Numerical simulation and experiment research of radiation performance in a dish solar collector system

Abstract

The Monte Carlo ray-tracing method is applied and coupled with optical properties to predict the radiation performance of solar concentrator/cavity receiver systems. Several different cavity geometries are compared on the radiation performance. A flux density distribution measurement system for dish parabolic concentrators is developed. The contours of the flux distribution for target placements at different distances from the dish vertex of a solar concentrator are taken by using an indirect method with a Lambert and a charge coupled device (CCD) camera. Further, the measured flux distributions are compared with a Monte Carlo-predicted distribution. The results can be a valuable reference for the design and assemblage of the solar collector system.

Keywords

Monte Carlo method / solar energy / radiation performance / cavity receiver

Introduction

Medium-high temperature application is an important topic in the solar energy field, such as the solar thermal electric power systems, solar electricity generating systems, solar dynamic space power systems, etc. A similar process is the scenario of a dish concentrator collecting energy that is transported optically to a central cavity receiver. Solar concentrating technologies are convenient for power generation due to the high temperature achieved by the higher power flux. However, manufacturing or assembly errors and unideal sunlight with an increased angular diameter can bring about a bigger energy spot in the focal region, a nonuniformity of heat flux distribution in the cavity receiver, or a local overheating in the cavity receiver. The thermal stress concentration induced by the abovementioned errors will further degrade the system performance.

The investigation into the flux distribution of solar concentrating systems is important to the optimization of the system configuration, especially when hydrogen is produced via the solar thermal gasification of biomass in supercritical condition, because the flux distribution in the cavity receiver/reactor has a strong effect on hydrogen production. The radiation flux distribution in the cavity receiver/reactor is dependent on the directional distribution and quantity of concentrated energy. Different techniques have been developed to measure the focal flux distribution using CCD cameras [1]. However, it is still necessary to evaluate, in detail, the radiative heat flux distribution in the focal region of the concentrator by developing modelling tools and thus optimize the design of solar concentrator systems.

The codes traditionally used for the design and simulation of solar thermal central receiver plants, such as HELIOS (heliostat) [2], CIRCE (convolution of incident radiation with concentrator errors) [3], MIRVAL (mirror evaluation) [4], etc., were written in 1980s in FORTRAN, whose philosophy and structure, in most cases, are neither modular nor user friendly. In addition, Daly [5] studied flux distributions produced by parabolic and circular cylinder solar concentrators using a backward ray tracing method. Jeter [6] calculated the distribution of concentrated flux in idealized paraboloidal solar collectors by introducing an integral relationship. Jones and Wang [7] computed solar concentrations on a cylindrical receiver in a paraboloidal concentrator using a geometric optics method. Johnston [8,9] predicted the flux mapping the 400 m² “Big Dish” by developing the COMPREC compound receiver code at The Australian National University. Imenes et al. [10] generated the flux distribution in the case of a surface error of 3.5 mrad and an ideal tracking regime using the ray-trace program. Jaramillo [11] evaluated the energy arriving at the focus of a small paraboloidal mirror by an analytical method. Doron and Kribus [12] demonstrated the importance of irradiation directional features to volumetric absorbers. In the previous works related to the performance of solar collector systems, only the energy flux density distribution in the focal plane is considered, while the directional characteristics of concentrated energy are neglected.

In this paper, radiation flux distributions in the focal plane of the solar collector system and in the wall of the cavity receiver/reactor are studied by employing the Monte Carlo ray-tracing method. A measuring system is developed to measure the focal radiative flux distribution using CCD cameras. Moreover, a series of flux measurements are performed for target placements at different distances from the dish vertex of a paraboloidal dish solar concentrator. Further, the measured flux distributions are compared with a Monte Carlo-predicted distribution.

