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Computational design for a wide-angle cermet-based solar selective absorber for high temperature applications
Journal of Quantitative Spectroscopy & Radiative Transfer 132 (2014) 80–89
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Journal of Quantitative Spectroscopy & Radiative Transfer journal homepage: www.elsevier.com/locate/jqsrt
Computational design for a wide-angle cermet-based solar selective absorber for high temperature applications Atsushi Sakurai a,n, Hiroya Tanikawa b, Makoto Yamada a a b
Department of Mechanical and Production Engineering, Niigata University, 8050, Ikarashi 2-no-cho, Niigata-city 950-2181, Japan Graduate School of Science and Technology, Niigata University, 8050, Ikarashi 2-no-cho, Niigata-city 950-2181, Japan
a r t i c l e in f o
abstract
Article history: Received 7 September 2012 Received in revised form 29 January 2013 Accepted 11 March 2013 Available online 26 March 2013
The purpose of this study is to computationally design a wide-angle cermet-based solar selective absorber for high temperature applications by using a characteristic matrix method and a genetic algorithm. The present study investigates a solar selective absorber with tungsten–silica (W–SiO2) cermet. Multilayer structures of 1, 2, 3, and 4 layers and a wide range of metal volume fractions are optimized. The predicted radiative properties show good solar performance, i.e., thermal emittances, especially beyond 2 μm, are quite low, in contrast, solar absorptance levels are successfully high with wide angular range, so that solar photons are effectively absorbed and infrared radiative heat loss can be decreased. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Solar selective absorber Radiative properties Genetic algorithm Optimization Cermet Multilayer
1. Introduction After the Fukushima nuclear accident on March 11, 2011, there is a growing need for renewable energy now more than ever before. Solar energy resources are capable of providing sustainable and safe energy to us and future generations. Solar thermal power, solar thermophotovoltaics, and solar thermoelectrics are of special interest because solar energy is a potentially large-scale energy resource and it can be converted into electricity with high efficiency. Solar selective absorbers can play an important role for improving power generation efficiency [1]. A solar selective absorber is an artificial material that has the ability to absorb sunlight efficiently with low levels of thermal emission. Fig. 1 shows the spectral energy distribution of solar energy and blackbody radiation. As the temperature of the absorber rises, the blackbody emission power significantly increases, resulting in large radiative heat loss from the absorber. Therefore, an ideal solar selective absorber should have high
n
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solar absorptance and low thermal emittance, and the ideal cutoff wavelength should be around 2.0 μm. Recent studies have proposed several types of solar selective absorber/emitter coating such as multilayer [2], photonic crystal [3–6], and metal/metal-oxide - dielectric composite [7,8]. Among these, a ceramic-metal composite called cermet is considered to have the potential for use in solar energy applications by mass production [9]. Zhang [10] proposed a double cermet film structure of Mo–Al2O3, Cu–SiO2, and AlN, and experimentally and numerically presented good solar performance. Previous research on cermet-based absorbers has focused on mid-temperature applications [11], but high-temperature applications beyond 1000 K have not been well-explored. Tungsten is a natural choice for high temperature applications because of its high melting point, and hence, the present study investigates a solar selective absorber with tungsten–silica (W–SiO2) cermet. Chester et al. [12] demonstrated the good performance of W–SiO2 cermet absorbers by using freely available computational electromagnetics software and the global optimization technique. Furthermore, their computational results were limited for the case of normal incidence that may be acceptable in low solar
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Fig. 1. Ideal reflectance of solar selective absorber for blackbody emissive power and solar energy.
concentration; however it is more realistic when we consider that the oblique solar light irradiates absorbers. The objective of this study is to optimize wide-angle cermet-based solar selective absorbers for and high temperature applications by using a different computational approach. We employ a characteristic matrix method [13] for solving the electromagnetics and a genetic algorithm for optimization. Effects of operating temperature, metal volume fraction and thickness of layers are investigated in order to show a valuable guidance for understanding and designing of solar selective absorbers. 2. Problem statement Fig. 2 shows a schematic of the solar selective absorber with cermet. The structure consists of an anti-reflection (AR) coating, wavelength selective cermet layers, and a highly reflective back layer. The silica (SiO2) is chosen for the AR coating due to the low refractive index. The first layer of cermet from the top is called “Cermet 1”, and the second layer is called “Cermet 2”. The geometric thicknesses of the cermet layers and the AR coating were varied in the range 20–100 nm. In addition, the metal volume fraction was varied in the range of 0.1–0.7. We assume that metal particles are distributed randomly inside ceramic. The infrared reflective back layer is tungsten having the thickness of 300 nm. Here, the solar zenith angle θ is set to 0 for normal incidence, and the other θ is for oblique incidence. There are many possibilities for evaluating the volume fractions of the metal-ceramic composites, layer thicknesses, and number of layers. Therefore, a numerical approach is required when considering the optimum design of a selective solar absorber. 3. Computational method 3.1. Electromagnetic calculation The radiative properties of nano/micro-scale materials depend not only on the properties of the materials but also on their electromagnetic behavior. To consider the electromagnetic effect, the amplitude and the phase of the electric field must be calculated, i.e., the Maxwell equation should be solved. Many computational tools have been
Fig. 2. Schematic of cermet-based solar selective absorber.
