Thermopile type heat flow sensor based on integral equation calibration method

Abstract

The invention provides a thermopile type heat flux sensor based on a calibration integral equation method. The thermopile type heat flux sensor is used for measuring the average heat flux density and the average temperature of the surface of an object through the calibration integral equation method. The sensor comprises a cylindrical thermal resistance layer, a thermal insulation material and a shell which are sequentially arranged from inside to outside. A thermopile is further arranged between the thermal resistance layer and the thermal insulation material, the thermopile 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 thermal insulation material. The device can measure the average heat flux density and the average temperature on the plane at the same time, and has the characteristics of high measurement accuracy, high sensitivity, simplicity in manufacturing, long-time measurement and the like.

Description

Technical Field

[0001] The present invention 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 Art

[0002] With technological advancements, improved energy efficiency, smarter equipment, and heightened environmental awareness, the demand for precise monitoring of heat flow and distribution is increasing. This is particularly true in the fields of industry, energy, and environmental monitoring, which place higher demands on real-time monitoring and optimization of heat flow. Heat flow sensors, as tools that accurately measure thermal energy flow and heat transfer, have garnered widespread attention and research in recent years.

[0003] The basic structure of currently produced thermopile temperature sensors is mostly to sputter a thin-film thermopile or thermistor onto a rigid and thermally insulating substrate such as a ceramic or silicon substrate. The hot end of the thermopile is then covered with a thermistor layer, and the cold end with an insulating material. The different covering materials create a temperature difference between the two ends of the thermopile, which is converted into a thermoelectric potential through the Seebeck effect. The temperature value is then compared with an initially calibrated thermoelectric potential vs. temperature plot. The temperature corresponds to the heat flux, enabling surface heat flux measurement. Compared to traditional heat flux sensors, thermopile sensors can detect even small changes in heat flux and temperature. However, improvements in sensor performance are limited by the development of the materials themselves, and the resulting thermopile sensors still suffer from low measurement accuracy and a narrow temperature measurement range. Currently, the most commonly used thermopile heat flux sensors often use platinum-platinum-rhodium thermopiles for heat flux measurement, which suffer from low sensitivity, high manufacturing costs, and difficulty in long-term measurements.

[0004] There are many methods to solve inverse problems, the most common ones are regularization method, conjugate gradient method, Bayesian method, reverse Monte Carlo method and so on.

[0005] The conjugate gradient method is a general iterative minimization method. The solution is defined as a linear combination of search directions. At each step, a new search vector is generated that is conjugate to all previous search directions. This ensures that an N-dimensional linear problem can be minimized in exactly N steps using exact algebra. This algorithm provides an exact solution h for the linear system in N steps, where N is the number of unknowns. For the inverse heat conduction problem, the conjugate gradient method continuously generates a forward value. By solving the forward problem, comparing the calculated value with the actual value, and repeatedly revising the forward value, the correct value for the inverse problem is obtained. This revision process is an iterative one. Each search vector is conjugate to the other. In theory, all solutions can be traversed, and the optimal solution can be gradually constructed to approximate the true solution, which can be solved in N steps. Therefore, to reduce computation time and achieve more accurate results, it is necessary to reduce the number of unknowns N. This requires precise measurement of sensor dimensions and thermophysical parameters. However, these parameters are not static and can change with temperature. Measurement errors cannot guarantee that the measured parameters match the true parameter data. These will bring errors and uncertainties to the final calculation results.

[0006] The Bayesian approach to solving inverse problems is a statistical inference method based on Bayesian theory. It combines prior knowledge with observed data to update probability estimates of unknown parameters. In the inverse heat conduction problem, the Bayesian method aims to infer the model parameters or distribution underlying the data using known observed data. The basic principle is as follows: To build a model, one must first establish a prior distribution for the model parameters and assume that the model parameters to be solved follow this distribution. Then, the observed data is used to update the estimates of the model parameters. The core of the Bayesian method lies in calculating the posterior distribution—the probability distribution of the model parameters given the observed data. The selection of the prior probability distribution is also crucial, as it embodies prior knowledge of the problem being solved and acts as a regularization parameter. Bayesian algorithms effectively integrate prior information with error information, reducing uncertainty in problem solving. However, the Bayesian method is heavily dependent on prior information. It requires setting a prior distribution, but the choice of the prior can be subjective. An inappropriate prior distribution can lead to biased results. In the absence of explicit prior knowledge, choosing a reasonable non-informative prior is a challenge. Bayesian methods are also computationally complex, often requiring complex integrals or summations. This computational complexity increases exponentially, especially in high-dimensional spaces. For small-sample problems, where data is minimal and prior knowledge is insufficient, inferences can be unreliable. For large-sample problems, computational complexity increases as the sample size increases.

