Open Access
Add to BibSonomy
Abstract
We propose a concept of a rotating tower reflector (TR) in a beam-down optical system to alternate concentrated solar irradiation of an array of solar receiver–reactors, realizing multi-step solar thermochemical redox cycles. Optical and radiative characteristics of the proposed system are explored analytically and numerically by Monte-Carlo ray-tracing simulations. We study the effects of the system geometrical and optical parameters on the optical and radiative performance. TR axis is required to be tilted for accommodating the receiver–reactor array, resulting in reduced optical efficiency. We demonstrate that the annual optical efficiency of a baseline system with the receiver–reactor located south of the tower decreases from 46% to 37% for the axis tilt angle of TR increasing from 2° to 20°. The optical analysis conducted in this study provides a general formulation to enable predictions of required gain of thermal-to-chemical efficiency of the receiver–reactor array for obtaining improved overall solar-to-chemical efficiency of the solar thermochemical plant.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Multi-step solar thermochemical metal-oxide redox cycles are a viable route to fast and efficient chemical fuel production or thermal energy storage [1–5]. Two-step cycles consist of: (1) a high-temperature solar endothermic reduction step and (2) a non-solar low-temperature exothermic oxidation step. The reduction step is driven by concentrated solar irradiation, which is supplied over a discrete time interval shorter than the cycle duration for temperature-swing redox cycles [6–9]. The operation of the cycle can be realized in a variety of ways, including (i) operating the two steps sequentially in a single cavity receiver–reactor with varied conditions [6,10]; (ii) operating the two steps in two separate receiver–reactors with the metal oxide cycled between the reduction and oxidation reactors [11]; (iii) operating the two steps in two separate reactors exchanging heat alternately within a single receiver [12]; (iv) placing the metal oxide in a rotating reactor component that passes through zones of different conditions [8]; and (v) alternating the solar input into two or more receiver–reactors by moving the focal point of the concentrating system, either directly [13–15] or by means of a secondary concentrator [16]. Dähler et al. summarized six design concepts based on method (v) for alternating the focal point in a solar dish system and experimentally investigated a design with a rotating flat secondary reflector [16]. With method (v), cycle steps can proceed simultaneously in different reactors under continuous irradiation of the receiver–reactor array. Heat recovery can be implemented in the receiver–reactor array, which is reported to result in dramatically improved thermal-to-chemical efficiency of receiver–reactors from 3.5% to 20% [7,17].
To explore the feasibility of method (v) in a large-scale concentrating solar system, we propose a novel concept of a rotating tower reflector (TR) in a beam-down optical system to alternate the concentrated solar irradiation of an array of receiver–reactors. The typical beam-down optical system comprises three main components: a heliostat field, a TR placed on top of a tower, and a receiver at the ground level. The receiver is typically coupled with a secondary optical concentrator such as a compound parabolic concentrator (CPC) [18]. The beam-down optical concept offers advantages for high-temperature solar thermochemical applications. The redirected convergent beam at the ground level enables simpler and cheaper installation and operation of the high-temperature receiver and auxiliary equipment. Besides, the beam-down optical concept enables novel designs of the solar receiver such as fluidized particle bed inside the receiver [6,19–29]. However, the use of the TR results in additional optical losses and magnification of the sun image, necessitating the application of a CPC to reduce the spillage loss and to attain a high concentration ratio (CR) [30,31]. The addition of a CPC also brings additional optical losses due to CPC backward reflection and surface absorption. Practical challenges for realizing the proposed system include manufacturing and maintenance of the complex optical components, such as a large hyperboloidal TR and three-dimensional CPCs. The rotation of the large TR also introduces engineering difficulties. Despite the challenges, the potential of achieving high system-level solar-to-chemical conversion efficiency and the convenience of operating high-temperature receiver–reactors at the ground level make the proposed idea worthwhile to be explored.
The optics of the beam-down system have been extensively studied [30,32–39]. The beam-down optical system has been successfully constructed and tested including demonstration-level systems [27,40,41] and a 50 MWe commercial system [42]. Despite a large number of previously studied solar beam-down systems, there are gaps in reports of useful optical characteristics such as the size of sun image on the target, required size of the TR, rim and tilt angles of the reflected beam from the TR, and the annual optical performance of overall systems. The majority of investigated systems include a TR with a vertical axis. For the novel system proposed in this study, the axis of its TR is tilted and the receiver–reactors are dislocated from an optimal position of a single-receiver system to accommodate the receiver–reactor array. Pertinent studies of beam-down systems with dislocated receivers are absent in the literature.
In this study, we investigate the optical and radiative performance of the proposed novel solar thermochemical beam-down system with a rotating TR and a receiver–reactor array. A simplified two-dimensional (2D) system and a more realistic three-dimensional (3D) system are investigated. Firstly, analytical ray tracing is conducted in the 2D system to explore parametrically the geometrical and optical characteristics, including the required size of the TR, size of the sun image on the CPC entry aperture, and rim and axis tilt angles of the incident beam on the CPC entry aperture, as a function of system geometrical parameters. Secondly, in-house developed Monte-Carlo ray-tracing (MCRT) simulations are used to study a 3D system. In the 3D system, we parametrically study the effects of system geometrical parameters on instantaneous (at autumn equinox noon) optical and radiative characteristics including optical efficiency of the heliostat field, the TR and the CPC, radiative power and concentrator ratio at the apertures of the receiver–reactor. Based on the parametric studies, we calculate and analyze the annual optical efficiency of the beam-down optical systems with the receiver–reactors positioned at different positions around the tower.
