Thermopile heat flux sensor based on the method of calibrated integral equation

Abstract

The application provides a heat flow sensor based on a calibration integral equation method, which is used for measuring average heat flow density and average temperature of an object surface by using a calibration integral equation method; the sensor comprises a cylindrical thermal resistance layer, heat insulation material and a shell which are sequentially arranged from inside to outside; a thermoelectric element is further arranged between the thermal resistance layer and the heat insulation material, the thermoelectric element comprises three hot end nodes and two cold end nodes, the hot end nodes are embedded in the thermal resistance layer, and the cold end nodes are located in the heat insulation material. The application can simultaneously measure average heat flow density and average temperature on a plane, and has the characteristics of high measurement accuracy, high sensitivity, simple production and long-time measurement.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of thermal measurement, and relates to a heat flow sensor, in particular to a thermopile type heat flow sensor based on a calibration integral equation method. BACKGROUND

[0002] With the progress of science and technology, the improvement of energy utilization efficiency, the intelligentization of equipment and the enhancement of environmental protection awareness, people's demand for accurate monitoring of heat flow and distribution is gradually increasing. In particular, in the fields of industry, energy and environmental monitoring, higher requirements are put forward for real-time monitoring and optimization of heat flow. As a tool for accurately measuring heat flow and heat transfer, heat flow sensors have also received extensive attention and research in recent years.

[0003] At present, the basic structure of the thermopile temperature sensor produced is mostly that a thin film thermopile or a thermal resistance is sputtered on the surface of a rigid and heat-insulating substrate such as ceramic or silicon substrate, then a thermal resistance layer is covered on the hot end of the thermopile, and the cold end is covered with heat-insulating material. Under the coverage of different materials, a temperature difference will be generated at the two ends of the thermopile, which will be converted into a thermoelectric potential through the Seebeck effect. By comparing with the initial calibration of the thermoelectric potential and temperature relationship diagram, the temperature value is obtained, and the temperature and heat flow have a corresponding relationship, so as to realize the measurement of surface heat flow. Compared with traditional heat flow sensors, thermopile sensors can reflect small heat flow and temperature changes. However, the performance progress of the sensor is limited by the development of the material itself, and the designed thermopile sensor still has problems of low measurement accuracy and low temperature measurement range. The most commonly used thermopile heat flow sensor at present often uses platinum-platinum rhodium thermopile for heat flow measurement, which has problems of low sensitivity, high preparation cost and difficulty in long-time measurement.

[0004] There are many methods for solving inverse problems, and common ones include regularization method, conjugate gradient method, Bayesian method, inverse Monte Carlo method and the like.

[0005] The conjugate gradient method is a general iterative minimization method. The solution is defined as a linear combination of search directions, and at each step a new search vector is generated, which is mutually conjugate with all previous search directions, thus ensuring that an N-dimensional linear problem can be minimized in exactly N steps using exact algebra. The algorithm provides an exact solution h for a linear system in N steps, where N is the unknown. In the inverse heat conduction problem, the conjugate gradient method is to constantly give a forward numerical value, by solving the forward problem, comparing the calculated value with the actual value, and repeatedly correcting the forward numerical value to obtain a correct value for the inverse problem. The correction process is the iteration process, and each search vector is mutually conjugate, which can theoretically traverse all solutions, gradually construct the optimal solution to approach the true solution, and solve it in N steps. Therefore, in order to reduce the calculation time and make the result more accurate, it is necessary to reduce the value of the unknown N. This requires accurate measurement of sensor size, thermal physical parameters, etc. However, these parameters are not constant, and thermal physical parameters will change with temperature; the measurement error cannot guarantee that the measured parameters meet the true parameter data. These will bring errors and uncertainties to the final calculation results.

[0006] The Bayesian method for solving inverse problems is a statistical inference method based on Bayesian theory, which updates the probability estimate of unknown parameters by combining prior knowledge and observed data. In the inverse heat conduction problem, the Bayesian method aims to infer the model parameters or distribution hidden behind the data from the known observation data. The basic principles include: establishing a model, first, a prior distribution of the model parameters needs to be established, and it is assumed that the model parameters to be solved follow this distribution; observing data, then updating the estimate of the model parameters through the observation data. The core of the Bayesian method is to calculate the posterior distribution, that is, the probability distribution of the model parameters given the observation data. At the same time, the selection of the prior probability distribution is also very important, because it contains the prior knowledge of the solution object and can play a role in regularizing the parameters. Bayesian algorithm can well integrate prior information and error information, and reduce the uncertainty of problem solving. However, Bayesian method has a serious dependence on prior information. It needs to set the prior distribution, but the selection of prior may be subjective. If the prior distribution is not appropriate, it may lead to biased results. When there is no explicit prior knowledge, how to choose a reasonable non-informative prior is a challenge. At the same time, the computational complexity of the Bayesian method is large, and it usually needs to calculate complex integrals or sums, especially in high-dimensional space, the computational complexity increases exponentially. For small sample problems, the data volume is very small and the prior knowledge is insufficient, and the inference result may be unreliable; for large sample problems, with the increase of sample size, the computational complexity will be further aggravated.

