Method for calculating error of radial thermal conductivity test of cylindrical sample

Abstract

The application discloses a kind of cylindrical sample radial heat conductivity test error calculation method, belongs to dry hot rock exploration technical field, it is characterized in that, include the following steps: a, distinguish the type of cylindrical sample, select the cylindrical sample to be measured;B, calculate the heat conductivity experimental test true value of cylindrical sample;C, calculate the test result simulation value of cylindrical sample;D, calculate the radial heat conductivity test error value ε of cylindrical sample.The application can carry out error analysis to the radial heat conductivity test of cylindrical sample, effectively estimate the accuracy of the radial heat conductivity test of cylindrical sample, carry out reliability evaluation to the radial heat conductivity test of cylindrical sample.

Description

Technical Field

[0001] This invention relates to the field of dry hot rock exploration technology, and in particular to a method for calculating the error of radial thermal conductivity testing of cylindrical samples. Background Technology

[0002] Thermal conductivity, also known as thermal conductivity coefficient, is a measure of a material's ability to conduct heat. It refers to the amount of heat transferred per unit time through a unit horizontal cross-sectional area when the temperature gradient is 1℃ / m vertically downward. The thermal conductivity values ​​of various materials are mainly determined experimentally, while theoretical estimation is an active topic in modern physics and physical chemistry. Theoretically, starting from the microscopic structure of matter and based on quantum mechanics and statistical mechanics, by studying the heat conduction mechanism of matter and establishing a physical model of heat conduction, thermal conductivity can be obtained through complex mathematical analysis and calculation. However, due to limitations in the applicability of the theory and the rapid increase in new materials, a sufficiently accurate and widely applicable theoretical equation has not yet been found. Therefore, the exploration of experimental testing methods and technologies for thermal conductivity remains the primary source of thermal conductivity data. In the energy industry, the radial thermal conductivity testing method for cylindrical samples has broad application prospects. When developing geothermal resources, the anisotropy of rock thermal conductivity in different directions is considered. Many core samples in the energy industry, obtained by drill bits, are cylindrical in shape. Cylindrical lithium-ion batteries typically employ spiral electrode assemblies. Due to the numerous interfaces between the electrodes and electrolyte layers in the radial conduction path that are absent in the axial direction, the thermal conductivity of cylindrical lithium-ion batteries differs by nearly two orders of magnitude between the radial and axial directions. Thermal conductivity is one of the important thermophysical performance parameters of lithium-ion batteries, and testing needs to cover the thermal conductivity of batteries of different specifications and in different directions. For industrial products like cylindrical batteries, which have specific morphological structures, mechanical cutting can cause product failure or damage. Existing technology is only suitable for testing the thermal conductivity of the cylindrical battery's end face, but cannot test the radial thermal conductivity.

[0003] Chinese patent document CN 112364577A, published on February 12, 2021, discloses a numerical simulation analysis method for thermal structural parameters of a subducting plate, characterized by comprising:

[0004] Calculate the initial conditions of the plate boundary temperature based on the subduction age and the plate free cooling model;

[0005] Based on the plate depth and subduction velocity, the regionalization and velocity field of the material inside the plate are defined, and relevant parameters of each region of the model are given. These relevant parameters include: density, viscosity, thermal conductivity, specific heat capacity, thermal expansion coefficient, and thermal emissivity.

[0006] Based on the initial boundary temperature conditions and the relevant parameters, the mass, temperature, velocity, and energy field of each dive step are iteratively calculated using the Navier-Stokes equations of mass, momentum, and energy conservation.

[0007] Once the dive is complete and the temperature has stabilized, the final mass field, temperature field, velocity field, and energy field are obtained.

[0008] By comparing the observed surface heat flow values, the relevant parameters of each region in the given model are adjusted to make the temperature field conform to the observed values:

[0009] Based on the temperature and velocity fields, the plate moisture content, dehydration rate, and rock phase transformation distribution are calculated.

[0010] Based on the calculated water content, dehydration rate, rock phase transformation distribution, and temperature field, a three-dimensional drawing is performed.

[0011] The numerical simulation analysis method for the thermal structure parameters of plate subduction disclosed in this patent document can calculate and represent the three-dimensional temperature field, plate water content, dehydration rate, and rock phase transition distribution of the subduction zone based on known plate depth and subduction velocity data. The calculation results can be further used in research on the deep Earth temperature field, rock phase transition exhumation processes, underground fluid fields of volcanic magma, and metamorphic rock mineral exploration and development. However, it cannot perform error analysis on the radial thermal conductivity test of cylindrical samples, cannot estimate the accuracy of the radial thermal conductivity test of cylindrical samples, and cannot conduct a reliability assessment of the radial thermal conductivity test of cylindrical samples. Summary of the Invention

[0012] To overcome the shortcomings of the prior art, this invention provides a method for calculating the error of radial thermal conductivity testing of cylindrical samples. This invention can perform error analysis on radial thermal conductivity testing of cylindrical samples, effectively estimate the accuracy of radial thermal conductivity testing of cylindrical samples, and conduct reliability assessment of radial thermal conductivity testing of cylindrical samples.

