An optimization method for the structure of a segmented thermoelectric generator

Abstract

The present invention relates to an optimization method for the structure of a segmented thermoelectric generator. By using Fourier's law and the calculation principle of calculus, the temperature distribution inside the segmented thermoelectric generator is analyzed, and the influence of temperature on the performance of thermoelectric materials is fully considered during the analysis, so as to optimize the calculation methods for the cross-sectional area of the thermoelectric arms inside the segmented thermoelectric generator and the heights of different thermoelectric materials, thereby improving the optimization accuracy of the structure of the segmented thermoelectric generator.

Description

Technical Field

[0001] The present invention relates to the technical field of optimizing the structure of thermoelectric generators, and particularly to an optimization method for the structure of a segmented thermoelectric generator. Background Art

[0002] The development of clean energy is currently a key research area. Thermoelectric power generation technology is a solid-state power generation technology based on the Seebeck effect, which can directly convert thermal energy into electrical energy. Thermoelectric generators (TEGs) have attracted attention due to their advantages such as small size, simple structure, long lifespan, and no pollution.

[0003] Although TEGs have many advantages, problems such as their low output efficiency have led to their limited widespread application. Applying the concept of functionally graded materials to thermoelectric materials enables each section of the thermoelectric material to operate within an optimal suitable temperature range, thereby improving the efficiency of the thermoelectric generator itself. This material is generally referred to as segmented thermoelectric material, and a thermoelectric generator constructed from this thermoelectric material is called a segmented thermoelectric generator (STEG).

[0004] The structural optimization of segmented generators is similar to that of thermoelectric generators. In traditional TEGs, the shapes of the P-type and N-type thermoelectric arms are cuboids, so the structural parameters that need to be optimized are the height and cross-sectional area of the thermoelectric arms. During the research process of optimizing the structure of traditional thermoelectric generators, the calculation formula for their output efficiency is shown in Formula (1):

[0005]

[0006] In the formula:

[0007] η —— is the output efficiency of the thermoelectric generator;

[0008] T h ,T c —— are the temperatures of the hot end and cold end of the thermoelectric TEG, respectively;

[0009] K —— is the thermal conductivity of the TEG;

[0010] R L ,R i —— are the external resistance and internal resistance of the TEG, respectively;

[0011] α PN —— is the equivalent Seebeck coefficient of the PN-type thermoelectric arms.

[0012] According to the formula, the output efficiency of the TEG is related to the performance of the thermoelectric material (Seebeck coefficient, thermal conductivity, resistivity), the temperatures of the hot and cold ends, and the magnitude of the external resistance.

[0013] In the calculation process of traditional TEGs, the performance of the thermoelectric materials of the PN-type thermoelectric arms is replaced by an average value for simplified calculation. After calculation, when the output efficiency reaches the maximum value, the calculation methods for the cross-sectional areas of the P-type and N-type thermoelectric arms are shown in Equation (2):

[0014]

[0015] A p ,A N —— The cross-sectional areas of the P-type and N-type thermoelectric arms, respectively;

[0016] κ P ,κ N —— The thermal conductivities of the P-type and N-type thermoelectric arms, respectively;

[0017] ρ P ,ρ N —— The resistivities of the P-type and N-type thermoelectric arms, respectively.

[0018] In the research process of thermoelectric material performance, the concept of the figure of merit Z was proposed to compare the magnitudes of thermoelectric material performance. Based on Equation (1), the calculation expression for the Z value corresponding to the PN-type thermoelectric arm was derived (as shown in Equation (3)).

[0019]

[0020] In the traditional research process, most did not consider the influence of temperature on the performance of thermoelectric materials, resulting in a deviation between the final calculation result and the actual result. Summary of the Invention

[0021] Aiming at the problems existing in the prior art, the purpose of the present invention is to provide an optimization method for the structure of a segmented thermoelectric generator, which fully considers the influence of temperature on materials to improve the design accuracy of the structure.

