CN109346595B - Stepped thermoelectric power generation sheet and pin height determination method thereof - Google Patents

Abstract

The invention discloses a stepped thermoelectric generation piece and a pin height determination method thereof, wherein the stepped thermoelectric generation piece consists of an upper end horizontal ceramic plate, a copper electrode plate, PN junction pins with the height increased in a stepped manner along the heat flow direction and a lower end stepped ceramic plate; because all PN junction pins of the thermoelectric generation piece are connected in series, when hot fluid flows through the thermoelectric generation piece, the temperature of the hot fluid is continuously reduced along the flowing direction, so that the output current of the PN junction in the uplink direction is higher than that of the PN junction in the downlink direction. In order to avoid the condition that the overall output current of the thermoelectric generation piece is limited by one minimum PN junction output current, the thermoelectric generation piece is designed into a ladder shape, the lower side of a pin of the PN junction is positioned in the upward direction of the hot fluid, and the higher side of the pin is positioned in the downward direction of the hot fluid. Meanwhile, the invention provides a method for calculating the heights of the PN junction pin in different steps, which is used for designing the optimal pin height value and has obvious optimization effect.

Description

A step-type thermoelectric power generation chip and its pin height determination method

technical field

The invention belongs to the fields of thermoelectric conversion, thermoelectric recovery, and thermoelectric power generation, and in particular relates to a stepped thermoelectric power generation chip and a method for determining the height of its pins. The method can improve the overall output of the thermoelectric power generation chip.

Background technique

In recent years, with the emergence of modern advanced material preparation technologies, such as nanotechnology, composite materials, etc., the conversion efficiency of thermoelectric materials has been greatly improved, which has attracted the attention of a wide range of researchers, and thermoelectric conversion technology has been applied to the field of thermoelectric recovery (such as aviation Aerospace, waste heat recovery from automobile exhaust, industrial waste heat recovery, etc.).

The thermoelectric power generation sheet is the core power generation unit in thermoelectric recovery. It consists of three parts: ceramic plates at the upper and lower ends, PN junction pins made of thermoelectric materials, and copper conductive sheets between the connecting pins. The output performance of the thermoelectric power generation sheet directly affects Performance of heat and electricity recovery. In order to increase the output voltage of the PN junction, some scholars proposed to change the PN junction with a quadrilateral cross-section into a PN junction with a hexagonal cross-section, and design the PN junction to have a variable cross-sectional area. These methods can improve the temperature difference power generation to a certain extent. The output voltage of the chip, etc., but these structures generally have the characteristics of complex structure and difficult fabrication, which are difficult to realize engineering applications. Some scholars take the topological connection relationship of thermoelectric generators as the research object. In order not to limit the overall output of the thermoelectric generator to the output of one of the smaller thermoelectric generators, the thermoelectric generators are connected in series and parallel. However, there are a large number of PN junction pins inside the thermoelectric generator, and the pins are connected in series. When the thermoelectric generator is placed between the hot-end heat exchanger and the cold-end heat exchanger, the thermoelectric generator The temperature difference between the two ends of the thermal fluid will continue to decrease along the flow direction of the thermal fluid, causing the output current of the PN junction in the downstream direction of the thermal fluid to be lower than the output current of the PN junction in the upward direction. The overall output current is limited by the smallest PN junction output current.

Contents of the invention

The purpose of the present invention is to overcome the influence that the overall output current of the thermoelectric power generation chip is limited by the minimum PN junction output current, and propose a stepped thermoelectric power generation chip and a method for determining the height of its pins. The height of the pins keeps the output current of the PN junction pins on each ladder consistent, thereby improving the overall output of the thermoelectric generator.