2. 3D beam-down optical system model
2.1 Model system
Figure 1 depicts the model of the 3D beam-down optical system comprising a heliostat field, a tower, a rotating hyperboloidal TR, and an example CPC array. Receiver–reactors are not shown in Fig. 1. A single CPC is shown in Fig. 1(b). As shown in Fig. 1(b), the global coordinate system is constructed with the origin at the center of the tower base, and the positive x- and y-axes pointing along the South and East directions, respectively. The local coordinate system of the hyperboloidal surface is constructed with its origin placed half-way between the primary and secondary foci, and the z1-axis is selected as the real axis of the hyperboloidal TR.
Fig. 1. Schematics of a 3D solar beam-down optical system. System components featuring a heliostat field, a tower, a hyperboloidal tower reflector, and an example array of 4 CPCs are depicted in (a). Coordinate systems and geometrical parameters are shown in (b). Receiver–reactors are not shown.
One of the hyperboloid foci is chosen as the primary focus, i.e. the focus of the primary optical concentrators—heliostats, that is located at a height h1 above the ground level (Fig. 1(b)). The CPC is positioned with its entrance at the secondary focus, i.e. the other focus of the hyperboloidal TR, which is located at a height h2 above the ground level and with an azimuthal angle ϕt relative to the positive x-axis. A height ratio γ between the secondary and primary foci is used, i.e. γ = h2/h1. The hyperboloid axis forms a tilt angle αr with the tower. The geometry of an un-truncated 3D CPC is determined by acceptance angle θCPC and entry aperture radius rin. CPC is oriented with an axis tilt angle αCPC with respect to the z-axis. The heliostat field is asymmetric about the y-axis (East–West direction) (shown in Fig. 1(b)). The maximum length of the heliostat field is given by distances d1 and d2 between the tower and the furthermost heliostats along the South and North directions, respectively. Hence, geometrical parameters investigated in this study are grouped into (i) CPC parameters: the CPC acceptance angle θCPC, the CPC entry aperture radius rin, the CPC axis tilt angle αCPC, and (ii) parameters excluding those of a CPC: the hyperboloidal TR eccentricity er, the TR axis tilt angle αr, the azimuthal angle ϕt, the primary focus height h1, the focal point height ratio γ, the distance d1 between the tower and the furthermost heliostat along the south direction.
The surface equation of a hyperboloid of revolution expressed in the local coordinate system is [43]
Figure 2 depicts an example array with 8 receiver–reactors in total. The receiver–reactor irradiated by the concentrated solar energy has an opened aperture and realizes a reduction reaction. All other receiver–reactors have closed apertures. The receiver–reactor on the opposite side to the reduction reactor realizes an oxidation reaction. Heat is exchanged between reactors other than the reduction and oxidation ones to pre-heat or pre-cool the active redox materials prior to their reduction and oxidation, respectively, allowing for significant gains in thermal-to-chemical efficiency [7–9,17].
2.2 Performance metrics
Figure 3 shows the power flow in a beam-down optical system. Compared with a solar ‘tower-receiver’ system, where the receiver is placed on the top of the tower [30], additional optical losses occur in the beam-down system including the spillage ${\dot{Q}_{\textrm{spill,r}}}$ and absorption losses ${\dot{Q}_{\textrm{abs,r}}}$ by the TR, the shading loss ${\dot{Q}_{\textrm{shade,r}}}$ of heliostats by the TR, the blocking loss ${\dot{Q}_{\textrm{block,rec}}}$ of heliostats by the CPC/receiver, and atmospheric attenuation loss ${\dot{Q}_{\textrm{aa,down}}}$ when rays travel from the TR to the CPC entry aperture. The simulated shading losses ${\dot{Q}_{\textrm{shade}}}$ include ${\dot{Q}_{\textrm{shade,r}}}$ and the shading loss ${\dot{Q}_{\textrm{shade,h}}}$ between heliostats. The simulated blocking losses ${\dot{Q}_{\textrm{block}}}$ include ${\dot{Q}_{\textrm{block,rec}}}$ and the blocking loss ${\dot{Q}_{\textrm{block,h}}}$ between heliostats.
The instantaneous optical performance of the beam-down optical system is evaluated with the overall optical efficiency of individual heliostats and heliostat field, ηh,opt and ηf,opt, respectively, CPC transmission efficiency, ηCPC, interception efficiency of TR and CPC, ηint,r and ηint,CPC, respectively, the radiative power ${\dot{Q}_{\textrm{rec,a}}}$ and concentration ratio CRrec,a at the receiver–reactor aperture, and the instantaneous optical efficiency ηsys,opt of the overall optical system. ηsys,opt is defined as the ratio of the radiative power ${\dot{Q}_{\textrm{rec,a}}}$ intercepted by the receiver–reactor aperture divided by ${\dot{Q}_{\textrm{f,}\max }}$, which in turn is the maximum total radiative power collected when solar rays are incident normally on an area equal to the total installed heliostat area Atotal,h. The instantaneous optical performance is obtained for autumn equinox noon, i.e. March 21st in the southern hemisphere. The overall optical efficiencies of an individual heliostat and a heliostat field, ηh,opt and ηf,opt, respectively, account for the cosine effect, shading, blocking, surface absorption, atmospheric attenuation, and spillage at the TR.