[0007] Compared to the above two algorithms, the calibrated integral equation method offers unique advantages. First, it does not require measurements of sensor dimensions and thermophysical properties, significantly reducing errors introduced by measured data. Furthermore, the key to the calibrated integral equation method lies in finding the relationship between the calibration equation and the experimental equation. Therefore, it can handle correspondences between multiple images or multiple formulas, offering high flexibility and a broad range of potential applications. Furthermore, the calibrated integral equation method may be more efficient for certain types of integral problems because it directly optimizes the properties of the integral equation. In contrast, the conjugate gradient method, while offering rapid convergence when solving linear systems, may not perform as well as the calibrated integral equation method for nonlinear problems. Regarding the processing of prior information, while Bayesian methods can effectively integrate prior knowledge with observed data, the calibrated integral equation method can also incorporate prior information through appropriate regularization techniques, while avoiding the subjective prior selection issues inherent in Bayesian methods. Furthermore, the calibrated integral equation method does not require the calculation of the exact Hessian matrix, a significant advantage in terms of computational complexity, especially when dealing with large-scale problems.

[0008] The calibration integral equation method (CIEM) is an analytical approach based on mathematical physics principles. It predicts surface heat flux by constructing a mathematical relationship between surface heat flux and the temperature at the measuring point. Compared to traditional inverse problem solving methods, it does not involve solving the forward heat conduction problem and therefore does not require specific system parameter inputs. This avoids the prediction uncertainty introduced by these system parameters and makes the final results more consistent with the specific circumstances of the reconstructed experimental surface heat flux. Although CIEM has been successfully applied in various fields, there are currently no thermopile heat flux and temperature measurement sensors based on the CIEM algorithm, which limits its widespread use in practical applications. Summary of the Invention

[0009] In response to the problems of low temperature measurement range, insufficient measurement accuracy, and difficulty in long-term measurement in existing thermopile sensors, the present invention designs a thermopile heat flux sensor based on the calibration integral equation method, which can simultaneously measure the average heat flux density and average temperature on a plane. It has the characteristics of high measurement accuracy, high sensitivity, simple production, and the ability to measure for a long time.

[0010] To achieve the above object, the present invention provides the following technical solutions:

[0011] A thermopile-type heat flux sensor based on a 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 a measuring end and the other end being a tail end. The sensor comprises a cylindrical thermal resistance layer, a thermal insulation material, and a shell arranged in sequence from the inside out. A thermopile is also provided between the thermal resistance layer and the thermal insulation material. The thermopile 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 thermal insulation material.

[0012] Preferably, the thermopile is composed of three thermocouples connected in series, each thermocouple includes a first wire and a second wire, and one end of the first wire and the second wire of the same thermocouple are connected to form a hot end node; 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 end nodes.

[0013] Preferably, three holes are provided on the side of the measuring end of the thermal resistance layer, the three holes are located on the same circle, and the angle between two adjacent holes is 120°; the hot end nodes of the three thermocouples are in contact with the bottoms of the three holes respectively, and the remaining parts of the three holes are filled with adhesive, and the thermocouples and the thermal resistance layer are fixed by the adhesive.

[0014] Preferably, the adhesive includes a graphite adhesive (Graphi-Bond 669) glue and a high-temperature two-phase adhesive (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 to the thermocouple.

[0015] Preferably, the first wire of the first thermocouple is welded to the signal output wire to form a positive lead, the second wire of the third thermocouple is welded to the signal output wire to form a negative lead, and the positive lead and the negative 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 includes an insulating layer and a metal shell, the first wire and the second wire are respectively wrapped with insulating layers, and the insulating layers of the first wire and the second wire are together wrapped with the metal shell.

[0018] Preferably, a thermocouple is embedded in the tail end of the thermal resistance layer in the same way as the thermocouple in the thermopile, and is used to detect whether the temperature of the thermal resistance layer meets the insulation condition.

[0019] Preferably, the sensor's tail end is also equipped with a thermal insulation plug, consisting of a cylindrical and annular insulation plug, which cooperate to secure the thermal resistance layer, the insulation material, and the housing. The thermal insulation plug is also provided with a plurality of holes for leading out the positive and negative leads, as well as the wires of the tail-end thermocouple.

