Mathematical Models for Simulation and Optimization of High-Flux Solar Furnaces

Abstract

High-flux solar furnaces distributed throughout the world have been designed and constructed individually, i.e., on a one-by-one basis because there are several possible optical configurations that must take into account the geographical location and the maximum power to be attained. In this work, three ray-tracing models were developed to simulate the optical paths travelled by sun rays in solar furnaces of high concentration using as an example, the solar furnace SF60 of the Plataforma Solar de Almería, in Spain. All these simulation models are supported by mathematical constructions, which are also presented. The first model assumes a random distribution of sun rays coming from a concentrator with spherical curvature. The second model assumes that a random distribution of parallel rays coming from the heliostat is reflected by a concentrator with spherical curvature. Finally, the third model considers that the random parallel rays are reflected by a concentrator with a paraboloid curvature. The three models are all important in optical geometry, although the paraboloid model is more adequate to optimize solar furnaces. The models are illustrated by studying the influence of mirror positioning and shutter attenuation. Additionally, ray-tracing simulations confirmed the possibility to attain homogenous distribution of flux by means of double reflexion using two paraboloid surfaces.

Computer Modelling of the Optical Behavior of Homogenizers in High-Flux Solar Furnaces

“…In high-flux solar concentration systems, the flux of solar radiation that reaches the target is non-homogeneous, as discussed in our previous modelling work [1,2] and illustrated by considerable experimental evidence. Therefore, to expand the application field of solar-driven high-temperature technologies it is essential to improve the temperature homogeneity conditions, because for many applications, it is important to obtain a radiation distribution as homogeneous as possible over the working area [3].…”

“…In solar furnaces, the test table is movable in three directions (East-West, North-South, up and down) thus allowing to place the test samples at a chosen location (near the high-concentration zone, but not necessarily at the focus). When necessary, a 45°-tilted flat mirror (not shown in Figure 1) may be placed at a certain distance between the concentrator and the focal point in order to reflect vertically the solar radiation so that the concentrated solar beam becomes vertically oriented [1,2]. Figure 1.…”

“…For this work, we improved our own ray tracing software (named LAM, Light Analysis Modelling) [1,2] to model the radiation output for several different homogenizers, with different geometries and operating conditions. The software works thus as a laboratory to study homogenizers, allowing us to learn as much as possible about these devices.…”

Solar Heat for Materials Processing: A Review on Recent Achievements and a Prospect on Future Trends

“…Additionally, the flux of solar radiation that reaches the target is theoretically non-homogeneous. In fact, a circle illuminated with a higher concentration in the middle (see Figure 5) is theoretically obtained when the paraboloid reflection model [1] is applied to the traditional solar concentrators utilizing a point focusing solar concentrating panel assembly.…”

“…MoSi 2 is very refractory with a melting point of 2030 • C, has excellent resistance to oxidation and a moderate density (6.24 g/cm 3 ) [69]. Recent work by Pereira et al [1] has shown that theoretically there exists the possibility to attain homogenous distribution of concentrated solar flux by means of double reflexion using two paraboloid surfaces. As schematically presented in Figure 8, the parallel rays of solar light are reflected by the "concentrator" (concave paraboloid); then, before being concentrated to the focal point F, if these rays are reflected by a smaller paraboloid (with the same focal point of the "concentrator")-which can be convex such as paraboloid reflector A or concave such as paraboloid reflector B-our calculations show that the reflected rays are simultaneously highly concentrated and equally distributed over the illuminated region (with a very small hole in the middle due to the shadow produced by the second paraboloid, probably too small to be detectable).…”