Towards an analysis of the performance of lightwell skylights under overcast sky conditions

1  Towards an analysis of the performance of lightwell skylights under overcast sky conditions Authors’ names and affiliations: Ignacio Acosta, University of Seville, Lecturer PhD. Corresponding Author. Jaime Navarro, University of Seville, Professor PhD. Juan José Sendra, University of Seville, Professor PhD. Corresponding Author: Ignacio Acosta, University of Seville, Corresponding Author Tel. number: 0034647550654 Email: [email protected] Permanent address: Institute of Architecture and Building Science, University of Seville, 41012 Seville. Spain Abstract The main aim of this article is to analyze the performance of lightwell skylights under overcast sky conditions, determining the daylight factors and luminous distribution produced inside a room. Four different studies are carried out considering a room with a lightwell skylight. The first analyzes the daylight factors according to the size and height/width ratio of the skylight, the second evaluates illuminance depending on the reflection index of the lightwell, the third studies different room proportions and the fourth establishes suitable spacing between skylights. All tests were carried out using Lightscape 3.2 software. Following the trials it was concluded that daylight factors are almost directly proportional to the size of the skylights and inversely proportional to their height. There is also an approximate quantification of the influence of the reflection index of the lightwell on interior lighting. Finally, it is confirmed that, in the absence of a reflected component, the suitable spacing between openings is proportional to the height/width ratio of the skylight. Keywords: skylight, lightwell, daylighting, overcast sky, lighting software. 1. Introduction and objective 1.1. State of the art The use of skylights is frequent in modern architecture since these allow access to daylight in rooms lacking façades, while providing homogeneous lighting over the horizontal plane. Most researchers in this field have based their methodology on classic treatises on daylighting [1] and computer simulation [2]. One of the many formsof providing daylight in rooms is that of lightwell skylights, horizontal openings placed on a prism which acts as a reflector and prevents the incidence of the sun on the interior. One of the first authors to define this type of skylight was Lam [3], who states that lightwell skylights allow sufficient daylighting in rooms below attic level. He also concludes that this type of skylight projects the light onto the floor, and in most cases this results in dim lighting of walls. 2  One of the most comprehensive studies on lightwell skylights is by Bouchet et al. [4] and establishes the design rules to allow an adequate amount of daylight into underground spaces. Using daylight simulation software Genelux, based on the ray-tracing method, the authors carried out a series of tests which basically conclude that the reflection index of lightwells is a determining factor in the lighting of a space. They also determined that specular reflectors allow greater illuminance than diffuse reflectors. Lightwell skylights have a highly practical application in architecture, as can be observed in the research on their use in residential buildings. Kristl et al. [5] researched the distribution of daylight factors produced by the use of lightwells in residential buildings. The authors determined the variation in lighting in rooms depending on the shape and width of the skylight, thus confirming the usefulness of this architectural element. In addition, practical cases can be observed in the research carried out by Kotani et al. [6] where the authors analyze the assessment of the environmental conditions carried out by the occupants. As described above, lightwell skylights mainly project light on the floor and produce a very characteristic daylight distribution. Nabil et al. [7] applied new metrics and assessed the lighting distribution produced by this type of skylight. This research emphasizes the interpretation of daylight factors compared to daylight autonomy and useful daylight illuminances. In addition to their application in daylighting, lightwell skylights favour natural ventilation in buildings. This can be noted in the research carried out by Kotani et al. [8], analyzing the ventilation produced by lightwells in different case studies. Moreover, Lomas [9] concludes that lightwells act as a passive system favouring the natural ventilation of buildings. A rather unique form of lightwell skylights not included in this research are daylight collectors, which allow daylight to reach the darker areas of the rooms. Specifically, Wittkopf et al. [10] assessed the performance of different shapes of daylight collectors, and concluded that lightwells are a very practical element in daylighting in architecture. 