Optimization method of multilayer thermal emitter parameters in thermophotovoltaics based on mathematical modeling

Abstract

The present invention discloses a method for optimizing the parameters of multi-layer thermal emitters in thermophotovoltaics based on mathematical modeling, which belongs to the technical field of parameter design methods. Thermal emitters mainly use different dielectric structures to adjust the emission of absorbed heat, so that most of the emitted photons are below the bandgap wavelength of the photovoltaic cell. Photovoltaic cells mainly convert high-energy photons below a specific bandgap wavelength. They have a certain bandgap energy and therefore a corresponding bandgap wavelength. In order to optimize the multi-layer thermal emitter, the present invention repeatedly uses optimization algorithms to optimize the number of layers, thickness, and materials of each layer, selects the best combination, and finally analyzes the optimal solution for each combination, selects the combination of maximum energy and minimum wavelength, and obtains the various parameters of the thermal emitter. A new set of thermal emitter models is designed to maximize the efficiency of photovoltaic cells in absorbing infrared radiation from thermal emitters and converting it into electrical energy.

Description

Technical Field

[0001] The invention relates to a method for optimizing parameters of a multilayer thermal emitter in thermophotovoltaics based on mathematical modeling, and belongs to the technical field of parameter design methods. Background Art

[0002] Currently, research on thermophotovoltaic radiators is limited, particularly experiments focused on metamaterial radiators. Wu Xi studied the system efficiency of different selective radiators (Yb2O3 and ErO3) paired with different photovoltaic cells (Si and GaSb). He also investigated the effects of air-fuel ratio, fuel mass flow rate, and radiator size on system efficiency, ultimately building a large-scale thermophotovoltaic system. Liu Guangping et al. investigated the impact of one-dimensional Si / SiO2 photonic crystal filters on the efficiency of thermophotovoltaic systems. Liu Ting of Nanjing University of Science and Technology found that ErAg doped with erbium has good compatibility with GaSb cells and fabricated the coated radiators using both sol-gel and thermochemical methods. Wang Qiang of Hubei University of Technology designed a cross-structured metamaterial radiator through simulation and investigated the influence of structural parameters on radiator performance. Wang Hujun of the University of Science and Technology of China conducted theoretical and experimental studies on erbium oxide-coated selective radiators, nickel-oxygen-doped magnesium oxide eutectic ceramic selective radiators, and vanadium dioxide selective radiators, comparing the performance and influencing factors of different selective radiators. Cao Shun et al. from the University of the Chinese Academy of Sciences discovered that a windmill-type metamaterial radiator can be used in terahertz detectors, achieving an average absorption rate of 95% at 1.516, 2.205, 2.424, and 2.565 THz. Peng Zhan et al. from Nanjing University proposed a near-infrared dual-broadband complete absorber based on a plasmon-photonic hybrid structure, achieving an absorption rate exceeding 90% in the near-infrared band.

[0003] Peng Yingcai and other researchers have proposed that GaSb is an important III-V binary compound semiconductor material with a band gap of approximately 0.72 eV, which matches well with the spectra of various radiators. Due to the low surface carrier recombination rate of p-type GaSb, researchers have mostly adopted the method of diffusing p-type impurities onto the surface of n-type GaSb to prepare homojunction GaSb solar cells. These cells exhibit high quantum efficiency. In recent years, with the deepening of GaSb research, the Zn diffusion method has become mainstream due to its simplicity and low cost, and has been adopted in commercial production. GaSb is generally used as the bottom cell in a tandem solar cell. Khvostikvo et al. fabricated a GaAs / GaSb solar cell using the LPE method, with GaAs as the top cell and GaSb as the bottom cell. The efficiency was measured to be 6% under 300 suns.

[0004] A thermophotovoltaic power generation device converts heat generated by various sources, such as fuel combustion heat, waste heat, solar energy, and radioisotope heat sources, into infrared radiation energy through a thermal radiation emitter. This radiation energy is then projected onto thermophotovoltaic cells and converted into electrical energy. Thermophotovoltaic power generation systems have high energy output density and theoretical efficiency, a wide range of energy utilization options, and more importantly, the ability to achieve cogeneration of heat and power. Therefore, this technology will have enormous practical value and application prospects in the fields of industry, commerce, military, and aerospace. Currently, the existing technology lacks effective optimization design methods for the parameters of multi-layer thermal reflectors, making it impossible to select the best combination and derive the parameters of the thermal emitter. Therefore, how to achieve the optimal design of the parameters of multi-layer thermal emitters in thermophotovoltaics based on mathematical modeling has become an urgent need. Summary of the Invention

[0005] In view of the deficiencies of the prior art, the present invention aims to provide a method for optimizing the parameters of multi-layer thermal emitters in thermophotovoltaics based on mathematical modeling, thereby solving the problems encountered in the prior art.