[0007] Compared to the two algorithms mentioned above, the calibration integral equation method has unique advantages. First, this algorithm does not require measurements of sensor size and thermal properties, significantly reducing errors caused by measurement data. Secondly, the key to the calibration integral equation method lies in finding the relationship between the calibration equation and the experimental equation, thus it can handle correspondences between multiple images or formulas, offering high flexibility and a wide range of potential applications. Furthermore, the calibration integral equation method may be more efficient in handling specific types of integration problems because it directly optimizes for the characteristics of the integral equation. In contrast, while the conjugate gradient method converges quickly when solving linear equations, it may be inferior to the calibration integral equation method in nonlinear problems. Regarding the handling of prior information, although Bayesian methods can effectively integrate prior knowledge and observational data, the calibration integral equation method can also integrate prior information through appropriate regularization techniques, while avoiding the subjectivity of prior selection in Bayesian methods. Additionally, the calibration integral equation method does not require calculating an exact Hessian matrix, which is a significant advantage in terms of computational cost, especially when dealing with large-scale problems.

[0008] The calibration integral equation method (CIEM) is a mathematical physics-based approach that predicts surface heat flux by constructing a mathematical relationship between surface heat flux and the temperature at the measurement point. Compared to traditional inverse problem-solving methods, it avoids the process of solving the direct heat conduction problem, thus eliminating the need for specific system parameter inputs and avoiding prediction uncertainties introduced by system parameters. This results in a final result that more closely matches the specific situation of the reconstructed experimental surface heat flux. Although CIEM has been successfully applied in several fields, a thermopile-based heat flux density and temperature measurement sensor based on the CIEM algorithm has yet to emerge, limiting its widespread adoption in practical applications. Summary of the Invention

[0009] To address the problems of low temperature measurement range, insufficient measurement accuracy, and difficulty in long-term measurement of existing thermopile sensors, this invention designs a thermopile-type heat flux sensor based on the calibration integral equation method. It can simultaneously measure the average heat flux density and average temperature on a plane, and features high measurement accuracy, high sensitivity, simple manufacturing, and the ability to perform long-term measurements.

[0010] To achieve the above objectives, the present invention provides the following technical solution:

[0011] A thermopile type heat flux sensor based on a calibration integral equation method is used for measuring the average heat flux density and average temperature of an object surface by using the calibration integral equation method; the sensor body is cylindrical, one end of which is a measurement end and the other end is a tail end; it comprises a cylindrical thermal resistance layer, a thermal insulation material and an outer shell arranged in sequence from inside to outside; a thermoelectric element is arranged between the thermal resistance layer and the thermal insulation material, the thermoelectric element comprises three hot junctions and two cold junctions, the hot junctions are embedded in the thermal resistance layer, and the cold junctions are located in the thermal insulation material.

[0012] Preferably, the thermoelectric element is composed of three series-connected thermocouples, each thermocouple comprising a first wire and a second wire, one end of the first wire and the second wire of the same thermocouple being connected to form a hot junction; at the other end of the first wire and the second wire, the second wire of the first thermocouple is connected with the first wire of the second thermocouple, and the second wire of the second thermocouple is connected with the first wire of the third thermocouple to form two cold junctions.

[0013] Preferably, three holes are formed on the side of the measurement end of the thermal resistance layer, the three holes are located on the same circle, and the included angle between adjacent two holes is 120°; the hot junctions of the three thermocouples are respectively in contact with the bottoms of the three holes, the remaining part of the three holes is filled with an adhesive, and the thermocouples are fixed to the thermal resistance layer by the adhesive.

[0014] Preferably, the adhesive comprises a Graphi-Bond 669 glue and a CERAMABOND 571 adhesive, the Graphi-Bond 669 glue is poured into the holes of the thermal resistance layer, and the CERAMABOND 571 adhesive is coated on the surface of the Graphi-Bond 669 glue and bonded with the thermocouples.

[0015] Preferably, the first wire of the first thermocouple is welded with a signal output line to form a positive electrode lead, the second wire of the third thermocouple is welded with a signal output line to form a negative electrode lead, and the positive electrode lead and the negative electrode lead are led out through the thermal insulation material.

[0016] Preferably, the depth of the hole is half of the radius of the thermal resistance layer.

[0017] Preferably, the thermocouple further comprises an insulating layer and a metal shell, the outer parts of the first wire and the second wire are respectively wrapped with an insulating layer, and the insulating layers of the first wire and the second wire are wrapped with a metal shell together.

