Nonimaging behavior of circular trough concentrators with tubular receivers

Abstract

This paper presents a detailed analysis of the optical performance of circular trough concentrators with tubular receivers. First, a simple analytical formula for the achievable geometric concentration ratio as a function of the rim angle and acceptance angle is developed. Notably, the development reveals the existence of three distinct concentration ratio regimes: a first regime where the receiver is sized based on reflection of the edge rays from the rim alone; a second regime where the receiver is sized based on the rim and the edge ray caustics; and a third regime where two reflections from the mirror are permitted. Several exemplary designs are proposed and further analyzed using Monte Carlo ray tracing to obtain transmission angle curves and receiver flux distributions. For an acceptance angle of 1°, the circular trough concentrator with circular receiver is found to achieve a maximum geometric concentration ratio of 7.695× with a peak flux of 30 suns. For large acceptance angles (10°), the circular trough achieves a geometric concentration ratio as high as 82% of that of a parabolic trough. This noteworthy performance, together with the fact that a circular mirror is amenable to an inflated polymer construction, make this configuration promising for low-cost, low-concentration solar thermal applications.