to effective transmission sunlight. Though an optical fiber system has advantages of less damage to the room space and the flexibility of installation, it obviously has at least two defects. One is that there’s always a tracking system undoubtedly having a mechanical moving component and accordingly requires an external power to drive it, so that should make the system more complex, lower the working reliability of system, shorten the system’s life time, and increase the cost of the initiative investment and operation. The second defect of existing optical fiber system for MSRT type is that, to increase the reflectivity of the parabolic surface, a high reflecting coating layer that is directly exposed to the air is needed. This layer is apt to be corroded by pollution weather, which would result in the attenuation of the reflectivity of the layer with time going on. It can be easily seen that the advantages of the light pipe have a simple and almost maintenance-free structure, no movable components and a high working reliability, but its shortcomings are of having a big space occupation and less installation flexibility. Based on the above analysis, we put forward a new type of solar
2. The constitution and working principle of a fixed optical fiber solar daylighting system 2.1. System constitution A fixed optical fiber solar daylighting system is composed of multiple light concentrating units and a support frame. A single row of concentrating unit could be arranged in a fan-shaped structure, as shown in Fig. 3. In practice application, the system could be made by several rows of the concentrating unit. Therefore, the proposed daylighting system could be grouped by an arbitrary number of light concentration unit. A light concentrating unit is the core part of the daylighting system, as shown in Fig. 4. It has three parts: 1- concentrator, 2- coupler and 3-
Fig. 1. The schematic of an imaging CPC with mirror reflection.
Fig. 2. The optical path in an imaging CPC with mirror reflection. 462
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Fig. 3. Schematic of a fixed daylighting system.
Fig. 5. Photo of the concentrator.
effectively the diffuse component. We attempt to make a try that at the cost of adding more units a fixed daylighting system can be built without tracking component. Therefore, the magnitude of the tracing error tolerance (TET) of the light concentrating unit is the key factor to realize the fixed daylighting system.
2.2. The conceptual design of components and their working principal
Fig. 4. Schematic of a light concentrating unit.
2.2.1. The design of the concentrator The concentrator in Fig. 4 is the key part of a light concentrating unit. It was integrally made of a block of solid transparent material, as shown in Fig. 5. Light transmitting through it is realized by total internal reflection instead of the specular reflection in MSRT. To distinguish this type of concentrator from the MSRT type, it is designated as total internal reflection type (abbreviated as TIRT). From the outside outline, based on Fig. 2, its bottom end is slightly extended, and then a semicircular lens is added. The operation principle of this part has been studied in the literature (Kaiyan et al., 2011) and its internal light paths are shown in Fig. 6 (except those inside the hemispherical lens). Compared to MSRT concentrator, TIRT concentrator possesses two advantages, that is, highly integrative and high-strength structure; and no coating layer. To make sure the incoming rays meet the condition of the total internal reflection principle so that all incoming light would be transmitted to the outlet aperture, the geometrical parameters of the concentrator and the refractive index of the material must be properly determined. Fig. 6 shows the optical path in a concentrator. Let us put the lower section below the EG aside. A beam of parallel light between ray 1 and ray 2 strikes on the parabolic segment CB that is the interface between the air and the transparent material with the incident angle of ray 1 minimal. As long as ray 1 satisfies the condition of the total internal reflection, all other rays to the right of it will satisfy the condition as well. Suppose the refractive index of the selected transparent material is n , the width of the outlet of the concentrator AB = l . If the cost of the
optical fiber. We will not discuss the luminaries in this paper. The geometrical structure of the concentrator in Fig. 4 is the modified type of the one in Fig. 2. It is made of a block of solid glass or other appropriate transparent material. Its function is to collect and concentrate sunlight. The coupler is a hollow cylinder with a highly reflective inner surface. It has two functions. One is the structural connection. It connects and fixes the concentrator and the fiber together as a whole. Another one is the optical power connection. When the incident light deviates from the normal line of the concentrator, part of the outgoing light may spill out of the receiving area of the optical fiber receiving end. The inner surface of the coupler can reflect these sun light into the receiving end of the fiber. The optical fiber is charge of the transmission of the sunlight power. The working process of the daylighting system is described as follows: The daylighting system facing to the sky is fixed on a base, without a tracking device. The light concentrating units (also concentrators) arranged in a fan shape faces to the sun's orbit. Benefiting from the ingenious design, each light concentrating unit has a certain ability of tracing error tolerance (abbreviated as TET, defined as an angle in Section 3.1.2). By proper arrangement with multiple units, there are always several units called effective receiving group who can simultaneously receive and transmit effectively the beam component of the sun light in different degrees respectively at an instant. In the form of a relay with the effective receiving group, the system can continuously receive sunlight during a certain time interval. For the other units that are beyond the allowable range of TET can still receive and transmit 463
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resistance. 2.2.2. The design of the coupler Fig. 7(b) shows that the outgoing light beam is a scattering beam, which is still not benefit to the energy transmission by optical fiber. The convergent beam is more convenient and more efficient to transmit to the optical fiber inlet end than the divergent beam. To deal with this problem, a part called coupler is needed. It is a hollow cylinder with a reflective inner surface. Its upper end is connected to the lower end of the concentrator, as shown in Fig. 8, its lower end will be connected to the receiving end of the fiber (undrawn in Fig. 8). From the rays tracing simulation in Fig. 8, it can be clearly seen that a convergent beam goes out from the outlet of the coupler, which would greatly improve the coupling efficiency between concentrator and fiber. For advancement of the reflectivity, the inner surface of the coupler needs coating. That is the only part that needs to be coated in the whole system. Moreover, the coated region is only a small area of the inner surface. Appropriate measures to isolate the coated surface from the air can be made easier for a small area of the inner surface of the coupler than for a large area of the outer surface of the MSRT concentrator. The coupler is also a structural piece. it firmly connects the concentrator and optical fiber, as shown in Fig. 4. 3. Efficiency attenuation curve of the light concentrating unit As mentioned in Section 2.1, the tracing error tolerance (TET) of the light concentrating unit is the key factor to realize the fixed daylighting system. The definition of the TET is based on efficiency attenuation curve. Therefore, we must first measure the efficiency attenuation curve that is one about the relation between the transmission efficiency and incident deviation angle. In this section, the efficiency attenuation curve of a light concentrating unit is investigated by computer simulation and by field measurement respectively.
Fig. 6. Optical path in an across section of the concentrator above its focus portion.