Note that the model optical systems investigated in this study use one receiver–reactor only of a variable position relative to the tower. The evaluation of the optical performance of the system with multiple receiver–reactors is not included in this study since it requires detailed information on the geometry, thermal design, and operation of the receiver–reactor array, such as the receiver–reactor dimension as a function of incident radiative power, the clearance between receiver–reactors, the duration time of each receiver–reactor being irradiated, and the rotating speed of the TR.
2.3 MCRT model assumptions
Optical modeling of the 3D beam-down optical system is implemented using an in-house developed MCRT program. The optical models for simulating the CPC and the heliostat field as used in the present study were previously developed and verified in [31] and [45], respectively. The modeled plant location is Alice Springs, Australia (–23.7°N, 133.9°E). The sun position relative to an observer on the ground is calculated as a function of solar time and site latitude using the method described in [46] and [47]. Buie sun shape model with an assumed radial displacement of σsun = 4.65 mrad and a circumsolar ratio of 0.02 is used [48]. A single-facet, point-focusing, and square heliostat is taken, with a surface area of 16 m2. The heliostat, TR and CPC surfaces are assumed to have specular, wavelength- and direction-independent reflectance equal to 0.93, 0.95 and 0.95, respectively. We use the Campo field layout pattern [49]. Reflections from optical surfaces are modeled by considering optical errors [50]. Gaussian surface normal error distributions with assumed standard deviations of 1.5, 1.4 and 0.5 mrad are applied for the heliostat, TR and CPC surfaces, respectively. The assumptions of the reflectance and slope errors of studied optical surfaces are based on the commercial beam-down plant in [42]. Atmospheric attenuation accounts for radiative losses incurred in the atmosphere. The atmospheric attenuation is calculated as a function of the slant distance that rays travel as discussed in [51]. The annual heliostat field performance is evaluated using the method given in [52] and by employing bi-cubic spline interpolation of results for discrete sun positions [53].
The 3D optical model is employed to explore the effects (i) of the system geometrical parameters excluding CPC parameters (defined in Subsection 2.1) and the TR size, on system optical and radiative characteristics (see Subsection 4.2.1); (ii) of CPC parameters (defined in Subsection 2.1) on instantaneous (at autumn equinox noon) system optical efficiency and concentration ratio at the receiver–reactor aperture (see Subsection 4.2.2), and (iii) to predict annual system optical efficiency for the receiver–reactor placed at selected positions around the tower (see Subsection 4.3). The selection of the geometry and orientation of the CPC used in (iii) is guided by the results of the analysis in (ii).
3. Simplified 2D optical system model
To establish the initial size of the TR and the geometry and orientation of the CPC for the 3D MCRT simulations, we employ a simplified 2D model and perform analytical ray tracing to predict geometrical and optical characteristics including the TR size lr for capturing all reflected rays from heliostat field, the radius rm of the sun image at the CPC entry aperture, and the rim and axis tilt angles of the incident beam on the CPC entry aperture, Φm and αm, respectively. These predictions are based on the edge-ray principle [18], hence, only edge rays are simulated. Figure 4 depicts the simplified 2D model with the investigated geometrical parameters and predicted geometrical and optical characteristics.
Fig. 4. Model of the simplified 2D beam-down optical system. Parameters in black and blue are the investigated geometrical parameters and predicted geometrical and optical characteristics, respectively. Red lines represent the edges of the incident beam at the CPC entry aperture.
The rationale for predicting the parameters lr, rm, Φm, and αm is given next. The distance lr,min between the two intersection points P1 and P2 of the TR with the two edge rays incident on the TR (Fig. 4) is calculated to characterize the required size of the TR. A larger TR leads to higher TR interception efficiency at the expense of an increased shading loss. The size of CPC entry aperture in the 3D MCRT simulation is matched with the size of the sun image on the CPC entry aperture. With the 2D model, we examine the sun image magnification due to the finite size of the sun and the reflection by optical surfaces, the so-called coma aberration [54]. The pillbox-distributed sun shape model is used for the 2D estimation of the sun image radius rm [55]. Sun rays can be assumed to originate from a sun disk subtending a cone half angle σsun of 4.65 mrad. When sun rays are reflected by perfect, specular primary and secondary optical concentrators, their distribution on a focal plane forms a sun image of radius rm. The determination of CPC acceptance and axis tilt angles, θCPC and αCPC, respectively, in the 3D MCRT simulation, is guided by the values of Φm and αm obtained with the 2D model.
Using the simplified 2D system, we explore the effects of (i) the system geometrical parameters excluding CPC parameters (defined in Subsection 2.1) on the above-discussed parameters lr,min, rm, Φm, and αm; and (ii) the optical imperfections of the heliostat and the TR surface, introduced by modifying the ideal surface normal vector by modelling its polar angle using the pillbox distribution with half-angles of σh and σr, respectively (see Subsection 4.1).
4. Results and discussion
Firstly, we present the results of the parametric studies with the 2D (Subsection 4.1) and 3D (Subsection 4.2) optical system models. In Subsection 4.3, we discuss the effects of the rotation of the TR and the dislocation of the receiver–reactor on the annual optical performance. The baseline parameter set listed in Table 1 is selected according to preliminary parametric studies and based on the parameters of the existing commercial solar beam-down system presented in [42]. One parameter is varied at a time while other parameters are taken from the baseline set.
