Diffuse reflections within CPCs and its effect on energy collection

In practical applications, part of solar rays incidence on reflectors of compound parabolic concentrators (CPC, in short) undergoes diffuse reflections instead of specular reflections due to imperfect reflector profile, rough surface and dust deposition, leading a considerable fraction of solar rays escape from the cavity of CPCs and making their optical performance decrease. In this article, a detailed mathematical procedure to estimate the optical efficiency factor of CPCs with semi-diffuse reflectors and one-sided flat absorber is developed based on the knowledge of two-dimensional radiation transfer, and the effect of diffuse reflections within the CPC on its energy collection is theoretically investigated. Ray-tracing analysis shows that the use of semi-diffuse reflectors in CPCs can not make solar flux on the absorber more uniform except using perfect diffuse reflectors, in turn leads the optical efficiency decrease. Comparisons of the optical efficiency factors between theoretically expected and those obtained by ray-tracing simulation indicate that the mathematical model proposed in this work can accurately estimate the optical performance of such CPC. Theoretical calculations show that the contribution of diffuse reflections within CPCs to the radiation collection of CPCs is limited as a result of the fact that the diffuse radiation transfer shape factor from the reflectors to the absorber is very small, and the annual average optical concentration decreases with the increase of diffuse reflectivity of reflectors for CPCs with a given total reflectivity.