material and concentrating efficiency of the concentrator are all comprehensively considered, and if the condition of the total internal reflection should be met, then according to the relative equations in the literature (Kaiyan et al., 2011), the configuration parameters of the concentrator, including x C , xB , yC , yB , and yF , can be determined (see appendix). To make the light energy effectively be transmitted to the receiving end of fiber, some modifications must be made in the lower part of the concentrator below its focus. Compared to the MSRT concentrator as shown in Fig. 2, the rays transmitting through the outlet of the TIRT concentrator have a different feature. By computer rays tracing simulation, as shown in Fig. 7(a), if exit aperture is flat, owing to the nonlinear relation between incident and refractive angle for the light ray, the outgoing beam will not converge into its focus anymore. What makes things become worse is that the scattering angle of the whole outgoing light beam becomes larger than that in Fig. 2. This phenomenon would affect the coupling efficiency between the concentrator and the fiber. To make the scattering angle of the outgoing beam smaller, the cylindrical portion of the lower part of the concentrator is stretched to a proper position below its focus, as shown in Fig. 7(b). The focused beam will continue running down inside the cylinder. Then the rays will strike on the wall of the cylinder for the second time. The lowest end of the cylindrical portion is stretched to the position on where the outermost ray strikes for the second time. Then, a hemispheric converging lens is added to the lowest end of the cylindrical portion. Computer rays tracing simulation in Fig. 7(b) clearly indicates that the scattering angle of the entire outlet beam becomes smaller than that on Fig. 7(a). Namely, the outgoing beam is collimated to some extent for optical fiber coupling purposes. All the modifications on the concentrator are made on a whole block material. Now, an integral and compact transparent solid TIRT concentrator is formed, as shown in Fig. 5. A whole block solid material can guaranty the mechanical strength and the geometric shape of the concentrator. Glass material, if used, can ensure long life and low cost of the device. All the reflective surfaces that is exposed to the air is the natural outer surfaces of the transparent solid concentrator, which need polished only, don’t need coating a reflective layer, which will help to improve system’s weather
3.1. Computer simulation measurement of the efficiency attenuation curve 3.1.1. Model building A computer model was first made before ray tracing simulation was conducted. To compare the simulation results with that in experiment, the parameters of the concentrator that were set for a computer model were generally based on the available material we would get easily from the market and the test accessibility in our laboratory. Let the refractive index of the transparent material n = 1.500, the diameter of the outlet of the concentrator l = 1.200 × 10−2 m. According to Eq. (7) in the appendix, eigen parameter of the con3 centrator should be k ⩽ 10 5 = 0.671. After considering various factors as discussed in the appendix, set k =
2 3
= 0.667. With these three
Fig. 7. Optical path inside the solid concentrator. 464
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attenuates with φ increasing. The ray pattern in Fig. 11 can help us understand the decay trend of the attenuation curve. From the rays tracing simulation in Fig. 11, we find that when the incident parallel light beam gradually deviates the normal line, the change in the propagation process for rays is very complicated. When φ ≠ 0 , the light beam no longer converges on the focus of the concentrator, instead, it scatters as an asymmetrical non-focusing beam. Some rays do not satisfy the total internal reflection condition. These rays leak out to the outside. Though some rays might not leak out and reach the receiving end of the fiber, but if their incident angles at the inlet end of the fiber are larger than 37.5° (the maximum receiving angle of the fiber), these rays can still not be received by fiber. Therefore, when the deviation angle becomes larger and larger, the transmission efficiency will be less and less. But, from another perspective, though the incident rays deviate the normal line of the concentrator, the transmission efficiency still does not immediately or quickly become zero, instead, it gradually become less. From red line in Fig. 10, it can be seen that when φ = 3° , η still larger than 0.5. This result shows that if the light concentrating unit is stationary (no tracking component), it can still receive sunlight within an angle of 6° with a ray transmission efficiency η larger than 0.5. This result implies that the light concentrating unit has an ability of tracing error tolerance (TET). This feature of the light concentrating unit suggests that if multiple fixed units are arranged in a row, they would be able to continuously receive the sun light in relay model. That is just the basis on which a fixed fiber daylighting system can be formed. To quantitatively describe the TET more accurately, we define a quantity to characterize it, denoted as φTET . It is the deviation angle at which the transmission efficiency attenuates to half of the maximum, actually like the half-value breadth. It is used to describe the ability for a light concentrating unit to tolerate the deviation of tracking accuracy. Setting aside the specific device, suppose that TET of a light concentrating unit is φTET and its full transmission attenuation curve is shown in Fig. 12. Suppose a daylighting system with 5 identical light concentrating units. They are arranged along an arc and are apart by 2φTET , as shown in Fig. 13. Then the attenuation curve of the whole system should be as the red ling in Fig. 14. It shows that in a certain range, the output graph of the transmission efficiency is constant. It means that no matter where the sun goes in the designed range the
Fig. 8. The optical path in a reflective cylindrical surface coupler. p
known quantities n, l, k, relation k = l , Eqs. (8), (9), (10) and (11) in
p = 3 l = 8.000 × 10−3 m, the appendix, we could find xB = 6.000 × 10−3 m, yB = 2.025 × 10−2 m, xC = 3.280 × 10−2 m, yC = 0.1254 m. Accordint to the related equations in the literature (Kaiyan et al., 2011), the maximal effective width of the inlet aperture of the concentrator d = 2xC = 6.550 × 10−2 m (corresponding to DC in Fig. 6), and the total height of the concentrator H = 0.133 m were obtained. Let the numerical aperture of the fiber NA = 0.6. This parameter means that the inlet end of the fiber can receive those rays whose incident angle are not larger than 37.5°. Both diameters of the fiber and the inner diameter of the coupler were all 1.200 × 10−2 m. According to the data above, a computer model of the light concentrating unit was built, as shown in Fig. 9. 2
3.1.2. Rays tracing simulation and the draw of the efficiency attenuation curve The established model was imported into an optical simulation software for ray tracing simulation. Our main purpose of the ray tracing simulation for the light concentrating unit here was to find how its transmission efficiency varied with the deviation angle, the real value of the transmission efficiency itself was irrelevant. For simplicity, all loss was omitted. Let the wavelength of the incident light was 550 nm. What we considered only here was the loss caused by light ray’s deviating about the normal line of the concentrator. The transmission efficiency was defined as
η=
effective emergent rays effective incident rays
(i)
where the effective emergent rays are the rays going out the terminal end of the fiber. The effective incident rays are the rays intercepted by inlet aperture of the concentrator. For each deviation angle of the incident ray about the normal line of the concentrator, we selected a ray grid including a certain number (say 90,000) of the parallel rays as the incident rays and conducted the rays tracing simulation. Effective incident rays and effective emergent rays were found and substituted into Eq. (i), a η value could be gained corresponding to a certain deviation angle φ . A series of corresponding transmission efficiency values η could be obtained by changing the different deviation angles φ for measurement. Therefore, a η − φ diagram called efficiency attenuation curve could be gained, as the red line (round points) shown in Fig. 10. A note about the attenuation curve is that, when φ = 0° , η is set to be 1, namely, the maximum is normalized, the reason why we do so is that our focus is set on the change of η with φ , not on the value of η itself. From the attenuation curve in Fig. 10, it can be seen that η gradually
Fig. 9. Computational model of a light concentrating unit. 465
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Fig. 13. Schematic of a daylighting system.
Fig. 10. Ray transmission efficiency vs. deviation angle.
Fig. 14. Total efficiency attenuation curve of a daylighting system.
reception effect of a fixed daylighting system is the same. 3.2. Field measurement of the attenuation curve for a light concentrating unit 3.2.1. Experimental device To get real data about TET, a field measurement on a light concentrating unit is needed. This is actually a dynamic test under the real solar condition. A device including two light concentrating units and a tracking system was made to be tested on the TET of the light concentrating units under the real solar condition, as shown in Fig. 15. The concentrator used in the device was made from acrylic material, with the same parameters as that of the computer model mentioned above with a solar receiving area of 3.38 × 10−3 m2. A plastic optical fiber, Fig. 11. Ray pattern when tilt incidence.
Fig. 12. Efficiency attenuation curve.
Fig. 15. Experimental device used in field measurements. 466
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with its 1.2 × 10−2 m diameter that is equal to that of the cylindrical part of the concentrator and its 2.5 m length, is connected to each outlet end of the concentrator to form a light concentrating unit. To enhance the test effect and decrease the error, we used two units with their normal line parallel to each other. The terminal ends of two fibers are connected to an integral sphere with its diameter of 0.3 m. The latitude of the experiment site is 23°.
corresponding to this period of time, the change and fluctuation of the solar irradiance are not much that big, which is very close to the static experiment condition. So, it can be considered as a quasi-static test in this period of time. The incident solar irradiance is considered approximately constant. Therefore, the incident illuminance on the inlet aperture of the concentrator could also be constant. The graph in Fig. 17 can be approximately seen as an efficiency attenuation curve under the real solar condition. The curve shows that the double TET is approximately equal to 11°, namely φTET = 5. 5° , which is larger than that of φTET = 4° we have obtained in Section 3.2.2. This result is in line with the discussion near the end of the previous section. The reason is that the acquisition of two TET was under different weather patterns, corresponding to the different intensities of the diffuse component.
3.2.2. Dynamic measurement of the efficiency attenuation curve of a light concentrating unit The ratio of illuminance inside integral sphere to that outside is defined as illuminance transmission efficiency η′ (φ) .
η′ (φ) =
G (φ) inside illuminance = ouside illuminance F (φ)
(ii) 4. Test on the fixed optical fiber system
where G (φ) and F (φ) , respectively, denote the illuminance function of the outgoing light (from the terminal ends of the fibers) and the illuminance function of the incoming light (striking to the inlet of the concentrator). The same reason as for the η , what we care most here is the change trend of η′. So also let η′ (0) = 1, namely, the normalization of maximum. In fact, a data point η′ (φ) can be measured at an instant as for a certain deviation angle. To obtain more accurate data, the system was tracking the sun with a given deviation angle φ during a certain time interval. In this period, data record can be conducted many times, so a series of transmission efficiency values can be gained by Eq. (ii) under a different solar irradiances and their average value was found, which stands for a final value of η′ (φ) , corresponding a point on the black line (square points) in Fig. 10. Measured points were conducted once every 1 degree of deviation angle apart, namely Δφ = 1° . In terms of general trends, similar to the computer simulation result, η′ (φ) decreases with increasing φ . But the decay rate of η′ (φ) is slower than η. The black line in Fig. 10 indicates that the TET under the real solar condition is larger than that (it is 3°, which corresponds to the red line in Fig. 10) in computer simulation condition, it reaches φTET = 4° . The reason is that in the case of simulation, only the beam component of the incident light is considered, but under the field measurement condition, both beam and diffuse component of the solar radiation exist simultaneously, and that the diffuse component is insensitive to spatial orientation within the range of experimental angle. The total attenuation curve in field test is the superposition of a decay line of the beam component and an almost horizontal line of the diffuse component. The larger the proportion of scattering component, the more it can slow down the decline of the total attenuation curve. So, TET of a light concentrating unit also depends on the pattern of the weather. In another word, TET has a different value under different weather conditions. Owing to the treatment of the normalization of the maximum at φ = 0° , the absolute sizes of both transmission efficiency in Fig. 10 are not comparable. It means that only from Fig. 10 we cannot say which transmission efficiency is larger.