[0013] This invention is achieved through the following technical solution:

[0014] A method for calculating the radial thermal conductivity test error of a cylindrical sample, characterized by comprising the following steps:

[0015] a. Differentiate the types of cylindrical samples and select the cylindrical sample to be tested;

[0016] b. Calculate the true value of the thermal conductivity of the cylindrical sample. When the cylindrical sample is a rock core, if the texture of the rock core is parallel to the end face of the cylinder, then observe the development of the laminae through CT scans or nuclear magnetic resonance images to divide the cylindrical sample into layers 1, 2, ..., and n, with the thermal conductivity of each layer corresponding to λ1, λ2, ..., and λn.n The thicknesses of each layer are h1, h2, ... and h. n The true value of thermal conductivity λ was calculated experimentally when the texture of the rock core was parallel to the end face of the cylinder using Equation 1. / / ;

[0017]

[0018] Where, λ / / h represents the true value of thermal conductivity measured experimentally when the texture of the rock core is parallel to the end face of the cylinder. i Let λ be the thickness of the i-th layer of the cylindrical sample. i Let be the thermal conductivity of the i-th layer of the cylindrical sample;

[0019] If the core's texture is perpendicular to the cylinder's end face, and heat flows in along the lamellar development direction, then the cylindrical sample can be divided into layers 1, 2, ..., and n according to the lamellar development, as observed by CT scans or nuclear magnetic resonance imaging. The thermal conductivity of each layer corresponds to λ1, λ2, ..., and λn. n The areas of each layer are S1, S2, ... and S. n The true value of thermal conductivity was calculated experimentally when the texture of the rock core was perpendicular to the end face of the cylinder using Equation 2.

[0020]

[0021] in, S represents the true value of thermal conductivity measured experimentally when the texture of the rock core is perpendicular to the end face of the cylinder. i Let λ be the area of ​​the i-th layer of the cylindrical sample. i Let be the thermal conductivity of the i-th layer of the cylindrical sample;

[0022] If the core texture is perpendicular to the end face of the cylinder, and heat flows in perpendicularly to the direction of lamellar development, then the cylindrical sample can be divided into layers 1, 2, ..., and n according to the development of the lamellar structures, as observed by CT scans or nuclear magnetic resonance imaging. The thermal conductivity of each layer corresponds to λ1, λ2, ..., and λn. n The thicknesses of each layer are H1, H2, ... and H. nA cuboid was constructed, with its end faces squared using the diameter of the cylindrical sample as the side length. The height of the cuboid was the height of the cylindrical sample. The thermal conductivity of each layer was designed based on the end faces, and the thickness distribution ratio was consistent with the end faces of the cylindrical sample. The cuboid was designed with a temperature of 1K on the left side and 0K on the right side, with no heat flow on other faces. A finite element mesh was established, and the temperature field distribution of the cuboid was obtained according to the current equation. The cuboid core was divided into 2l+1 equal parts from top to bottom. The average heat flux values ​​qc1, qc2, ..., qc of each section were read from the numerical simulation results of the temperature field. 2m+1 The true value of thermal conductivity was calculated experimentally when the texture of the rock core was perpendicular to the end face of the cylinder using Equation 3.

[0023]

[0024] in, This represents the experimentally measured true value of thermal conductivity when the texture of the rock core is perpendicular to the end face of the cylinder. The average heat flux value of the i-th cross section;

[0025] When the cylindrical sample is a battery, the true value λ of the battery's thermal conductivity is calculated using Equation 4. hb ;

[0026]

[0027] Where r is the radius of the battery, λ hb Here, r1 represents the true value of the battery's thermal conductivity as measured in an experiment, r2 represents the thickness of the first separator layer, and r is the thickness of the second separator layer. n Let λ be the thickness of the nth separator layer of the battery, λ1 be the thermal conductivity of the first separator layer of the battery, and λ2 be the thermal conductivity of the second separator layer of the battery. n Let be the thermal conductivity of the nth layer of the battery separator;

[0028] c. Calculate the simulated test results for the cylindrical sample. Set up a three-dimensional cylindrical model, with the thermal conductivity of each layer according to λ1, λ2, ... and λ... n The system is configured such that heat flows in from point A and out from point C. The boundary temperature at point A is set to be 1-5°C above room temperature, the boundary temperature at point C is room temperature, and there is no heat flow at boundaries B and D. A finite element mesh is established, and the temperature field distribution map can be obtained according to Fourier's law. The core sample is divided into 2m+1 equal parts from the outside to the inside. The average heat flow values ​​q1, q2, ..., q of each section are read from the numerical simulation results of the temperature field. 2m+1 The simulated value λ of the test result for the cylindrical sample is calculated using Equation 5. * ;

[0029]

[0030] Where, λ * q represents the simulated test result for a cylindrical sample. i The average heat flux value of the i-th cross section;

[0031] d. Calculate the radial thermal conductivity test error value ε of the cylindrical sample using Equation 6;

[0032]

[0033] Where ε is the radial thermal conductivity test error value of the cylindrical sample, and λ * For the simulated test results of the cylindrical sample, λ = λ i , λ i For λ / / , or λ hb .

[0034] In step a, distinguishing the type of cylindrical sample means checking whether the cylindrical sample is a rock core formed under natural conditions or an artificially made battery.

[0035] In step a, if the cylindrical sample is a rock core generated under natural conditions, then it is determined whether the end face of the cylindrical sample is parallel to the rock core texture or perpendicular to the rock core texture. When the end face of the rock core is perpendicular to the rock core texture, the direction of heat flow is observed.

[0036] The observation of the heat flow direction specifically refers to whether the heat flows in along the direction of lamellar development or perpendicular to the direction of lamellar development. If the heat flow direction is at an angle to the direction of lamellar development, the position of the cylindrical sample is readjusted until the heat flows in along the direction of lamellar development or perpendicular to the direction of lamellar development.

[0037] In step a, the cylindrical sample to be tested is selected if there is a fold or turn in the fingerprint layer development direction. If so, a new cylindrical sample is prepared and a cylindrical sample with a single fingerprint layer development direction is selected as the cylindrical sample to be tested.

[0038] In step b, the thermal conductivity values ​​of each layer are obtained by using a common thermal conductivity testing method on cylindrical samples of the same material.

[0039] In step b, when the cylindrical sample is a rock core, the thickness and area of ​​each layer are obtained through CT scans or nuclear magnetic resonance imaging images; when the cylindrical sample is a battery, the thickness and area are obtained through actual measurements of the same type of battery.

