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Lambertian transmission efficiency of the CPC calculated as function of the angular aperture of the Lambertian beam, θ m , for a unitary wall reflectivity
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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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... plot of dir m , simulated for a unitary wall reflectivity, is shown in Fig. 4. It is interesting to compare the behavior of τ dir lamb ( θ m ) with that of η dir coll ( θ in ) (see Fig.2). We obtain a step-like transmission efficiency curve also for a Lambertian beam irradiation, with the efficiency almost constant until about the acceptance angle ( θ acc coll = 5°), but, differently from the transmission efficiency curve η dir coll ( θ in ) , now the τ dir lamb ( θ m ) curve decreases slowly at increasing θ m . The reason is that, for θ m > θ acc coll , a constant portion of the input beam is always collected, and the Lambertian transmission efficiency at these conditions can be expressed by (on the assumption that R ...
Context 2
... Eq. (7) we have put dir in , as it can be seen from the curve of Fig. 2 corresponding to R w =1.0. Fig. 4 shows the Lambertian transmission efficiency of the CPC compared to the sin 2 θ acc coll sin 2 θ m function. The perfect correspondence between the two curves when θ m > θ acc coll is clearly evident. Now we are able to define a new optical quantity, the angular aperture of the input Lambertian beam corresponding to the halving of the direct Lambertian transmittance at θ = 0°. We call this angle the “Lambertian acceptance angle” , acc , indicated in Fig. 4 together with θ acc coll , the acceptance angle at parallel beam irradiation. The quantity θ acc lamb is immediately derived from Eq. (7), and is about 7.1° for our CPC with θ acc coll = ...
Context 3
... Eq. (7) we have put dir in , as it can be seen from the curve of Fig. 2 corresponding to R w =1.0. Fig. 4 shows the Lambertian transmission efficiency of the CPC compared to the sin 2 θ acc coll sin 2 θ m function. The perfect correspondence between the two curves when θ m > θ acc coll is clearly evident. Now we are able to define a new optical quantity, the angular aperture of the input Lambertian beam corresponding to the halving of the direct Lambertian transmittance at θ = 0°. We call this angle the “Lambertian acceptance angle” , acc , indicated in Fig. 4 together with θ acc coll , the acceptance angle at parallel beam irradiation. The quantity θ acc lamb is immediately derived from Eq. (7), and is about 7.1° for our CPC with θ acc coll = ...
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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.
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