[0018] Preferably, the tail end of the thermal resistance layer is also embedded with a thermocouple in the same way as the thermocouple in the thermoelectric pile, for detecting whether the temperature of the thermal resistance layer meets the adiabatic condition.

[0019] Preferably, the tail end of the sensor is also provided with a thermal insulation plug, which is composed of a cylindrical thermal insulation plug and a circular ring-shaped thermal insulation plug, and the two cooperate to fix the thermal resistance layer, the thermal insulation material and the shell. The thermal insulation plug is also provided with a plurality of holes for leading out the positive electrode lead and the negative electrode lead and the lead wire of the tail end thermocouple.

[0020] More preferably, the thermal insulation material is mullite, and the thermal insulation plug adopts zirconia material.

[0021] Compared with the prior art, the present application has the following beneficial effects:

[0022] Compared with other heat flow sensors, the present application based on the calibration integral equation method has the characteristics of high precision, long measurement time, high sensitivity and wide application range. The present application can accurately measure the average temperature on a plane. By arranging the hot end of the thermoelectric pile on a complete thermal resistance layer, the boundary effect caused by dividing the area can be effectively avoided, so that the accuracy is greatly improved. At the same time, by connecting the thermocouples in series to form a thermoelectric pile to measure the temperature, the small temperature change can be more sensitively reflected, so that the measured temperature is more close to the average temperature of the plane. By adjusting the thickness of the thermal resistance layer, the sensitivity of the sensor can be adjusted.

[0023] The CIEM algorithm on which the present application is based can avoid the limitation conditions of one-dimensional heat transfer, and can more truly reflect the heat flow and temperature change in a plane. At the same time, the thermoelectric pile of the present application is embedded in the thermal resistance layer, compared with general thin film heat flow sensors, it can still maintain strong sensitivity and measurement performance in high temperature and high heat flow environment. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 It is a front view of the thermoelectric pile type heat flow sensor based on the calibration integral equation algorithm in the embodiment of the present application.

[0025] Figure 2 It is a schematic diagram of the sensor thermoelectric pile hot end embedding in the embodiment of the present application.

[0026] Figure 3 It is a schematic diagram of the sensor thermoelectric pile cold end in the embodiment of the present application.

[0027] Figure 4 It is a configuration diagram of the thermocouple after being made in the embodiment of the present application.

[0028] Figure 5 It is a size diagram of the thermal insulation plug provided in the embodiment of the present application.

[0029] Figure 6 This is a flowchart of the method for measuring the average heat flux on the surface of an object provided in an embodiment of the present invention.

[0030] Among them, 1 is the thermal resistance layer, 2 is the thermal insulation material, 3 is the outer shell, 4 is the hot end junction, 5 is the cold end junction, 6 is the positive electrode lead, 7 is the negative electrode lead, 8 is the insulation layer, 9 is the metal outer shell, 10 is the annular heat insulation plug, and 11 is the cylindrical heat insulation plug. Detailed Implementation

[0031] This invention, based on the calibration integral equation method, designs a thermopile sensor using the CIEM method. Without needing to know the object's thermal properties, only the local average temperature obtained from the pre-embedded thermopile is required. The average heat flux and average temperature of the measured surface can then be derived using the CIEM algorithm.

[0032] The technical solution of the present invention will be further described clearly and in detail below with reference to the accompanying drawings and specific examples.

[0033] like Figure 1 As shown, a thermopile-type heat flux sensor based on the calibration integral equation method is used to measure the average heat flux density and average temperature of an object surface using the calibration integral equation method. The sensor body is cylindrical, with one end being the measuring end and the other end being the tail end. It includes a cylindrical thermal resistance layer 1, a thermal insulation material 2, and a shell 3 arranged sequentially from the inside out. A thermopile is also provided between the thermal resistance layer 1 and the thermal insulation material 2. The thermopile includes three hot-end nodes 4 and two cold-end nodes 5. The hot-end nodes 4 are embedded in the thermal resistance layer 1, and the cold-end nodes 5 are located in the thermal insulation material 2.

[0034] The thermopile consists of three thermocouples connected in series. Each thermocouple includes a first and a second conductor. One end of the first and second conductors of the same thermocouple is connected to form a hot end node 4. At the other end of the first and second conductors, the second conductor of the first thermocouple is connected to the first conductor of the second thermocouple, and the second conductor of the second thermocouple is connected to the first conductor of the third thermocouple to form two cold end nodes 5.

[0035] The heat resistance layer 1 is provided with three holes on the measuring end side, the three holes are located on the same circle, the included angle between the adjacent two holes is 120°, and the depth of the hole is half of the radius of the heat resistance layer 1; the hot junction 4 of the three thermocouples is in contact with the bottom of the three holes respectively, the remaining part of the three holes is filled with an adhesive, and the thermocouples are fixed with the heat resistance layer 1 through the adhesive. The adhesive includes Graphi-Bond 669 glue and CERAMABOND 571 adhesive, the Graphi-Bond 669 glue is injected into the hole of the heat resistance layer 1, and the CERAMABOND 571 adhesive is coated on the surface of the Graphi-Bond 669 glue and bonded with the thermocouple.