Table 1. Baseline simulation parameters
4.1 Parametric studies using simplified 2D optical system model
Figure 5 shows the analytical ray-tracing results of the effects of the geometrical parameters excluding those of a CPC (defined in Subsection 2.1) on the required size lr,min of the TR and the radius rm of the sun image. Schematics showing ray paths for three example values of each parameter are included in the plots to visualize the effects of each parameter. According to Fig. 5(a,d), lr,min and rm have reverse trends for an increasing TR eccentricity er or focal point height ratio γ. An increase in er leads to a significant decrease in rm, especially for er < 2, and a significant increase in lr,min. Placing the receiver–reactor closer to the ground level greatly increases lr,min. Figure 5(b, c, e) show that a smaller TR axis tilt angle αr, a smaller primary focus height h1, or a smaller distance d1 of the furthermost heliostat to the tower result in smaller both lr,min and rm.
Fig. 5. Optical characteristics including required tower reflector (TR) size lr,min and radius rm of sun image on CPC entry aperture, as a function of (a) hyperboloidal TR eccentricity er, (b) TR axis tilt angle αr, (c) primary focus height h1, (d) focal point height ratio γ, and (e) distance d1 from the furthermost heliostat to tower.
Figure 6 exhibits the magnitude of the increase of lr,min and rm with the increase of the optical imperfections of the heliostat and TR surfaces, characterized by σh and σr, respectively. It is found that the increase of σh from 0 to around 10 mrad leads to lr,min and rm increased by about 1.5% and 178%, respectively. σh has a significant influence on rm but minor impact on lr,min. For σr increasing from 0 to around 10 mrad, rm increases by approximately 27.5%. Compared with σr, σh has a greater impact on rm due to an optical path from the heliostat surface to the CPC entry aperture longer than that from the TR to the CPC entry aperture.
Fig. 6. Effects of slope errors of the heliostat and tower reflector (TR) surfaces, σh and σr, respectively, on required TR size lr,min and radius rm of sun image on CPC entry aperture.
Figure 7 shows the rim and axis tilt angles of the incident beam on the CPC entry aperture, Φm and αm, respectively, as functions of the system geometrical parameters excluding those of the CPC. As indicated in Fig. 7(a), Φm is mainly affected by er, followed by h1. A smaller er or a larger h1 lead to a smaller Φm, allowing the selection of a CPC with a smaller θCPC for achieving a larger theoretical CR boost from the 3D CPC, equal to 1/sin2θCPC. This is consistent with the findings of the study presented in Ref [56]. Figure 7(b) shows that αm is significantly affected by αr, followed by h1 and er.
Fig. 7. Optical characteristics of the incident beam on the CPC entry aperture including (a) rim angle Φm and (b) axis tilt angle αm, as a function of hyperboloidal tower reflector eccentricity er, TR axis tilt angle αr, primary focus height h1, focal point height ratio γ, and distance d1 from the furthermost heliostat to tower.
4.2 Parametric studies using 3D optical system model
In the 3D system model, we select a heliostat field with its boundary determined by removing the heliostats with overall instantaneous optical efficiency ηh,opt lower than a selected trimming threshold of 0.6 (see Fig. 8). The distances from the furthermost heliostats to the tower along the South and North directions of 242 m and 164 m, respectively, are set as the baseline values of d1 and d2 for the 2D analysis (Table 1). Table 1 also includes the baseline parameters of the 3D system for parametric studies presented in this subsection.
Fig. 8. The heliostat field for the baseline MCRT simulation. The color scale indicates the overall instantaneous (at autumn equinox noon) optical efficiency of each heliostat, ηh,opt. The tower is at the origin point. The heliostats near the origin point have low overall optical efficiency due to the shading by the tower reflector.
Figure 9 and Table 2 show the instantaneous optical and radiative performance of the baseline system with one receiver–reactor located south of the tower, i.e. ϕt = 0°, and with a TR axis tilt angle αr = 10°. The instantaneous optical efficiency of the overall system is around 51% and radiative power of around 15.9 MW is provided to the receiver–reactor. The main optical losses are ascribed to the cosine effect, the spillage at the CPC entry aperture, and the absorption and rejection by the CPC. The system optical efficiency of 51% is lower than the values of approx. 60–70% for a typical beam-down system as discussed in [30] while a high concentration ratio of 2588 is achieved for the present system.
Fig. 9. Sankey diagram of instantaneous (at autumn equinox noon) optical losses for the baseline system with the parameter set of Table 1.
Table 2. Instantaneous optical performance of the baseline case
The following sections explore the effects of geometrical parameters excluding those of a CPC (Part 1) and CPC parameters (Part 2) on system optical and radiative performance metrics defined in Section 2.
4.2.1 Parametric study: Part 1
To accommodate the receiver–reactor array in the proposed system, the receiver–reactors are moved away from the locations corresponding to the maximum optical performance. For that purpose, we investigate the effects of geometrical parameters excluding those of a CPC in a 3D system with an example dislocated receiver–reactor for which the position is given by αr = 10° and ϕt = 0°, on the instantaneous system optical and radiative performance characterized by the metrics defined in Subsection 2.2.
