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Concentrating the concept of a beam-down solar tower with linear Fresnel heliostat (PLCF) is one of the feasible choices and has great potential in reducing spot size and improving optical efficiency. Optical characteristics of a PLCF system with the hyperboloid reflector are introduced and investigated theoretically. Taking into account solar position and optical surface errors, a Monte Carlo ray-tracing (MCRT) analysis model for a PLCF system is developed and applied in a comparison-based study on the optical performance between the PLCF system and the conventional beam-down solar tower system with flat and spherical heliostats. The optimal square facet of linear Fresnel heliostat is also proposed for matching with the 3D-CPC receiver.
© 2016 Optical Society of America
1. Introduction
It is well known that the energy and environmental crisis has been promoting the development of solar thermal technologies, where concentrating solar tower technology has been proven to be a fairly efficient way of converting solar energy into thermal energy or electricity [1]. As for traditional solar tower system, solar energy from a large array of heliostats is focused onto a top tower that captures heat by a receiver, where this heat is converted to electricity using a steam generator and a steam turbine. However, it can be pretty arduous in terms of building a low heat loss tower and pumping heat transfer fluid (HTF) such as molten salt up to the tower top that usually mounted at hundreds of meters high to the ground. In order to overcome these shortcomings, beam-down solar tower (BST) has been proposed and developed, where the second set of the beam-down concentrator (BC) directs the solar radiation back down to a central receiver (CR) placed on the ground. On account of aforementioned merits, BST technology is considered as one of the promising ways to harvest solar energy and is worth further research.
A variety of studies on optical characteristics of various BST systems is in the literature. The concept of BST was proposed for the first time by Rabl [2] and then developed at the Weizmann Institute in Israel [3]. Segal and Epstein [4–6] described the optics of the BST system, where two types of secondary reflectors, namely hyperboloid and elliptical, were investigated for a comparative study. However, a single solar ray per heliostat was considered, and shading and blocking effects have been neglected. Detailed optical analysis of BST systems with the hyperboloid concentrators and the compound parabolic concentrator (CPC) has been performed [7,8].
The initial concept of the point-line-coupling-focus (PLCF) system was proposed by Li et al. [9], where the superior wind-resistance linear Fresnel heliostat (line focus) and the beam-down concentrator (point focus) were integrated. It has been proven that PLCF is one of feasible focusing concepts in the beam-down solar tower system. In this paper, optical characteristics of PLCF system with the hyperboloid beam-down reflector are introduced and investigated theoretically. Considering the incident angle, solar position, optical surface errors, and sun-tracking angles, the Monte Carlo ray-tracing (MCRT) optical analysis model for PLCF system is developed and applied in comparison-based study on the optical performance between the PLCF system and the conventional beam-down solar tower system with flat heliostats (FH) and spherical heliostats (SH).
2. PLCF system description
A schematic of concentrating concept of PLCF system employing linear Fresnel heliostats (LFH) and a beam-down concentrator (BC) is shown in Fig. 1. A hyperboloid reflector is used as the BC of PLCF system. The heliostat tracks the sun and reflects incident rays (IA and IB) to the BC, and then these rays are concentrated downwards to the final focal point F2 at the focal plane. The concentrating process of this PLCF is mainly composed of focusing effects of heliostat and BC. The detailed geometrical parameters and sun-tracking models of LFH have been introduced by Li et al. [9]. As shown in Fig. 1, lm and Hh are the length and the height of the LFH, respectively. D is the distance between the heliostat and the receiver. H and Hmax are the height of point A and the maximum height of the hyperboloid reflector, respectively. F1 and F2 are the upper focus (target point) and lower focus (focal point), respectively. rmax is the maximum radius of the hyperboloid reflector. zg is defined as the height at Zenith direction.
Fig. 1 Schematic diagram of the PLCF system with the hyperboloid reflector. (a) concentrating concept. (b) optical geometric parameters.