[0022] To achieve the above purpose, the technical solution adopted by the present invention is:

[0023] An optimization method for the structure of a segmented thermoelectric generator, the optimization method analyzes the temperature distribution inside the segmented thermoelectric generator by using Fourier's law and the calculation principle of calculus, and fully considers the influence of temperature on the performance of thermoelectric materials during the analysis process, thereby optimizing the calculation methods for the cross-sectional areas of the thermoelectric arms and the heights of different thermoelectric materials inside the segmented thermoelectric generator:

[0024] For both the P-type and N-type thermoelectric arms, each is composed of n layers of thermoelectric arms, where n ≥ 3; the temperatures at the junction between the i-th layer of thermoelectric material and the (i + 1)-th layer of thermoelectric material are T sbi and T sai , the thermal conductivities of the i-th layer of thermoelectric material are κ SPi and κ SNi , the electrical resistivities of the i-th layer of thermoelectric material are ρ SPi and ρ SNi . Meanwhile, ignoring the influence of the thermal conductivities of the copper current collectors and ceramics on temperature propagation, the hot and cold end temperatures of the P-type and N-type segmented thermoelectric arms are both T c and T h , T sb0 = T sa0 = T c ; T sbn = T san = T h ;

[0025] Within the range of the hot end temperature T h and the cold end temperature T c , set the temperature at the junction between every two layers of thermoelectric materials according to the properties of the thermoelectric materials, and obtain the internal resistance of the segmented thermoelectric generator as follows:

[0026]

[0027]

[0028] R St = R SN + R SP

[0029] where R SP , R SN —are the resistances of the P-type and N-type segmented thermoelectric arms respectively;

[0030] R St —is the resistance of the PN-type segmented thermoelectric arm;

[0031] H S —is the total height of the segmented thermoelectric arm;

[0032] A SP , A SN —are the cross-sectional areas of the P-type and N-type segmented thermoelectric arms respectively, and are calculated as follows:

[0033]

[0034] Then, calculate the maximum output efficiency of the segmented thermoelectric generator according to the following formula:

[0035]

[0036] In the formula:

[0037] η —— is the maximum output efficiency;

[0038] K —— is the thermal conductivity;

[0039] R L and R i —— are respectively the external resistance and internal resistance of the TEG, and R i is R St ;

[0040] α PN —— is the equivalent Seebeck coefficient of the PN-type thermoelectric arm;

[0041] Within the range of the hot-end temperature T h and the cold-end temperature T c , reset the temperature at the junction of every two layers of thermoelectric materials according to the properties of the thermoelectric materials, and then calculate the new maximum output efficiency according to the above method;

[0042] Repeat the above operations to obtain multiple maximum output efficiencies, select the largest one among them, and calculate the structural parameters of the segmented thermoelectric generator according to the temperature at the junction of every two layers of thermoelectric materials corresponding to the largest maximum output efficiency, as follows:

[0043] The height values of the i-th layer of thermoelectric materials of the P-type and N-type segmented thermoelectric arms are as follows:

[0044]

[0045] The ratio of the cross-sectional areas of the P-type thermoelectric arm and the N-type thermoelectric arm is as follows:

[0046]

[0047] The figure of merit Z of the segmented thermoelectric generator is calculated as follows:

[0048]

[0049] After adopting the above scheme, the temperature distribution inside the segmented thermoelectric generator is analyzed by using Fourier's law and the calculation principle of calculus, and the influence of temperature on the performance of thermoelectric materials is fully considered during the analysis process, so as to optimize the calculation methods of the cross-sectional area of the thermoelectric arms and the height of different thermoelectric materials inside the segmented thermoelectric generator, thereby improving the structural optimization accuracy of the segmented thermoelectric generator. Description of the Drawings

[0050] Figure 1 It is a schematic diagram of the PN-type thermoelectric arm structure inside the segmented thermoelectric generator;

[0051] Figure 2 Schematic diagram of one-dimensional steady-state heat conduction of a single-layer homogeneous flat plate;

[0052] Figure 3 Schematic diagram of one-dimensional steady-state heat conduction of a two-layer homogeneous flat plate;

[0053] Figure 4 Schematic diagram of one-dimensional steady-state heat conduction of an n-layer homogeneous flat plate;

[0054] Figure 5 Schematic diagram of the hot-spot performance of the material selected in the embodiment of the present invention;

[0055] Figure 6 Schematic diagram of the relationship between Tsa and Tsb and the maximum output efficiency in the embodiment of the present invention. Detailed implementation manners

[0056] The present invention discloses an optimization method for the structure of a segmented thermoelectric generator, which analyzes the temperature distribution inside the segmented thermoelectric generator by using Fourier's law and the calculation principle of calculus, and fully considers the influence of temperature on the performance of thermoelectric materials during the analysis process, so as to optimize the calculation methods for the cross-sectional area of the thermoelectric arms and the heights of different thermoelectric materials inside the segmented thermoelectric generator, thereby improving the optimization accuracy of the structure of the segmented thermoelectric generator.

