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Tracing of daylight through circular light pipes with anidolic concentrators
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ScienceDirect Solar Energy 110 (2014) 818–829 www.elsevier.com/locate/solener
Tracing of daylight through circular light pipes with anidolic concentrators Thanyalak Taengchum a, Surapong Chirarattananon a,b,⇑, Robert H.B. Exell a,b, Pipat Chaiwiwatworakul a,b a
Joint Graduate School of Energy and Environment, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand b Science and Technology Postgraduate Education and Research Development Office, Ministry of Education, Thailand Received 10 July 2014; received in revised form 24 September 2014; accepted 30 September 2014 Available online 11 November 2014 Communicated by: Associate Editor J.-L. Scartezzini
Abstract Light pipes can bring both daylight from the sun and the sky into deep interior spaces of a building. Adding an anidolic concentrator at the entry port of a light pipe will increase daylight capture and may reduce the overall cost per unit of delivered daylight flux, especially for long pipes or pipes with bends. This paper presents results of modeling, experiments, and simulation of transmission of beam and diffuse daylight through tubular light pipes attached with an anidolic concentrator at the entry port. Analytic method is used for tracing light rays from the sun and sources in the sky zones through the anidolic concentrator to the straight section of a pipe through to the exit port. The vertical curvature surface of the anidolic concentrator is modeled as a parabolic section. The ASRC-CIE sky luminance distribution model is used to generate luminance of daylight from the sky. The algorithms are coded in a MATLAB program. The physical anidolic concentrator and pipe are fabricated from off-the-shelf materials commonly available. The interior surface of each section is lined with a film of reflectance of 99%. Results from calculation of transmission of global and diffuse daylight through the tubular pipe with anidolic concentrator match well with those from experiments. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Daylighting; Light pipe; Anidolic concentrator; Sky luminance; Sunlight
1. Introduction Electric lighting accounts directly for 20% of electricity consumption in air-conditioned buildings in Thailand while daylight is plentiful, (Chirarattananon et al., 2010). Daylighting is attractive and can greatly help reduce lighting energy. The common method of daylighting letting ⇑ Corresponding author at: Joint Graduate School of Energy and Environment, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand. Tel.: +66 (2) 4708309. E-mail addresses: [email protected] (T. Taengchum), surapong. [email protected] (S. Chirarattananon), [email protected] (R.H.B. Exell), [email protected] (P. Chaiwiwatworakul).
http://dx.doi.org/10.1016/j.solener.2014.09.046 0038-092X/Ó 2014 Elsevier Ltd. All rights reserved.
daylight in through windows is practical only for the areas near windows. Light pipes and reflector systems that can utilize direct sunlight have been shown to be more effective in bringing daylight into deeper interior spaces, (Rosemann and Kraase, 2005; Scartezzini and Courret, 2002). Light pipes commonly used are passive tubular pipes that comprise an entry port, a hollow tubular pipe for transmission of daylight, and an exit port for delivering it into the intended space. In most cases and in this paper, all sections of a light pipe possess specularly reflective interior surfaces. It is often desirable to capture daylight from a large part of sky through a larger entry aperture, then concentrate the captured daylight and re-direct it to a smaller pipe section.
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Nomenclature /s cs as # / hent Aent U q E DEext %Nrt CR hext Aext Evg Evd
solar zenith angle, radian solar azimuth angle solar altitude angle acceptance half-angle, radian or degree 90° complement of the acceptance half-angle entry angle, radian area of entry port, m2 light flux, lumen surface reflectance illuminance, lux incremental illuminance at exit port percentage of number of rays transmitted concentration ratio exit angle, radian area of exit port, m2 total illuminance, lux diffuse illuminance, lux
Performance of such light collector can be improved if it is designed using the principle of anidolic, or non-imaging, optics, Scartezzini and Courret (2002). Molteni et al. rationalizing that basement and underground spaces were increasingly used in urban areas, studied the use of anidolic collectors connected to a vertical pipe, (Molteni et al., 2000). Two collectors were designed separately, one to capture and concentrate daylight from the sky, and one to capture summer sunlight. The authors used a scanning artificial sky as light source for a light pipe and collector model and found that the collectors increase transmitted light fluxes considerably. Wittkopf (2006), reports the use of Photopia, a raytracing calculation tool, to study comparative performance of a fac¸ade installed with an ‘anidolic integrated ceiling’, or AIC, against two other common configurations when the facades are illuminated with different sky luminance distributions. The author concludes that the fac¸ade with AIC performs better in terms of improving illuminance ratio and reducing glare. Wittkopf et al. (2010), used Photopia to study comparative luminous intensity distributions of light that passes through seven collectors of an anidolic integrated ceiling. Light uniformly distributed from a half hemisphere in front of the collector is simulated to enter each collector. The collector with a main anidolic concentrator and an opposite de-concentrator was found to offer the least spread of luminous intensity distribution. This is deemed to transmit light along the pipe with least attenuation. Linhart et al. (2010), modeled a ‘virtual sky dome’ that emanates daylight whose luminance distribution represents that of Singapore sky and used Photopia to simulate transmission of light from such model. The authors tested comparative performance of daylight transmission through the AIC against change in the reflectance of the surfaces, change in dimensions of the AIC, and extent of shading by objects above the collector.