The geometric schematic of linear Fresnel heliostat is shown in Fig. 2. The heliostat has superior concentration ratio and wind-resistance performance respectively compared with plat and spherical heliostats that are commonly used in the solar tower system. As shown in Fig. 2, the mirror facet of LFHs is a set of linear Fresnel reflectors with flat mirrors. With respect to the sun-tracking mechanism of the heliostat, rotation movements of the frame and the facet are driven by two independent stepper motors with frame and mirror tracking angles (i.e., βh and βm), respectively. When standing on the location of the lower focus and orienting to a heliostat, clockwise rotation of a mirror facet represents plus value of βm, corresponding counterclockwise rotation is defined as minus value of βm. Wm and Wh represent the width of a single mirror facet and a heliostat, respectively. ΔW is defined as the distance of two adjacent sub-mirrors. lh and lm are the length of a heliostat and a facet. Here, the upper and lower facet are assumed as a whole mirror facet, where lh = 2lm, and lh = nWm. n is the number of mirror facets for LFH. In this paper, the distance between two adjacent facets is neglected (ΔW = Wm), besides the proposed models of sun-tracking angles and angle differences [9] are used.
3. Optical analysis models
3.1 Sunshape
Because sun rays are not strictly parallel, the sun rays hitting on the facet surface are modeled as a conic bundle where the rays of the bundle are weighted with a non-uniform energy distribution. Based on the concept of sun-shape profile, the intensity distribution I of solar disk proposed by Johnston [10] can be calculated as
where ϑ denotes the angle of a surface element on the solar sphere. Io is the intensity in the center of the solar disk. β is the limb darkening parameter. ϑs is angular half-width of the solar disk (4.65 mrad).3.2 Optical surface errors
It is generally assumed that all surface errors follow a Gaussian distribution [11] characterized by the standard deviation. The variances of each individual error distribution can be summed to one total equivalent variance, σerr, which describes the composite effect of all errors, namely the specularity error, the slope error, the shape error, the alignment error, and the tracking error. The simple Rayleigh method of surface error [12] for generating surface error is given as
where θerr and ϕerr are defined as the azimuthal angular and circumferential components of the surface error, respectively. U is the random number with uniform distribution in the interval of 0 and 1. M is specularly reflected vector. M′ is deviant reflected vector with surface error. ux and uy are unit vectors in the Cartesian x-component and y-component directions, respectively.3.3 Optical efficiency
The optical efficiency of the PLCF system is related to significant factors involving cosine efficiency ηcos, shading and blocking efficiency ηsb, interception efficiency ηit, and the atmospheric attenuation efficiency ηaa. Instantaneous optical efficiency with respect to above efficiencies, proposed by Schmitz et al. [13], is expressed as
where ρh and ρBC indicate the facet reflectivity of LHF and BC, respectively.4. Results and discussion
4.1 The effect of geometric of hyperboloid reflector
The geometrical structure of the hyperboloid reflector has a direct influence on the concentrating properties of PLCF system. Considering the geometric parameters of F1 = 75 m, F2 = 5 m, lm = 5 m, rmax = 44.1 m, solar azimuth γ = 0°, solar altitude α = 90°, and Hm = 5 m, the magnification M is the ratio of the image size of the upper focal plane to the image size of lower focal plane. Based on the MCRT optical analysis method, considering sun angle effects, the single ray reflected from the geometric center (point C shown in Fig. 1) of the LFH is used to reveal characteristics of the spot on the lower focal plane. Figure 3 shows the effects of the parameter D and hyperboloid eccentricity e on the spot characteristics. Figure 3(a) shows the effect of the parameters of e and D on the spot sizes of the upper and lower focal planes. With the increase of e, the spot size on lower focal plane decreases. When e trends to infinity, the spot sizes on the upper and lower focal planes trend to be identical. Figure 3(b) reveals the relationship between e and M that increases sharply with the increasing e from 1.0 to 4.5, and the amplification factor decreases sharply. Therefore, the increase of D in a certain extent can weaken the negative effect caused by the magnification of the hyperboloid. The comparison-based results show that the MCRT optical analysis model developed in this work has the reasonable accuracy.
Fig. 3 The effects of D and e on the spot characteristics of a single ray reflected from the geometric center of LFH. (a) The effect on the spot size. (b) The effect on the magnification M.
4.2 The effect of structure parameters of LFH
The effect of heliostat structure parameters on optical properties is analyzed under the conditions of Hh = 5 m, F1 = 75 m, F2 = 5 m, rmax = 44.1 m, γ = 0°, α = 90°, D = 150 m, and e = 3. In this case, the aperture of each heliostat is considered with the diameter of 10 m, where the LFH is divided into five separate facets. The focal length of SH is defined as f = R/2. The curvature radius R of SH is 331 m. Figure 4(a) shows comparison results of the spot sizes of LFH, SH and FH at the upper and lower focal planes. As shown in Fig. 4(a), the SH has the smaller spot sizes compared to LFH and FH.
