Biomimetic hierarchical structure for enhancing concentrated solar energy converting and utilizing efficiency

Xinping Zhang; Xuhang Shi; Xuhang Shi; Yang Li; Fuqiang Wang; Fuqiang Wang; Bo Lin

doi:10.1364/OE.433119

1. Introduction

Energy shortage and environmental pollution are two major problems that need to be solved to realize sustainable development of human society, for which many explorations and studies have been carried out [1–7]. In recent decades, the issues of fossil fuel consumption and climate change have contributed to development of solar industrial technology solutions [8–13]. Concentrated solar technology can significantly enhance the solar energy density per unit area, which provides the possibility to utilize solar energy efficiently and convert it into electrical, thermal, and chemical forms through photovoltaic, photothermal, and photochemical technology [14–18]. In addition, concentrated solar technology can provide sufficient light intensity and temperature conditions for the photocatalytic reaction, thereby achieving high efficiency and high yield of the photocatalytic reaction [19]. Yet, concentrated solar technology also has some negative effects. For example, the problem of local overheating and inadequate light absorption of solar cells is prone to occur in concentrated photovoltaic systems [20,21], and the problem of insufficient diffusion of solar irradiation energy flow exists in the process of concentrated solar thermochemical and photocatalytic reactions [22,23]. In order to eliminate these adverse effects, a mass of studies have been conducted.

Researches show that one of the reasons for low photovoltaic conversion efficiency is the heat load [24]. Scholars have conducted a lot of researches to solve the problem of overheating and improve concentrated photovoltaic (CPV) conversion efficiency in order to save the expenditure per unit power generation. And a considerable part of these researches attempts to solve the overheating problem and improve photovoltaic conversion efficiency by regulating the structure of solar cells. However, these two goals seem difficult to achieve together. For example, PV cells are made ultra-thin and flexible in order that their temperature can be decreased [25], while the reduction of the thickness of PV cells can decrease the optical path length of light and lead to unsaturated light absorption and low conversion efficiency of PV cells [26]. Furthermore, although several approaches, such as grating, prism arrays, and nanoholes, have been proposed to increase the light absorption [27–31], they will also enhance carrier recombination and reduce the efficiency of solar cells [32,33]. Therefore, it is important to develop an efficient photon management strategy that can both solve the overheating problem and improve photovoltaic conversion efficiency, thereby enhancing the concentrated solar energy utilizing efficiency.

The insufficient diffusion of solar irradiation energy flow is another urgent problem to be solved in concentrated solar technology. Yu et al. [22] found that the concentrated solar energy flux followed Gaussian distribution model, and the solar irradiation was concentrated on the entrance of the receiver. In recent years, in order to improve the thermal performance of solar collectors in photothermal and solar thermochemical technology, porous materials have been employed in many studies. Saedodin et al. [15] applied porous metal foam to a flat plate collector and enhanced the maximum thermal efficiency up to 18.5%. Porous materials are a category of artificial materials with a three-dimensional network skeleton and porous material collectors have high contact surface area per solar irradiation unit and can control the fluid vortex in the channel [15,34]. Porous structures have also been utilized to enhance light absorption, charge separation efficiency, and eventually enhance the conversion efficiency of photo electrocatalytic technology by Prof. Zou [35] and Prof. Gratzel. [36] Yet, the strong absorption of porous structures will cause poor penetration of the incident solar irradiation [37], and the absorption of solar energy only occurs in the surface region where the radiation is received [23], so the thermochemical and photocatalytic reaction region is limited, resulting in low conversion efficiency. Thus, it is necessary to propose an alternative scheme to solve the above problem.

The biomimetic hierarchical structure might be a feasible alternative. Recently, hierarchical structures inspired by nature have been developed and applied in energy storage and conversion, catalysis, photocatalysis [38–41]. These hierarchical structures have two or more different pore sizes in the same host material, have the advantages of various kinds of porous structures, and own the advantages that single-pored structures do not have. According to the definition of the International Union of Pure and Applied Chemistry (IUPAC), the hierarchical structure was divided into micropores (< 2 nm), mesopores (2–50 nm), and large pores (> 50 nm) [42]. Nevertheless, in concentrated solar technology, this division is not quite reasonable, because the wavelength range of useful solar radiation ranges from several hundred nanometers to several micrometers, and the wavelength size is far beyond the size of the large pores mentioned above, so we need to redefine the size of large pores. In our previous work, the hierarchical structure was adopted to design solar high-temperature thermochemical reaction chambers and the conversion efficiency could be increased by up to 5.9% [43]. Yet, the size of the previous hierarchical structure was in the millimeter range and did not consider the effect of the hierarchical structure on radiation regulation.

