Small-sized long-term measurement heat flux sensor and measurement method suitable for two inverse problem algorithms

Abstract

The present invention provides a small, long-term heat flow sensor and measurement method suitable for two inverse problem algorithms, used to measure heat flow using a calibrated integral equation method and a spatial propulsion method. The sensor comprises a housing, a thermal insulation material, a thermally conductive material, a first thermocouple, and a second thermocouple. The housing is a cylindrical structure with one end open, and a coaxial cylindrical thermally conductive material is provided inside the housing. The first and second thermocouples are provided between the thermally conductive material and the housing, and the collection ends of the first and second thermocouples are embedded in the thermally conductive material. The other area between the thermally conductive material and the housing is filled with thermal insulation material. The sensor of the present invention has a compact structure and small size, and can be embedded within a material for measurement. At the same time, the sensor has high accuracy and stability, and can accurately output the predicted solution of the measurement point in both short-term and long-term measurements, thus having a wide range of applications and practicality.

Description

Technical Field

[0001] The present invention belongs to the field of thermal measurement, relates to a heat flow sensor, and in particular to a small-sized long-time measurement heat flow sensor and a measurement method suitable for two inverse problem algorithms. Background Art

[0002] With the development of society and technological advancement, a large number of unresolved heat transfer problems have emerged in fields such as industrial and agricultural production, scientific research, aerospace, and energy and power. Heat flux is a core parameter describing the heat transfer process. Accurately measuring and evaluating the heat flux distribution in the system under test can provide critical thermal information for heat transfer problems, which is of great significance for optimizing thermal protection design and improving system performance. The increasing demand for heat flux data places higher demands on the functionality of heat flux sensors.

[0003] The inverse problem of heat conduction is a type of problem that studies the inverse prediction of surface heat flux. It refers to special situations when the heated outer surface is in an extremely high temperature environment. Because the sensors arranged on the outer surface will not work or be burned through, or it is difficult to install sensors in a small space, the sensors can only be buried inside the material, and the heat flux and temperature of the outer surface can be obtained by inverting the internal temperature measurement data. At present, there are many calibration methods and numerical methods for solving the inverse problem of heat conduction, such as the conjugate gradient method, the Bayesian method, the reverse Monte Carlo method, the calibrated integral equation method, the spatial marching method, etc. Gradient algorithms have many steps, a large amount of calculation, and a long time to solve. In addition, a small deviation in the calculation process may lead to large discrepancies in the results. The Bayesian method also requires a large amount of calculation and is very dependent on prior information. In the case of insufficient prior information, the deduction results will have large errors.

[0004] The calibration integral equation method (CIEM) and the space marching method (SMM) are two commonly used methods for solving inverse heat conduction problems. Unlike these two methods, which suffer from long iteration times and significant limitations, CIEM and SMM both rapidly and accurately predict the temperature and heat flux of the measured surface based on data from internal points, without requiring repeated iterations. CIEM does not rely on system parameters such as the experimental material's thermophysical properties, the thermocouple's internal position, and the dynamic response time, eliminating the need for repeated iterations to obtain the optimal solution. Instead, CIEM uses pre-established calibration experiments to predict the heat flux density or temperature of the reconstructed experimental surface, rapidly providing an accurate prediction. SMM, on the other hand, eliminates the need for calibration experiments and directly inverts the heat flux and temperature of the measured surface, regardless of whether the thermophysical parameters are linear or not, without requiring repeated iterations. Currently, CIEM and SMM have successfully solved various types of inverse heat conduction problems. However, there is currently no heat flow sensor that is compatible with the CIEM and SMM algorithms, which limits the practical application scope of these two inverse problem algorithms.

[0005] Among the various types of heat flow sensors currently studied, coaxial thermocouples, circular foil heat flow sensors, Schmidt-Boelter heat flow sensors, and thermopile heat flow sensors are relatively common. The advantage of coaxial thermocouples is that they can perform point measurements and internal measurements. However, their main disadvantage is that they cannot achieve long-term continuous heat measurement. Circular foil heat flow sensors require external water cooling equipment when operating in high-temperature environments. These sensors are large, complex to install, and significantly interfere with the thermal environment, thus limiting their use. Schmidt-Boelter heat flow sensors offer high output, good linearity, and a wide dynamic range, but they have a long response time to rapidly changing heat fluxes. Thermopile heat flow sensors offer advantages such as a wide measurement range, good stability, and high accuracy, and are widely used to measure heat flux density in harsh, high-temperature environments. However, their processing is complex and their cost is high. In summary, currently commonly used heat flow sensors generally suffer from large size, long response time, inability to measure over a long period of time, and high cost.

[0006] In order to solve the shortcomings of the above-mentioned heat flux sensor in measuring heat flux density, the present invention designs a heat flux sensor based on CIEM and SMM algorithms, which can be embedded in the material to be measured and can accurately measure the heat flux density at the measuring point for a long period of time. Summary of the Invention

[0007] To address the problems of existing heat flux sensors, which are large in size, unable to measure internal points, and most unable to meet the requirements of high precision, low cost, and long-term measurement, the present invention proposes a small, long-term measurement heat flux sensor and measurement method suitable for two inverse problem algorithms. Based on CIEM and SMM, the present invention designs a small, built-in sensor capable of measuring heat flux density and temperature over long periods of time. The sensor has a compact structure and small size, allowing it to be embedded within materials for measurement. Furthermore, thanks to the advantages of CIEM and SMM, the sensor has high accuracy and stability, and can quickly output accurate prediction solutions for measurement points in both short-term and long-term measurements, thus having a wide range of applications and practicality.