[0040] In step c, the boundary temperature of A is 1°C higher than room temperature.

[0041] The finite element mesh of this invention is established by Zeng Pan's "Fundamental Tutorial of Finite Element Analysis", Higher Education Press, July 2009, "Finite Element Analysis in Heat Transfer Processes", pp. 290-311.

[0042] The heat flow of this invention is calculated using the finite element numerical simulation software COMSOL. After obtaining the temperature field distribution curve through numerical simulation, the surface integral of the heat flow curve to be calculated is selected to obtain the heat flow through the interface.

[0043] The beneficial effects of this invention are mainly reflected in the following aspects:

[0044] 1. This invention can perform error analysis on the radial thermal conductivity test of cylindrical samples, effectively estimate the accuracy of the radial thermal conductivity test of cylindrical samples, and conduct reliability assessment on the radial thermal conductivity test of cylindrical samples.

[0045] 2. This invention can objectively evaluate the accuracy or systematic error of radial thermal conductivity test results for cylindrical samples, solving the problem that there were no other effective methods to evaluate the accuracy of radial thermal conductivity test results.

[0046] 3. This invention provides different calculation methods for different internal results of the sample to numerically simulate the true value of the thermal conductivity test, effectively ensuring the objectivity of the calculation of the true value of the thermal conductivity test, improving the accuracy of the evaluation of system error, and avoiding general descriptions of complex problems.

[0047] 4. In this invention, the numerical simulation method can be adapted to different computational costs by the operator based on the actual sample, thereby improving the flexibility and adaptability of system error evaluation calculation.

[0048] 5. In calculating the true value of thermal conductivity experimental test, this invention fully considers the usual practice of measuring thermal conductivity, making it convenient for operators to compare with the axial thermal conductivity test method.

[0049] 6. The calculation method of this invention is simple and clear, and has strong operability and practicality.

[0050] 7. This invention provides a feasible algorithm that can effectively evaluate the impact of conformal transformation using a "complex function" on the test results when the radial thermal conductivity test assumes isotropic properties.

[0051] 8. This invention can be used to study the degree of influence of the difference in the properties of the components on the overall thermal conductivity of a system composed of materials with different properties, based on simulation calculations. Attached Figure Description

[0052] The present invention will now be further described in detail with reference to the accompanying drawings and specific embodiments, wherein:

[0053] Figure 1 This is a schematic diagram of the cylindrical sample structure of the present invention, showing the flow of heat from end A to end C. Detailed Implementation

[0054] Example 1

[0055] See Figure 1 A method for calculating the radial thermal conductivity test error of a cylindrical sample, comprising the following steps:

[0056] a. Differentiate the types of cylindrical samples and select the cylindrical sample to be tested;

[0057] b. Calculate the true value of the thermal conductivity of the cylindrical sample. When the cylindrical sample is a rock core, if the texture of the rock core is parallel to the end face of the cylinder, then observe the development of the laminae through CT scans or nuclear magnetic resonance images to divide the cylindrical sample into layers 1, 2, ..., and n, with the thermal conductivity of each layer corresponding to λ1, λ2, ..., and λn. n The thicknesses of each layer are h1, h2, ... and h. n The true value of thermal conductivity λ was calculated experimentally when the texture of the rock core was parallel to the end face of the cylinder using Equation 1. / / ;

[0058]

[0059] Where, λ / / h represents the true value of thermal conductivity measured experimentally when the texture of the rock core is parallel to the end face of the cylinder. i Let λ be the thickness of the i-th layer of the cylindrical sample. i Let be the thermal conductivity of the i-th layer of the cylindrical sample;

[0060] If the core's texture is perpendicular to the cylinder's end face, and heat flows in along the lamellar development direction, then the cylindrical sample can be divided into layers 1, 2, ..., and n according to the lamellar development, as observed by CT scans or nuclear magnetic resonance imaging. The thermal conductivity of each layer corresponds to λ1, λ2, ..., and λn. n The areas of each layer are S1, S2, ... and S. n The true value of thermal conductivity was calculated experimentally when the texture of the rock core was perpendicular to the end face of the cylinder using Equation 2.

[0061]

[0062] in, S represents the true value of thermal conductivity measured experimentally when the texture of the rock core is perpendicular to the end face of the cylinder. i Let λ be the area of ​​the i-th layer of the cylindrical sample. i Let be the thermal conductivity of the i-th layer of the cylindrical sample;

[0063] If the core texture is perpendicular to the end face of the cylinder, and heat flows in perpendicularly to the direction of lamellar development, then the cylindrical sample can be divided into layers 1, 2, ..., and n according to the development of the lamellar structures, as observed by CT scans or nuclear magnetic resonance imaging. The thermal conductivity of each layer corresponds to λ1, λ2, ..., and λn. n The thicknesses of each layer are H1, H2, ... and H. n A cuboid was constructed, with its end faces squared using the diameter of the cylindrical sample as the side length. The height of the cuboid was the height of the cylindrical sample. The thermal conductivity of each layer was designed based on the end faces, and the thickness distribution ratio was consistent with the end faces of the cylindrical sample. The cuboid was designed with a temperature of 1K on the left side and 0K on the right side, with no heat flow on other faces. A finite element mesh was established, and the temperature field distribution of the cuboid was obtained according to the current equation. The cuboid core was divided into 2l+1 equal parts from top to bottom. The average heat flux values ​​qc1, qc2, ..., qc of each section were read from the numerical simulation results of the temperature field. 2m+1 The true value of thermal conductivity was calculated experimentally when the texture of the rock core was perpendicular to the end face of the cylinder using Equation 3.