Although a lot of researches have been conducted to apply hierarchical structure to energy conversion and utilization, the application of hierarchical structure to concentrated solar energy from the perspective of radiation regulation and photon management is rarely seen. In this study, inspired by the efficient photon management of hierarchical structure in leaf [44,45]. A biomimetic hierarchical structure is proposed to solve the problems of local overheating, inadequate light absorption, and insufficient diffusion of solar irradiation energy flow in concentrated solar technology. The performance of radiation regulation and photon management are researched to enhance concentrated solar energy converting and utilizing efficiency. The effects of the ratio, diameter, and filling factor of the biomimetic hierarchical structure on effective light absorption and energy flow diffusion efficiency are investigated. The particle swarm optimization algorithm is employed to explore the full potential of the biomimetic hierarchical structure from the perspective of optics. And the feature sizes which can serve as the boundary between large pores and small pores in concentrated solar technology are searched in this study. The calculated analysis results can provide general and valuable guidance for enhancing solar energy converting and utilizing efficiency of high-temperature solar thermochemical reactors, solar cells, and photocatalytic carriers.

2. Methodology

2.1 Design of biomimetic hierarchical structure

The photon management of leaf is brilliant because of the unconventional hierarchical structures, which is provided for highly efficient solar light utilizing: leaf epidermal cells generally concentrate light; palisade cells commonly channel light; the air spaces between the cells intensely scatter light, which improves the light absorption and utilization for photosynthesis in chloroplasts [45]. Based on the above solar light utilizing advantages of hierarchical structures observed in leaf, a biomimetic hierarchical structure is designed for enhancing the solar light utilizing efficiency of concentrated solar technology. As shown in Fig. 1(a), the biomimetic hierarchical structure is composed of two-pore structures with different diameters, and the top view and front view of this biomimetic hierarchical structure are displayed in the schematic. In concentrated solar technology, the solar radiation is concentrated by the solar concentrator and the incident energy flux follows the Gaussian distribution model. The incident concentrated solar light is channeled by the large holes in the biomimetic hierarchical structure and the situation is similar to the light transportation in palisade cells; the solar light is scattered by the ribs between large and small holes in the biomimetic hierarchical structure and the situation is similar to the light scatteration in intercellular spaces.

Fig. 1. (a) Schematic diagram of the biomimetic leaf-type hierarchical structure; (b) Schematic of the light management and radiation regulation in the biomimetic hierarchical structure.

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The solar radiation and energy flux in the biomimetic hierarchical structure is displayed in Fig. 1(b). This graph shows the schematic of the light management and radiation regulation mechanism in the proposed hierarchical structure. The biomimetic hierarchical structure can effectively scatter concentrated solar radiation, thereby avoiding excessive energy flow density in local areas, avoiding generating extremely high temperatures and avoiding damaging the reaction chambers of concentrated solar technology. At the same time, the solar radiation energy is dispersed to a wider area of the hierarchical structure, which increases the probability of solar energy being absorbed and utilized, thus enhancing the utilizing efficiency of solar radiation.

2.2 Numerical analysis description

The Maxwell’s equations can be employed to analyze the electromagnetic field distribution in the biomimetic hierarchical structure, which can analyze the characteristics of solar spectral radiation in the biomimetic hierarchical structure. In this study, the FDTD numerical method is employed to compute the Maxwell’s equations [46,47]. This is one of the advanced techniques to obtain electromagnetic solutions in the optics regime, because it is versatile and can accurately determine all the optical effects at play [48]. The Maxwell’s curl equations can be expressed as

(1)$$\nabla \times {\boldsymbol H} = \frac{{\partial {\boldsymbol D}}}{{\partial t}} + {\boldsymbol J}\textrm{,}$$

(2)$$\nabla \times {\boldsymbol E} ={-} \frac{{\partial {\boldsymbol B}}}{{\partial t}} - {{\boldsymbol J}_{\boldsymbol m}},$$

(3)$${\boldsymbol D} = {\varepsilon _\textrm{0}}{\varepsilon _r}{\boldsymbol E},$$

(4)$${\boldsymbol B} = {\mu _0}{\mu _r}{\boldsymbol H}\textrm{,}$$

where E is the electric field intensity; D is the electric flux density; H is the magnetic field intensity; B is the magnetic flux density; J is the current density, and J_m is the corresponding magnetic flux density; $\nabla$ is the Laplace operator; ${\varepsilon _0}$ is the dielectric constant in vacuum; ${\varepsilon _r}$ is the complex relative dielectric constant. ${\mu _0}$ is the magnetic conductivity in vacuum; ${\mu _r}$ is the complex relative magnetic conductivity.