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

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

[0022] Compared to other heat flow sensors, the present invention, based on a calibration integral equation method, boasts high precision, long measurement time, high sensitivity, and a wide range of applications. The present invention can accurately measure the average temperature on a plane. By placing the hot end of the thermopile on a complete thermal resistance layer, boundary effects caused by regional divisions can be effectively avoided, significantly improving accuracy. Furthermore, by connecting thermocouples in series to form a thermopile for temperature measurement, it can more sensitively reflect small temperature changes, bringing the measured temperature closer to the average temperature of the plane. Adjusting the thickness of the thermal resistance layer allows for adjustment of the sensor's sensitivity.

[0023] The CIEM algorithm, based on this invention, avoids the limitations of one-dimensional heat transfer and more realistically reflects heat flow and temperature changes within a plane. Furthermore, the thermopile in this invention is embedded within a thermal resistance layer. Compared to conventional thin-film heat flow sensors, it maintains superior sensitivity and measurement performance in high-temperature and high-heat-flow environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 It is a front cross-sectional view of a thermopile type thermal flow sensor based on a calibration integral equation algorithm in an embodiment of the present invention.

[0025] Figure 2 Schematic diagram of the embedded hot end of the sensor thermopile in an embodiment of the present invention.

[0026] Figure 3 Schematic diagram of the cold end of the sensor thermopile in an embodiment of the present invention.

[0027] Figure 4 This is a diagram of the thermocouple configuration after fabrication in an embodiment of the present invention.

[0028] Figure 5 Dimensions of the thermal insulation plug provided in an embodiment of the present invention.

[0029] Figure 6 This is a flow chart of a method for measuring the average heat flux on an object surface 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 shell, 4 is the hot end node, 5 is the cold end node, 6 is the positive lead, 7 is the negative lead, 8 is the insulation layer, 9 is the metal shell, 10 is the annular thermal insulation plug, and 11 is the cylindrical thermal insulation plug. DETAILED DESCRIPTION

[0031] This paper, centered on the calibration integral equation method, designs a thermopile sensor based on the CIEM method. Without knowing the object's thermophysical properties, the CIEM algorithm can be used to invert the average heat flux and average temperature of the measured surface, simply by using the local average temperature obtained from a pre-embedded thermopile.

[0032] The technical solution of the present invention will be further described 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 a measuring end and the other end being a tail end. It includes a cylindrical thermal resistance layer 1, a thermal insulation material 2, and a shell 3 arranged in sequence 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 is composed of three thermocouples connected in series, each thermocouple includes a first and a second wire, and one end of the first wire and the second wire of the same thermocouple are connected to form a hot end node 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 end nodes 5.

[0035] The measuring end side of the thermal resistance layer 1 is provided with three holes. These holes are located on the same circle, with the angle between adjacent holes being 120°. The depth of each hole is half the radius of the thermal resistance layer 1. The hot end junctions 4 of the three thermocouples contact the bottoms of the three holes, respectively. The remaining portions of the three holes are filled with an adhesive, which secures the thermocouples to the thermal resistance layer 1. The adhesive comprises Graphi-Bond 669 and CERAMABOND 571. The Graphi-Bond 669 is poured into the holes of the thermal resistance layer 1, and the CERAMABOND 571 is applied to the surface of the Graphi-Bond 669 to bond with the thermocouples.

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

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

[0038] A thermocouple is also embedded in the tail end of the thermal resistance layer 1 in the same way as the thermocouple in the thermopile, and is used to detect whether the temperature of the thermal resistance layer 1 meets the insulation condition.

[0039] The tail end of the sensor is also provided with a heat-insulating plug, which is composed of a cylindrical heat-insulating plug (11) and an annular heat-insulating plug (10), which cooperate to fix the thermal resistance layer, the heat-insulating material and the shell; the heat-insulating plug is provided with a plurality of holes for leading out the positive lead 6 and the negative lead 7 as well as the wires of the tail end thermocouple.

[0040] The present invention first considers the problem of response sensitivity, and its sensitivity is related to the distance between the thermopile hot end node 4 and the thermal resistance layer measuring end plane. Therefore, it is foreseeable that the closer the distance is, the more sensitive the sensor is, and the more it can respond to tiny heat flux changes. However, considering the manufacturing process of the thermal resistance layer and the preparation problem of the thermopile, its thickness is not the thinner the better. Taking these two factors into consideration, the thermal resistance layer with a diameter of 3mm is selected, and its material is stainless steel. The distance between the thermopile hot end node position and the thermal resistance layer measuring end plane is set to 2mm.

