Abstract
A novel three-dimensional elliptical-shaped Fresnel lens (ESFL) analytical model is presented to evaluate and maximize the solar energy concentration of Fresnel-lens-based solar concentrators. AutoCAD, Zemax and Ansys software were used for the ESFL design, performance evaluation and temperature calculation, respectively. Contrary to the previous modeling processes, based on the edge-ray principle with an acceptance half-angle of ±0.27° as the key defining parameter, the present model uses, instead, a Gaussian distribution to define the solar source in Zemax. The results were validated through the numerical analysis of published experimental data from a flat Fresnel lens. An in-depth study of the influence of several ESFL factors, such as focal length, arch height and aspect ratio, on its output performance is carried out. Moreover, the evaluation of the ESFL output performance as a function of the number/size of the grooves is also analyzed. Compared to the typical 1–16 grooves per millimeter reported in the previous literature, this mathematical parametric modeling allowed a substantial reduction in grooves/mm to 0.3–0.4, which may enable an easy mass production of ESFL. The concentrated solar distribution of the optimal ESFL configuration was then compared to that of the best flat Fresnel lens configuration, under the same focusing conditions. Due to the elliptical shape of the lens, the chromatic aberration effect was largely reduced, resulting in higher concentrated solar flux and temperature. Over 2360 K and 1360 K maximum temperatures were found for ESFL and flat Fresnel lenses, respectively, demonstrating the great potential of the three-dimensional curved-shaped Fresnel lens on renewable solar energy applications that require high concentrations of solar fluxes and temperatures.
Highlights
This study reveals that the number of grooves necessary to maximize the concentrated solar flux could be significantly reduced in relation to that reported by the literature and market, which may enhance the cost efficiency of the manufacturing process of Fresnel lens solar concentrators
At Z = +30 mm in relation to the origin, the maximum concentrated solar flux of only 1.86 W/mm2 was reached, as shown in. For both the elliptical-shaped Fresnel lens (ESFL) and the flat Fresnel lens, the focal distributions at the origin (Z = 0 mm) do not correspond to the positions where the concentrated solar flux is maximum, as shown in Figures 17a and 18a. This phenomenon occurs due to the chromatic aberration, which is more abundant in the flat Fresnel lens
The modeling process took into account the solar Gaussian distribution based on the measured parameters by Vittitoe and Biggs [35], instead of the classical edge-ray principle method and the solar acceptance half-angle of 0.27◦
Summary
Equation (14) represents the calculation of the coordinates of point D considering an isolated prism, where point A is defined as the origin. The coordinates of the reduced output facet AD due to the pitch angle is represented in Equation (16). The grooves of the ESFL’s output surface were the first components to be modeled by drawing all the facets from coordinates An and Dn , starting from the outmost prism (n = 1) to the innermost prism N. This chaining process followed a sequence of A1 D1 A2 D2 .
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