Figure 10 shows the results of the parametric studies performed using MCRT simulations. As shown in Fig. 10(a), the TR interception efficiency ηint,r decreases with increasing hyperboloidal TR eccentricity er due to the increase of required TR size lr,min referring to Fig. 5(a). The CPC interception efficiency ηint,CPC increases with an increasing er due to the decrease of rm as indicated in Fig. 5(a). CPC transmission efficiency ηCPC decreases with the increase of er due to the increase of Φm as seen in Fig. 7(a). Hence, an optimal er can be identified that offers the maximum system optical efficiency ηsys,opt, radiative power and CR at the receiver–reactor aperture. Figure 10(b) shows that the system optical performance is decreased for a larger tilt angle αr of the TR axis, due to the increasing mismatch of the selected αCPC (= αr in the simulations) and αm (increasing with αr as seen in Fig. 7(b)).
Fig. 10. Instantaneous optical efficiencies, radiative power and concentration ratio at receiver–reactor aperture, as a function of (a) hyperboloidal tower reflector (TR) eccentricity er, (b) TR axis tilt angle αr, (c) primary focus height h1, (d) focal point height ratio γ, and (e) TR size lr.
Referring to Fig. 5(c), lr,min and rm increase with the increasing primary focus height h1, resulting in decreasing interception efficiency of the TR and CPC, ηint,r and ηint,CPC, respectively (Fig. 10(d)). As seen in Fig. 7(a), a higher primary focus results in the beam hitting the CPC entry aperture at a smaller rim angle Φm, allowing for higher CPC transmission efficiency ηCPC. ηCPC diminishes as h1 increases further, because of the increasing misalignment of the axes of the CPC and the incident beam, αCPC and αm, respectively. The optimum h1 can be identified that offers the maximum radiative power and/or CR. The difference between αCPC (= αr in the simulations) and αm (shown in Fig. 7(b)) increases with the increasing focal point height ratio γ, which in turn results in decreasing ηCPC (Fig. 10(d)). The increase of ηint,TR with the increase of γ is due to the decrease of lr,min as indicated in Fig. 5(d).
A larger TR leads to reduced TR spillage loss but more shading loss to the heliostat field by the TR. As the TR size increases, more rays reflected from the heliostat field are redirected by the TR, particularly the rays reflected from the heliostats further away from the tower. As a result, rm and Φm increase with a larger TR, which in turn decreases the CPC transmission and interception efficiencies, respectively (see Fig. 10(e)).
4.2.2 Parametric study: Part 2
Parameters determining the geometry and orientation of the CPC coupled with the receiver–reactor are the entry aperture radius rin, the acceptance angle θCPC, and the axis tilt angle αCPC. CPC transmission and interception efficiencies, ηCPC and ηint,CPC, respectively, are affected by the difference between αCPC and αm and the ray distribution of the incident beam. ηCPC and ηint,CPC are also influenced by the difference between αCPC and αm and the difference between rin and rm, respectively. Parametric studies on CPC parameters on the instantaneous system optical efficiency ηsys,opt and CRrec,a are carried out for each selected receiver–reactor position and presented in this subsection. Figure 11 shows ηsys,opt and CRrec,a as a function of θCPC (varying from 10° to 50° in 5° increments), rin (varying from 1 m to 10 m in 1 m increments), and αCPC (varying from 2° to 44° in approximately 3.8° increments), for the defined receiver–reactor positions with two TR axis tilt angles αr of 5° and 25° and four azimuthal angles ϕt of 0°, 90°, and 180°. Optical performance for ϕt = 270° and ϕt = 90° are the same due to the symmetry of the system geometry, for which the results for ϕt = 270° are omitted from Figs. 11 and 12.
Fig. 11. Effects of (a) acceptance angle θCPC, (b) entry aperture radius rin, and (c) axis tilt angle αCPC of a CPC on (1) the instantaneous (at autumn equinox noon) system optical efficiency ηsys,opt and (2) concentration ratio CRrec,a at the receiver–reactor aperture, for systems with the receiver–reactor placed at selected positions (characterized by tower reflector axis tilt angle αr and azimuthal angle ϕt).
Fig. 12. Annual system optical efficiency ${\bar{\eta }_{\textrm{sys,opt}}}$ of a beam-down optical system with one receiver–reactor placed at different relative positions to the tower. Receiver–reactor positions are expressed by (a) global coordinates x and y; and (b,c) tilt angle αr of tower reflector axis and azimuthal angle ϕt of secondary focus.
According to Fig. 11, larger θCPC and rin result in higher ηsys,opt due to higher ηCPC and ηint,CPC, respectively (Fig. 11(a-1), (b-1)), but decreased CRrec,a due to reduced maximum theoretical concentration ratio boost from the CPC of 1/sin2θCPC and lower mean radiative flux at the CPC entry aperture, respectively (Fig. 11(a-2), (b-2)). For the same αr, the highest and lowest ηsys,opt and/or CRrec are found at ϕt = 0° and 180°, respectively. For a smaller αr, the systems with different ϕt have close optical performance. Increasing differences between the optical performance of the systems with ϕt = 0° and ϕt = 180° are observed for the cases of larger αr. It is also found that the optimum θCPC for maximizing CRrec,a are different for αr = 5° and αr = 25°, indicating that different acceptance angles of CPCs may be required for the receiver–reactor positions with different TR axis tilt angle αr. Based on Fig. 11(c-1) and (c-2), the optimum αCPC leading to maximum ηsys,opt and CRrec are equal and close to the selected αr. Thus, αCPC can be determined by optimizing the optical performance, while θCPC and rin should be selected as a trade-off between maximizing ηsys,tot and maximizing CRrec,a.