[0041] The thermopile constructed in the present invention is composed of a series of thermocouples. The selected thermocouples should have characteristics such as fast response time and a wide temperature measurement range. Therefore, nickel-chromium-silicon and nickel-silicon-magnesium were selected as the two wires of the thermocouple, denoted as the first wire and the second wire, respectively. This is an N-type thermocouple.

[0042] Compared to the common K-type thermocouple, the N-type thermocouple successfully overcomes two drawbacks of the K-type thermocouple: unstable thermoelectromotive force between 300 and 500°C due to the short-range lattice order of the nickel-chromium alloy; and unstable thermoelectromotive force around 800°C due to preferential oxidation of the nickel-chromium alloy. The N-type thermocouple offers advantages such as good linearity, high thermoelectromotive force, high sensitivity, excellent stability and uniformity, strong oxidation resistance, low price, and immunity to short-range ordering.

[0043] Therefore, using nickel-chromium-silicon and nickel-silicon-magnesium as the primary materials for the thermopile can increase the temperature range of the sensor of the present invention. The sensor can still function effectively within the temperature range of 400 to 1300°C.

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

[0045] Considering the convenience and universality of thermocouple connection operation, the method of welding thermocouples is chosen to prepare the thermopile.

[0046] Taking into account the size of the thermal resistance layer and the length loss during welding, a thermocouple wire with a diameter of 0.1 mm was selected, and the length of nickel-chromium-silicon and nickel-silicon-magnesium was cut into 30 mm respectively.

[0047] Weld the first and second thermocouple wires together to form a spherical junction, or hot junction 4, with a diameter of approximately 0.5 mm to ensure good time response characteristics. Except for the junction, the thermocouple wires should be wrapped with insulation to ensure good insulation between the wires.

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

[0049] Extrusion is typically used to coat conductors with insulation. The extruder's output must be controlled to ensure uniformity and thickness. During the extrusion process, the insulating material is heated and melted, then squeezed through the extruder's die and tightly wrapped around the conductor.

[0050] However, the heat resistance of insulation materials is still insufficient. Polytetrafluoroethylene, the preferred material, can only be used for extended periods within a temperature range of -180 to 260°C. Therefore, a metal casing must be placed over the insulation layer, typically using an armoring process.

[0051] In order to facilitate the subsequent production of the thermopile, the two first and second wires, which have been wrapped with an insulation layer, are placed together in a metal shell. The metal shell is preferably made of a cobalt-based alloy material, whose operating temperature can reach 1200°C. It has the characteristics of high temperature resistance, strong corrosion resistance, good stability and good ductility.

[0052] The outer metal casing, inner insulation, and conductors are then placed in an air-heated furnace and heated to 750°C to 1500°C over 30 minutes. The heated material is then quickly placed in a hot rolling mill for rapid rolling. The speed of placement should ensure the outer metal casing temperature does not drop below 750°C. The rolling process should be completed within 1 minute. After rolling, the material is cooled in air or slowly while holding the material.

[0053] like Figure 4 FIG. 1 shows the completed thermocouple configuration, which includes a first wire A, a second wire B, an insulating layer 8 and a metal shell 9 .

[0054] The thermopile is installed inside the sensor and is realized by punching a hole and inserting a thermocouple. Figure 2 As shown, holes are placed in the thermal resistor layer 1 at appropriate spacing. The holes are distributed on a circle with a diameter of 0.75 mm, with an angle of 120° between each two holes. This effectively reflects the average temperature within the area while not excessively disrupting the heat conduction process within the thermal resistor layer. The hole diameter is selected to be approximately 0.8 mm, not too small to prevent contact between the wires at the rear end of the hot end node and the thermal resistor layer. The bottom surface of the hole should be tangent to the circle containing the hot end node of the thermopile, and the depth of each hole should be strictly equal, 0.75 mm.

[0055] The hot end of the thermocouple is buried in the hole, ensuring that it is completely in contact with the bottom of the hole, and then glue is poured to completely fix the thermocouple and the thermal resistance layer. The end point buried in the thermal resistance layer serves as the hot end of the thermopile.