[0064]

[0065] in, This represents the experimentally measured true value of thermal conductivity when the texture of the rock core is perpendicular to the end face of the cylinder. The average heat flux value of the i-th cross section;

[0066] When the cylindrical sample is a battery, the true value λ of the battery's thermal conductivity is calculated using Equation 4. hb ;

[0067]

[0068] Where r is the radius of the battery, λ hb Here, r1 represents the true value of the battery's thermal conductivity as measured in an experiment, r2 represents the thickness of the first separator layer, and r is the thickness of the second separator layer. n Let λ be the thickness of the nth separator layer of the battery, λ1 be the thermal conductivity of the first separator layer of the battery, and λ2 be the thermal conductivity of the second separator layer of the battery. n Let be the thermal conductivity of the nth layer of the battery separator;

[0069] c. Calculate the simulated test results for the cylindrical sample. Set up a three-dimensional cylindrical model, with the thermal conductivity of each layer according to λ1, λ2, ... and λ... n The system is configured such that heat flows in from point A and out from point C. The temperature at boundary A is set to be 1°C above room temperature, and the temperature at boundary C is set to room temperature. There is no heat flow at boundaries B and D. A finite element mesh is established, and the temperature field distribution diagram can be obtained according to Fourier's law. The core sample is divided into 2m+1 equal parts from the outside to the inside. The average heat flow values ​​q1, q2, ..., q at each cross-section are read from the numerical simulation results of the temperature field. 2m+1 The simulated value λ of the test result for the cylindrical sample is calculated using Equation 5. * ;

[0070]

[0071] Where, λ * q represents the simulated test result for a cylindrical sample. i The average heat flux value of the i-th cross section;

[0072] d. Calculate the radial thermal conductivity test error value ε of the cylindrical sample using Equation 6;

[0073]

[0074] Where ε is the radial thermal conductivity test error value of the cylindrical sample, and λ * For the simulated test results of the cylindrical sample, λ = λ i , λ i For λ / / , or λ hb .

[0075] This embodiment is the most basic implementation method, which can perform error analysis on the radial thermal conductivity test of cylindrical samples, effectively estimate the accuracy of the radial thermal conductivity test of cylindrical samples, and conduct a reliability assessment of the radial thermal conductivity test of cylindrical samples.

[0076] Example 2

[0077] See Figure 1 A method for calculating the radial thermal conductivity test error of a cylindrical sample, comprising the following steps:

[0078] a. Differentiate the types of cylindrical samples and select the cylindrical sample to be tested;

[0079] b. Calculate the true value of the thermal conductivity of the cylindrical sample. When the cylindrical sample is a rock core, if the texture of the rock core is parallel to the end face of the cylinder, then observe the development of the laminae through CT scans or nuclear magnetic resonance images to divide the cylindrical sample into layers 1, 2, ..., and n, with the thermal conductivity of each layer corresponding to λ1, λ2, ..., and λn. n The thicknesses of each layer are h1, h2, ... and h. n The true value of thermal conductivity λ was calculated experimentally when the texture of the rock core was parallel to the end face of the cylinder using Equation 1. / / ;

[0080]

[0081] Where, λ / / h represents the true value of thermal conductivity measured experimentally when the texture of the rock core is parallel to the end face of the cylinder. i Let λ be the thickness of the i-th layer of the cylindrical sample. i Let be the thermal conductivity of the i-th layer of the cylindrical sample;

[0082] If the core's texture is perpendicular to the cylinder's end face, and heat flows in along the lamellar development direction, then the cylindrical sample can be divided into layers 1, 2, ..., and n according to the lamellar development, as observed by CT scans or nuclear magnetic resonance imaging. The thermal conductivity of each layer corresponds to λ1, λ2, ..., and λn. n The areas of each layer are S1, S2, ... and S. n The true value of thermal conductivity was calculated experimentally when the texture of the rock core was perpendicular to the end face of the cylinder using Equation 2.

[0083]

[0084] in, S represents the true value of thermal conductivity measured experimentally when the texture of the rock core is perpendicular to the end face of the cylinder. i Let λ be the area of ​​the i-th layer of the cylindrical sample. i Let be the thermal conductivity of the i-th layer of the cylindrical sample;

[0085] If the core texture is perpendicular to the end face of the cylinder, and heat flows in perpendicularly to the direction of lamellar development, then the cylindrical sample can be divided into layers 1, 2, ..., and n according to the development of the lamellar structures, as observed by CT scans or nuclear magnetic resonance imaging. The thermal conductivity of each layer corresponds to λ1, λ2, ..., and λn. n The thicknesses of each layer are H1, H2, ... and H. nA cuboid was constructed, with its end faces squared using the diameter of the cylindrical sample as the side length. The height of the cuboid was the height of the cylindrical sample. The thermal conductivity of each layer was designed based on the end faces, and the thickness distribution ratio was consistent with the end faces of the cylindrical sample. The cuboid was designed with a temperature of 1K on the left side and 0K on the right side, with no heat flow on other faces. A finite element mesh was established, and the temperature field distribution of the cuboid was obtained according to the current equation. The cuboid core was divided into 2l+1 equal parts from top to bottom. The average heat flux values ​​qc1, qc2, ..., qc of each section were read from the numerical simulation results of the temperature field. 2m+1 The true value of thermal conductivity was calculated experimentally when the texture of the rock core was perpendicular to the end face of the cylinder using Equation 3.