Evtap
total daylight illuminance transmitted through the straight pipe with concentrator, lux Evtp total daylight transmitted through the pipe with no concentrator, lux Evdap diffuse daylight transmitted through a pipe with anidolic concentrator, lux Evdp diffuse daylight transmitted through a pipe with no concentrator, lux Evdap-exp measured transmitted diffuse illuminances, lux Evdap-cal calculated transmitted diffuse illuminances, lux Evbap-exp measured transmitted beam illuminances, lux Evbap-cal calculated transmitted beam illuminances, lux
Raytracing and flux transfer have been applied to the study of a facade-mounted rectangular pipes by Hien and Chirarattananon to obtain results that agree well with those from experiments, (Hien and Chirarattananon, 2009). Dutton and Shao (2008), use long thin rectangular sections to form approximate circular shaped pipes and simulate light transmission by the use of Photopia. Swift et al. (2008), develop theoretical model of transmission of light through rectangular pipe for collimated rays and report that results from the model agree well with experimental results. Zastrow and Wittwer (1986), considered transmission of light beam across cylindrical light pipes and offers a simple relationship for light transmission as a function of the length and diameter of the pipe, and the entry angle of the light beam. Kocifaj et al. (2008), developed a method called HOLIGILM for calculation of illuminance on an incremental area at the exit port of a circular light pipe by considering backward tracing of a light ray through the entry dome or port to a sky zone. Kocifaj et al. (2010), extends the HOLIGILM method to the case where two straight pipes are connected to form a bend. Kocifaj and Kundracik (2011), introduce an asymmetrical parameter and apply it with the HOLIGILM method to characterize the spread of luminous intensity of light exiting a pipe. Darula et al. (2010), applies the HOLIGILM method to study daylight transmission through a bended pipe on a roof and examines the patterns of illuminance distributions at exit port and at the work plane below for a standard sky luminance distribution (CIE Sky 12, clear with sun) and a number of room orientations. The authors conclude that effective design of bended tubular light pipe requires a study of interrelation between tube azimuth orientation and the angle of incidence of the sun beam. Kocifaj (2009) applies the HOLIGILM method to modeling of light transmission through hollow light guide with transparent exit port,
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similar to the configuration used in this paper. Similar configuration of bended pipe is considered by Kocifaj et al. (2012), who illustrate that a bended pipe with its upper section oriented in the direction of the brighter part of the sky dome near the path of travel of the sun attains maximum transmission efficiency. Samuhatananon et al. (2011), uses forward raytracing in a study on daylight transmission through cylindrical pipes with and without torus bends. The ASRC-CIE sky luminance distribution model, (Perez et al., 1990, 1992), is used to generate light rays that enter into vertical pipes from standard sky zones. The authors show that results from experiments under real sky agree well with calculation results. This paper utilizes the principle of forward ray tracing to trace transmission of light rays from sky through equal incremental areas on the aperture of an anidolic concentrator connected to a straight cylindrical light pipe. The anidolic section and the pipe are modeled analytically. The computational results from tracing of rays from sky, whose luminance is calculated by using the ASRC-CIE sky luminance model, are then compared to results from physical experiments conducted at the seaside campus of King Mongkut’s University of Technology. 2. Ray tracing method for circular pipes with anidolic concentrators In the method of forward raytracing, each individual ray is traced along its path of travel from a daylight source. At the point of interception with a specular surface, a part of radiative power in the ray is absorbed, and the other part is specularly reflected. In the method used, the cross section of the anidolic concentrator is modeled mathematically as a section of parabola. The method employed in this paper is applicable for both fac¸ade mounted and roof mounted light pipes. For the present work, the glazing elements at the entry and exit ports of a pipe are omitted in order to elucidate the mechanism of transmission of light rays
through the pipe and to distinguish its features from the effects of transmission by the port elements. Fig. 1 illustrates the geometrical position of a cylindrical pipe connected with an anidolic concentrator under the sky dome. In the figure, the center of a Cartesian coordinate with the z-coordinate coincident with the zenith direction is located at the center of the exit port of the anidolic concentrator. The x-axis points toward south. This is the reference direction for the azimuth angle. Rays from the sun and that from a sky zone enter the entry aperture of the anidolic concentrator with given altitude and azimuth angles. 2.1. Uniform entry of rays The rays that enter the entry port of the anidolic concentrator in this paper are modeled to enter at the center of equal incremental areas, similar to that used in Samuhatananon et al. (2011). Fig. 2 shows a plot of the positions of entries of 900 rays. 2.2. Mathematical relationships for ray traveling through the concentrator and the pipe Consider Fig. 3 where an imaginary surface is assumed to cover the entry port of the concentrator. A coordinate is located at the base of the concentrator. A ray enters the port at location Po and travels in the direction vo. It intersects with surface of the concentrator at P1. The normal of the surface at the point of intersection is n and the specularly reflected vector is v1. The conjunctive point P1 lies along the line parallel to vector vo and can be obtained from P1 ¼ Po þ to vo
ð1Þ
where to is a scalar quantity and the point P1 lies on the anidolic surface, so its x, y, and z coordinates follows the
Fig. 1. The geometry of a pipe with anidolic concentrator under the sky dome.
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2.3. Mathematical model of an anidolic concentrator The anidolic concentrator here is a compound parabolic concentrator that reflects incoming parallel rays to a focal point. Fig. 4 illustrates the two-dimensional configuration of the right hand side (RHS) of a compound parabolic concentrator (CPC). The vertex of the parabola is at (xo, yo), and the focus F is at (xo, yo + a), where ‘a’ is the distance between the vertex and the focus. In the figure, both xo and yo are zero. All rays parallel to y are reflected to the focal point F. The RHS of the CPC that comprises a parabolic section b and its base c is shown in Fig. 4. The height of this section is h, as shown in the figure. The LHS section comprises the mirror image of the section on the RHS. The focal point of the RHS parabola is at F while that of the LHS parabola is at F0 . The coordinate x* and y* form the coordinates of the RHS concentrator. The new coordinate (x*, y*) is rotated from the coordinate (x, y) clockwise by an angle #, which is the acceptance half-angle and is the 90° complement of /. In constructing a CPC, it is normal to first decide on the size of the diameter of the cylindrical pipe that is equal to c, the base of the CPC.
Fig. 2. A plot of the uniform positions of entries of 900 rays.
Table 1 Functional description of surfaces and normal vectors for parabolic and cylindrical surfaces. Surface function: parabolic S : ðx xo Þ2 þ ðy y o Þ2 4aðz zo Þ Surface normal o Þiþðyy o Þj2ak ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n ¼ pðxx 2 2 2 ðxxo Þ þðyy o Þ þ4a
Surface function: cylindrical S : x2 þ y 2 r2 Surface normal n ¼ xr i yr j
Fig. 3. The geometry of a ray entering the entry port of the anidolic concentrator and its reflection on the concentrator surface.
governing equation for the anidolic surface, where in this case is a parabolic function, given in Table 1. The vector v1 follow the law of specular reflection, the mathematical relationship for the vectors in Fig. 3 are v1 ¼ v0 2ðv0 ; nÞn
ð2Þ
Once the ray is reflected from the conjunctive point, it travels along v1 from P1. When the ray travels in the cylindrical section of the pipe, the coordinate of its intersection point follows the governing cylindrical function.
Fig. 4. Formation of the RHS of a compound parabolic concentrator.
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The second parameter to decide on is the acceptance half-angle # or its complement /. The other parameters ‘a’, focal length and ‘h’, height are obtained from c and # as follows a¼ h¼
cð1 þ sin #Þ 2 a sin / ðcos /Þ
2
ð3Þ ð4Þ
3. Computational procedure and results A set of MATLAB scripts and functions has been written to compute the transmission of daylight rays from the sky and the sun through the concentrator and pipe system. The acceptance half-angle of the concentrator was chosen to be 40° and its base or the diameter of exit port 0.15 m, then the distance between the focal point and vertex ‘a’ is 0.123 m, its height 0.2284 m, and the diameter at the entry port 0.2334 m. The 3D concentration ratio is then 2.42. The diameter of the exit port matches that of the straight pipe, here having a length of 1.00 m. 3.1. Computational algorithm A ray with a given direction of travel is tested if it will intersect the exit or entry ports of a given section (In the concentrator, a ray can be reflected back to the entry port). If not, then it must intersect the concentrator or the pipe surface. The locations of the intersection and reflection vectors are then computed, and the ray continues to travel. This is repeated until the ray intersects an entry or exit port of the given section. A counter is used to count the number of times a ray intersects the surface of each section. If the ray intersects the exit port of the concentrator, it continues to travel into the cylindrical pipe and enter into the coordinate of the pipe. A coordinate transformation is required when the coordinates between adjacent sections differ. When a ray leaves the exit port of the pipe, its position on the port and the direction of travel are recorded. 3.2. Results of computation for directional rays A series of computational runs was made for parallel rays that were assumed to enter into the concentrator (only) at certain angles to examine some transmission characteristics. 3.2.1. Three dimensional plots of ray trajectories Fig. 5 shows three sample plots of ray trajectories for rays that enter at 20° and 40°. The first two on the left show ray trajectories in the concentrator. The rays that enter at 20° are all transmitted through the concentrator, (a), and through the concentrator and straight pipe, (c). Half of the rays that enter at 40° are transmitted through the concentrator, (b).