[0006] The method for optimizing parameters of multilayer thermal emitters in thermophotovoltaics based on mathematical modeling according to the present invention comprises the following steps:

[0007] S1: Search for materials for making multilayer thermal emitters and find relevant characteristics of the materials, such as refractive index, extinction coefficient, wavelength and other data information;

[0008] S2: Fit all material properties to a single wavelength;

[0009] S3: Calculate the refractive index, extinction coefficient and other data information of various materials within a unified wavelength range;

[0010] S4: Using the Fresnel coefficient, find the light energy within different wavelength ranges in a single-layer heat reflector. Based on the relationship between the extinction coefficient and thickness of different media, deduce the absorbance in different media. The relationship between reflectivity and refractive index is derived from the law of reflection. Finally, the energy conservation theorem derives the relationship between the emission spectrum and the medium properties in a single-layer structure.

[0011] S5: In the multi-layer structure of the heat reflector, the Maxwell equations are used to calculate the Fresnel coefficient under vertical polarization. The Maxwell equations are then converted into a transmission matrix using the transfer matrix method. The transmittance and reflectance of the entire multi-layer structure are then calculated. Finally, the relationship between the absorbance and transmittance is used to derive the relationship between the emission spectrum and the medium properties of the multi-layer structure.

[0012] S6: Since the band gap wavelength of GaSb solar cells is 1710nm, an objective function expression is given based on this characteristic, and constraints are set on the number of layers of the multilayer thermal emitter, the thickness of each layer, and the wavelength.

[0013] S7: Use the particle swarm algorithm to optimize all media layer by layer, and obtain the optimal thickness combination under different media, forming a control test. Then use the particle swarm algorithm again to optimize the thickness of multiple layers, and thus obtain the optimal design parameter combination of the thermal emitter;

[0014] S8: The multilayer thermal emitter is heated by solar energy and chemical energy. The heated multilayer thermal emitter emits infrared radiation waves to the gallium antimonide cell. The internal structure of the thermal emitter adjusts the absorbed heat and then emits infrared radiation waves, so that the emitted photons are lower than the band gap wavelength of the gallium antimonide cell, thereby allowing the gallium antimonide cell to convert more electrical energy through the thermoelectric conversion effect.

[0015] In step S4, the relationship between the emission spectrum and the medium properties under the single-layer structure is derived from the energy conservation theorem, which specifically includes the following steps:

[0016] S11: The infrared radiation emitted by the thermal emitter is red light. The photons themselves have energy. The energy formula of photons is:

[0017]

[0018] Where: h is Planck's constant, c is the speed of light, λ is the wavelength, n is the refractive index,

[0019] S12: When the emitted light hits the medium vertically, part of it will be reflected vertically, and the other part will penetrate the medium. When the light passes through the medium, part of its own energy will be absorbed by the medium. The extinction coefficient of the same medium at different wavelengths is different, and the absorbance of the light energy absorbed by the medium is also different.

[0020] The formula for absorbance is:

[0021]

[0022] Where: k is the extinction coefficient, d is the thickness of the medium, so it can be concluded that the energy of light absorbed by the medium is:

[0023] E1=Ea (3)

[0024] S13: When light enters different media, it will undergo reflection and refraction. Assuming that the angle of incidence of light is 0, the relationship between the reflection coefficient and transmission coefficient of S-wave and P-wave is obtained through Snell's law.

[0025]

[0026] Where: r s is the reflection coefficient of s wave, t s is the transmission coefficient of s wave, r p is the reflection coefficient of the p wave, t p is the transmission coefficient of the p-wave, θ1 and θ2 are the incident angle and reflection angle respectively, n1 and n2 are the refractive index of the first medium and the refractive index of the second medium respectively, from which the relationship between reflectivity and transmittance is obtained as follows:

[0027] R S =|r s | 2

[0028] R P =|r p | 2

[0029] By the law of conservation of energy: R S +T S =1, R P +T P =1, at vertical incidence

[0030]

[0031] S14: The infrared radiation emitted by the thermal emitter is red light, and the relationship between the single-layer emission spectrum and the medium properties is obtained:

[0032]

[0033] Where: h is Planck's constant, c is the speed of light in a vacuum, λ0 is the wavelength of red light, λ is the wavelength in the medium, and d is the thickness of the medium.