Fig. 4 Comparison results of the spot characteristics of LFH and CH at the upper and lower focal planes (ρh = 0.9 and ρBC = 0.9). (a) Spot size. (b) Local concentration ratio of LFH. (c) Local concentration ratio of SH. (d) Local concentration ratio of FH.
The local concentrating ratio Ci, defined as the ratio of the flux on the focal plane to direct normal irradiance, is an important index to evaluate the solar concentrating characteristics. Figures 4(b)–4(d) illustrate comparison results of the local concentration ratio of the spot for LFH, SH and CH, respectively. The effect of optical surface errors σerr = 3.5 mrad has been considered herein. Analysis results show that the SH has obvious advantages in concentrating ratio and the spot size due to the point focusing characteristics. The spot characteristics of LFH are situated between SH and FH.
4.3 The effect of structure parameters of LFH facet
The shape of the LFH facet has an important effect on the spot size and interception efficiency. The geometry of LFH is considered with the total mirror area of 100 m2. The spot sizes of various length-width ratios (σ = lm/Wm) are investigated herein with the parameters of Hh = 5 m, F1 = 75 m, F2 = 5 m, rmax = 44.1 m, γ = 0°, α = 90°, D = 150 m, and e = 3. Figure 5 reveals the effect of length-width ratio σ on the characteristic of the spot at the lower focal plane. The diameter of compound parabolic concentrator (CPC) [9] is defined as 20 m. Figures 5(a)–5(c) represent the length-width ratios of 1:1, 5:1, and 1:2, respectively. As can be seen, when the length-width ratio is 1:1, the LFH has the lowest receiver spillage loss of 26.9%.
Fig. 5 The effect of length-width ratio σ on the characteristic of the spot at the lower focal plane (ρh = 0.9 and ρBC = 0.9). (a) Length-width ratio of 1:1 with spillage loss [13] of 26.9%. (b) Length-width ratio of 5:1 with spillage loss of 41%. (c) Length-width ratio of 1:2 with spillage loss of 31.2%.
4.4 Comparison-based analysis of optical efficiency
The comparison-based analysis of optical efficiency is implemented considering the length-width ratio of 1:1 for the square facet of LFH with lm = 2.236 m, Wm = 4.472 m, lh = 4.472 m, Wh = 22.4 m, Hh = 5 m, rmax = 44.1 m, f = R/2, and e = 3. The aperture area of heliostat is 100 m2 facing south for LFH, square SH (lh = 10 m, Wh = 10 m) and square FH (lh = 10 m, Wh = 10 m). Figure 6 shows the effect of the solar position and design parameters on the cosine efficiency as well as the shading and blocking efficiency.
Fig. 6 The effect of the solar position and design parameters on the cosine efficiency as well as the shading and blocking efficiency. (a) the effect of solar altitude. (b) the effect of solar azimuth. (c) the effect of the distance D. (d) the effect of the upper focus F1.
As shown in Fig. 6, under the same conditions, LFH, SH and FH have the closely related cosine efficiency, and this result is not affected by the parameters of solar position and the distance D. In addition, the shading and blocking efficiency of LFH is always lower than that of SH and FH, where the variation of solar position, parameters D and F1 has a greater influence on LFH.
The corresponding comparison results of interception efficiency as well as shading and blocking efficiency under various solar azimuths and altitudes are respectively listed in Table 1 and Table 2 considering with the parameters of Hh = 5 m, F1 = 75 m, F2 = 5 m, rmax = 44.1 m, D = 150 m, e = 3, R = 331 m, ρh = 0.9, and ρBC = 0.9. The aperture radius of CPC is 10 m, As can be seen, the interception efficiency of LFH with five square facets is obviously superior to that of FH, however, it is lower than that of SH, which results in the intermediate level of optical efficiency. The optical performance of LFH with the facet parameters of lm = 10 m, Wm = 2 m is significantly lower than LFH with rectangular facet (lm = 10 m, Wm = 2 m) as well as SH. It means LFH with square facets applied in BST system can reduce the spot size as well as receiver spillage loss, and improve the optical efficiency in a certain degree. Under the reasonable design of the mirror facet structure, the optical efficiency of LFH can be one of the feasible choices for the beam-down solar tower.
