Design method of multi-stage thermoelectric cooler adaptive to multi-component bismuth telluride temperature zone

Abstract

The invention discloses a design method of a multi-stage thermoelectric cooler adaptive to a multi-component bismuth telluride temperature zone. The design method comprises the following steps: preparing bismuth telluride materials with various components and different thermoelectric properties; testing the change relation of the thermoelectric parameters of the multiple groups of bismuth telluride materials in a near room temperature range along with the temperature; based on a test result, screening the bismuth telluride material with the highest thermoelectric figure of merit in different temperature zones, drawing a curve of thermoelectric parameters of the bismuth telluride material changing along with the temperature, and fitting to obtain a high-order term expression taking the temperature as a variable; setting an initial value of the logarithm and an initial value of the grain size of each layer of element of the multistage thermoelectric refrigerating unit, and substituting the obtained fitting expression into a heat balance equation set of the multistage thermoelectric refrigerating unit according to a temperature zone for analysis; and solving a heat balance equation set by iterating the logarithm and the grain size of each layer of element to obtain an optimal design parameter and finish the design. By means of the method, structural optimization of the multistage thermoelectric cooler can be achieved, material temperature zone adaptation and structural parameter collaborative optimization are achieved, and the refrigeration temperature difference and the refrigeration power are remarkably improved.

Description

Technical Field

[0001] This application belongs to the field of thermoelectric device design technology, and in particular to a design method for a multi-stage thermoelectric cooler with multi-component bismuth telluride temperature range adaptation. Background Technology

[0002] Thermoelectric coolers (TECs) are based on the Peltier effect and achieve solid-state cooling through direct current drive. They offer advantages such as no moving parts, high reliability, and compact size. To achieve a larger cooling temperature difference, multiple single-stage thermoelectric modules are typically cascaded and stacked to form a multi-stage thermoelectric cooler. In this structure, the cold end of a lower-stage thermoelectric module contacts the hot end of a higher-stage module, absorbing the heat released by the higher-stage module's hot end. This allows the cold end of the higher-stage module to reach a lower temperature, making it suitable for applications such as heat dissipation of electronic devices in cryogenic environments and temperature control of precision instruments.

[0003] As the number of stages increases, a large temperature gradient forms from the cold end to the hot end within a multi-stage thermoelectric cooler. For example, when achieving a temperature difference exceeding 100°C, the cold end temperature may drop below -90°C, while the hot end temperature remains in the near-room temperature range of 0-50°C. However, the bismuth telluride-based thermoelectric material, which forms the core of the thermoelectric cooler, exhibits a significant temperature dependence in its thermoelectric performance figure of merit (ZT value), with key parameters such as the Seebeck coefficient, electrical conductivity, and thermal conductivity all changing nonlinearly with temperature.

[0004] Currently, most multi-stage thermoelectric coolers are designed using the same bismuth telluride material with uniform composition and properties for each stage. This prevents the material from achieving optimal performance within its specific local temperature range, as it is difficult for a single material to maintain its peak ZT value across such a wide temperature span. Furthermore, existing design methods typically model the structure based solely on the thermoelectric parameters of a single material, failing to adequately consider the dynamic characteristics of material properties changing with temperature. Consequently, the device's performance is not optimal in actual operation, and its cooling efficiency and limiting temperature range are constrained. Summary of the Invention

[0005] This application provides a design method for a multi-stage thermoelectric cooler with multi-component bismuth telluride temperature range adaptation, aiming to solve the technical problem of how to achieve the optimal design of the overall device performance through temperature range matching of material properties and synergistic optimization of structural parameters.

[0006] To solve at least one of the above-mentioned technical problems, the technical solution adopted in this application is:

[0007] A design method for a multi-stage thermoelectric cooler with multi-component bismuth telluride temperature range adaptation, comprising the following steps:

[0008] S1. Preparation of bismuth telluride materials with various components and different thermoelectric properties;

[0009] S2. Test the thermoelectric parameters of multiple groups of the bismuth telluride materials as a function of temperature in the near-room temperature range;

[0010] S3. Based on the test results, select the bismuth telluride material with the highest thermoelectric figure of merit in different temperature zones, plot the curves of its thermoelectric parameters changing with temperature, and fit the obtained high-order expression with temperature as the variable.

[0011] S4. Set the initial values ​​of the logarithm and grain size of each level element of the multi-stage thermoelectric cooler, and substitute the fitting expression obtained in step S3 into the heat balance equation set of the multi-stage thermoelectric cooler according to the temperature zone for analysis.

[0012] S5. By iterating through the logarithms and grain sizes of each level of components, the heat balance equations are solved to obtain the optimal design parameters and complete the design of the multi-stage electrothermal cooler.

