A trough collector with parabolic profile has been simulated and studied by means of ray tracing analyses. The first study examines the geometrical deformations of the parabolic profile and their effects on solar light collection. For the application to solar light exploitation, the essential quantity to be considered is the collection efficiency. It is obtained as ratio between the light focused on the absorber and the light captured by the entrance aperture of the collector. The effects of mirror deformations are expressed using collection efficiency instead of focused light or collected energy: the results are illustrated in Section 3.

The application is a solar trough collector, whose principal component is the linear parabolic mirror. The parabolic profile of this reflecting surface has been optically designed to concentrate the sunlight on a cylindrical receiver, whose centre is placed in the parabola focus.

The methodology to reproduce mirror deformations is based on the use of a mathematical representation for parabolic and deformed profiles. The mathematical approach consists in introducing conic constant and conic equation to represent the profiles of the mirror surface.

Fig. 2 presents the border profile for two examples of deformed mirrors, compared to the correct parabolic curve.

It is important to note that the length of all deformed curves must correspond to the parabola extent, since they represent

deformations of a real solar collector.

The conic equation used in this reconstruction of mirror profiles can be expressed as:

where K is the conic constant and c is the mirror curvature, defined in Eq.(2) from the curvature radius R of the parabolic mirror.

1

c =

R

The reference value for the conic constant is -1: in fact, using the conic equation Eq.(1), the parabolic curve pertains to K = -1. The values of conic constant K different from -1 correspond to deformations of the parabolic mirror, as Fig. 2 illustrates comparing the border profiles of deformed mirrors to the parabolic edge profile.

For -1 < K < 0 the profile becomes elliptic and there is a reduction on the entrance aperture of the deformed collector. The corresponding curve in Fig. 2 is the upper and internal profile.

For K < -1 the profile is hyperbolic and the deformed mirror presents a larger entrance aperture with respect to the parabolic collector. The corresponding curve in Fig. 2 is the lower and external profile (see also Table 1).

Simplicity and efficacy are the advantages of the proposed procedure to simulate the deformations of a parabolic mirror. However the most important result is that it seems to reproduce the flexibility of a real solar collector and its imperfect rigidity. In fact considering a reflecting surface, laying over a set of ribs and centrally bonded, the major deformations appear at the borders.