[0086]

[0087] in, This represents the experimentally measured true value of thermal conductivity when the texture of the rock core is perpendicular to the end face of the cylinder. The average heat flux value of the i-th cross section;

[0088] When the cylindrical sample is a battery, the true value λ of the battery's thermal conductivity is calculated using Equation 4. hb ;

[0089]

[0090] Where r is the radius of the battery, λ hb Here, r1 represents the true value of the battery's thermal conductivity as measured in an experiment, r2 represents the thickness of the first separator layer, and r is the thickness of the second separator layer. n Let λ be the thickness of the nth separator layer of the battery, λ1 be the thermal conductivity of the first separator layer of the battery, and λ2 be the thermal conductivity of the second separator layer of the battery. n Let be the thermal conductivity of the nth layer of the battery separator;

[0091] c. Calculate the simulated test results for the cylindrical sample. Set up a three-dimensional cylindrical model, with the thermal conductivity of each layer according to λ1, λ2, ... and λ... n The system is configured such that heat flows in from point A and out from point C. The temperature at boundary A is set to be 2°C above room temperature, and the temperature at boundary C is set to room temperature. There is no heat flow at boundaries B and D. A finite element mesh is established, and the temperature field distribution diagram can be obtained according to Fourier's law. The core sample is divided into 2m+1 equal parts from the outside to the inside. The average heat flow values ​​q1, q2, ..., q at each cross-section are read from the numerical simulation results. 2m+1 The simulated value λ of the test result for the cylindrical sample is calculated using Equation 5. * ;

[0092]

[0093] Where, λ * q represents the simulated test result for a cylindrical sample. i The average heat flux value of the i-th cross section;

[0094] d. Calculate the radial thermal conductivity test error value ε of the cylindrical sample using Equation 6;

[0095]

[0096] Where ε is the radial thermal conductivity test error value of the cylindrical sample, and λ * For the simulated test results of the cylindrical sample, λ = λ i , λ i For λ / / , or λ hb .

[0097] In step a, distinguishing the type of cylindrical sample means checking whether the cylindrical sample is a rock core formed under natural conditions or an artificially made battery.

[0098] In step a, if the cylindrical sample is a rock core generated under natural conditions, then it is determined whether the end face of the cylindrical sample is parallel to the rock core texture or perpendicular to the rock core texture. When the end face of the rock core is perpendicular to the rock core texture, the direction of heat flow is observed.

[0099] This embodiment is a preferred implementation method, which can objectively evaluate the accuracy or systematic error of the radial thermal conductivity test results of cylindrical samples, and solves the problem that there are no other effective methods to evaluate the accuracy of radial thermal conductivity test results.

[0100] Different calculation methods are used to numerically simulate the true value of thermal conductivity test results for different internal results of the sample itself. This effectively ensures the objectivity of the calculation of the true value of thermal conductivity test results, improves the accuracy of systematic error evaluation, and avoids general descriptions of complex problems.

[0101] Example 3

[0102] See Figure 1 A method for calculating the radial thermal conductivity test error of a cylindrical sample, comprising the following steps:

[0103] a. Differentiate the types of cylindrical samples and select the cylindrical sample to be tested;

[0104] b. Calculate the true value of the thermal conductivity of the cylindrical sample. When the cylindrical sample is a rock core, if the texture of the rock core is parallel to the end face of the cylinder, then observe the development of the laminae through CT scans or nuclear magnetic resonance images to divide the cylindrical sample into layers 1, 2, ..., and n, with the thermal conductivity of each layer corresponding to λ1, λ2, ..., and λn. n The thicknesses of each layer are h1, h2, ... and h. n The true value of thermal conductivity λ was calculated experimentally when the texture of the rock core was parallel to the end face of the cylinder using Equation 1. / / ;

[0105]

[0106] Where, λ / / h represents the true value of thermal conductivity measured experimentally when the texture of the rock core is parallel to the end face of the cylinder. i Let λ be the thickness of the i-th layer of the cylindrical sample. i Let be the thermal conductivity of the i-th layer of the cylindrical sample;

[0107] If the core's texture is perpendicular to the cylinder's end face, and heat flows in along the lamellar development direction, then the cylindrical sample can be divided into layers 1, 2, ..., and n according to the lamellar development, as observed by CT scans or nuclear magnetic resonance imaging. The thermal conductivity of each layer corresponds to λ1, λ2, ..., and λn. n The areas of each layer are S1, S2, ... and S. n The true value of thermal conductivity was calculated experimentally when the texture of the rock core was perpendicular to the end face of the cylinder using Equation 2.

[0108]

[0109] in, S represents the true value of thermal conductivity measured experimentally when the texture of the rock core is perpendicular to the end face of the cylinder. i Let λ be the area of ​​the i-th layer of the cylindrical sample. i Let be the thermal conductivity of the i-th layer of the cylindrical sample;

[0110] If the core texture is perpendicular to the end face of the cylinder, and heat flows in perpendicularly to the direction of lamellar development, then the cylindrical sample can be divided into layers 1, 2, ..., and n according to the development of the lamellar structures, as observed by CT scans or nuclear magnetic resonance imaging. The thermal conductivity of each layer corresponds to λ1, λ2, ..., and λn. n The thicknesses of each layer are H1, H2, ... and H. nA cuboid was constructed, with its end faces squared using the diameter of the cylindrical sample as the side length. The height of the cuboid was the height of the cylindrical sample. The thermal conductivity of each layer was designed based on the end faces, and the thickness distribution ratio was consistent with the end faces of the cylindrical sample. The cuboid was designed with a temperature of 1K on the left side and 0K on the right side, with no heat flow on other faces. A finite element mesh was established, and the temperature field distribution of the cuboid was obtained according to the current equation. The cuboid core was divided into 2l+1 equal parts from top to bottom. The average heat flux values ​​qc1, qc2, ..., qc of each section were read from the numerical simulation results of the temperature field. 2m+1 The true value of thermal conductivity was calculated experimentally when the texture of the rock core was perpendicular to the end face of the cylinder using Equation 3.