[0013] Furthermore, in step S1, the bismuth telluride material is an N-type bismuth telluride crystal rod and a P-type bismuth telluride crystal rod prepared by zone melting or hot extrusion; wherein, the compressive strength is ≥80MPa.

[0014] Furthermore, the bismuth telluride material used to prepare N-type bismuth telluride crystal rods has the following chemical formula: Where 0 ≤ x ≤ 0.8, 0 ≤ y ≤ 0.5;

[0015] The bismuth telluride material used to prepare p-type bismuth telluride crystal rods has the following chemical formula: , where 0≤x≤0.8, 0≤y≤0.5.

[0016] Furthermore, the bismuth telluride material used in the N-type bismuth telluride crystal rod is doped with a Group VIIA halogen compound, wherein the halogen compound has a mass percentage of 0-1.0 wt% and is selected from... , , , , One or more of them.

[0017] Furthermore, in step S2, the thermoelectric parameters are tested using a low-temperature property measurement system or by introducing liquid nitrogen into the thermoelectric performance test bench. The test temperature points include 173K, 198K, 223K, 248K, 273K, 298K, and 323K. The thermoelectric parameters include electrical conductivity σ, Seebeck coefficient α, and thermal conductivity κ.

[0018] Furthermore, the different temperature zones in step S3 include at least:

[0019] First temperature zone: [173K, 223K);

[0020] Second temperature zone: [223K, 273K);

[0021] Third temperature zone: [273K, 323K];

[0022] For each temperature range, at least one component of the N-type and P-type bismuth telluride material with the highest thermoelectric figure of merit (ZT) in that temperature range is selected.

[0023] Furthermore, using a numerical fitting method, the conductivity of the N-type and P-type bismuth telluride materials with optimal thermoelectric performance in each temperature range was established. Seebeck coefficient Thermal conductivity The mathematical expression for higher-order terms that change with temperature, where m = 1, 2, 3, corresponding to the three temperature zones respectively.

[0024] Furthermore, in the structure of the multi-stage thermoelectric cooler constructed in step S4:

[0025] The top layer is the first stage cold end;

[0026] The intermediate levels, from top to bottom, are level 2 to level i-1;

[0027] The bottom layer is the i-th level hot end;

[0028] Where i is the total number of stages in the multi-stage thermoelectric cooler, 3≤i≤6;

[0029] And set the initial number of pairs of components in each level from the first-level cold end to the i-th-level hot end as follows: , … The initial cross-sectional area of ​​each layer of components is ; , … The initial height of each level of component is ; , … .

[0030] Furthermore, the heat balance equations for the multi-stage thermoelectric cooler in step S4 are established based on the Peltier heat, Joule heat, and Fourier heat conduction of the thermoelectric effect, specifically as follows:

[0031] For level 1, a fitting function is used. , , The heat flow equations for the cold and hot ends are constructed as follows: The heat flow equation for the cold end is shown in equation (1), and the heat flow equation for the hot end is shown in equation (2).

[0032] (1)

[0033] (2)

[0034] For the intermediate levels 2 to (i-1), a fitting function is used. , , The heat flow equations for the cold and hot ends are constructed as follows: the heat flow equation for the cold end is shown in equation (3), and the heat flow equation for the hot end is shown in equation (4).

[0035] (3)

[0036] (4)

[0037] For the i-th level, the fitting function is used. , , The heat flow equations for the cold and hot ends are constructed as follows: the heat flow equation for the cold end is shown in equation (5), and the heat flow equation for the hot end is shown in equation (6).

[0038] (5)

[0039] (6)

[0040] in, and These are the cold and hot end temperatures of the i-th stage cooling component, respectively. and These represent the heat at the cold and hot ends of the i-th stage cooling component, respectively; c represents the cold end; h represents the hot end; and I represents the current. Represents the number of pairs of elements at level i, which is greater than 1 and is an integer; These represent the electrical conductivity, Seebeck coefficient, and thermal conductivity of bismuth telluride materials, respectively. Represents the height of the i-th level component; This represents the cross-sectional area of ​​the i-th level element.

[0041] Furthermore, in step S5, the iteration condition includes ensuring temperature continuity between adjacent levels. With heat flow continuity The iteration terminates when the maximum cold temperature difference is obtained. Or the maximum cold end absorbs heat .

[0042] The design method of a multi-stage thermoelectric cooler with multi-component bismuth telluride temperature range adaptability, as proposed in this application, is based on the core of which is to achieve structural optimization of the multi-stage thermoelectric cooler through the selection of multi-component, temperature range adaptable bismuth telluride materials and iterative thermal balance modeling. This method solves the problem that multi-stage thermoelectric coolers have a large operating temperature range and it is difficult for a single material to maintain optimal performance across the entire temperature range. It achieves synergistic optimization of material temperature range adaptability and structural parameters, significantly improving the cooling temperature difference and cooling power. Attached Figure Description

[0043] Figure 1 A flowchart of the design method proposed in this application;

[0044] Figure 2 This is a schematic diagram of the material distribution of the five-stage thermoelectric cooler in Embodiment 1 of this application;

[0045] Figure 3 The optimal electrical conductivity curves of the N-type bismuth telluride material in this application are shown in various temperature ranges.