proposed to solve the Maxwell equation. Among these, rigorous coupled-wave analysis [14] and finite difference time domain [15] are popular solution method because these are computationally effective and robust for dealing with complicated 3D geometry. Since a 1D multilayer structure is relatively simple, this study employs the characteristic matrix method, which is often referred to as thin-film optics [13]. This method is computationally efficient for modeling the optical properties of multilayer structures. We developed in-house code for the characteristic matrix method using MATLAB [16]. A brief introduction to the method follows. The medium in each layer is assumed to be isotropic and homogenous with a spectrally dependent complex relative permittivity. A multilayer absorber consists of a number of interfaces between various media. When the boundary conditions of electromagnetic wave propagation are applied for each interface, the characteristic matrix of q layers is described as #)" # ( q " 1 cosδr ðisinδr Þ=Y r B ¼ ∏ ð1Þ Ys cosδr C r ¼ 1 iY r sinδr where B and C are the normalized electric and magnetic fields at the front interface. The phase factor of the positivegoing wave and the negative-going wave will be multiplied by exp(iδ) and exp(−iδ) for the tangential components of the electric and magnetic fields, respectively. δ is defined as δr ¼
2πNr dr cosyr λ
ð2Þ
where Nr is the refractive index of the r-th layer, dr is the thickness of r-th layer, yr is the angle obtained from Snell’s law, and λ is the wavelength. Note that this calculation can deal with a solid angle dependent problem. Optical admittance Yr is given by Y r ¼ Y 0 Nr cosθr ; For TE wave Yr ¼
Y 0 Nr ; For TM wave cosθr
ð3Þ
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where Y0 is the optical admittance in free space. Ys, the optical admittance in the substrate, is given by Y s ¼ Y 0 Ns cosθs ; For TE wave
Ys ¼
Y 0 Ns ; For TM wave cosθs
ð4Þ
Reflectance of a multilayer absorber can be calculated by solving Eq. (1). When the characteristic matrices, B and C, are derived by a numerical procedure, the reflectance is given by Y 0 B−C Y 0 B−C n ð5Þ R¼ Y 0B þ C Y0B þ C where ( )n indicates a complex conjugate. If the refractive indices of the cermet, metal, and ceramic are known, one can calculate the reflectance, and then solar absorptance and thermal emittance. The refractive indices of dielectrics can be modeled by a constant refractive index over the full spectrum. Metals can be modeled by the Lorentz–Drude model [17] matching the reference data [18]. The refractive indices of cermet materials can be modeled by the effective medium theory [19]. The Maxwell–Garnett model [20] is known to be a successful approximation for smaller metal volume fractions, but it fails for fractions beyond 0.4. In contrast, the Bruggeman model [21] is relatively accurate over a wide range of metal volume fractions. For identical spherical metal particles immersed in a ceramic, the average dielectric function ζBR of a cermet is given by the Bruggeman approximation: fv
ζ m −ζ BR ζ −ζ BR þð1−f v Þ d ¼0 BR ζ m þ2ζ ζ d þ2ζ BR
ð6Þ
where ζm and ζd are the dielectric functions of the metal and ceramic, respectively, and fv is the volume fraction of metal. For calculation of the thermal emittance of a selective surface, the temperature dependence of the complex refractive indices of the metals should be considered. To model the temperature dependence of a metal, we use a dielectric function given by the Lorentz–Drude model modifying the electron collision frequency [22]. Chester et al. [12] recommended the use of a semi-empirical model to match experimental observations over a wide temperature range, and we have also confirmed the modified Lorentz–Drude model can precisely predict the spectral emissivity of tungsten with measurements by Roberts [23]. As for SiO2, it was shown that the extinction coefficient in the infrared region can be neglected compared with the extinction coefficient of the tungsten, and hence, the refractive index is set to 1.5 for the full spectrum [24]. Solar absorptance and thermal emittance are commonly quoted parameters of the performance of solar selective absorbers [10]. The spectrally averaged hemispherical solar absorptance α and thermal emittance ε are defined by α¼
2π
R π=2 R ∞ 0
0
f1−Rðθ,λÞgI sol ðλÞcosθsinθdλdθ R∞ π 0 I sol ðλÞdλ
ε¼
2π
R π=2 R ∞ 0
0
f1−Rðθ,λÞgI b ðT,λÞcosθsinθdλdθ R∞ π 0 I b ðT,λÞdλ
ð8Þ
where Isol(λ) is the spectral solar radiance (air mass of 1.5) [25], and Ib(T,λ) is the spectral blackbody radiative intensity. The following photo-thermal conversion efficiency is used as the figure of merit (FOM): ηFOM ¼ Bα−
εsT 4 CI
ð9Þ
where s, T, C, and I are the Stefan–Boltzmann constant, the operating temperature, the solar concentration, and the solar flux intensity, respectively. B is related to the transmittance of glass envelope, and is typically chosen to be 0.91 [9]. In this study, the computational conditions were as follows: operating temperature of 1000 K, solar concentration of 100 suns, and solar flux intensity of 863 W/m2. 3.2. Optimization by genetic algorithm Next, we explain the optimization design of the solar selective absorber. In the design process of a multilayer cermet absorber, there are many approaches to optimize the appropriate thicknesses of the layers and the volume fraction of the metal. A genetic algorithm (GA) is a wellknown optimization tool for multilayer design [26,27]. A GA is a method for solving optimization problems that is based on natural process of biological evolution [28]. The GA imitates a code string of DNA, i.e., each individual is assigned the parameters of the layer thicknesses and the metal volume fractions as a code string. Fig. 3 shows the flowchart of the present optimization procedure. The major procedure of the GA is as follows: (1) Generate 20 initial population of structures having various code strings, i.e., thicknesses of layers and volume fractions.
ð7Þ Fig. 3. Flowchart of the present GA.
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(2) Evaluate the FOM, as shown in Eq. (9), of each structures by the characteristic matrix method. (3) Select elite a pair of structures for mating. (4) In the crossover and mutation operations, the code strings are randomly and partially exchanged, resulting in producing new offspring. (5) Based on the new code strings, the current structures are replaced with the new population. (6) Check the termination criterion, and finding the best structure. In the present calculation, the GA developed 400 generations; we confirmed that convergence was successfully ensured. The geometric thicknesses of the cermet layers and the AR coating were varied in the range 20–100 nm. In addition, the metal volume fraction was varied in the range of 0.1–0.7. We employed the GA software involved in the commercially available MATLAB optimization toolbox [16], that is capable of finding the maximum of the FOM. Obtained optimization results were re-confirmed using other algorithm such as the constrained nonlinear optimization by trust region algorithm involved in the above toolbox, and then their differences were within 0.2%.