[0057] First, as Figure 2 shown, the present invention can change the mathematical expression of the transferred heat Q k to Equation (4) by using Fourier's law of heat conduction:

[0058]

[0059] As Figure 3 shown, when the thermal conductivity is a constant and the two surface temperatures are of a homogeneous flat plate with uniform and constant temperatures, the rate of heat flow entering from the left surface is opposite to that exiting from the right, so Equation (5) can be obtained.

[0060]

[0061] In the formula:

[0062] Q - the transferred heat;

[0063] q - the transfer velocity of heat flow.

[0064] Generalizing it to an n-layer composite flat plate, Equation (6) can be obtained.

[0065]

[0066] For the thermoelectric materials in the TEG, the thermal conductivity changes with temperature. Taking △T as the standard, it is evenly divided into an n-layer flat plate structure (asFigure 4 As shown in the figure, using Equation (6), Equation can be obtained.

[0067]

[0068] where

[0069]

[0070] Equation (9) can be simplified from Equation (7).

[0071]

[0072] When the height of the thermoelectric arm is H n According to the formula, the temperature T w and T w+1 For the flat plate of this layer, the expression of its height is as shown in the equation.

[0073]

[0074] Both the P-type and N-type thermoelectric arms in common TEGs are cuboids. When the conductivity of the material is determined, the expression of its resistance is as shown in Equation (11).

[0075]

[0076] In the formula:

[0077] R——is the resistance of the conductor;

[0078] L——is the height of the conductor;

[0079] A——is the cross-sectional area of the conductor;

[0080] ρ——is the resistivity of the conductor;

[0081] σ——is the conductivity of the conductor.

[0082] For the PN-type segmented thermoelectric arms in STEG, after adding the hot-end temperature and the cold-end temperature, its schematic diagram is as Figure 1 shown. Assume that the temperature at the boundary of different materials of the N-type thermoelectric arm is T sa , and the temperature at the boundary of different materials of the P-type thermoelectric is T sb . For the P-type and N-type segmented thermoelectric arms, assume that the thermal conductivities of the thermoelectric materials close to the high-temperature region are κ SPh and κ SNh , and the thermal conductivities of the thermoelectric materials close to the low-temperature region are κ SPc and κ SNc . At the same time, ignoring the influence of the thermal conductivities of the copper current collector and the ceramic on the temperature propagation, the hot and cold end temperatures of the P-type and N-type segmented thermoelectric arms are both Tc and T h , so the formula can be used to obtain the equation.

[0083]

[0084] In the equation:

[0085] k, j, e, and f are arbitrary constants, and K, J, E, and F are arbitrary integers between 0 and k, j, e, and f respectively;

[0086] q P , q N —— are the heat outflow transfer rates of the P-type and N-type thermoelectric arms respectively;

[0087] κ SPh , κ SNh —— are the thermal conductivities of the thermoelectric materials at the high-temperature ends of the P-type and N-type segmented thermoelectric arms respectively;

[0088] κ SPc , κ SNc —— are the thermal conductivities of the thermoelectric materials at the low-temperature ends of the P-type and N-type segmented thermoelectric arms respectively;

[0089] If it is assumed that in the STEG, the height of the segmented thermoelectric arm is H S , then after simplifying and arranging the formula, equation (13) can be obtained.

[0090]

[0091] In the equation:

[0092] H SPh , H SNh —— are the heights of the thermoelectric materials at the high-temperature ends of the P-type and N-type segmented thermoelectric arms respectively;

[0093] H SPc , H SNc —— are the heights of the thermoelectric materials at the low-temperature ends of the P-type and N-type segmented thermoelectric arms respectively;

[0094] H S —— is the total height of the segmented thermoelectric arm.

[0095] When △T approaches zero infinitely, k, j, e, and f will approach infinity, and according to the knowledge of calculus, equation (14) is obtained.

