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Research Papers

Distribution of Emerged Energy for Daylight Illuminate on Prismatic Elements

[+] Author and Article Information
Shih-Chuan Yeh1

 National Taiwan University of Science and Technology/ De Lin Institute of Technology, No. 1, Lane 380, Qingyun Road, Tucheng City, Taipei County 236, Taiwanyehsc@dlit.edu.tw National Taiwan University of Science and Technology, T2-507, No. 43, Sec. 4, Keelung Road, Taipei 10607, Taiwanyehsc@dlit.edu.tw National Taiwan University of Science and Technology, EE-602-1, No. 43, Sec. 4, Keelung Road, Taipei 10607, Taiwanyehsc@dlit.edu.tw Dongguan University of Technology, No. 1, University Road, Songshan Lake, Dongguan City 523808, Guangdong Province, Chinayehsc@dlit.edu.tw National Taiwan University of Science and Technology, T2-507, No. 43, Sec. 4, Keelung Road, Taipei 10607, Taiwanyehsc@dlit.edu.tw

Allen Jong-Woei Whang, Horng-Ching Hsiao, Xi-Duo Hu, Yi-Yung Chen

 National Taiwan University of Science and Technology/ De Lin Institute of Technology, No. 1, Lane 380, Qingyun Road, Tucheng City, Taipei County 236, Taiwanyehsc@dlit.edu.tw National Taiwan University of Science and Technology, T2-507, No. 43, Sec. 4, Keelung Road, Taipei 10607, Taiwanyehsc@dlit.edu.tw National Taiwan University of Science and Technology, EE-602-1, No. 43, Sec. 4, Keelung Road, Taipei 10607, Taiwanyehsc@dlit.edu.tw Dongguan University of Technology, No. 1, University Road, Songshan Lake, Dongguan City 523808, Guangdong Province, Chinayehsc@dlit.edu.tw National Taiwan University of Science and Technology, T2-507, No. 43, Sec. 4, Keelung Road, Taipei 10607, Taiwanyehsc@dlit.edu.tw

1

Corresponding author.

J. Sol. Energy Eng 133(2), 021007 (Mar 23, 2011) (9 pages) doi:10.1115/1.4003587 History: Received June 16, 2010; Revised February 01, 2011; Published March 23, 2011; Online March 23, 2011

Prismatic elements are typical devices of natural light illumination system for redirecting and collecting daylight. Based on the principles of optics, this paper presents a simple mathematical 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. We also present the distribution of the secondary emerged intensity from a prism illuminated by the emerged light of an adjacent prism. 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 prismatic element presented that most of daylight are directly emerged out and are confined in some directions at earlier morning and afternoon, and the emerged light re-incident into the adjacent prism at noon around. 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.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) An illustration of sunshine illuminate the prismatic element. (b) An illustration of the prismatic element with a fixed coordinate and a temporary imagined coordinate; a photograph of a model of the optical brick is also presented.

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Figure 2

(a) An illustration of a light ray is incident to a prism. (b) An illustration of the interface of mediums, plane of incidence, unit vectors of incident ray, reflective ray, refracted ray, and the angles δir and δit.

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Figure 3

Definitions of surface number of the right-angle prism: (a) 3D and (b) 2D

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Figure 4

The components −θ and −φ of reflective and refractive rays for the external ray is incident from surface S2, where the vertical angle-axis and horizontal-axis in these figures describe the propagated direction of the incident ray: (a) θ of reflective rays, (b) ψ of reflective ray, (c) θ of refractive ray, and (d) ψ of refractive ray.

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Figure 5

Illustrations of the divided light beams and the calculated results of criterion positions relative to the polar angle of external incident from each surface of the prism: (a) external incident from S1 (b) external incident from S2 (c) external incident from S3.

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Figure 6

The intensity and surface of the main emerged light relative to the direction of external incidence from S1: (a) incident from (0.2, 1.0), (b). (0.5, 1.0), and (c). (0.8, 1.0)

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Figure 7

(a) The concentration ratios of S2 and S3, (b) the transmittances of the main emerged on S2 and S3, and (c) the intensity of emerged light

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Figure 8

The normalized intensity and polar angle of the main emerged light for the light illuminated on S1: (a) the normalized intensities and (b) the polar angle

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Figure 9

(a) An illustration of the emerged light from S2 of prism A; (b) the components −y of the top ye22 and bottom end ye21 of the emerged region of S2 and criterion positions (x23 min,y23 min); (c) the distribution of energy of the main emerged from S2; (d) the distribution of intensity that emerged out to space

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Figure 10

(a) An illustration of emerged light of S3, (b) the distribution of relative energy of the emerged light of S of prism A, (c) an illustration of distribution of energy that intersected S1 and S3, and (d) the distribution of intensity that emerged out to space

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Figure 11

Comparison of measured radiation of clear acrylic window and main emerged light of S2

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