[0046] Figure 4 The optimal Seebeck coefficient curves for the N-type bismuth telluride material in this application are shown in various temperature ranges.

[0047] Figure 5 The optimal thermal conductivity curves of the N-type bismuth telluride material in this application are shown in various temperature ranges.

[0048] Figure 6 The optimal ZT values ​​for the N-type bismuth telluride material in this application are shown in various temperature ranges.

[0049] Figure 7 The optimal electrical conductivity curves of the P-type bismuth telluride material in this application are shown in various temperature ranges.

[0050] Figure 8 The optimal Seebeck coefficient curves for the P-type bismuth telluride material in this application are shown in various temperature ranges.

[0051] Figure 9 The optimal thermal conductivity curves of the P-type bismuth telluride material in this application are shown in various temperature ranges.

[0052] Figure 10 The optimal ZT values ​​for the P-type bismuth telluride material in this application are shown in various temperature ranges.

[0053] Figure 11 The hot surface of the five-stage thermoelectric cooler assembly in Embodiment 1 of this application. The curve showing the change in cooling temperature difference with current during design;

[0054] Figure 12 The hot surface of the five-stage thermoelectric cooler assembly in Comparative Example 1 of this application The curve showing the change in cooling temperature difference with current during the design process. Detailed Implementation

[0055] The present application will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0056] This embodiment proposes a design method for a multi-stage thermoelectric cooler with multi-component bismuth telluride temperature range adaptation, such as... Figure 1 As shown, the steps include:

[0057] S1. Prepare bismuth telluride materials with various components and different thermoelectric properties.

[0058] The preparation process of bismuth telluride materials is either zone melting or hot extrusion, yielding N-type and P-type bismuth telluride crystal rods. The compressive strength must be ≥80 MPa to ensure the integrity of the material's crystal lattice structure and provide sufficient mechanical support.

[0059] The bismuth telluride material used in the preparation of N-type bismuth telluride crystal rods has the following chemical formulas: Bi, Sb, Te, and Se. , where 0≤x≤0.8, 0≤y≤0.5.

[0060] The bismuth telluride material used in the preparation of p-type bismuth telluride crystal rods has the following chemical formulas: Bi, Sb, Te, and Se. Where 0 ≤ x ≤ 0.8 and 0 ≤ y ≤ 0.5. The composition is controlled by adjusting the chemical formulas of Bi, Sb, Te, and Se, thereby changing the band structure, carrier concentration, and mobility of the material.

[0061] The bismuth telluride material used in N-type bismuth telluride crystal rods is doped with a Group VIIA halogen compound, with a doping ratio (mass percentage) of 0-1.0 wt%. , , , , One or more of these are used to optimize the balance between electrical conductivity and thermal conductivity.

[0062] By adjusting the ratio of chemical formulas (x and y) to dopants, multi-component bismuth telluride materials with different trends in thermoelectric properties (conductivity, Seebeck coefficient, and thermal conductivity) with temperature were prepared, enabling them to exhibit different thermoelectric figures of merit (ZT values) in different temperature ranges, laying the foundation for selecting the optimal material in different temperature regions.

[0063] S2. Test the thermoelectric parameters of multiple groups of bismuth telluride materials as a function of temperature in the near-room temperature range.

[0064] Near-room temperature refers to a wide temperature range from a low temperature of 173K (-100℃) to a typical hot-end temperature of 323K (50℃), which covers the entire operating temperature range of multi-stage thermoelectric coolers from the cold end to the hot end.

[0065] Thermoelectric parameters of multiple bismuth telluride materials from step S1 were tested using a low-temperature property measurement system or by introducing liquid nitrogen into the thermoelectric performance testing platform. These thermoelectric parameters included electrical conductivity σ, Seebeck coefficient α, and thermal conductivity κ. The test temperatures were 173K, 198K, 223K, 248K, 273K, 298K, and 323K; seven discrete temperature points were used to plot continuous curves. The aim was to obtain continuous or discrete data on the thermoelectric parameters of each material as a function of temperature. The test results were directly used for fitting higher-order terms, providing input functions for modeling and experimental basis for subsequent selection of optimal materials in each temperature range and establishment of fitting functions.