4.3 Annual simulations of 3D optical systems with selected receiver–reactor positions
Here, we present the annual simulation results for systems with selected receiver–reactor positions, i.e. the TR axis tilt angle αr varying from 2° to 40° in 1.6° increments and the azimuthal angle ϕt varying from 0° to 360° in 15° increments. The results of the parametric studies presented in Subsection 4.2.2 indicate that the optimal CPC geometry for the maximized system optical performance may be different for each receiver–reactor position. However, it is pragmatic to manufacture CPCs with the same geometry, although with possible differences in their orientations as evident from results presented in Subsections 4.1 and 4.2. Based on the results shown in Fig. 11, we select example values of CPC parameters, i.e. θCPC of 30°, rin of 2.8 m, and αCPC equal to the relevant αr for each receiver–reactor position.
Annual system optical efficiency ${\bar{\eta }_{\textrm{sys,opt}}}$ for each system with the selected receiver–reactor position and the designed CPC is calculated and plotted in Fig. 12. Figure 12(a) and (b,c) show the results for the receiver–reactor positions expressed by the global coordinates x and y, and αr and ϕt, respectively. A maximum ${\bar{\eta }_{\textrm{sys,opt}}}$ of 46% is found at αr = 2° (the smallest simulated αr) and ϕt = 0°. ${\bar{\eta }_{\textrm{sys,opt}}}$ decreases with an increasing αr. For a smaller αr, ${\bar{\eta }_{\textrm{sys,opt}}}$ varies little for different ϕt. The difference between ${\bar{\eta }_{\textrm{sys,opt}}}$ of the cases with different ϕt increases with increasing αr. The system with ϕt = 0° performs best, followed by ϕt = 90° and ϕt = 180°. The same ${\bar{\eta }_{\textrm{sys,opt}}}$ is observed for the receiver–reactor positions symmetric about the x-axis (the North–South direction).
The optical performance of the system with a receiver–reactor array is maximized for αr and ϕt equal to 2° and 0°, respectively. The average optical efficiency of the system with the receiver–reactor array is affected by factors such as the selected total number of receivers, the finite receiver size, and the inter-receiver clearance required to accommodate potential auxiliary equipment in the receiver–reactor array.
5. Summary and conclusions
A novel beam-down optical system with a rotating tower reflector and an array of receiver–reactors has been proposed to realize multi-step solar thermochemical redox cycles for solar fuel production or thermal energy storage applications. Analytical and Monte-Carlo ray-tracing simulations were performed for a simplified two-dimensional model system and a realistic three-dimensional beam-down optical model system, respectively. Instantaneous and annual optical characteristics were predicted for the proposed system.
The optimal geometrical parameters that offer the maximum system optical efficiency and radiative input to a receiver–reactor were identified. The heliostat surface slope error was found to have a greater influence on the sun image size than the slope error of the tower reflector surface. The baseline system was found to provide a flux concentration ratio of 2588 with an instantaneous system optical efficiency and radiative power to the receiver–reactor of 51% and 16 MW, respectively. We demonstrated that the annual system optical efficiency of the baseline system with a receiver–reactor placed to the south of the tower decreases from 46% to 37% for the axis tilt angle of the tower reflector increasing from 2° to 20°. Locating the receiver–reactor array south of and as close as possible to the tower offers the most promising optical configuration.
Funding
Australian Renewable Energy Agency (2014/RND005); China Scholarship Council ([2017]3109).
Acknowledgments
This research was undertaken with the assistance of resources and services from the National Computational Infrastructure (NCI), which is supported by the Australian Government.
Disclosures
The authors declare no conflict of interest.
References
1. M. Sturzenegger and P. Nüesch, “Efficiency analysis for a manganese-oxide-based thermochemical cycle,” Energy 24(11), 959–970 (1999). [CrossRef]
2. M. Romero and A. Steinfeld, “Concentrating solar thermal power and thermochemical fuels,” Energy Environ. Sci. 5(11), 9234–9245 (2012). [CrossRef]
3. R. Bader and W. Lipiński, “Solar thermal processing,” in Advances in Concentrating Solar Thermal Research and Technology (Elsevier, 2017), 403–459.