[0111]

[0112] in, This represents the experimentally measured true value of thermal conductivity when the texture of the rock core is perpendicular to the end face of the cylinder. The average heat flux value of the i-th cross section;

[0113] When the cylindrical sample is a battery, the true value λ of the battery's thermal conductivity is calculated using Equation 4. hb ;

[0114]

[0115] Where r is the radius of the battery, λ hb Here, r1 represents the true value of the battery's thermal conductivity as measured in an experiment, r2 represents the thickness of the first separator layer, and r is the thickness of the second separator layer. n Let λ be the thickness of the nth separator layer of the battery, λ1 be the thermal conductivity of the first separator layer of the battery, and λ2 be the thermal conductivity of the second separator layer of the battery. n Let be the thermal conductivity of the nth layer of the battery separator;

[0116] c. Calculate the simulated test results for the cylindrical sample. Set up a three-dimensional cylindrical model, with the thermal conductivity of each layer according to λ1, λ2, ... and λ... n The system is configured such that heat flows in from point A and out from point C. The boundary temperature at point A is set to be 3°C above room temperature, the boundary temperature at point C is room temperature, and there is no heat flow at boundaries B and D. A finite element mesh is established, and the temperature field distribution diagram can be obtained according to Fourier's law. The core sample is divided into 2m+1 equal parts from the outside to the inside. The average heat flow values ​​q1, q2, ..., q of each section are read from the numerical simulation results of the temperature field. 2m+1 The simulated value λ of the test result for the cylindrical sample is calculated using Equation 5. * ;

[0117]

[0118] Where, λ * q represents the simulated test result for a cylindrical sample. i The average heat flux value of the i-th cross section;

[0119] d. Calculate the radial thermal conductivity test error value ε of the cylindrical sample using Equation 6;

[0120]

[0121] Where ε is the radial thermal conductivity test error value of the cylindrical sample, and λ * For the simulated test results of the cylindrical sample, λ = λ i , λ i For λ / / , or λ hb .

[0122] In step a, distinguishing the type of cylindrical sample means checking whether the cylindrical sample is a rock core formed under natural conditions or an artificially made battery.

[0123] In step a, if the cylindrical sample is a rock core generated under natural conditions, then it is determined whether the end face of the cylindrical sample is parallel to the rock core texture or perpendicular to the rock core texture. When the end face of the rock core is perpendicular to the rock core texture, the direction of heat flow is observed.

[0124] The observation of the heat flow direction specifically refers to whether the heat flows in along the direction of lamellar development or perpendicular to the direction of lamellar development. If the heat flow direction is at an angle to the direction of lamellar development, the position of the cylindrical sample is readjusted until the heat flows in along the direction of lamellar development or perpendicular to the direction of lamellar development.

[0125] In step a, the cylindrical sample to be tested is selected if there is a fold or turn in the fingerprint layer development direction. If so, a new cylindrical sample is prepared and a cylindrical sample with a single fingerprint layer development direction is selected as the cylindrical sample to be tested.

[0126] In step b, the thermal conductivity values ​​of each layer are obtained by using a common thermal conductivity testing method on cylindrical samples of the same material.

[0127] This embodiment is another preferred implementation. The numerical simulation method can be adopted by the operator according to the actual sample, using numerical simulation methods with different computational costs, which improves the flexibility and adaptability of system error evaluation calculation.

[0128] The calculation of the true value of thermal conductivity experimental test fully considers the usual practice of measuring thermal conductivity, making it convenient for operators to compare with the axial thermal conductivity test method.

[0129] The calculation method is simple and clear, and has strong operability and practicality.

[0130] Example 4

[0131] See Figure 1 A method for calculating the radial thermal conductivity test error of a cylindrical sample, comprising the following steps:

[0132] a. Differentiate the types of cylindrical samples and select the cylindrical sample to be tested;

[0133] b. Calculate the true value of the thermal conductivity of the cylindrical sample. When the cylindrical sample is a rock core, if the texture of the rock core is parallel to the end face of the cylinder, then observe the development of the laminae through CT scans or nuclear magnetic resonance images to divide the cylindrical sample into layers 1, 2, ..., and n, with the thermal conductivity of each layer corresponding to λ1, λ2, ..., and λn. n The thicknesses of each layer are h1, h2, ... and h. n The true value of thermal conductivity λ was calculated experimentally when the texture of the rock core was parallel to the end face of the cylinder using Equation 1. / / ;

[0134]

[0135] Where, λ / / h represents the true value of thermal conductivity measured experimentally when the texture of the rock core is parallel to the end face of the cylinder. i Let λ be the thickness of the i-th layer of the cylindrical sample. i Let be the thermal conductivity of the i-th layer of the cylindrical sample;

[0136] If the core's texture is perpendicular to the cylinder's end face, and heat flows in along the lamellar development direction, then the cylindrical sample can be divided into layers 1, 2, ..., and n according to the lamellar development, as observed by CT scans or nuclear magnetic resonance imaging. The thermal conductivity of each layer corresponds to λ1, λ2, ..., and λn. n The areas of each layer are S1, S2, ... and S. n The true value of thermal conductivity was calculated experimentally when the texture of the rock core was perpendicular to the end face of the cylinder using Equation 2.

[0137]

[0138] in, S represents the true value of thermal conductivity measured experimentally when the texture of the rock core is perpendicular to the end face of the cylinder. i Let λ be the area of ​​the i-th layer of the cylindrical sample. i Let be the thermal conductivity of the i-th layer of the cylindrical sample;

[0139] If the core texture is perpendicular to the end face of the cylinder, and heat flows in perpendicularly to the direction of lamellar development, then the cylindrical sample can be divided into layers 1, 2, ..., and n according to the development of the lamellar structures, as observed by CT scans or nuclear magnetic resonance imaging. The thermal conductivity of each layer corresponds to λ1, λ2, ..., and λn. n The thicknesses of each layer are H1, H2, ... and H. n A cuboid was constructed, with its end faces squared using the diameter of the cylindrical sample as the side length. The height of the cuboid was the height of the cylindrical sample. The thermal conductivity of each layer was designed based on the end faces, and the thickness distribution ratio was consistent with the end faces of the cylindrical sample. The cuboid was designed with a temperature of 1K on the left side and 0K on the right side, with no heat flow on other faces. A finite element mesh was established, and the temperature field distribution of the cuboid was obtained according to the current equation. The cuboid core was divided into 2l+1 equal parts from top to bottom. The average heat flux values ​​qc1, qc2, ..., qc of each section were read from the numerical simulation results of the temperature field. 2m+1 The true value of thermal conductivity was calculated experimentally when the texture of the rock core was perpendicular to the end face of the cylinder using Equation 3.

