Geometric characteristics and design optimization of parabolic trough concentrators with a flat mirror as the secondary reflector designed based on two components of a solar source

Abstract

Parabolic trough concentrators with a tubular receiver (PTCs) are widely used for the production of solar thermal power. However, the geometric concentration ratio (CR) of PTCs falls short of thermodynamic concentration limit (C0) by a factor larger than π, and restricted by the angle subtended by solar sources (Δs = 2θa). To increase CR, a novel idea by dividing a solar source into two components in the open angle is proposed for the design of PTC equipped with a secondary reflector (SR), and PTC with a flat mirror (FM) is designed as a trial of the idea. For such design idea, rays incident at rims of primary parabolic reflector (PR) from one component (S1) are required to directly redirect onto on the absorber tube (AT) and those from another component (S2) are required to arrive on the AT after reflections from PR first then from FM. To investigate effects of the angular division factor (k) of solar sources (Δs2 = kΔs) and rim angle (ϕe) of PR on the effective CR (Cg), a mathematical procedure to characterize the geometry is suggested and examined by ray-tracing technique. The analysis shows that the geometry of PTC-FM is dependent on k, ϕe and θa, and a set of optimal k and ϕe for maximizing Cg can be obtained when θa is given. Calculation results show that the optimal k for maximizing Cg is 0.5 regardless of θa, but the optimal ϕe of PTC-FM for maximizing Cg, is sensitive to θa. As compared to conventional PTCs, the Cg of optimized PTC-FM is increased more than 80%, larger than 56.5% of C0, for k = 0.5 and θa < 1.0°. Empirical expressions for a quick estimation of optimal ϕe are also proposed based on numerical calculations. Results by ray-tracing analysis indicate that the optimal ϕe for maximizing CR and average solar concentration ratio are almost identical when the reflectivity of PR and FM is higher than 0.8. In principle, the novel idea is applicable for the design of other solar concentrators, therefore a further increase of Cg of PTCs is possible by using other imaging and non-imaging optics as the SR.