According to the conceptual designed system as in Fig. 13, a real system with 5 light concentrating units with 8° apart between two adjacent units (each has a φTET = 4° ) has been made, as shown in Fig. 18. The system has a total acceptance angle of 32°, (namely 4 × 8° = 32°), which covers solar track for 128 min. According to the local geographic position and experimental date and time, the system was adjusted to a proper orientation, specifically, let the normal line of the middle concentrator pointed to the sun at solar noon of the day and fixed the system firmly. The ends of 5 fibers were bundled and inserted into the chamber mentioned in Section 3.2.3. The detector of the illuminometer was put on a distance of 0.40 m from the ends of the fibers. This daylighting system would have a total transmission efficiency attenuation curve like that in Fig. 14 with a flat middle region. It means that in the range of the deviation angle from − 4φTET to 4φTET , here should be −16° to 16°, the transmission efficiency η′ is approximately a constant. According to Eq. (ii), we get G (φ) = η′F (φ) . Therefore, the outgoing light illuminance will follow the incoming light illuminance. It can be considered that the outgoing light illuminance will follow the fluctuation of the incoming light irradiance. Through field measurement, the above conclusion has been generally proven by Fig. 19 and Fig. 20. The two test results were gained under different weather patterns. Though the physical units of the incident light (in irradiance) and outgoing light (in illuminance) are not the same, we think it will not harm our conclusion that the outgoing light intensity is in step of the incoming light intensity. It also proves that our proposed system without a tracking component has the same receiving effect as the traditional fiber system with a tracking component. In addition, for this small system with only 5 light concentrating units, the test results show that, on average, about 180 lx of illuminance can be gained under about 600 W/m2 of solar irradiance (see Fig. 19), 300 lx gained under 800 W/ m2 (see Fig. 20), respectively. Therefore, theoretical and experimental
3.2.3. Quasi-static measurement of the efficiency attenuation curve of a light concentrating unit The TET of the light concentrating unit could be studied from another angle. The attenuation curve was measured directly. The sun was used as the light source. The device was oriented to the direction of the sun’s ray at solar noon of the day without its tracking system running. The bundled ends of the fibers were inserted into a small chamber with its dimension being 1.2 × 1.2 × 1.2 m3, and with its inside walls painted matte white. The detector of the illuminometer (accuracy: ± 3%) was placed at a distance of 0.4 m from the fiber terminal ends. The graph of illuminance at the measurement point versus local time is shown in Fig. 16 with its maximal value 561.8 lx at 12:11 (at solar noon on the test day). The time interval in which the illuminance is larger than half max-value 280.9 lx is from 11:54 to 12:36, lasting for 43 min, corresponding to the range of the change of the solar azimuth angle by 11°. Fig. 17 is the enlarged view of that region. It can be seen that,
Fig. 16. Graph of the illuminance of the measured point. 467
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Fig. 20. Graph of the illuminance of a fixed optical fiber system under weather pattern 2.
Fig. 17. The partial enlargement of the Fig. 16.
can only receive the diffuse sun light from this direction at a moment. However, owing to the spherical arrangement, all concentrators in our new system can simultaneously receive diffuse sun light from the different directions at a moment, including some reflected sun light from surrounding objects such as building walls. 5. Conclusions A new type of optical fiber daylighting system that integrates the advantage of traditional light pipe and optical fiber system has been proposed. Benefiting from ingenious design, a single light concentrating unit has good performance of the light transmission and an ability of tracing error tolerance. With multiple light concentrating units, arranged in an arc shape in a row, and with multiple rows, a fixed optical fiber daylighting system can be formed. Its receiving surface is like a spherical sunflower. For a spherical receiving surface fixed on ground, any direction of the incident light is equivalent. Exactly, the results of computer simulation and field measurement have proved that it's reception effect of solar energy is independent on the position of the sun within the designed range of receiving angle. In terms of reception effect alone, it is the same as a traditional system with a tracking device. In another word, the output illuminance of the fixed multi-unit compound system is almost independent of the incident angle of sunlight, only dependent on the strength of sunlight. It might also be said: The traditional optical fiber system uses tracking device to ensure that the normal of a flat receiving surface follows the solar rays at any time. The new system employs a spherical receiving surface to prearrange normals pointing in different directions in space at the same time, waiting for the arrival of the sun's rays. In addition, the fixed system with only five units in only one row (with a total receiving area of 1.69 × 10−2 m2) shows that, on average, the output illuminance inside a small test room is up to about 180 lx in a distance of 0.4 m from the bundled end of the fibers with the solar irradiance being about 600 W/ m2 (see Fig. 19), about 300 lx under about 800 W/m2 (see Fig. 20). The results of computer simulation and field measurement show that this non-tracking fixed optical fiber daylighting system is feasible. Although the system proposed in this paper is formed at the cost of
Fig. 18. Photo of the fixed optical fiber system.
Fig. 19. Graph of the illuminance of a fixed optical fiber system under weather pattern 1.
results prove the proposed fixed fiber lighting system is feasible. It is safe to speculate that if more units (in partially spherical shape, as shown in Fig. 21) are applied, the system will supply stronger illuminance for longer time intervals in a day, and give a wider space receiving angle for sunlight. Thus, a completely non-tracking component, namely a fixed optical fiber daylighting system would be realized. It can be easily seen from Fig. 21, the new system can receive not only direct sunlight but also diffuse and partially reflected light. For a conventional fiber optic daylighting system with solar tracking, the normal line of its receiving area directs to a single direction, it means it
Fig. 21. Schematic of a fixed optical fiber system with multi-row. 468
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light pipe system, the use of fine soft fibers as light transmission portion make system flexible in installation, easy to integrate the lighting system to buildings and less space occupation. These merits will facilitate the mass production of daylighting system, and help the realization of viable commercialization.
adding more light concentrating units, it is still worth it. It can be understood why it is worth doing so from the fact that, until now, few solar products with a tracking system have been widely realized commercialization in civilian market. Fig. 2 fully illustrates the simplicity of the structure of a light concentrating unit. Through industrial design, it is easy to be modularized, then a tapered module can be made. Side by side combination of multiple tapered module spontaneously compose a fan-shaped single row system. If the support frame and fiber are excluded (because the traditional system also needs them), the cost of the system lies mainly with concentrators (usually made of glass) and couplers. Low costs are to be expected. Moreover, compared to the traditional optical fiber system, the new system has no tracking component. It means no bulky and complex mechanical moving components and additional power supply to drive the moving components. Its simple and fixed structure is bound to have these advantages: its maintenance is almost free, its operational reliability would be greatly enhanced, its life span would increase considerably. Compared to the
Declaration of Competing Interest We declare that we have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment This work is supported by both of the National Natural Science Foundation of China under grant number 51166001 & 51868002, and Guangxi Natural Science Fund under grant number 20150954.