[0036] The first wire of the first thermocouple is welded with the signal output line to form a positive electrode lead 6, and the second wire of the third thermocouple is welded with the signal output line to form a negative electrode lead 7, and the positive electrode lead 6 and the negative electrode lead 7 are led out through the heat insulation material 2.

[0037] The thermocouple further comprises an insulating layer 8 and a metal shell 9, and the outer parts of the first wire and the second wire are wrapped with the insulating layer 8 respectively, and the insulating layers of the first wire and the second wire are wrapped with the metal shell 9.

[0038] The heat resistance layer 1 tail end is further embedded with a thermocouple in the same way as in the thermoelectric pile, for detecting whether the temperature of the heat resistance layer 1 meets the heat insulation condition.

[0039] The sensor tail end is further provided with a heat insulation plug, the heat insulation plug is composed of a cylindrical heat insulation plug (11) and a circular heat insulation plug (10), and the two cooperate to fix the heat resistance layer, the heat insulation material and the shell; a plurality of holes are arranged on the heat insulation plug, for leading out the positive electrode lead 6, the negative electrode lead 7 and the wires of the tail end thermocouple.

[0040] The present application first considers the response sensitivity problem, and the sensitivity is related to the distance between the hot junction 4 of the thermoelectric pile and the measuring end plane of the heat resistance layer. Therefore, it can be predicted that the closer the distance, the more sensitive the sensor, and the more responsive to the small heat flow change. However, considering the manufacturing process of the heat resistance layer and the preparation of the thermoelectric pile, the thickness is not the thinner the better. Considering these two factors, the heat resistance layer with a diameter of 3mm is selected, the material is stainless steel, and the distance between the hot junction position of the thermoelectric pile and the measuring end plane of the heat resistance layer is 2mm.

[0041] The thermoelectric pile constructed in the present application is composed of thermocouples in series. The selected thermocouples should meet the characteristics of fast time response and wide measurement temperature range. Therefore, nickel-chromium-silicon and nickel-silicon-magnesium are selected as the two wires of the thermocouple, which are respectively marked as the first wire and the second wire. That is, N-type thermocouple.

[0042] Compared with the common K-type thermocouple, the N-type thermocouple can successfully overcome two shortcomings of the K-type thermocouple: the instability of the thermoelectric electromotive force of the K-type thermocouple caused by the short-range order of the nickel-chromium alloy crystal lattice at 300-500 ℃; and the instability of the thermoelectric electromotive force caused by the preferential oxidation of the nickel-chromium alloy at about 800 ℃. The N-type thermocouple has the advantages of good linearity, large thermoelectric electromotive force, high sensitivity, good stability and uniformity, strong oxidation resistance, low price, and no influence of short-range ordering.

[0043] Therefore, taking nickel-chromium-silicon and nickel-silicon-magnesium as the main materials of the thermoelectric pile can increase the temperature range measured by the sensor of the present application. The present sensor can still effectively function at a temperature range of 400-1300 ℃.

[0044] When the measured temperature is in the temperature range of -200-400 ℃, the K-type thermocouple is preferred.

[0045] Considering the convenience and universality of the thermocouple connection operation, the welding method of the thermocouple is selected to prepare the thermoelectric pile.

[0046] Considering the size of the thermal resistance layer and the length loss in the welding process, a thermocouple wire with a diameter of 0.1 mm is selected, and the lengths of the nickel-chromium-silicon and nickel-silicon-magnesium are 30 mm.

[0047] The first lead and the second lead of the thermocouple are welded together to form a spherical node, i.e., the hot junction node 4, with a diameter of about 0.5 mm, which ensures that the thermocouple has good time response characteristics. In addition to the node, the thermocouple leads should be wrapped with an insulating layer to ensure good insulation between the leads.

[0048] Common insulating materials include polyvinyl chloride (PVC), polytetrafluoroethylene (PTFE), FEP (perfluoroethylene propylene copolymer), PFA (perfluoroalkoxy ethylene vinyl ether), etc. For environments with high heat resistance requirements, polytetrafluoroethylene is preferably used as the insulating layer material.

[0049] The insulating layer is usually wrapped around the lead surface by extrusion. The extrusion amount of the extruder needs to be controlled to ensure the uniformity and thickness of the insulating layer. During the extrusion process, the insulating material is heated and melted, then extruded through the die of the extruder and tightly wrapped around the lead.