[0034] Said S2 also includes a double-layer heat reflector structure, and the relationship between the emission spectrum and the medium characteristics in the two-layer heat reflector structure is:

[0035]

[0036] Where: r1 is the reflectivity of the first medium, r2 is the reflectivity of the second medium, d1 and d2 are the thicknesses of the two media respectively, and λ1 and λ2 are the absorbances of the two media respectively.

[0037] Tungsten and silicon dioxide are selected as two media in the double-layer heat reflector structure.

[0038] In step S2, in the multilayer structure of the heat reflector, the Fresnel coefficients under vertical polarization are calculated using the Maxwell equations, and the Maxwell equations are converted into the form of a transfer matrix using the transfer matrix method, which specifically includes the following:

[0039] S21: The refractive index of the layers in the multilayer structure in the xy plane is expressed as:

[0040]

[0041] Where: d is the thickness, n is the refractive index, and the type of polarization depends on the angle at which the wave falls on the surface of the medium. If the light is perpendicular to the medium surface and the falling angle is 0, then the polarization type produced by the light is vertical polarization, s polarization, or TE polarization.

[0042] S22: Use Maxwell's equations to derive the Fresnel coefficients for vertical polarization.

[0043]

[0044]

[0045] S23: Then use the transfer matrix method to transform Maxwell's equations into a transfer matrix form, which becomes an eigenvalue solution problem.

[0046] The step S23 specifically includes the following:

[0047] S31: Maxwell's equations are used to solve the electric and magnetic fields on two adjacent layers to obtain the transmission matrix. The conclusions for a single layer are then extended to the entire medium space to calculate the transmission coefficient and reflection coefficient of the entire multilayer medium. The formula is as follows:

[0048]

[0049]

[0050] Among them, δ j is the phase thickness, k j is the wave number, η j The following formula is derived for the intrinsic impedance:

[0051]

[0052]

[0053]

[0054] As shown in formula (11), M j Expressed as a 2×2 matrix, the transmittance t and reflectance r are expressed by the total transmission matrix, and the relationship between the emission spectrum of the multilayer structure and the refractive index and thickness of the medium is found as follows:

[0055]

[0056] Where i represents the relevant characteristics of the i-th layer of medium.

[0057] The constraints set in step S3 for the number of layers of the multilayer thermal emitter, the thickness of each layer of material, and the wavelength are:

[0058]

[0059] The optimal design parameters of the thermal emitter obtained in step S4 specifically include the following: setting the design parameters as variables, where the variable L is the number of layers, randomly extracting a medium from the attachment for each layer, the second variable is the thickness under a certain medium, and the third variable is the wavelength range. In order to find the optimal design parameters, a particle swarm algorithm is used for global optimization. Since if the number of layers is too large, light cannot reach the surface of the photovoltaic cell and infrared thermal radiation cannot be converted into electrical energy, after optimizing the thickness of various materials, the optimal thickness of each material is selected, and the particle swarm algorithm is used again to optimize the thickness of multiple layers to obtain the specific parameters of the material characteristics.

[0060] The multilayer thermal radiation emitter comprises five layer groups, which are SiC-ZnO-W-SiC-W from top to bottom.

[0061] The wavelength of the multi-layer thermal radiation emitter is in the range of 780nm-1mm.

[0062] Compared with the prior art, the present invention has the following beneficial effects:

[0063] The present invention describes a method for optimizing the parameters of multilayer thermal emitters in thermophotovoltaics based on mathematical modeling. This technology utilizes various heat sources to heat the thermal emitters, then converts the thermal emitters' infrared radiation into electrical energy via photovoltaic cells. The thermal emitters in this system primarily utilize different dielectric structures to regulate the emission of absorbed heat, ensuring that the majority of emitted photons are below the photovoltaic cell's bandgap wavelength. Photovoltaic cells primarily convert high-energy photons below a specific bandgap wavelength. They possess a specific bandgap energy and, therefore, a corresponding bandgap wavelength. To optimize the multilayer thermal emitters, the present invention utilizes multiple optimization algorithms to optimize the number of layers, thickness, and materials used in each layer, selecting the best combination. Finally, each combination is analyzed for optimal solutions, selecting the combination with the highest energy and lowest wavelength to determine the thermal emitter parameters. This design maximizes the efficiency of the photovoltaic cell's absorption of the thermal emitter's infrared radiation and its conversion into electrical energy. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 A flowchart of the overall steps of an embodiment of the present invention;