4. G. Levêque, R. Bader, W. Lipiński, and S. Haussener, “High-flux optical systems for solar thermochemistry,” J. Sol. Energy Eng. 156, 133–148 (2017). [CrossRef]
5. A. J. Carrillo, J. González-Aguilar, M. Romero, and J. M. Coronado, “Solar energy on demand: A review on high temperature thermochemical heat storage systems and materials,” Chem. Rev. 119(7), 4777–4816 (2019). [CrossRef]
6. W. C. Chueh, C. Falter, M. Abbott, D. Scipio, P. Furler, S. M. Haile, and A. Steinfeld, “High-flux solar-driven thermochemical dissociation of CO2 and H2O using nonstoichiometric ceria,” Science 330(6012), 1797–1801 (2010). [CrossRef]
7. J. Lapp, J. H. Davidson, and W. Lipiński, “Efficiency of two-step solar thermochemical non-stoichiometric redox cycles with heat recovery,” Energy 37(1), 591–600 (2012). [CrossRef]
8. J. Lapp, J. H. Davidson, and W. Lipiński, “Heat transfer analysis of a solid-solid heat recuperation system for solar-driven nonstoichiometric redox cycles,” J. Sol. Energy Eng. 135(3), 031004 (2013). [CrossRef]
9. J. Lapp and W. Lipiński, “Transient three-dimensional heat transfer model of a solar thermochemical reactor for H2O and CO2 splitting via nonstoichiometric ceria redox cycling,” J. Sol. Energy Eng.136 (2014). [CrossRef]
10. D. Marxer, P. Furler, M. Takacs, and A. Steinfeld, “Solar thermochemical splitting of CO2 into separate streams of CO and O2 with high selectivity, stability, conversion, and efficiency,” Energy Environ. Sci. 10(5), 1142–1149 (2017). [CrossRef]
11. B. Wang, L. Li, R. Bader, J. Pottas, V. Wheeler, P. Kreider, and W. Lipiński, “Thermal model of a solar thermochemical reactor for metal oxide reduction,” J. Sol. Energy Eng. 142(5), 051002 (2020). [CrossRef]
12. A. Steinfeld, P. Furler, A. Haselbacher, and L. Geissbühler, “A thermochemical reactor system for a temperature swing cyclic process with integrated heat recovery and a method for operating the same,” U.S. Patent Application No. 16/342 (2019).
13. M. Roeb, J.-P. Säck, P. Rietbrock, C. Prahl, H. Schreiber, M. Neises, L. de Oliveira, D. Graf, M. Ebert, and W. Reinalter, “Test operation of a 100 kW pilot plant for solar hydrogen production from water on a solar tower,” Sol. Energy 85(4), 634–644 (2011). [CrossRef]
14. E. Koepf, S. Zoller, S. Luque, M. Thelen, S. Brendelberger, J. González-Aguilar, M. Romero, and A. Steinfeld, “Liquid fuels from concentrated sunlight: An overview on development and integration of a 50 kW solar thermochemical reactor and high concentration solar field for the SUN-to-LIQUID project,” in AIP Conference Proceedings, (AIP Publishing LLC, 2019), 180012.
15. C. Sattler, M. Roeb, C. Agrafiotis, and D. Thomey, “Solar hydrogen production via sulphur based thermochemical water-splitting,” Sol. Energy 156, 30–47 (2017). [CrossRef]
16. F. Dähler, M. Wild, R. Schäppi, P. Haueter, T. Cooper, P. Good, C. Larrea, M. Schmitz, P. Furler, and A. Steinfeld, “Optical design and experimental characterization of a solar concentrating dish system for fuel production via thermochemical redox cycles,” Sol. Energy 170, 568–575 (2018). [CrossRef]
17. C. Yuan, C. Jarrett, W. Chueh, Y. Kawajiri, and A. Henry, “A new solar fuels reactor concept based on a liquid metal heat transfer fluid: Reactor design and efficiency estimation,” Sol. Energy 122, 547–561 (2015). [CrossRef]
18. R. Winston, J. C. Miñano, and P. G. Benitez, Nonimaging Optics (Elsevier, 2005).
19. H. Hasuike, Y. Yoshizawa, A. Suzuki, and Y. Tamaura, “Study on design of molten salt solar receivers for beam-down solar concentrator,” Sol. Energy 80(10), 1255–1262 (2006). [CrossRef]
20. M. Epstein, G. Olalde, S. Santén, A. Steinfeld, and C. Wieckert, “Towards the industrial solar carbothermal production of zinc,” J. Sol. Energy Eng. 130(1), 014505 (2008). [CrossRef]
21. E. Koepf, S. G. Advani, A. Steinfeld, and A. K. Prasad, “A novel beam-down, gravity-fed, solar thermochemical receiver/reactor for direct solid particle decomposition: Design, modeling, and experimentation,” Int. J. Hydrogen Energy 37(22), 16871–16887 (2012). [CrossRef]
22. A. Lenert and E. N. Wang, “Optimization of nanofluid volumetric receivers for solar thermal energy conversion,” Sol. Energy 86(1), 253–265 (2012). [CrossRef]
23. M. Mokhtar, S. A. Meyers, P. R. Armstrong, and M. Chiesa, “Performance of a 100 kWth concentrated solar beam-down optical experiment,” J. Sol. Energy Eng. 136(4), 041007 (2014). [CrossRef]
24. G. Xiao, K. Guo, Z. Luo, M. Ni, Y. Zhang, and C. Wang, “Simulation and experimental study on a spiral solid particle solar receiver,” Appl. Energy 113, 178–188 (2014). [CrossRef]
25. X. Li, Y. Dai, and R. 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]
26. M. Martins, U. Villalobos, T. Delclos, P. Armstrong, P. G. Bergan, and N. Calvet, “New concentrating solar power facility for testing high temperature concrete thermal energy storage,” Energy Procedia 75, 2144–2149 (2015). [CrossRef]
27. T. Kodama, N. Gokon, H. S. Cho, K. Matsubara, T. Etori, A. Takeuchi, S.-N. Yokota, and S. Ito, “Particles fluidized bed receiver/reactor with a beam-down solar concentrating optics: 30-kWth performance test using a big sun-simulator,” in AIP Conference Proceedings, (AIP Publishing, 2016), 120004.