[0008] The technical solution adopted in the present invention is as follows:

[0009] A small-scale long-time measurement heat flow sensor suitable for two inverse problem algorithms, the sensor comprising a shell, a thermal insulation material, a thermal conductive material, a first thermocouple and a second thermocouple; the shell is a cylindrical structure with one end open, a coaxial cylindrical thermal conductive material is provided inside the shell, the first thermocouple and the second thermocouple are provided between the thermal conductive material and the shell, and the collection ends of the first thermocouple and the second thermocouple are embedded in the thermal conductive material, and the other area between the thermal conductive material and the shell is filled with thermal insulation material.

[0010] Furthermore, the first thermocouple and the second thermocouple are exposed-type thermocouples.

[0011] Furthermore, a first measuring point and a second measuring point are provided on the central axis inside the thermal conductive material, and a first hole and a second hole are radially provided at the first measuring point and the second measuring point respectively, and the collecting ends of the first thermocouple and the second thermocouple are embedded in the first hole and the second hole respectively.

[0012] Furthermore, the collecting ends of the first thermocouple and the second thermocouple are both wrapped with a silicone grease layer and fixed in the first hole and the second hole respectively by an adhesive. The adhesive includes a high-temperature thermally conductive adhesive (Graphi-Bond 669 glue) and a high-viscosity two-phase adhesive (CERAMABOND 571 adhesive). The high-temperature thermally conductive adhesive is poured into the first hole and the second hole, and the high-viscosity two-phase adhesive is coated on the surface of the high-temperature thermally conductive adhesive to reinforce the first thermocouple and the second thermocouple.

[0013] Furthermore, the thermal conductive material includes a measuring end and a tail end, the measuring end is aligned with the open end of the shell, and the tail end is aligned with the sealed end of the shell; the distance between the first measuring point and the measuring end is 10~20 mm; the distance between the second measuring point and the measuring end is 40~45 mm.

[0014] Furthermore, the diameter of the thermal conductive material is 2.5-4 mm, and the length is 45-55 mm; the thickness of the thermal insulation material is 1-1.25 mm; the outer diameter of the shell is 5-7 mm, the thickness is 0.5-0.7 mm, and the length is 45-55 mm.

[0015] Furthermore, two openings are provided on the bottom surface of the sealed end of the shell, and the leads of the first thermocouple and the second thermocouple are led along the axial direction between the heat-conducting material and the shell to the tail end of the heat-conducting material, and are respectively led to the outside of the shell through the two openings.

[0016] Furthermore, the heat insulating material is mullite to ensure that one-dimensional heat conduction occurs in the heat conducting material 3 during the measurement process. The heat conducting material 3 is stainless steel.

[0017] Furthermore, when the temperature of the measured point is below 600°C, the sensor is suitable for the calibration integral equation method; when the temperature of the measured object point is 600°C and above, the sensor is suitable for the space propulsion method.

[0018] A heat flow measurement method based on two inverse problem algorithms, implemented using the above-mentioned sensor, includes the following steps:

[0019] The sensor is connected to a data acquisition board to acquire temperature data; the data acquisition board is connected to a computer to transmit the temperature data to the computer; the computer has a built-in calibration integral equation algorithm and a space propulsion algorithm;

[0020] The algorithm to be used is selected based on the temperature data of the measured point. When the temperature is below 600°C, the calibration integral equation algorithm is selected; when the temperature is above 600°C, the space advancement algorithm is selected.

[0021] After post-processing the temperature data using the selected algorithm, the predicted values ​​of the temperature and heat flux at the measuring point are output and an image is generated.

[0022] Compared with the prior art, the present invention has the following beneficial effects:

[0023] (1) Compared with coaxial thermocouples, thanks to the accuracy and stability of CIEM and SMM algorithms, the present invention can realize heat flow measurement over a long period of time, making up for the defect that the former is only suitable for short-term measurement and has a wider range of application scenarios.

[0024] (2) Compared with circular foil heat flux meters and other sensors with complex and large structures, the present invention has the advantages of a slender diameter and a small size. It can drill a hole to allow the probe to penetrate deep into the object to be measured, thereby achieving heat flow data measurement at internal points while maintaining the accuracy of the measurement within the error range. This is more in line with the application characteristics and practical requirements in industrial production.

[0025] (3) Compared with the conjugate gradient method, Bayesian method and other heat conduction inverse problem solving methods, CIEM and SMM algorithms do not require repeated iterations, have smaller computational complexity, and are faster to solve, which is more than ten times faster than other inverse problem algorithms. Moreover, unlike the Bayesian method which requires a large amount of prior information, CIEM and SMM algorithms have fewer dependent conditions. CIEM algorithm only requires the temperature of two measuring points and calibration experimental data, while SMM only requires the temperature of two measuring points, the thermophysical parameters of the main material and the embedded position of the thermocouple, which is very flexible and lightweight. In addition, CIEM has high accuracy in predicting solutions under linear conditions and is very fast to solve, while SMM can invert a more accurate prediction solution regardless of whether the thermophysical parameters are linear or not, but is slightly slower to solve. The combination of the two can obtain accurate solutions more quickly over a wider temperature range.