[0066] Formula (7) for calculating the thermoelectric figure of merit ZT using electrical conductivity σ, Seebeck coefficient α, and thermal conductivity κ is:

[0067] (7)

[0068] T represents the temperature of the bismuth telluride material, measured in K.

[0069] Because the properties of thermoelectric materials are strongly temperature-dependent, the same material may have drastically different ZT values ​​at different temperatures, so these values ​​must be obtained experimentally. , and Only by understanding the true trend of temperature changes can precise temperature zone adaptation be achieved.

[0070] S3. Based on the test results, select the bismuth telluride material with the highest thermoelectric figure of merit in different temperature zones, plot the curves of its thermoelectric parameters as a function of temperature, and fit the obtained high-order expression with temperature as the variable.

[0071] Based on the test temperature point in step S2, three different temperature zones are set, including:

[0072] The first temperature zone, which ranges from [173K, 223K);

[0073] The second temperature zone, which ranges from [223K, 273K);

[0074] The third temperature zone is [273K, 323K].

[0075] Since each stage of a multi-stage thermoelectric cooler operates within a different temperature range, the material properties change significantly with temperature. Temperature zone adaptation selects the material with the highest ZT value for each temperature zone, ensuring that each stage operates at its optimal performance. Without screening, using a single material can lead to poor performance at certain stages, limiting the overall temperature difference and cooling capacity.

[0076] Therefore, for each temperature range, at least one type of N-type and P-type bismuth telluride material with the highest thermoelectric figure of merit (ZT) in that temperature range was selected.

[0077] For each of the selected optimal materials, plot its electrical conductivity. Seebeck coefficient Thermal conductivity The curves illustrating the temperature-dependent properties of the materials visually demonstrate the changing trends within corresponding temperature ranges. Numerical fitting methods were used to establish the conductivity parameters for the N-type and P-type bismuth telluride materials with the best thermoelectric performance in each temperature range. Seebeck coefficient Thermal conductivity The mathematical expression for higher-order terms that change with temperature. Where m = 1, 2, 3, corresponding to the three temperature zones respectively.

[0078] Numerical fitting was used to establish the conductivity of N-type and P-type bismuth telluride materials with optimal thermoelectric performance in each temperature range. Seebeck coefficient Thermal conductivity Mathematical expression for higher-order terms that change with temperature.

[0079] Where m = 1, 2, 3, corresponding to the three temperature zones; optimal conductivity Seebeck coefficient Thermal conductivity The performance relationship between N-type and P-type bismuth telluride materials is as follows:

[0080] ;

[0081] ;

[0082] .

[0083] Accordingly, the mathematical expressions for the three higher-order terms are as follows:

[0084] ;

[0085] ;

[0086] .

[0087] In this model, the coefficients are replaced by constants a, b, and c. Thermoelectric parameters typically change nonlinearly with temperature, and higher-order polynomials can better approximate the actual changes. The fitted function can be easily substituted into the heat balance equation for analytical calculations, avoiding the complexity and errors caused by discrete data interpolation. In this embodiment, a fourth-order polynomial is used to illustrate that the impact of temperature change on performance is significant and requires a higher-order description.

[0088] Ultimately, three sets of functions are obtained for each temperature range, corresponding to the optimal material properties for the three temperature ranges, as follows:

[0089] The N-type bismuth telluride material with the highest thermoelectric figure of merit in the first temperature range exhibits the best electrical conductivity, Seebeck coefficient, and thermal conductivity. In order , and The performance curves are as follows: Figure 3 , Figure 4 , Figure 5 As shown; the electrical conductivity, Seebeck coefficient, and thermal conductivity of the P-type bismuth telluride material with the highest thermoelectric figure of merit within the first temperature range. In order , and The performance curves are as follows: Figure 7 , Figure 8 , Figure 9 As shown.

[0090] The N-type bismuth telluride material with the highest thermoelectric figure of merit in the second temperature range exhibits the best electrical conductivity, Seebeck coefficient, and thermal conductivity. In order , and The performance curves are as follows: Figure 3 , Figure 4 , Figure 5 As shown; the mathematical expressions for the higher-order terms of the electrical conductivity, Seebeck coefficient, and thermal conductivity of the P-type bismuth telluride material with the highest thermoelectric figure of merit within the second temperature range are, in order: , and The performance curve is as follows Figure 7 , Figure 8 , Figure 9 As shown.

[0091] The N-type bismuth telluride material with the highest thermoelectric figure of merit in the third temperature zone exhibits the best electrical conductivity, Seebeck coefficient, and thermal conductivity. In order , and The performance curve is as follows Figure 3 , 4 As shown in Figure 5, the P-type bismuth telluride material with the highest thermoelectric figure of merit in the third temperature range exhibits the following electrical conductivity, Seebeck coefficient, and thermal conductivity. In order , and The performance curves are as follows: Figure 7 , Figure 8 , Figure 9 As shown;

[0092] The aim is to provide a continuous and differentiable input function for the subsequent analytical solution of the heat balance equation, which facilitates numerical solution and iterative optimization.

