Research Papers

Optical Analysis of the Fixed Mirror Solar Concentrator by Forward Ray-Tracing Procedure

[+] Author and Article Information
Ramon Pujol Nadal, Víctor Martínez Moll

Departament de Física,  Universitat de les Illes Balears, Ctra de Valldemossa km 7,5, 07122 Palma de Mallorca, Illes Balears, Spainramon.pujol@uib.es

J. Sol. Energy Eng 134(3), 031009 (May 22, 2012) (14 pages) doi:10.1115/1.4006575 History: Received September 07, 2011; Revised April 04, 2012; Published May 21, 2012; Online May 22, 2012

The fixed mirror solar concentrator (FMSC) is a mobile focus concentrator whose design emerged in the 1970s in an effort to reduce electricity production costs in solar thermal power plants. This geometry has not yet been analyzed with 3D ray-tracing procedures. The geometry of FMSC is defined using three parameters: the number of mirrors N, the ratio of focal length and reflector width F/W, and the intercept factor γ (in order to represent different receiver widths). For the analysis, a 3D ray-tracing code that allows the characterization of solar concentrators was developed. A standard evacuated tube was used as a receiver. The geometric concentration ratio, the optical efficiency, and the transversal and longitudinal incidence angle modifier (IAM) curves for different values of design parameters were calculated. High concentrations imply low F/W values and for high efficiencies, large intercept factor values are required. Increasing the F/W ratio has a positive effect on the transversal IAM, yet a negative one for the longitudinal IAM. Increasing the number of mirrors has a negative effect on both IAM curves due to the self-shadowing between the adjacent steps. Increasing the intercept factor only has a significant positive effect on the longitudinal IAM. The goodness of the IAM factorization approach was analyzed, and it was found that it can be used as long as a new correction factor to account for the focus displacement is introduced. The results presented in this paper provide information, in form of curves, regarding the optical behavior of the FMSC in terms of different design parameters in order to know the possibility to use the FMSC in medium range temperature applications.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

θt and θl are the transverse and longitudinal angles that are the projected incidence angles on the two reference planes perpendicular and along the axis of the collector

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Figure 2

Optical principle of the FMSC. The receiver is moving in a circular path.

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Figure 3

A geometrical demonstration of the existence of the focus. (a) Lines r1 , r2 , r3 , and r4 are sun rays, the lines are reflected by the mirrors 1 and 2. r1 || r2 and r3 || r4 . The centres of mirrors 1 and 2 are points A and B, respectively. The parallel rays are reflected to points P and Q, respectively. (b) By construction and reflexion law ζ=β=υ=δ. Since ϕ=ψ the βψχ¯ and δλϕ¯ triangles are similar. Then, λ=χ, so this means that points A, B, P, and Q belong to the same circle according to the inscribed angle property. Hence, it exists a point on the circle which is a focal point for any incidence angle.

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Figure 4

Mirrors and focus positioning. (a) Two mirrors are shown, the central mirror, n = 1, and its neighbouring mirror, n = 2. (b) The position of the focus (xf , zf ) for the 2D is shown. Only one parameter is needed to position the focus, the θf angle referred to the circle centre. It is easy to prove that θf  = 2Θs .

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Figure 5

Reflector for the case N = 11 and F/W = 1.5

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Figure 6

Dimensions of the evacuated tube in 1000 × u units for one case analyzed with N = 25 and F/W = 1.0

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Figure 7

Ray-tracing simulation with 300 rays emitted. (a) Total view of the concentrator, sun rays, and sun window. (b) Frontal projection of the same ray-tracing in the region of the receiver.

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Figure 8

Normalized flux density on the receiver in the case of N = 25, F/W = 1.0, σ = 8 mrad, and CSR = 0.05 for different values of intercept factor and the case of receiver width equal to mirror width (γ = 0.82). The longitudinal length of the concentrator was considered as 1u. Total reflectivity was equal to 1, and an ideal receiver (on both sides) was considered for this experiment. A total of 100,000 rays were emitted.

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Figure 9

Geometric concentration as a function N for the values of F/W and γ chosen

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Figure 10

Optical efficiency for direct normal radiation as a function of N. Reflector length L = 1u has been considered.

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Figure 11

Transversal IAM curves depending on the F/W ratio as a function of transversal angle for different numbers of mirrors and intercept factor values

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Figure 12

Transversal IAM curves depending on the number of mirrors as a function of the transversal angle for different F/W ratios and intercept factor values

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Figure 13

Transversal IAM curves depending on the intercept factor as a function of the transversal angle for different N and F/W values

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Figure 14

Longitudinal IAM curves depending on the F/W, N, and γ values

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Figure 15

Case analyzed N = 45, F/W = 1.0, and γ = 0.92. (a) Factorized incidence angle modifier and calculated by ray-tracing. (b) Error in the calculation of energy collected from direct radiation if K(θt,0)K(0,θl)f(θt,θl) is used instead of K(θt,θl). The values of the error estimators are RMSE = 0.0252, MBE = − 0.0021, MAE = 21.43, and ME = 16.31.

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Figure 16

Case analyzed N = 25, F/W = 1.25, and γ = 0.98. (a) Factorized incidence angle modifier and calculated by ray-tracing. (b) Error in the calculation of energy collected from direct radiation if K(θt,0)K(0,θl)f(θt,θl) is used instead of K(θt,θl). The values of the error estimators are RMSE = 0.0154, MBE = − 0.0041, MAE = 3.56, and ME = − 0.55.



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