3.2.2. Geometric patterns at exit ports of concentrator At smaller entry angles the positions where the rays leave the exit port of the concentrator form geometric patterns. Fig. 6(a) shows a pattern for the case when the entry angle 10° and Fig. 6(b) for the case of 40°, the acceptance half-angle. When the ray entry angle is small and the rays travel through to the straight pipe, patterns similar to mirror images to those of the concentrator only are discernible, but appear to be imposed with random dots, as in Fig. 7(a). When the ray entry angle is large the random dots appear to dominate as in Fig. 7(b). 3.2.3. Characteristics of transmission of rays through the concentrator 3.2.3.1. Ray transmissions through a concentrator. A part of parallel light rays that enters the concentrator at an angle smaller than the acceptance half-angle will transmit through the exit port without intersecting the surface of the concentrator. Another part of parallel rays intersect the concentrator surface and are reflected. The closer is the size of the entry angle of the parallel rays to that of the acceptance half-angle, the smaller is the proportion of the rays that transmit through the port without intersecting the concentrator surface. In this latter case, the other part of rays experience a larger number of reflections by the concentrator surface. When the entry angle of the parallel rays equals the acceptance half-angle, half of the total number of rays transmits through the concentrator, and the other half is reflected out through the entry port. Fig. 8 illustrates the configuration when the entry angle of rays is smaller than the acceptance half-angle. Table 2 shows sample result of transmission of 100 rays with entry angle of 39° through a concentrator with an acceptance half-angle of 40°. The table shows the number of reflections of ray number 1, 40, and 85 that are transmitted through the exit port. It also shows that ray number 100 transmits through without any reflection. Ray number 19 and 76 are reflected a number of times each before being reflected back out through the entry port. It also shows the position and the direction as each ray leaves the exit port. The coordinate (x, y) is at the base of the concentrator and z is coincident with the zenith direction, hence all rays that travel through the exit port have the z components in the position vectors equal to zero. The negative exit angles in the direction vector mean that the rays travel in the direction opposite to the z-coordinate. 3.2.3.2. Illuminance of transmitted rays. Suppose a beam of light of illuminance E lux in the direction of the beam enters the entry port of area Aent of a concentrator at an entry angle hent. The amount of light flux U reaching the entry port is then given as U ¼ ðE cos hent ÞAent
ð5Þ
Suppose n parallel rays are used to represent the entry light flux, each ray then represents DU lumen where
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Fig. 5. Three-dimensional plots of ray travels. (a) Rays entering at angle 20°. (b) Rays entering at angle 40°. (c) Rays entering at angle 20° and traveling through the pipe system.
DU ¼
U n
ð6Þ
A representative ray is reflected mi times at the concentrator surface when it reaches the exit port, where the concentrator surface has a reflectance of q. Its light flux is now reduced to
DUext ¼ DUðqmi Þ
ð7Þ
This ray leaves the exit port at an angle hext. If the exit port has an area of Aext, then the illuminance this ray contributes to the total is DEext where ðDUext Þ cos hext DEext ¼ ð8Þ Aext
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Fig. 6. Geometric patterns at exit port of concentrator. (a) Entry angle 10°. (b) Entry angle 40°.
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Fig. 7. Geometric patterns at exit port of pipe. (a) Entry angle 10°. (b) Entry angle 40°.
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Fig. 8. The configuration that illustrates that some rays transmit directly through the exit port when the entry angle of rays is smaller than the acceptance half-angle.
The total illuminance of the light flux leaving the exit port Eext is the sum of the illuminance contributed by each transmitted ray. The method of deriving transmitted illuminance used here is applicable to the whole pipe system where the system has more than one section. Fig. 9(a) shows, for a concentrator with an acceptance half-angle of 30°, plots of percentage of the number of rays transmitted (%Nrt) against the 90° complement of the ray entry angle on the horizontal scale. The figure also shows plots of illuminance at the exit port for two cases, when the reflectance of the concentrator surface is 0.95 and when it is 1.0, for when the illuminance of the entering beam light is 100 klux on a surface normal to the beam. The number of rays used in the calculation is 2500 for each entry angle and the increment of entry angle is 2°. The plots of percentage of the number of rays transmitted in Fig. 9(a) shows rather sharp transition between the entry angle that all rays are reflected out (33°) and the angle that all rays are transmitted (27°). The plot of illuminance at exit port for the case where the surface reflectance of the concentrator is 1.0 show that it rises from zero at an entry angle of 32–335 klux at the entry angle of 0°. For the case where the surface reflectance is 0.95, the exit illuminance only reaches 318 klux at entry angle of zero. The concentration ratio for this concentrator is 4 (or 400%). Even when the entry angle is zero, a small proportion of rays is transmitted without intersecting the concentrator surface, a larger proportion is reflected and the angles of intersection at the exit port of the rays in this portion is less than 90°.
Fig. 9. Plots of percentage number of rays transmitted and illuminance at exit port for the case where the acceptance half-angle of the concentrator is 30° and 40°. (a) Plots for the case where the acceptance half-angle of the concentrator is 30°. (b) Plots for the case where the acceptance half-angle of the concentrator is 40°.
Fig. 9(b) shows similar plots for the case where the acceptance half-angle of the concentrator is 40°, and the concentration ratio (CR) is 2.42 (or 242%). The maximum illuminance at exit port for surface reflectance of 1.0 and 0.95 are 218 and 210 klux respectively. Fig. 10 shows similar plots for the case where the acceptance half-angle of the concentrator is 40° connected to circular pipe of 1 m long, and the concentration ratio is 2.42 (or 242%). The maximum illuminance at exit port for surface reflectance of 1.0 and 0.95 are 218 and 190 klux respectively. 4. Experimental and calculation results and discussion A number of experiments on transmission of daylight through straight pipes only and pipes with anidolic concentrator were conducted in March 2014. The light pipes and concentrators were constructed with the same dimensions
Table 2 Sample result of ray tracing for a concentrator with acceptance half-angle 40°. Ray no.