Methodology

A Monte Carlo ray-tracing method, which is based on the radiative exchange factor (REF), is developed to predict the energy distributions in the focal region of the concentrator. Monte Carlo (MC) method is a statistical simulation method for radiative transfer, which can be performed by tracing a finite number of energy bundles through their transport histories. These energy bundles are similar to photons in their behaviour, and their histories are traced from their emission points to their absorption points. What happens to an individual bundle depends on its emissive, scattering, and absorptive behavior within the surface or the medium, which can be denoted by a set of statistical relationships. Modest [13] and Siegel and Howell [14] have described the MC simulation in detail, respectively.

The REF RD_ij is defined as the fraction of the emissive power of surface element i, which is absorbed by surface element j, due to both direct radiation and all possible reflections within the enclosure. The value of the REF depends not only on the geometry but also on the radiative characteristics of the computation elements. When total bundles N_i are emitted from surface element i within the spectral band Δλ_k (k=1,2,…,M_b), with N_ij bundles absorbed by surface element j, the REF within the spectral band Δλ_k can be calculated with

(1)\mathrm{R}{\mathrm{D}}_{i,j,\mathrm{\Delta }{\lambda }_k}=N_{ij}/N_i,

where M_b is the total spectral bands of the wavelength-dependent radiation characteristics for the surface (or the medium).

For an enclosure consisting of M surface elements, the REF within the spectral band Δλ_k has the following important attributes:

1) Conservation of energy

(2){\displaystyle \sum _{j=\mathrm{1}}^M\mathrm{R}{\mathrm{D}}_{i,j,\mathrm{\Delta }{\lambda }_k}}=\mathrm{1.0},\mathrm{1}\le i\le M.

2) Reciprocity relationship between two surface elements i and j

(3){ϵ}_{i,\mathrm{\Delta }{\lambda }_k}{A}_i\mathrm{R}{\mathrm{D}}_{i,j,\mathrm{\Delta }{\lambda }_k}={ϵ}_{j,\mathrm{\Delta }{\lambda }_k}{A}_j\mathrm{R}{\mathrm{D}}_{j,i,\mathrm{\Delta }{\lambda }_k},\mathrm{1}\le i\le M,\mathrm{1}\le j\le M.

3) Combination of reciprocity and conservation of energy

(4){\displaystyle \sum _{j=\mathrm{1}}^M{ϵ}_j{A}_j\mathrm{R}{\mathrm{D}}_{j,i,\mathrm{\Delta }{\lambda }_k}}={ϵ}_{i,\mathrm{\Delta }{\lambda }_k}{A}_i,\mathrm{1}\le i\le M,

where ϵ and A are the emissivity and area of the surface, respectively.

As shown in Fig. 1, the radiation flux on the cavity aperture (surface 3) of the receiver/reactor, q_ca, can be calculated by

(5)q_{\mathrm{c}\mathrm{a}}={\displaystyle \frac{A_{\mathrm{1}}}{A_{\mathrm{3}}}}{\displaystyle \sum _{k=\mathrm{1}}^{M_{\mathrm{b}}}\mathrm{R}{\mathrm{D}}_{1,3,\mathrm{\Delta }{\lambda }_k}}{E}_{\mathrm{s}\mathrm{u}\mathrm{n},\mathrm{\Delta }{\lambda }_k},

where RD_1,3,Δλk refers to the fraction of the emissive power of imaginary emission surface (surface 1) that is reflected by the solar concentrator and finally arrives at the cavity aperture (surface 3), A₁ is the area of the imaginary emission surface, A₃ is the area of the cavity aperture, and E_sun,Δλk is the Sun average spectral irradiance in the spectral band Δλ_k.

The wall radiation flux of the cavity receiver (surface 4) can be obtained by

(6)q_{\mathrm{c}\mathrm{r},i}={\displaystyle \frac{A_{\mathrm{1}}}{A_{\mathrm{4}i}}}{\displaystyle \sum _{k=\mathrm{1}}^{M_{\mathrm{b}}}\mathrm{R}{\mathrm{D}}_{1,4i,\mathrm{\Delta }{\lambda }_k}{E}_{\mathrm{s}\mathrm{u}\mathrm{n}\mathrm{\Delta }{\lambda }_k},}

where q_cr,i is the wall radiation flux of the i th surface element of the cavity receiver (surface 4), and A_4i is the corresponding area.