The purpose of the present invention is achieved through the following technical solutions:

沿热流方向，阶梯式温差发电片分别为第1阶梯、第2阶梯、…第i阶梯…、第n阶梯，其中，第1阶梯上的PN结引脚高度最低，第n阶梯上的PN结引脚高度最高；第i阶梯的引脚高度为h_i、下陶瓷板第i阶梯的高度为h_ci，且上陶瓷板的高度h_c1和铜电极片的高度h_co保持不变，h_c1等于下陶瓷板第一阶梯的高度，各高度间满足下述关系：h_c1+h₁＝h_i+h_ci。A stepped thermoelectric power generation sheet, comprising an upper horizontal ceramic plate, a copper electrode sheet, a PN junction pin whose height increases stepwise along the heat flow direction, and a lower end stepped ceramic plate, the contact surface between the lower ceramic plate and the copper electrode sheet is stepped; After the PN junction pins are connected in series by copper electrode sheets, they are sandwiched between the upper horizontal ceramic plate and the lower end stepped ceramic plate; the number of columns R of the PN junction pins on each step is consistent, and the same step The heights of the PN junction pins on different ladders are the same, and the heights of the PN junction pins on different steps are different, where R is determined by the total number of columns R _all and the number of steps n of the PN junction pins of the thermoelectric power generation sheet, namely:

Along the direction of heat flow, the stepped thermoelectric power generation sheets are respectively the first step, the second step, ... the i-th step..., and the n-th step. Among them, the PN junction pin height on the first step is the lowest, and the PN junction on the n-th step is the lowest. The pin height is the highest; the pin height of the i-th step is h _i , the height of the i-th step of the lower ceramic plate is h _ci , and the height h _c1 of the upper ceramic plate and the height h _co of the copper electrode remain unchanged, h _c1 It is equal to the height of the first step of the lower ceramic plate, and the following relationship is satisfied between each height: h _c1 +h ₁ =h _i +h _ci .

A method for determining the pin height of a stepped thermoelectric power generation chip, which determines the hot end temperature and cold end temperature of the i-th step PN junction pin, and calculates the PN of the i-th step according to the hot end temperature and the cold end temperature of the PN junction pin Junction output current, so as to calculate the pin height h _i of the i-th step.

Further, the specific process of determining the hot end temperature of the i-th ladder PN junction pin is:

Calculate the inner wall temperature T _iwh of the heat exchanger at the hot end;

为热流体的质量流量，Th_i为第i阶梯的热流体入口温度、Th_i+1为第i阶梯的热流体出口温度，h₁为热流体对流换热系数，A₁为热流体与热端换热器的内壁面接触面积，

为第i阶梯的热流体平均温度，且

where C _h is the specific heat capacity of the thermal fluid,

is the mass flow rate of the thermal fluid, Th _i is the thermal fluid inlet temperature of the ith step, Th _i+1 is the thermal fluid outlet temperature of the ith step, h ₁ is the convective heat transfer coefficient of the thermal fluid, A ₁ is the thermal fluid and the thermal fluid The inner wall surface contact area of the end heat exchanger,

is the average temperature of the thermal fluid in the i-th step, and

Calculate the hot junction temperature Th _leg of the PN junction pin;

根据热流密度相等，则

式中λ₁为热端换热器材料的热导率，δ_h为热端换热器底板厚度，λ_ce为陶瓷板的材料热导率，T_owh为热端换热器外壁面温度；The heat flux _q1 at the hot end is:

According to the heat flux is equal, then

Where λ ₁ is the thermal conductivity of the heat exchanger material at the hot end, δ _h is the thickness of the bottom plate of the heat exchanger at the hot end, λ _ce is the thermal conductivity of the ceramic plate material, and T _owh is the temperature of the outer wall of the heat exchanger at the hot end;

Then the hot junction temperature of the PN junction pin

Further, the specific process of determining the cold junction temperature of the i-th ladder PN junction pin is:

Calculate the inner wall surface temperature T _iwc of the cold end heat exchanger;

为冷流体的质量流量，Tc_i为冷流体的入口温度、Tc_i+1为冷流体出口温度，h₂为冷流体对流换热系数，A₂为冷流体与冷端换热器的内壁面接触面积，

为第i阶梯的冷流体平均温度，且

In the formula, C _w is the specific heat capacity of the cold fluid,

is the mass flow rate of the cold fluid, Tc _i is the inlet temperature of the cold fluid, Tc _i+1 is the outlet temperature of the cold fluid, h ₂ is the convective heat transfer coefficient of the cold fluid, A ₂ is the inner wall surface of the cold fluid and the cold end heat exchanger Contact area,

is the average temperature of the cold fluid in the i-th step, and

Calculate the cold junction temperature Tc _leg of the PN junction pin;

根据热流密度相等，则

式中λ₂为冷端换热器材料的热导率，δ_c为冷端换热器底板厚度，T_owc为冷端换热器外壁面温度；h_c1为上陶瓷板的高度等于下陶瓷第一阶梯的高度。The heat flux _q2 at the cold end is:

According to the heat flux is equal, then

In the formula, λ ₂ is the thermal conductivity of the material of the cold end heat exchanger, δ _c is the thickness of the bottom plate of the cold end heat exchanger, T _owc is the temperature of the outer wall of the cold end heat exchanger; h _c1 is the height of the upper ceramic plate equal to that of the lower ceramic plate The height of the first step.