4. Validating test The present characteristic matrix method is validated via comparison with the existing results from the literature. Esposito et al. [29] reported the fabrication and characterization of a Mo–SiO2 cermet-based solar selective coating. They evaluated the refractive index and the extinction coefficient of the cermet by ellipsometric measurement. Thus, we can check the validity of our code with completely experimental results. Table 1 presents the recipe of the Mo–SiO2 cermet-based solar selective coating. Fig. 4 shows a comparison between the calculated and measured reflectances. The reflectance of the present simulation shows excellent agreement with that of the experimental measurements. Next, the present characteristic matrix method with the predicted dielectric functions is validated by comparing it with the previous work on W–SiO2 cermet-based solar selective coating [12]. Table 2 presents the recipe of the double layer W–SiO2 cermet-based solar selective coating. Fig. 5 shows a comparison between the present reflectance results and the reflectance in the reference data. The present result shows good agreement with the results in reference data. Although both the results are obtained by calculation, we confirmed that our simulation code, comprising the characteristic matrix method and the Table 1 Recipe of the Mo–SiO2 cermet-based solar selective absorber. Layer
Material
Volume fraction
Thickness (nm)
AR coating Cermet 1 Cermet 2 Reflective back
SiO2 (n¼ 1.50) Mo–SiO2 Mo–SiO2 Mo
0.0 0.3 0.5 1.0
50 30 35 500
Fig. 4. Comparison between the calculated and measured reflectance. Table 2 Recipe of the W–SiO2 cermet-based solar selective absorber. Layer
Material
Volume fraction
Thickness (nm)
AR coating Cermet 1 Cermet 2 Reflective back
SiO2 (n ¼1.24) W–SiO2 W–SiO2 W
0.0 0.1751 0.4939 1.0
96.3 68.3 54.4 300
Fig. 5. Comparison between the present reflectance result and the reflectance in the reference data.
optical properties modeling, works well for appropriate prediction of cermet-based solar selective absorbers. 5. Results and discussion 5.1. Effect of metal volume fraction and thickness of layers Fig. 6 shows a contour plot of the spectral averaged solar absorptance, the spectral averaged thermal emittance and the FOM for a 2 layer cermet-based selective absorber as a function of metal volume fraction at 1000 K. The left-hand side of column indicates the result of normal incidence and the right-hand side of column
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indicates the result of oblique incidence with the other parameters set identical to the selective absorber given in Fig. 10. For the normal and hemispherical solar absorptance, the maximum area can be found in the range of 0.2–0.3 for the first cermet layer and the range of 0.4–0.5
for the second layer. If a metal volume fraction of the first cermet layer is high, a reflected light is increased so that the solar absorptance becomes low. The maximum value of normal solar absorptance is higher than that of hemispherical solar absorptance due to the directional
Fig. 6. Effect of metal volume fraction for a 2 layer cermet-based selective absorber: (a) spectral averaged solar absorptance (Normal and Hemispherical solar absorptance), (b) spectral averaged thermal emittance (FOM with normal and oblique incidence) and (c) FOM. Left-hand side of column indicates a normal incidence and right-hand side of column indicates an oblique incidence.
A. Sakurai et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 132 (2014) 80–89
dependence. For the normal and hemispherical thermal emittance, the maximum are can be found in the range of 0.3–0.4 for both layers. Tungsten itself is a good reflector for infrared light, however the cermet layers act as an AR coating for this situation. Therefore, the maximum values
85
of the FOM with normal and oblique incidences are located avoiding the area of high thermal emittance. Fig. 7 shows a contour plot of the spectral averaged solar absorptance, the spectral averaged thermal emittance and the FOM for a 2 layer cermet-based selective
Fig. 7. Effect of layer thickness for a 2 layer cermet-based selective absorber: (a) spectral averaged solar absorptance (Normal and Hemispherical solar absorptance), (b) spectral averaged thermal emittance (Normal and Hemispherical thermal absorptance) and (c) FOM. Left-hand side of column indicates a normal incidence and right-hand side of column indicates an oblique incidence.
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absorber as a function of layer thickness at 1000 K, and the other parameters are identical to Fig. 10 as well. The normal and hemispherical solar absorptance and thermal emittance increase as thickness of cermet layer increase. For a thermal emittance, the interference effect tends to occur in thicker layers due to the long wavelength of light. The maximum values of the FOM can be found in the range of 40–60 nm of each cermet layers, and the FOM with normal incidence is higher than that with hemispherical one due to the directional dependence.
5.2. Optimization of W–SiO2 cermet-based selective absorber Fig. 8(a) shows the optimized normal reflectance with varying numbers of layers at 1000 K and Fig. 8(b) shows the corresponding metal volume fraction in AR coating and cermet layers. In addition, the FOM, the solar absorptance, and the thermal emittance are listed in Table 3. All results show good solar performance. The thermal emittance values, especially beyond 2 μm, are quite low because of the tungsten infrared reflector. In contrast, the solar absorptances are successfully high, and thus, the solar photons are effectively absorbed by the cermet and by phase interference.
The performance of a solar selective absorber was a solar absorptance value of 0.9556, thermal emittance of 0.1573, and an FOM of 0.7663 with the double-layered cermet-based absorber. However, the results of the cermets with three and four layers were very similar to those of the doublelayered cermet. The FOM of the single-layered cermet was relatively smaller than that of others. It is difficult to directly compare our results with those from previous studies [12] because we used a different refractive index and calculation code in this study. Such comparison is not our purpose, but the previously reported values were a solar absorptance of 0.945 and a thermal emittance of 0.172. Thus, our GA results also show good solar performance. 5.3. Angular dependence of W–SiO2 cermet-based solar selective absorber In Fig. 9, the directional dependence of the reflectance for 2-layer W–SiO2 cermet-based solar selective absorber is shown at 1000 K. The identical parameters are set to Fig. 8 for the case of normal incidence, then the incident angle is changed from 0 to 901. Fig. 10(a) shows the comparison between the optimized normal and hemispherical reflectance with 2 layer cermet-based selective absorber and Fig. 10(b) shows the corresponding metal volume fraction in AR coating and cermet layers. In addition, the FOM, the solar absorptance, and the thermal emittance are listed in Table 4. Since the largely oblique incident light cannot be absorbed effectively for a visible light in the cermet layers as shown in Fig. 9, the hemispherical reflectance for visible range is slightly higher
Table 3 Normal solar absorptance, thermal emittance, and FOM with varying number of cermet layers.