[0056] The preferred adhesive is Graphi-Bond 669, which offers excellent thermal stability and chemical resistance, allowing it to withstand long-term use in harsh, high-temperature environments without degradation. It also exhibits excellent electrical and thermal conductivity, ensuring consistent electrical and thermal performance at high temperatures. This effectively prevents the impact of perforations on heat flow within the thermal resistance layer.

[0057] However, Graphi-Bond 669 lacks viscosity and may cause loosening during use. Therefore, CERAMABOND 571 is also recommended. Its strong adhesiveness, with a viscosity between 20,000 and 90,000 cP, effectively prevents thermopiles from loosening due to shock and vibration. It is commonly used for assembling and insulating ceramic and metal components in high-temperature equipment, meeting the bonding and filling requirements of the present invention at higher temperatures. Furthermore, because this glue is applied to the surface of the thermal resistance layer, its low thermal conductivity does not significantly affect heat transfer within the thermal resistance layer.

[0058] Before applying the adhesive, CERAMABOND 571 requires preparation. CERAMABOND 571 is a mixture of powder and liquid adhesive. To use, mix the powder and liquid in a 1.5:1 ratio (by weight). Slowly add the powder to the liquid while stirring gently with a low-speed agitator. Mix thoroughly and slowly to ensure the powder is completely wetted and free of lumps, achieving a uniform color, and avoiding the incorporation of air that could cause bubbles. If the viscosity of the mixture needs to be adjusted, add an appropriate amount of diluent (such as 571-T), up to 20% by weight. The thoroughly mixed material should form a homogeneous paste with no separation or delamination, similar to liquid cement. The mixed adhesive should be used promptly to prevent premature curing. Best results are typically achieved within 1 to 4 hours of mixing.

[0059] The following describes the specific gluing process. First, inject Graphi-Bond 669 into the hole. Given the slender structure of the hole, this is done using a syringe. Insert the needle of the syringe into the hole and slowly inject until the glue overflows. Wipe away any residual glue from the surface. Then insert the hot end of the thermopile into the hole, ensuring full contact with the bottom surface. Wait for the adhesive to fully cure, which usually takes about a day. Apply CERAMABOND 571 to the hole surface to fully secure the thermocouple, which usually takes a day.

[0060] After completing the above steps, each thermocouple will have two wires, A and B, extending from it. 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 junctions, or cold junctions 5, which serve as the cold ends of the thermopile. This completes the series connection of the thermocouples, and the measured temperature fully reflects the average temperature of the two-dimensional region in which they are located.

[0061] To ensure that the thermal resistance layer is strictly insulated, a thermocouple is added near the end of the thermal resistance layer to detect whether the temperature at that location meets the insulation conditions. The thermocouple is embedded in the same way as the thermopile.

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

[0063] The thermal insulation material is mullite, and the thermal insulation plug is zirconia. The thermal insulation plug is composed of a ring with an inner diameter of 3 mm, an outer diameter of 5 mm, and a length of 1 mm and a cylinder with a diameter of 5 mm and a length of 1 mm.

[0064] Mullite is a high-quality refractory material characterized by high temperature resistance, high strength, and low thermal conductivity. It also exhibits excellent high-temperature stability and thermal shock resistance, making it widely used in heat-resistant materials such as crucibles, protective tubes, and thermocouple tubes. As the primary thermal insulation material for sensors, mullite effectively insulates the surrounding thermal resistance layer. Furthermore, its fibrous nature allows for compaction and complete integration with the cold end, ensuring thermal insulation. Compared to thermal insulation materials with fixed shapes, the use of fibrous mullite significantly reduces the impact of machining precision. The cold end and thermal resistance layer maintain full contact with the insulation material, ensuring strict thermal insulation, a prerequisite for the subsequent operation of the CIEM algorithm.

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

[0066] The shell 3 is made of stainless steel, and its cylindrical inner diameter is 5 mm and its thickness is 0.5 mm.

[0067] Place the annular insulation plug, the metal cylinder of the thermal resistance layer (with the thermopile already embedded), and the stainless steel shell in that order, and fill them with mullite fiber. It's best to compact the material after partially filling it to avoid voids that could compromise the insulation and damage the thermopile structure caused by compaction. Once fully filled, cover the back with a cylindrical insulation plug. This completes the insulation. The signal leads pass through the insulation material and emerge from the circular hole in the cylindrical insulation plug. The thermopile cold end is placed within the insulation.