[0065] Figure 2 This is a structural diagram of a multilayer heat reflector in an embodiment of the present invention;

[0066] Figure 3 This is a structural diagram of a single-layer heat reflector in an embodiment of the present invention;

[0067] Figure 4 This is a structural diagram of a double-layer heat reflector in an embodiment of the present invention;

[0068] Figure 5 Flowchart of the steps of the particle swarm algorithm in an embodiment of the present invention. DETAILED DESCRIPTION

[0069] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0070] Example 1:

[0071] like Figure 1 As shown, the method for optimizing the parameters of multi-layer thermal emitters in thermophotovoltaics based on mathematical modeling described in the present invention finds the light energy in different wavelength ranges under a single-layer structure, and calculates the absorbance under different media based on the relationship between the extinction coefficient and thickness of different media. The relationship between reflectivity and refractive index and the energy conservation theorem are derived from the law of reflection. Its purpose is to provide a relationship between the emission spectrum and the medium characteristics under a single-layer structure.

[0072] In a multilayer structure, light passes through the interface between the L and L+1 layers of dielectric. Since light generates two different polarization types, S and P polarization, and the light enters the multilayer thermal emitter vertically, Maxwell's equations are used to calculate the Fresnel coefficients for vertical polarization. The transfer matrix method is then used to convert Maxwell's equations into a transfer matrix. The transmittance and reflectance of the entire multilayer structure are then calculated. Finally, the relationship between absorbance and transmittance yields a relationship between the emission spectrum and dielectric characteristics for the multilayer structure.

[0073] Since the band gap wavelength of gallium antimonide (GaSb) cells is 1.71 microns, it is necessary to design a new thermal emitter to make its infrared radiation wave as small as possible below 1.71 microns, so as to maximize the thermoelectric conversion efficiency of the gallium antimonide (GaSb) cells. The particle swarm algorithm is used to obtain the optimal design parameter combination of the thermal emitter.

[0074] like Figure 3 As shown, under the single-layer tungsten structure:

[0075] The characteristics of the medium mainly include the refractive index, refractive index and thickness. The relationship between the emission spectrum and the characteristics of the medium is the relationship between the emission spectrum and the refractive index and thickness. According to the information, the emission spectrum refers to the spectrum emitted by the light source, and the spectrum is composed of light with continuously distributed wavelengths. Therefore, the emission spectrum can be understood as having a continuously distributed wavelength, so that the relationship between the emission spectrum and the characteristics of the medium can be converted into the relationship between the wavelength and the refractive index and thickness. The infrared radiation emitted by the thermal emitter is red light, and the wavelength of red light is 620~760nm. The photon itself has energy, and the energy formula of the photon is:

[0076]

[0077] Where h is Planck's constant, c is the speed of light, λ is the wavelength, and n is the refractive index. When emitted light hits a medium vertically, part of it will be reflected vertically, and the other part will penetrate the medium. When the light passes through the medium, part of its own energy will be absorbed by the medium. The extinction coefficient of the same medium at different wavelengths is different, and the absorbance of the light energy absorbed by the medium is also different. The formula for absorbance is:

[0078]

[0079] Where k is the extinction coefficient and d is the thickness of the medium. Therefore, the energy of light absorbed by the medium can be obtained as:

[0080] E1=Ea (3)

[0081] When light enters different media, reflection and refraction will occur. Assuming that the angle of incidence of light is 0, the relationship between the reflection coefficient and transmission coefficient of S-wave and P-wave is obtained through Snell's law.

[0082]

[0083] where r s : reflection coefficient of s-wave, t s : transmission coefficient of s-wave, r p : reflection coefficient of p-wave, t p : The transmission coefficient of the p-wave. θ1 and θ2 are the angle of incidence and the angle of reflection, respectively. n1 and n2 are the refractive index of the first medium and the refractive index of the second medium, respectively. The relationship between reflectivity and transmittance is:

[0084] R S =|r s | 2

[0085] R P =|r p | 2

[0086] By the law of conservation of energy: R S +T S =1, R P +T P =1, at vertical incidence

[0087]

[0088] The infrared radiation emitted by the thermal emitter is red light. The relationship between the emission spectrum of a single layer of 50nm tungsten and the dielectric properties is as follows:

[0089]

[0090] Where h is Planck's constant, c is the speed of light in a vacuum, λ0 is the wavelength of red light, λ is the wavelength in the medium, and d is the thickness of the medium.