Then the cold junction temperature of the PN junction pin

Further, the specific process of calculating the PN junction output current of the i-th step is:

Calculate the PN junction output voltage U _i of the i-th step;

U _i ＝R×m(α _P -α _N )×(Th _leg -Tc _leg )

In the formula, m is the number of PN junctions contained in each column of PN junction pins, α _P is the Seebeck coefficient of the P pole, and α _N is the Seebeck coefficient of the N pole;

Calculate the PN junction internal resistance R _i of the i-th step;

In the formula, ρ _P is the resistivity of the P pole, ρ _N is the resistivity of the N pole, and A _leg is the cross-sectional area of the PN junction pin.

Further, calculate the PN junction output current I _i of the ith step:

当i＝2，3，…，n时，h_i未知，根据I_i＝I₁可求解得到，即

Furthermore, when i=1, h ₁ is known, and obtain

When i=2, 3,..., n, h _i is unknown, and it can be obtained by solving according to I _i =I ₁ , namely

The beneficial effects of the present invention are:

The thermoelectric power generation sheet of the present invention designs the lower ceramic plate into a stepped shape, and the height of the PN junction pins increases stepwise along the flow direction of the thermal fluid, and provides a method for determining the height of the pins, so that the steps on each step in the stepped thermoelectric power generation sheet The output current of the PN junction pins is the same, which can greatly improve the performance of the thermoelectric power generation chip.

Description of drawings

Fig. 1 is a structural schematic diagram of a stepped thermoelectric power generation sheet;

Figure 2 is the front view of the stepped thermoelectric power generation sheet and its working principle diagram;

Figure 3 shows the relevant parameters of the i-th step of the stepped thermoelectric power generation sheet.

Detailed ways

The technical solution of the present invention will be described below in conjunction with a specific stepped thermoelectric generation chip structure.

As shown in Figure 1, the stepped thermoelectric power generation sheet includes an upper horizontal ceramic plate, a copper electrode sheet, a PN junction pin with a stepwise increase in height along the heat flow direction, and a lower stepped ceramic plate. The contact surface between the lower ceramic plate and the copper electrode sheet is designed In a stepped shape, it is used to place PN junction pins; the PN junction pins are connected in series by copper electrode sheets, sandwiched between the upper horizontal ceramic plate and the lower end stepped ceramic plate; the PN junction pins are in each step The number of columns R on the same ladder remains the same, and the heights of the PN junction pins on the same ladder are the same, and the heights of the PN junction pins on different ladders are different, where R is determined by the total number of columns R _{all of} the thermoelectric chip PN junction pins and The number of steps n is determined, namely:

Along the flow direction of the thermal fluid, the stepped thermoelectric power generation sheets are respectively the first step, the second step, ... the i-th step..., and the n-th step. Among them, the height of the PN junction pin on the first step is the lowest, and the height of the PN junction on the n-th step is the lowest. The pin height of the PN junction is the highest; the pin height of the i-th (i=1,2,...,n) step is h _i , the height of the lower ceramic plate of the i-th step is h _ci , and the height of the upper ceramic plate is h _c1 (equal to the height of the first step of the lower ceramic plate) and the height h _co of the copper electrode remain unchanged, and the following relationship is satisfied between each height:

h _c1 +h ₁ =h _i +h _ci (2)

热端换热器内壁面温度为T_iwh、热端换热器外壁面温度为T_owh、PN结引脚热端温度为Th_leg、PN结引脚冷端温度为Tc_leg、冷端换热器的外壁面温度为T_owc、冷端换热器的内壁面温度为T_iwc、冷流体的平均温度为