[0050] However, the heat resistance of the insulating material is still insufficient. The preferred polytetrafluoroethylene can only be used for a long time at a temperature range of -180-260 ℃. Therefore, a metal shell needs to be added outside the insulating layer. The armoring process is usually used.

[0051] In order to facilitate the subsequent thermoelectric pile production, the two first wires and the second wire wrapped with the insulating layer are put into the metal shell together, and the metal shell is preferably cobalt-based alloy material, which can be used at a temperature of 1200 ℃, has the characteristics of high temperature resistance, strong corrosion resistance, good stability and good ductility.

[0052] Then the outer metal shell and the internal insulating layer and the wire are placed in an air heating furnace and heated to 750 ℃ ~ 1500 ℃ within 30 minutes. The heated material is quickly put into a hot rolling mill for rapid rolling, and the speed of putting into the hot rolling mill should ensure that the temperature of the metal shell sleeve is not lower than 750 ℃. The rolling speed should ensure that the rolling is completed within 1 minute. After rolling, air cooling or slow cooling under heat preservation.

[0053] As shown in Figure 4 , it is the configuration of the completed thermocouple, which includes the first wire A, the second wire B, the insulating layer 8 and the metal shell 9.

[0054] The thermoelectric pile is installed inside the sensor and realized by punching and inserting in the form of thermocouple. As shown in Figure 2 , holes are applied in the thermal resistance layer 1 with appropriate spacing. The hole positions are distributed on a circle with a diameter of 0.75 mm, and the included angle between every two holes is 120°, which can effectively reflect the average temperature in the area without excessively damaging the heat conduction process inside the thermal resistance layer. The diameter of the hole is selected to be about 0.8 mm, which should not be too small to prevent the hot end node from contacting the thermal resistance layer. The bottom surface of the hole should be tangent to the circle where the hot end node of the thermoelectric pile is located, and the depth of each hole should be strictly equal to 0.75 mm.

[0055] After the hot end node 4 of the thermocouple is buried in the hole and ensures that it is completely matched with the bottom surface of the hole, glue is poured to completely fix the thermocouple and the thermal resistance layer. The end point buried in the thermal resistance layer is used as the hot end of the thermoelectric pile.

[0056] The glue is preferably Graphi-Bond 669, which has excellent thermal stability and chemical corrosion resistance, and can be used for a long time in severe high temperature environment without performance degradation. At the same time, it also has good electrical conductivity and thermal conductivity, which ensures that the electrical and thermal performance remains consistent at high temperature. Therefore, the influence of the heat flow conduction inside the thermal resistance layer caused by punching can be effectively avoided.

[0057] However, Graphi-Bond 669 is not viscous enough and can be loose during use, so CERAMABOND 571 is also selected. It has strong adhesion and viscosity between 20,000-90,000 cP, which can effectively prevent the thermoelectric element from loosening due to impact and vibration. It is commonly used for the assembly and insulation of ceramic and metal components of high-temperature equipment, and can meet the adhesion and filling requirements of the application at higher temperatures. At the same time, because the glue is used on the surface of the thermal resistance layer, its low thermal conductivity will not significantly affect the heat transfer inside the thermal resistance layer.

[0058] Before the specific gluing, CERAMABOND 571 also needs to be processed. CERAMABOND 571 is a mixture of powder and liquid adhesive, and when used, the powder and liquid need to be mixed in a ratio of 1.5:1 (by weight). Slowly add the powder to the liquid while using a low-speed stirrer for slow stirring. The mixing process should be thorough and slow to ensure that the powder is completely wet and there are no dry powder lumps, and the color is uniform, while avoiding air mixing to cause bubbles. If you need to adjust the viscosity of the mixture, you can add an appropriate amount of diluent (such as 571-T) to achieve it, and at most 20% of the diluent (by weight) can be added. The well-mixed material should be in a uniform paste state without separation or stratification, similar to liquid cement. The mixed adhesive should be used as soon as possible to avoid premature curing. Generally, the best results are achieved within 1-4 hours after mixing.

[0059] The following is the specific gluing process. First, fill the hole with Graphi-Bond 669, considering the elongated structure of the hole, use a syringe to fill it. Insert the needle tube of the syringe into the hole and slowly inject it until the glue overflows. Wipe off the surface of the remaining glue. Then insert the hot end of the thermoelectric element into the hole and make sure the hot end is in full contact with the bottom surface of the hole. After waiting for the adhesive to fully solidify, usually wait for about 1 day. Use CERAMABOND 571 on the surface of the hole to completely fix the thermocouple, usually need to wait for a day.

[0060] After the above steps are completed, each thermocouple will lead out two wires A and B. The second wire of the first thermocouple is welded to the first wire of the second thermocouple, and the second wire of the second thermocouple is welded to the first wire of the third thermocouple, forming two spherical nodes, i.e. cold end node 5, which is used as the cold end of the thermoelectric element. In this way, the thermocouples are connected in series, and the measured temperature can fully reflect the average temperature of the two-dimensional area where they are located.