Fig. 8. W–SiO2 selective absorber at 1000 K: (a) optimized normal reflectance for 1–4 layer structures and (b) corresponding metal volume fraction in AR coating and cermet layers.
No. layers
Solar absorptance
Thermal emittance
FOM
1 2 3 4
0.9344 0.9556 0.9556 0.9559
0.1684 0.1573 0.1572 0.1576
0.7397 0.7663 0.7663 0.7664
Fig. 9. Spectral directional reflectance of W–SiO2 2 layer cermet-based selective absorber at 1000 K.
A. Sakurai et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 132 (2014) 80–89
Fig. 10. Comparison between (a) the optimized normal and hemispherical reflectance with 2 layer cermet-based selective absorber and (b) corresponding metal volume fraction in AR coating and cermet layers.
Table 4 Normal and hemispherical solar absorptance, thermal emittance, and FOM.
Normal Hemispherical
Solar absorptance
Thermal emittance
FOM
0.9556 0.9073
0.1573 0.1646
0.7663 0.7175
than the normal reflectance. Even though there is a limitation for a solar absorption, the optimized structure show good spectral selectivity over a wide angular range, and would therefore be good candidate for solar thermal applications. 5.4. Comparison with the Ni–SiO2 cermet-based solar selective absorber Nickel is a candidate metal that had been used for the cermet-based solar selective absorber [11]. Here, the solar performance is compared between the Ni–SiO2 and W–SiO2 cermet-based solar selective absorber. The refractive index of Ni–SiO2 cermet can be obtained by the same manner with W–SiO2 cermet as described in Section 3.1. Fig. 11(a) shows the comparison between the optimized normal reflectance
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Fig. 11. Comparison between (a) the optimized normal reflectance with 2 layer W–SiO2 and Ni–SiO2 cermet-based selective absorber and (b) corresponding metal volume fraction in AR coating and cermet layers.
Table 5 Comparison of materials of solar absorptance, thermal emittance, and FOM. Cermet
Solar absorptance
Thermal emittance
FOM
W–SiO2 Ni–SiO2
0.9556 0.9580
0.1573 0.1962
0.7663 0.7429
with 2 layer W–SiO2 and Ni–SiO2 cermet-based selective absorber and Fig. 11(b) shows the corresponding metal volume fraction in AR coating and cermet layers. In addition, the FOM, the solar absorptance, and the thermal emittance are listed in Table 5. The solar absorptance of W–SiO2 and Ni–SiO2 cermet-based selective absorber shows successfully low value, on the other hand, the thermal emittance of Ni–SiO2 selective absorber is higher than that of W–SiO2. Tungsten itself has a higher reflectance for infrared range compared with nickel, therefore W–SiO2 selective absorber shows good solar performance. In addition, the melting temperature of tungsten is very higher than the other metals.
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5.5. Effect of temperature of W–SiO2 cermet-based solar selective absorber The effect of operating temperature for W–SiO2 cermet-based selective absorber is investigated. Fig. 12(a) shows the optimized normal reflectance with varying temperature and Fig. 12(b) shows the corresponding metal volume fraction in AR coating and cermet layers. In addition, the FOM, the solar absorptance, and the thermal emittance are listed in Table 6. The temperature dependence of the refractive indices of W–SiO2 cermet can be obtained by the same manner as described in Section 3.1.
In Eq. (9), the operating temperature of 400 K, 700 K and 1000 K is assumed to be given by the solar concentration 1, 50 and 100 suns, respectively. As shown in Fig. 1, the peak of the blackbody emissive power is located at shorter wavelength as increasing temperature. Accordingly, the high reflectance region for infrared light shifts to the shorter wavelength at 1000 K. The thermal emittance increases as the operating temperature becomes high. The results indicate the optimized selective absorber shows good solar performance with wide range of operating temperature.
6. Conclusion This paper has described the computational design for a wide-angle and high-temperature cermet-based solar selective absorber by a characteristic matrix method and a genetic algorithm. Our conclusions are summarized as follows:
Fig. 12. Effect of operating temperature for W–SiO2 cermet-based selective absorber: (a) the optimized normal reflectance with varying temperature and (b) corresponding metal volume fraction in AR coating and cermet layers.
Table 6 Effect of temperature of solar absorptance, thermal emittance, and FOM. Temperature (K)
Solar absorptance
Thermal emittance
FOM
400 700 1000
0.9772 0.9805 0.9556
0.0370 0.1050 0.1573
0.8270 0.8591 0.7663
1. The present simulation model using a characteristic matrix method was validated by comparing it with existing results. In addition, we confirmed that our code, which uses optical properties modeling with the Bruggeman approximation, is suitable for predicting the radiative properties of cermet-based solar selective absorbers. 2. The effects of metal volume fraction and thickness of layers were investigated for designing of selective absorber. The local maximum area was found for the normal and hemispherical solar absorptance and thermal emittance. Especially, it was found that the metal volume fraction of the first cermet layer from the top should be low compared with that of the second layer for the enhancement of solar light absorption. 3. The structure design was optimized by using a genetic algorithm. The multilayer structures having 1, 2, 3, and 4 layers and a wide range of metal volume fractions were optimized. Consequently, the performance of a solar selective absorber was a solar absorptance of 0.9556, thermal emittance of 0.1573, and FOM of 0.7663, with a double-layered cermet-based absorber. However, the results of the cermets with three and four layers were very similar to those of the double-layered cermet. 4. The double layer tungsten-silica cermet-based selective absorber showed the good spectral selectivity over a wide angular range and a wide operating temperature range. Since tungsten itself is a good reflector for infrared light and has the high melting temperature compared with other metals, a tungsten–silica cermetbased solar selective absorber is a good candidate for high-temperature applications. In our future work, experimental demonstrations will be performed. The magnetron sputtering technology is suitable for fabricating multi-layer cermet-based solar selective absorbers. Spectroscopic measurement system will be utilized to evaluate the optical properties with wide angular range and wide temperature range.