1 19 40 76 85 100
Incident point x
y
z
Direction x
y
z
Ray exit angle (degree)
No. reflections of rays transmitted through
No. reflections of rays reflected back
0.0683 0.0965 0.0717 0.0709 0.0383 0.0748
0 0.0322 0.0121 0.065 0.0636 0
0 0.2284 0 0.2284 0 0
0.8813 0.6592 0.8698 0.3841 0.6609 0.6307
0 0.0769 0.4763 0.4963 0.6714 0
0.4726 0.748 0.1286 0.7786 0.3354 0.776
28.2 48.4 7.4 51.1 19.6 50.9
1 – 2 – 3 0
– 4 – 6 – –
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Fig. 10. Plots of percentage number of rays transmitted and illuminance at exit port for the case where the acceptance half-angle of the concentrator is 40° and is connected to circular pipe of 1 m long.
as those used for computation and are as described in the first paragraph of Section 3. The interior surface of the pipe and concentrator is lined with a film that has a specular reflectance of over 0.99. Fig. 11 shows the experimental setup. Two straight pipes were erected vertically, one with a shading ball to shade out beam illuminance, so that only diffuse illuminance from sky enters the entry port. For the unshaded pipe, total illuminance enters its port. Similar arrangement was made for two other pipes that were connected with anidolic concentrators at the tops of the pipes. To measure exit illuminance, illuminance sensors were placed at the exit of the pipes and all were housed in a box painted diffusively black. There was a daylight measurement station near the experimental site, but the total and diffuse illuminance measurements used in this paper were measured by illuminance sensors on the experimental site. 4.1. Experimental results on transmission of daylight through pipes with and without concentrators Fig. 12 shows plots of total (second line from top, Evg) and diffuse (fourth line from top, Evd) illuminance measured by two sensors on site on March 23. The sky ratio as can be surmised from the graphs varies mostly between about 0.4 to about 0.8. So the sky is partly cloudy during the experiment, However, for the period around
Fig. 11. Experimental setup for the experiments during March 2014.
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Fig. 12. Graphs of un-obstructed daylight and transmitted daylight through pipes.
11.20–11.35, clouds appear to shade out sunlight. So this period is overcast. The top line is the plot of total daylight illuminance transmitted through the straight pipe with concentrator (Evtap). The bottom line in the figure is a plot of diffuse daylight transmitted through a pipe with anidolic concentrator (Evdap). The line above it is a plot of diffuse daylight transmitted through a pipe with no concentrator (Evdp). Immediately above the three bottom lines is a plot of total daylight transmitted through the pipe with no concentrator (Evtp). Examining the results described above, it can be surmised that in cases of transmission of total illuminance, the pipe with concentrator performs better. In cases of transmission of diffuse illuminance, the pipes with no concentrator perform better. The relative performance is more pronounced for transmission of total illuminance where illuminance transmitted through the pipe with concentrator is higher (0–30%) than global illuminance and clearly higher (0–35%) than that transmitted through the pipe without concentrator. 4.2. A Comparison between calculated and measured daylight transmitted through pipes with concentrators The set of MATLAB scripts and functions described in Section 3 were used in the computation of transmission of daylight from the sky and beam daylight through the pipe system with anidolic concentrator. For beam daylight, measurement from the nearby station was used in the calculation. For daylight from the sky, the values of luminance used in the computation were generated using the ASRC-CIE sky luminance model. The model uses beam and diffuse radiation as well as the angular position of the sun at the given time to calculate clearness index and brightness index of Perez, (Perez et al., 1990). The values of the two parameters are then used to choose a combination of four standard sky luminance models. The combined model was used in a MATLAB function to generate luminance of 145 standard sky zones. A number of rays were assumed emitted in each of the 145 directions in the sky
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beam normal illuminance were obtained from a sun illuminance sensor attached to a suntracker at the station. In the figure, the measured transmitted beam illuminance is obtained as the difference between transmitted total illuminance and transmitted diffuse illuminance, from two different concentrator and pipes. The plot in Fig. 13(b) shows this derived value to vary from very small value to around 90 klux near noon. The values of calculated and measured transmitted beam illuminance are close and are larger than the beam normal illuminance. Within 10.50 and 14.07, when the angle of beam illuminance from the sun fell within the acceptance half-angle, the concentration ratio varies between 1.2 and 2. The results here show that the concentration ratio of a concentrator is a function of its acceptance half-angle and the reflectance of its surface. 5. Conclusion
Fig. 13. Plots of measured and calculated values of transmitted diffuse and beam daylight illuminance. (a) Plots of measured and calculated values of transmitted diffuse daylight illuminance. (b) Plots of measured and calculated values of transmitted beam daylight illuminance.
and entered into the entry port of the concentrator at each given time of 5-min duration. Each ray from each sky zone is traced until it leaves the exit port of the straight pipe. The number of times a ray is reflected from each section of the pipe system and the angle at which it leaves the exit port are recorded for computation of the illuminance at the outlet as described in Section 3.1. Results from the computation shows that beam illuminance is concentrated and transmitted through the pipe system with concentrator during 10.50 and 14.07 h. The resultant concentration ratio (CR in Fig. 13) is larger than one. For diffuse illuminance, the concentration ratio is less than one. The calculated and measured transmitted diffuse illuminance are plotted with measured horizontal diffuse illuminance in Fig. 13(a). The calculated and measured values are very close and both are smaller than the measured horizontal diffuse illuminance, with a concentration ratio between 0.5 and 0.9. This shows that even though the concentrator may be able to concentrate the part of sky daylight within the acceptance half-angle of the concentrator, the rejected part of the sky daylight was larger. Fig. 13(b) shows plots of calculated and measured transmitted beam illuminances and beam normal illuminance. The values of
Anidolic concentrator has the potential to enhance performance of a light pipe by increasing capture of more light flux into a pipe. This paper demonstrates that analytic method can be directly applied to trace rays through the light pipe system. The sky luminance values corresponding to a given sky condition are directly calculated for each time by a built-in function. The method can be used for analysis and design of such system. However, in certain configuration and certain situation, the specific character of an anidolic concentrator that sharply rejects rays of angles larger the acceptance half-angle may result in adverse effects. The configuration of the concentrator used in this study might not be able to clearly demonstrate the advantage of concentration for transmission of daylight that includes sunlight. Alternative configurations should be considered in the attempt to concentrate and bring more uniform transmitted daylight into interior spaces. Acknowledgements The research work reported in this paper is funded by the National Research Council of Thailand through the Thai-China Joint Research Program and the National Research University Project of the Commission for Higher Education of the Ministry of Education, the Royal Government of Thailand. Financial support is also given by the Thailand Research Fund through the Royal Golden Jubilee Ph.D. Program (Grant No. PHD/0010/2555) to Ms. Thanyalak Taengchum (student) and Professor Surapong Chirarattananon (advisor). References Chirarattananon, S., Chaiwiwataorakul, P., Hien, V.D., Rakwamsuk, P., Kubaha, K., 2010. Assessment of energy savings from the revised building energy code of Thailand. Energy, 1741–1753. Darula, S., Kocifaj, M., Kittler, R., Kundracik, F., 2010. Illumination of interior spaces by bended hollow light guides: application of the theoretical light propagation method. Solar Energy 84, 2112–2119.
