## Abstract

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 * p{sup n/T}. Deviations between exact and approximate optical efficiency increase as n increases or as p decreases. For troughs with C ≤ 2.5 the maximal error for beam radiation is 3.4% for p ≥ 0.8 (8.3% for p ≥ 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 p = 0.8, were obtained. Increasing the concentration
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Fraidenraich, N.;

^{[1] }Almeida, G. J.- Universidade Federal de Pernambuco, Recife, PE Brasil (Brazil)

## Citation Formats

Fraidenraich, N., and Almeida, G. J.
Optical properties of V-trough concentrators.
FAO: N. p.,
1991.
Web.
doi:10.1016/0038-092X(91)90073-6.

Fraidenraich, N., & Almeida, G. J.
Optical properties of V-trough concentrators.
FAO.
doi:10.1016/0038-092X(91)90073-6.

Fraidenraich, N., and Almeida, G. J.
1991.
"Optical properties of V-trough concentrators."
FAO.
doi:10.1016/0038-092X(91)90073-6.
https://www.osti.gov/servlets/purl/10.1016/0038-092X(91)90073-6.

@misc{etde_22342452,

title = {Optical properties of V-trough concentrators}

author = {Fraidenraich, N., and Almeida, G. J.}

abstractNote = {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 * p{sup n/T}. Deviations between exact and approximate optical efficiency increase as n increases or as p decreases. For troughs with C ≤ 2.5 the maximal error for beam radiation is 3.4% for p ≥ 0.8 (8.3% for p ≥ 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 p = 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 p = 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. (author)}

doi = {10.1016/0038-092X(91)90073-6}

journal = {Solar energy}

issue = {3}

volume = {47}

journal type = {AC}

place = {FAO}

year = {1991}

month = {Jul}

}

title = {Optical properties of V-trough concentrators}

author = {Fraidenraich, N., and Almeida, G. J.}

abstractNote = {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 * p{sup n/T}. Deviations between exact and approximate optical efficiency increase as n increases or as p decreases. For troughs with C ≤ 2.5 the maximal error for beam radiation is 3.4% for p ≥ 0.8 (8.3% for p ≥ 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 p = 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 p = 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. (author)}

doi = {10.1016/0038-092X(91)90073-6}

journal = {Solar energy}

issue = {3}

volume = {47}

journal type = {AC}

place = {FAO}

year = {1991}

month = {Jul}

}