[0091] like Figure 4 As shown, under the double-layer structure of tungsten and silicon dioxide:

[0092] For the relationship under the double-layer structure, tungsten and silicon dioxide are selected as two media.

[0093]

[0094] Where r1 is the reflectivity of the first medium, r2 is the reflectivity of the second medium, d1 and d2 are the thicknesses of the two media, and λ1 and λ2 are the absorbances of the two media. For silicon dioxide and tungsten, the order of precedence is uncertain, but the wavelength, refractive index, and absorbance of these two media differ, and the energy lost when infrared light passes through them also differs. At the same wavelength, the transmittance of silicon dioxide is much greater than that of tungsten. Tungsten is a refractory metal with a high melting point, making it an excellent material for high-temperature solar thermal absorbers. Tungsten exhibits high loss in the visible and near-infrared spectra, which enhances its absorption of sunlight. Therefore, tungsten is used as the primary absorber in thermal emitters.

[0095] like Figure 2 As shown, in the case of more than two layers of dielectric structure:

[0096] In a multilayer structure, the refractive index of the layers in the xy plane is expressed as:

[0097]

[0098] Where d is the thickness and n is the refractive index. The type of polarization depends on the angle at which the wave strikes the surface of the medium. In our study, the light is perpendicular to the surface of the medium, with a falling angle of 0. Therefore, the resulting polarization type is vertical, s, or TE polarization. Maxwell's equations can be used to derive the Fresnel coefficients for vertical polarization.

[0099]

[0100]

[0101] Then the transfer matrix method is used to transform Maxwell's equations into a transfer matrix form, which becomes an eigenvalue solution problem.

[0102] Specifically, Maxwell's equations are used to solve the electric and magnetic fields on two adjacent layers to obtain the transmission matrix. The conclusions for a single layer are then extended to the entire medium space, thereby calculating the transmission coefficient and reflection coefficient of the entire multilayer medium.

[0103] The formula is as follows:

[0104]

[0105]

[0106] Among them, δ j is the phase thickness, k j is the wave number, η j The following formula is derived for the intrinsic impedance:

[0107]

[0108]

[0109]

[0110] As shown in formula (11), M j It is represented as a 2×2 matrix. Each element in the matrix has no actual physical meaning and is only a calculation result. We can express the transmittance t and reflectance r from the total transmission matrix. To this end, we can find the relationship between the emission spectrum of the multilayer structure and the refractive index and thickness of the medium properties:

[0111]

[0112] Where i represents the relevant characteristics of the i-th layer of medium. The purpose of designing a multi-layer thermal radiation emitter is to improve the thermoelectric conversion efficiency of the thermoelectric device, that is, to improve the external quantum efficiency. For this purpose, the objective function is set as formula (15). However, since gallium antimonide (GaSb) cells are relatively advanced among other cells, and the band gap wavelength of gallium antimonide (GaSb) is 1.71 microns. According to the data, photovoltaic cells mainly convert high-energy photons below a specific band gap wavelength. It has a certain band gap energy and therefore also has a corresponding band gap wavelength. Therefore, gallium antimonide (GaSb) cells can only absorb high-energy photons below 1710 nanometers and convert them into electrical energy, while low-energy photons with wavelengths above 1710 nanometers will not be absorbed and can only be converted into thermal energy, which will lead to a decrease in the photoelectric conversion efficiency of gallium antimonide (GaSb) cells.

[0113] The following constraints are set for the above requirements:

[0114]

[0115] By controlling the material selection, material order, and material thickness of the multilayered thermal emitter, the intensity of the infrared thermal radiation wave is adjusted, keeping the wavelength of the generated infrared thermal radiation as short as possible from the band gap wavelength of the gallium antimonide (GaSb) solar cell. Because specific design parameters are required, they are set as variables. The variable L is the number of layers, and each layer is randomly selected from the attached dielectric. The second variable is the thickness of a specific dielectric layer, and the third variable is the wavelength range.