28. S. Bellan, K. Matsubara, C. H. Cheok, N. Gokon, and T. Kodama, “CFD-DEM investigation of particles circulation pattern of two-tower fluidized bed reactor for beam-down solar concentrating system,” Powder Technol. 319, 228–237 (2017). [CrossRef]
29. G. Manikandan, S. Iniyan, and R. Goic, “Enhancing the optical and thermal efficiency of a parabolic trough collector – A review,” Appl. Energy 235, 1524–1540 (2019). [CrossRef]
30. A. Segal and M. Epstein, “Comparative performances of ‘tower-top’ and ‘tower-reflector’ central solar receivers,” Sol. Energy 65(4), 207–226 (1999). [CrossRef]
31. L. Li, B. Wang, J. Pottas, and W. Lipiński, “Design of a compound parabolic concentrator for a multi-source high-flux solar simulator,” Sol. Energy 183, 805–811 (2019). [CrossRef]
32. C. E. Mauk, H. W. Prengle Jr, and E. C.-H. Sun, “Optical and thermal analysis of a Cassegrainian solar concentrator,” Sol. Energy 23(2), 157–167 (1979). [CrossRef]
33. A. Yogev, A. Kribus, M. Epstein, and A. Kogan, “Solar “tower reflector” systems: a new approach for high-temperature solar plants,” Int. J. Hydrogen Energy 23(4), 239–245 (1998). [CrossRef]
34. A. Segal and M. Epstein, “The optics of the solar tower reflector,” Sol. Energy 69, 229–241 (2001). [CrossRef]
35. A. Segal and M. Epstein, “Practical considerations in designing large scale “beam down” optical systems,” J. Sol. Energy Eng. 130(1), 011009 (2008). [CrossRef]
36. X. Wei, Z. Lu, W. Yu, and W. Xu, “Ray tracing and simulation for the beam-down solar concentrator,” Renewable Energy 50, 161–167 (2013). [CrossRef]
37. L. Vant-Hull, “Issues with beam-down concepts,” Energy Procedia 49, 257–264 (2014). [CrossRef]
38. E. Leonardi, “Detailed analysis of the solar power collected in a beam-down central receiver system,” Sol. Energy 86(2), 734–745 (2012). [CrossRef]
39. L. Li, J. Coventry, R. Bader, J. Pye, and W. Lipiński, “Optics of solar central receiver systems: a review,” Opt. Express 24(14), A985–A1007 (2016). [CrossRef]
40. B. Grange, V. Kumar, A. Gil, P. R. Armstrong, D. S. Codd, A. Slocum, and N. Calvet, “Preliminary optical, thermal and structural design of a 100 kWth CSPonD beam-down on-sun demonstration plant,” Energy Procedia 75, 2163–2168 (2015). [CrossRef]
41. Magaldi, retrieved 26 October, 2019, https://www.magaldi.com/en/products-solutions/csp-concentrating-solar-power.
42. HELIOSCSP, retrieved 26 October, 2019, http://helioscsp.com/three-solar-modules-of-worlds-first-commercial-beam-down-tower-concentrated-solar-power-project-to-be-connected-to-grid/.
43. I. N. Bronshtein and K. A. Semendyayev, Handbook of Mathematics (Springer Science & Business Media, 2013).
44. M. F. Modest, Radiative Heat Transfer (Academic, 2013).
45. L. Li, B. Wang, J. Pye, and W. Lipiński, “Temperature-based optical design, optimization and economics of solar polar-field central receiver systems with an optional compound parabolic concentrator,” Sol. Energy, doi:10.1016/j.solener.2020.05.088 (2020).
46. J. A. Duffie and W. A. Beckman, Solar Engineering of Thermal Processes (John Wiley & Sons, 2013).
47. A. B. Sproul, “Derivation of the solar geometric relationships using vector analysis,” Renewable Energy 32(7), 1187–1205 (2007). [CrossRef]
48. D. Buie, A. Monger, and C. Dey, “Sunshape distributions for terrestrial solar simulations,” Sol. Energy 74(2), 113–122 (2003). [CrossRef]
49. F. J. Collado and J. Guallar, “Campo: Generation of regular heliostat fields,” Renewable Energy 46, 49–59 (2012). [CrossRef]
50. R. Bader, S. Haussener, and W. Lipiński, “Optical design of multisource high-flux solar simulators,” J. Sol. Energy Eng. 137(2), 021012 (2015). [CrossRef]
51. P. Leary and J. Hankins, “User's guide for MIRVAL: a computer code for comparing designs of heliostat-receiver optics for central receiver solar power plants,” (Sandia National Laboratories, Livermore, CA (USA), 1979).
52. V. Grigoriev, C. Corsi, and M. Blanco, “Fourier sampling of sun path for applications in solar energy,” in AIP Conference Proceedings, (AIP Publishing, 2016), 020008.
53. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 90 (Cambridge University, 1996), Vol. 2.
54. W. J. Smith, Modern Optical Engineering, 4th ed. (McGraw-Hill, 2008).
55. Y. Wang, D. Potter, C.-A. Asselineau, C. Corsi, M. Wagner, C. Caliot, B. Piaud, M. Blanco, J.-S. Kim, and J. Pye, “Verification of optical modelling of sunshape and surface slope error for concentrating solar power systems,” Sol. Energy 195, 461–474 (2020). [CrossRef]
56. L. Li, B. Wang, R. Bader, J. Zapata, and W. Lipiński, “Reflective optics for redirecting convergent radiative beams in concentrating solar applications,” Sol. Energy 191, 707–718 (2019). [CrossRef]