Appendix Suppose the refractive index of the selected transparent material is n , the width of the outlet of the concentrator AB = l , the abscissa of point B is 1 l xB = 2 , the curvilinear equation of the parabolic segment CB is y = 2p (x + l)2 . According to the constructing method described in the literature (Kaiyan et al., 2011), we get yB =
9l2 , 8p
the slope of the tangent of curve CB through point B is y′|x = 1 l = 2
called eigen parameter of the concentrator with its value range being 0 < k <
θ = arctan
3 . 2
3l 2p
=
3 , 2k
p
where the dimensionless factor k = l ,
The angle between the tangent and x axis is
3 2k
(1)
which is just the angle between the ray 1 and the normal line of the parabolic segment CB at B , namely the incident angle of ray 1 at B in the interface. Suppose the optical medium outside the concentrator is air with its refractive index approximately being 1. When the angle θ satisfies Eq. (2),
sin θ ⩾
1 n
(2)
Then the total internal reflection would occur everywhere on both parabolic segment DA and CB for the incoming light beam that is parallel to the y axis. From Eqs. (1) and (2), we obtain eigen parameter as
k⩽
3 2 n −1 2
(3)
This is the condition that insures the satisfaction of total internal reflection occurring in the first reflection on the interface (corresponding to parabolic segment DA and CB ). Let us follow the ray 1 to its second reflection. After reflecting from the point B , ray 1 will strike on straight line AE at E . Apparently, its incident angle at E is also the minimum compared to the other rays among the incoming light beam mentioned above. According to the equations in the literature (Kaiyan et al., 2011), the incident angle at E can be found as
δ = arccot
k 3 4
−
k2 3
(4)
To meet the condition of the total internal reflection, this angle should also satisfy Eq. (5).
sin δ ⩾
1 n
(5)
From Eqs. (4) and (5), we obtain Eq. (6)
k⩽
3 n2 − 1 2 n+1
(6)
To assure the condition of the total internal reflection being simultaneously satisfied for two reflections, eigen parameter of the concentrator k should be the small one among k should satisfy Eq. (7)
k⩽
3 2
n2 − 1 (for the first reflection) and
3 2
n2 − 1 n+1
3 n2 − 1 2 n+1
(for the second reflection). Since n ⩾ 1, so
n2 − 1 n+1
<
n2 − 1 , therefore,
(7)
This means that as long as the condition of total internal reflection on the wall of the cylindrical portion of the concentrator is satisfied, so does on the wall of the parabolic portion. If the condition of the total internal reflection is the only consideration, the smaller k is better. However, from the perspective of the material saving, larger k is better. Larger k means larger ratio α of the width to the height of the concentrator according to the literature (Kaiyan et al., 2011), that means less material. Another concentrator’s parameter significantly affected by k is the ratio β of the entrance width to exit width. This parameter affects the concentrating efficiency of the energy, which larger β is better. Actually, 469
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the value of β is larger when k smaller. Therefore, the selection of k ’s value depends on the actual demand in terms of three factors: Eq. (7), α and β . To sum up, total internal reflection condition needs less k, concentrating efficiency needs less k, but material saving needs larger k. Given the above, the structure parameters of the transparent solid concentrator can be determined as follows: 1) For the convenience of coupling, let the exit width l of the concentrator be the diameter of the fiber. 2) Once transparent material is selected, the refractive index n would be determined. Then maximal value of k can be found by Eq. (7) as 3
n2 − 1
km = 2 n + 1 . 3) Considering the effect of both α and β on the cost of the material and the efficiency of the concentrator, k can be finally determined. p 4) According to k = l , focal parameter p can be found and the coordinates of point B and C can be found by the following equations from the literature (Kaiyan et al., 2011).
xD = yD =
1 l 2
(8)
9l 2 8p
(9) 2
xC =
p2 5l − + 4 l
2 ⎛ 9l − p ⎞ + p2 l ⎠ ⎝4
yC =
p2 1 ⎛ 9l − + ⎜ 2p 4 l ⎝
⎜
⎟
2
(10) 2
2 ⎛ 9l − p ⎞ + p2 ⎞ ⎟ l ⎠ ⎝4 ⎠ ⎜
⎟
(11)
p yF = 2
(12)
So far, the configuration parameters of the concentrator are determined.
Malet-Damour, Bruno, Guichard, Stéphane, Bigot, Dimitri, Boyer, Harry, 2016. Study of tubular daylight guide systems in buildings: experimentation, modelling and validation. Energy Build 129, 308–321. Ngoc-Hai, Vu., Pham, Thanh-Tuan, Shin, Seoyong, 2016. Modified optical fiber daylighting system with sunlight transportation in free space. Optics Express 26, 1528–1545. Obianuju, Onubogu Nneka, Chong, Kok-Keong, 2017. High acceptance angle optical fiber based on daylighting system using two-stage reflective non-imaging dish concentrator. Energy Procedia 105, 498–504. Petržala, J., Kocifaj, M., Kómar, L., 2018. Accurate tool for express optical efficiency analysis of cylindrical light-tubes with arbitrary aspect ratios. Solar Energy 169, 264–269. Schlegel, G.O., Burkholder, F.W., et al., 2004. Analysis of a full spectrum hybrid lighting system. Solar Energy 76, 359–368. Sedki, Laila, Maaroufi, Mohamed, 2017. Design of parabolic solar daylighting systems based on fiber optic wires: a new heat filtering device. Energy Build 152, 434–441. Shuxiao, Wang, Jianping, Zhao, Lixiong, Wang, 2015. Research on energy saving analysis of tubular daylight devices. Energy Procedia 78, 1781–1786. Tao, T., Hongfei, Z., Kaiyan, H., Mayere, A., 2011. A new trough solar concentrator and its performance analysis. Solar Energy 85, 198–207. Tsangrassoulis, A., Doulos, L., Fontoynont, M., et al., 2005. On the energy efficiency of a prototype hybrid daylighting system. Solar Energy 79, 56–64. Vu, N.H., Shin, S., 2016. Cost-effective optical fiber daylighting system using modified compound parabolic concentrators. Solar Energy 136, 145–152. Xiaodi, X., Hongfei, Z., Kaiyan, H., Zhili, C., Tao, T., Guo, X., 2010. Experimental study on a new solar boiling water system with holistic track solar funnel concentrator. Energy 35, 692–697.
Reference Andre′, Erik, Schade, Jutta, 2002. Daylighting by Optical Fiber. Master’s thesis. University of Technology, Luleaa˚, pp. 21–27. Darula, Stanislav, Kittler, Richard, Kocifaj, Miroslav, 2010. Luminous effectiveness of tubular light-guides in tropics. Appl. Energy 87, 3460–3466. Feuermannt, D., Gordon, J.M., 1999. Solar fiber-optic mini-dishes: a new approach to the efficient collection of sunlight. Solar Energy 65, 159–170. Garcia-Hansen, Veronica, Edmonds, Ian, 2015. Methods for the illuminance of multilevel buildings with vertical light pipes. Solar Energy 117, 74–88. Kaiyan, He, Hongfei, Zheng, Yixin, Liu, Ziqian, Chen, 2007. An imaging compounding parabolic concentrator. In: Proceedings of ISES Solar World Congress, pp. 589–592. Kaiyan, He, Hongfei, Zheng, Tao, Tao, Xiaodi, Xue, 2009b. Experimental investigation of high temperature congregating energy solar stove with sun light funnel. Energy Convers. Manage. 50, 3051–3055. Kaiyan, He, Hongfei, Zheng, Zhengliang, Li, Tao, Tao, Jing, Dai, 2009a. Design and investigation of a novel concentrator used in solar fiber lamp. Solar Energy 83, 2086–2091. Kaiyan, H., Hongfei, Z., Tao, T., 2011. A novel multiple curved surfaces compound concentrator. Solar Energy 85, 523–529. Kandilli, Canan, et al., 2008. Exergetic assessment of transmission concentrated solar energy systems via optical fibres for building applications. Energy Build 40, 1505–1512. Kocifaj, Miroslav, Kundracik, Frantisˇek, Darula, Stanislav, Kittler, Richard, 2010. Theoretical solution for light transmission of a bended hollow light guide. Solar Energy 84, 1422–1432. Lv, Yuexia, Xia, Longyu, Yan, Jinyue, Bi, Jinpeng, 2018. Design of a hybrid fiber optic daylighting and PV solar lighting system. Energy Procedia 145, 586–591.
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A solar fiber daylighting system without tracking component ⁎
T
Kaiyan He , Ziqian Chen, Shiuku Zhong, Yingda Qian, Haoyue Liu, Junhua Yin, Bangdi Zhou School of Physical Science and Technology, Guangxi University, Nanning 530004, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Solar light guiding Solar concentrating Non-tracking system Optical fiber daylighting
A fixed optical fiber solar system for long distance daylighting used in buildings is proposed. Its structure and working principle have been introduced. The proposed system takes the advantages of both light pipe and traditional optical fiber system and overcomes their shortcomings. The receiving surface of the new system is like a spherical sunflower. It has a simple structure, good integrity, flexible light transmission and light redistribution characteristics. Especially, it does not require a tracking device. Both the theoretical analysis and field test have proved that the system has the same reception feature as the traditional optical fiber system with a tracking device. Its graph of the illuminance roughly follows the fluctuation of the curve of the solar irradiance. A small test system with a solar receiving area of 1.69 × 10−2 m2 and receiving angle of 32° was made to verify the feasibility of the fixed optical fiber system. Experimental result had proved that the proposed system is feasible. On average, the output illuminance inside a small test room is up to about 180 lx in a distance of 0.4 m from the bundled end of the fibers with the solar irradiance being about 600 W/m2, approximately 300 lx under approximately 800 W/m2. The simple structure, expectable low cost, almost maintenance-free and a predictable long life of the new system will facilitate the mass production and the viable commercialization of daylighting systems.