[0093] S4. Set the initial values ​​of the logarithm and grain size of each level element of the multi-stage thermoelectric cooler, and substitute the fitting expression obtained in step S3 into the heat balance equation set of the multi-stage thermoelectric cooler according to the temperature zone for analysis.

[0094] like Figure 2 As shown, the structure of the constructed multi-stage thermoelectric cooler includes:

[0095] The top layer is the first stage cold end;

[0096] The intermediate levels, from top to bottom, are level 2 to level i-1;

[0097] The bottom layer is the i-th level hot end;

[0098] Where i is the total number of stages in the multi-stage thermoelectric cooler, 3≤i≤6.

[0099] And set the initial number of pairs of components in each level from the first-level cold end to the i-th-level hot end as follows: , … The initial cross-sectional area of ​​each layer of components is ; , … The initial height of each level of component is ; , … The initial value provides a starting point for iterative optimization; it can be based on experience, a simplified model, or historical design data.

[0100] Based on the mathematical expression of the higher-order terms in step S3, and based on the Peltier thermoelectric effect... Joule fever and Fourier heat conduction The heat balance equations for a multi-stage thermoelectric cooler are as follows:

[0101] For level 1, a fitting function is used. , , The heat flow equations for the cold and hot ends are constructed as follows: The heat flow equation for the cold end is shown in equation (1), and the heat flow equation for the hot end is shown in equation (2).

[0102] (1)

[0103] (2)

[0104] For the intermediate levels 2 to (i-1), a fitting function is used. , , The heat flow equations for the cold and hot ends are constructed as follows: the heat flow equation for the cold end is shown in equation (3), and the heat flow equation for the hot end is shown in equation (4).

[0105] (3)

[0106] (4)

[0107] For the i-th level, the fitting function is used. , , The heat flow equations for the cold and hot ends are constructed as follows: the heat flow equation for the cold end is shown in equation (5), and the heat flow equation for the hot end is shown in equation (6).

[0108] (5)

[0109] (6)

[0110] in, and These are the cold and hot end temperatures of the i-th stage cooling component, respectively. and These represent the heat at the cold and hot ends of the i-th stage cooling component, respectively; c represents the cold end; h represents the hot end; and I represents the current. Represents the number of pairs of elements at level i, which is greater than 1 and is an integer; These represent the electrical conductivity, Seebeck coefficient, and thermal conductivity of bismuth telluride materials, respectively. Represents the height of the i-th level component; This represents the cross-sectional area of ​​the i-th level element.

[0111] In this step, based on the number of stages of the multi-stage thermoelectric cooler (usually 3 to 6 stages), initial values ​​for the logarithm, cross-sectional area, and height of each stage of the components are set. The three temperature zone material performance fitting functions obtained in step S3 are substituted into different stages of the cooler to construct and analyze a multi-stage heat balance equation system that considers the Peltier effect, Joule heating, and heat conduction. This establishes a theoretical model that couples materials, temperature zones, structure, and performance, providing a mathematical model basis and initial performance evaluation for subsequent iterative optimization.

[0112] S5. By iterating through the logarithms and grain sizes of each level of components, the heat balance equations are solved to obtain the optimal design parameters and complete the design of the multi-stage electrothermal cooler.

[0113] In this step, the iteration conditions include ensuring temperature continuity between adjacent levels. With heat flow continuity The iteration terminates when the maximum cold temperature difference is obtained. Or the maximum cold end absorbs heat .

[0114] Using the heat balance equations constructed in step S4 as the mathematical model, and aiming to maximize the cooling temperature difference or cooling capacity, a numerical iterative algorithm is employed to systematically adjust the structural parameters such as the logarithm, cross-sectional area, and height of each stage component in the multi-stage thermoelectric cooler. Under the condition of satisfying the constraints on temperature and heat flow continuity between stages, the algorithm automatically searches for and determines a set of structural parameters that optimizes the overall performance, thereby outputting the final design result of the high-performance multi-stage thermoelectric cooler.

[0115] To enable those skilled in the art to further understand the method of the present invention, the technical solution of the present invention will be explained in detail below with reference to specific embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0116] Example 1:

[0117] S1. Prepare bismuth telluride materials with various components and different thermoelectric properties.

[0118] High-strength bismuth telluride materials were prepared by hot extrusion. The compressive strength of N-type bismuth telluride crystal rods was 170 MPa, and the compressive strength of P-type bismuth telluride crystal rods was 150 MPa.