The Poynting vector represents the energy flow density of the electromagnetic field, and it is in the following form:

(5)$${\boldsymbol S}\textrm{ = }{\boldsymbol E} \times {\boldsymbol H}\textrm{ = }\frac{1}{2}\textrm{Re}[{\boldsymbol E} \times {\boldsymbol H^{\prime}}],$$

where Re is the real part of the complex quantity; and ${\boldsymbol H^{\prime}}$ is the complex conjugate of the magnetic field vector. The time-averaged energy power flow across one surface can be defined by

(6)$$p = \int_a {S\cdot da} ,$$

where a is the area of a surface. The reflectivity $\rho$ can be defined as follows:

(7)$$\rho = {P_r}/{P_0} = \int_{{a_r}} {{S_r}\cdot da} /\int_{{a_0}} {{S_0}\cdot da} ,$$

where S_r is the Poynting vector of the reflected light; S₀ is the Poynting vector of the incident light; P₀ is the power of the incident light; P_r is the power of the reflected light. The transmissivity $\tau$ can be defined as follows:

(8)$$\tau = {P_t}/{P_0} = \int_{{a_t}} {{S_t}\cdot da} /\int_{{a_0}} {{S_0}\cdot da} .$$

where P_t is the power of the transmitted light. Then the absorptivity $\alpha$ can be obtained by the formula $\alpha \textrm{ = 1}-\rho -\tau$. The computational domain is a three-dimensional body; P_t and P_r are obtained by the power monitor; P₀ is initialized by the inner computer.

By employing the FDTD method to calculate the radiative parameters and the electromagnetic field distribution, the bottom and top of the three-dimensional computational domain are set as the perfectly matched layer (PML) boundary [49]. When the light direction is normal, the sides around the structure computational domain can be treated as the periodic boundary conditions [50]. The light source is set as a Gaussian light source which is near to the light condition in the solar reaction cavity. And the waist size and position of the Gaussian light source can be adjusted to make the light condition closed to the actual situation in the structure. The time, refractive index, reflectance, transmittance, and field intensity monitors are set in the analysis area to track the changes in the electromagnetic field over time. In this study, we performed 3D field electromagnetic simulations with Lumerical FDTD Solutions [50] to predict the optimal size of the biomimetic hierarchical structure. In this work, the biomimetic hierarchical structure is made of silicon carbide, so that the structure is similar to a solar thermochemical reactor and can provide general and valuable guidance for designing highly efficient solar cells and photocatalytic carriers. Meanwhile, from the perspective of the solar thermochemical reactor, aluminum oxide is also an alternative material. The optical properties of silicon carbide and other materials used in this paper are shown in Fig. S1. [51,52] (See Supplement 1 for supporting content).

2.3 Methodologies of performance analysis

In this study, the effective light absorption and energy flow diffusion efficiency are the evaluation indexes of concentrated solar energy utilization efficiency. This section introduces the analysis objects and the methods of results processing in this study. In a three-dimensional Finite-Difference Time-Domain (FDTD) solver, the memory required to perform calculations increases as the minimum wavelength decreases. Therefore, in order to ensure the feasibility and accuracy of calculations, it is significant to select a suitable wavelength range as the research object. It is noted that the solar radiation energy in the 0.4–1.8 µm wavelength range accounts for more than 90% of the total radiation energy [12]. Meanwhile, the efficient working band of most solar cells starts from 400nm, and the wavelength of the light quantum (photon) that maintains the photocatalytic reaction is 473nm. Thus, the radiation characteristics in the 0.4–1.8 µm band are chosen as the research object, and the solar radiation in this band is defined as total radiation. According to the distribution of solar spectral radiation power at AM (Air mass)1.5, the total absorption rate can be defined as follows.

(9)$${A_{Total}}\textrm{ = }\int_{400nm}^{1800nm} {A(\lambda )I(\lambda )d\lambda } /\int_{400nm}^{1800nm} {I(\lambda )d\lambda } .$$

where A(λ) is the spectral solar energy absorptivity, and I(λ) is the solar spectral radiation power at AM=1.5.