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Perez, R., Ineichen, P., Seals, R., Mechaels, J., Stewart, R., 1990. Modeling daylight availability and irradiance components from direct and global irradiance. Solar Energy 44 (5), 271–289. Perez, R., Michalsky, J., Seals, R., 1992. Modeling sky luminance angular distribution for real sky conditions: experimental evaluation of existing algorithms. Illum. Eng. Soc. J. 212, 84–92. Rosemann, A., Kraase, H., 2005. Lightpipe applications for daylighting systems. Solar Energy 78, 772–780. Samuhatananon, S., Chirarattananon, S., Chirarattananon, P., 2011. An experimental and analytical study of transmission of daylight through circular light pipes. Leukos 7 (4), 203–219. Scartezzini, J.L., Courret, G., 2002. Anidolic daylighting systems. Solar Energy 73 (2), 123–135. Swift, P.D., Lawlor, R., Smith, G.B., Gentle, A., 2008. Rectangularsection mirror light pipes. Sol. Energy Mater. Sol. Cells 92, 969–975. Wittkopf, S.K., 2006. Daylight performance of anidolic ceiling under different sky conditions. Solar Energy 81, 151–161. Wittkopf, S.K., Grobe, L., Geisler-Moroder, D., Compagnon, R., Kampf, J., Linhart, F., Scartezzini, J.L., 2010. Ray tracing study for nonimaging daylight collectors. Solar Energy 84, 986–996. Zastrow, A., Wittwer, V., 1986. Daylighting with mirror light pipes and with fluorescent planar concentrators, results from the demonstration project Stuttgart-Hohenheim. International Society for Optical Engine, vol. 69, pp. 227–234.
ScienceDirect Solar Energy 110 (2014) 818–829 www.elsevier.com/locate/solener
Tracing of daylight through circular light pipes with anidolic concentrators Thanyalak Taengchum a, Surapong Chirarattananon a,b,⇑, Robert H.B. Exell a,b, Pipat Chaiwiwatworakul a,b a
Joint Graduate School of Energy and Environment, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand b Science and Technology Postgraduate Education and Research Development Office, Ministry of Education, Thailand Received 10 July 2014; received in revised form 24 September 2014; accepted 30 September 2014 Available online 11 November 2014 Communicated by: Associate Editor J.-L. Scartezzini
Abstract Light pipes can bring both daylight from the sun and the sky into deep interior spaces of a building. Adding an anidolic concentrator at the entry port of a light pipe will increase daylight capture and may reduce the overall cost per unit of delivered daylight flux, especially for long pipes or pipes with bends. This paper presents results of modeling, experiments, and simulation of transmission of beam and diffuse daylight through tubular light pipes attached with an anidolic concentrator at the entry port. Analytic method is used for tracing light rays from the sun and sources in the sky zones through the anidolic concentrator to the straight section of a pipe through to the exit port. The vertical curvature surface of the anidolic concentrator is modeled as a parabolic section. The ASRC-CIE sky luminance distribution model is used to generate luminance of daylight from the sky. The algorithms are coded in a MATLAB program. The physical anidolic concentrator and pipe are fabricated from off-the-shelf materials commonly available. The interior surface of each section is lined with a film of reflectance of 99%. Results from calculation of transmission of global and diffuse daylight through the tubular pipe with anidolic concentrator match well with those from experiments. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Daylighting; Light pipe; Anidolic concentrator; Sky luminance; Sunlight
1. Introduction Electric lighting accounts directly for 20% of electricity consumption in air-conditioned buildings in Thailand while daylight is plentiful, (Chirarattananon et al., 2010). Daylighting is attractive and can greatly help reduce lighting energy. The common method of daylighting letting ⇑ Corresponding author at: Joint Graduate School of Energy and Environment, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand. Tel.: +66 (2) 4708309. E-mail addresses: [email protected] (T. Taengchum), surapong. [email protected] (S. Chirarattananon), [email protected] (R.H.B. Exell), [email protected] (P. Chaiwiwatworakul).
http://dx.doi.org/10.1016/j.solener.2014.09.046 0038-092X/Ó 2014 Elsevier Ltd. All rights reserved.
daylight in through windows is practical only for the areas near windows. Light pipes and reflector systems that can utilize direct sunlight have been shown to be more effective in bringing daylight into deeper interior spaces, (Rosemann and Kraase, 2005; Scartezzini and Courret, 2002). Light pipes commonly used are passive tubular pipes that comprise an entry port, a hollow tubular pipe for transmission of daylight, and an exit port for delivering it into the intended space. In most cases and in this paper, all sections of a light pipe possess specularly reflective interior surfaces. It is often desirable to capture daylight from a large part of sky through a larger entry aperture, then concentrate the captured daylight and re-direct it to a smaller pipe section.
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Nomenclature /s cs as # / hent Aent U q E DEext %Nrt CR hext Aext Evg Evd
solar zenith angle, radian solar azimuth angle solar altitude angle acceptance half-angle, radian or degree 90° complement of the acceptance half-angle entry angle, radian area of entry port, m2 light flux, lumen surface reflectance illuminance, lux incremental illuminance at exit port percentage of number of rays transmitted concentration ratio exit angle, radian area of exit port, m2 total illuminance, lux diffuse illuminance, lux
Performance of such light collector can be improved if it is designed using the principle of anidolic, or non-imaging, optics, Scartezzini and Courret (2002). Molteni et al. rationalizing that basement and underground spaces were increasingly used in urban areas, studied the use of anidolic collectors connected to a vertical pipe, (Molteni et al., 2000). Two collectors were designed separately, one to capture and concentrate daylight from the sky, and one to capture summer sunlight. The authors used a scanning artificial sky as light source for a light pipe and collector model and found that the collectors increase transmitted light fluxes considerably. Wittkopf (2006), reports the use of Photopia, a raytracing calculation tool, to study comparative performance of a fac¸ade installed with an ‘anidolic integrated ceiling’, or AIC, against two other common configurations when the facades are illuminated with different sky luminance distributions. The author concludes that the fac¸ade with AIC performs better in terms of improving illuminance ratio and reducing glare. Wittkopf et al. (2010), used Photopia to study comparative luminous intensity distributions of light that passes through seven collectors of an anidolic integrated ceiling. Light uniformly distributed from a half hemisphere in front of the collector is simulated to enter each collector. The collector with a main anidolic concentrator and an opposite de-concentrator was found to offer the least spread of luminous intensity distribution. This is deemed to transmit light along the pipe with least attenuation. Linhart et al. (2010), modeled a ‘virtual sky dome’ that emanates daylight whose luminance distribution represents that of Singapore sky and used Photopia to simulate transmission of light from such model. The authors tested comparative performance of daylight transmission through the AIC against change in the reflectance of the surfaces, change in dimensions of the AIC, and extent of shading by objects above the collector.