[0096]

[0097] Combining formula (13) and formula (14) can obtain the expressions of H SNc , H SNh , H SPc and H SPh as shown in equation (15).

[0098]

[0099] Through formula (15), the height ratio of different thermoelectric materials in the PN-type segmented thermoelectric arm can be obtained, and thus the actual heights of different thermoelectric materials can be calculated.

[0100] Combining formula (10) and formula (11), it can be obtained that in the thermoelectric generator, the resistances of the thermoelectric materials at the high-temperature ends and low-temperature ends of the N-type and P-type segmented thermoelectric arms are as shown in formula (16).

[0101]

[0102] In the formula:

[0103] R SPh and R SNh —— are the resistances of the thermoelectric materials at the high-temperature ends of the P-type and N-type segmented thermoelectric arms respectively;

[0104] R SPc and R SNc —— are the resistances of the thermoelectric materials at the low-temperature ends of the P-type and N-type segmented thermoelectric arms respectively;

[0105] A SP and A SN —— are the cross-sectional areas of the P-type and N-type segmented thermoelectric arms respectively;

[0106] σ SPh and σ SNh —— are the conductivities of the thermoelectric materials at the high-temperature ends of the P-type and N-type segmented thermoelectric arms respectively;

[0107] σ SPc and σ SNc —— are the conductivities of the thermoelectric materials at the low-temperature ends of the P-type and N-type segmented thermoelectric arms respectively;

[0108] Multiply both the numerator and denominator in formula (16) by △T, and according to the method of calculus, the resistances of the P-type and N-type segmented thermoelectric arms can be obtained, and their resistance values are as shown in formula (17).

[0109]

[0110] In the formula:

[0111] R SP and R SN —— are the resistances of the P-type and N-type segmented thermoelectric arms respectively;

[0112] R St —— is the resistance of the PN-type segmented thermoelectric arm.

[0113] Substituting formula (17) into formula (1) and calculating, it can be obtained that when the output efficiency reaches the maximum value, the cross-sectional area calculation method of the P-type and N-type segmented thermoelectric arms ( Figure 1 ) is as shown in formula (18):

[0114]

[0115] In the formula:

[0116] ρ SPh , ρ SNh ——Resistivities of the thermoelectric materials at the high-temperature ends of the P-type and N-type segmented thermoelectric arms, respectively;

[0117] ρ SPc , ρ SNc ——Resistivities of the thermoelectric materials at the low-temperature ends of the P-type and N-type segmented thermoelectric arms, respectively.

[0118] Within the range of the hot-end temperature T h and the cold-end temperature T c , multiple sets of Ts b and Ts a are taken. For each set of Ts b and Ts a , the thermoelectric arm resistance values are calculated according to formula (17). Each set of Ts b and Ts a corresponds to a maximum output efficiency value, and the maximum output efficiency under this set of Ts b and Ts a is calculated according to formula (1). Then, the maximum value is selected from all the maximum output efficiency values. Then, using the T b and T a corresponding to this maximum value, the corresponding structural parameters are calculated, which are the finally optimized structural parameters; specifically as follows:

[0119] Calculate the height ratio of different thermoelectric materials in the P-type and N-type thermoelectric arms according to formula (15), and then calculate the actual heights of different thermoelectric materials;

[0120] Calculate the cross-sectional area ratio of the P-type and N-type thermoelectric arms according to formula (18).

[0121] In addition, through calculation, it can be obtained that on the premise of considering the influence of temperature on thermoelectric materials, the calculation of the figure of merit Z of the PN-type segmented thermoelectric arm in a certain temperature range is as shown in formula (19), and this formula provides a new reference for the performance comparison of the PN-type segmented thermoelectric arm in any temperature range.

[0122]

[0123] The present invention analyzes the temperature distribution inside a segmented thermoelectric generator by using Fourier's law and the calculation principle of calculus, and fully considers the influence of temperature on the performance of thermoelectric materials during the analysis process, thereby optimizing the calculation methods for the cross-sectional area of the thermoelectric arms inside the segmented thermoelectric generator and the heights of different thermoelectric materials, so as to improve the structural optimization accuracy of the segmented thermoelectric generator. In addition, on the premise of considering the influence of temperature on thermoelectric materials, the present invention optimizes the calculation formula for the figure of merit Z of the PN-type segmented thermoelectric arm within a certain temperature range, providing a new reference for the comparison of the performance of STEGs in the future.