In order to analyze the regulation performance of biomimetic hierarchical structure on the distribution of concentrated solar energy flow, we utilize a 3D FDTD solver to calculate the distribution of the energy flow density vector (Poynting vector) inside the biomimetic hierarchical structure. The results obtained are Poynting vectors at a certain wavelength and a certain cross-section, and the output data are presented in the form of a matrix. Taking the standard solar irradiance function at AM1.5 as the weight, Eq. (10) is adopted to calculate the overall distribution of solar irradiation energy flow under a certain cross-section.

(10)$${S_{Total,mn}}\textrm{ = }\sum\limits_{\lambda = 400nm}^{1800nm} {[{{S_{mn}}(\lambda )\cdot I(\lambda )} ]} .$$

where S_mn(λ) is the Poynting vector-matrix at a certain wavelength, and S_Total,mn represents the overall distribution of solar irradiation energy flow under a certain cross-section.

In this study, the Gaussian light source is employed, and it is incident from the center of the biomimetic hierarchical structure. For each biomimetic hierarchical structure, the distribution of solar irradiation energy flow under the central cross-section and the central longitudinal section are selected as the analysis objects. The regulation performance of biomimetic hierarchical structure on the distribution of concentrated solar energy flow is evaluated by the diffusion efficiency of concentrated solar energy flow, and the diffusion efficiency is described in detail in Section 4.1.

3. Model validation

In order to verify the accuracy and validity of the FDTD method adopted in this work, the absorptivity of nickel porous material in Ref. [53] is comparatively calculated, and the results are presented in Fig. 2(a). Solar energy is the energy source of driving thermochemical reactors, photocatalysis and photovoltaic conversion, and the efficient absorption of solar energy is the root of ensuring the thermochemical reactors, photocatalysis and photovoltaic conversion of solar energy. And the solar energy utilizing efficiency is enhanced through improving the effective light absorption and the energy flow diffusion efficiency. Thus, the absorption of porous materials was figured in the manuscript. The nickel porous material is produced by applying the ordered inverse opal structure and it has a diameter of 0.4 µm and a height of 0.35 µm. The comparison is shown in Fig. 2(a). It can be seen from the graph that the two results can agree well with each other. Another validation case was presented as well. We compared the FDTD results with those numerical results in Ref. [54]. The numerical results were obtained by implementing a computer program based on the characteristic matrix method. We chose TiO₂/Ag/TiO₂ film as the calculation object, and all the optical properties are the same as those in Ref. [54]. The FDTD calculation results of this study and those in Ref. [54] are all presented in Fig. 2(b), from which it can be seen that the two calculation results are basically consistent. Based on the above two verification cases, the FDTD method employed in this work is reliable for the prediction of spectral radiative properties of the solar reaction cavity with a biomimetic hierarchical structure.

Fig. 2. (a) The absorptivity of nickel porous material calculated by FDTD method in Ref. [53] and by FDTD method in this study; (b) the transmissivity of TiO₂/Ag/TiO₂ film calculated by characteristic matrix method in Ref. [54] and by FDTD method in this study

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The grid independence is checked as well, the absorptivities of three-dimensional biomimetic hierarchical structure with a large diameter of 0.4 µm and small diameter of 0.2 µm calculated by adopting different mesh sizes are shown in Fig. 3. Considering the accuracy and computational resource, enough accuracy can be obtained by applying a mesh size of λ/50 from Fig. 3.

Fig. 3. The absorptivities with different meshing sizes for grid independence verification

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4. Results and discussions

4.1 Performance of uniform porous structure and biomimetic hierarchical structure

The structural diagrams of uniform porous structure and biomimetic hierarchical structure are shown in Fig. 4. In this study, the definition of large holes and small holes is different from the definition in materials discipline. We have raised the magnitude of the pore size to the micron level instead of tens of nanometers so that the biomimetic hierarchical structure can regulate solar radiation through absorption and scatteration. The ratio (R) is adopted to define the ratio between the diameter of the large holes and the diameter of the small holes, which can be calculated by a dimensionless coefficient:

(11)$$R = \frac{{{d_l}}}{{{d_s}}}.$$

The filling factor (FF) is adopted to define the distance between the two adjacent large holes and evaluate the compactness of biomimetic hierarchical structure, which can be calculated by a dimensionless coefficient (FF):

(12)$$FF = \frac{L}{{{d_l}}}\textrm{ = }\frac{l}{{{d_s}}}.$$

where d_l is the diameter of the large holes, d_s is the diameter of the small holes, and L is the distance between the two adjacent holes.