[0026] (4) The present invention can not only measure heat flow, but also obtain temperature data of the measured location at the same time.

[0027] (5) The present invention can conveniently transmit and interact with a computer. The temperature data of the thermocouple can be directly connected to the computer through the lead. After algorithm processing, the specific data and change curve of the heat flow and temperature of the measured point during the measurement time period can be displayed on the computer, which is convenient for subsequent digital processing of experimental measurements.

[0028] (6) Thanks to the advantages of CIEM and SMM, the heat flow sensor of the present invention does not require a complex and precise structure, has a simple structure, low cost, a wide range of applications, and is suitable for mass production. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Schematic diagram of the cross-sectional structure of the heat flow sensor in an embodiment of the present invention.

[0030] Figure 2 3D schematic diagram of the thermal flow sensor from the rear end perspective in an embodiment of the present invention.

[0031] Figure 3 It is a front view of the measuring end of the heat flow sensor in an embodiment of the present invention.

[0032] Figure 4 This is a partial enlarged view of the temperature measuring point of the thermocouple of the heat flow sensor in an embodiment of the present invention.

[0033] Figure 5This is a flow chart of the use of the heat flow sensor in an embodiment of the present invention.

[0034] Figure 6 is the surface heat flux inverted by the CIEM algorithm in the embodiment of the present invention 's effect diagram.

[0035] Figure 7 is the surface heat flux inverted by the SMM algorithm in the embodiment of the present invention 's effect diagram.

[0036] Figure 8 is the surface temperature inverted by the SMM algorithm in the embodiment of the present invention 's effect diagram.

[0037] Figure 9 These are the parameters used in the SMM algorithm inversion in the embodiment of the present invention.

[0038] Among them, 1 is the shell, 2 is the thermal insulation material, 3 is the thermal conductive material, 4 is the first thermocouple, 5 is the second thermocouple, ① is the first measuring point, and ② is the second measuring point. DETAILED DESCRIPTION

[0039] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific examples.

[0040] Example

[0041] like Figures 1-4 As shown, Figure 1 Schematic diagram of the cross-sectional structure of the heat flow sensor in this embodiment; Figure 2 This is a three-dimensional schematic diagram of the heat flow sensor from the rear end perspective in this embodiment; Figure 3 This is a front view of the measuring end of the heat flow sensor in the embodiment; Figure 4 This is a partial enlarged view of the thermocouple temperature measurement point of the heat flow sensor in this embodiment. This invention, based on CIEM and SMM, provides a small, long-term measurement heat flow sensor based on two algorithms. This sensor can be used in applications requiring accurate measurement of heat flux density or temperature at points within an object over long periods of time and display of their continuous changes. The sensor is cylindrical in shape and comprises five components: a housing 1, thermal insulation material 2, thermally conductive material 3, a first thermocouple 4, and a second thermocouple 5.

[0042] The housing 1 is a cylindrical structure with one end open. A coaxial cylindrical heat-conducting material 3 is provided inside the housing 1. A first thermocouple 4 and a second thermocouple 5 are provided between the heat-conducting material 3 and the housing 1. The heat-collecting ends of the first and second thermocouples 4 and 5 are embedded in the heat-conducting material 3. The remaining area between the heat-conducting material 3 and the housing 1 is filled with a heat-insulating material 2. The first and second thermocouples 4 and 5 are exposed-type thermocouples.

[0043] The thermally conductive material 3 is provided with a first and a second measuring point on its inner central axis. The thermally conductive material 3 is provided with a first and a second radial hole at the first and second measuring points, respectively. The tips of the temperature-measuring lotus root wires of the first and second thermocouples 4 and 5 are respectively embedded in the first and second holes. An adhesive layer is provided in each of the first and second holes. The tips of the temperature-measuring lotus root wires of the first and second thermocouples 4 and 5 are each coated with a silicone grease layer embedded in the adhesive layer. The tops of the temperature-measuring lotus root wires are in contact with the bottoms of the holes. A highly viscous two-phase adhesive is applied to the tops of the first and second holes to reinforce the first and second thermocouples 4 and 5.

[0044] The first temperature measurement point can be set within the range of 10~20 mm from the measuring end. The purpose is to be relatively close to the measuring end, which can reflect the heat flow and temperature properties of the measuring end to a greater extent and improve the accuracy of the algorithm inversion. It cannot be too close to the measuring end, otherwise the temperature will be too high and the thermocouple will be at risk of burning out. It cannot be too far from the measuring end, otherwise the volume of the heat flow sensor will increase, which is not conducive to internal measurement; the second temperature measurement point can be set within the range of 40~45 mm. The purpose is to increase the distance from the first temperature measurement point as much as possible to allow the heat conduction process to proceed more fully, so as to obtain a greater degree of differentiation between the two sets of temperature data, which is conducive to improving the accuracy of the algorithm inversion. It cannot be too close to the measuring end, otherwise the distance from the first temperature measurement point cannot be increased, the temperature data differentiation is small, and the error is large. It cannot be too far from the measuring end, otherwise the volume of the heat flow sensor will increase, which is not conducive to internal measurement.