[0061] In order to ensure that the thermal resistance layer is strictly in the heat insulation state, a thermocouple is added near the tail end of the thermal resistance layer to detect whether the temperature at this position meets the heat insulation condition. The internal embedding mode of the thermocouple is the same as that of the thermocouple.

[0062] The remaining two wires of the thermocouple in the thermocouple are welded together with the signal output line, and are marked as positive lead 6 and negative lead 7, respectively. The signal output line is led out through the heat insulation material, and the cold end node 5 is placed in the heat insulation material.

[0063] The heat insulation material is selected as mullite, the heat insulation plug is selected as zirconia, and the heat insulation plug is composed of a circular ring with an inner diameter of 3mm, an outer diameter of 5mm and a length of 1mm, and a cylindrical column with a diameter of 5mm and a length of 1mm.

[0064] Mullite is a high-quality refractory material, which has the characteristics of high temperature resistance, high strength, small thermal conductivity, good high temperature stability and good thermal shock resistance, and is widely used in crucibles, protective tubes and thermocouple tubes. As the main heat insulation material of the sensor, on the one hand, it can effectively ensure that the thermal resistance layer is in the heat insulation state, and on the other hand, it is fibrous and can be combined with the cold end through compaction technology to make it in the heat insulation state. Compared with the heat insulation material with fixed shape, the use of fibrous mullite can significantly reduce the influence caused by the machining precision. The cold end and the thermal resistance layer will be in full contact with the heat insulation material and strictly in the heat insulation condition, which is the condition for the subsequent CIEM algorithm to run.

[0065] Zirconia material is used as a fixed plug, which is dense, hard and has excellent heat insulation performance, and can ensure that the mullite is in full contact with the thermal resistance layer, but not too loose. Its structure is shown in Figure 5 .

[0066] The shell 3 is selected from stainless steel material, and the inner diameter of the cylinder is 5mm and the thickness is 0.5mm.

[0067] The annular heat insulation plug, the thermal resistance layer metal cylinder (on which the internal embedding of the thermocouple has been completed), and the stainless steel shell are placed in sequence, and the mullite fiber is filled therein. It is best to compact after filling a part to avoid the generation of gaps that destroy the heat insulation condition and the damage of the compaction action to the structure of the thermocouple. After the filling is completed, the cylindrical heat insulation plug is covered on the back. At this time, the heat insulation material part is completed. The signal lead is led out from the circular hole of the cylindrical heat insulation plug through the heat insulation material, and the cold end of the thermocouple is placed in the heat insulation material.

[0068] The measurement principle of the thermocouple type heat flow sensor based on the calibration integral equation method is as follows:

[0069] The CIEM algorithm that the sensor is based on needs to be completed under adiabatic condition, so it is necessary to monitor the adiabatic condition to ensure that the sensor is in normal working state.

[0070] A thermocouple is added at the position close to the tail end of the thermal resistance layer to detect the temperature at the position .

[0071] Excess temperature is defined wherein

[0072]

[0073] wherein, is the instantaneous temperature at this position, is the initial temperature at this position.

[0074] When the plane where the thermoelectric pile is located has reached a high temperature, < 10 ℃. At this time, the entire thermal resistance layer has fully conducted heat, but the back surface still maintains a low temperature, less than 5 ℃, which can be considered to meet the adiabatic condition.

[0075] But when the plane where the thermoelectric pile is located is not high in temperature, It may still meet the condition of less than 10 ℃. At this time, the temperature difference between the two is not much, and the back surface may conduct heat to the plane where the thermoelectric pile is located, which will affect the final result. Therefore, we can consider that the adiabatic condition is not met at this time.

[0076] Before solving the surface average heat flux by using the CIEM algorithm, calibration needs to be performed first.

[0077] According to the derivation of the CIEM algorithm, the ratio of the average heat flux after Laplace transform to the average excess temperature is a constant value. Therefore, calibration is needed.

[0078] Uniform heat flux q is applied in the vertical direction of the surface of the sensor, and the potential difference collected by the thermoelectric pile is processed to obtain the average temperature of the plane.

[0079] The potential difference of a single thermocouple and the temperature are in a linear relationship.

[0080]

[0081] wherein, is the hot end temperature of the thermocouple, is the cold end temperature of the thermocouple, both in K (the same below).

[0082] The sensor of the present application forms a thermoelectric pile by connecting three thermocouples in series, and the potential difference collected by the thermoelectric pile has the relationship

[0083]

[0084] Thus the relationship between the average temperature and the potential difference can be obtained

[0085]

[0086] where, is the potential difference of a single thermocouple, is the potential difference of a thermopile, is the average temperature difference between the hot end and the cold end of the thermopile.