1. Introduction Nowadays, two schemes of solar light guiding, light pipe and the optical fiber, are often adopted in long distance daylighting for buildings. The light pipe technology is relative mature and has been commercially used in buildings. Recently, there are still some researchers studying light pipe, but their looked only at the details of the application (Garcia-Hansen and Edmonds, 2015; Bruno Malet-Damour et al., 2016; Darula et al., 2010), or new analysis method (Petržala et al., 2018; Shuxiao et al., 2015; Kocifaj, et al., 2010). There is no major breakthrough in technical route so far. The technology of optical fiber light guiding is not yet very mature. Several technologies of optical fiber daylighting have been proposed in the past few decades (Schlegel et al., 2004; Feuermannt and Gordon, 1999; Tsangrassoulis et al., 2005; Kandilli et al., 2008; Sedki and Maaroufi, 2017; Lv et al., 2018; Obianuju and Chong, 2017; Vu and Shin, 2016). Several commercial products made with different technologies of the optical fiber daylighting, such as the Himawari (Japan), Hybrid lighting (USA) and SOLUX (Germany) was reported by Andre′ and Schade (2002). The differences in these optical fiber technologies mainly lie in light concentrating component which usually resorts to typical lens (or Fresnel lens) and parabolic concentrator to collect sunlight. A parabolic
⁎
concentrator usually uses reflective surfaces to transmit solar energy, which is called the mirror surface reflection type (abbreviated as MSRT). An optical fiber system using a special designed compounded parabolic concentrator, called imaging CPC, as its light concentrating unit was introduced by Kaiyan et al. (2009a), , which still a MSRT type (Kaiyan et al. (2009b)). The idea of the special designed compounded parabolic concentrator was originally proposed in 2008 (Kaiyan et al., 2007). Since then, this type of concentrator has been studied further. Several papers involving its experimental results for two dimensions or three dimensions structure have been published subsequently (Kaiyan et al., 2009; Xiaodi et al., 2010; Tao et al., 2011). Especially in literature (Kaiyan et al., 2011), its working principle and several performance parameters have been theoretically studied in more detail. The schematic of its working principle is shown in Fig. 1. Tow parabolic line l1 and l2, with their symmetrical axes parallel to each other, are separated by a distance 2l. Take parabolic segments DA and CB, together with straight lines AE and BG, as the contour of the concentrator. When the contour is rotated around its symmetrical axis, a concentrator is formed, which looks like a funnel with a cylindrical lower portion. For a given solar ray as shown in Fig. 1, when it strikes on CB, parallel to the central axis of the parabola, it should be reflected to the focus F1, but
Corresponding author. E-mail address: [email protected] (K. He).
https://doi.org/10.1016/j.solener.2019.10.058 Received 10 July 2019; Received in revised form 18 October 2019; Accepted 23 October 2019 0038-092X/ © 2019 International Solar Energy Society. Published by Elsevier Ltd. All rights reserved.
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Nomenclature MSRT TIRT TET η
K P N α β
mirror surface reflection type total internal reflection type tracing error tolerance transmission efficiency
eigen parameter of the concentrator focal parameter of the parabola refractive index of the selected transparent material ratio of the width to the height of the concentrator ratio of the entrance width to exit width
daylighting system that integrates the advantages of both light pipe and the optical fiber system and overcomes their shortcomings, which is called a fixed optical fiber solar daylighting system. The proposed system has a simple, compact and integral structure, especially, without tracking system. In this paper, the system structure and its important components are first introduced, and then the conceptual design of components and their working principals are discussed. By computer simulation and field testing, the efficiency attenuation curves of a light concentrating unit and a five-unit daylighting system are researched.
due to the specular reflection of the AE, it will actually reach F, which is just the focus of the concentrator. The same physical process will happen for the opposite symmetrical side of the contour, namely DA l and BG. As long as F1 E = EF = FG = GF2 = 2 , all optical rays parallel to the central axis of the concentrator will converge on concentrator’s focus F. The light path pattern from a computer simulation of the concentrator is shown in Fig. 2. Some researchers have tried using A. Rabl and R. Winston’s CPC (non-imaging CPC) as concentrator in fiber optical daylighting systems. For example, Ngoc-Hai Vu and Seoyong Shin have come up with such a design with modified non-imaging CPCs, but still with a tracking system (Ngoc-Hai et al., 2016). Actually, for a normal non-imaging CPC, even when light is incident normally, the angle of divergence of the output light beam is colossal, let alone when the incident light is deflected from the normal line. Therefore, non-imaging CPC is unsuitable for connecting to a fiber to effective transmission sunlight. Though an optical fiber system has advantages of less damage to the room space and the flexibility of installation, it obviously has at least two defects. One is that there’s always a tracking system undoubtedly having a mechanical moving component and accordingly requires an external power to drive it, so that should make the system more complex, lower the working reliability of system, shorten the system’s life time, and increase the cost of the initiative investment and operation. The second defect of existing optical fiber system for MSRT type is that, to increase the reflectivity of the parabolic surface, a high reflecting coating layer that is directly exposed to the air is needed. This layer is apt to be corroded by pollution weather, which would result in the attenuation of the reflectivity of the layer with time going on. It can be easily seen that the advantages of the light pipe have a simple and almost maintenance-free structure, no movable components and a high working reliability, but its shortcomings are of having a big space occupation and less installation flexibility. Based on the above analysis, we put forward a new type of solar
2. The constitution and working principle of a fixed optical fiber solar daylighting system 2.1. System constitution A fixed optical fiber solar daylighting system is composed of multiple light concentrating units and a support frame. A single row of concentrating unit could be arranged in a fan-shaped structure, as shown in Fig. 3. In practice application, the system could be made by several rows of the concentrating unit. Therefore, the proposed daylighting system could be grouped by an arbitrary number of light concentration unit. A light concentrating unit is the core part of the daylighting system, as shown in Fig. 4. It has three parts: 1- concentrator, 2- coupler and 3-
Fig. 1. The schematic of an imaging CPC with mirror reflection.
Fig. 2. The optical path in an imaging CPC with mirror reflection. 462
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Fig. 3. Schematic of a fixed daylighting system.
Fig. 5. Photo of the concentrator.
effectively the diffuse component. We attempt to make a try that at the cost of adding more units a fixed daylighting system can be built without tracking component. Therefore, the magnitude of the tracing error tolerance (TET) of the light concentrating unit is the key factor to realize the fixed daylighting system.
2.2. The conceptual design of components and their working principal
Fig. 4. Schematic of a light concentrating unit.