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

[0069] The CIEM algorithm on which the sensor of the present invention is based needs to be completed under adiabatic conditions, so it is very necessary to monitor the adiabatic conditions to ensure that the sensor is in a normal working state.

[0070] Add a thermocouple near the end of the thermal resistance layer to detect the temperature at this location .

[0071] Defining excess temperature ,in

[0072]

[0073] in, For the instantaneous temperature here, This is the initial temperature here.

[0074] When the temperature of the thermopile plane has reached a high level, < 10 ℃. At this point, the entire thermal resistance layer has fully transferred heat, but the back surface still maintains a relatively low temperature. When it is below 5 ℃, it can be considered to meet the insulation conditions.

[0075] But when the temperature of the plane where the thermopile is located is not high, The condition of less than 10°C may still be met. At this point, the temperature difference between the two is not much, and the back surface may transfer heat to the plane where the thermopile is located, which will affect the final result. Therefore, we can conclude that the adiabatic condition is not met at this time.

[0076] Before using the CIEM algorithm to solve the surface average heat flux, calibration must be performed first.

[0077] According to the derivation of the CIEM algorithm, the ratio of the average heat flux after Laplace transformation to the average residual temperature is a constant, so calibration is required.

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

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

[0080]

[0081] in, is the temperature of the thermocouple hot end, is the cold junction temperature of the thermocouple, and the unit is K (the same below).

[0082] The sensor of the present invention forms a thermopile by connecting three thermocouples in series. The potential difference collected by the sensor is related to

[0083]

[0084] So we can get the relationship between the average temperature and the potential difference

[0085]

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

[0087] During this process, because the cold end is in adiabatic 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 average temperature of the sensor surface is obtained by calibration.

[0091] When the external environment applies heat to the sensor, it is transferred through the thermal resistance layer to the hot junction of the thermopile. Since the cold junction is enclosed in the insulation material, it can be assumed to be at a constant temperature. Due to the Seebeck effect, a corresponding potential difference is generated across the thermopile. By processing this potential difference, the average residual temperature of the surface over time can be calculated.

[0092] After the data is collected and connected to the computer, the average heat flow and average temperature of the object surface can be inverted through the CIEM algorithm built into the program.

[0093] The following is the derivation of the CIEM algorithm in three dimensions.

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

[0095]

[0096] The boundary conditions are

[0097]

[0098] remember

[0099]

[0100]

[0101] have to

[0102]

[0103] Will Substitute into In, get

[0104]

[0105] exist Considering boundary conditions ,have

[0106]

[0107]

[0108]

[0109]

[0110] Bring in In, get

[0111]

[0112] make

[0113]

[0114] Substitution ,have to

[0115]

[0116] in

[0117]

[0118]

[0119] Perform Laplace transform to get

[0120]

[0121] Will Substitute, and we get

[0122]

[0123] On the left

[0124]

[0125] Combined and, there is

[0126]

[0127] Its analytical solution is

[0128]

[0129] Substitute it into the solution and we get

[0130]

[0131] Substituting into , we get

[0132]

[0133] Also because

[0134]

[0135] Performing Laplace transform, we get

[0136]

[0137] Comprehensive comparison and

[0138]

[0139] Among them, L and W are the dimensions of the thermal resistance layer in the x and y directions, H is the dimension of the thermal resistance layer in the z direction (the axis direction of the thermal resistance layer), w is the position of the thermopile in the z direction of the thermal resistance layer, α is the thermal diffusion coefficient of the thermal resistance layer, and k is the thermal conductivity of the thermal resistance layer. When the sensor is completed, W, L, k, α, H, and w remain unchanged, so it can be known that

[0140]

[0141] Under the condition of ensuring the above conditions remain unchanged, there is an identity under different heat flow conditions

[0142]

[0143] Among them, subscript c represents the calibration group data, and subscript r represents the experimental group data.

[0144] Where, 、 、 Known, we can calculate it by the identity .

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

[0146] First, the heat flux sensor of the present invention needs to be calibrated. Select the "Calibration Group" module in the software and click "Start Measurement". Apply a uniform heat flux that changes with time vertically to the surface of the sensor (if the purpose of the experiment is to measure temperature, change the surface temperature of the sensor to obtain a temperature change curve over time). Through the data collected by the sensor, the average thermal residual temperature curve of the thermopile position that changes with time can be obtained. Import the data and curve of the heat flux applied on the sensor surface into the software. Click "Start Calculation", the software will automatically fit the above two curves to obtain the formula for the average heat flux and average thermal residual temperature changing with time, and obtain the calibration group data.