[0119] By altering the chemical formulas of Bi, Sb, Te, and Se in N- and P-type materials, multi-component hot-extruded bismuth telluride materials are prepared. The corresponding components include:

[0120] For N-type bismuth telluride materials, the components containing Bi, Te, Se, and dopants are as follows: , , , , , .

[0121] For p-type bismuth telluride materials, the components containing Bi, Te, and Se are as follows: , , , , , .

[0122] S2. Test the thermoelectric parameters of multiple groups of bismuth telluride materials as a function of temperature in the near-room temperature range.

[0123] The thermoelectric parameters of the above-mentioned multi-component bismuth telluride material, namely conductivity σ, Seebeck coefficient α, and thermal conductivity κ, were tested using a low-temperature property measurement system at temperatures of 173K, 198K, 223K, 248K, 273K, 298K, and 323K, and the ZT value was calculated.

[0124] Based on these temperature points, three temperature zones are divided: the first temperature zone, which ranges from [173K to 223K]; the second temperature zone, which ranges from [223K to 273K]; and the third temperature zone, which ranges from [273K to 323K].

[0125] S3. Based on the test results, select the bismuth telluride material with the highest thermoelectric figure of merit in different temperature zones, plot the curves of its thermoelectric parameters as a function of temperature, and fit the obtained high-order expression with temperature as the variable.

[0126] For these three temperature ranges, three different N-type and P-type bismuth telluride materials with the highest thermoelectric figure of merit and ZT value were selected for each temperature range.

[0127] Among them, the conductivity-temperature curve of N-type bismuth telluride material is as follows: Figure 3 As shown, the Seebeck coefficient-temperature curve is as follows: Figure 4 As shown, the thermal conductivity-temperature curve is as follows: Figure 5 As shown, and the ZT value-temperature curve as shown... Figure 6 As shown.

[0128] The conductivity-temperature curve of p-type bismuth telluride material is as follows: Figure 7 As shown, the Seebeck coefficient-temperature curve is as follows: Figure 8 As shown, the thermal conductivity-temperature curve is as follows: Figure 9 As shown, and the ZT value-temperature curve as shown... Figure 10 As shown.

[0129] From the above appendix Figures 3-9 It can be seen that the electrical conductivity, Seebeck coefficient, and thermal conductivity of N- and P-type bismuth telluride materials #1, #2, and #3 exhibit similar trends with temperature: electrical conductivity decreases with increasing temperature, while the Seebeck coefficient increases. The optimal N- and P-type bismuth telluride material in the first temperature region has the lowest overall electrical conductivity and the highest Seebeck coefficient. The optimal N- and P-type bismuth telluride material in the second temperature region has intermediate electrical conductivity and Seebeck coefficient. The optimal N- and P-type bismuth telluride material in the third temperature region has the highest overall electrical conductivity and the lowest Seebeck coefficient.

[0130] S4. Set the initial values ​​of the logarithm and grain size of each level element of the multi-stage thermoelectric cooler, and substitute the fitting expression obtained in step S3 into the heat balance equation set of the multi-stage thermoelectric cooler according to the temperature zone for analysis.

[0131] like Figure 2 As shown, a five-stage thermoelectric cooler is constructed, with each layer having the following structure:

[0132] The top layer is the first stage cold end;

[0133] The intermediate levels, from top to bottom, are level 2, level 3, and level 4;

[0134] The bottom layer is the 5th level hot end.

[0135] The initial values ​​for the number of components in each stage, from the cold end of stage 1 to the hot end of stage 5, are set to... The initial cross-sectional area of ​​each layer of components is ; The initial height of each level of component is ; .

[0136] The above initial values ​​and fitting function , , The first stage heat balance equation set in the five-stage thermoelectric cooler is constructed together, and its cold end heat flow equation is as shown in equation (1) and its hot end heat flow equation is as shown in equation (2):

[0137] (1)

[0138] (2)

[0139] For levels 2 through 4 in the middle, the above initial values ​​are compared with the fitted function. , , Together, they construct the heat flow equations for the cold and hot ends, where i = 2, 3, 4; the heat flow equation for the cold end is shown in equation (3), and the heat flow equation for the hot end is shown in equation (4):

[0140] (3)

[0141] (4)

[0142] For level 5, the above initial values ​​are compared with the fitted function. , , Together, they construct the heat flow equations for the cold and hot ends, where i=5; the heat flow equation for the cold end is as shown in equation (5), and the heat flow equation for the hot end is as shown in equation (6):

[0143] (5)

[0144] (6)

[0145] S5. By iterating through the logarithms and grain sizes of each level of components, the heat balance equations are solved to obtain the optimal design parameters and complete the design of the multi-stage electrothermal cooler.

