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Average number of reflections experienced by the transmitted rays, as function of the angular aperture of the Lambertian beam, calculated for three pairs of wall reflectivities: (1.0-0.9); (1.0-0.8); (0.9-0.8)
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The optical properties of nonimaging solar concentrators irradiated in direct mode by diffused Lambertian beams are investigated in detail adopting original simulation methods. These methods were not limited to investigate useful properties for the practical application of the concentrators, but were also used to study them as optical elements with...
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Context 1
... τ w m represents the number of transmitted rays. The average number of reflections has been calculated by using three pairs of wall reflectivities: (1.0-0.9); (1.0-0.8); (0.9-0.8). The results are reported in Fig. 6 and show that the average number of reflections of the transmitted rays is practically independent on the angular aperture of the Lambertian beam and equal to ≈ 2. This result is in good agreement with what was found [2] by analyzing the average number of reflections of the transmitted beam when the CPC is irradiated with a parallel beam at different polar angles respect to the optical axis. We now introduce the quantity “direct Lambertian concentration ratio” , C dir lamb , defined in [1] as the ratio between the average output, or transmitted, radiance and the constant input radiance. When the lambertian beam at input has an angular aperture θ m , the direct Lambertian concentration ratio is indicated as C dir lamb ( θ m ) . We start calculating the average output ...
Context 2
... absorption efficiency dir w m , calculated for the wall reflectivities R w = 0.9 and 0.8, is shown in Fig. 31. The simulation with R w = 1.0 is useless in this case, as it would give a systematic zero absorption efficiency. For θ m < θ acc coll = 5°, the absorption of light is due to the internal reflections of mainly the transmitted rays, these reflections being about 2, as we see in Fig. 6. As a result, the absorption of the incident flux will be ≈ 2x10% when R w = 0.9, and ≈ 2x20% when R w = 0.8, as it can be seen in Fig. 31. For θ m > θ acc coll , the absorption of light inside the CPC increases due to the contribution given by the back reflected rays, whose average number of ...
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We analytically derive the mean path length of light rays diffusely incident on refractive regular polygons of n sides (n-gons), analyzed from the dynamical billiards perspective and from ray optics. In polygons with sufficiently low refractive index, the mean path length is found to be equal to that in the invariant scattering case, i.e. the produ...
Citations
... Different approaches can be followed to perform it; here we will focus our attention on two of them, directly derived by our recent research on this subject: the "direct method" and the "inverse method", distinguished by the modality in which the concentrator is irradiated, if from the input or the output aperture, respectively. In the "direct method" [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], the angle-resolved transmission efficiency is obtained irradiating the input aperture by a suitably oriented parallel beam, of known irradiance, and measuring the output flux; this must be repeated for all the significant directions of incidence, which are strictly dependent on the geometrical symmetry of the concentrator. From the transmission efficiency curve obtained for the different azimuthal directions the "acceptance angle" is derived; it is a parameter that defines the angular limit within which the incident radiation is collected. ...
... Different approaches can be followed to perform it; here we will focus our attention on two of them, directly derived by our recent research on this subject: the "direct method" and the "inverse method", distinguished by the modality in which the concentrator is irradiated, if from the input or the output aperture, respectively. In the "direct method" [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], the angle-resolved transmission efficiency is obtained irradiating the input aperture by a suitably oriented parallel beam, of known irradiance, and measuring the output flux; this must be repeated for all the significant directions of incidence, which are strictly dependent on the geometrical symmetry of the concentrator. From the transmission efficiency curve obtained for the different azimuthal directions the "acceptance angle" is derived; it is a parameter that defines the angular limit within which the incident radiation is collected. ...