[0140]

[0141] in, q represents the true value of thermal conductivity measured experimentally when the texture of the rock core is perpendicular to the end face of the cylinder. Ci The average heat flux value of the i-th cross section;

[0142] When the cylindrical sample is a battery, the true value λ of the battery's thermal conductivity is calculated using Equation 4. hb ;

[0143]

[0144] Where r is the radius of the battery, λ hb Here, r1 represents the true value of the battery's thermal conductivity as measured in an experiment, r2 represents the thickness of the first separator layer, and r is the thickness of the second separator layer. n Let λ be the thickness of the nth separator layer of the battery, λ1 be the thermal conductivity of the first separator layer of the battery, and λ2 be the thermal conductivity of the second separator layer of the battery. n Let be the thermal conductivity of the nth layer of the battery separator;

[0145] c. Calculate the simulated test results for the cylindrical sample. Set up a three-dimensional cylindrical model, with the thermal conductivity of each layer according to λ1, λ2, ... and λ... nThe system is configured so that heat flows in from point A and out from point C. The boundary temperature at point A is set to be 5°C above room temperature, and the boundary temperature at point C is set to room temperature. There is no heat flow at boundaries B and D. A finite element mesh is established, and the temperature field distribution diagram can be obtained according to Fourier's law. The core sample is divided into 2m+1 equal parts from the outside to the inside. The average heat flow values ​​q1, q2, ..., q of each section are read from the numerical simulation results. 2m+1 The simulated value λ of the test result for the cylindrical sample is calculated using Equation 5. * ;

[0146]

[0147] Where, λ * is the simulated value of the test results for the cylindrical sample, and qi is the average heat flow value of the i-th cross section;

[0148] d. Calculate the radial thermal conductivity test error value ε of the cylindrical sample using Equation 6;

[0149]

[0150] Where ε is the radial thermal conductivity test error value of the cylindrical sample, and λ * For the simulated test results of the cylindrical sample, λ = λ i , λ i For λ / / , or λ hb .

[0151] In step a, distinguishing the type of cylindrical sample means checking whether the cylindrical sample is a rock core formed under natural conditions or an artificially made battery.

[0152] In step a, if the cylindrical sample is a rock core generated under natural conditions, then it is determined whether the end face of the cylindrical sample is parallel to the rock core texture or perpendicular to the rock core texture. When the end face of the rock core is perpendicular to the rock core texture, the direction of heat flow is observed.

[0153] The observation of the heat flow direction specifically refers to whether the heat flows in along the direction of lamellar development or perpendicular to the direction of lamellar development. If the heat flow direction is at an angle to the direction of lamellar development, the position of the cylindrical sample is readjusted until the heat flows in along the direction of lamellar development or perpendicular to the direction of lamellar development.

[0154] In step a, the cylindrical sample to be tested is selected if there is a fold or turn in the fingerprint layer development direction. If so, a new cylindrical sample is prepared and a cylindrical sample with a single fingerprint layer development direction is selected as the cylindrical sample to be tested.

[0155] In step b, the thermal conductivity values ​​of each layer are obtained by using a common thermal conductivity testing method on cylindrical samples of the same material.

[0156] In step b, when the cylindrical sample is a rock core, the thickness and area of ​​each layer are obtained through CT scans or nuclear magnetic resonance imaging images; when the cylindrical sample is a battery, the thickness and area are obtained through actual measurements of the same type of battery.

[0157] In step c, the boundary temperature of A is 1°C higher than room temperature.

[0158] This embodiment represents the best implementation method and provides a feasible algorithm that can effectively evaluate the impact of conformal transformation using a "complex function" on the test results when the radial thermal conductivity test assumes isotropic properties.

[0159] It can be used to simulate and calculate the effect of a system composed of materials with different properties on the overall thermal conductivity, and to study the degree of influence of the degree of difference in the properties of the components on the system error.