Fig. 4. Comparison of uniform porous structure and biomimetic hierarchical structure

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The influence of biomimetic hierarchical structure on the solar light absorption and concentrated solar energy flow distribution regulation has been investigated and the results are presented in Fig. 5 and 6. As shown in Fig. 5, under the same incident condition of Gaussian light source and the same porosity condition of 0.58, the maximum energy flow intensity in the biomimetic hierarchical structure is apparently lower than that of the uniform porous structure under both horizontal and vertical directions, the diffusion efficiency of solar irradiation energy flow is higher than that of uniform porous structure, and the problem of local irradiation energy flow concentration is alleviated. Especially, the analysis sections under the horizontal and vertical directions are displayed in Fig. 4. In order to quantitatively evaluate the diffusion efficiency of solar irradiation energy flow, referring to the concept of half-life in the field of atomic physics, the proportion percentage of the diffused area to the total area, when the intensity of the energy flow in the hierarchical structure decays to half of the initial value, is defined as the effective area percentage. The larger the effective area rate is, the higher the diffusion efficiency is.

Fig. 5. The concentrated solar energy flow distribution in the biomimetic hierarchical structure and uniform porous structure under both horizontal and vertical directions: (a) the energy flow distribution of biomimetic hierarchical structure under horizontal direction; (b) the energy flow distribution of uniform porous structure under horizontal direction; (c) the energy flow distribution of biomimetic hierarchical structure under vertical direction; (d) the energy flow distribution of uniform porous structure under vertical direction

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Fig. 6. (a) The effective light absorption of uniform porous structure, biomimetic hierarchical structure with increasing pore size (S-L) and biomimetic hierarchical structure with decreasing pore size (L-S); (b) spectral absorption characteristic of these three structures; (c) the energy flow diffusion efficiency of these three structures under horizontal direction; (d) the energy flow diffusion efficiency of these three structures under vertical direction

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The effective light absorption and energy flow diffusion efficiency of uniform porous structure, biomimetic hierarchical structure with increasing pore size, and biomimetic hierarchical structure with decreasing pore size are presented in Fig. 6. As shown in the graph (Fig. 6(b)), the effective light absorption of small-large pore to visible light (0.4–0.8 µm) is higher than that of large-small pore and uniform pore. From the perspective of effective light absorption, the hierarchical structure with small-large pore can enhance the utilization of high-frequency photon energy by photovoltaic cells and photocatalytic reactions. In this section, the diameters of the above three pore structures are d_s=0.5 µm, d=0.7 µm, d_l=1 µm, respectively. Due to the coherent scattering effect, the effective absorption of small-large pore to solar radiation near the wavelength of 0.5 µm is enhanced, which causes the above results. It is also indicated in the graph that the effective light absorption of small-large pore to total radiation is higher than that of large-small pore and uniform pore. From the perspective of effective light absorption, the hierarchical structure with small-large pore can promote the utilization of total solar radiation by solar high-temperature thermochemical reaction. From the perspective of photovoltaic and photocatalysis, 0.5-µm size is a notable feature size, which is the boundary between large pores and small pores. From the perspective of solar thermochemistry, 1-µm size is a notable feature size, which is the boundary between large pores and small pores.

The energy flow diffusion efficiency of uniform porous structure, biomimetic hierarchical structure with increasing pore size (S-L) and biomimetic hierarchical structure with decreasing pore size (L-S) are displayed in Fig. 6(c) (d). Specifically, the proportion percentages of the diffused area to the total area, when the intensity of the energy flow in the pore structure decays to 87.5%, 75%, 62.5%, and 50% of the initial value, are presented in the graph. It can be seen from the graph that the energy flow diffusion efficiency of the biomimetic hierarchical structure is evidently superior to that of the porous structure, and the biomimetic hierarchical structure with increasing pore size is a little bit better than the biomimetic hierarchical structure with decreasing pore size comprehensively considering both horizontal and vertical directions. Specifically, the effective light absorption of the biomimetic hierarchical structure with increasing pore size is 3.4% higher than that of the uniform porous structure under the same porosity condition, and the energy flow diffusion efficiency of the biomimetic hierarchical structure with increasing pore size has an enhancement of 25.9% under horizontal direction and an enhancement of 30% under vertical direction compared with the energy flow diffusion efficiency of the uniform porous structure.