[0087] In this process, because the cold end is in an insulated condition, its temperature is the same as the initial temperature.

[0088] The average excess temperature can be obtained

[0089]

[0090] The relationship between the average excess temperature of the plane where the thermopile is located and the average heat flux and the average temperature of the surface of the sensor is calibrated.

[0091] When the external environment exerts a heat flux on the sensor, the heat is transferred to the hot end node of the thermopile through the thermal resistance layer, and at the same time, because the cold end node is sealed and insulated in the insulating material, it can be considered as a constant temperature. According to the Seebeck effect, a corresponding potential difference is generated between the two ends of the thermopile. By processing the potential difference, the average excess temperature of the plane over time can be obtained.

[0092] After the data is collected and accessed to the computer, the average heat flux and the average temperature of the surface of the object can be obtained by the CIEM algorithm built in the program.

[0093] The following is the derivation of the CIEM algorithm in the three-dimensional case.

[0094] The heat conduction equation in three-dimensional conditions is

[0095]

[0096] The boundary condition is

[0097]

[0098] Let

[0099]

[0100]

[0101] obtained

[0102]

[0103] Substitute into

[0104]

[0105] In

[0106]

[0107]

[0108]

[0109]

[0110] Substitute into

[0111] Let

[0112]

[0113] Substitute

[0114]

[0115]

[0116] Where

[0117]

[0118]

[0119] Take

[0120]

[0121] Substitute into

[0122] ​​​​​​​​

[0123] Left with

[0124]

[0125] Simultaneously and, with

[0126]

[0127] Its analytical solution is

[0128]

[0129] Will be substituted into the solution, get

[0130]

[0131] Will be substituted into the solution, get

[0132]

[0133] Because

[0134]

[0135] Will be substituted into the solution, get

[0136]

[0137] Comprehensive comparison and get

[0138]

[0139] Where, L, W for the thermal resistance layer x, y direction size, H for the thermal resistance layer z direction (thermal resistance layer axis direction) size, w for the thermal resistance layer z direction on the location of thermoelectric power, α for the thermal resistance layer of thermal diffusivity, k for the thermal resistance layer of thermal conductivity. When the sensor is completed, W, L, k, α, H, w is constant, can be known

[0140]

[0141] In the case of ensuring that the above conditions do not change, under different heat flow conditions, there is an identity

[0142]

[0143] Wherein, subscript c represents the calibration group data, subscript r represents the experimental group data.

[0144] In the formula, , , Known, can be calculated by identity .

[0145] The following is the specific use process of the sensor of the present application:

[0146] Firstly, the heat flow sensor of the present application needs to be calibrated. Select the "calibration group" module in the software and click "start measurement". Apply a uniform heat flow changing with time vertically on the surface of the sensor (if the purpose of the experiment is to measure temperature, change the temperature of the surface of the sensor to obtain the temperature-time curve), and through the data collected by the sensor, the average heat excess temperature curve at the position of the thermoelectric element changing with time can be obtained. Import the data and curve of the heat flow applied on the surface of the sensor into the software. Click "start calculation", and the software will automatically fit the above two curves to obtain the average heat flow and average heat excess temperature-time formula, and obtain the calibration group data.

[0147] Further, the experimental data is obtained. The measurement end of the sensor (i.e. the exposed side of the thermal resistance layer) is tightly attached to the surface of the object to be measured.

[0148] Further, because the size of the sensor is small, in order to make the result more accurate, the plug-in method can be adopted. A hole with a diameter of 6.5 mm and a depth of about 5 mm is applied on the surface of the object, and the sensor is plugged into it. When it cannot be inserted further, the sensor is in close contact with the object. A mark can also be made on the sensor at 5 mm in advance, and the position of the mark can be used to judge whether the sensor has been fully inserted. In order to ensure that the sensor and the object are in close contact, an adhesive or other means can be used to fix it, and if the position of the sensor in the measured object remains stable after applying external force, it has been fixed sufficiently.

[0149] Further, the positive and negative leads of the sensor are connected to the computer. Select the "experimental group" module in the software and click "start measurement", and the system will automatically record the heat excess temperature θ t at the position of the thermoelectric element until "stop measurement" is clicked.

[0150] Further, the object is heated.

[0151] Further, the average heat excess temperature θ1 at the position of the thermoelectric element and the heat excess temperature θ2 at the back surface position of the sensor are compared to determine whether the sensor is working normally.

[0152] Further, when the value of θ1 is high and θ2≤ 10 ℃, the sensor can be used for measurement; when the value of θ1 is not high, if the difference between θ1 and θ2 is not large, the sensor cannot be used.

[0153] Further, after the measurement is completed, the software in the calculator will process the potential difference obtained by the sensor to obtain the average heat excess temperature-time curve. The curve is fitted to obtain the formula of the average heat excess temperature changing with time.