The concentration of solar radiation plays a key role in the field of renewable energies, as it can be effectively applied to thermal, thermodynamic, photovoltaic (PV) and even hybrid thermal/photovoltaic technologies. In concentrating photovoltaic systems (CPV) the size of the photovoltaic receiver (solar cell) is reduced by a factor equal to the geometric concentration ratio, and this has a strong, positive impact on the cost of the total PV concentrator, opening perspectives for the use of more sophisticated and more efficient devices. The concentrating optics is one specific component of the photovoltaic concentrator. It must be designed to transfer the incident solar radiation to the receiver searching the maximal optical efficiency achievable within an angular range limited by physical constrains]. The concentrating optics should produce a concentrated flux with reduced non-uniformity on the receiver to minimize ohmic losses [12, 15], and should be designed with great attention on many aspects related to its final industrial application. These are: compactness, tolerance on assembling errors, low cost of manufacturing processes, optimal placement of the receiver for electrical and thermal issues, use of materials of high reliability, high durability and low cost, high efficiency at the module and array level. All the previously indicated characteristics must be considered in the design of photovoltaic concentrators; many optical configurations have been proposed during the last years; a large spectrum of possible designs, with different levels of effectiveness, can be achieved by applying the “nonimaging” optics.
... A review of the theoretical models of light irradiation and collection in solar concentrators (SC) was presented in the first part of this work [1]. In the second part [2], we presented the application of these models to nonimaging SC of the type 3D-CPC (Three-Dimensional Compound Parabolic Concentrator) irradiated by direct and collimated beams, whereas in the third part [3] the same models were applied to SC irradiated by direct and lambertian beams. In this paper, we continue the analysis of the optical properties of 3D-CPC irradiated by the direct method with collimated beams. ...
... The aim of the present study is to develop maps of transmittance/reflectance of the kind displayed by Winston in publications [6][7][8], but made by following different methods of simulation. In the previous works [2,3] we analyzed a 3D-CPC with coll acc θ = 5°; in this work, we will continue to report results obtained on this CPC. With our method, maps relating to transmitted rays are obtained by irradiating inversely the CPC with Lambertian beams applied to the output opening, whereas the maps relating to the reflected rays are obtained by irradiating directly the CPC with Lambertian beams applied to the input opening. ...
... Fig. 1 shows the 3D-CPC used in our simulations. The 3D-CPC, with coll acc θ = 5°, is the same used in the previous papers of this series [2,3] and is shown in Fig. 1. The CPC is characterized by a maximum angular divergence of rays at exit aperture equal to 90° when the incidence angle is equal to the acceptance angle. ...
The transmission and reflection properties of nonimaging solar concentrators irradiated in direct mode by parallel light are investigated adopting original simulation methods. These methods were not limited to investigate useful properties for practical application of the concentrators, but were also used to study them as optical elements with specific transmission, absorption and reflection characteristics. In this work, we investigate the flux transmitted to the receiver and that back-reflected towards the entrance opening, by measuring the average number of reflections that the transmitted or reflected rays make on the internal wall of the concentrator. Results of this study are maps of the entrance opening, in which the different regions crossed by the transmitted or reflected rays are distinguishable and characterized by a different number of internal reflections. These maps are plotted for different values of the incidence angle of the parallel beam with respect to the optical axis of the concentrator. The presented simulation methods can be fruitfully applied to any other type of solar concentrator.
The problem of absorption of diffuse light by a 2D array of identical spherical particles is considered. The equations to solve this problem are derived on the basis of statistical approach. They can be used to match parameters of the array and the illumination system to get maximum absorption. The numerical results are presented for absorption coefficients of arrays with the imperfect triangular lattice and partially ordered structures of crystalline silicon and silver particles embedded in nonabsorbing medium, in the wavelength range 0.35 μm – 0.80 μm. The size of particles and their concentration are chosen so as to illustrate the dependence of light absorption on the angle of incidence under conditions of resonances due to the high spatial ordering of particles. The absorption coefficients of the arrays at diffuse and directional light illumination are compared.
Advances in Optics Reviews Vol. 5 is devoted to optics, lasers, optical communication and networks, and written by 53 authors from academia and industries from 12 countries.
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