[0146] and These represent the cold and hot end temperatures of a 5-stage thermoelectric cooling system, respectively. The iteration condition must satisfy temperature continuity. With heat flow continuity The iteration termination condition is obtaining the cold temperature difference. .

[0147] The output yields the hot surface of the five-stage thermoelectric cooler assembly. The curve of the design cooling temperature difference versus current is shown below. Figure 11 As shown, the maximum temperature difference is obtained after traversal. The output obtained , , The parameters are shown in Table 1.

[0148] Table 1. Parameters F1~F5, S1~S5, and H1~H5 obtained from the output of Example 1 and Comparative Example 1.

[0149] category Logarithms F1 to F5 Component height H1~H5 (mm) Component cross-sectional area S1~S5 (mm) Example 1 [7,13,27,54,119] [1.80,1.10,1.10,1.10,0.90] [8.80,5.30,5.30,5.30,3.80] Comparative Example 1 [8,14,29,58,120] [1.60,1.60,1.60,1.60,1.60] [4.0,4.0,4.0,4.0,4.0]

[0150] From Table 1 and Figure 11 The results show that by adapting the multi-component bismuth telluride material to the corresponding temperature range in Example 1, the design optimization of the maximum temperature difference parameter of the multi-level device was achieved. Compared with the product using the single-component material design method, the maximum temperature difference is increased by about 5%, which can provide an optimization scheme and theoretical support for the design and manufacturing of multi-level devices with high temperature difference of various models.

[0151] Comparative Example 1:

[0152] The difference between Comparative Example 1 and Example 1 is as follows:

[0153] In step S3, only the N-type bismuth telluride material and the P-type bismuth telluride material with the highest thermoelectric figure of merit within the third temperature region are selected. The fitting formula for the higher-order terms is as follows:

[0154] ;

[0155] ;

[0156] .

[0157] In step S4, substitute the following equation (i=1,…,5) into the equation.

[0158] (8)

[0159] (9)

[0160] In step 6, the hot surface of the five-stage thermoelectric cooler assembly is output. The curve of the design cooling temperature difference versus current is shown below. Figure 12 As shown.

[0161] The maximum temperature difference was obtained after traversal. The output obtained , , The parameters are shown in Table 1.

[0162] Hot surface of the five-stage thermoelectric cooler assembly in Comparative Example 1 The curve of the design cooling temperature difference versus current is shown below. Figure 12 As shown.

[0163] From Table 1 and Figure 12 The results show that, due to the failure to properly match the material properties with different temperature zones in Comparative Example 1, it is difficult to simultaneously meet the characteristic requirements of the first and second temperature zones by using the material with the best performance in the third temperature zone. Therefore, the maximum temperature difference obtained by simulation calculation is about 5% different from that in Example 1.

[0164] The design method of a multi-stage thermoelectric cooler with multi-component bismuth telluride temperature range adaptability, as proposed in this application, is based on the core of which is to achieve structural optimization of the multi-stage thermoelectric cooler through the selection of multi-component, temperature range adaptable bismuth telluride materials and iterative thermal balance modeling. This method solves the problem that multi-stage thermoelectric coolers have a large operating temperature range and it is difficult for a single material to maintain optimal performance across the entire temperature range. It achieves synergistic optimization of material temperature range adaptability and structural parameters, significantly improving the cooling temperature difference and cooling power.

[0165] The embodiments of this application have been described in detail above. These descriptions are merely preferred embodiments and should not be construed as limiting the scope of this application. All equivalent variations and modifications made within the scope of this application should still fall within the patent coverage of this application.

Claims

1. A design method for a multi-stage thermoelectric cooler with multi-component bismuth telluride temperature range adaptation, characterized in that the steps include... include: S1. Preparation of bismuth telluride materials with various components and different thermoelectric properties; S2. Test the thermoelectric parameters of multiple groups of the bismuth telluride materials as a function of temperature in the near-room temperature range; S3. Based on the test results, select the bismuth telluride material with the highest thermoelectric figure of merit in different temperature zones, plot the curves of its thermoelectric parameters changing with temperature, and fit the obtained high-order expression with temperature as the variable. S4. Set the initial values ​​of the logarithm and grain size of each level element of the multi-stage thermoelectric cooler, and substitute the fitting expression obtained in step S3 into the heat balance equation set of the multi-stage thermoelectric cooler according to the temperature zone for analysis. S5. By iterating through the logarithms and grain sizes of each level of components, the heat balance equations are solved to obtain the optimal design parameters and complete the design of the multi-stage electrothermal cooler.

2. The design method for a multi-component bismuth telluride temperature-range adapted multi-stage thermoelectric cooler according to claim 1, characterized in that, In step S1, the bismuth telluride material is an N-type bismuth telluride crystal rod and a P-type bismuth telluride crystal rod prepared by zone melting or hot extrusion; wherein the compressive strength is ≥80MPa.

