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With the high population growth rate, especially in developing countries, and the scarcity of land resources, buildings are becoming so close to each other, depriving the lower floors and the alleys from sunlight and consequently causing health problems. Therefore, there is an urgent need for cost-effective efficient light redirecting panels that guide sun rays into those dim places. In this paper, we address this problem. A novel sine wave based panel is presented to redirect/diverge light downward and enhance the illumination level in those dark places. Simulation results show that the proposed panel improves the illuminance values by more than 200% and 400% in autumn and winter respectively, operates over wide solar altitude ranges, and redirects light efficiently. Experimental and simulation results are in good agreement.
© 2014 Optical Society of America
1. Introduction
In recent years the population growth rate has increased rapidly and buildings have become so close to each other in many areas in the world, an example is shown in Fig. 1, depriving lower floors and alleys from good level of sun light. Hence, it is important to provide not only a good level of lighting but also a healthy environment. However, as we need to save energy and reduce carbon emissions, sustainable sources of energy have to replace conventional old expensive sources to illuminate these places. The best sustainable substitute is the redirection of sunlight to provide homogeneous light for long periods of time throughout most of the day.
Fig. 1 Dim light wells and streets in dense urban areas (a) real case in Egypt (b) model to be simulated.
To redirect sun light, several structures were recently developed [1–7]. They use either redirecting panels [1–4] or guiding tubes [5–7]. Some of the panel-based structures depend on reflecting light, e.g. LUMITOP® where stacked polymethyl methacrylate (PMMA) profiles are used as light conductors [1] and light shelf, which is designed to shade and reflect light on its top surface and to shield direct glare from the sky [2]. Other structures depend on refracting light as the one presented in [3], which consists of micro lenses that focus the incident rays on one side and prisms that redirect light upwards to aim the ceiling on the other side, and the micro-prismatic panels presented in [2, 4], which are thin and planar, have the shape of saw tooth and are made of clear PMMA. Unfortunately, these panels, though they are cost effective, simple and fixed, they direct the light upwards into the depth of the room and are not suitable for redirecting the sun light into the depth of narrow streets. Moreover, these systems are optimized only for a certain solar altitude range and are adopting the conditions of a certain geographical region (Middle Europe).
In this paper a new panel based on a sine wave structure, as shown in Fig. 2, is proposed. Placed on building roofs and facing the sun, it uses the idea of light divergence to redirect sun light downward into alleys. Because of its shape, the proposed panel operates over a wide range of solar altitudes and can be tilted to fit different building conditions.
The paper is organized as follows; section 2 introduces the proposed structure, section 3 presents the simulations. Fabrication techniques are explained in section 4, the measurement results are presented in section 5, environmental aspects of the proposed technique are discussed in section 6 and finally conclusion is provided in section 7.
2. Proposed structure and problem formulation
In this paper, a sine wave shaped panel, as shown in Fig. 2, is developed to redirect sunlight to cover dark alleys between tall buildings by diverging it. The underlying idea is that the sine wave has a varying slope (plane of incidence of the sunlight rays) across its period, as shown in Fig. 3(a), so the refracted rays diverge within the sine period emerging with different angles according to Snell’s law, Eq. (1):
where and are the first and the second medium refractive indices respectively, is the angle of incidence and is the angle of refraction. In principle, this idea is similar to Powell lens [8], however the later deals with narrow beams while the proposed structure deals with plane waves (the sunlight).The fan out angle, which is the difference between the maximum output angle (θmax) and the minimum output angle (θmin), varies with varying either the sine amplitude or period. As the amplitude increases -for the same period- the fan out angle becomes wider. This is due to the fact that with increasing amplitude the slope becomes steeper and changes faster, Fig. 3(b), leading to wider fan outs. Also, as the period decreases for the same amplitude a wider fan out angle is observed, Fig. 3(c). The last parameter that affects the fan out angle is the material refractive index, which provides wider fan outs as it increases. Figure 4 shows the emergence angle across the sine period calculated by an algebraic-graphical method (GeoGebra [9]).
The mathematical formulation of the investigated problem is shown in Fig. 5. It is necessary for the maximum emerging angle to comply with Eq. (2) to ensure that the redirected light reaches the far left end of the alley or well, while the minimum emerging angle has to comply with Eq. (3) to guarantee that no redirected light is lost in space and stays within the building.