Evtap
total daylight illuminance transmitted through the straight pipe with concentrator, lux Evtp total daylight transmitted through the pipe with no concentrator, lux Evdap diffuse daylight transmitted through a pipe with anidolic concentrator, lux Evdp diffuse daylight transmitted through a pipe with no concentrator, lux Evdap-exp measured transmitted diffuse illuminances, lux Evdap-cal calculated transmitted diffuse illuminances, lux Evbap-exp measured transmitted beam illuminances, lux Evbap-cal calculated transmitted beam illuminances, lux
Raytracing and flux transfer have been applied to the study of a facade-mounted rectangular pipes by Hien and Chirarattananon to obtain results that agree well with those from experiments, (Hien and Chirarattananon, 2009). Dutton and Shao (2008), use long thin rectangular sections to form approximate circular shaped pipes and simulate light transmission by the use of Photopia. Swift et al. (2008), develop theoretical model of transmission of light through rectangular pipe for collimated rays and report that results from the model agree well with experimental results. Zastrow and Wittwer (1986), considered transmission of light beam across cylindrical light pipes and offers a simple relationship for light transmission as a function of the length and diameter of the pipe, and the entry angle of the light beam. Kocifaj et al. (2008), developed a method called HOLIGILM for calculation of illuminance on an incremental area at the exit port of a circular light pipe by considering backward tracing of a light ray through the entry dome or port to a sky zone. Kocifaj et al. (2010), extends the HOLIGILM method to the case where two straight pipes are connected to form a bend. Kocifaj and Kundracik (2011), introduce an asymmetrical parameter and apply it with the HOLIGILM method to characterize the spread of luminous intensity of light exiting a pipe. Darula et al. (2010), applies the HOLIGILM method to study daylight transmission through a bended pipe on a roof and examines the patterns of illuminance distributions at exit port and at the work plane below for a standard sky luminance distribution (CIE Sky 12, clear with sun) and a number of room orientations. The authors conclude that effective design of bended tubular light pipe requires a study of interrelation between tube azimuth orientation and the angle of incidence of the sun beam. Kocifaj (2009) applies the HOLIGILM method to modeling of light transmission through hollow light guide with transparent exit port,
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similar to the configuration used in this paper. Similar configuration of bended pipe is considered by Kocifaj et al. (2012), who illustrate that a bended pipe with its upper section oriented in the direction of the brighter part of the sky dome near the path of travel of the sun attains maximum transmission efficiency. Samuhatananon et al. (2011), uses forward raytracing in a study on daylight transmission through cylindrical pipes with and without torus bends. The ASRC-CIE sky luminance distribution model, (Perez et al., 1990, 1992), is used to generate light rays that enter into vertical pipes from standard sky zones. The authors show that results from experiments under real sky agree well with calculation results. This paper utilizes the principle of forward ray tracing to trace transmission of light rays from sky through equal incremental areas on the aperture of an anidolic concentrator connected to a straight cylindrical light pipe. The anidolic section and the pipe are modeled analytically. The computational results from tracing of rays from sky, whose luminance is calculated by using the ASRC-CIE sky luminance model, are then compared to results from physical experiments conducted at the seaside campus of King Mongkut’s University of Technology. 2. Ray tracing method for circular pipes with anidolic concentrators In the method of forward raytracing, each individual ray is traced along its path of travel from a daylight source. At the point of interception with a specular surface, a part of radiative power in the ray is absorbed, and the other part is specularly reflected. In the method used, the cross section of the anidolic concentrator is modeled mathematically as a section of parabola. The method employed in this paper is applicable for both fac¸ade mounted and roof mounted light pipes. For the present work, the glazing elements at the entry and exit ports of a pipe are omitted in order to elucidate the mechanism of transmission of light rays
through the pipe and to distinguish its features from the effects of transmission by the port elements. Fig. 1 illustrates the geometrical position of a cylindrical pipe connected with an anidolic concentrator under the sky dome. In the figure, the center of a Cartesian coordinate with the z-coordinate coincident with the zenith direction is located at the center of the exit port of the anidolic concentrator. The x-axis points toward south. This is the reference direction for the azimuth angle. Rays from the sun and that from a sky zone enter the entry aperture of the anidolic concentrator with given altitude and azimuth angles. 2.1. Uniform entry of rays The rays that enter the entry port of the anidolic concentrator in this paper are modeled to enter at the center of equal incremental areas, similar to that used in Samuhatananon et al. (2011). Fig. 2 shows a plot of the positions of entries of 900 rays. 2.2. Mathematical relationships for ray traveling through the concentrator and the pipe Consider Fig. 3 where an imaginary surface is assumed to cover the entry port of the concentrator. A coordinate is located at the base of the concentrator. A ray enters the port at location Po and travels in the direction vo. It intersects with surface of the concentrator at P1. The normal of the surface at the point of intersection is n and the specularly reflected vector is v1. The conjunctive point P1 lies along the line parallel to vector vo and can be obtained from P1 ¼ Po þ to vo
ð1Þ
where to is a scalar quantity and the point P1 lies on the anidolic surface, so its x, y, and z coordinates follows the
Fig. 1. The geometry of a pipe with anidolic concentrator under the sky dome.
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2.3. Mathematical model of an anidolic concentrator The anidolic concentrator here is a compound parabolic concentrator that reflects incoming parallel rays to a focal point. Fig. 4 illustrates the two-dimensional configuration of the right hand side (RHS) of a compound parabolic concentrator (CPC). The vertex of the parabola is at (xo, yo), and the focus F is at (xo, yo + a), where ‘a’ is the distance between the vertex and the focus. In the figure, both xo and yo are zero. All rays parallel to y are reflected to the focal point F. The RHS of the CPC that comprises a parabolic section b and its base c is shown in Fig. 4. The height of this section is h, as shown in the figure. The LHS section comprises the mirror image of the section on the RHS. The focal point of the RHS parabola is at F while that of the LHS parabola is at F0 . The coordinate x* and y* form the coordinates of the RHS concentrator. The new coordinate (x*, y*) is rotated from the coordinate (x, y) clockwise by an angle #, which is the acceptance half-angle and is the 90° complement of /. In constructing a CPC, it is normal to first decide on the size of the diameter of the cylindrical pipe that is equal to c, the base of the CPC.
Fig. 2. A plot of the uniform positions of entries of 900 rays.
Table 1 Functional description of surfaces and normal vectors for parabolic and cylindrical surfaces. Surface function: parabolic S : ðx xo Þ2 þ ðy y o Þ2 4aðz zo Þ Surface normal o Þiþðyy o Þj2ak ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n ¼ pðxx 2 2 2 ðxxo Þ þðyy o Þ þ4a
Surface function: cylindrical S : x2 þ y 2 r2 Surface normal n ¼ xr i yr j
Fig. 3. The geometry of a ray entering the entry port of the anidolic concentrator and its reflection on the concentrator surface.
governing equation for the anidolic surface, where in this case is a parabolic function, given in Table 1. The vector v1 follow the law of specular reflection, the mathematical relationship for the vectors in Fig. 3 are v1 ¼ v0 2ðv0 ; nÞn
ð2Þ
Once the ray is reflected from the conjunctive point, it travels along v1 from P1. When the ray travels in the cylindrical section of the pipe, the coordinate of its intersection point follows the governing cylindrical function.
Fig. 4. Formation of the RHS of a compound parabolic concentrator.