[0124] For the optimized design of STEGs, compared with the optimized design methods considering the influence of temperature on thermoelectric materials in other articles, the new method provided by this patent has a simpler structure and more convenient calculation.

[0125] In the above embodiments, the PN-type thermoelectric arm is composed of two layers of thermoelectric materials, but it can be analogously extended to PN-type segmented thermoelectric arms composed of three, four, or even multiple layers of thermoelectric materials.

[0126] For P-type and N-type thermoelectric arms, each of them is composed of n layers of thermoelectric arms, where n ≥ 3; the temperatures at the junction between the i-th layer of thermoelectric material and the (i + 1)-th layer of thermoelectric material are T sbi and T sai , the thermal conductivities of the i-th layer of thermoelectric material are κ SPi and κ SNi , the resistivities of the i-th layer of thermoelectric material are ρ SPi and ρ SNi , and meanwhile, ignoring the influence of the thermal conductivities of copper current collectors and ceramics on temperature propagation, the hot and cold end temperatures of the P-type and N-type segmented thermoelectric arms are both T c and T h , T sb0 =T sa0 =T c ; T sbn =T san =T h ;

[0127] Within the range of the hot end temperature T h and the cold end temperature T c , set the temperature at the junction between every two layers of thermoelectric materials according to the properties of the thermoelectric materials, and obtain the internal resistance of the segmented thermoelectric generator as follows:

[0128]

[0129]

[0130] R St =R SN +R SP

[0131] Among them, R SP , R SN —— are the resistances of the P-type and N-type segmented thermoelectric arms respectively;

[0132] R St —— is the resistance of the PN-type segmented thermoelectric arm;

[0133] H S —— is the total height of the segmented thermoelectric arm;

[0134] A SP , A SN —— are the cross-sectional areas of the P-type and N-type segmented thermoelectric arms respectively, and are calculated as follows:

[0135]

[0136] Then, the maximum output efficiency of the segmented thermoelectric generator is calculated according to the following formula (1):

[0137]

[0138] In the formula:

[0139] η—— is the maximum output efficiency;

[0140] K—— is the thermal conductivity coefficient;

[0141] R L , R i —— are the external resistance and internal resistance of the TEG respectively, and R i is R St ;

[0142] α PN —— is the equivalent Seebeck coefficient of the PN-type thermoelectric arm;

[0143] Within the range of the hot-end temperature T h and the cold-end temperature T c , the temperature at the junction of every two layers of thermoelectric materials is reset according to the properties of the thermoelectric materials, and then the new maximum output efficiency is calculated according to the above method;

[0144] Repeat the above operations to obtain multiple maximum output efficiencies, select the largest one among them, and calculate the structural parameters of the segmented thermoelectric generator according to the temperature at the junction of every two layers of thermoelectric materials corresponding to the largest maximum output efficiency, as follows:

[0145] The height values of the i-th layer of thermoelectric materials of the P-type and N-type segmented thermoelectric arms are as follows:

[0146]

[0147] The ratio of the cross-sectional areas of the P-type and N-type thermoelectric arms is as follows:

[0148]

[0149] The figure of merit coefficient Z of the segmented thermoelectric generator is calculated as follows:

[0150]

[0151] In the present invention, κ SNi (T), ρ SNi (T) is a function of temperature T and changes with the temperature value. For convenience, in some formulas, it is abbreviated as κ SNi 、ρ SNi .

[0152] To better illustrate the technical effects of the present invention, specific embodiments will be listed below for illustration.

[0153] The thermoelectric performance parameters of the materials selected in this embodiment are as Figure 3 shown. According to the size parameters of the existing TEGs on the market, it can be assumed that the height of the PN-type thermoelectric arms is 2 mm (excluding the current collectors), and the sum of the cross-sectional areas of the P-type and N-type thermoelectric arms is 2 mm 2 , and for convenience of calculation, it can be assumed that the width of the PN-type thermoelectric arms is constantly 1 mm. Copper material is used as the current collector of the PN-type thermoelectric arms, and its dimensions of length, width and height are 2.5 mm, 1.0 mm and 0.2 mm respectively. At the same time, considering the possible application scenarios in the future, it can be assumed that the working environment of the TEG is a hot-end temperature of 800 K and a cold-end temperature of 300 K, and the N-type and P-type thermoelectric materials used in this STEG are both Bi2Te3 (low temperature) and PbTe (high temperature).