[0045] The diameter of the thermal conductive material 3 ranges from 2.5 to 4 mm. A diameter that is too small is not conducive to processing and assembly with the thermocouple. A diameter that is too large will cause the overall volume of the heat flow sensor to be too large, and the object itself will be greatly damaged when opening a hole for internal measurement, affecting the user experience. The length range is 45 to 55 mm. A length that is too small is not conducive to the setting of the two temperature measurement points, and it is difficult to increase the distance to produce temperature differentiation, resulting in a large error. A length that is too long will waste materials and increase the volume of the heat flow sensor, which is not conducive to internal measurement.

[0046] Regarding the choice of CIEM or SMM algorithm, when the measured surface temperature is below 600°C, the thermal properties of the thermal conductive material change linearly with temperature. In this case, the CIEM algorithm should be used to reduce reliance on the uncertain thermal properties and improve measurement accuracy. When the measured surface temperature is 600°C or above, the thermal properties of the thermal conductive material begin to change nonlinearly with temperature. The CIEM algorithm has poor inversion effect under nonlinear conditions, and the SMM algorithm can obtain a more accurate prediction solution.

[0047] Furthermore, the algorithms used in the present invention are all based on a one-dimensional heat transfer model. The thermal conductive material 3 needs to be well insulated. Therefore, the thermal insulation material 2 uses HM1800 mullite insulation material, which has excellent thermal insulation properties but is prone to dust generation after forming. Therefore, a cylindrical shell 1 is designed. The shell 1 is made of stainless steel, which has good strength, hardness, and corrosion resistance. The thermal conductive material 3 is also made of stainless steel. Due to its excellent thermal conductivity, this material can quickly reflect the heat flow through temperature changes. At the same time, its thermal resistance is moderate, which will not make the temperature difference between the two measurement points too small, thereby avoiding large errors when the algorithm inverse predicts the measured surface temperature. The first thermocouple 4 and the second thermocouple 5 used need to meet the following characteristics simultaneously: a wide temperature measurement range, a fast response time, and a small volume structure. Based on these requirements, the basic specification can be selected from the SCAXL-020E-6 exposed thermocouple.

[0048] In this embodiment, the cylindrical stainless steel housing 1 has an outer diameter of 6 mm, a thickness of 0.5 mm, and a length of 50 mm. The thermal conductive material 3 has a diameter of 3 mm and a length of approximately 50 mm, with one end serving as the measuring end and the other as the tail end. Two temperature measurement points, namely the first and second measuring points, are provided on the central axis of the thermal conductive material 3. Two radial holes are provided at each of the two temperature measurement points, with the first measuring point 15 mm from the measuring end and the second measuring point 40 mm from the measuring end. The holes have a diameter of approximately 0.5 mm and a depth of 1.5 mm. This ensures that the temperature measurement point of the thermocouple is located along the axis of the thermal conductive material, making it more consistent with one-dimensional heat transfer.

[0049] The tips of the first thermocouple 4 and the second thermocouple 5 temperature measuring wires are respectively embedded in the two holes of the thermal conductive material 3. The specific embedding and fixing operation is as follows: First, use a syringe to inject high-temperature thermal conductive adhesive Graphi-Bond 669 with good thermal conductivity into the hole. After the needle touches the bottom, push the piston to inject the adhesive while moving the needle upward until it begins to overflow from the hole to ensure that the hole is completely filled with adhesive and no air remains. After removing the part of the glue that overflows the hole, wrap the tip of the thermocouple temperature measuring wire with a layer of silicone grease, and then insert the tip of the thermocouple temperature measuring wire into the hole to ensure that it is completely in contact with the bottom surface. Wait for more than ten minutes for the filling adhesive layer to solidify, and then cover the hole on the surface of the thermal conductive material 3 with a layer of high-viscosity two-phase adhesive CERAMABOND 571. Let it stand for about a day to ensure that the thermocouples are completely fixed at the first measuring point ① and the second measuring point ②. After securing the tips of the temperature-measuring wires of the first and second thermocouples 4 and 5 to the thermally conductive material 3, the thermally conductive material 3 is placed in a cylindrical stainless steel housing 1. The ends of the thermally conductive material 3 are aligned with the ends of the housing 1, and the thermally conductive material 3 and the housing 1 are coaxially arranged. The leads of the first and second thermocouples 4 and 5 are guided axially to the tail ends of the thermally conductive material 3 between the thermally conductive material 3 and the stainless steel housing 1. The bottom surface of the housing 1 has two openings, through which the leads of the first and second thermocouples 4 and 5 are led to the outside. The thermally conductive material 3 and the stainless steel housing 1 are then secured together by welding or other integrated processing. After the above installation is completed, the gap between the thermally conductive material 3 and the stainless steel housing 1 is filled with powdered HM1800 mullite insulation material 2 and compacted. The leads of the first and second thermocouples 4 and 5 are encased in the HM1800 mullite powder.

[0050] The advantages of using exposed thermocouples in the present invention are:

[0051] Currently, commonly used thermocouples can be divided into three types according to their structural form: exposed type, grounded type and embedded type, each with its own characteristics and applicable scenarios.

[0052] The exposed end of the thermocouple is directly exposed to the environment being measured, allowing it to quickly sense temperature changes. It has excellent response characteristics for rapidly changing temperature measurements and can react quickly to subtle temperature changes. It is suitable for applications requiring rapid responsiveness, such as engine testing. Compared to other types of thermocouples, it has a simpler structure, does not require complex insulation or grounding designs, and is relatively low in cost.