Therefore, based on the effective light absorption and energy flow diffusion efficiency, it can be concluded that the biomimetic hierarchical structure with increasing pore size (i.e., the small hole is at the top and the large hole is in the bottom) has a preferable performance than the biomimetic hierarchical structure with decreasing pore structure (i.e., the large hole is in the top and the small hole is in the bottom) and the uniform porous structure under the same condition.

4.2 Effects of diameter (d_s) on performance of biomimetic hierarchical structure

In this study, ascertaining the feature pore size that can serve as the boundary between large pores and small pores for the total radiation is a significant objective. Thus, the effects of diameter (d_s) on performance of the biomimetic hierarchical structure are investigated firstly. In this section, the ratio (R) between the diameter of small pore and the diameter of large pore is set to 1:4 initially. The influence of the diameter of small pore (d_s) on the performance of biomimetic hierarchical structure is firstly investigated by scanning this parameter from 0.4 µm to 1.2 µm, and the optimization method is the particle swarm optimization algorithm in FDTD Solutions software. The influence of the diameter of small pore (d_s) on the effective light absorption and energy flow diffusion efficiency of the biomimetic hierarchical structure is studied by the FDTD method and the numerical results are presented in Fig. 7 and Fig. 8, respectively. As shown in Fig. 7, the spectral mean absorptivity of the biomimetic leaf-type hierarchical structure has two peak values when the diameter of small pore (d_s) is 0.5 µm and 1 µm, and the spectral mean absorptivity of the uniform porous structure has two peak values when its diameter is 0.6 µm and 0.7 µm. These results account for the basis on which we chose the pore sizes in the last chapter. After optimization, the maximum spectral mean absorptivity of the biomimetic hierarchical structure is 88.68%, while that of the uniform porous structure is 88.2%. Meanwhile, the average level of the spectral mean absorptivity of the biomimetic hierarchical structure is higher than that of the uniform porous structure. Thus, the biomimetic hierarchical structure can enhance effective light absorption compared with the uniform porous structure. Based on Fig. 6 and Fig. 7, it can be concluded that the 0.5-µm small hole mainly improves the absorption of short-wavelength solar radiation, while the 1-µm small hole mainly enhances the absorption of long-wavelength solar radiation.

Fig. 7. (a) Effects of diameter (d_s) of biomimetic hierarchical structure on the effective spectral mean absorptivity and effects of diameter (d) of uniform porous structure on the effective spectral mean absorptivity; (b) spectral absorption characteristic of biomimetic hierarchical structure with five types of diameters (d_s)

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Fig. 8. Effects of diameter (d_s) of biomimetic hierarchical structure and effects of diameter (d) of uniform porous structure on the effective diffusion area percentage: (a) under horizontal direction; (b) under vertical direction

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The influence of the diameter of the small pore (d_s) on the energy flow diffusion efficiency under the central cross-section and the central longitudinal section is presented in Fig. 8. As shown in the graph, the energy flow diffusion efficiency of the biomimetic hierarchical structure under the central cross-section is basically higher than that of the uniform porous structure, and the maximum efficiency is realized when the diameter of the small pore (d_s) is 1 µm. The maximum energy flow diffusion efficiency of the biomimetic hierarchical structure under the central longitudinal section is also realized when the diameter of the small pore (d_s) is 1 µm. It is indicated that the uniform porous structure cannot take both effective light absorption and energy flow diffusion efficiency into account. That is, under the condition of the optimal pore size (d=0.6 µm) which has the best spectral mean absorptivity, the diffusion efficiency of the uniform porous structure is very low. On the contrary, the biomimetic hierarchical structure can take both effective light absorption and energy flow diffusion efficiency into account. When the diameter of the small pore (d_s) is 1 µm, the spectral mean absorptivity and effective diffusion area percentage of the biomimetic hierarchical structure are both the best. It is worth noting that the porosities of the biomimetic hierarchical structure are different from those of the uniform porous structure in this optimization process (it is difficult to control the same porosity of these two structures in the simulation process). In this section, the optimized parameters are utilized in Section 4.1, and the porosity of the biomimetic hierarchical structure is the same as that of the uniform porous structure in Section 4.1. Therefore, the comparison between these two structures and the performance enhancement are only discussed in Section 4.1. In this study, the parameter optimization process is divided into two parts. In both parts, each parameter of the structure is optimized while holding all other parameters constant. In part I, the effects of diameter (d_s) on the performance of the biomimetic hierarchical structure are investigated firstly by scanning this parameter from 0.4 µm to 1.2 µm, and the initial values of other parameters are chosen based on our previous works [20][38], they may not be the best values in this study. The results indicate that the light absorption performance of the biomimetic hierarchical structure has two peak values when the diameter of small pore (d_s) is 0.5 µm and 1 µm, while the energy flow diffusion performance of the biomimetic hierarchical structure reaches the only peak value when the diameter of small pore (d_s) is 1 µm. Thus, the diameter value of 1 µm is selected as the optimized parameter. Then, other parameters are optimized according to the order in the article and the best values are found in turn. In part II, the effects of diameter (d_s) on the performance of the biomimetic hierarchical structure are investigated by scanning this parameter from 0.4 µm to 1.2 µm, while the initial values of other parameters are the optimized values in part I. According to Eq. (10), the energy flow diffusion efficiency in this study is for the entire 0.4–1.8 µm solar radiation. It can be concluded that the biomimetic hierarchical structure with a small pore of 1-µm length has a significant performance of radiation regulation and photon management, thus enhancing the light absorption and energy flow diffusion efficiency in the 0.4–1.8 µm band. Meanwhile, the pore size of 1 µm is a notable feature size for the total radiation, which is the boundary between large pores and small pores.