[0116] In order to find the best design parameters, a particle swarm algorithm (POS) is used for global optimization. When using the particle swarm algorithm (POS) for global optimization, two issues need to be considered. First, avoid too few layers, which will lead to the material's ability to adjust infrared thermal radiation light waves being too weak, resulting in a wavelength greater than the band gap wavelength of gallium antimonide (GaSb); second, avoid too many layers, which will cause some photons to fail to reach the surface of the photovoltaic cell, thus failing to convert infrared thermal radiation into electrical energy, which will also lead to material waste and affect the economic benefits of practical applications. Considering these two issues is to find the optimal number of material layers while ensuring the photoelectric conversion efficiency of gallium antimonide (GaSb) cells. Formula (15) is used as the objective function, and formula (16) is the constraint condition of each variable. The data in the entire article are all optimized data under appropriate assumptions. First, the objective function is used to optimize various materials layer by layer to obtain a series of material order and thickness relationships.

[0117] like Figure 5As shown in the figure, the particle swarm algorithm (PSO) process is as follows: The basic idea of ​​the PSO is to simulate the random foraging behavior of a flock of birds. The flock adjusts its search path based on its own experience and communication within the flock, ultimately finding the location with the most food. Each bird's position / path is a combination of independent variables, and the food density at each location is the function value. Each search adjusts its search direction and speed based on its own experience (its own historical search results for the optimal location) and communication within the flock (its historical search results for the optimal location). This process is called tracking the extreme value, which leads to the optimal solution. The objective function is used to calculate the fitness of each particle. Using the mathematical software Matlab, the resulting objective function and the constraints of each variable are input into Matlab, and the PSO software is used to find the optimal solution.

[0118] When the number of material layers is three, infrared radiation waves are emitted after adjustment by the SiC-ZnO-W structure inside the thermal emitter. Most of the emitted photons have a wavelength of 1820nm, which cannot meet the requirements of being absorbed by gallium antimonide (GaSb) batteries.

[0119] When the number of material layers is four, infrared radiation waves are emitted after adjustment by the SiC-ZnO-W-SiC structure inside the thermal emitter. Most of the emitted photons have a wavelength of 1760nm, which cannot meet the requirements of being absorbed by gallium antimonide (GaSb) batteries.

[0120] When the number of material layers is five, infrared radiation waves are emitted after adjustment of the SiC-ZnO-W-SiC-W structure inside the thermal emitter. Most of the emitted photons have a wavelength of 1700nm, which is smaller than the band gap wavelength of gallium antimonide (GaSb) of 1710nm. Therefore, when the number of material layers is five, the requirements for being absorbed by gallium antimonide (GaSb) batteries can be met.

[0121] When the number of material layers is six, the SiC-ZnO-W-SiC-WW structure inside the thermal emitter is adjusted to emit infrared radiation waves, and most of the emitted photons have a wavelength of 1640nm, which can meet the requirements of being absorbed by gallium antimonide (GaSb) batteries. However, considering that too many material layers may lead to waste in actual applications, thus failing to achieve maximum economic benefits, and too many material layers will prevent photons from reaching the surface of the photovoltaic cell, six or more material layers are not considered.

[0122] Secondly, in this series of data relationships, it is concluded that the optimal parameter order of the multilayer thermal emitter is SiC-ZnO-W-SiC-W and the thickness of each material. The specific results are shown in Table 1 below.

[0123] Finally, the design parameters of the multiple thermal emitter are shown in Table 1.

[0124] Table 1 Design parameters of multi-layer heat radiator

[0125] Number of layers Material Thickness (nm) D1 SiC 111 D2 ZnO 57 D1 W 17 D4 SiC 105 D5 W 153

[0126] This multilayer thermal radiation emitter consists of five layers (SiC-ZnO-W-SiC-W from top to bottom). The top SiC and ZnO layers have zero absorbance and are very sensitive to light wavelength. Therefore, they act as anti-reflection coatings to reduce light reflection and increase light absorption. The bottom W-SiC-W layer forms an FP resonant cavity. After being reflected by a parallel plane mirror, the light in the FP resonant cavity propagates parallel to the axis and never escapes the cavity, thereby increasing light absorption and improving thermoelectric conversion efficiency.

[0127] The multilayer thermal emitter is heated by solar energy and chemical energy. After heating, the multilayer thermal emitter emits infrared radiation light waves with a wavelength range of 780nm-1mm to the gallium antimonide (GaSb) cell. Since the band gap wavelength of the gallium antimonide (GaSb) cell is 1710nm, the gallium antimonide (GaSb) cell can only absorb high-energy photons below 1710nm. The SiC-ZnO-W-SiC-W structure inside the thermal emitter regulates the absorption of heat and then emits infrared radiation light waves, so that most of the emitted photons are below the band gap wavelength of the gallium antimonide (GaSb) cell. This allows the gallium antimonide (GaSb) cell to convert more electrical energy through the thermoelectric conversion effect, thereby improving the thermoelectric conversion efficiency.