Table 1. Comparison Results of the Optical Efficiency of LFH, SH and FH in a Beam-Down System Under Various Solar Azimuths (ρh = 0.9, ρBC = 0.9 and α = 40°)
Table 2. Comparison Results of the Optical Efficiency of LFH, SH and FH in a Beam-Down System Under Various Solar Altitudes (ρh = 0.9, ρBC = 0.9 and γ = 60°)
5. Conclusion
A novel point-line-coupling-focus solar thermal system, employed beam-down solar tower technology and linear Fresnel heliostat with superior wind resistance performance, is investigated theoretically in this paper. Comparison-based optical investigation between the PLCF system and the conventional beam-down solar tower with flat and spherical heliostats is implemented. Considering the sunshape and optical surface errors, the MCRT method is used to analyse the effects of geometric parameters for hyperboloid and LFH, as well as solar position on spot characteristics and optical efficiencies.
The shape of the heliostat facet has an important effect on the concentrating performance. By comparison analysis, the optimal shape of LFH facet for matching with the 3D-CPC receiver is the length-width ratio of 1:1 in order to achieve the lowest spillage loss. Under the same investigating conditions, the total optical efficiency of LFH is obviously superior to that of FH, but lower than that of SH. It is feasible for PLCF system to reduce the spot size as well as receiver spillage loss, and improve the optical efficiency. It proves that PLCF is one of the feasible options used in the beam-down solar tower system due to its simple structure and manufacture as well as superior wind resistance performance. Further work is under development to take account of the optimization on heliostat layout and solar-thermal performance for the large-scale PLCF system.
Acknowledgment
This work was supported by National Natural Science Foundation Project of China (NSFC) under the Contract No. 51276112.
References and links
1. S. A. Kalogirou, “Solar thermal collectors and applications,” Pror. Energy Combust. Sci. 30(3), 231–295 (2004). [CrossRef]
2. A. Rabl, “Tower reflector for solar power plants,” Sol. Energy 18(3), 269–271 (1976). [CrossRef]
3. A. Segal and M. Epstein, “Modelling of solar receiver for cracking of liquid petroleum gas,” J. Sol. Energy Eng. 119(1), 48–51 (1997). [CrossRef]
4. A. Segal and M. Epstein, “Comparative performances of ‘tower-top’ and ‘tower reflector’ central solar receivers,” Sol. Energy 65(4), 207–226 (1999). [CrossRef]
5. A. Segal and M. Epstein, “The optics of the solar tower reflector,” Sol. Energy 69, 229–241 (2001). [CrossRef]
6. A. Segal and M. Epstein, “Optimized working temperatures of a solar central receiver,” Sol. Energy 75(6), 503–510 (2003). [CrossRef]
7. E. Leonardi, “Detailed analysis of the solar power collected in a beam-down central receiver system,” Sol. Energy 86(2), 734–745 (2012). [CrossRef]
8. X. D. Wei, Z. W. Lu, W. X. Yu, and W. B. Xu, “Ray tracing and simulation for the beam-down solar concentrator,” Renew. Energy 50, 161–167 (2013). [CrossRef]
9. X. Li, Y. J. Dai, and R. Z. Wang, “Performance investigation on solar thermal conversion of a conical cavity receiver employing a beam-down solar tower concentrator,” Sol. Energy 114, 134–151 (2015). [CrossRef]
10. G. Johnston, “Focal region measurements of the 20 m2 tiled dish at the Australian national university,” Sol. Energy 63(2), 117–124 (1998). [CrossRef]
11. A. Rabl, Active Solar Collectors and Their Applications (Oxford University, 1985).
12. T. Cooper and A. Steinfeld, “Derivation of the angular dispersion error distribution of mirror surfaces for Monte Carlo ray-tracing applications,” J. Sol. Energy Eng. 133(4), 044501 (2011). [CrossRef]
13. M. Schmitz, P. Schwarzbozl, R. Buck, and R. Pitz-Paal, “Assessment of the potential improvement due to multiple apertures in central receiver systems with secondary concentrators,” Sol. Energy 80(1), 111–120 (2006). [CrossRef]
