Influence of the size of facets on point focus solar concentrators David Riveros-Rosas a , Marcelino Sánchez-González b , Camilo A. Arancibia-Bulnes c, * , Claudio A. Estrada c a Instituto de Geofísica, Universidad Nacional Autónoma de México, Ciudad Universitaria, Col. Copilco, Coyoacán, CP 04510 DF, México b Centro Nacional de Energías Renovables, c/Somera 7-9, CP 28026 Madrid, Spain c Centro de Investigación en Energía, Universidad Nacional Autónoma de México, Priv. Xochicalco s/n, Morelos, México article info Article history: Received 19 August 2009 Accepted 26 August 2010 Keywords: Solar concentrator Faceted concentrator Optical design Ray tracing Radiative flux distribution Optical error abstract It is a common practice in the development of point focus solar concentrators to use multiple identical reflecting facets, as a practical and economic alternative for the design and construction of large systems. This kind of systems behaves in a different manner than continuous paraboloidal concentrators. A theoretical study is carried out to understand the effect of the size of facets and of their optical errors in multiple facet point focus solar concentrating systems. For this purpose, a ray tracing program was developed based on the convolution technique, in which the brightness distribution of the sun and the optical errors of the reflecting surfaces are considered. The study shows that both the peak of concen- tration and the optimal focal distance of the system strongly depend on the size of the facets, and on their optical errors. These results are useful to help concentrator developers to have a better under- standing of the relationship between manufacturing design restrictions and final optical behavior. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction Several different methods have been investigated for the construction of point focus solar concentration systems. These range from segmented parabolas made with metal or glass mirrors, to single surface mirrors that approximate the required geometry, and are fabricated by applying tensions to stretch reflective metallic or polymeric membranes to suitable shapes. A practical solution when very high concentration is required, as for instance in solar furnaces is the formation of the concentrator with individual mirrors of spherical curvature, which can be fabricated in conventional optical workshops. In any case, it is usually assumed that the best focal distance for the system coincides with the focal distance of the continuous parabola one is trying to emulate, or else a simulation is carried out to determine this optimal focal distance for the particular case at hand. Ray tracing simulations are very effective for the design and optimization of parameters in solar concentration systems [1,2]. They are also used to characterize optical errors in such systems by comparison with experimental results, and for the design of receivers [3e5]. By these techniques it is possible to model large dimensions optical systems like central receivers and faceted concentrators. In the present work ray tracing simulations by the convolution method are employed to analyze the effect of the facet size and optical error in the irradiance distribution of point focus concen- trators, as well as on the effective value of the ratio between the focal distance and the concentrator width (F/D ratio). 2. Methodology The analysis was carried out by means of a ray tracing program called Tonalli (rising sun in Nahuatl, the Aztec language) [6], developed in Matlab platform in collaboration with CIEMAT, Spain. The program obtains the radiation cone incident in a receiving plane by means of the convolution [7] of a Gaussian distribution of optical errors with the standard solar radiation cone [8], as for instance in the CIRCE2 ray tracing code [9]. There are other tech- niques for ray tracing to obtain the irradiance distribution on a receiver, like direct ray tracing, in which every considered point on the solar disk, generates a ray that will be reflected on the mirror surface; or the Monte Carlo technique, that use a random set of incidence points. However, the convolution technique is faster for this kind of simulations, because less rays need to be traced. The simulated system is a faceted concentrator consisting of a paraboloidal structure (frame) where the individual mirrors are attached to their respective positions. However, the curvature of each mirror does not correspond with the part of the frame it covers; It is considered that for ease of fabrication all facets are spherical mirrors; i.e., facets are not fabricated as sections of * Corresponding author. Tel./fax: þ52 55 56229791. E-mail address: caab@cie.unam.mx (C.A. Arancibia-Bulnes). Contents lists available at ScienceDirect Renewable Energy journal homepage: www.elsevier.com/locate/renene 0960-1481/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2010.08.038 Renewable Energy 36 (2011) 966e970