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Journal of Quantitative Spectroscopy & Radiative Transfer journal homepage: www.elsevier.com/locate/jqsrt
Computational design for a wide-angle cermet-based solar selective absorber for high temperature applications Atsushi Sakurai a,n, Hiroya Tanikawa b, Makoto Yamada a a b
Department of Mechanical and Production Engineering, Niigata University, 8050, Ikarashi 2-no-cho, Niigata-city 950-2181, Japan Graduate School of Science and Technology, Niigata University, 8050, Ikarashi 2-no-cho, Niigata-city 950-2181, Japan
a r t i c l e in f o
abstract
Article history: Received 7 September 2012 Received in revised form 29 January 2013 Accepted 11 March 2013 Available online 26 March 2013
The purpose of this study is to computationally design a wide-angle cermet-based solar selective absorber for high temperature applications by using a characteristic matrix method and a genetic algorithm. The present study investigates a solar selective absorber with tungsten–silica (W–SiO2) cermet. Multilayer structures of 1, 2, 3, and 4 layers and a wide range of metal volume fractions are optimized. The predicted radiative properties show good solar performance, i.e., thermal emittances, especially beyond 2 μm, are quite low, in contrast, solar absorptance levels are successfully high with wide angular range, so that solar photons are effectively absorbed and infrared radiative heat loss can be decreased. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Solar selective absorber Radiative properties Genetic algorithm Optimization Cermet Multilayer
1. Introduction After the Fukushima nuclear accident on March 11, 2011, there is a growing need for renewable energy now more than ever before. Solar energy resources are capable of providing sustainable and safe energy to us and future generations. Solar thermal power, solar thermophotovoltaics, and solar thermoelectrics are of special interest because solar energy is a potentially large-scale energy resource and it can be converted into electricity with high efficiency. Solar selective absorbers can play an important role for improving power generation efficiency [1]. A solar selective absorber is an artificial material that has the ability to absorb sunlight efficiently with low levels of thermal emission. Fig. 1 shows the spectral energy distribution of solar energy and blackbody radiation. As the temperature of the absorber rises, the blackbody emission power significantly increases, resulting in large radiative heat loss from the absorber. Therefore, an ideal solar selective absorber should have high
n
Corresponding author. Tel.: þ 81 252 627 004. E-mail address: [email protected] (A. Sakurai).
0022-4073/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jqsrt.2013.03.004
solar absorptance and low thermal emittance, and the ideal cutoff wavelength should be around 2.0 μm. Recent studies have proposed several types of solar selective absorber/emitter coating such as multilayer [2], photonic crystal [3–6], and metal/metal-oxide - dielectric composite [7,8]. Among these, a ceramic-metal composite called cermet is considered to have the potential for use in solar energy applications by mass production [9]. Zhang [10] proposed a double cermet film structure of Mo–Al2O3, Cu–SiO2, and AlN, and experimentally and numerically presented good solar performance. Previous research on cermet-based absorbers has focused on mid-temperature applications [11], but high-temperature applications beyond 1000 K have not been well-explored. Tungsten is a natural choice for high temperature applications because of its high melting point, and hence, the present study investigates a solar selective absorber with tungsten–silica (W–SiO2) cermet. Chester et al. [12] demonstrated the good performance of W–SiO2 cermet absorbers by using freely available computational electromagnetics software and the global optimization technique. Furthermore, their computational results were limited for the case of normal incidence that may be acceptable in low solar
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Fig. 1. Ideal reflectance of solar selective absorber for blackbody emissive power and solar energy.
concentration; however it is more realistic when we consider that the oblique solar light irradiates absorbers. The objective of this study is to optimize wide-angle cermet-based solar selective absorbers for and high temperature applications by using a different computational approach. We employ a characteristic matrix method [13] for solving the electromagnetics and a genetic algorithm for optimization. Effects of operating temperature, metal volume fraction and thickness of layers are investigated in order to show a valuable guidance for understanding and designing of solar selective absorbers. 2. Problem statement Fig. 2 shows a schematic of the solar selective absorber with cermet. The structure consists of an anti-reflection (AR) coating, wavelength selective cermet layers, and a highly reflective back layer. The silica (SiO2) is chosen for the AR coating due to the low refractive index. The first layer of cermet from the top is called “Cermet 1”, and the second layer is called “Cermet 2”. The geometric thicknesses of the cermet layers and the AR coating were varied in the range 20–100 nm. In addition, the metal volume fraction was varied in the range of 0.1–0.7. We assume that metal particles are distributed randomly inside ceramic. The infrared reflective back layer is tungsten having the thickness of 300 nm. Here, the solar zenith angle θ is set to 0 for normal incidence, and the other θ is for oblique incidence. There are many possibilities for evaluating the volume fractions of the metal-ceramic composites, layer thicknesses, and number of layers. Therefore, a numerical approach is required when considering the optimum design of a selective solar absorber. 3. Computational method 3.1. Electromagnetic calculation The radiative properties of nano/micro-scale materials depend not only on the properties of the materials but also on their electromagnetic behavior. To consider the electromagnetic effect, the amplitude and the phase of the electric field must be calculated, i.e., the Maxwell equation should be solved. Many computational tools have been
Fig. 2. Schematic of cermet-based solar selective absorber.