The average temperature of the thermal fluid in the i-th step is

The inner wall temperature of the hot end heat exchanger is T _iwh , the outer wall temperature of the hot end heat exchanger is T _owh , the hot end temperature of the PN junction pin is Th _leg , the cold end temperature of the PN junction pin is Tc _leg , and the cold end heat transfer The temperature of the outer wall of the heat exchanger is T _owc , the temperature of the inner wall of the cold end heat exchanger is T _iwc , and the average temperature of the cold fluid is

The implementation steps are as follows:

比热容C_h和对流换热系数h₁，以及冷流体的质量流量

比热容C_w和对流换热系数h₂均为已知。The prerequisites for the realization of the present invention are: (1) ignoring the contact thermal resistance between the hot end heat exchanger, the cold end heat exchanger and the thermoelectric generation sheet; (2) the i (i=1,2,...,n) step The inlet temperature Th _i of the hot fluid, the outlet temperature Th _i+1 of the hot fluid, the inlet temperature _Tci of the cold fluid, and the outlet temperature Tc _i+1 of the cold fluid are known; (3) The mass flow rate of the hot fluid

Specific heat capacity C _h and convective heat transfer coefficient h ₁ , and mass flow rate of cold fluid

Both the specific heat capacity _Cw and the convective heat transfer coefficient _h2 are known.

Step 1, determine the hot end temperature of the i-th ladder PN junction pin;

(1) The reduction of the internal energy of the thermal fluid at the hot end is equal to the convective heat transfer amount between the thermal fluid and the inner wall of the heat exchanger at the hot end, and the inner wall temperature T _iwh of the heat exchanger at the hot end is calculated;

In the formula, A ₁ is the contact area between the i-th step thermal fluid and the inner wall of the hot end heat exchanger;

(2) It can be known from Fourier's law that when the heat is transferred to the PN junction pin from the inner wall of the hot end heat exchanger, the heat flux remains constant, and the hot end temperature Th _leg of the PN junction pin is calculated accordingly;

The heat flux q ₁ is:

According to the equal heat flux, there are:

In the formula, λ ₁ is the thermal conductivity of the material of the heat exchanger at the hot end, λ _ce is the thermal conductivity of the material of the ceramic plate, and δ _h is the thickness of the bottom plate of the heat exchanger at the hot end;

Due to the high thermal conductivity and small thickness of the copper electrode sheet, the thermal conductivity of the copper electrode sheet is negligible, so the hot end temperature of the PN junction pin can be calculated by formulas (3), (4), and (5) Th _leg , namely:

Step 2, determine the cold junction temperature of the i-th ladder PN junction pin;

(1) The increase of the internal energy of the cold fluid at the cold end is equal to the convective heat transfer between the cold fluid and the inner wall of the cold end heat exchanger, and the temperature T _iwc of the inner wall of the cold end heat exchanger is calculated;

In the formula, _A2 is the contact area between the i-th step cold fluid and the inner wall of the cold end heat exchanger;

(2) It can be known from Fourier's law that when the heat is transferred from the PN junction pin to the inner wall of the cold-end heat exchanger, the heat flux remains constant, and the cold-end temperature Tc _leg of the PN junction pin is calculated accordingly;

The heat flux _q2 at the cold end is:

According to the equal heat flux, there are:

In the formula, _λ2 is the thermal conductivity of the material of the cold-end heat exchanger, and _δc is the thickness of the bottom plate of the cold-end heat exchanger;

The cold junction temperature Tc _leg of the PN junction pin can be calculated from formulas (7), (8) and (9), namely:

Step 3, according to the hot end temperature Th _leg of the PN junction pin obtained in step 1 and the cold end temperature Tc _{leg of} the PN junction pin obtained in step 2, calculate the PN junction output current of the i-th step;

(1) Calculate the PN junction output voltage U _i of the i-th step;

U _i =R×m(α _P −α _N )×(Th _leg −Tc _leg ) (11)

In the formula, m is the number of PN junctions contained in each column of PN junction pins, α _P is the Seebeck coefficient of the P pole, and α _N is the Seebeck coefficient of the N pole;

(2) Calculate the PN junction internal resistance R _i of the i-th step;

In the formula, ρ _P is the resistivity of the P pole, ρ _N is the resistivity of the N pole, and A _leg is the cross-sectional area of the PN junction pin;

(3) Calculate the PN junction output current I _i of the i-th step;

再由第i阶梯的输出电流都等于第1阶梯的输出电流(I_i＝I₁)，计算得到第i阶梯的引脚高度

由此使得每一阶梯的PN结输出电流保持一致，提高温差发电片的整体输出。Given the pin height h ₁ of the first step and the height h _c1 of the ceramic plate, the current output of the first step is calculated by formula (13)

Then, the output current of the i-th step is equal to the output current of the first step (I _i =I ₁ ), and the pin height of the i-th step is calculated

In this way, the output current of the PN junction of each step is kept consistent, and the overall output of the thermoelectric power generation sheet is improved.