2.2.1. The design of the concentrator The concentrator in Fig. 4 is the key part of a light concentrating unit. It was integrally made of a block of solid transparent material, as shown in Fig. 5. Light transmitting through it is realized by total internal reflection instead of the specular reflection in MSRT. To distinguish this type of concentrator from the MSRT type, it is designated as total internal reflection type (abbreviated as TIRT). From the outside outline, based on Fig. 2, its bottom end is slightly extended, and then a semicircular lens is added. The operation principle of this part has been studied in the literature (Kaiyan et al., 2011) and its internal light paths are shown in Fig. 6 (except those inside the hemispherical lens). Compared to MSRT concentrator, TIRT concentrator possesses two advantages, that is, highly integrative and high-strength structure; and no coating layer. To make sure the incoming rays meet the condition of the total internal reflection principle so that all incoming light would be transmitted to the outlet aperture, the geometrical parameters of the concentrator and the refractive index of the material must be properly determined. Fig. 6 shows the optical path in a concentrator. Let us put the lower section below the EG aside. A beam of parallel light between ray 1 and ray 2 strikes on the parabolic segment CB that is the interface between the air and the transparent material with the incident angle of ray 1 minimal. As long as ray 1 satisfies the condition of the total internal reflection, all other rays to the right of it will satisfy the condition as well. Suppose the refractive index of the selected transparent material is n , the width of the outlet of the concentrator AB = l . If the cost of the
optical fiber. We will not discuss the luminaries in this paper. The geometrical structure of the concentrator in Fig. 4 is the modified type of the one in Fig. 2. It is made of a block of solid glass or other appropriate transparent material. Its function is to collect and concentrate sunlight. The coupler is a hollow cylinder with a highly reflective inner surface. It has two functions. One is the structural connection. It connects and fixes the concentrator and the fiber together as a whole. Another one is the optical power connection. When the incident light deviates from the normal line of the concentrator, part of the outgoing light may spill out of the receiving area of the optical fiber receiving end. The inner surface of the coupler can reflect these sun light into the receiving end of the fiber. The optical fiber is charge of the transmission of the sunlight power. The working process of the daylighting system is described as follows: The daylighting system facing to the sky is fixed on a base, without a tracking device. The light concentrating units (also concentrators) arranged in a fan shape faces to the sun's orbit. Benefiting from the ingenious design, each light concentrating unit has a certain ability of tracing error tolerance (abbreviated as TET, defined as an angle in Section 3.1.2). By proper arrangement with multiple units, there are always several units called effective receiving group who can simultaneously receive and transmit effectively the beam component of the sun light in different degrees respectively at an instant. In the form of a relay with the effective receiving group, the system can continuously receive sunlight during a certain time interval. For the other units that are beyond the allowable range of TET can still receive and transmit 463
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resistance. 2.2.2. The design of the coupler Fig. 7(b) shows that the outgoing light beam is a scattering beam, which is still not benefit to the energy transmission by optical fiber. The convergent beam is more convenient and more efficient to transmit to the optical fiber inlet end than the divergent beam. To deal with this problem, a part called coupler is needed. It is a hollow cylinder with a reflective inner surface. Its upper end is connected to the lower end of the concentrator, as shown in Fig. 8, its lower end will be connected to the receiving end of the fiber (undrawn in Fig. 8). From the rays tracing simulation in Fig. 8, it can be clearly seen that a convergent beam goes out from the outlet of the coupler, which would greatly improve the coupling efficiency between concentrator and fiber. For advancement of the reflectivity, the inner surface of the coupler needs coating. That is the only part that needs to be coated in the whole system. Moreover, the coated region is only a small area of the inner surface. Appropriate measures to isolate the coated surface from the air can be made easier for a small area of the inner surface of the coupler than for a large area of the outer surface of the MSRT concentrator. The coupler is also a structural piece. it firmly connects the concentrator and optical fiber, as shown in Fig. 4. 3. Efficiency attenuation curve of the light concentrating unit As mentioned in Section 2.1, the tracing error tolerance (TET) of the light concentrating unit is the key factor to realize the fixed daylighting system. The definition of the TET is based on efficiency attenuation curve. Therefore, we must first measure the efficiency attenuation curve that is one about the relation between the transmission efficiency and incident deviation angle. In this section, the efficiency attenuation curve of a light concentrating unit is investigated by computer simulation and by field measurement respectively.
Fig. 6. Optical path in an across section of the concentrator above its focus portion.
material and concentrating efficiency of the concentrator are all comprehensively considered, and if the condition of the total internal reflection should be met, then according to the relative equations in the literature (Kaiyan et al., 2011), the configuration parameters of the concentrator, including x C , xB , yC , yB , and yF , can be determined (see appendix). To make the light energy effectively be transmitted to the receiving end of fiber, some modifications must be made in the lower part of the concentrator below its focus. Compared to the MSRT concentrator as shown in Fig. 2, the rays transmitting through the outlet of the TIRT concentrator have a different feature. By computer rays tracing simulation, as shown in Fig. 7(a), if exit aperture is flat, owing to the nonlinear relation between incident and refractive angle for the light ray, the outgoing beam will not converge into its focus anymore. What makes things become worse is that the scattering angle of the whole outgoing light beam becomes larger than that in Fig. 2. This phenomenon would affect the coupling efficiency between the concentrator and the fiber. To make the scattering angle of the outgoing beam smaller, the cylindrical portion of the lower part of the concentrator is stretched to a proper position below its focus, as shown in Fig. 7(b). The focused beam will continue running down inside the cylinder. Then the rays will strike on the wall of the cylinder for the second time. The lowest end of the cylindrical portion is stretched to the position on where the outermost ray strikes for the second time. Then, a hemispheric converging lens is added to the lowest end of the cylindrical portion. Computer rays tracing simulation in Fig. 7(b) clearly indicates that the scattering angle of the entire outlet beam becomes smaller than that on Fig. 7(a). Namely, the outgoing beam is collimated to some extent for optical fiber coupling purposes. All the modifications on the concentrator are made on a whole block material. Now, an integral and compact transparent solid TIRT concentrator is formed, as shown in Fig. 5. A whole block solid material can guaranty the mechanical strength and the geometric shape of the concentrator. Glass material, if used, can ensure long life and low cost of the device. All the reflective surfaces that is exposed to the air is the natural outer surfaces of the transparent solid concentrator, which need polished only, don’t need coating a reflective layer, which will help to improve system’s weather
3.1. Computer simulation measurement of the efficiency attenuation curve 3.1.1. Model building A computer model was first made before ray tracing simulation was conducted. To compare the simulation results with that in experiment, the parameters of the concentrator that were set for a computer model were generally based on the available material we would get easily from the market and the test accessibility in our laboratory. Let the refractive index of the transparent material n = 1.500, the diameter of the outlet of the concentrator l = 1.200 × 10−2 m. According to Eq. (7) in the appendix, eigen parameter of the con3 centrator should be k ⩽ 10 5 = 0.671. After considering various factors as discussed in the appendix, set k =
2 3
= 0.667. With these three
Fig. 7. Optical path inside the solid concentrator. 464
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attenuates with φ increasing. The ray pattern in Fig. 11 can help us understand the decay trend of the attenuation curve. From the rays tracing simulation in Fig. 11, we find that when the incident parallel light beam gradually deviates the normal line, the change in the propagation process for rays is very complicated. When φ ≠ 0 , the light beam no longer converges on the focus of the concentrator, instead, it scatters as an asymmetrical non-focusing beam. Some rays do not satisfy the total internal reflection condition. These rays leak out to the outside. Though some rays might not leak out and reach the receiving end of the fiber, but if their incident angles at the inlet end of the fiber are larger than 37.5° (the maximum receiving angle of the fiber), these rays can still not be received by fiber. Therefore, when the deviation angle becomes larger and larger, the transmission efficiency will be less and less. But, from another perspective, though the incident rays deviate the normal line of the concentrator, the transmission efficiency still does not immediately or quickly become zero, instead, it gradually become less. From red line in Fig. 10, it can be seen that when φ = 3° , η still larger than 0.5. This result shows that if the light concentrating unit is stationary (no tracking component), it can still receive sunlight within an angle of 6° with a ray transmission efficiency η larger than 0.5. This result implies that the light concentrating unit has an ability of tracing error tolerance (TET). This feature of the light concentrating unit suggests that if multiple fixed units are arranged in a row, they would be able to continuously receive the sun light in relay model. That is just the basis on which a fixed fiber daylighting system can be formed. To quantitatively describe the TET more accurately, we define a quantity to characterize it, denoted as φTET . It is the deviation angle at which the transmission efficiency attenuates to half of the maximum, actually like the half-value breadth. It is used to describe the ability for a light concentrating unit to tolerate the deviation of tracking accuracy. Setting aside the specific device, suppose that TET of a light concentrating unit is φTET and its full transmission attenuation curve is shown in Fig. 12. Suppose a daylighting system with 5 identical light concentrating units. They are arranged along an arc and are apart by 2φTET , as shown in Fig. 13. Then the attenuation curve of the whole system should be as the red ling in Fig. 14. It shows that in a certain range, the output graph of the transmission efficiency is constant. It means that no matter where the sun goes in the designed range the
Fig. 8. The optical path in a reflective cylindrical surface coupler. p
known quantities n, l, k, relation k = l , Eqs. (8), (9), (10) and (11) in
p = 3 l = 8.000 × 10−3 m, the appendix, we could find xB = 6.000 × 10−3 m, yB = 2.025 × 10−2 m, xC = 3.280 × 10−2 m, yC = 0.1254 m. Accordint to the related equations in the literature (Kaiyan et al., 2011), the maximal effective width of the inlet aperture of the concentrator d = 2xC = 6.550 × 10−2 m (corresponding to DC in Fig. 6), and the total height of the concentrator H = 0.133 m were obtained. Let the numerical aperture of the fiber NA = 0.6. This parameter means that the inlet end of the fiber can receive those rays whose incident angle are not larger than 37.5°. Both diameters of the fiber and the inner diameter of the coupler were all 1.200 × 10−2 m. According to the data above, a computer model of the light concentrating unit was built, as shown in Fig. 9. 2
3.1.2. Rays tracing simulation and the draw of the efficiency attenuation curve The established model was imported into an optical simulation software for ray tracing simulation. Our main purpose of the ray tracing simulation for the light concentrating unit here was to find how its transmission efficiency varied with the deviation angle, the real value of the transmission efficiency itself was irrelevant. For simplicity, all loss was omitted. Let the wavelength of the incident light was 550 nm. What we considered only here was the loss caused by light ray’s deviating about the normal line of the concentrator. The transmission efficiency was defined as
η=
effective emergent rays effective incident rays
(i)
where the effective emergent rays are the rays going out the terminal end of the fiber. The effective incident rays are the rays intercepted by inlet aperture of the concentrator. For each deviation angle of the incident ray about the normal line of the concentrator, we selected a ray grid including a certain number (say 90,000) of the parallel rays as the incident rays and conducted the rays tracing simulation. Effective incident rays and effective emergent rays were found and substituted into Eq. (i), a η value could be gained corresponding to a certain deviation angle φ . A series of corresponding transmission efficiency values η could be obtained by changing the different deviation angles φ for measurement. Therefore, a η − φ diagram called efficiency attenuation curve could be gained, as the red line (round points) shown in Fig. 10. A note about the attenuation curve is that, when φ = 0° , η is set to be 1, namely, the maximum is normalized, the reason why we do so is that our focus is set on the change of η with φ , not on the value of η itself. From the attenuation curve in Fig. 10, it can be seen that η gradually
Fig. 9. Computational model of a light concentrating unit. 465
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Fig. 13. Schematic of a daylighting system.