proposed to solve the Maxwell equation. Among these, rigorous coupled-wave analysis [14] and finite difference time domain [15] are popular solution method because these are computationally effective and robust for dealing with complicated 3D geometry. Since a 1D multilayer structure is relatively simple, this study employs the characteristic matrix method, which is often referred to as thin-film optics [13]. This method is computationally efficient for modeling the optical properties of multilayer structures. We developed in-house code for the characteristic matrix method using MATLAB [16]. A brief introduction to the method follows. The medium in each layer is assumed to be isotropic and homogenous with a spectrally dependent complex relative permittivity. A multilayer absorber consists of a number of interfaces between various media. When the boundary conditions of electromagnetic wave propagation are applied for each interface, the characteristic matrix of q layers is described as #)" # ( q " 1 cosδr ðisinδr Þ=Y r B ¼ ∏ ð1Þ Ys cosδr C r ¼ 1 iY r sinδr where B and C are the normalized electric and magnetic fields at the front interface. The phase factor of the positivegoing wave and the negative-going wave will be multiplied by exp(iδ) and exp(−iδ) for the tangential components of the electric and magnetic fields, respectively. δ is defined as δr ¼
2πNr dr cosyr λ
ð2Þ
where Nr is the refractive index of the r-th layer, dr is the thickness of r-th layer, yr is the angle obtained from Snell’s law, and λ is the wavelength. Note that this calculation can deal with a solid angle dependent problem. Optical admittance Yr is given by Y r ¼ Y 0 Nr cosθr ; For TE wave Yr ¼
Y 0 Nr ; For TM wave cosθr
ð3Þ
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where Y0 is the optical admittance in free space. Ys, the optical admittance in the substrate, is given by Y s ¼ Y 0 Ns cosθs ; For TE wave
Ys ¼
Y 0 Ns ; For TM wave cosθs
ð4Þ
Reflectance of a multilayer absorber can be calculated by solving Eq. (1). When the characteristic matrices, B and C, are derived by a numerical procedure, the reflectance is given by Y 0 B−C Y 0 B−C n ð5Þ R¼ Y 0B þ C Y0B þ C where ( )n indicates a complex conjugate. If the refractive indices of the cermet, metal, and ceramic are known, one can calculate the reflectance, and then solar absorptance and thermal emittance. The refractive indices of dielectrics can be modeled by a constant refractive index over the full spectrum. Metals can be modeled by the Lorentz–Drude model [17] matching the reference data [18]. The refractive indices of cermet materials can be modeled by the effective medium theory [19]. The Maxwell–Garnett model [20] is known to be a successful approximation for smaller metal volume fractions, but it fails for fractions beyond 0.4. In contrast, the Bruggeman model [21] is relatively accurate over a wide range of metal volume fractions. For identical spherical metal particles immersed in a ceramic, the average dielectric function ζBR of a cermet is given by the Bruggeman approximation: fv
ζ m −ζ BR ζ −ζ BR þð1−f v Þ d ¼0 BR ζ m þ2ζ ζ d þ2ζ BR
ð6Þ
where ζm and ζd are the dielectric functions of the metal and ceramic, respectively, and fv is the volume fraction of metal. For calculation of the thermal emittance of a selective surface, the temperature dependence of the complex refractive indices of the metals should be considered. To model the temperature dependence of a metal, we use a dielectric function given by the Lorentz–Drude model modifying the electron collision frequency [22]. Chester et al. [12] recommended the use of a semi-empirical model to match experimental observations over a wide temperature range, and we have also confirmed the modified Lorentz–Drude model can precisely predict the spectral emissivity of tungsten with measurements by Roberts [23]. As for SiO2, it was shown that the extinction coefficient in the infrared region can be neglected compared with the extinction coefficient of the tungsten, and hence, the refractive index is set to 1.5 for the full spectrum [24]. Solar absorptance and thermal emittance are commonly quoted parameters of the performance of solar selective absorbers [10]. The spectrally averaged hemispherical solar absorptance α and thermal emittance ε are defined by α¼
2π
R π=2 R ∞ 0
0
f1−Rðθ,λÞgI sol ðλÞcosθsinθdλdθ R∞ π 0 I sol ðλÞdλ
ε¼
2π
R π=2 R ∞ 0
0
f1−Rðθ,λÞgI b ðT,λÞcosθsinθdλdθ R∞ π 0 I b ðT,λÞdλ
ð8Þ
where Isol(λ) is the spectral solar radiance (air mass of 1.5) [25], and Ib(T,λ) is the spectral blackbody radiative intensity. The following photo-thermal conversion efficiency is used as the figure of merit (FOM): ηFOM ¼ Bα−
εsT 4 CI
ð9Þ
where s, T, C, and I are the Stefan–Boltzmann constant, the operating temperature, the solar concentration, and the solar flux intensity, respectively. B is related to the transmittance of glass envelope, and is typically chosen to be 0.91 [9]. In this study, the computational conditions were as follows: operating temperature of 1000 K, solar concentration of 100 suns, and solar flux intensity of 863 W/m2. 3.2. Optimization by genetic algorithm Next, we explain the optimization design of the solar selective absorber. In the design process of a multilayer cermet absorber, there are many approaches to optimize the appropriate thicknesses of the layers and the volume fraction of the metal. A genetic algorithm (GA) is a wellknown optimization tool for multilayer design [26,27]. A GA is a method for solving optimization problems that is based on natural process of biological evolution [28]. The GA imitates a code string of DNA, i.e., each individual is assigned the parameters of the layer thicknesses and the metal volume fractions as a code string. Fig. 3 shows the flowchart of the present optimization procedure. The major procedure of the GA is as follows: (1) Generate 20 initial population of structures having various code strings, i.e., thicknesses of layers and volume fractions.
ð7Þ Fig. 3. Flowchart of the present GA.
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(2) Evaluate the FOM, as shown in Eq. (9), of each structures by the characteristic matrix method. (3) Select elite a pair of structures for mating. (4) In the crossover and mutation operations, the code strings are randomly and partially exchanged, resulting in producing new offspring. (5) Based on the new code strings, the current structures are replaced with the new population. (6) Check the termination criterion, and finding the best structure. In the present calculation, the GA developed 400 generations; we confirmed that convergence was successfully ensured. The geometric thicknesses of the cermet layers and the AR coating were varied in the range 20–100 nm. In addition, the metal volume fraction was varied in the range of 0.1–0.7. We employed the GA software involved in the commercially available MATLAB optimization toolbox [16], that is capable of finding the maximum of the FOM. Obtained optimization results were re-confirmed using other algorithm such as the constrained nonlinear optimization by trust region algorithm involved in the above toolbox, and then their differences were within 0.2%.