This example adopts the more common size of thermoelectric power generation sheet, the size of the ceramic plate is 40mm*40mm (length*width), there are 8 columns of PN junction pins, and each column has 8 PN junction thermocouples (that is, 4 PN junctions, The number of thermocouples in the first column and the last column is only 7 because a positive and negative interface is reserved), and the number of steps R=4, so there are 2 columns of PN junction pins on each step. Seebeck coefficient, resistivity and other parameters of PN junction thermocouple are shown in Table 1.

Table 1 Seebeck coefficient and resistivity of PN junction thermocouple

Note: T in the table is the average temperature of the hot and cold ends of the PN junction pins, that is, T=(Th _leg +Tc _leg )/2

The known dimensional parameters of the thermoelectric power generation sheet, such as the height of the first column of ceramic plates, the height of the pins, the height of the copper electrode sheet, the thickness of the hot end heat exchanger δ _h , the thickness of the cold end heat exchanger δ _c , and the cold fluid The relevant parameters of (high temperature exhaust gas) and thermal fluid (cooling water) are shown in Table 2.

Table 2 Known parameters of thermoelectric power generation sheet and related parameters of cold and hot ends

Assuming that the inlet temperature of the hot fluid is 771K, the temperature drops by 0.5K from the i-th step to the i+1 step, that is, Th _i -Th _i+1 = 0.5, the inlet temperature of the cold fluid is 365K, and flows from the i-th step to the i-th step The +1 step temperature increases by 0.1K, that is, Tc _i+1 −Tc _i =0.1.

The temperature of the cold and hot ends of the PN junction pins of each step and the temperature of the outer wall surface of the heat exchanger at the hot end are calculated from the above known parameters, as shown in Table 3.

Table 3 Hot and cold junction temperatures of each stepped PN junction pin

Therefore, the Seebeck coefficient of the P pole of the first step is 83.4066μv/K, the Seebeck coefficient of the N pole is -95.8313μv/K, the resistivity of the P pole is 2.3554×10 ^-5 Ωm, and the resistivity of the N pole is 2.3676 ×10 ^-5 Ωm, calculated by the formula (13), the current output of the first step is I ₁ =2.27A, so the output current of the i-th step must also be 2.27A, calculated with the help of matlab calculation tools: 2nd, 3rd , PN junction pin heights of 4 steps are 1.608mm, 1.616mm, 1.624mm respectively.

The specific implementation manner has been described in detail above according to the technical solution of the present invention. According to the technical solution of the present invention, without changing the essence and spirit of the present invention, those skilled in the art can propose multiple structural modes and implementation modes that can be replaced with each other. Therefore, the specific implementation methods and drawings described above are only exemplary illustrations of the technical solution of the present invention, and should not be regarded as the entirety of the present invention or as a limitation or limitation on the technical solution of the present invention.

Claims (5)

1. A method for determining the pin height of a stepped thermoelectric generator, characterized in that, the method for determining the pin height is based on a stepped thermoelectric generator, and the stepped thermoelectric generator includes an upper horizontal ceramic plate , copper electrode sheets, PN junction pins with a stepwise increase in height along the heat flow direction, and a stepped ceramic plate at the lower end. After the PN junction pins are connected in series with each other by copper electrode sheets, they are sandwiched between the upper horizontal ceramic plate and the lower end stepped ceramic plate. In the middle, the contact surface between the lower ceramic plate and the copper electrode sheet is stepped; along the heat flow direction, the stepped thermoelectric generation sheets are respectively the first step, the second step, ... the i step ..., the n step, where the first step The pin height of the PN junction on the upper is the lowest, and the pin height of the PN junction on the nth step is the highest; the pin height of the i-th step is h _i , the height of the i-th step on the lower ceramic plate is h _ci , and the height of the upper ceramic plate h _c1 and the height h _co of the copper electrode sheet remain unchanged, h _c1 is equal to the height of the first step of the lower ceramic plate, and the following relationship is satisfied between each height: h _c1 +h ₁ =h _i +h _ci ; The number of columns R of the PN junction pins on each step remains the same, and the heights of the PN junction pins on the same step are the same, and the heights of the PN junction pins on different steps are different, wherein R is determined by the thermoelectric power generation sheet PN The total number of columns R _{all of} the junction pins and the number of steps n are determined, namely:

