Investigation of the impact of apex angle in prismatic elements on the efficiency of prismatic daylight collectors using matrix ray-tracing model

• Main Authors: Shih-Chuan Yeh, 葉世川
• Other Authors: Allen Jong-Woei Whang
• Format: Others
• Language: en_US
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/64742215922845119897

博士 === 國立臺灣科技大學 === 電子工程系 === 100 === In buildings, efficient lighting systems and excellent design of interior natural light illumination can contribute to energy savings; meanwhile, natural light illumination systems have the potential to improve human health, mood, performance and productivity. Prismatic elements are widely used in natural light illumination systems for redirecting and collect daylight. Prismatic elements can be part of a daylight illuminate system located on the roof or façade of buildings and can be used as collectors to collect and guide daylight to reduce glare and save energy. An analysis of the distribution of the energy and ray-tracing can improve the performance of daylight guiding systems and aid in the design of natural light illumination systems. The characteristics of the light that emerges from the surface of a right-angled prism vary with the apex of the prism and the incident angle of the sunshine illuminating the surface of the prismatic daylight collector. Based on the principles of optics, this article presents a simple mathematical three dimensional matrix ray-tracing methodology through which a detailed intensity distribution of parallel light beam incident onto a right angled prism from different incident angles can be calculated precisely. The direction, concentration and distribution of intensity of the emerged light from the parallel light incident onto a surface of the right-angle prism, as well as daylight illuminate on a prismatic collector are precisely calculated. The detailed calculation of the emerged light re-incident onto the adjacent prism or emerged out of the right angled prismatic element with a 45° apex angle presented that most of daylight are directly emerged out and are confined in some directions at earlier morning and afternoon; the emerged light re-incident into the adjacent prism at noon around. This paper also investigates the effect of the apex angle of a right-angled prismatic collector on the performance of the collector using this matrix ray tracing model and the edge principle. It was found that the majority of the light emerges from the hypotenuse of the right-angled prism when sunshine is incident on the surface of the prismatic daylight collector; furthermore, the distribution of the light can be shifted by changing the apex of the right-angled prismatic collector. The direct illumination level of the light emerging from the hypotenuse decreases as the apex of the right-angled prism is increased. The intensity distribution of the majority of the light emerging from the hypotenuse of a right-angled prism can be used to guide the design of natural light illumination systems and enhance their performance. The percentage of light emerging from the hypotenuse decreases with the number of prismatic elements because the relative area of the emerging light that reaches the adjacent prism increases with the number of prismatic elements. The analysis of the relative area of the emerging light that reaches the adjacent prism according to the edge ray principle shows that the total area is constant when the number of prismatic elements is greater than 10; an economical prismatic daylight collector can be realized with less material due to the larger number of smaller prisms with the same apex. This detailed calculation model of parallel light beam incident to a prismatic element can be applied to the hybrid natural light illumination system as well as to the prism-relative solar illumination system for the improvement of efficiency. This paper proposes a model of a natural light illumination system that would improve the efficiency of solar energy use. This model is composed of a prismatic daylight collector, a reflector for re-directing daylight into the room and a diffuse reflector for indoor illumination. The prismatic daylight collector and the daylight canopy not only decrease the discomfort of glare but also collect daylight for the natural lighting system.