4. Validating test The present characteristic matrix method is validated via comparison with the existing results from the literature. Esposito et al. [29] reported the fabrication and characterization of a Mo–SiO2 cermet-based solar selective coating. They evaluated the refractive index and the extinction coefficient of the cermet by ellipsometric measurement. Thus, we can check the validity of our code with completely experimental results. Table 1 presents the recipe of the Mo–SiO2 cermet-based solar selective coating. Fig. 4 shows a comparison between the calculated and measured reflectances. The reflectance of the present simulation shows excellent agreement with that of the experimental measurements. Next, the present characteristic matrix method with the predicted dielectric functions is validated by comparing it with the previous work on W–SiO2 cermet-based solar selective coating [12]. Table 2 presents the recipe of the double layer W–SiO2 cermet-based solar selective coating. Fig. 5 shows a comparison between the present reflectance results and the reflectance in the reference data. The present result shows good agreement with the results in reference data. Although both the results are obtained by calculation, we confirmed that our simulation code, comprising the characteristic matrix method and the Table 1 Recipe of the Mo–SiO2 cermet-based solar selective absorber. Layer
Material
Volume fraction
Thickness (nm)
AR coating Cermet 1 Cermet 2 Reflective back
SiO2 (n¼ 1.50) Mo–SiO2 Mo–SiO2 Mo
0.0 0.3 0.5 1.0
50 30 35 500
Fig. 4. Comparison between the calculated and measured reflectance. Table 2 Recipe of the W–SiO2 cermet-based solar selective absorber. Layer
Material
Volume fraction
Thickness (nm)
AR coating Cermet 1 Cermet 2 Reflective back
SiO2 (n ¼1.24) W–SiO2 W–SiO2 W
0.0 0.1751 0.4939 1.0
96.3 68.3 54.4 300
Fig. 5. Comparison between the present reflectance result and the reflectance in the reference data.
optical properties modeling, works well for appropriate prediction of cermet-based solar selective absorbers. 5. Results and discussion 5.1. Effect of metal volume fraction and thickness of layers Fig. 6 shows a contour plot of the spectral averaged solar absorptance, the spectral averaged thermal emittance and the FOM for a 2 layer cermet-based selective absorber as a function of metal volume fraction at 1000 K. The left-hand side of column indicates the result of normal incidence and the right-hand side of column
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indicates the result of oblique incidence with the other parameters set identical to the selective absorber given in Fig. 10. For the normal and hemispherical solar absorptance, the maximum area can be found in the range of 0.2–0.3 for the first cermet layer and the range of 0.4–0.5
for the second layer. If a metal volume fraction of the first cermet layer is high, a reflected light is increased so that the solar absorptance becomes low. The maximum value of normal solar absorptance is higher than that of hemispherical solar absorptance due to the directional
Fig. 6. Effect of metal volume fraction for a 2 layer cermet-based selective absorber: (a) spectral averaged solar absorptance (Normal and Hemispherical solar absorptance), (b) spectral averaged thermal emittance (FOM with normal and oblique incidence) and (c) FOM. Left-hand side of column indicates a normal incidence and right-hand side of column indicates an oblique incidence.
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dependence. For the normal and hemispherical thermal emittance, the maximum are can be found in the range of 0.3–0.4 for both layers. Tungsten itself is a good reflector for infrared light, however the cermet layers act as an AR coating for this situation. Therefore, the maximum values
85
of the FOM with normal and oblique incidences are located avoiding the area of high thermal emittance. Fig. 7 shows a contour plot of the spectral averaged solar absorptance, the spectral averaged thermal emittance and the FOM for a 2 layer cermet-based selective
Fig. 7. Effect of layer thickness for a 2 layer cermet-based selective absorber: (a) spectral averaged solar absorptance (Normal and Hemispherical solar absorptance), (b) spectral averaged thermal emittance (Normal and Hemispherical thermal absorptance) and (c) FOM. Left-hand side of column indicates a normal incidence and right-hand side of column indicates an oblique incidence.
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absorber as a function of layer thickness at 1000 K, and the other parameters are identical to Fig. 10 as well. The normal and hemispherical solar absorptance and thermal emittance increase as thickness of cermet layer increase. For a thermal emittance, the interference effect tends to occur in thicker layers due to the long wavelength of light. The maximum values of the FOM can be found in the range of 40–60 nm of each cermet layers, and the FOM with normal incidence is higher than that with hemispherical one due to the directional dependence.
5.2. Optimization of W–SiO2 cermet-based selective absorber Fig. 8(a) shows the optimized normal reflectance with varying numbers of layers at 1000 K and Fig. 8(b) shows the corresponding metal volume fraction in AR coating and cermet layers. In addition, the FOM, the solar absorptance, and the thermal emittance are listed in Table 3. All results show good solar performance. The thermal emittance values, especially beyond 2 μm, are quite low because of the tungsten infrared reflector. In contrast, the solar absorptances are successfully high, and thus, the solar photons are effectively absorbed by the cermet and by phase interference.
The performance of a solar selective absorber was a solar absorptance value of 0.9556, thermal emittance of 0.1573, and an FOM of 0.7663 with the double-layered cermet-based absorber. However, the results of the cermets with three and four layers were very similar to those of the doublelayered cermet. The FOM of the single-layered cermet was relatively smaller than that of others. It is difficult to directly compare our results with those from previous studies [12] because we used a different refractive index and calculation code in this study. Such comparison is not our purpose, but the previously reported values were a solar absorptance of 0.945 and a thermal emittance of 0.172. Thus, our GA results also show good solar performance. 5.3. Angular dependence of W–SiO2 cermet-based solar selective absorber In Fig. 9, the directional dependence of the reflectance for 2-layer W–SiO2 cermet-based solar selective absorber is shown at 1000 K. The identical parameters are set to Fig. 8 for the case of normal incidence, then the incident angle is changed from 0 to 901. Fig. 10(a) shows the comparison between the optimized normal and hemispherical reflectance with 2 layer cermet-based selective absorber and Fig. 10(b) shows the corresponding metal volume fraction in AR coating and cermet layers. In addition, the FOM, the solar absorptance, and the thermal emittance are listed in Table 4. Since the largely oblique incident light cannot be absorbed effectively for a visible light in the cermet layers as shown in Fig. 9, the hemispherical reflectance for visible range is slightly higher
Table 3 Normal solar absorptance, thermal emittance, and FOM with varying number of cermet layers.