[0128] The method for optimizing the parameters of multi-layer thermal emitters in thermophotovoltaics based on mathematical modeling of the embodiment of the present invention described above in conjunction with the accompanying drawings is used. The present invention repeatedly uses optimization algorithms to optimize the number of layers, thickness, and materials of each layer, selects the best combination, and finally analyzes the optimal solution for each combination, selects the combination of maximum energy and minimum wavelength, and obtains the various parameters of the thermal emitter. A new set of thermal emitter models is designed to maximize the efficiency of photovoltaic cells absorbing infrared radiation from thermal emitters and converting it into electrical energy. The problems existing in the prior art are solved. However, the present invention is not limited to the described embodiments. Changes, modifications, substitutions, and deformations to the embodiments without departing from the principles and spirit of the present invention still fall within the scope of protection of the present invention.

Claims

1. A method for optimizing parameters of multilayer thermal emitters in thermophotovoltaics based on mathematical modeling, characterized by: The following steps are involved: S1: Search for materials for making multilayer thermal emitters and find relevant characteristics of the materials; S2: Fit all material properties to a single wavelength; S3: Calculate the refractive index and extinction coefficient data of various materials within a unified wavelength range; S4: Under a single-layer heat reflector structure, the Fresnel coefficient is used to find the light energy within different wavelength ranges. Based on the relationship between the extinction coefficient and thickness of different media, the absorbance of different media is calculated. The relationship between reflectivity and refractive index is obtained from the law of reflection. Finally, the energy conservation theorem is used to derive the relationship between the emission spectrum and the medium characteristics under a single-layer structure. S5: In the multi-layer structure of the heat reflector, the Maxwell equations are used to calculate the Fresnel coefficient under vertical polarization. The Maxwell equations are then converted into a transmission matrix using the transfer matrix method. The transmittance and reflectance of the entire multi-layer structure are then calculated. Finally, the relationship between the absorbance and transmittance is used to derive the relationship between the emission spectrum and the medium properties in the multi-layer structure. S6: Since the band gap wavelength of the GaSb cell is a fixed value, an objective function expression is given based on this characteristic according to the relationship obtained in step S5, and constraints are set on the number of layers of the multilayer thermal emitter, the thickness of each layer of material, and the wavelength; S7: Use the particle swarm algorithm to optimize all media layer by layer, and obtain the optimal thickness combination under different media, forming a control test. Then use the particle swarm algorithm again to optimize the thickness of multiple layers, and thus obtain the optimal design parameter combination of the thermal emitter; S8: The multilayer thermal emitter is heated by solar energy and chemical energy. The heated multilayer thermal emitter emits infrared radiation waves to the gallium antimonide cell. The internal structure of the thermal emitter adjusts the absorbed heat and then emits infrared radiation waves, so that the emitted photons are lower than the band gap wavelength of the gallium antimonide cell, thereby allowing the gallium antimonide cell to convert more electrical energy through the thermoelectric conversion effect.

2. The method for optimizing parameters of multi-layer thermal emitters in thermophotovoltaics based on mathematical modeling according to claim 1, characterized in that: In step S4, the relationship between the emission spectrum and the medium properties under the single-layer structure is derived from the energy conservation theorem, which specifically includes the following steps: S11: The infrared radiation emitted by the thermal emitter is red light. The photons themselves have energy. The energy formula of photons is: （1） Where: h is Planck's constant, c is the speed of light, is the wavelength; S12: When the emitted light hits the medium vertically, part of it will be reflected vertically, and the other part will penetrate the medium. When the light passes through the medium, part of its own energy will be absorbed by the medium. The extinction coefficient of the same medium at different wavelengths is different, and the absorbance of the light energy absorbed by the medium is also different. The formula for absorbance is: （2） Where: k is the extinction coefficient, d is the thickness of the medium, so it can be concluded that the energy of light absorbed by the medium is: （3） S13: When light enters different media, it will be reflected and refracted. Assuming that the angle of incidence of light is 0, the relationship between the reflection coefficient and transmission coefficient of S-wave and P-wave is obtained by Snell's law. （4） Where: r s is the reflection coefficient of s wave, t s is the transmission coefficient of s wave, r p is the reflection coefficient of the p wave, t p is the transmission coefficient of p-wave, and are the angle of incidence and the angle of reflection, n1 and n2 are the refractive index of the first medium and the refractive index of the second medium, respectively. The relationship between reflectivity and transmittance is: （5） By the law of conservation of energy: R S +T S =1, R P +T P =1, at vertical incidence S14: The infrared radiation emitted by the thermal emitter is red light, and the relationship between the single-layer emission spectrum and the medium properties is obtained: （6） Where: h is Planck's constant, c is the speed of light in vacuum, is the wavelength of red light, is the wavelength in the medium, and d is the thickness of the medium.