Fig. 10. Ray transmission efficiency vs. deviation angle.
Fig. 14. Total efficiency attenuation curve of a daylighting system.
reception effect of a fixed daylighting system is the same. 3.2. Field measurement of the attenuation curve for a light concentrating unit 3.2.1. Experimental device To get real data about TET, a field measurement on a light concentrating unit is needed. This is actually a dynamic test under the real solar condition. A device including two light concentrating units and a tracking system was made to be tested on the TET of the light concentrating units under the real solar condition, as shown in Fig. 15. The concentrator used in the device was made from acrylic material, with the same parameters as that of the computer model mentioned above with a solar receiving area of 3.38 × 10−3 m2. A plastic optical fiber, Fig. 11. Ray pattern when tilt incidence.
Fig. 12. Efficiency attenuation curve.
Fig. 15. Experimental device used in field measurements. 466
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with its 1.2 × 10−2 m diameter that is equal to that of the cylindrical part of the concentrator and its 2.5 m length, is connected to each outlet end of the concentrator to form a light concentrating unit. To enhance the test effect and decrease the error, we used two units with their normal line parallel to each other. The terminal ends of two fibers are connected to an integral sphere with its diameter of 0.3 m. The latitude of the experiment site is 23°.
corresponding to this period of time, the change and fluctuation of the solar irradiance are not much that big, which is very close to the static experiment condition. So, it can be considered as a quasi-static test in this period of time. The incident solar irradiance is considered approximately constant. Therefore, the incident illuminance on the inlet aperture of the concentrator could also be constant. The graph in Fig. 17 can be approximately seen as an efficiency attenuation curve under the real solar condition. The curve shows that the double TET is approximately equal to 11°, namely φTET = 5. 5° , which is larger than that of φTET = 4° we have obtained in Section 3.2.2. This result is in line with the discussion near the end of the previous section. The reason is that the acquisition of two TET was under different weather patterns, corresponding to the different intensities of the diffuse component.
3.2.2. Dynamic measurement of the efficiency attenuation curve of a light concentrating unit The ratio of illuminance inside integral sphere to that outside is defined as illuminance transmission efficiency η′ (φ) .
η′ (φ) =
G (φ) inside illuminance = ouside illuminance F (φ)
(ii) 4. Test on the fixed optical fiber system
where G (φ) and F (φ) , respectively, denote the illuminance function of the outgoing light (from the terminal ends of the fibers) and the illuminance function of the incoming light (striking to the inlet of the concentrator). The same reason as for the η , what we care most here is the change trend of η′. So also let η′ (0) = 1, namely, the normalization of maximum. In fact, a data point η′ (φ) can be measured at an instant as for a certain deviation angle. To obtain more accurate data, the system was tracking the sun with a given deviation angle φ during a certain time interval. In this period, data record can be conducted many times, so a series of transmission efficiency values can be gained by Eq. (ii) under a different solar irradiances and their average value was found, which stands for a final value of η′ (φ) , corresponding a point on the black line (square points) in Fig. 10. Measured points were conducted once every 1 degree of deviation angle apart, namely Δφ = 1° . In terms of general trends, similar to the computer simulation result, η′ (φ) decreases with increasing φ . But the decay rate of η′ (φ) is slower than η. The black line in Fig. 10 indicates that the TET under the real solar condition is larger than that (it is 3°, which corresponds to the red line in Fig. 10) in computer simulation condition, it reaches φTET = 4° . The reason is that in the case of simulation, only the beam component of the incident light is considered, but under the field measurement condition, both beam and diffuse component of the solar radiation exist simultaneously, and that the diffuse component is insensitive to spatial orientation within the range of experimental angle. The total attenuation curve in field test is the superposition of a decay line of the beam component and an almost horizontal line of the diffuse component. The larger the proportion of scattering component, the more it can slow down the decline of the total attenuation curve. So, TET of a light concentrating unit also depends on the pattern of the weather. In another word, TET has a different value under different weather conditions. Owing to the treatment of the normalization of the maximum at φ = 0° , the absolute sizes of both transmission efficiency in Fig. 10 are not comparable. It means that only from Fig. 10 we cannot say which transmission efficiency is larger.
According to the conceptual designed system as in Fig. 13, a real system with 5 light concentrating units with 8° apart between two adjacent units (each has a φTET = 4° ) has been made, as shown in Fig. 18. The system has a total acceptance angle of 32°, (namely 4 × 8° = 32°), which covers solar track for 128 min. According to the local geographic position and experimental date and time, the system was adjusted to a proper orientation, specifically, let the normal line of the middle concentrator pointed to the sun at solar noon of the day and fixed the system firmly. The ends of 5 fibers were bundled and inserted into the chamber mentioned in Section 3.2.3. The detector of the illuminometer was put on a distance of 0.40 m from the ends of the fibers. This daylighting system would have a total transmission efficiency attenuation curve like that in Fig. 14 with a flat middle region. It means that in the range of the deviation angle from − 4φTET to 4φTET , here should be −16° to 16°, the transmission efficiency η′ is approximately a constant. According to Eq. (ii), we get G (φ) = η′F (φ) . Therefore, the outgoing light illuminance will follow the incoming light illuminance. It can be considered that the outgoing light illuminance will follow the fluctuation of the incoming light irradiance. Through field measurement, the above conclusion has been generally proven by Fig. 19 and Fig. 20. The two test results were gained under different weather patterns. Though the physical units of the incident light (in irradiance) and outgoing light (in illuminance) are not the same, we think it will not harm our conclusion that the outgoing light intensity is in step of the incoming light intensity. It also proves that our proposed system without a tracking component has the same receiving effect as the traditional fiber system with a tracking component. In addition, for this small system with only 5 light concentrating units, the test results show that, on average, about 180 lx of illuminance can be gained under about 600 W/m2 of solar irradiance (see Fig. 19), 300 lx gained under 800 W/ m2 (see Fig. 20), respectively. Therefore, theoretical and experimental
3.2.3. Quasi-static measurement of the efficiency attenuation curve of a light concentrating unit The TET of the light concentrating unit could be studied from another angle. The attenuation curve was measured directly. The sun was used as the light source. The device was oriented to the direction of the sun’s ray at solar noon of the day without its tracking system running. The bundled ends of the fibers were inserted into a small chamber with its dimension being 1.2 × 1.2 × 1.2 m3, and with its inside walls painted matte white. The detector of the illuminometer (accuracy: ± 3%) was placed at a distance of 0.4 m from the fiber terminal ends. The graph of illuminance at the measurement point versus local time is shown in Fig. 16 with its maximal value 561.8 lx at 12:11 (at solar noon on the test day). The time interval in which the illuminance is larger than half max-value 280.9 lx is from 11:54 to 12:36, lasting for 43 min, corresponding to the range of the change of the solar azimuth angle by 11°. Fig. 17 is the enlarged view of that region. It can be seen that,
Fig. 16. Graph of the illuminance of the measured point. 467
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Fig. 20. Graph of the illuminance of a fixed optical fiber system under weather pattern 2.