Fig. 8. W–SiO2 selective absorber at 1000 K: (a) optimized normal reflectance for 1–4 layer structures and (b) corresponding metal volume fraction in AR coating and cermet layers.
No. layers
Solar absorptance
Thermal emittance
FOM
1 2 3 4
0.9344 0.9556 0.9556 0.9559
0.1684 0.1573 0.1572 0.1576
0.7397 0.7663 0.7663 0.7664
Fig. 9. Spectral directional reflectance of W–SiO2 2 layer cermet-based selective absorber at 1000 K.
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Fig. 10. Comparison between (a) the optimized normal and hemispherical reflectance with 2 layer cermet-based selective absorber and (b) corresponding metal volume fraction in AR coating and cermet layers.
Table 4 Normal and hemispherical solar absorptance, thermal emittance, and FOM.
Normal Hemispherical
Solar absorptance
Thermal emittance
FOM
0.9556 0.9073
0.1573 0.1646
0.7663 0.7175
than the normal reflectance. Even though there is a limitation for a solar absorption, the optimized structure show good spectral selectivity over a wide angular range, and would therefore be good candidate for solar thermal applications. 5.4. Comparison with the Ni–SiO2 cermet-based solar selective absorber Nickel is a candidate metal that had been used for the cermet-based solar selective absorber [11]. Here, the solar performance is compared between the Ni–SiO2 and W–SiO2 cermet-based solar selective absorber. The refractive index of Ni–SiO2 cermet can be obtained by the same manner with W–SiO2 cermet as described in Section 3.1. Fig. 11(a) shows the comparison between the optimized normal reflectance
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Fig. 11. Comparison between (a) the optimized normal reflectance with 2 layer W–SiO2 and Ni–SiO2 cermet-based selective absorber and (b) corresponding metal volume fraction in AR coating and cermet layers.
Table 5 Comparison of materials of solar absorptance, thermal emittance, and FOM. Cermet
Solar absorptance
Thermal emittance
FOM
W–SiO2 Ni–SiO2
0.9556 0.9580
0.1573 0.1962
0.7663 0.7429
with 2 layer W–SiO2 and Ni–SiO2 cermet-based selective absorber and Fig. 11(b) shows the corresponding metal volume fraction in AR coating and cermet layers. In addition, the FOM, the solar absorptance, and the thermal emittance are listed in Table 5. The solar absorptance of W–SiO2 and Ni–SiO2 cermet-based selective absorber shows successfully low value, on the other hand, the thermal emittance of Ni–SiO2 selective absorber is higher than that of W–SiO2. Tungsten itself has a higher reflectance for infrared range compared with nickel, therefore W–SiO2 selective absorber shows good solar performance. In addition, the melting temperature of tungsten is very higher than the other metals.
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5.5. Effect of temperature of W–SiO2 cermet-based solar selective absorber The effect of operating temperature for W–SiO2 cermet-based selective absorber is investigated. Fig. 12(a) shows the optimized normal reflectance with varying temperature and Fig. 12(b) shows the corresponding metal volume fraction in AR coating and cermet layers. In addition, the FOM, the solar absorptance, and the thermal emittance are listed in Table 6. The temperature dependence of the refractive indices of W–SiO2 cermet can be obtained by the same manner as described in Section 3.1.
In Eq. (9), the operating temperature of 400 K, 700 K and 1000 K is assumed to be given by the solar concentration 1, 50 and 100 suns, respectively. As shown in Fig. 1, the peak of the blackbody emissive power is located at shorter wavelength as increasing temperature. Accordingly, the high reflectance region for infrared light shifts to the shorter wavelength at 1000 K. The thermal emittance increases as the operating temperature becomes high. The results indicate the optimized selective absorber shows good solar performance with wide range of operating temperature.
6. Conclusion This paper has described the computational design for a wide-angle and high-temperature cermet-based solar selective absorber by a characteristic matrix method and a genetic algorithm. Our conclusions are summarized as follows:
Fig. 12. Effect of operating temperature for W–SiO2 cermet-based selective absorber: (a) the optimized normal reflectance with varying temperature and (b) corresponding metal volume fraction in AR coating and cermet layers.
Table 6 Effect of temperature of solar absorptance, thermal emittance, and FOM. Temperature (K)
Solar absorptance
Thermal emittance
FOM
400 700 1000
0.9772 0.9805 0.9556
0.0370 0.1050 0.1573
0.8270 0.8591 0.7663
1. The present simulation model using a characteristic matrix method was validated by comparing it with existing results. In addition, we confirmed that our code, which uses optical properties modeling with the Bruggeman approximation, is suitable for predicting the radiative properties of cermet-based solar selective absorbers. 2. The effects of metal volume fraction and thickness of layers were investigated for designing of selective absorber. The local maximum area was found for the normal and hemispherical solar absorptance and thermal emittance. Especially, it was found that the metal volume fraction of the first cermet layer from the top should be low compared with that of the second layer for the enhancement of solar light absorption. 3. The structure design was optimized by using a genetic algorithm. The multilayer structures having 1, 2, 3, and 4 layers and a wide range of metal volume fractions were optimized. Consequently, the performance of a solar selective absorber was a solar absorptance of 0.9556, thermal emittance of 0.1573, and FOM of 0.7663, with a double-layered cermet-based absorber. However, the results of the cermets with three and four layers were very similar to those of the double-layered cermet. 4. The double layer tungsten-silica cermet-based selective absorber showed the good spectral selectivity over a wide angular range and a wide operating temperature range. Since tungsten itself is a good reflector for infrared light and has the high melting temperature compared with other metals, a tungsten–silica cermetbased solar selective absorber is a good candidate for high-temperature applications. In our future work, experimental demonstrations will be performed. The magnetron sputtering technology is suitable for fabricating multi-layer cermet-based solar selective absorbers. Spectroscopic measurement system will be utilized to evaluate the optical properties with wide angular range and wide temperature range.
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