1.2. Objective The main objective of this research is to determine the performance of lightwell skylights under overcast sky conditions. In order to do so four trials were carried out to obtain the variation of performance depending on multiple variables, such as the size and the height/width ratio of the skylight, as well as the reflection index of the reflector or the spacing between openings. 2. Description of Methodology for Calculation 2.1. Choosing the calculation conditions By definition, the calculation of daylight factor components is carried out considering an unobstructed sky of assumed or known illuminance distribution, excluding direct sunlight. The definition of traditional overcast sky is used to calculate the sky component. The overcast sky model, used in the methodology, is that defined by Moon-Spencer [11], where the luminance values are distributed according to the following: L = LZ · (1+2sin)/3 where “LZ” is the luminance at the zenith of the sky vault and “” the projection angle. This implies that the lowest luminance value in an overcast sky vault occurs on the horizon, and is equivalent to a third of the maximum luminance at the zenith: L0 = LZ /3 3  The formulation established by Moon-Spencer corresponds to the definition of overcast sky accepted by the CIE [12], which is known as traditional overcast sky: Sky type 16. 2.2. Choosing the calculation program The analysis of the daylight factors was carried out using simulation program Lightscape 3.2, which calculates luminous distribution using a radiosity process. Several studies have confirmed the correct behaviour of this calculation program [13,14]. The calculation parameters used by this program are shown in table 1. Lightscape 3.2 Sky Conditions Overcast Sky Mesh Spacing Min 0.10 m Max 0.20 m Subdivision Contrast Threshold 0.40 Skylight Accuracy 0.60 Source Direct Source Min 0.20 Subdivision Accuracy 0.70 Indirect Source Min 0.40 Subdivision Accuracy 0.70 Shadow Grid Size Five Tolerances Length 0.0005 Ray Offset 0.001 Initialization Min Area 0.01 Table 1: Parameters of the calculation program. 2.3. Choosing the calculation model The initial model used for the trials was a room 9 m wide by 9 m long by 4.5 m high. A lightwell skylight, with a square floor and variable height (H) and width (W) (fig. 1), was placed in the centre of the roof. The work plane on which daylight factors are studied is located 1.00 m above the floor. The model represents the typical dimensions of a museum or library room. The low height of the ceiling in relation to the measurements of the space allows a distribution of light that is largely dependent on the Sky Component and is therefore suitable for analyzing the efficiency of the skylight proportions under study. 4  Figure 1: Initial calculation model. To adapt the results to the skylight proportions, the optical properties of surfaces –reflection, inter-reflection and transmission– are considered invariable. The inter-reflection of all the surfaces is completely diffuse under Lambert’s cosine law, and as a result the light falling on a surface is reflected in all directions. Each surface has a different reflection index: the ceiling and skylight have an index of 0.9, the walls 0.7, and the floor 0.5, normal values in the design of interiors. 3. Calculation 3.1. Trial 1: Size and ratio of the lightwell skylight The first trial analyzed the performance of a lightwell skylight, considering variations in size and the height/width ratio of the reflector. In order to carry out this first study, three skylight models were established, according to the base measurements:  M1: lightwell skylight with 1.00 x 1.00 m base and variable height.  M1.5: lightwell skylight with 1.50 x 1.50 m base and variable height.  M2: lightwell skylight with 2.00 x 2.00 m base and variable height. Eight skylights of different heights were measured according to the base of each model. The height of the skylights varied between 1 and 4.5 times the width of the base (fig. 2). Figure 2: Trial 1: Variation in size and height/width ratio of the lightwell skylights. 