4.3 Effects of ratio (R) on performance of biomimetic hierarchical structure

In this section, the diameter of the small pore (d_s) is set to 1 µm. The ratio (R) is adopted to define the ratio between the diameter of the small pore and the diameter of the large pore. The influence of the ratio (R) on the effective light absorption and energy flow diffusion efficiency of the biomimetic hierarchical structure is studied by the FDTD method and the numerical results are displayed in Fig. 9 and Fig. 10, respectively. As shown in Fig. 9, the spectral mean absorptivity of the biomimetic leaf-type hierarchical structure has two peak values when the ratio (R) is 1:2 and 1:4, the spectral mean absorptivity with different ratios (R) in Fig. 9 is generally higher than that with different small pore diameter (d_s) in Fig. 8, and the difference of the spectral mean absorptivity with different ratios (R) in Fig. 9 is less than that with different small pore diameter (d_s) in Fig. 7. Thus, once the feature size for the total radiation is ascertained, the effective light absorption of the biomimetic hierarchical structure can be maintained at a high level, and the effect of the ratio (R) on the effective light absorption is not remarkable.

Fig. 9. (a) Effects of the ratio (R) of biomimetic hierarchical structure on the effective spectral mean absorptivity; (b) spectral absorption characteristic of biomimetic hierarchical structure with five types of ratios

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Fig. 10. Effects of the ratio (R) of biomimetic hierarchical structure on the effective diffusion area percentage

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The influence of the ratio (R) on the energy flow diffusion efficiency of the biomimetic leaf-type hierarchical structure is presented in Fig. 10. The effect of the ratio (R) on the effective diffusion area percentage of the biomimetic hierarchical structure under the horizontal direction is relatively significant, while the effect of the ratio (R) on the effective diffusion area percentage of the biomimetic hierarchical structure under the vertical direction is relatively ordinary. When the ratio (R) is 1:4, the effective diffusion area percentage reaches the best value under both horizontal and vertical directions. It can be concluded that the ratio (R) has ordinary effects on the effective light absorption of the biomimetic hierarchical structure and has remarkable effects on the energy flow diffusion efficiency of the biomimetic hierarchical structure.

4.4 Effects of filling factor (FF) on performance of biomimetic hierarchical structure

In this section, the influence of the filling factor (FF) of large and small pores on the effective light absorption and energy flow diffusion efficiency of the biomimetic hierarchical structure is studied by the FDTD method and the numerical results are presented in Fig. 11 and Fig. 12, respectively. The ratio (R) between the diameter of the small pore (d_s) and the diameter of the large pore (d_l) is set to 1:4. The diameter of the small pore (d_s) is set to 1 µm. After the ratio (R) and diameters of small and large pores are determined, the value of filling factor (FF) determines the value of porosity. As shown in Fig. 11, the spectral mean absorptivity of the biomimetic hierarchical structure reaches the only peak value when the filling factor (FF) is 1, and the oversize or undersize porosity and filling factor (FF) are unfavorable to the effective light absorption. The influence of the filling factor (FF) on the energy flow diffusion efficiency of the biomimetic hierarchical structure is displayed in Fig. 12. It can be also concluded that the best value of the filling factor (FF) is 1, when it comes to the energy flow diffusion efficiency of the biomimetic hierarchical structure.