Claims

1. A method for calculating the error in testing the radial thermal conductivity of a cylindrical sample, characterized in that, Includes the following steps: a. Differentiate the types of cylindrical samples and select the cylindrical sample to be tested; b. Calculate the true value of the thermal conductivity of the cylindrical sample. When the cylindrical sample is a rock core, if the texture of the rock core is parallel to the end face of the cylinder, then observe the development of the laminae through CT scans or nuclear magnetic resonance images to divide the cylindrical sample into layers 1, 2, ..., and n, with the thermal conductivity of each layer corresponding to λ1, λ2, ..., and λn. n The thicknesses of each layer are h1, h2, ... and h. n The true value of thermal conductivity λ was calculated experimentally when the texture of the rock core was parallel to the end face of the cylinder using Equation 1. / / ; Where, λ / / h represents the true value of thermal conductivity measured experimentally when the texture of the rock core is parallel to the end face of the cylinder. i Let λ be the thickness of the i-th layer of the cylindrical sample. i Let be the thermal conductivity of the i-th layer of the cylindrical sample; If the core's texture is perpendicular to the cylinder's end face, and heat flows in along the lamellar development direction, then the cylindrical sample can be divided into layers 1, 2, ..., and n according to the lamellar development, as observed by CT scans or nuclear magnetic resonance imaging. The thermal conductivity of each layer corresponds to λ1, λ2, ..., and λn. n The areas of each layer are S1, S2, ... and S. n The true value of thermal conductivity was calculated experimentally when the texture of the rock core was perpendicular to the end face of the cylinder using Equation 2. in, S represents the true value of thermal conductivity measured experimentally when the texture of the rock core is perpendicular to the end face of the cylinder. i Let λ be the area of ​​the i-th layer of the cylindrical sample. i Let be the thermal conductivity of the i-th layer of the cylindrical sample; If the core texture is perpendicular to the end face of the cylinder, and heat flows in perpendicularly to the direction of lamellar development, then the cylindrical sample can be divided into layers 1, 2, ..., and n according to the development of the lamellar structures, as observed by CT scans or nuclear magnetic resonance imaging. The thermal conductivity of each layer corresponds to λ1, λ2, ..., and λn. n The thicknesses of each layer are H1, H2, ... and H. n A cuboid was constructed, with its end faces squared using the diameter of the cylindrical sample as the side length. The height of the cuboid was the height of the cylindrical sample. The thermal conductivity of each layer was designed based on the end faces, and the thickness distribution ratio was consistent with the end faces of the cylindrical sample. The cuboid was designed with a temperature of 1K on the left side and 0K on the right side, with no heat flow on other faces. A finite element mesh was established, and the temperature field distribution of the cuboid was obtained according to the current equation. The cuboid core was divided into 2l+1 equal parts from top to bottom. The average heat flux values ​​qc1, qc2, ..., qc of each section were read from the numerical simulation results of the temperature field. 2m+1 The true value of thermal conductivity was calculated experimentally when the texture of the rock core was perpendicular to the end face of the cylinder using Equation 3. in, This represents the experimentally measured true value of thermal conductivity when the texture of the rock core is perpendicular to the end face of the cylinder. The average heat flux value of the i-th cross section; When the cylindrical sample is a battery, the true value of the battery's thermal conductivity λ is calculated using Equation 4. hb ; Where r is the radius of the battery, λ hb Here, r1 represents the true value of the battery's thermal conductivity as measured in an experiment, r2 represents the thickness of the first separator layer, and r is the thickness of the second separator layer. n Let λ be the thickness of the nth separator layer of the battery, λ1 be the thermal conductivity of the first separator layer of the battery, and λ2 be the thermal conductivity of the second separator layer of the battery. n Let be the thermal conductivity of the nth layer of the battery separator; c. Calculate the simulated test results for the cylindrical sample. Set up a three-dimensional cylindrical model, with the thermal conductivity of each layer according to λ1, λ2, ... and λ... n The system is configured so that heat flows in from point A and out from point C. The boundary temperature at point A is set to be 1-5°C above room temperature, the boundary temperature at point C is room temperature, and there is no heat flow at boundaries B and D. A finite element mesh is established, and the temperature field distribution map can be obtained according to Fourier's law. The core sample is divided into 2m+1 equal parts from the outside to the inside. The average heat flow values ​​q1, q2, ..., q of each section are read from the numerical simulation results. 2m+1 The simulated value λ of the test result for the cylindrical sample is calculated using Equation 5. * ; Where, λ * q represents the simulated test result for a cylindrical sample. i The average heat flux value of the i-th cross section; d. Calculate the radial thermal conductivity test error value ε of the cylindrical sample using Equation 6; Where ε is the radial thermal conductivity test error value of the cylindrical sample, and λ * For the simulated test results of the cylindrical sample, λ = λ i , λ i For λ / / , or λ hb .

2. The method for calculating the radial thermal conductivity test error of a cylindrical sample according to claim 1, characterized in that: In step a, distinguishing the type of cylindrical sample means checking whether the cylindrical sample is a rock core formed under natural conditions or an artificially made battery.

3. The method for calculating the radial thermal conductivity test error of a cylindrical sample according to claim 2, characterized in that: In step a, if the cylindrical sample is a rock core generated under natural conditions, then it is determined whether the end face of the cylindrical sample is parallel to the rock core texture or perpendicular to the rock core texture. When the end face of the rock core is perpendicular to the rock core texture, the direction of heat flow is observed.

4. The method for calculating the radial thermal conductivity test error of a cylindrical sample according to claim 3, characterized in that: The observation of the heat flow direction specifically refers to whether the heat flows in along the direction of lamellar development or perpendicular to the direction of lamellar development. If the heat flow direction is at an angle to the direction of lamellar development, the position of the cylindrical sample is readjusted until the heat flows in along the direction of lamellar development or perpendicular to the direction of lamellar development.

5. The method for calculating the radial thermal conductivity test error of a cylindrical sample according to claim 1, characterized in that: In step a, the cylindrical sample to be tested is selected if there is a fold or turn in the fingerprint layer development direction. If so, a new cylindrical sample is prepared and a cylindrical sample with a single fingerprint layer development direction is selected as the cylindrical sample to be tested.

6. The method for calculating the radial thermal conductivity test error of a cylindrical sample according to claim 1, characterized in that: In step b, the thermal conductivity values ​​of each layer are obtained by using a common thermal conductivity testing method on cylindrical samples of the same material.

7. The method for calculating the radial thermal conductivity test error of a cylindrical sample according to claim 1, characterized in that: In step b, when the cylindrical sample is a rock core, the thickness and area of ​​each layer are obtained through CT scans or nuclear magnetic resonance imaging images; when the cylindrical sample is a battery, the thickness and area are obtained through actual measurements of the same type of battery.

8. The method for calculating the radial thermal conductivity test error of a cylindrical sample according to claim 1, characterized in that: In step c, the boundary temperature of A is 1°C higher than room temperature.

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