5  From figure 2 it is deduced that models M1, M1.5 and M2 are proportional to each other, thus helping us assess the variations in illuminance caused by the size and height/width ratio of the lightwell. A total of 24 simulations was carried out for this test. Table 2 shows the maximum, average and minimum daylight factors on the work plane for each calculation model under the conditions described in the methodology and the variation in size and ratio of the skylight: TRIAL 1: SIZE AND RATIO LIGHTWELL SKYLIGHT. BASE OF 1x1 (M1) SKYLIGHT HEIGHT DAYLIGHT FACTOR MAX AVE MIN 1.00 1.95% 0.59% 0.17% 1.50 1.65% 0.42% 0.12% 2.00 1.44% 0.33% 0.09% 2.50 1.24% 0.25% 0.07% 3.00 1.07% 0.20% 0.06% 3.50 0.94% 0.16% 0.04% 4.00 0.82% 0.13% 0.03% 4.50 0.72% 0.10% 0.02% LIGHTWELL SKYLIGHT. BASE OF 1.5x1.5 (M1.5) SKYLIGHT HEIGHT DAYLIGHT FACTOR MAX AVE MIN 1.50 3.93% 1.36% 0.39% 2.25 3.27% 1.00% 0.28% 3.00 2.71% 0.78% 0.21% 3.75 2.30% 0.59% 0.17% 4.50 1.93% 0.47% 0.13% 5.25 1.63% 0.37% 0.10% 6.00 1.39% 0.30% 0.08% 6.75 1.19% 0.23% 0.06% LIGHTWELL SKYLIGHT. BASE OF 2x2 (M2) SKYLIGHT HEIGHT DAYLIGHT FACTOR MAX AVE MIN 2.00 6.38% 2.49% 0.71% 3.00 5.11% 1.81% 0.52% 4.00 4.20% 1.41% 0.39% 5.00 3.44% 1.07% 0.30% 6.00 2.84% 0.86% 0.23% 7.00 2.38% 0.67% 0.18% 8.00 1.98% 0.54% 0.14% 9.00 1.66% 0.41% 0.11% Table 2: Trial 1: Maximum, average and minimum daylight factors on the work plane. Variable size and ratio of the skylight. As can be observed in table 2, the daylight factors measured on the work plane decrease as the height of the lightwell increases. Considering the calculation model used, where the reflection index of the skylight is 0.9, it is deduced that daylight factors decrease in inverse proportion to the height of the lightwell. This behaviour can also be seen in figure 3, which shows the daylight factors measured using the simulation program and those established following the hypothesis that the results obtained are inversely proportional to the height of the lightwell, using the average daylight factors produced by each skylight model as a starting point. 6  Figure 3: Trial 1: Average daylight factors (DF.ave.) on the work plane according to simulation software (S) and hypothesis (H). Variable size and ratio of the skylight. As can be deduced from figure 3, considering the calculation model conditions, the hypothesis that average daylight factors are inversely proportional to the height of the lightwell provides results similar to those of the simulation program, with an average relative difference of 9.47%. The margin of error of the simulation program results and the hypothesis proposed increases as the height of the skylight increases and decreases as the height decreases. The hypothesis proposed makes it possible to calculate the relative variation in lighting in a room as a result of the modification in height of lightwell skylights. From table 2 it is also possible to deduce that daylight factors are almost directly proportional to the size of the skylight. This can be seen when comparing lightwells of equal height/width ratio but different size, so that with identical ratios, model M1.5, which is 1.5 m wide produces daylight factors almost 1.5 times those measured for model M1, which is 1 m wide. An equivalent observation can be made for model M2, which is 2 m wide and produces approximately double the daylight factors measured in model M1. Thus, it can be deduced that the quotient of daylight factors and the surface base of the skylight is practically invariable, providing the height/width ratio remains constant. Figure 4 shows the relative difference for models M1.5 and M2 compared to model M1, considering the daylight factors and the surface base of the skylight. 7  Figure 4: Trial 1: Relative difference of the quotient of average daylight factors on the work plane and the surface base of the skylight, according to simulation software. Models 1.5 (M1.5) and 2 (M2) with respect to model 1 (M1). Variable size and ratio of the skylight. As can be observed in figure 4, the relative difference for models M1.5 and M2 with respect to model M1 has a maximum value of 7.25% and an average of 4.72%. Thus, it can be stated that the daylight factors produced by a lightwell skylight are almost directly proportional to size. This statement allows us to calculate the relative variation in daylight for a room, caused by the modification of the size of the lightwell skylight. 