A novel method for determining sky view factor for isotropic diffuse radiations for a collector in obstacles-free or urban sites

Abstract

A novel method for computing sky view factor for isotropic diffuse radiations on tilted collectors located in obstacle free and urban sites has been introduced in this paper. The proposed method involves disintegrating the hemispherical sky vault around collector into small portions (sky elements). Collector is a flat receiving surface, positioned at a particular tilt angle and facing a specific azimuthal orientation. The three-dimensional celestial vault is transformed into a two-dimensional plane. This plane is converted into a computer graphic raster image for computing. Each pixel of raster image represents a sky element. Color (gray shade) of every pixel describes specific weight which depends upon sky element's solid angle and incidence angle with respect to collector. Sky view factor is evaluated by taking ratio of the sum of color codes of all the pixels for tilted collector to that of horizontal collector. Sky view factors at different tilt angles for obstacle free sites are evaluated and results are found in good agreement with Liu Jordan method. To evaluate sky view factor for urban sites having obstacles (e.g., buildings, trees, etc.) that may cause sky blocking, the obstacles are taken into account by projecting them onto the celestial vault. Their projections are transformed onto a two dimensional plane and then onto the raster image. For enhancing the applicability of the proposed method, so as to analyze sites with complex sky blocking obstacles, the approach is developed such that it can be computer programmed easily. Small portions of sky can be located and analyzed in a program using a specially developed coordinate system recognized by various programing languages. The program results in grey scaled raster images presenting radiances received by the collector, coming from different portions of the sky. Comparison of sky view factors obtained from the proposed method with existing methods published in literature is also presented. Results show that the proposed methodology is in good agreement with Liu Jordan method and provides more logical results as compared to results published in literature for urban sites with obstacles. The deviations between results are quantified and discussed.