3. The method for optimizing parameters of multi-layer thermal emitters in thermophotovoltaics based on mathematical modeling according to claim 2, characterized in that: The S5 also includes a double-layer heat reflector structure. The relationship between the emission spectrum and the medium characteristics in the double-layer heat reflector structure is: Where: r1 is the reflectivity of the first medium, r2 is the reflectivity of the second medium, d1 and d2 are the thicknesses of the two media respectively, and λ1 and λ2 are the absorbances of the two media respectively.

4. The method for optimizing parameters of multi-layer thermal emitters in thermophotovoltaics based on mathematical modeling according to claim 3, characterized in that: Tungsten and silicon dioxide are selected as two media in the double-layer heat reflector structure.

5. The method for optimizing parameters of multi-layer thermal emitters in thermophotovoltaics based on mathematical modeling according to claim 4, characterized in that: In the step S5, the Fresnel coefficients under vertical polarization are calculated using the Maxwell equations under the multilayer structure of the heat reflector, and the Maxwell equations are converted into the form of a transfer matrix using the transfer matrix method. the following: S21: The refractive index of different layers in the multilayer structure in the xy plane is expressed as: （8） Where: d is the thickness, n is the refractive index, and the type of polarization depends on the angle at which the wave falls on the surface of the medium. If the light is perpendicular to the medium surface and the falling angle is 0, then the polarization type produced by the light is vertical polarization, s polarization, or TE polarization. S22: Use Maxwell's equations to derive the Fresnel coefficients for vertical polarization. （9） S23: Use the transfer matrix method to transform Maxwell's equations into a transfer matrix form, which becomes an eigenvalue solution problem.

6. The method for optimizing parameters of multi-layer thermal emitters in thermophotovoltaics based on mathematical modeling according to claim 5, characterized in that: The step S23 specifically includes the following: S31: Maxwell's equations are used to solve the electric and magnetic fields on two adjacent layers to obtain the transmission matrix. The conclusion of a single layer is then extended to the entire medium space to calculate the transmission coefficient and reflection coefficient of the entire multilayer medium. The formula is as follows: （10） （11） in, is the phase thickness; is the wave number, The intrinsic impedance is derived from the following formula: （12） （13） （14） As shown in formula (11), Represented as a The total transmission matrix expresses the transmittance t and reflectance r, and the relationship between the emission spectrum of the multilayer structure and the refractive index and thickness of the medium is found as follows: Where i represents the relevant characteristics of the i-th layer of medium.

7. The method for optimizing parameters of multi-layer thermal emitters in thermophotovoltaics based on mathematical modeling according to claim 6, characterized in that: The constraints set in step S6 for the number of layers of the multilayer thermal emitter, the thickness of each layer of material, and the wavelength are: （16）。 8. The method for optimizing parameters of multi-layer thermal emitters in thermophotovoltaics based on mathematical modeling according to claim 6, characterized in that: The optimal design parameters of the heat emitter obtained in step S7 specifically include: As follows: Set the design parameters as variables, variable L is the number of layers, and the medium is randomly selected for each layer. The second variable is the thickness under a certain medium, and the third variable is the wavelength range. In order to find the optimal design parameters, the particle swarm algorithm is used for global optimization. If there are too many layers, light cannot reach the surface of the photovoltaic cell and infrared thermal radiation cannot be converted into electrical energy. After optimizing the thickness of various materials, the optimal thickness of each material is selected, and the particle swarm algorithm is used again to optimize the thickness of multiple layers to obtain the specific parameters of the material characteristics.

9. The method for optimizing parameters of multi-layer thermal emitters in thermophotovoltaics based on mathematical modeling according to claim 1, characterized in that: The multilayer thermal emitter comprises five layers, SiC-ZnO-W-SiC-W from top to bottom.

10. The method for optimizing parameters of multi-layer thermal emitters in thermophotovoltaics based on mathematical modeling according to claim 9, characterized in that: The wavelength of the multi-layer thermal emitter is in the range of 780nm-1mm.

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