3.2. Trial 2: Reflection index of the lightwell skylight The second trial analyzed the performance of a lightwell skylight, considering the variation of the reflection index of its surfaces. For this study, skylight model M1.5 was used for the room described in the calculation model. Eight skylight models of varying heights were analyzed. The height of the skylight varied between 1 and 4.5 times the width of the base (fig. 2). Thus, a skylight measuring 1.5 x 1.5 m and with a height varying between 1.5 and 6.75 m was used. The reflection index of the skylight varied between 0.3 and 0.9. A total of 24 simulations was carried out in this trial, complementing the previous one, which simulated a skylight with a reflection index of 0.9. Table 3 shows the maximum, average and minimum daylight factors on the work plane for each calculation model under the conditions described in the methodology and with a variation in the height and reflection index of the skylight: 8  TRIAL 2: SKYLIGHT REFLECTION LIGHTWELL SKYLIGHT. REFLECTION OF 0.7 (R0.7) SKYLIGHT HEIGHT DAYLIGHT FACTOR MAX AVE MIN 1.50 3.48% 1.09% 0.28% 2.25 2.73% 0.72% 0.17% 3.00 2.15% 0.48% 0.12% 3.75 1.74% 0.34% 0.08% 4.50 1.42% 0.24% 0.06% 5.25 1.17% 0.18% 0.04% 6.00 0.98% 0.13% 0.02% 6.75 0.83% 0.10% 0.02% LIGHTWELL SKYLIGHT. REFLECTION OF 0.5 (R0.5) SKYLIGHT HEIGHT DAYLIGHT FACTOR MAX AVE MIN 1.50 3.20% 0.92% 0.21% 2.25 2.44% 0.56% 0.12% 3.00 1.90% 0.36% 0.07% 3.75 1.52% 0.24% 0.05% 4.50 1.24% 0.17% 0.03% 5.25 1.02% 0.12% 0.02% 6.00 0.86% 0.09% 0.02% 6.75 0.74% 0.07% 0.01% LIGHTWELL SKYLIGHT. REFLECTION OF 0.3 (R0.3) SKYLIGHT HEIGHT DAYLIGHT FACTOR MAX AVE MIN 1.50 3.00% 0.76% 0.16% 2.25 2.27% 0.45% 0.09% 3.00 1.76% 0.28% 0.06% 3.75 1.41% 0.19% 0.04% 4.50 1.16% 0.13% 0.02% 5.25 0.96% 0.09% 0.02% 6.00 0.81% 0.07% 0.01% 6.75 0.70% 0.06% 0.01% Table 3: Trial 2: Maximum, average and minimum daylight factors on the work plane. Variable reflection index of the skylight. As was concluded in the previous trial, the daylight factors on the work plane decrease proportionally as the height of the skylight increases, although this tendency is more noticeable when the reflection index is lower. As can be observed in table 3, the average daylight factors obtained on the work plane vary considerably depending on the reflection index of the skylight, and the difference can be noticed mainly in the higher lightwells. Specifically, the skylight with a reflection index of 0.7 produces an increase of around 30% in comparison with the skylight with an index of 0.5 which produces a similar increase over the skylight with an index of 0.3. These increases become much more noticeable the higher the skylight is, as there is a larger surface for reflection. These observations show that despite the high performance of lightwell skylights, their reflection index is a determining factor for an efficient use of lighting, particularly in the case of lightwells with a high height/width ratio. 9  Disregarding the daylight factors observed in extreme cases where the reflection index of the lightwell is below 0.3 or above 0.9, it can be deduced that the average daylight factors are almost directly proportional to the skylight reflection, providing the lightwell is high enough to reflect daylight. The lower the skylight, the lower the influence of the reflection index on the resulting daylight factors, as the reflection surface is smaller and therefore less of a determining factor in generating the reflected component. As is represented in figure 5, considering a height/width ratio of the skylight over 2.00, in cases where the reflection index of the lightwell is between 0.5 and 0.7, average daylight factors are almost directly proportional to this index. Figure 5: Trial 2: Average daylight factors (DF.ave.) on the work plane according to simulation software (S) and hypothesis (H). Variable reflection index and height of the skylight. As can be deduced from figure 5, the hypothesis that daylight factors are directly proportional to the reflection index of the lightwell is true for skylights with a height/width ratio over 2.00, where the index is between 0.5 and 0.7, with an average relative difference of 2.53%. As can be deduced from table 3, the lower the lightwell, the lower the influence of the reflection index as a determining factor, meaning that the daylight factors tend to converge as the height/width ratio tends towards 0 and do not comply with the proportionality between reflection indexes, as observed in figure 5.