In the next section, simulations are carried out to determine an optimum design, best amplitude to period ratio and tilt angle (θtilt), that fits most of the year conditions, i.e., fulfilling Eqs. (2) and (3), providing maximum percentage of the transmitted power with respect to the incident power averaged over the year and offering uniform power distribution at the output.
3. Simulation results
By using GeoGebra, it is possible to visualize the effect of different parameters (such as the solar angle and the panel design on the emerging light rays), calculate the fan out angles and observe the behavior of emerging rays. However, the developed model does neither consider the blockage effect of neighboring sine periods, Fig. 6, nor does it track rays experiencing total internal reflection. Therefore, a ray tracing algorithm has to be applied to accurately model the proposed structure.
The simulation methodology includes designing the panel in a horizontal position and directing a visible light source (550 nm wavelength) of a fixed number of rays, 100 rays having 100 watts, towards a 6 mm clear PMMA panel, p = 6 mm and a varies, with different incident angles starting from 10° to 90° as shown in Fig. 7. The results are visually analyzed for the fan out angle, and the percentage of power transmission is recorded.
Figures 8(a) and 8(b) show, respectively, the phenomena of total internal reflections and blocking. Simulation results show that blocking is so significant in the lower incident angles where light rays are entirely blocked by the repetition of the sine wave causing the effective area to become smaller (green area) as shown in Fig. 8(b).
Fig. 8 Ray tracing simulations showing the effect of: (a) total internal reflections (b) blockage of neighboring sine periods.
Samples with different amplitude to period ratios are simulated. Emerging versus incident rays are shown in Fig. 9 for the 1:4 ratio. Similar results are obtained for different designs. Figure 10 shows the relation of the transmitted power percentage, maximum and minimum emergence angles versus the incident angle for the different designs.
Fig. 9 Simulation results for 1:4 amplitude to period ratio at 0° tilt for incident angles ranging from 10° to 90°.
Fig. 10 Transmitted power percentage, maximum and minimum emergence angles versus incident angles for different design ratios (a) 2:1, (b) 1:1, (c) 1:2, (d) 1:4, (e) 1:8, and (f) isosceles (80°, 80°, 20°).
To consider the effect of tilting the panel, the emergence angles and transmitted power percentage are re-plotted versus the solar altitude (SA), which is given by Eq. (4):
Figure 11 shows a sample of the updated results. It also shows that as the tilt angle changes the curve’s maximum and minimum emergence angles for different incident angles shift to the left.
Fig. 11 Panel performance after considering the tilt angle, design ratio is 1:4. (a) 10° tilt angle (b) 20° tilt angle.
To get an optimum design that fits most of the year conditions, the ranges of the transmitted power percentage that satisfy the boundaries set by Eq. (2) and Eq. (3) are summed up over the solar altitude range from 10° to 80° for different design ratios and different tilt angles. Results are depicted in Table 1 and are plotted in Fig. 12. Both show that for the problem described in Fig. 5 the optimum design ratio is 1:1 with 35° tilt angle.
Table 1. Transmitted Power Percentage Integrated over Solar Altitude Range 10° to 80° for Different Designing Ratios and Different Tilt Angles
The transmitted power uniformity, shown in Fig. 13 for different designs, is further studied by calculating the ratio between maximum power density to minimum power density after neglecting edge effect on a 1m flat screen located at 15 cm beneath the panel. The closer the number to unity the more uniform the power transmitted is. Figure 14 shows the updated results, which reveals that the best design ratio for the problem described above is 1:4 with 10° tilt angle.
Fig. 14 Integrated transmitted power percentage for different designs after considering the uniformity condition.
To validate the proposed structure, a 3D model of two buildings of 12 meters height and 4 meters separation, as shown in Fig. 1, is then built and simulated using Radiance [10]. To include the panel, which is a complex redirecting device, into the simulator the bidirectional scattering distribution function (BSDF) has to be defined [11]. This function is generated using Radiance’s GenBSDF function, whose input is a .cad file and output is an .xml file, containing all the numerical BSDF data, i.e. transmittance and angle output data for different hemispherical incident angles. The .xml file is then fed-back to Radiance to simulate the light direction.
Figure 15 shows the simulations at two different timings, autumn and winter, both at noon, while Fig. 16 shows the isolux on the ground. Illumination has been significantly improved. Averaging the illuminance in the alley, Table 2 shows that enhancements are 242%, 411% in autumn and winter, respectively.
Fig. 16 Isolux at the ground with and without the proposed panel at two timings: (a) Autumn, b) Winter.