3. The design method for a multi-component bismuth telluride temperature-range adapted multi-stage thermoelectric cooler according to claim 2, characterized in that, The bismuth telluride material used to prepare N-type bismuth telluride crystal rods has the following chemical formula: Where 0 ≤ x ≤ 0.8, 0 ≤ y ≤ 0.5; The bismuth telluride material used to prepare p-type bismuth telluride crystal rods has the following chemical formula: , where 0≤x≤0.8, 0≤y≤0.

5.

4. A design method for a multi-component bismuth telluride temperature-range adapted multi-stage thermoelectric cooler according to claim 2 or 3, characterized in that, The bismuth telluride material used in the N-type bismuth telluride crystal rod is doped with a Group VIIA halogen compound, wherein the halogen compound has a mass percentage of 0-1.0 wt% and is selected from... , , , , One or more of them.

5. The design method for a multi-component bismuth telluride temperature-range adapted multi-stage thermoelectric cooler according to claim 1, characterized in that, In step S2, the thermoelectric parameters are tested using a low-temperature property measurement system or by introducing liquid nitrogen into the thermoelectric performance test bench. The test temperature points include 173K, 198K, 223K, 248K, 273K, 298K, and 323K. The thermoelectric parameters include electrical conductivity σ, Seebeck coefficient α, and thermal conductivity κ.

6. The design method for a multi-component bismuth telluride temperature-range adapted multi-stage thermoelectric cooler according to claim 5, characterized in that, The different temperature zones in step S3 include at least: First temperature zone: [173K, 223K); Second temperature zone: [223K, 273K); Third temperature zone: [273K, 323K]; For each temperature range, at least one component of the N-type and P-type bismuth telluride material with the highest thermoelectric figure of merit (ZT) in that temperature range is selected.

7. The design method for a multi-component bismuth telluride temperature-range adapted multi-stage thermoelectric cooler according to claim 6, characterized in that, Numerical fitting was used to establish the conductivity of the N-type and P-type bismuth telluride materials with optimal thermoelectric performance in each temperature range. Seebeck coefficient Thermal conductivity The mathematical expression for higher-order terms that change with temperature, where m = 1, 2, 3, corresponding to the three temperature zones respectively.

8. A design method for a multi-component bismuth telluride temperature-range adapted multi-stage thermoelectric cooler according to any one of claims 4-7, characterized in that, In the structure of the multi-stage thermoelectric cooler constructed in step S4: The top layer is the first stage cold end; The intermediate levels, from top to bottom, are level 2 to level i-1; The bottom layer is the i-th level hot end; Where i is the total number of stages in the multi-stage thermoelectric cooler, 3≤i≤6; And set the initial number of pairs of components in each level from the first-level cold end to the i-th-level hot end as follows: , … The initial cross-sectional area of ​​each layer of components is ; , … The initial height of each level of component is ; , … .

9. The design method for a multi-component bismuth telluride temperature-range adapted multi-stage thermoelectric cooler according to claim 8, characterized in that, The heat balance equations for the multi-stage thermoelectric cooler in step S4 are established based on Peltier heat, Joule heat, and Fourier heat conduction of the thermoelectric effect, specifically as follows: For level 1, a fitting function is used. , , The heat flow equations for the cold and hot ends are constructed as follows: The heat flow equation for the cold end is shown in equation (1), and the heat flow equation for the hot end is shown in equation (2). （1） （2） For the intermediate levels 2 to (i-1), a fitting function is used. , , The heat flow equations for the cold and hot ends are constructed as follows: the heat flow equation for the cold end is shown in equation (3), and the heat flow equation for the hot end is shown in equation (4). （3） （4） For the i-th level, the fitting function is used. , , The heat flow equations for the cold and hot ends are constructed as follows: the heat flow equation for the cold end is shown in equation (5), and the heat flow equation for the hot end is shown in equation (6). （5） （6） in, and These are the cold and hot end temperatures of the i-th stage cooling component, respectively. and These represent the heat at the cold and hot ends of the i-th stage cooling component, respectively; c represents the cold end; h represents the hot end; and I represents the current. Represents the number of pairs of elements at level i, which is greater than 1 and is an integer; These represent the electrical conductivity, Seebeck coefficient, and thermal conductivity of bismuth telluride materials, respectively. Represents the height of the i-th level component; This represents the cross-sectional area of ​​the i-th level element.

10. The design method for a multi-component bismuth telluride temperature-range adapted multi-stage thermoelectric cooler according to claim 1, characterized in that, In step S5, the iteration condition includes ensuring temperature continuity between adjacent levels. With heat flow continuity ; The iteration terminates when the maximum cold temperature difference is obtained. Or the maximum cold end absorbs heat .

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