A unified geometric design and optical evaluation of a V-shaped secondary reflector for parabolic trough collectors

Parabolic trough collectors are the most mature concentrating solar power technology, yet their optical performance is constrained by two coupled limitations: a limited geometric concentration ratio and a strongly non-uniform flux on the absorber tube. This study proposes a V-shaped secondary reflector that, by introducing a reflector-inclination angle absent in the conventional flat secondary reflector, provides an additional geometric degree of freedom for exploring the trade-off between concentration enhancement and flux homogenization. A unified geometric-design framework combining the split-source method with the boundary-ray principle is established; it classifies the absorber–reflector coupling into four geometric cases and yields closed-form solutions for the size and position of both the secondary reflector and the absorber. Two key findings emerge from the analysis. First, the effective geometric concentration ratio closely tracks the ray-traced average local concentration ratio in the examined sweeps, supporting its use for rapid pre-screening before targeted ray tracing. Second, the V-shaped configuration provides two complementary advantages over its flat counterpart: an equal or higher concentration ratio for rim angles up to 90°, with gains of up to 36% near the feasibility boundary, and continued geometric feasibility at rim angles beyond 90°, where the flat secondary-reflector configuration considered here is no longer feasible. A sensitivity analysis shows only limited degradation for equivalent per-surface slope errors up to about 2 mrad and for a secondary-reflector reflectivity as low as 0.90.