[0053] The measuring end of the grounded thermocouple is directly welded to the front end of the sheath, so the heat transfer is relatively direct. The response speed is slower than that of the exposed thermocouple, but faster than that of the insulated thermocouple. It can quickly reflect temperature changes. The structure is relatively simple and the grounding performance is good. Although grounding can reduce some electrical interference, its anti-interference ability is still relatively weak in environments with strong electromagnetic interference or electrical noise, which may affect the measurement accuracy. Its application range is limited and the maintenance requirements are high.

[0054] There is a layer of insulating material between the two measuring ends of the insulated thermocouple, which electrically isolates the measuring part from the measured temperature environment. It can effectively reduce the electrical interference between the measuring end and the external environment, and improve the accuracy and stability of the measurement. It is suitable for occasions with high measurement accuracy requirements and large electrical interference. It has strong anti-interference ability and can be used in various harsh environmental conditions. It has a wide range of applications and a long service life. However, due to the existence of the insulating layer, the speed of heat transfer to the measuring end is relatively slow, resulting in a long response time. There may be a certain lag in the measurement of rapidly changing temperatures. The responsiveness is not as good as the grounded type and exposed type, and the structure is complex and the maintenance cost is high.

[0055] The present invention uses an exposed thermocouple. Since the algorithm requires a data set with a one-to-one correspondence between temperature and time, in the embedded measurement, it is necessary to quickly respond to the temperature change of the measuring point, which places high demands on the response speed of the thermocouple. At the same time, since it is necessary to punch a hole in the thermal conductive material to bury the thermocouple to the center, in order to minimize the impact on the heat conduction process, the volume of the embedded part of the thermocouple should be as small as possible. Compared with the grounded and embedded types, the temperature measuring element of the exposed thermocouple is directly exposed to the measured environment, which can minimize the hysteresis phenomenon in the heat transfer process and achieve a rapid response to temperature changes. At the same time, since the temperature measuring lotus root is not covered with insulating material and is directly exposed, its volume embedded in the thermal conductive material is very small and will not cause major damage to the heat conduction process.

[0056] The advantages of using adhesives in this invention include the use of high-temperature thermally conductive adhesive Graphi-Bond 669 and high-viscosity two-phase adhesive CERAMABOND 571 as adhesives to secure thermocouples. Graphi-Bond 669, due to its excellent thermal stability and chemical resistance, performs exceptionally well in high-temperature environments, maintaining good performance even after long-term use. Furthermore, this adhesive possesses excellent electrical and thermal conductivity, ensuring stable electrical and thermal performance under high-temperature conditions, thereby reducing the impact of drilling on internal heat conduction in the thermally conductive material. However, due to its insufficient viscosity, it may loosen during use. Therefore, the use of high-viscosity two-phase adhesive CERAMABOND 571 is necessary for securing the thermocouples. CERAMABOND 571 has strong adhesion, with a viscosity range of 20,000 to 90,000 cP, effectively preventing loosening of thermocouples caused by shock and vibration. This adhesive is commonly used for the assembly and insulation of ceramic and metal components in high-temperature equipment, meeting the requirements of this invention for bonding and filling at higher temperatures. At the same time, its low thermal conductivity ensures that when applied to the hole surface, it will not significantly affect the overall heat transfer.

[0057] Before applying the adhesive, it's necessary to prepare the highly viscous two-phase adhesive, CERAMABOND 571. CERAMABOND 571 is a combination of powder and liquid adhesive. Before use, mix in a powder-to-liquid ratio of 1.5:1 by weight. To achieve uniformity, slowly add the powder to the liquid, stirring gently with a low-speed stirrer. The mixing process should be meticulous, ensuring complete immersion of all powders without lumps, consistent color, and the formation of air bubbles. To adjust viscosity, add a diluent (such as 571-T) up to 20% of the total volume. After thorough mixing, the ideal result is a homogeneous paste with no noticeable separation or separation, resembling liquid cement. This adhesive should be used as soon as possible after preparation to prevent premature hardening. Application within 1 to 4 hours of preparation is generally recommended for optimal performance.

[0058] The specific gluing and fixing process is as follows: When embedding the thermocouple, to minimize measurement error and response time between the thermocouple and the measuring point, we first coat the tip of the thermocouple's sheathed conductor with a layer of silicone grease, which has a very high thermal conductivity. At the same time, we inject Graphi-Bond 669, a high-performance, high-temperature thermal adhesive, into the hole in the thermally conductive material. Due to the slender structure of the hole, we recommend using a syringe for injection. Insert the needle into the hole and slowly inject the glue until it begins to overflow from the opening. Then, remove any excess glue from the surface. Next, insert the tip of the thermocouple into the hole, ensuring full contact with the bottom surface. Wait for about ten minutes for the filler adhesive layer to solidify. Then, apply a layer of CERAMABOND 571, a pre-cured, high-viscosity two-phase adhesive, around the outside of the hole. Finally, let it sit for about a day to fully secure the thermocouple to the thermally conductive material.