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The second parameter to decide on is the acceptance half-angle # or its complement /. The other parameters ‘a’, focal length and ‘h’, height are obtained from c and # as follows a¼ h¼
cð1 þ sin #Þ 2 a sin / ðcos /Þ
2
ð3Þ ð4Þ
3. Computational procedure and results A set of MATLAB scripts and functions has been written to compute the transmission of daylight rays from the sky and the sun through the concentrator and pipe system. The acceptance half-angle of the concentrator was chosen to be 40° and its base or the diameter of exit port 0.15 m, then the distance between the focal point and vertex ‘a’ is 0.123 m, its height 0.2284 m, and the diameter at the entry port 0.2334 m. The 3D concentration ratio is then 2.42. The diameter of the exit port matches that of the straight pipe, here having a length of 1.00 m. 3.1. Computational algorithm A ray with a given direction of travel is tested if it will intersect the exit or entry ports of a given section (In the concentrator, a ray can be reflected back to the entry port). If not, then it must intersect the concentrator or the pipe surface. The locations of the intersection and reflection vectors are then computed, and the ray continues to travel. This is repeated until the ray intersects an entry or exit port of the given section. A counter is used to count the number of times a ray intersects the surface of each section. If the ray intersects the exit port of the concentrator, it continues to travel into the cylindrical pipe and enter into the coordinate of the pipe. A coordinate transformation is required when the coordinates between adjacent sections differ. When a ray leaves the exit port of the pipe, its position on the port and the direction of travel are recorded. 3.2. Results of computation for directional rays A series of computational runs was made for parallel rays that were assumed to enter into the concentrator (only) at certain angles to examine some transmission characteristics. 3.2.1. Three dimensional plots of ray trajectories Fig. 5 shows three sample plots of ray trajectories for rays that enter at 20° and 40°. The first two on the left show ray trajectories in the concentrator. The rays that enter at 20° are all transmitted through the concentrator, (a), and through the concentrator and straight pipe, (c). Half of the rays that enter at 40° are transmitted through the concentrator, (b).
3.2.2. Geometric patterns at exit ports of concentrator At smaller entry angles the positions where the rays leave the exit port of the concentrator form geometric patterns. Fig. 6(a) shows a pattern for the case when the entry angle 10° and Fig. 6(b) for the case of 40°, the acceptance half-angle. When the ray entry angle is small and the rays travel through to the straight pipe, patterns similar to mirror images to those of the concentrator only are discernible, but appear to be imposed with random dots, as in Fig. 7(a). When the ray entry angle is large the random dots appear to dominate as in Fig. 7(b). 3.2.3. Characteristics of transmission of rays through the concentrator 3.2.3.1. Ray transmissions through a concentrator. A part of parallel light rays that enters the concentrator at an angle smaller than the acceptance half-angle will transmit through the exit port without intersecting the surface of the concentrator. Another part of parallel rays intersect the concentrator surface and are reflected. The closer is the size of the entry angle of the parallel rays to that of the acceptance half-angle, the smaller is the proportion of the rays that transmit through the port without intersecting the concentrator surface. In this latter case, the other part of rays experience a larger number of reflections by the concentrator surface. When the entry angle of the parallel rays equals the acceptance half-angle, half of the total number of rays transmits through the concentrator, and the other half is reflected out through the entry port. Fig. 8 illustrates the configuration when the entry angle of rays is smaller than the acceptance half-angle. Table 2 shows sample result of transmission of 100 rays with entry angle of 39° through a concentrator with an acceptance half-angle of 40°. The table shows the number of reflections of ray number 1, 40, and 85 that are transmitted through the exit port. It also shows that ray number 100 transmits through without any reflection. Ray number 19 and 76 are reflected a number of times each before being reflected back out through the entry port. It also shows the position and the direction as each ray leaves the exit port. The coordinate (x, y) is at the base of the concentrator and z is coincident with the zenith direction, hence all rays that travel through the exit port have the z components in the position vectors equal to zero. The negative exit angles in the direction vector mean that the rays travel in the direction opposite to the z-coordinate. 3.2.3.2. Illuminance of transmitted rays. Suppose a beam of light of illuminance E lux in the direction of the beam enters the entry port of area Aent of a concentrator at an entry angle hent. The amount of light flux U reaching the entry port is then given as U ¼ ðE cos hent ÞAent
ð5Þ
Suppose n parallel rays are used to represent the entry light flux, each ray then represents DU lumen where
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Fig. 5. Three-dimensional plots of ray travels. (a) Rays entering at angle 20°. (b) Rays entering at angle 40°. (c) Rays entering at angle 20° and traveling through the pipe system.
DU ¼
U n
ð6Þ
A representative ray is reflected mi times at the concentrator surface when it reaches the exit port, where the concentrator surface has a reflectance of q. Its light flux is now reduced to
DUext ¼ DUðqmi Þ
ð7Þ
This ray leaves the exit port at an angle hext. If the exit port has an area of Aext, then the illuminance this ray contributes to the total is DEext where ðDUext Þ cos hext DEext ¼ ð8Þ Aext
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Fig. 6. Geometric patterns at exit port of concentrator. (a) Entry angle 10°. (b) Entry angle 40°.
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Fig. 7. Geometric patterns at exit port of pipe. (a) Entry angle 10°. (b) Entry angle 40°.
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Fig. 8. The configuration that illustrates that some rays transmit directly through the exit port when the entry angle of rays is smaller than the acceptance half-angle.
The total illuminance of the light flux leaving the exit port Eext is the sum of the illuminance contributed by each transmitted ray. The method of deriving transmitted illuminance used here is applicable to the whole pipe system where the system has more than one section. Fig. 9(a) shows, for a concentrator with an acceptance half-angle of 30°, plots of percentage of the number of rays transmitted (%Nrt) against the 90° complement of the ray entry angle on the horizontal scale. The figure also shows plots of illuminance at the exit port for two cases, when the reflectance of the concentrator surface is 0.95 and when it is 1.0, for when the illuminance of the entering beam light is 100 klux on a surface normal to the beam. The number of rays used in the calculation is 2500 for each entry angle and the increment of entry angle is 2°. The plots of percentage of the number of rays transmitted in Fig. 9(a) shows rather sharp transition between the entry angle that all rays are reflected out (33°) and the angle that all rays are transmitted (27°). The plot of illuminance at exit port for the case where the surface reflectance of the concentrator is 1.0 show that it rises from zero at an entry angle of 32–335 klux at the entry angle of 0°. For the case where the surface reflectance is 0.95, the exit illuminance only reaches 318 klux at entry angle of zero. The concentration ratio for this concentrator is 4 (or 400%). Even when the entry angle is zero, a small proportion of rays is transmitted without intersecting the concentrator surface, a larger proportion is reflected and the angles of intersection at the exit port of the rays in this portion is less than 90°.
Fig. 9. Plots of percentage number of rays transmitted and illuminance at exit port for the case where the acceptance half-angle of the concentrator is 30° and 40°. (a) Plots for the case where the acceptance half-angle of the concentrator is 30°. (b) Plots for the case where the acceptance half-angle of the concentrator is 40°.
Fig. 9(b) shows similar plots for the case where the acceptance half-angle of the concentrator is 40°, and the concentration ratio (CR) is 2.42 (or 242%). The maximum illuminance at exit port for surface reflectance of 1.0 and 0.95 are 218 and 210 klux respectively. Fig. 10 shows similar plots for the case where the acceptance half-angle of the concentrator is 40° connected to circular pipe of 1 m long, and the concentration ratio is 2.42 (or 242%). The maximum illuminance at exit port for surface reflectance of 1.0 and 0.95 are 218 and 190 klux respectively. 4. Experimental and calculation results and discussion A number of experiments on transmission of daylight through straight pipes only and pipes with anidolic concentrator were conducted in March 2014. The light pipes and concentrators were constructed with the same dimensions
Table 2 Sample result of ray tracing for a concentrator with acceptance half-angle 40°. Ray no.
