Optical concentration ratio of a parabolic trough collector with flat receiver and concentrator with surface irregularities

In a parabolic trough collector (PTC), the geometric concentration ratio (C_g), which is the ratio of the aperture width of the concentrator and the width of the receiver, is generally used for evaluating the solar radiation collected by the flat receiver. This paper argues that this approach is valid only up to a certain width of receiver and that the optical concentration ratio (C_opt) should be used when the receiver exceeds that width. A model for evaluating C_opt has been developed in this work. It is based on tracing a large number of rays, sampled probabilistically using the Latin Hypercube Sampling (LHS) technique. The model also considers the incidence angle of individual rays, and concentrator surface irregularities, which are ignored in the analytical relationships for C_g. For a perfect parabolic surface where \(100\leq C_{g}\leq 10\), the C_opt was found to be between ≈80% to 90% of C_g. Also, the concentration ratio was found to be significantly affected by surface irregularities. A useful graphical tool, a set of mathematical relationships and an online program are presented to help designers and researchers evaluate the C_opt by providing the design parameters.