Fig. 11. (a) Effects of filling factor (FF) of biomimetic hierarchical structure on the effective spectral mean absorptivity; (b) spectral absorption characteristic of biomimetic hierarchical structure with five types of filling factors (FF)

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Fig. 12. Effects of FF of biomimetic hierarchical structure on the effective diffusion area percentage

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5. Conclusions

The problems of local overheating, inadequate light absorption, and insufficient diffusion of solar irradiation energy flow usually occur in concentrated solar technology. In this study, the idea of using biomimetic hierarchical structure inspired by the efficient photon management of hierarchical structure in leaf is proposed for enhancing concentrated solar energy utilizing efficiency. The geometrical parameters (diameters, ratio, and filling factor) of the biomimetic hierarchical structure are investigated and optimized to enhance the effective light absorption and energy flow diffusion efficiency of concentrated solar energy. The particle swarm optimization algorithm is employed to explore the full potential of biomimetic hierarchical structure from the perspective of optics. The results can provide general and valuable guidance for enhancing solar energy converting and utilizing efficiency of high-temperature solar thermochemical reactors, solar cells, and photocatalytic carriers. The following conclusions can be drawn:

1. The biomimetic leaf-type hierarchical structure can significantly enhance the effective light absorption and energy flow diffusion efficiency of concentrated solar energy, and the biomimetic hierarchical structure with increasing pore size is a little superior to the biomimetic hierarchical structure with decreasing pore size.
2. From the perspective of photovoltaic and photocatalysis, 0.5-µm size is a notable feature size, which is the boundary between large pores and small pores; from the perspective of solar thermochemistry, 1-µm size is a notable feature size, which is the boundary between large pores and small pores.
3. The diameter, ratio, and filling factor of the biomimetic hierarchical structure mainly influence the effective light absorption and energy flow diffusion efficiency of concentrated solar energy in the total radiation band (0.4–1.8 µm), and 1 µm is the best pore size, 1:4 is the best pore size ratio, 1 is the best filling factor value.
4. As for the effective light absorption, the biomimetic hierarchical structure has an enhancement of 3.4%, as for the energy flow diffusion efficiency, the biomimetic hierarchical structure has an enhancement of 25.9% under horizontal direction and 30% under vertical direction, compared with the uniform porous structure.

Funding

National Natural Science Foundation of China (No.52006094, No.52076064); National Key Research and Development Program of China (2018YFA0702300); Taishan Scholar Foundation of Shandong Province (tsqn201812105).

Acknowledgments

This work was supported by National Natural Science Foundation of China Grant (No. 52076064, No. 52006094), National Key Research and Development Program of China (2018YFA0702300), and Taishan Scholar Foundation of Shandong Province (tsqn201812105).

Disclosures

The authors declare no conflicts of interest.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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Biomimetic hierarchical structure for enhancing concentrated solar energy converting and utilizing efficiency

Abstract

1. Introduction

2. Methodology

2.1 Design of biomimetic hierarchical structure

2.2 Numerical analysis description

2.3 Methodologies of performance analysis

3. Model validation

4. Results and discussions

4.1 Performance of uniform porous structure and biomimetic hierarchical structure

4.2 Effects of diameter (d_s) on performance of biomimetic hierarchical structure

4.3 Effects of ratio (R) on performance of biomimetic hierarchical structure

4.4 Effects of filling factor (FF) on performance of biomimetic hierarchical structure

5. Conclusions

Funding

Acknowledgments

Disclosures

Data availability

Supplemental document

References

Supplementary Material (1)

Data availability

Cited By

Figures (12)

Equations (12)

Optics Express

Abstract

1. Introduction

2. Methodology

2.1 Design of biomimetic hierarchical structure

2.2 Numerical analysis description

2.3 Methodologies of performance analysis

3. Model validation

4. Results and discussions

4.1 Performance of uniform porous structure and biomimetic hierarchical structure

4.2 Effects of diameter (ds) on performance of biomimetic hierarchical structure

4.3 Effects of ratio (R) on performance of biomimetic hierarchical structure

4.4 Effects of filling factor (FF) on performance of biomimetic hierarchical structure

5. Conclusions

Funding

Acknowledgments

Disclosures

Data availability

Supplemental document

References

Supplementary Material (1)

Data availability

Cited By

Figures (12)

Equations (12)

Optics Express

4.2 Effects of diameter (d_s) on performance of biomimetic hierarchical structure