The method for determining the pin height is: Determine the hot end temperature and cold end temperature of the i-th step PN junction pin, calculate the PN junction output current of the i-th step from the hot-end temperature and the cold end temperature of the PN junction pin, and thus calculate the pin height of the i-th step h _i . 2. the method for determining the pin height of a kind of stepped thermoelectric generating sheet according to claim 1, is characterized in that, the specific process of determining the hot end temperature of the i-th step PN junction pin is: Calculate the inner wall temperature T _iwh of the heat exchanger at the hot end;

where C _h is the specific heat capacity of the thermal fluid,

is the mass flow rate of the thermal fluid, Th _i is the thermal fluid inlet temperature of the ith step, Th _i+1 is the thermal fluid outlet temperature of the ith step, h ₁ is the convective heat transfer coefficient of the thermal fluid, A ₁ is the thermal fluid and the thermal fluid The inner wall surface contact area of the end heat exchanger,

is the average temperature of the thermal fluid in the i-th step, and

Calculate the hot junction temperature Th _leg of the PN junction pin; The heat flux q1 at the hot end is:

According to the heat flux is equal, then

Where λ ₁ is the thermal conductivity of the heat exchanger material at the hot end, δ _h is the thickness of the bottom plate of the heat exchanger at the hot end, λ _ce is the thermal conductivity of the ceramic plate material, and T _owh is the temperature of the outer wall of the heat exchanger at the hot end; Then the hot junction temperature of the PN junction pin

3. the method for determining the pin height of a kind of stepped thermoelectric generating sheet according to claim 2, is characterized in that, the specific process of determining the cold junction temperature of the i-th step PN junction pin is: Calculate the inner wall surface temperature T _iwc of the cold end heat exchanger;

In the formula, C _w is the specific heat capacity of the cold fluid,

is the mass flow rate of the cold fluid, Tc _i is the inlet temperature of the cold fluid, Tc _i+1 is the outlet temperature of the cold fluid, h ₂ is the convective heat transfer coefficient of the cold fluid, A ₂ is the inner wall surface of the cold fluid and the cold end heat exchanger Contact area,

is the average temperature of the cold fluid in the i-th step, and

Calculate the cold junction temperature Tc _leg of the PN junction pin; The heat flux _q2 at the cold end is:

According to the heat flux is equal, then

In the formula, λ ₂ is the thermal conductivity of the material of the cold end heat exchanger, δ _c is the thickness of the bottom plate of the cold end heat exchanger, T _owc is the temperature of the outer wall of the cold end heat exchanger; h _c1 is the height of the upper ceramic plate equal to that of the lower ceramic plate the height of the first step; Then the cold junction temperature of the PN junction pin

. 4. the method for determining the pin height of a kind of step type thermoelectric generating sheet according to claim 3, is characterized in that, the specific process of calculating the PN junction output current of the i step is: Calculate the PN junction output voltage U _i of the i-th step; U _i ＝R×m(α _P -α _N )×(Th _leg -Tc _leg ) In the formula, m is the number of PN junctions contained in each column of PN junction pins, α _P is the Seebeck coefficient of the P pole, and α _N is the Seebeck coefficient of the N pole; Calculate the PN junction internal resistance R _i of the i-th step;

In the formula, ρ _P is the resistivity of the P pole, ρ _N is the resistivity of the N pole, and A _leg is the cross-sectional area of the PN junction pin; Calculate the PN junction output current I _i of the i-th step:

5. the method for determining the pin height of a kind of stepped thermoelectric power generation sheet according to claim 4, is characterized in that, when i=1, h ₁ is known, obtains

When i=2, 3,..., n, h _i is unknown, and it can be obtained by solving according to I _i =I ₁ , namely

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