[0154] Further, after clicking "start calculation", the software in the calculator will solve the calibration integral equation by simultaneously solving the calibration group average heat surplus temperature and surface heat flow variation formula with experimental group data, and obtain the surface average heat flow variation formula in the experimental group, while drawing the corresponding curve.

[0155] The above detailed description is used to explain and illustrate the present application, rather than limiting the present application, and any modification and change made to the present application within the spirit and protection scope of the claims of the present application, falls into the protection scope of the present application.

Claims

1. A thermopile-type heat flux sensor based on a calibration integral equation method, characterized in that, Used to measure the average heat flux density and average temperature of an object surface using a calibration integral equation method; the sensor body is cylindrical, with one end being the measuring end and the other end being the tail end; it includes a cylindrical thermal resistance layer (1), a thermal insulation material (2), and a shell (3) arranged sequentially from the inside out; a thermopile is also provided between the thermal resistance layer (1) and the thermal insulation material (2), the thermopile including three hot end nodes (4) and two cold end nodes (5), the hot end nodes (4) being embedded in the thermal resistance layer (1), and the cold end nodes (5) being located in the thermal insulation material (2); The thermal resistance layer (1) has three holes on the side of the measuring end, and the three holes are located on the same circle; the hot junctions (4) of the three thermocouples are in contact with the bottom of the three holes respectively; A thermocouple is also embedded in the tail end of the thermal resistance layer (1), and the embedding method is the same as that of the thermocouple in the thermopile, which is used to detect whether the temperature of the thermal resistance layer (1) meets the insulation conditions. While ensuring the dimensions L in the x-direction, W in the y-direction, H in the z-direction, and the thermal conductivity k and thermal diffusivity of the thermal resistance layer are maintained... α With the position w of the thermopile along the z-direction of the thermal resistance layer remaining constant, the sensor exhibits an identity under different heat flux application conditions: ， in, θ is the excess temperature, representing the difference between the transient temperature and the initial temperature; s is a parameter of the Laplace transform. For calibration group heat flow, For calibration group excess temperature, For the heat flow of the experimental group, The excess temperature for the experimental group. , , It is known that It can be calculated using identities.

2. A thermopile-type heat flux sensor based on a calibration integral equation method according to claim 1, characterized in that, The thermopile consists of three thermocouples connected in series. Each thermocouple includes a first wire and a second wire. One end of the first wire and the second wire of the same thermocouple are connected to form a hot junction (4). At the other end of the first wire and the second wire, the second wire of the first thermocouple is connected to the first wire of the second thermocouple, and the second wire of the second thermocouple is connected to the first wire of the third thermocouple to form two cold junctions (5).

3. A thermopile-type heat flux sensor based on a calibration integral equation method according to claim 2, characterized in that, The included angle between two adjacent holes is 120°; the remaining parts of the three holes are filled with adhesive, and the thermocouple and the thermal resistance layer (1) are fixed by the adhesive.

4. A thermopile-type heat flux sensor based on a calibration integral equation method according to claim 3, characterized in that, The adhesive includes graphite adhesive and high-temperature two-phase adhesive. The graphite adhesive is poured into the pores of the thermal resistance layer (1), and the high-temperature two-phase adhesive is applied to the surface of the graphite adhesive and bonded to the thermocouple.

5. A thermopile-type heat flux sensor based on a calibration integral equation method according to claim 2, characterized in that, The first wire of the first thermocouple is welded to the signal output line to form a positive lead (6), and the second wire of the third thermocouple is welded to the signal output line to form a negative lead (7). The positive lead (6) and the negative lead (7) are led out through the heat insulation material (2).

6. A thermopile-type heat flux sensor based on a calibration integral equation method according to claim 2, characterized in that, The depth of the hole is half the radius of the thermal resistance layer (1).

7. A thermopile-type heat flux sensor based on a calibration integral equation method according to claim 2, characterized in that, The thermocouple also includes an insulating layer (8) and a metal shell (9). The first conductor and the second conductor are respectively wrapped with an insulating layer (8), and the insulating layers of the first conductor and the second conductor are together wrapped with a metal shell (9).

8. A thermopile-type heat flux sensor based on a calibration integral equation method according to claim 5, characterized in that, The sensor is also provided with a heat insulation plug at the tail end. The heat insulation plug is composed of a cylindrical heat insulation plug (11) and an annular heat insulation plug (10). The two work together to fix the thermal resistance layer, the heat insulation material and the shell. The heat insulation plug is also provided with several holes for leading out the positive electrode lead (6) and the negative electrode lead (7) as well as the wires of the thermocouple at the tail end.

9. A thermopile-type heat flux sensor based on a calibration integral equation method according to claim 1, characterized in that, The heat insulation material (2) is mullite, and the heat insulation plug is made of zirconium oxide.

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