A computer code based on the preceding calculation procedure is written. A number of ray-sampling studies are also performed for the physical model to ensure that the essential physics is independent of the ray-sampling number. For the numerical study in this paper, the number density of energy bundles is equal to 20 W/mm² [15].

Numerical simulation of radiation characteristics

To examine the correctness of the code, the same cases (f=1 m, ϕ_rim=45°, 60°), as given in Ref. [1] and Ref. [6], are calculated, and the results are compared with those obtained by Johnston [1] using COMPREC code and Jeter [6] using analytical calculations. As can be seen in Fig. 2, they are in good agreement.

According to the geometry relations, the radius of the focal spot (

r_{\mathrm{f}\mathrm{o}\mathrm{c}}^{\mathrm{a}\mathrm{s}}

) of ideal paraboloidal dish concentrator (in view of a hat-top distribution sunshape) can be deduced as

(7)r_{\mathrm{f}\mathrm{o}\mathrm{c}}^{\mathrm{a}\mathrm{s}}={\displaystyle \frac{f\times {\theta }_{\mathrm{p}\mathrm{a}\mathrm{r}}}{\cos {\phi }_{\mathrm{r}\mathrm{i}\mathrm{m}}(\mathrm{1}+\cos {\phi }_{\mathrm{r}\mathrm{i}\mathrm{m}})}},

where θ_par denotes the solar disk angle in the annular circumsolar region, f and ϕ_rim are the focal length and the rim angle of the paraboloidal concentrator, respectively.

Table 1 shows a comparison between the numerical (r^ns_foc) and analytic solution (r^as_foc) of the radius of focal spot whose size increases with the rim angle when the focal length is the same, and it also increases with the focal length when the rim angle is the same. It is found that all the simulation solutions are in good agreement with the analytic solutions, only with a maximum relative error of 0.172% for f=1.5 m and ϕ_rim=45°, 60°.

With regard to the solar cavity receiver, the shape can be selected to capture the solar energy effectively while accommodating the unusually challenging conditions with the smallest possible size. Six classical cavity receivers (cylindrical, dome, heteroconical, elliptical, spherical, and conical) are chosen to simulate radiation characteristics, as shown in Fig. 3. The walls of those receivers are assumed to be black, while the reflection and the emission are assumed to be diffuse.

Figure 4 shows the radiative flux distribution with the focal length of 3 m, the rim angle of 45°, the surface slope error of 3.5 mrad, and the concentrator reflectivity of 0.9. It can be seen that there is an approximately Gaussian shape distribution with the peak value close to 13.5 W/mm² and a small extent of 23-mm-radius circle for 90% of flux capture.

Figure 5 shows the wall flux distributions of six cavity receivers. It is seen that the nonuniformity in the radiative heat flux distribution at the wall is generated for those receivers. The sunshape and surface slope error can lead to a decrease in the nonuniformity [15], but it is at the expense of concentrated radiative energy.

Based on the radiation attributes (including quantity and spatial characteristic) of focal flux, a new shape (called “upside-down tear drop”) of cavity receiver has been developed in order to provide an almost uniform radiation flux field in the cavity receiver / reactor [15]. The dimensionless radiation flux distributions for three different cavity receivers are studied, as shown in Fig. 6. It is seen obviously that the uniformity of flux in the conical receiver is the worst, but the uniformity of flux in the “upside-down tear drop” receiver is the best. As it can also be seen in Fig. 6 that for the “upside-down tear drop” receiver, the flux intensity has a sharp gradient at R=R_max and a zero value at the bottom wall (R<R_max). The main reason for this is that only the incident radiation is considered in the present study.

