OPTICAL-PROPERTIES OF V-TROUGH CONCENTRATORS

A new approach to study the optical behavior of V-trough concentrators is developed, based on the use of three characteristic angles defining the appearance, disappearance and return to the outside space of the cavity of a reflection mode. The probability of occurrence of a given number of reflections for beam radiation is determined as a function of these angles and the optical efficiency calculated. It is shown that the optical efficiency can be approximated by a function of two parameters, the angular acceptance function, T, and the mean number of reflections, n, as T.rho-n/T. Deviations between exact and approximate optical efficiency increase as n increases or as rho-decreases. For troughs with C less-than-or-equal-to 2.5 the maximal error for beam radiation is 3.4% for rho greater-than-or-equal-to 0.8 (8.3% for rho greater-than-or-equal-to 0.7). For diffuse radiation the maximal error is less than 2% for configurations whose optical efficiency is above 0.6. A further simplification was introduced to obtain the optical efficiency for diffuse radiation, approximating T by an analytical expression and n by an empirical linear function of the inverse of the vertex angle. Results accurate up to 5% for rho = 0.8, were obtained. Increasing the concentration ratio, C, from 1.5 to 2.5 for a vertex angle being one third of the acceptance angle, decreased the optical efficiency from 0.74 to 0.59, for rho = 0.8. For a given C, the dependence of the optical efficiency on the vertex angle is rather weak, suggesting that large trough angles might be favoured by cost-benefit analysis.