Fig. 17. The partial enlargement of the Fig. 16.
can only receive the diffuse sun light from this direction at a moment. However, owing to the spherical arrangement, all concentrators in our new system can simultaneously receive diffuse sun light from the different directions at a moment, including some reflected sun light from surrounding objects such as building walls. 5. Conclusions A new type of optical fiber daylighting system that integrates the advantage of traditional light pipe and optical fiber system has been proposed. Benefiting from ingenious design, a single light concentrating unit has good performance of the light transmission and an ability of tracing error tolerance. With multiple light concentrating units, arranged in an arc shape in a row, and with multiple rows, a fixed optical fiber daylighting system can be formed. Its receiving surface is like a spherical sunflower. For a spherical receiving surface fixed on ground, any direction of the incident light is equivalent. Exactly, the results of computer simulation and field measurement have proved that it's reception effect of solar energy is independent on the position of the sun within the designed range of receiving angle. In terms of reception effect alone, it is the same as a traditional system with a tracking device. In another word, the output illuminance of the fixed multi-unit compound system is almost independent of the incident angle of sunlight, only dependent on the strength of sunlight. It might also be said: The traditional optical fiber system uses tracking device to ensure that the normal of a flat receiving surface follows the solar rays at any time. The new system employs a spherical receiving surface to prearrange normals pointing in different directions in space at the same time, waiting for the arrival of the sun's rays. In addition, the fixed system with only five units in only one row (with a total receiving area of 1.69 × 10−2 m2) shows that, on average, the output illuminance inside a small test room is up to about 180 lx in a distance of 0.4 m from the bundled end of the fibers with the solar irradiance being about 600 W/ m2 (see Fig. 19), about 300 lx under about 800 W/m2 (see Fig. 20). The results of computer simulation and field measurement show that this non-tracking fixed optical fiber daylighting system is feasible. Although the system proposed in this paper is formed at the cost of
Fig. 18. Photo of the fixed optical fiber system.
Fig. 19. Graph of the illuminance of a fixed optical fiber system under weather pattern 1.
results prove the proposed fixed fiber lighting system is feasible. It is safe to speculate that if more units (in partially spherical shape, as shown in Fig. 21) are applied, the system will supply stronger illuminance for longer time intervals in a day, and give a wider space receiving angle for sunlight. Thus, a completely non-tracking component, namely a fixed optical fiber daylighting system would be realized. It can be easily seen from Fig. 21, the new system can receive not only direct sunlight but also diffuse and partially reflected light. For a conventional fiber optic daylighting system with solar tracking, the normal line of its receiving area directs to a single direction, it means it
Fig. 21. Schematic of a fixed optical fiber system with multi-row. 468
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light pipe system, the use of fine soft fibers as light transmission portion make system flexible in installation, easy to integrate the lighting system to buildings and less space occupation. These merits will facilitate the mass production of daylighting system, and help the realization of viable commercialization.
adding more light concentrating units, it is still worth it. It can be understood why it is worth doing so from the fact that, until now, few solar products with a tracking system have been widely realized commercialization in civilian market. Fig. 2 fully illustrates the simplicity of the structure of a light concentrating unit. Through industrial design, it is easy to be modularized, then a tapered module can be made. Side by side combination of multiple tapered module spontaneously compose a fan-shaped single row system. If the support frame and fiber are excluded (because the traditional system also needs them), the cost of the system lies mainly with concentrators (usually made of glass) and couplers. Low costs are to be expected. Moreover, compared to the traditional optical fiber system, the new system has no tracking component. It means no bulky and complex mechanical moving components and additional power supply to drive the moving components. Its simple and fixed structure is bound to have these advantages: its maintenance is almost free, its operational reliability would be greatly enhanced, its life span would increase considerably. Compared to the
Declaration of Competing Interest We declare that we have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment This work is supported by both of the National Natural Science Foundation of China under grant number 51166001 & 51868002, and Guangxi Natural Science Fund under grant number 20150954.
Appendix Suppose the refractive index of the selected transparent material is n , the width of the outlet of the concentrator AB = l , the abscissa of point B is 1 l xB = 2 , the curvilinear equation of the parabolic segment CB is y = 2p (x + l)2 . According to the constructing method described in the literature (Kaiyan et al., 2011), we get yB =
9l2 , 8p
the slope of the tangent of curve CB through point B is y′|x = 1 l = 2
called eigen parameter of the concentrator with its value range being 0 < k <
θ = arctan
3 . 2
3l 2p
=
3 , 2k
p
where the dimensionless factor k = l ,
The angle between the tangent and x axis is
3 2k
(1)
which is just the angle between the ray 1 and the normal line of the parabolic segment CB at B , namely the incident angle of ray 1 at B in the interface. Suppose the optical medium outside the concentrator is air with its refractive index approximately being 1. When the angle θ satisfies Eq. (2),
sin θ ⩾
1 n
(2)
Then the total internal reflection would occur everywhere on both parabolic segment DA and CB for the incoming light beam that is parallel to the y axis. From Eqs. (1) and (2), we obtain eigen parameter as
k⩽
3 2 n −1 2
(3)
This is the condition that insures the satisfaction of total internal reflection occurring in the first reflection on the interface (corresponding to parabolic segment DA and CB ). Let us follow the ray 1 to its second reflection. After reflecting from the point B , ray 1 will strike on straight line AE at E . Apparently, its incident angle at E is also the minimum compared to the other rays among the incoming light beam mentioned above. According to the equations in the literature (Kaiyan et al., 2011), the incident angle at E can be found as
δ = arccot
k 3 4
−
k2 3
(4)
To meet the condition of the total internal reflection, this angle should also satisfy Eq. (5).
sin δ ⩾
1 n
(5)
From Eqs. (4) and (5), we obtain Eq. (6)
k⩽
3 n2 − 1 2 n+1
(6)
To assure the condition of the total internal reflection being simultaneously satisfied for two reflections, eigen parameter of the concentrator k should be the small one among k should satisfy Eq. (7)
k⩽
3 2
n2 − 1 (for the first reflection) and
3 2
n2 − 1 n+1
3 n2 − 1 2 n+1
(for the second reflection). Since n ⩾ 1, so
n2 − 1 n+1
<
n2 − 1 , therefore,
(7)
This means that as long as the condition of total internal reflection on the wall of the cylindrical portion of the concentrator is satisfied, so does on the wall of the parabolic portion. If the condition of the total internal reflection is the only consideration, the smaller k is better. However, from the perspective of the material saving, larger k is better. Larger k means larger ratio α of the width to the height of the concentrator according to the literature (Kaiyan et al., 2011), that means less material. Another concentrator’s parameter significantly affected by k is the ratio β of the entrance width to exit width. This parameter affects the concentrating efficiency of the energy, which larger β is better. Actually, 469
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the value of β is larger when k smaller. Therefore, the selection of k ’s value depends on the actual demand in terms of three factors: Eq. (7), α and β . To sum up, total internal reflection condition needs less k, concentrating efficiency needs less k, but material saving needs larger k. Given the above, the structure parameters of the transparent solid concentrator can be determined as follows: 1) For the convenience of coupling, let the exit width l of the concentrator be the diameter of the fiber. 2) Once transparent material is selected, the refractive index n would be determined. Then maximal value of k can be found by Eq. (7) as 3
n2 − 1
km = 2 n + 1 . 3) Considering the effect of both α and β on the cost of the material and the efficiency of the concentrator, k can be finally determined. p 4) According to k = l , focal parameter p can be found and the coordinates of point B and C can be found by the following equations from the literature (Kaiyan et al., 2011).
xD = yD =
1 l 2
(8)
9l 2 8p
(9) 2
xC =
p2 5l − + 4 l
2 ⎛ 9l − p ⎞ + p2 l ⎠ ⎝4
yC =
p2 1 ⎛ 9l − + ⎜ 2p 4 l ⎝
⎜
⎟
2
(10) 2
2 ⎛ 9l − p ⎞ + p2 ⎞ ⎟ l ⎠ ⎝4 ⎠ ⎜
⎟
(11)
p yF = 2
(12)
So far, the configuration parameters of the concentrator are determined.
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