1 19 40 76 85 100
Incident point x
y
z
Direction x
y
z
Ray exit angle (degree)
No. reflections of rays transmitted through
No. reflections of rays reflected back
0.0683 0.0965 0.0717 0.0709 0.0383 0.0748
0 0.0322 0.0121 0.065 0.0636 0
0 0.2284 0 0.2284 0 0
0.8813 0.6592 0.8698 0.3841 0.6609 0.6307
0 0.0769 0.4763 0.4963 0.6714 0
0.4726 0.748 0.1286 0.7786 0.3354 0.776
28.2 48.4 7.4 51.1 19.6 50.9
1 – 2 – 3 0
– 4 – 6 – –
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Fig. 10. Plots of percentage number of rays transmitted and illuminance at exit port for the case where the acceptance half-angle of the concentrator is 40° and is connected to circular pipe of 1 m long.
as those used for computation and are as described in the first paragraph of Section 3. The interior surface of the pipe and concentrator is lined with a film that has a specular reflectance of over 0.99. Fig. 11 shows the experimental setup. Two straight pipes were erected vertically, one with a shading ball to shade out beam illuminance, so that only diffuse illuminance from sky enters the entry port. For the unshaded pipe, total illuminance enters its port. Similar arrangement was made for two other pipes that were connected with anidolic concentrators at the tops of the pipes. To measure exit illuminance, illuminance sensors were placed at the exit of the pipes and all were housed in a box painted diffusively black. There was a daylight measurement station near the experimental site, but the total and diffuse illuminance measurements used in this paper were measured by illuminance sensors on the experimental site. 4.1. Experimental results on transmission of daylight through pipes with and without concentrators Fig. 12 shows plots of total (second line from top, Evg) and diffuse (fourth line from top, Evd) illuminance measured by two sensors on site on March 23. The sky ratio as can be surmised from the graphs varies mostly between about 0.4 to about 0.8. So the sky is partly cloudy during the experiment, However, for the period around
Fig. 11. Experimental setup for the experiments during March 2014.
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Fig. 12. Graphs of un-obstructed daylight and transmitted daylight through pipes.
11.20–11.35, clouds appear to shade out sunlight. So this period is overcast. The top line is the plot of total daylight illuminance transmitted through the straight pipe with concentrator (Evtap). The bottom line in the figure is a plot of diffuse daylight transmitted through a pipe with anidolic concentrator (Evdap). The line above it is a plot of diffuse daylight transmitted through a pipe with no concentrator (Evdp). Immediately above the three bottom lines is a plot of total daylight transmitted through the pipe with no concentrator (Evtp). Examining the results described above, it can be surmised that in cases of transmission of total illuminance, the pipe with concentrator performs better. In cases of transmission of diffuse illuminance, the pipes with no concentrator perform better. The relative performance is more pronounced for transmission of total illuminance where illuminance transmitted through the pipe with concentrator is higher (0–30%) than global illuminance and clearly higher (0–35%) than that transmitted through the pipe without concentrator. 4.2. A Comparison between calculated and measured daylight transmitted through pipes with concentrators The set of MATLAB scripts and functions described in Section 3 were used in the computation of transmission of daylight from the sky and beam daylight through the pipe system with anidolic concentrator. For beam daylight, measurement from the nearby station was used in the calculation. For daylight from the sky, the values of luminance used in the computation were generated using the ASRC-CIE sky luminance model. The model uses beam and diffuse radiation as well as the angular position of the sun at the given time to calculate clearness index and brightness index of Perez, (Perez et al., 1990). The values of the two parameters are then used to choose a combination of four standard sky luminance models. The combined model was used in a MATLAB function to generate luminance of 145 standard sky zones. A number of rays were assumed emitted in each of the 145 directions in the sky
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beam normal illuminance were obtained from a sun illuminance sensor attached to a suntracker at the station. In the figure, the measured transmitted beam illuminance is obtained as the difference between transmitted total illuminance and transmitted diffuse illuminance, from two different concentrator and pipes. The plot in Fig. 13(b) shows this derived value to vary from very small value to around 90 klux near noon. The values of calculated and measured transmitted beam illuminance are close and are larger than the beam normal illuminance. Within 10.50 and 14.07, when the angle of beam illuminance from the sun fell within the acceptance half-angle, the concentration ratio varies between 1.2 and 2. The results here show that the concentration ratio of a concentrator is a function of its acceptance half-angle and the reflectance of its surface. 5. Conclusion
Fig. 13. Plots of measured and calculated values of transmitted diffuse and beam daylight illuminance. (a) Plots of measured and calculated values of transmitted diffuse daylight illuminance. (b) Plots of measured and calculated values of transmitted beam daylight illuminance.
and entered into the entry port of the concentrator at each given time of 5-min duration. Each ray from each sky zone is traced until it leaves the exit port of the straight pipe. The number of times a ray is reflected from each section of the pipe system and the angle at which it leaves the exit port are recorded for computation of the illuminance at the outlet as described in Section 3.1. Results from the computation shows that beam illuminance is concentrated and transmitted through the pipe system with concentrator during 10.50 and 14.07 h. The resultant concentration ratio (CR in Fig. 13) is larger than one. For diffuse illuminance, the concentration ratio is less than one. The calculated and measured transmitted diffuse illuminance are plotted with measured horizontal diffuse illuminance in Fig. 13(a). The calculated and measured values are very close and both are smaller than the measured horizontal diffuse illuminance, with a concentration ratio between 0.5 and 0.9. This shows that even though the concentrator may be able to concentrate the part of sky daylight within the acceptance half-angle of the concentrator, the rejected part of the sky daylight was larger. Fig. 13(b) shows plots of calculated and measured transmitted beam illuminances and beam normal illuminance. The values of
Anidolic concentrator has the potential to enhance performance of a light pipe by increasing capture of more light flux into a pipe. This paper demonstrates that analytic method can be directly applied to trace rays through the light pipe system. The sky luminance values corresponding to a given sky condition are directly calculated for each time by a built-in function. The method can be used for analysis and design of such system. However, in certain configuration and certain situation, the specific character of an anidolic concentrator that sharply rejects rays of angles larger the acceptance half-angle may result in adverse effects. The configuration of the concentrator used in this study might not be able to clearly demonstrate the advantage of concentration for transmission of daylight that includes sunlight. Alternative configurations should be considered in the attempt to concentrate and bring more uniform transmitted daylight into interior spaces. Acknowledgements The research work reported in this paper is funded by the National Research Council of Thailand through the Thai-China Joint Research Program and the National Research University Project of the Commission for Higher Education of the Ministry of Education, the Royal Government of Thailand. Financial support is also given by the Thailand Research Fund through the Royal Golden Jubilee Ph.D. Program (Grant No. PHD/0010/2555) to Ms. Thanyalak Taengchum (student) and Professor Surapong Chirarattananon (advisor). References Chirarattananon, S., Chaiwiwataorakul, P., Hien, V.D., Rakwamsuk, P., Kubaha, K., 2010. Assessment of energy savings from the revised building energy code of Thailand. Energy, 1741–1753. Darula, S., Kocifaj, M., Kittler, R., Kundracik, F., 2010. Illumination of interior spaces by bended hollow light guides: application of the theoretical light propagation method. Solar Energy 84, 2112–2119.
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