[0147] To obtain further experimental data, place the sensor's measuring end (i.e., the exposed side of the thermal resistance layer) close to the surface of the object to be measured.

[0148] Furthermore, due to the sensor's small size, a push-in method can be used for even more accurate results. A 6.5mm diameter and approximately 5mm deep hole is created on the surface of the object, and the sensor is inserted. When it reaches its limit of penetration, the sensor is in close contact with the object. A mark 5mm above the sensor can be placed beforehand to determine if the sensor has fully penetrated the object. To ensure close contact between the sensor and the object, secure it with adhesive or other means. If the sensor remains stable in the object even after applying light force, it is securely fixed.

[0149] Then, connect the positive and negative leads of the sensor to the computer. Select the "Experimental Group" module in the software and click "Start Measurement". The system will automatically record the residual temperature θ of the thermopile during this period. t , until you click "Stop Measuring".

[0150] Furthermore, the object is subjected to a heating treatment.

[0151] Furthermore, the average residual heat temperature θ1 at the location of the thermopile and the residual heat temperature θ2 at the back surface of the sensor are compared to determine whether the sensor is working properly.

[0152] Furthermore, 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 and the difference between θ1 and θ2 is not large, the sensor cannot be used.

[0153] Furthermore, after the measurement is completed, the software in the calculator processes the potential difference obtained by the sensor to obtain a curve showing the average residual temperature changing over time. The curve is then fitted to obtain a formula showing the average residual temperature changing over time.

[0154] Further, click "Start Calculation", and the software in the calculator will combine the formula for the average residual heat temperature and surface heat flux of the calibration group with the time variation formula of the experimental group data. By solving the calibration integral equation, the formula for the average surface heat flux of the experimental group with time is obtained, and the corresponding curve is drawn at the same time.

[0155] The above specific embodiments are used to illustrate the present invention rather than to limit the present invention. Any modifications and changes made to the present invention within the spirit of the present invention and the protection scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A thermopile type heat flow sensor based on the 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, one end of which is a measuring end and the other end is a tail end; it comprises a cylindrical thermal resistance layer (1), a thermal insulation material (2) and a shell (3) arranged in sequence from the inside out; a thermopile is further provided between the thermal resistance layer (1) and the thermal insulation material (2), the thermopile comprising 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).

2. The thermopile type heat flow sensor based on the calibration integral equation method according to claim 1, characterized in that: The thermopile is composed of three thermocouples connected in series, each thermocouple including 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 end node (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 end nodes (5).

3. The thermopile type heat flow sensor based on the calibration integral equation method according to claim 2, characterized in that: The measuring end side of the thermal resistance layer (1) is provided with three holes, the three holes are located on the same circle, and the angle between two adjacent holes is 120°; the hot end nodes (4) of the three thermocouples are in contact with the bottoms of the three holes respectively, and the remaining parts of the three holes are filled with adhesive, and the thermocouples and the thermal resistance layer (1) are fixed by the adhesive.

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

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

6. The thermopile type heat flow sensor based on the 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. The thermopile type heat flow sensor based on the calibration integral equation method according to claim 2, characterized in that: The thermocouple further comprises an insulating layer (8) and a metal shell (9), the first wire and the second wire are respectively wrapped with the insulating layer (8), and the insulating layers of the first wire and the second wire are together wrapped with the metal shell (9).

8. The thermopile type heat flow sensor based on the calibration integral equation method according to claim 2, characterized in that: A thermocouple is also embedded in the tail end of the thermal resistance layer (1), in the same way as the thermocouple in the thermopile, and is used to detect whether the temperature of the thermal resistance layer (1) meets the insulation condition.

9. The thermopile type heat flow sensor based on the calibration integral equation method according to claim 1, characterized in that: The tail end of the sensor is also provided with a heat-insulating plug, which is composed of a cylindrical heat-insulating plug (11) and an annular heat-insulating plug (10), which cooperate to fix the thermal resistance layer, the heat-insulating material and the shell; the heat-insulating plug is also provided with a plurality of holes for leading out the positive lead (6) and the negative lead (7) as well as the wires of the tail end thermocouple.

10. The thermopile type heat flow sensor based on the calibration integral equation method according to claim 1, characterized in that: The thermal insulation material (2) is mullite, and the thermal insulation plug is made of zirconium oxide.

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