A measurement system for focal flux of a dish concentrator

Figure 7 shows the schematic layout of the measurement system that is first developed by Dr. Liu [16]. The design assignments include the structures of the concentrator and Lambert target, and the whole frame of measuring system that consists of a CCD camera and a neutral density (ND) filter. The CCD camera is CASIO EX-Z1000 module with a pixel of 3648×2736. Figure 8 shows the actual picture of the concentrator in this measurement system, which has a focal of 0.462 m and an aperture area of 4.52 m². The dish concentrator consists of 832 isosceles trapezoid mirror panels with the thickness of 2 mm mounted on a television satellite antenna frame dish structure. The focal spot is projected onto a circular iron target, 0.2 m in diameter, mounted onto a movable slide that allows motion of the target in the focal region along a direction parallel to the axis of the dish, as shown in Fig. 9. The front surface of the target is spray painted with a white and matt finish high-temperature paint to create an approximately Lambert reflecting surface.

In order to investigate the spectral selectivity of reflective mirrors, the UV-3101PC (from Shimadzu Corporation, Japan) is used to measure the spectral reflectance of the glass in the experiment system, as shown in Fig. 10. Table 2 shows the nine approximation parameters of spectral reflectivity of glass. The effect of the reflectivity on the concentration ratio is presented in Fig. 11. The spectral selectivity of the reflective mirror makes a big difference on the concentration ratio, which increases with the rim angle of the concentrator.

While 0.462 m is the nominal focal point of the dish concentrator, a series of flux measurements are performed for the Lambert target placements at distances of 0.397 to 0.467 m from the dish vertex, in 1 cm increments. Figure 12 shows the flux image by the CCD camera with the distances of 0.397 and 0.447 m from the dish vertex. Figure 13 shows the corresponding infrared thermal image in the Lambert target. The flux intensity of the focal spot with a distance of 0.397 m is stronger than one with a distance of 0.447 m. Furthermore, the temperature of the focal spot in the Lambert target is 45 degrees Celsius lower than the corresponding temperature for the distance of 0.447 m, but the focal spot size of the latter is much bigger than the former.

As can be seen in Fig. 14, these measurements indicate that a distribution with the highest peak flux and minimum extent occurs at the distance of 0.447 m. Figure 14(b) also shows that the flux field exhibits a flat-topped non-Gaussian type of distribution that comes from the contributions of the flat mirror panels of the dish. The experiments show that the focal spot size and the peak flux density decrease when the target is far away from the focal point along the symmetry axis of the dish, and the flux distributions are getting more and more irregular.

The abovementioned method is used to compare the experiment results with numerical calculations. Figures 15 and 16 show the results of these comparisons for the dish with a focal length of 0.462 m and an aperture diameter of 1.2 m. In order to compare the spread of the two distributions, the Monte Carlo ray-traced distribution shown in Fig .15 is reduced to match the peak intensity of the measured distribution by adjusting error parameters. The maximum error of the focal spot size is 15% when the distance of the target placement from the dish vertex is 0.437 m, as shown in Fig. 16. The distribution of the experiment is broadened in the base region due to systematic errors [16], such as nonlinear error of the CCD camera, non-Lambert properties of the target, calibration error, etc.

Conclusion

Radiation performance of a dish solar concentrator/cavity receiver system is studied using Monte Carlo ray-tracing method based on the radiative exchange factor. Good agreement is observed between numerical results of the present Monte Carlo method and the published data.

Different cavity geometries are evaluated on the uniformity of wall radiation flux. The results indicate that cavity geometry has a significant effect on overall flux distribution. The “upside-down tear drop” cavity receiver with an almost uniform radiation flux distribution can provide qualitative guidelines for the cavity receiver design.

A measurement system for flux distributions in the focal regions of solar concentrating devices using CCD imaging cameras and neutral density (ND) filter is developed. The spot distribution contours on the focal plane and defocused planes of the concentrator are obtained, and numerical results obtained are in good agreement with the experiment data. The use of photogrammetry proves itself to be a valuable aid to concentrator analysis and design.

References

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