[0059] The advantages of the thermal insulation material selected in the present invention are:

[0060] The thermal insulation material HM1800 mullite used in this invention exhibits excellent thermal insulation and high-temperature resistance. Its low thermal conductivity, typically around 0.18-0.25 W / (m·K), and low heat capacity effectively prevent heat transfer and reduce heat storage, resulting in significant energy savings. It also exhibits excellent high-temperature resistance, with a melting point as high as 1810°C and structural stability at temperatures up to 1500°C. Its low thermal expansion coefficient and strong thermal shock resistance allow for long-term stable operation in high-temperature equipment. It also boasts high mechanical strength, with a compressive strength exceeding 5–10 MPa, excellent wear resistance, and the ability to withstand pressure and impact, making it less susceptible to damage during use. It also exhibits excellent chemical stability, resistance to acid, alkali, and salt corrosion, and excellent oxidation resistance, allowing for stable operation in complex chemical environments. It is also lightweight and environmentally friendly, making it easy to transport and install, and can be easily processed, with cuts and processed on demand. It has a long service life and can operate stably and continuously under harsh conditions, reducing maintenance and replacement times and costs.

[0061] The method of using the heat flow sensor is as follows:

[0062] like Figure 5 As shown, when measuring, first check whether the instrument is complete. If it is complete and undamaged, connect the leads of the first thermocouple 4 and the second thermocouple 5 to the data acquisition module, record the numbers corresponding to the different thermocouple leads, and then connect the bus of the data acquisition module to the computer.

[0063] Before the actual measurement, the user can use the computer's built-in test platform to select the pre-test module to perform a pre-test to check if there are any faults in the measurement process. After the pre-test results are normal, the actual measurement can begin.

[0064] Place the measuring end of the heat flux sensor at the location to be measured. To measure the heat flux and temperature on the surface of an object, hold the tail end of the sensor and place the measuring end close to the surface to be measured. To measure the heat flux and temperature inside the object, first determine the diameter and depth of the hole according to the present invention and the size of the object to be measured. Then, place the measuring end of the sensor close to the target location through the hole and secure it with adhesive or other means. If the position of the sensor in the object to be measured remains stable after a slight external force is applied, it is fully fixed and data collection can begin. After installing the sensor, click "Start Measurement" on the test platform. The system will begin to continuously record the temperature data of the first measuring point ① and the second measuring point ② during this period of time until you click "Stop Measurement". The system will then terminate the temperature data collection. After the collection is completed, you can directly perform an inversion prediction for the entire time period, or you can select the temperature data of the measuring points in a certain time period for solution.

[0065] After acquiring temperature data at a measurement point over a period of time, the corresponding algorithm module must be substituted for the data to perform calculations and solve the problem. At this point, the algorithm to be used must be determined based on the temperature of the measured point. Regarding the choice between the CIEM or SMM algorithm, when the measured surface temperature is below 600°C, the thermal properties of the thermally conductive material stainless steel vary linearly with temperature. In this case, the CIEM algorithm is recommended to reduce reliance on the uncertain thermal properties and improve measurement accuracy. When the measured surface temperature is 600°C or above, the thermal properties of the thermally conductive material stainless steel begin to vary nonlinearly with temperature. The CIEM algorithm performs poorly under nonlinear conditions, and the SMM algorithm provides a more accurate prediction solution.

[0066] If the temperature is above 600°C, the SMM algorithm is used to directly substitute the known thermal properties of the thermally conductive material 3, the embedded locations of the first and second thermocouples 4 and 5, and the collected temperature data at the measuring point into a pre-set program. The program then outputs predicted values ​​for the temperature and heat flux at the measuring point and plots their variations over time. If the temperature is below 600°C, the CIEM algorithm is used. The system calibration database is first searched for suitable data. If so, the calibration data is directly substituted into the program. If not, a set of calibration experiments is performed at the measuring point. Once reasonable calibration data is obtained, the calibration data and the collected temperature data at the measuring point are substituted into the pre-set program to calculate and output predicted values ​​and a plot of the temperature and heat flux at the measuring point. Finally, the temperature and heat flux at the measuring point, as well as their temporal variations, are clearly displayed on the test platform interface and can be exported for further analysis.

[0067] After completing the experiment, first disconnect the computer from the output end of the data acquisition module, then remove the connection between the thermocouple wire and the input end of the data acquisition module, then release the fixation between the sensor and the object to be measured, and finally slowly remove the sensor from the measuring point. After a simple cleaning and tidying up, check whether the sensor is damaged. After checking, let it stand and dissipate heat for the next use.

[0068] The CIEM algorithm is specifically:

[0069] x represents the distance from the test end, and t represents the time.

[0070] definition is the temperature at a distance x from the test end and a time t;

[0071] is the heat flux density at a distance of x from the test end and a time of t.

[0072] The initial condition at t = 0 is

[0073] (1.1)

[0074] in, Represents the initial temperature of the environment.

[0075] Define the temperature and heat flow at x = 0 as

[0076] (1.2)

[0077] (1.3)

[0078] The excess temperature is defined as

[0079] (1.4)

[0080] The corresponding initial conditions become

[0081] (1.5)

[0082] The excess temperature at x = 0 is

[0083] (1.6)

[0084] Then the one-dimensional linear heat conduction equation and heat flux defined by excess temperature are

[0085] (1.7)

[0086] (1.8)

[0087] in is the thermal diffusivity, is the thermal conductivity.

