Analytical solutions for the geometric properties of compound parabolic solar collectors

In this study, a series of geometrical analysis of compound parabolic solar collectors with a different type of receiver revealed by nonimaging optics is made. Firstly, solar energy is defined, and types of collectors are classified. Then, the definitions of edge ray principle, acceptance function, half acceptance angle and etendue, which are basic concepts in the formation process of nonimaging optics and compound parabolic collectors, are given. The limit of geometric theoretical maximum concentration is respectively calculated by means of geometrical properties and etendue. Moreover, basic geometrical definitions used in geometrical analysis of compound parabolic collectors are put forth. Geometrical properties of compound parabolic solar collectors with a different kind of receiver are worked out through these definitions. This thesis also gives a total of analytical solutions and comparisons made on compound parabolic solar collectors with flat receiver and edge receiver. Analysed flat receivers are classified as horizontal and vertical receivers. The study of compound parabolic collectors with flat receiver have been published in literature. The analysis in this thesis is compared with the study in literature and the based calculations are confirmed. As to collectors with edge receiver, they are studied in two case according to vertex angle of receiver and half acceptance angle of collector. In the first case, vertex angle of receiver is bigger than half acceptance angle. The study on this first case published in literature is taken as a reference to this thesis. The analytical solutions are verified by the reference study. The second case is that vertex angle of collectors with edge receiver is narrower than half acceptance angle. Analytical solutions are made on the second case designated as the last receiver type. By making geometrical anaylsis, equations of collector concentration ratio, collector height, collector gap, reflector surface lenght are determined. These quations are presented on a chart and diagram by using 30°,45° ve 60° half acceptance angles and different truncation angles. Analytic solution of geometrical properties made in this study opens up an opportunity of comparing compound parabolic collectors especially for different receivers. Besides, this analytic solution offers absolute scores for design to be made in regard to ray tracing simulations. Considering the solutions found in this study, it is observed that contrentration ratio is not changed significantly when reflectors of compound parabolic solar collectors are truncated. Particularly, in collectors with flat horizontal receiver and the ones whose vertex angles are bigger than their half acceptance angle, collector cost of reflector truncations, in respect to manufacturing cost, is cheaper than other types of collectors. The fact that the difference between vertex angle and half acceptance angle gets bigger, especially considering collectors with edge receivers, provides collectors with more convinient criteria for design of collectors. In this study, it is also seen that different half acceptance angles and truncation angles are ideal for compound parabolic solar collectors with different reflectors