[0154] When the hot and cold-end temperatures are assumed to be 300 K and 800 K respectively, and the traditional optimization method and the optimization method proposed in this patent are used for optimization respectively, the corresponding optimal structural parameters are shown in Table 1.

[0155] Table 1 When T h = 800 K, T c = 300 K, the size parameters of the PN-type segmented thermoelectric arms corresponding to different optimization methods

[0156]

[0157] Using mathematical knowledge, it can be calculated that the relationship between the temperatures (T Sa , T Sb ) at the junctions of different thermoelectric materials in the N-type and P-type segmented thermoelectric arms and the output efficiency is as Figure 6 shown.

[0158] Substitute the data in Table 1 intoFigure 6 As can be seen from the results, the maximum output efficiencies obtained by using the method of the present invention and the traditional method are 14.703% and 14.693% respectively. It can be seen therefrom that the output efficiency obtained by using the method of the present invention is superior to the traditional method.

[0159] As described above, it is only an embodiment of the present invention, and does not impose any limitation on the technical scope of the present invention. Therefore, any minor modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. An optimization method for the structure of a segmented thermoelectric generator, characterized in that: The optimization method analyzes the temperature distribution inside the segmented thermoelectric generator by using Fourier's law and the calculation principle of calculus, and fully considers the influence of temperature on the performance of thermoelectric materials during the analysis process, so as to optimize the calculation methods of the cross-sectional area of the thermoelectric arms and the heights of different thermoelectric materials inside the segmented thermoelectric generator: For both the P-type and N-type thermoelectric arms, each consists of n layers of thermoelectric arms, where n ≥ 3; the temperatures at the junction between the i-th layer of thermoelectric material and the (i + 1)-th layer of thermoelectric material are T sbi and T sai , the thermal conductivities of the i-th layer of thermoelectric material are κ SPi and κ SNi , the resistivities of the i-th layer of thermoelectric material are ρ SPi and ρ SNi . Meanwhile, neglecting the influence of the thermal conductivities of the copper current collectors and ceramics on temperature propagation, the hot and cold end temperatures of the P-type and N-type segmented thermoelectric arms are both T c and T h , T sb0 = T sa0 = T c ; T sbn = T san = T h ; At the hot-end temperature T h and the cold-end temperature T c within the range, set the temperature at the junction of every two layers of thermoelectric materials according to the properties of the thermoelectric materials, and obtain the internal resistance of the segmented thermoelectric generator as follows: R St = R SN + R SP Among them, R SP , R SN —— are the resistances of the P-type and N-type segmented thermoelectric arms, respectively; R St —— Resistance of the PN-type segmented thermoelectric arm; H S —— Total height of segmented thermoelectric arm; A SP ,A SN —— are the cross-sectional areas of the P-type and N-type segmented thermoelectric arms, respectively, and are calculated as follows: Then, the maximum output efficiency of the segmented thermoelectric generator is calculated according to the following formula: In the formula: η —— is the maximum output efficiency; K —— is the thermal conductivity; R L and R i —— are the external resistance and internal resistance of TEG respectively, and R i is R St ; α PN —— is the equivalent Seebeck coefficient of the PN-type thermoelectric arm; Within the range of the hot-end temperature T h and the cold-end temperature T c reset the temperature at the junction of every two layers of thermoelectric materials according to the properties of the thermoelectric materials, and then calculate the new maximum value of the output efficiency according to the above method; Repeat the above operations to obtain multiple maximum output efficiencies, select the largest one among them, and calculate the structural parameters of the segmented thermoelectric generator according to the temperature at the junction of every two layers of thermoelectric materials corresponding to the largest maximum output efficiency, as follows: The height values of the i-th layer of thermoelectric materials of the P-type and N-type segmented thermoelectric arms are as follows: The ratio of the cross-sectional areas of the P-type thermoelectric arm and the N-type thermoelectric arm is as follows:

2. The optimization method of a segmented thermoelectric generator structure according to claim 1, characterized in that: The figure of merit Z of the segmented thermoelectric generator is calculated as follows:

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