A mathematical procedure to predict optical efficiency of CPCs with tubular absorbers

To evaluate the performance of compound parabolic solar concentrators (CPCs) with a tubular absorber, the ray-tracing analysis is commonly employed to determine the optical efficiency of CPCs for radiation incident at any angle. However, ray-tracing analysis is time-consuming especially as one investigates effects of the CPC’s geometry on the performance of CPC based solar systems. In this article, an attempt is first made to develop a mathematical procedure to predict the optical efficiency of CPCs with a tubular absorber. Results obtained based on one-, two-, three- and four-reflections models are compared to those from ray-tracing analysis. Analysis shows that multiple-reflections commonly occur for the radiation incident on reflectors near the aperture at small angles, and multiple-reflections after the third reflection usually occur on cusped reflectors near the bottom of tubular absorbers. Results show that a considerable fraction of incident radiation arrives on the tube after more than two reflections, but the fraction of incident radiation that arrives on the tube after more than four reflections is considerably small. Hence, the one-reflection model, where the incident radiation that arrives on the tube after more than one reflection is simply regarded as the one that arrives after one reflection, can’t reasonably predict the optical performance of CPCs except for those with a very high reflectivity. It is found that three-reflections models, where the radiation arriving on the tube after more than three reflections is regarded as the one that arrives after three reflections, can accurately predict the optical performance of CPCs.