Table 2. Average Illuminance Enhancement at the Ground before and after Using the Panel
4. Fabrication
The designed structure with 1:4 sine wave amplitude to period ratio is manufactured using the compression moulding technique on a flat PMMA sheet of 6 mm thickness. A hydraulic thermal press of 30 ton capacity was used, equipped with a pressure gauge and temperature controller for both upper and lower platens. A 85 × 85 × 6 mm PMMA sheet was placed between two chromated tool steel flat plates and slowly heated between the press platens (at no pressure) to a temperature above the glass transition temperature (Tg = 107 °C) and further kept at 160 °C for 90 minutes until the sheet is homogeneously heated up across the thickness
The press is then opened and the upper die with the designed sine wave chromated tool steel, as indicated in Fig. 17, is placed on top of the hot sheet and further partially pressed up to a pressure of 0.2 bar. Pressure drop is observed indicating material flow and the cease of normal stresses caused by shear forces during pressing. This is of vital importance in order to reduce material’s memory effect targeting dimensional accuracy. When the pressure falls back to zero, indicating diminished material resistance, pressing up to 0.2 bar is repeated till the requested shape is achieved. The PMMA sheet is then left to cool down to room temperature inside the closed mould. Figure 18 shows the picture of the fabricated sample.
Fig. 17 The die used in manufacturing. Mould material is chromated tool steel. Dimensions are in (mm).
5. Experimental measurements
The fabricated sample is tested using the setup shown in Fig. 19. A tungsten light source (C-type CIE illuminant) illuminates the fabricated sample and the angles of the emerging rays are measured. Simulated and experimentally measured angles, which are shown in Fig. 20, are in good agreement. Discrepancies may be due to the fabricated sample roughness.
Fig. 19 (a) Experimental test setup. (b) Output light from the 1:4 sample with 0° tilt and 90° incident angle.
6. Environmental aspects of the proposed technique
One of the prospective applications of the proposed panel is lighting a well enclosed in a 4-store building. Well dimensions are typically 4 m × 4 m × 12 m, as illustrated in Fig. 21 for a 1:10 scaled prototype. Corresponding dimensions are thus 40cm × 40 cm × 120 cm. Figure 21 also shows a simple structure that is designed to support the sunlight guiding panel and to measure the tilting angle. By visual inspection, the proposed panel has improved significantly the illuminance.
Fig. 21 Well prototype with and without panel, dimensions are 40cm × 40 cm × 120 cm. a) Without panel, b) with panel θtilt = 10°, c) maximum illumination can be achieved inside the well.
As presented by the prototype, the proposed panels montage should not cover the entire well or the street shown in Fig. 1. If this was the case, streets would turn into greenhouses, which is definitely an undesired side effect. In actual cases, the panels will be mounted on roof tops, thus covering 1m only of the 5-6 m width of the street, providing sufficient free spaces that allow the exit of heat. In other words panels are designed to only redirect and spread the same amount of heat and light entering the street to needed areas but do not enclose them.
Regular panel maintenance and cleaning is a necessary process, as commonly the case for all solar technologies. The installation of panels at roof tops, which are habitable and accessible places, makes it easy to reach and clean the panels from the roof as it extends only for 1m beyond the roof edge.
From the production point of view, the mould material used to produce the panel sample is chromated tool steel. This ensures high production rates at high surface quality, leading to high transparency (and thus transmittance). PMMA as a polymeric material naturally exhibits high aging resistance and excellent weatherability, if compared to other thermoplastics, also including UV radiation. Thus, outdoor exposure does not cause discoloration or embrittlement of PMMA. The outstanding stability of PMMA to sunlight results primarily from weak absorption properties in the UV-region [12–14]. In this respect, industry offers a long term guarantee against yellowing and light loss.
7. Conclusion
A novel sine-wave panel that diverges light and directs it downward was proposed. The fan-out angle exceeds 80° for certain solar altitudes and the transmitted power percentage varies from 40% to 90% as the solar altitude varies from 10° to 80°. The panel was made from polymethyl methacrylate (PMMA), which is a synthetic glass similar thermoplastic material commonly available at low cost under the terms Plexiglas or Acrylic. Fabrication was achieved at low cost using common press forming equipment. The proposed structure provides a good solution for the problem of sun light deprivation in dense populated areas as illumination enhancement exceeds 400% in winter. Experimental results are in good agreement with the theoretical expectations.
Acknowledgment
This work was supported by the Science and Technology Development Fund (STDF), Cairo, Egypt, grant number 2799.
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