[0088] Perform Laplace transform on (1.7), and we get

[0089] (1.9)

[0090] Under zero initial condition (1.5), equation (1.9) can be transformed into

[0091] (1.10)

[0092] The solution of formula (1.10) is

[0093] (1.11)

[0094] Taking the derivative of (1.11), we get the residual temperature gradient:

[0095] (1.12)

[0096] The heat flux after Laplace transformation is

[0097] (1.13)

[0098] Let b represent the position of the first measuring point and c represent the position of the second measuring point. Substituting x = b and x = c into (1.11), we can obtain

[0099] (1.14)

[0100] (1.15)

[0101] Among them, the unknown coefficients A(s) and B(s) are unknown coefficients.

[0102] By transforming (1.14) and (1.15), the unknown coefficients A(s) and B(s) can be expressed as

[0103] (1.16)

[0104] (1.17)

[0105] Substituting it into (1.11), we get

[0106] (1.18)

[0107] in

[0108] (1.19)

[0109] (1.20)

[0110] At this time, the heat flux can be converted into

[0111] (1.21)

[0112] Then the excess temperature and heat flow at x = 0 can be expressed as

[0113] (1.22)

[0114] (1.23)

[0115] In order to eliminate the two and , conduct calibration experiments to obtain the temperatures at the two measuring points x = b and x = c,

[0116] (1.24)

[0117] (1.25)

[0118] Assuming that b, c, α and the thermocouple characteristics do not change between two calibration tests, the calibration temperature of the two measuring points is expressed as and , and then substitute the result back into formula (1.22), we get

[0119] (1.26)

[0120] or

[0121] (1.27)

[0122] Using the three-term convolution formula, (1.27) can be finally simplified to

[0123] (1.28)

[0124] in

[0125] (1.29)

[0126] (1.30)

[0127] It can be seen that and They are all defined by the calibration data, so after obtaining the temperatures of the two measuring points through the calibration experiment, the temperature at x = 0 can be solved by formula (1.28).

[0128] Similarly, using the calibration temperatures of the two measuring points, we can convert and Eliminate, and then use the three-term convolution formula to get

[0129] (1.31)

[0130] in

[0131] (1.32)

[0132] (1.33)

[0133] Therefore, after obtaining the temperatures of the two measuring points through the calibration experiment, the heat flux at x = 0 can also be calculated using formula (1.31).

[0134] The SMM algorithm is specifically:

[0135] x represents the distance from the test end, and t represents the time.

[0136] definition is the temperature at a distance x from the test end and a time t;

[0137] is the heat flux density at a distance of x from the test end and a time of t.

[0138] The one-dimensional heat conduction equation with extraordinary physical properties is

[0139] (2.1)

[0140] in, is the density, is the specific heat capacity.

[0141] The initial conditions are

[0142] (2.2)

[0143] in, Represents the initial temperature of the environment.

[0144] Assume that the temperature measured by the thermocouple is The actual temperature of the measuring point ,by Indicates the position of the first measuring point, The position of the second measuring point is

[0145] (2.3)

[0146] Get and Then, the heat flow at x = b1 can be obtained by the direct problem .

[0147] Use index i and j to represent spatial node x respectively i and time node t j , the first spatial node when i = 0 is x0 = b1, and the last spatial node when i = M is x M = 0. The temperature and heat flux at the starting point of the spatial advancement are defined as

[0148] (2.4)

[0149] (2.5)

[0150] Then there is

[0151] (2.6)

[0152] (2.7)

[0153] in

[0154] (2.8)

[0155] (2.9)

[0156] (2.10)

[0157] (2.11)

[0158] The initial condition at t = 0 is

[0159] (2.12)

[0160] (2.13)

[0161] With the one-sided boundary conditions (2.5), (2.6) and the initial conditions (2.12), (2.13), we can start from x = b1 and solve the temperature and heat flux at x = 0 by inversion.

[0162] The order of this scheme is Currently, due to and It is not completely accurate, and solving it this way will result in large errors. In order to stabilize the results, regularization is also required.

[0163] Therefore, we choose a low-pass Gaussian filter and define it as

[0164] (2.14)

[0165] in , is the circular cutoff frequency, is the cutoff frequency.

[0166] Obviously, the cutoff frequency f c The regularization parameter is defined. Therefore, the selection of the optimal regularization parameter involves determining the optimal cutoff frequency f c We calculate the heat flux rate by Perform phase plane and cross-correlation analysis based on a predefined cutoff frequency f n (n=1,2,…,P) spectrum prediction to determine the optimal cutoff frequency f of the digital filter shown in Equation (2.14) c .

[0167] The specific algorithm is as follows:

[0168] 1. Filter the raw thermocouple (TC) temperature using a Gaussian low-pass filter at x = b1 and x = b2, and fix the cutoff frequency f according to (2.14) n .

[0169] 2. Solve the direct heat conduction problem for the spatial domain defined between x = b1 and x = b2, using the filtered TC temperatures obtained in step 1 as the boundary conditions for the specified direct region. Assuming the sampling frequency is high enough, use the same sampling rate in the finite difference scheme.

[0170] 3. Calculate the local heat flux at x = b1 by evaluating the control volume. So far, the temperature at x = b1 has been obtained. and heat flow , with the unilateral boundary condition of advancing from x = b1 to the origin x = 0 space.

[0171] 4. Using the local heat flux calculated in step 3, filter the TC temperature at x = b1 in step 1 and use the above formula to propagate to the surface at x = 0 to obtain the surface heat flux and surface temperature.

[0172] 5. For a fixed cutoff frequency, calculate the surface temperature and heat flux density in step 4. Next, express the first derivative of the heat flux using simple finite differences to obtain the heat flux rate , and then perform phase plane and cross-correlation analysis.

[0173] 6. For each selected cutoff frequency f n, n = 1, 2, ..., P perform steps 1-5 and store them for later use in phase plane and cross-correlation analysis. Determine the optimal regularization parameter f based on the observed output n (opt).

[0174] Simulation results:

[0175] The simulation was performed using stainless steel for 5 seconds with a data collection frequency of 300 Hz. The optimal regularization parameter was selected by phase plane and cross-correlation analysis according to the above method. The results are shown in Figure 2. Figure 7 and Figure 8 shown. Figure 7 The predicted surface heat flux is shown , Figure 8 Shows the surface temperature used , where f = 4.0 Hz. Figure 9 The parameters used in the short-time simulations are listed.

[0176] It can be seen that the SMM algorithm has a high accuracy in the inversion prediction solution of heat flux density and temperature, and the results still maintain good accuracy and stability in a large range of heat flux and temperature, which has good application value.

[0177] 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 small-scale long-term measurement heat flow sensor suitable for two inverse problem algorithms, characterized in that: Used to measure heat flow using a calibration integral equation method and a space propulsion method; the sensor comprises a housing (1), a heat insulating material (2), a heat conducting material (3), a first thermocouple (4), and a second thermocouple (5); the housing (1) is a cylindrical structure with an open end, a coaxially arranged cylindrical heat conducting material (3) is provided inside the housing (1), the first thermocouple (4) and the second thermocouple (5) are provided between the heat conducting material (3) and the housing (1), and the collecting ends of the first thermocouple (4) and the second thermocouple (5) are embedded in the heat conducting material (3), and the other area between the heat conducting material (3) and the housing (1) is filled with heat insulating material (2); The first thermocouple (4) and the second thermocouple (5) are exposed thermocouples; A first measuring point and a second measuring point are provided on the inner central axis of the heat-conducting material (3); a first hole and a second hole are provided radially at the first measuring point and the second measuring point, respectively; and collection ends of the first thermocouple (4) and the second thermocouple (5) are embedded in the first hole and the second hole, respectively; The thermal conductive material (3) comprises a measuring end and a tail end, the measuring end is aligned with the open end of the housing (1), and the tail end is aligned with the sealed end of the housing (1); the distance between the first measuring point and the measuring end is 10-20 mm; the distance between the second measuring point and the measuring end is 40-45 mm; When the temperature of the measured point is below 600°C, the sensor is suitable for the calibration integral equation method; when the temperature of the measured point is 600°C or above, the sensor is suitable for the space propulsion method.

2. A small-scale long-term measurement heat flow sensor suitable for two inverse problem algorithms according to claim 1, characterized in that: The collecting ends of the first thermocouple (4) and the second thermocouple (5) are both wrapped with a silicone grease layer and fixed in the first hole and the second hole respectively by an adhesive, wherein the adhesive comprises a thermally conductive adhesive and a high-viscosity two-phase adhesive, the thermally conductive adhesive is poured into the first hole and the second hole, and the high-viscosity two-phase adhesive is coated on the surface of the thermally conductive adhesive to reinforce the first thermocouple (4) and the second thermocouple (5).

3. The small-sized long-time measurement heat flow sensor applicable to two inverse problem algorithms according to claim 1, characterized in that: The heat-conducting material (3) has a diameter of 2.5 to 4 mm and a length of 45 to 55 mm; the heat-insulating material (2) has a thickness of 1 to 1.25 mm; and the outer shell (1) has an outer diameter of 5 to 7 mm, a thickness of 0.5 to 0.7 mm, and a length of 45 to 55 mm.

4. A small-scale long-time measurement heat flow sensor suitable for two inverse problem algorithms according to claim 1, characterized in that: The bottom surface of the sealed end of the shell (1) is provided with two openings, and the leads of the first thermocouple (4) and the second thermocouple (5) are led between the heat-conducting material (3) and the shell (1) along the axial direction to the tail end of the heat-conducting material (3), and are respectively led to the outside of the shell (1) through the two openings.

5. The small-sized long-time measurement heat flow sensor applicable to two inverse problem algorithms according to claim 1, characterized in that: The heat insulating material (2) is mullite, and the heat conducting material (3) is stainless steel.

6. A heat flow measurement method based on two inverse problem algorithms, characterized in that: The method is implemented using the sensor according to any one of claims 1 to 5, comprising the following steps: The sensor is connected to a data acquisition board to acquire temperature data; the data acquisition board is connected to a computer to transmit the temperature data to the computer; the computer has a built-in calibration integral equation algorithm and a space propulsion algorithm; The algorithm used is selected based on the temperature data of the measured point. When the temperature is below 600°C, the calibration integral equation algorithm is selected; when the temperature is above 600°C, the spatial advancement algorithm is selected. After post-processing the temperature data using the selected algorithm, the predicted values ​​of the temperature and heat flux density at the measuring point are output and an image is generated.

Images